A STUDYOF CASTING DISTORTION AND RESIDUAL
STRESSES IN DIE CASTING
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate School
of The Ohio State University
By
Abelardo Garza-Delgado, M.S.
*****
The Ohio State University 2007
Dissertation Committee: Approved by: Professor R. Allen Miller, Adviser Professor Jerald Brevick _______________________ Dr. Khalil Kabiri-Bamoradian Adviser
Industrial and Systems Engineering Graduate Program
ii
ABSTRACT
The use of numerical methods to analyze the design and performance of
mechanical components has been widely used in industry for many years. The
results obtained have been used to improve the design of the products by
providing useful insights into the critical areas of the component during operation.
However, the numerical analysis of the manufacturing process that integrates
machine, tooling and products has not been widely done due to the greater
complexity of the physical phenomena involved. This dissertation work presents
a computer modeling methodology developed to predict the final dimensions and
residual stresses in a die casting. The determination of the temperature and
strain-rate dependent mechanical properties of the casting material needed for
the computer model is also presented here. Furthermore, to validate the
adequacy of the modeling methodology computer model predictions are
compared against experimental measurements taken on productions castings.
The methodology uses the finite element method to analyze the
solidification and cooling conditions of a casting during the die casting process.
The die and machine components were incorporated into the analysis and were
modeled as deformable bodies. An innovative method that uses a shell mesh is
presented that allows tracking the elastic deflections in the die cavity resulting
iii
from the die casting process loads. A fully coupled thermal-mechanical analysis
was done to model the die casting process. The finite element model was solved
using the commercially available finite element package Abaqus.
The determination of the casting constitutive model needed for the
computer model was done as part of this dissertation work. Tensile bars made of
die casting aluminum alloy A380.0 in compliance with industrial testing standards
were produced using an existing tooling. A series of tensile tests at different
combinations of temperatures and strain rates were conducted to determine the
casting constitutive behavior. The tests were performed using a Gleeble 1500
thermo-mechanical simulator.
An experimental Design of Experiments was done to validate the
adequacy of the computer model predictions and to study the effect of process
variables on final casting dimensions. Castings were produced and different
features were selected to characterize the in-cavity and across parting plane
distortion. The production castings were then precisely measured using a
Coordinate Measurement Machine. An Analysis of Variance was performed
using the experimental data and the statistical significance of the main variables
was determined. The experimental results were compared against computer
models simulating the same runs. The comparisons between the experimental
and computer model distortion results are discussed. Computer model residual
stress predictions are discussed as well.
iv
Dedicated to my family, my father Alfonso, my mother Ana Maria, my
brother Ismael and my sister Ana Patricia
v
ACKNOWLEDGMENTS
I wish to thank my adviser, Dr. R. Allen Miller, for the opportunity he gave
me to pursue my graduate studies here at The Ohio State University under his
guidance. I am extremely grateful for his dedication towards developing good
people with sound engineering judgment and for providing the means and the
freedom that let me explore and experiment my ideas throughout the course of
my studies. I am particularly thankful for the countless hours of intellectual
discussion we had during all these years.
I would like to thank my coadviser Dr. Khalil Kabriri-Bamoradian for the
unconditional support he provided throughout these years. I appreciate
intellectual exchanges we had in discussing the finite element models, the
casting experiments as well as the tensile tests. I owe much of my success in
my studies to him.
I am grateful to my colleagues and friends at the Center for Die Casting. I
would like to thank Adham Ragab, Karthik Murugesan, Jeeth Kinatingal and
Hung Yu Xu. The countless hours we spend discussing our difficulties and
enjoying our studies will be always in my mind.
I would like to thank Dr. Jerald Brevick for the joy he always brought while
advising me throughout all these years. I am appreciative of the effort he made
revising this dissertation and also in guiding me while conducting my elevated
vi
temperature tensile tests. I would like to thank him for motivating me and my
colleagues to study and contribute towards the improvement of the die casting
industry.
I am extremely grateful to Cedric Sze and to Shih-Kwang Chen for the
outstanding job they do in keeping the CAD/CAM Laboratory running. I
appreciate all the help provided that allowed me to run my finite element models.
I would like to thank the following people for helping during the various
stages of the tensile tests project. I am grateful to Professor John Lippold for
allowing me to use the Gleeble 3800 at the Welding Engineering facilities. To
Morgan Gallagher for instructing me on how to operate the Gleeble. To
Professor Hamish Fraser at the Materials Science and Engineering Department
for letting me use the Gleeble 1500 to conduct my experiments. To Rick
Tomazin for modifying the tooling to die cast the tensile bars. To Mark Kubicki
from Empire Die Casting for casting the tensile bars and for providing the cycle
design for the production.
vii
VITA June 23, 1979 Born, Monclova, Coah, Mexico Dec. ‘00 B.S. Mechanical Engineering ITESM Campus Monterrey Dec. ‘03 M.S. Industrial Engineering The Ohio State University Sept. ‘01-Sept. ’07 Graduate Research Associate The Ohio State University
PUBLICATIONS Research Publication 1. Garza, A., Kabiri-Bamoradian, K., Miller, R.A., “Using Die Distortion Modeling to Predict Component Failure in a Miniature Zinc Die”, NADCA Transactions, 2003 2. Garza, A., Kabiri-Bamoradian, K., Miller, R.A., “Finite Element Modeling of Die Casting Die Distortion by Coupled Thermal-Fluid-Structural Analysis”, NADCA Transactions, 2004 3. Garza, A., Kabiri-Bamoradian, K., Miller, R.A., “Finite Element Modeling of Casting Distortion in Die Casting”, NADCA Transactions, 2007
FIELDS OF STUDY Major Field: Industrial and Systems Engineering Minor Field: Manufacturing Engineering
viii
TABLE OF CONTENTS Page Abstract ii
Dedication iv
Acknowledgments v
Vita vii
List of Tables xi
List of Figures xii
1 CHAPTER 1 ................................................................................................................. 1
1.1 Motivation ............................................................................................................. 1 1.2 Die casting process .............................................................................................. 3 1.3 Problem statement ............................................................................................... 7 1.4 Research objectives ............................................................................................. 9 1.5 Research contributions ...................................................................................... 10 1.6 Dissertation outline ............................................................................................. 11
2 CHAPTER 2 ............................................................................................................... 13 2.1 Basic concepts of stress development in castings ............................................. 13
2.1.1 Cooling ........................................................................................................... 13 2.1.2 Development of stresses ............................................................................... 15 2.1.3 Shrinkage ....................................................................................................... 19
2.2 Casting distortion ............................................................................................... 22 2.2.1 Mold restraint ................................................................................................. 22 2.2.2 Casting restraint ............................................................................................. 26
2.3 Casting and die distortion in die casting ............................................................ 28 2.3.1 Die distortion .................................................................................................. 28 2.3.2 Casting distortion ........................................................................................... 30
2.4 Computer modeling of solidification ................................................................... 32 2.4.1 Fluid flow modeling ........................................................................................ 35 2.4.2 Stress modeling ............................................................................................. 39
2.5 Finite element method in solidification modeling ............................................... 43 2.6 Computer modeling of casting and die distortion in die casting ......................... 47
2.6.1 Die distortion modeling .................................................................................. 48 2.6.2 Casting distortion modeling ........................................................................... 51
2.7 Casting distortion studies ................................................................................... 55
ix
2.8 Summary ............................................................................................................ 59 3 CHAPTER 3 ............................................................................................................... 61
3.1 Introduction ......................................................................................................... 61 3.2 Die distortion modeling ....................................................................................... 62
3.2.1 Clamping force modeling ............................................................................... 64 3.2.2 Thermal load modeling .................................................................................. 67 3.2.3 Intensification pressure modeling .................................................................. 72
3.3 Modeling of part distortion .................................................................................. 73 3.3.1 Modeling the tracking of cavity distortion ....................................................... 74 3.3.2 Modeling the cooling of casting inside the die ............................................... 77 3.3.3 Modeling cooling of casting post-ejection ...................................................... 80
3.4 Constitutive model for the casting material ........................................................ 80 3.4.1 Finite element selection for casting ............................................................... 83
3.5 Modeling die distortion using Fluid-Structure-Interaction (FSI) in ADINA .......... 83 3.5.1 Fluid Structure Interaction (FSI) Model .......................................................... 85
4 CHAPTER 4 ............................................................................................................... 89 4.1 Introduction ......................................................................................................... 89 4.2 Background ........................................................................................................ 91 4.3 Literature review ................................................................................................. 95
4.3.1 Die casting alloys ........................................................................................... 96 4.3.2 Aluminum casting alloys ................................................................................ 98 4.3.3 Gleeble testing ............................................................................................. 105
4.4 Determination of aluminum A380.0 mechanical properties ............................. 108 4.4.1 Machine and specimen selection ................................................................ 108 4.4.2 Design of experiments matrix ...................................................................... 114 4.4.3 Specimen production and preparation ......................................................... 117 4.4.4 Testing methodology ................................................................................... 118
4.4.4.1 Velocity controlled ................................................................................. 119 4.4.4.2 Force controlled .................................................................................... 128 4.4.4.3 Results .................................................................................................. 137
4.5 Summary .......................................................................................................... 164 5 CHAPTER 5 ............................................................................................................. 166
5.1 Introduction ....................................................................................................... 166 5.2 Part distortion experiments .............................................................................. 167
5.2.1 Dimensional measurements on production castings ................................... 171
x
5.2.2 Statistical analysis ....................................................................................... 174 5.2.3 In-cavity dimensions .................................................................................... 175 5.2.4 Across parting plane dimensions ................................................................. 182
5.3 Computer model predictions ............................................................................ 190 5.3.1 Model preparation ........................................................................................ 190 5.3.2 Distance calculations ................................................................................... 191
5.3.2.1 Coordinate transformation ..................................................................... 191 5.3.2.2 Distance calculation .............................................................................. 197
5.3.3 In cavity dimensions .................................................................................... 198 5.3.4 Across parting plane dimensions ................................................................. 201
5.4 Comparison of experimental and computer model results .............................. 204 5.5 Testing the adequacy of part distortion modeling assumptions ....................... 210 5.6 Stress results .................................................................................................... 216 5.7 Summary .......................................................................................................... 227
6 CHAPTER 6 ............................................................................................................. 230 6.1 Introduction ....................................................................................................... 230 6.2 Research contributions .................................................................................... 231 6.3 Conclusions ...................................................................................................... 232
6.3.1 Finite element modeling ............................................................................... 232 6.3.2 Determination of mechanical properties for casting material ...................... 235 6.3.3 Design of Experiments ................................................................................. 238
6.3.3.1 Experimental results .............................................................................. 238 6.3.3.2 Computer model results ........................................................................ 239
6.3.4 Adequacy of different sets of modeling assumptions .................................. 241 6.3.5 Analysis of residual stress profiles .............................................................. 242
REFERENCES 260
APPENDIX A Test bars insert 267
APPENDIX B Tensile bars material chemical composition and die casting process
control parameters 269
APPENDIX C Collected data during tensile tests 272
APPENDIX D Sample measurements obtained from coordinate measurement
machine 276
APPENDIX E Research casting insert dimensions 284
xi
LIST OF TABLES Table Page Table 3.1 Boundary conditions applied on the simulated thermal cycles ......................... 69
Table 3.2 Physical properties for H-13 tool steel .............................................................. 70
Table 3.3 Physical properties for a typical 4140 steel alloy .............................................. 71
Table 3.4 Physical properties for aluminum A380.0 die casting alloy .............................. 71
Table 4.1 Experimental array for tensile tests ................................................................ 116
Table 5.1 Matrix design for experimental DOE ............................................................... 170
Table 5.2 ANOVA results for distance D1 ...................................................................... 176
Table 5.3 ANOVA results for distance D2 ...................................................................... 177
Table 5.4 ANOVA results for distance D3 ...................................................................... 178
Table 5.5 ANOVA results for distance H2 ...................................................................... 184
Table 5.6 ANOVA results for distance H3 ...................................................................... 185
Table 5.7 ANOVA results for distance H4 ...................................................................... 186
Table 5.8 Proposed sets of modeling assumptions ........................................................ 212
Table C.1 Data collection for tensile tests 273
xii
LIST OF FIGURES Figure Page Fig. 1.1 Schematic of a hot chamber die casting process wild [1 ] ..................................... 4
Fig. 1.2 Schematic of a cold chamber die casting process [1 ] .......................................... 5
Fig. 1.3 Process stages in a typical die casting cycle [1 ] ................................................... 6
Fig. 2.1 Temperature profile across casting/mold interface [4] ......................................... 14
Fig. 2.2 Mechanical behavior of solidifying aluminum alloy under tension [5] .................. 17
Fig. 2.3 Stress-elongation curves at different temperatures [5] ........................................ 18
Fig. 2.4 Residual stresses as a function of ejection time [4] ............................................. 19
Fig. 2.5 Types contractions experienced by a solidifying material [4] .............................. 21
Fig. 2.6 Contraction of three different casting shapes [4] ................................................. 23
Fig. 2.7 Pattern's maker contraction as a function of casting envelope density [4] .......... 24
Fig. 2.8 Contraction of steel castings for different degrees of mold constrain [4] ............. 25
Fig. 2.9 Effect of mold constrain in casting distortion [4] .................................................. 26
Fig. 2.10 Effect of casting geometry in casting distortion pattern [4] ................................ 28
Fig. 2.11 Schematic of different types of analyses for solidification modeling [10] .......... 34
Fig. 2.12 Typical stages in a comprehensive solidification model [10] ............................. 35
Fig. 2.13 Relationship between specific heat and enthalpy [11] ....................................... 39
Fig. 3.1 Machine model finite element mesh .................................................................... 63
Fig. 3.2 Schematic of clamping method ............................................................................ 65
Fig. 3.3 Location of clamping pressure on platens ........................................................... 66
Fig. 3.4 Casting finite element mesh ................................................................................. 74
Fig. 3.5 Shell element mesh ............................................................................................. 77
Fig. 3.6 Temperature dependence of Young’s Modulus [45 ]. .......................................... 82
Fig. 3.7 FSI cavity displacement predictions .................................................................... 86
xiii
Fig. 4.1 Creep properties for die casting aluminum alloy A380.0 [52] .............................. 98
Fig. 4.2 Testing devices used for determining flow stress a) below 300 ºC and b) above
300 ºC [53] ...................................................................................................................... 100
Fig. 4.3 Flow stress for Al-Si alloys at temperatures below the solidus [53] ................... 101
Fig. 4.4 Flow stress for Al-Si alloys at temperatures above the solidus [53] .................. 102
Fig. 4.5 Material properties for an Al-7%Si-0.3%Mg alloy [54] ....................................... 103
Fig. 4.6 Schematic of a typical Gleeble test [57] ............................................................. 110
Fig. 4.7 Schematic of the test bar used for tensile tests ................................................. 112
Fig. 4.8 Strain and strain rate plots for a 0.001mm/s jaw velocity .................................. 122
Fig. 4.9 Strain rate distribution for a 0.001mm/s jaw velocity ......................................... 123
Fig. 4.10 Strain and strain rate plots for a 1mm/s jaw velocity ....................................... 124
Fig. 4.11 Strain rate distribution for a 1mm/s jaw velocity .............................................. 125
Fig. 4.12 Strain and strain rate plots for a 100mm/s jaw velocity ................................... 126
Fig. 4.13 Strain rate distribution for a 100mm/s jaw velocity .......................................... 127
Fig. 4.14 Strain rate vs. jaw velocity correlation plot ....................................................... 128
Fig. 4.15 Strain vs. time curve for a 1.0KN force at 381 ºC ............................................ 130
Fig. 4.16 Strain vs. time curve for a 1.5KN force at 381 ºC ............................................ 131
Fig. 4.17 Strain vs. time curve for a 2.0KN force at 381 ºC ............................................ 132
Fig. 4.18 Strain rate force vs. force correlation plot at 300 ºC ........................................ 133
Fig. 4.19 Strain rate force vs. force correlation plot at 381 ºC ........................................ 134
Fig. 4.20 Strain rate force vs. force correlation plot at 445 ºC ........................................ 135
Fig. 4.21 Strain rate force vs. force correlation plot at 485 ºC ........................................ 136
Fig. 4.22 Strain rate force vs. force correlation plot at 500 ºC ........................................ 137
Fig. 4.23 Stress vs. strain curves at 500 ºC and 1x10-4 s-1 strain rate ............................ 138
Fig. 4.24 Stress vs. strain curves at 485 ºC and 1x10-3 s-1 strain rate ............................ 139
xiv
Fig. 4.25 Stress vs. strain curves at 445 ºC and 1x10-2 s-1 strain rate ............................ 140
Fig. 4.26 Stress vs. strain curves at 381 ºC and 1x10-2 s-1 strain rate ............................ 141
Fig. 4.27 Stress vs. strain curves at 304 ºC and 1x10-2 s-1 strain rate ............................ 142
Fig. 4.28 Stress vs. strain curves at 221 ºC and 1x10-2 s-1 strain rate ............................ 143
Fig. 4.29 Stress vs. strain curves at 145 ºC and 1x10-2 s-1 strain rate ............................ 144
Fig. 4.30 Stress vs. strain curves at 81 ºC and 1x10-2 s-1 strain rate .............................. 145
Fig. 4.31 Stress vs. strain curves at 39 ºC and 1x10-3 s-1 strain rate .............................. 146
Fig. 4.32 Stress vs. strain curves at 25 ºC and 1x10-4 s-1 strain rate .............................. 147
Fig. 4.33 Stress vs. strain curves at 25 ºC and 1x10-4 s-1 strain rate .............................. 148
Fig. 4.34 Stress vs. strain curves at 39 ºC and 1x10-5 s-1 strain rate .............................. 149
Fig. 4.35 Stress vs. strain curves at 81 ºC and 1x10-6 s-1 strain rate .............................. 150
Fig. 4.36 Stress vs. strain curves at 145 ºC and 1x10-6 s-1 strain rate ............................ 151
Fig. 4.37 Stress vs. strain curves at 220 ºC and 1x10-6 s-1 strain rate ............................ 152
Fig. 4.38 Stress vs. strain curves at 305 ºC and 1x10-6 s-1 strain rate ............................ 153
Fig. 4.39 Stress vs. strain curves at 381 ºC and 1x10-6 s-1 strain rate ............................ 154
Fig. 4.40 Stress vs. strain curves at 445 ºC and 1x10-6 s-1 strain rate ............................ 155
Fig. 4.41 Stress vs. strain curves at 485 ºC and 1x10-5 s-1 strain rate ............................ 156
Fig. 4.42 Stress vs. strain curves at 263 ºC and 1x10-4 s-1 strain rate ............................ 157
Fig. 4.43 Stress vs strain curves for temperatures below 300 ºC ................................... 159
Fig. 4.44 Stress vs strain curves for temperatures above 300 ºC .................................. 160
Fig. 4.45 Simulation material properties for strain rate of 1x10-6 s-1 ............................... 161
Fig. 4.46 Simulation material properties for strain rate of 1x10-5 s-1 ............................... 162
Fig. 4.47 Simulation material properties for strain rate of 1x10-4 s-1 ............................... 162
Fig. 4.48 Simulation material properties for strain rate of 1x10-3 s-1 ............................... 163
Fig. 4.49 Simulation material properties for strain rate of 1x10-2 s-1 ............................... 163
xv
Fig. 5.1 Selected casting ................................................................................................. 168
Fig. 5.2 Casting dimensions in millimeters (2º draft on interior walls formed by the insert
and 1º draft on walls formed by the insert and die shoe, see Appendix E) .................... 169
Fig. 5.3 Location of fixture gauging points ...................................................................... 172
Fig. 5.4 Selected casting dimensions ............................................................................. 173
Fig. 5.5 Experimental main effect plots for in-cavity dimensions .................................... 179
Fig. 5.6 Experimental interaction plots for in-cavity dimensions ..................................... 181
Fig. 5.7 Box plots for in-cavity dimensions ..................................................................... 182
Fig. 5.8 Experimental main effect plots for across parting plane dimensions ................. 187
Fig. 5.9 Experimental interaction plots for across parting plane dimensions .................. 189
Fig. 5.10 Box plots for across parting plane dimensions ................................................ 190
Fig. 5.11 Sampling order of casting nodes for coordinate transformation ...................... 192
Fig. 5.12 Simulation main effect plots for in-cavity dimensions ...................................... 199
Fig. 5.13 Simulation interaction plots for in-cavity dimensions ....................................... 200
Fig. 5.14 Simulation main effect plots for across parting plane dimensions ................... 202
Fig. 5.15 Simulation interaction plots for across parting plane dimensions .................... 203
Fig. 5.16 Comparison of results for in-cavity dimensions ............................................... 205
Fig. 5.17 Comparisons of results for across parting plane dimensions .......................... 206
Fig. 5.18 Distribution of across parting plane experimental dimensions ........................ 208
Fig. 5.19 Distribution of across parting plane simulation dimensions ............................. 210
Fig. 5.20 Comparisons of results for in-cavity dimensions predicted by the different sets
of modeling assumptions ................................................................................................ 214
Fig. 5.21 Comparison of results for across parting plane dimensions predicted by the
different sets of modeling assumptions........................................................................... 215
Fig. 5.22 Analyzed stress locations at the symmetry plane ............................................ 217
xvi
Fig. 5.23 Stress and temperature profiles at location 1 .................................................. 219
Fig. 5.24 Stress and temperature profiles at location 2 .................................................. 220
Fig. 5.25 Stress and temperature profiles at location 3 .................................................. 221
Fig. 5.26 Stress and temperature profiles at location 4 .................................................. 222
Fig. 5.27 Strain profiles at location 1 ............................................................................... 224
Fig. 5.28 Strain profiles at location 2 ............................................................................... 225
Fig. 5.29 Strain profiles at location 3 ............................................................................... 226
Fig. 5.30 Strain profiles at location 4 ............................................................................... 227
1
1 CHAPTER 1
INTRODUCTION
1.1 Motivation
The ever-demanding quest for lighter components that help reduce weight
in these energy-driven times places a great deal of pressure on mechanical
component designers. Designers are often challenged by selecting the
appropriate manufacturing process that would yield products in the least number
of steps and with the dimensional and functional requirements that the given
application demands. Castings are often among the most sophisticated
mechanical components that due to their processing routes lend themselves to a
large degree of component consolidation, allowing designers to reduce parts
weight.
Casting processes are widely known for their ability to manufacture
products with a very attractive interplay of product complexity and dimensional
accuracy. Among the many casting processes, die casting is often selected
because of its ability to produce thin-walled parts with a great degree of
complexity, accuracy, and at the same time meeting the economies of scale
2
needed for competing with other mass manufacturing processes. However, the
freedom that component designers exercise by merging many parts into one
comes often with the price of very long lead times before a casting can be
successfully produced. Dimensional non-conformance, or casting distortion, is
among the most critical factors driving these long lead times.
Casting distortion is among the many defects that cause a product to be
scraped. It has been estimated that more than $50 million are spent in distortion
related casting defects. Casting distortion arises from two main sources, namely,
uneven cooling of the different sections of the casting due to their different
geometries, and the constraint imposed by the mold walls that limits the ability of
the casting to shrink freely. Distortions may also be induced by post-processing
operations such as fixturing, machining, and quenching.
In die casting the majority of the long lead times afore mentioned is often
spent reworking the tooling. The main source of this reworking is the so called
shrinkage or allowance factor, which tool designers usually apply uniformly
throughout the cavity, implicitly assuming that the casting shrinks evenly.
However, because castings are often made of complex irregular shapes, cooling
of these sections is often uneven. Additionally, due to the high degree of
restraint imposed by the die, die castings may be ejected with residual stresses,
a key factor that plays a major role in post-ejection casting distortion.
Thus, in order to position die casting in a more competitive position among
the other net shape manufacturing processes, it becomes of paramount
importance that lead times be reduced. A significant reduction of lead times can
3
only be achieved when the prediction of casting dimensions is done before the
tooling is produced and all the tool reworking can be eliminated. The prediction
of casting dimensions requires a good understanding of the factors that drive
casting distortion, so shrinkage factors can be applied in a more intelligent
fashion, rather than by trial and error.
1.2 Die casting process
Die casting is high production rate manufacturing process which consists
of the injection of non-ferrous alloys under high pressures and high velocities into
metallic reusable dies. The main characteristics that differentiate this process
from other casting processes are: the high injection velocities, high injection
pressures, short cycle times, the use of metallic reusable dies, thin-walled
casting designs, excellent surface finish attainable, good casting mechanical
properties, dimensional repeatability, etc. Die castings are also prone to higher
porosity contents when compared to other castings mainly due to the entrapment
of air bubbles during the turbulent filling of the die cavity. The majority of the
alloys processed by die casting include aluminum, magnesium, and zinc.
The die casting process presents two main variants, namely, hot chamber
and cold chamber. The schematics of these two processes are presented in Fig.
1.1 and Fig. 1.2 [1 ]. As illustrated in Fig. 1.1, in the hot chamber process the
injection mechanism is in direct contact with the molten metal. On the other
hand, in the cold chamber process the molten metal is in direct contact with the
injection mechanism only during a very small fraction of time, usually in the order
4
of one to two seconds. The differentiation of these two processes comes due the
inability of the injection mechanism to handle highly chemically attacking alloys
such as aluminum, which tends to dissolve iron fairly quickly, and thus, due to the
short exposure times, cold chamber machines are designed to process these
types of alloys, whereas magnesium and zinc alloys are processed in hot
chamber machines.
Fig. 1.1 Schematic of a hot chamber die casting process wild [1 ]
Plunger
HydraulicCylinder
Liquid Metal
Furnace
Gooseneck
Nozzle
Holding Pot
Ejector Platen
Cover DieEjector Die
Ejector Box
Stationary Platen
Die Cavity
Plunger
HydraulicCylinder
Liquid Metal
Furnace
Gooseneck
Nozzle
Holding Pot
Ejector Platen
Cover DieEjector Die
Ejector Box
Stationary Platen
Die Cavity
5
Fig. 1.2 Schematic of a cold chamber die casting process [1 ]
Both die casting processes follow similar processing stages. Fig. 1.3
depicts the most common steps during a cold chamber injection cycle. The
process starts with the metal ladling in which the material is transported from the
holding furnace to the injection chamber by the use of a ladle. Injection of the
metal is carried out in two phases, namely slow shot and fast shot. During slow
shot the metal is carried from the injection chamber to the runner under small
velocities. The fast shot stage is triggered to get the metal at the gate under
velocities that range from 30 to 40 m/s (1200 to 1600 in/s). During this stage the
Ladle
Hydraulic Cylinder
Plunger
Shot Sleeve
Cover DieEjector Die
Ejector Box
Stationary PlatenEjector Platen
Die CavityLadle
Hydraulic Cylinder
Plunger
Shot Sleeve
Cover DieEjector Die
Ejector Box
Stationary PlatenEjector Platen
Die CavityLadle
Hydraulic Cylinder
Plunger
Shot Sleeve
Cover DieEjector Die
Ejector Box
Stationary PlatenEjector Platen
Die Cavity
6
metal actually fills the die cavity in the order of a few milliseconds. Immediately
after the end of filling the metal is pressurized. Pressurization is achieved in a
small time window before the gate freezes and is carried out by the release of
stored energy in an accumulator located by the injection end of the machine.
After the casting has solidified and cooled, the die is open and the injection
plunger is retracted as illustrated. The casting is finally ejected by the use of
ejector pins driven by a mechanism located behind the movable die half.
Fig. 1.3 Process stages in a typical die casting cycle [1 ]
(d)
(a)
(c)
(e) (f)
(b)
(d)
(a)
(c)
(e) (f)
(b)
7
As already mentioned, one of the characteristics of die casting is the use
of metallic dies. It is precisely the metallic nature of the die that enables the
process to be carried out with short cycle times due to its relatively high thermal
conductivity. The die consists of two halves, namely the cover or fixed half, and
the ejector or movable half. Each half of the die is mounted onto a machine
platen. The machine provides a sturdy frame with three main functions:
repeatedly clamp the die with proper alignment and withstand the high injection
pressures, provide the means for injecting the metal into the cavity, and lastly,
provide the means of extracting the part.
1.3 Problem statement
Die casting as a manufacturing and forming process is subjected to two
sources of errors that can cause parts to be produced out of tolerances and be
rejected. Karve [2] identified these two sources as: random variability in process
conditions and incorrect die dimensions. Typical sources of random variability in
die casting can be attributed to: variations in cycle time, injection pressure,
injection velocity, metal temperature, spraying patterns, cooling line conditions,
etc. All these factors have a definite effect on the repeatability of the process
and nowadays more than ever efforts are being made by machine and peripheral
equipment builders to control them more precisely so they can be kept within the
desired magnitudes. On the other hand, incorrect die dimensions represent a
systematic source of error leading to the production of castings with dimensions
that are consistently off target magnitudes regardless of any variability in the
8
process conditions. Because of the trial and error approach used in dealing with
this issue, long lead times are usually experienced before a die can be released
to the production floor.
The systematic nature of this source of error is usually attributed to the
incorrect oversizing of the die cavity. Because metals experience shrinkage
when they cool down, die cavities are usually oversized to compensate for this
physical phenomenon. Thus, when built die cavities are usually enlarged by an
amount commonly known as the shrinkage or allowance factor. For simplicity
tool builders apply this factor uniformly throughout the cavity shape, inherently
assuming that the casting would cool down evenly. However, because of the
irregular shapes usually encounter in die castings, cooling does not progress
uniformly and some sections of the casting cool faster than others. This uneven
cooling behavior is one of the major causes of casting distortion that represents a
major challenge for tool builders when trying to size die cavities properly.
Another factor that poses a major challenge in properly sizing the die
cavity is the distortion the die cavity experiences due to the operating conditions.
The causes and effects of die distortion in die casting have been identified by
Ahuett [3]. This research work and many others that followed from the same
research group have supported the claim that, as a result of the combined effect
of some mechanical and thermal loads, dies in fact elastically deflect and their
operating dimensions are somewhat different, and usually unknown, from the
intended ones by the tool builder. This cavity distortion complicates matters
further for tool builders when trying to size cavities because of their inability to
9
predict what the operating conditions of the die are, and for that matter, what the
operating cavity dimensions are.
In addition to the cavity distortion issue, the restrained cooling the casting
experiences while cooling inside the die leads to generation of thermal strains.
At high temperatures, when the casting material yields easily, these thermal
strains result in plastic deformation. However, when the material has cooled
down enough and is no longer able to yield, these thermal strains lead to the
appearance of elastic residual stresses, which at the point of ejection may have a
marked effect on the way the casting distorts while cooling to room temperature.
Elastic residual stresses may also be caused as a result of thermal strains
generated while the casting cools outside the die due to uneven cooling of
different sections.
As can be appreciated, the complex interplay of the described physical
phenomena that are involved when trying to accurately size die cavities poses a
major challenge for tool builders. The large complexity of this problem has been
traditionally resolved by tool builders iteratively, usually modifying the cavity
dimensions many times before a die can be released to the shop floor. Clearly,
this approach is lengthy and cumbersome limiting to a large degree the
competitiveness of the die casting industry due to the long lead times involved.
1.4 Research objectives
This research work was focused on the development of a computer model
to simulate the die casting process in order to predict the final deformation and
10
residual stresses in a die casting. Experimental validation of the computer model
predictions formed part of the main objective of this research work as well. The
results of this investigation have the main goal of providing practitioners and tool
designers a better understanding of how process and tool design related factors
affect the final deformation and residual stresses in a die casting.
Among many other things, computer model predictions rely heavily upon
the correct representation of the system being analyzed as well the use of
appropriate constitutive models and physical properties that describe the
physical/mechanical behavior of the components involved. An important side
objective of this research work was the determination of some of the high
temperature mechanical properties of the die casting alloy employed in the
model. The availability and use of these properties was of paramount
importance to have a high degree confidence in the predictions provided by the
computer model.
1.5 Research contributions
Modeling of part distortion in die casting has been a subject of study for
many years. Nonetheless, all of the existing approaches made use of simplifying
assumptions that limit to varying degrees the respective predictions. Accounting
for the contact conditions between the casting and the die, and thus the
development of important deformations and residual stresses in the casting, has
been among the most common simplifications taken. Proper consideration of the
described situation requires incorporating the deforming die into the model. The
11
main contribution of this work is the development of a modeling methodology that
allows the proper establishment of the contact conditions between the casting
and the die prior to solidification and cooling. This modeling approach takes into
account the cavity deformations caused by the elastic deflections experienced by
the die during operation, and through a proper spatial mapping applies this
deformation to the casting shape at the end of filling; thus, accurately
establishing the contact conditions between the casting and the die walls at the
onset of cooling and solidification.
The degree of confidence in computer model predictions was increased by
the determination of the high-temperature mechanical properties of the die
casting aluminum alloy A380.0 used in this study. In particular, temperature and
strain rate dependent stress-strain curves were obtained experimentally using a
thermo-mechanical simulator available at the Materials Science and Engineering
facilities at The Ohio State University. The generated data was used as input
data in the computer model developed as part of this research work. The
benefits of this experimental work will help the modeling community by providing
a reliable set of experimental data that can be readily used in part distortion
models.
1.6 Dissertation outline
The dissertation is structured as follows. Chapter 2 presents a literature
review on casting distortion and the computer modeling techniques developed to
analyze it. Chapter 3 describes the methodology developed in this research
12
work to model residual stresses and distortion in die castings. Chapter 4
presents the experimental work done to determine the elevated temperature
mechanical properties for the die casting alloy used in this study. Chapter 5
describes and compares the results of an experimental design of experiments
with the computer model results. Lastly, the conclusions of this dissertation are
presented in Chapter 6.
13
2 CHAPTER 2
LITERATURE REVIEW
2.1 Basic concepts of stress development in castings
2.1.1 Cooling
In its most crude description, casting involves the pouring of a hot liquid
metal into a mold, which provides a negative print of the desired final product so
that when the liquid metal solidifies a shaped product is obtained. Very intricate
shapes can be obtained via this route, provided properly designed passages are
used to get the liquid metal to fill all the regions of the mold. From a broad
perspective, it can be seen that understanding of a casting process requires the
understanding of the thermal exchange phenomena that take place and govern
the described operation.
Therefore, in order for a casting to be produced the heat content stored in
the hot liquid metal must be taken out by a shaped mold whose main functions
are to extract the heat from the casting and to provide a structurally sound and
stable shape to be filled by the liquid metal. From a thermal point of view, the
mold must be kept at a lower temperature than that of the liquid metal, so a
te
m
ta
a
emperature
mold. Witho
ake place.
rrangemen
e gradient is
out a tempe
A typical de
nt is illustrat
Fig. 2
s imposed a
erature grad
epiction of
ted in Fig. 2
2.1 Temperat
14
and heat ca
dient, no he
the temper
2.1 [4]
ture profile ac
4
an flow from
eat flux is p
rature profil
cross casting/
m the liquid
resent and
e in a casti
mold interfac
metal to th
no cooling
ng-mold
e [4]
he
can
15
2.1.2 Development of stresses
Upon cooling, the hot liquid metal starts to freeze and becomes solid at
the melting point if it is a pure substance or a eutectic, or over a temperature
range if it is an alloy. As the liquid is turning into a solid it starts to develop
stresses as a result of the denser and more crystalline regularity present in the
atomic arrangement, which is held by stronger interatomic binding forces than in
the liquid state. An illustration of the progression of the stress development in an
aluminum alloy subject to tension is shown in Fig. 2.2 [5]. In order to understand
this process, Fig. 2.3 depicts the stress-elongation curves for this material as a
function of the temperatures experienced at the same locations as those
highlighted in Fig. 2.2.
In stage 1 when the metal is still completely liquid the applied stress would
just cause the liquid to follow the end plates, since a liquid cannot develop any
stresses. Looking at Fig. 2.3, it can be predicted that any stress applied at this
stage would cause it to elongate quite substantially. Following the next stage,
when a small amount of solid is present in the liquid, the application of a tensile
stress will cause this mixture to deform quite substantially since there is no
coherency among the solid particles that can provide any obstruction to the
tensile load. In stage 3, when the mixture is mostly solid with some liquid, a
coherent network between the solid particles or grains has already been
established, thus upon application of the tensile load the weak solid would
deform and break easily as shown in Fig. 2.3. The rupture tears apart the grains
and since the small amount of liquid present is isolated, it cannot fill the cracks
16
thus the very well known defect of hot tears develops. Stretching of the metal
below the solidus temperature as shown in stage 4 causes the metal to deform
plastically under very low stress magnitudes. In this stage the ductility of the
material is high and cracking is not observed unless there exist a brittle phase
that can cause it. At this stage recrystallization of the grains may be obtained if
the grains are deformed such that they begin to recrystallize. A twin effect that is
difficult to distinguish but which is also present in this stage is the phenomenon of
creep, which is characterized by a continuous elongation of the material with time
under the application of a constant load. Creep causes the material to further
deform plastically and contributes to the total plastic elongation of the material.
Finally, once the material has cooled enough such that the flow stress is
substantially large, any applied stress smaller in magnitude than the achieved
flow stress will produce only elastic strains, which are not relieved by any plastic
deformation but rather when the load is removed causing the material to spring
back.
18
Fig. 2.3 Stress-elongation curves at different temperatures [5]
The time the casting remains under the application of a given stress
magnitude, either due to a restraint offered by the mold or due to stronger
sections of the casting that have cooled earlier as will be shown later, determines
the magnitude of the elastic residual stresses with which the casting is ejected
from the mold. This behavior is depicted in Fig. 2.4, which shows the effect of
the time the casting remains in the mold on the magnitude of the residual
stresses.
19
Fig. 2.4 Residual stresses as a function of ejection time [4]
2.1.3 Shrinkage
As is well known in foundries, the mold is made slightly larger than the
size of the final product because the liquid metal occupies more volume than the
final casting. This behavior is illustrated in Fig. 2.5 [4]. Three different types of
shrinkage are experienced when a liquid molten metal becomes solid. The first
20
one is liquid-to-liquid shrinkage, which represents no challenge for the
foundryman since the contraction experienced in this stage can be easily made
up for by pouring slightly more metal. The second stage is liquid-to-solid
shrinkage. This shrinkage is experienced due to the denser arrangement of the
atoms in the solid state as compared with the liquid state. Problems may arise
due to this type of shrinkage mainly if the feeding of liquid or solid metal is not
adequate, leading to the formation of shrinkage cavities. The last type of
shrinkage is solid-to-solid shrinkage. This type of solid contraction represents no
problem to the foundryman if the casting is free to contract by itself. Typically
this is not the case, and due to the complex shapes usually cast, the cooling of
some regions of the casting is often constrained by other regions that have
cooled earlier and thus are stronger, causing the weaker regions to plastically
deform. Another type of constrain typically present while the solid casting is
cooling is that offered by the mold walls. The mold, which is usually made of a
stronger material than the casting, exerts a force in the opposite direction to that
exerted by the casting upon it while contracting, thus offering a rather strong
obstacle to the free contracting action of the casting causing it to enlarge and
build up residual stresses at the latter stages of cooling. After removal of the
casting from the mold has taken place, it can be expected that the casting being
perhaps with some shrinkage porosity, somewhat distorted, and out of tolerances
in some regions making the predictability of the dimensions troublesome for the
foundryman. This leads to difficulties in estimating the size of the mold since the
21
contraction and deformation experienced by each region of the casting might be
really challenging to predict.
Fig. 2.5 Types contractions experienced by a solidifying material [4]
22
2.2 Casting distortion
2.2.1 Mold restraint
As was mentioned before, as a result of the solid-to-solid contraction, the
casting shrinks in a magnitude proportional to the temperature difference and
also proportional to the coefficient of linear thermal expansion. However, the
amount of shrinkage a given casting can experience in actuality depends on the
degree of restraint imposed by other regions of the casting cooling faster at
earlier stages and also the degree of restraint imposed by the mold walls. Thus,
the amount of allowance applied to the die in order to account for the shrinkage
of the casting while cooling can be rather cumbersome since different regions of
the casting may require different allowance, depending on the contribution of
each of the restraints to which the regions of the casting are subjected to while
cooling.
Campbell [4] proposed a rather simplistic method to assess the degree of
restraint offered by sand molds and in this way predict the pattern/mold
allowance based purely on the geometry of the casting. It is proposed that a
straight bar such as that shown in Fig. 2.6 would experience zero restraint and
would be allowed to cool and shrink freely. On the other hand, a box-shaped
casting with thin walls cast around a rather big and stiff sand core would
experience theoretically infinity constrain as the walls of the casting get thinner
and thinner. In this case the casting contraction would be theoretically zero. The
results of these two cases can be thought to provide the points for a calibration
curve in which the first one represents the case of a fully dense casting, whereas
th
b
d
d
c
T
F
he second o
e obtained
ensities of
ivided by th
ontraction v
The results o
Fig. 2.7.
one represe
by using d
the geome
he overall v
values are
of such ana
Fig
ents the ca
ifferent geo
tries are co
volume occu
measured o
alysis can b
g. 2.6 Contrac
23
se of a null
ometries su
omputed by
upied by th
once the pa
be presente
ction of three
3
l dense cas
uch as those
y taking the
e envelope
art as reach
ed in curves
different cas
sting. Differ
e shown in
weight of t
e of the cas
hed room te
s such as th
ting shapes [4
rent points
Fig. 2.6. T
the casting
ting, and th
emperature
hose shown
4]
can
The
he
e.
n in
d
a
re
te
F
F
The r
egrees of r
re shown in
esults of the
emperature
Fig. 2.8.
ig. 2.7 Pattern
results of an
restraint offe
n Fig. 2.8.
e previously
e match the
n's maker con
n experime
ered by gre
The results
y discussed
predicted c
24
ntraction as a
ntal investi
een sand m
s published
d method, s
contraction
4
a function of c
gation in w
molds in stee
more than
since the 4
percentag
casting envelo
hich the eff
el castings
70 years a
points obta
es for the s
ope density [4
fect of diffe
was studie
ago confirm
ained at roo
steel curve
4]
rent
ed
m the
om
in
g
s
th
ill
F
In act
eometries s
ections of t
he pattern/m
lustrates th
Fig. 2.8 Contr
tuality, mos
such as tho
the casting
mold allowa
is scenario
raction of stee
st of casting
ose shown
be restrain
ance will dif
o is the cast
25
el castings for
gs are comp
in Fig. 2.6,
nted by diffe
ffer from se
ting shown
5
r different deg
prised of a
thus one m
erent amou
ection to sec
in Fig. 2.9.
grees of mold
series of si
might expec
nts by the m
ction. A sim
Upon coo
d constrain [4]
mple
ct that differ
mold, and t
mple case t
oling, it can
]
rent
hus
that
be
s
d
m
o
2
b
c
c
m
a
s
een that the
irection, bu
maximum co
btained is t
.2.2 Casti
Aside
e distorted
ool at differ
onductivity
mold which
core, etc.
hrinkage al
e long horiz
ut it is being
onstraint fro
that one sh
Fi
ng restraint
e from the m
by the effe
rent rates d
of the mold
affect the w
All these fa
llowance ev
zontal bar w
g restrainted
om the mold
own in das
g. 2.9 Effect o
t
mold restrai
ect of uneve
depending o
d/die they c
way the hea
actors make
ven more d
26
wants to sh
d by the ve
d and as a
hed line.
of mold const
int, it has b
en cooling.
on the volum
contact, the
at is extract
e the proble
ifficult to pr
6
rink and pu
rtical bars,
result of th
train in castin
een mentio
Different s
me to surfa
e design of t
ted by the m
em of deter
redict as ca
ull in the ho
which expe
is, the final
g distortion [4
oned that th
sections of t
ace area rat
the cooling
mold/die, th
rmining the
an be imagi
rizontal
erienced ne
geometry
4]
he casting c
the casting
tio, the
lines in the
e presence
e amount of
ned.
early
can
can
e
e of
f
27
As an illustration of the effect of casting design on the casting distortion,
Fig. 2.10 shows two scenarios that can yield quite different results as far as
casting distortion is concerned. The distortion or eventual crack that results in
the top case can be explained as follows. Upon cooling, the thinner sections of
the casting solidify the first, and their supply of material upon shrinkage is fed by
the thicker section that remains hotter for longer time. Once these sections cool
enough, they become strong, and the shrinkage action of the thicker section can
cause bending of the thin section or even produce a crack if the thicker section is
weak enough not being able to withstand the tensile load. The bottom case
shows a slightly different scenario. In this case, the outer sides bow because the
inner section cools the slowest due to the fact that it is surrounded by hotter
cores and thus the dissipation of the heat from the cores takes longer. Upon
cooling, the inner section starts to pull the outer ones, and cause them to bow, or
if it is weak enough it may crack as shown.
28
Fig. 2.10 Effect of casting geometry in casting distortion pattern [4]
2.3 Casting and die distortion in die casting
2.3.1 Die distortion
During a typical die casting cycle a certain set of loads are present that
undoubtedly affect the performance of the die, the machine, and ultimately the
productivity of the process. In this section, a description of the loads that affect
the performance of the die are highlighted with the goal of setting the background
for the even more complex phenomena of part distortion.
As a broad classification, the loads experienced by the dies are classified
as mechanical or thermal. Due to their nature, the mechanical loads can be
29
subdivided into static and dynamic. Among the static loads, the clamping force
exerted by the toggle mechanism is the simplest. This force is applied,
depending on the toggle location relative to the ejector platen back surface,
either on the top and bottom or nearly equally distributed on the center of the
ejector platen back surface. This load strains the tie bars in tension so that a
constant, but non-uniform, pressure keeps the die halves in contact during the
injection and dwell stages. As a simplification to the characterization of the static
loads, the intensification pressure is considered in this category. After the filling
of the cavity is completed, high pressure stored in an accumulator is released so
that the injection piston can further push the molten metal into the cavity,
guaranteeing filling of intricate regions in the cavity and also compressing the
pores of entrapped air caused by the traveling of the molten metal.
In the dynamic loads category, the well-known pressure spike at the end
of filling is definitely the most important one. This phenomenon has been
observed and documented in the die casting literature for years. It is all a result
of the inertia of moving masses coming to rest in a very short period of time. At
the start of filling of the die cavity the plunger is accelerated to achieve the fast
shot speed. However, the filling time does not last long (on the order of
milliseconds) and suddenly all moving masses including hydraulic oil, piston, and
the rod come to rest once the cavity is filled. This sudden stop imparts a
tremendous pressure spike onto the die and machine structure that sometimes
has been identified to be the cause of flashing problems.
30
The thermal load affecting the dies is undoubtedly very critical. When built
at room temperature the die halves come perfectly in contact. However, due to
the continuous injection and cooling of the metal inside the die cavity, the dies
absorb heat, causing some elastic deflection. Moreover, since during the
injection and dwell stages the die is not free to expand, the thermal distortion
usually causes the die to grow inside the cavity, affecting its dimensions.
The combined effect of all these loads imparts some distortion in the die,
which under most circumstances is not easy to predict. As a result of this, the
process of producing a die is usually iterative requiring many trials before a die
can be released to production, leading to a decrease in the productivity of the
industry due to the long lead times incurred.
2.3.2 Casting distortion
The process of producing a die casting starts with the injection of the
molten metal into the die. As was already discussed, due to the thermal and
mechanical loads experienced by the die during operation, the cavity shape the
liquid encounters once it fills it is somewhat distorted from its nominal shape at
room temperature. These important small cavity deformations have an important
effect in that they determine the initial casting shape just prior to the onset of
solidification and cooling.
During solidification and cooling, the casting releases its heat content to
the die. The effect of this heat exchange produces reversed effects on the
casting and die, leading to shrinkage of the casting while causing expansion of
the die, thus affecting once more the cavity dimensions. In die casting as in any
31
other casting process, self induced as well as mold induced restraints occur while
the casting is cooling inside the mold. It should be mentioned that because die
casting relies in using metallic dies, the degree of restraint imposed by the die
walls is much higher than other processes such as sand casting, having a
marked effect on casting shrinkage. This phenomenon leads to plastic
deformation in casting during the early stages of cooling, while during the later
stages it leads to the formation of important residual stresses as was already
discussed.
One interesting feature that differentiates die casting from the rest of the
casting processes is the use of an intensification pressure that helps in reducing
porosity levels as well as in feeding material to intricate regions. As a result of
the high pressures applied, the hot liquid metal is left pressurized before it starts
to solidify. It is conjectured that this pressurization may affect the early plastic
and visco-plastic behavior of the newly formed solid, which experiences higher
plastic deformation due to the large hydrostatic state of stress to which it is
initially subjected. Thus, the fact that the liquid experiences a phase change
under pressure may lead to additional plastic deformation at the early stages of
solidification.
After a predetermined time the casting is ejected from the die. At the point
of ejection the casting may possess some residual stresses as well as a non-
uniform temperature profile due to its cooling process. Under these conditions,
die castings are usually left to cool at room temperature. Sometime, parts are
quenched or trimmed for subsequent post-processing operations such as
32
machining. The final casting obtained is the result of all deformations induced
during the various process stages it goes through.
2.4 Computer modeling of solidification
From a metallurgical standpoint the phenomenon of solidification is a
process of nucleation and growth as outlined by Wallace et al [6]. A wide variety
of physical phenomena take place when a liquid metal solidifies. The range of
these physical phenomena can vary from a few atomic distances when the
clustering of the atoms is taking place during the growth of a solid grain, to a few
millimeters or centimeters when the solid transport of a few solid particles or
grains takes place, leading to macrosegregation problems in castings. From a
mechanical engineering point of view, solidification might be regarded as a fluid
flow, heat transfer, and stress development problem, with their respective
physical equations developed based on continuum mechanics principles. The
solution of these “macroscopic” phenomena provide the basis on which the
analysis and study of a mold filling, heat flow, and residual stress and distortion
of casting can be done to gain understanding in the design of molds and parts for
instance. Due to the scope of these analyses, little or no attention is paid to the
nucleation and growth of solid grains and other microscopic phenomena that take
place and in most instances, the solution of the macroscopic phenomena is used
to make gross predictions of the “microscopic” ones and vice versa. Because of
the nature of the wide variety physical phenomena as well as the wide range of
length and time scales in which these take place, when one speaks of computer
33
modeling solidification a clear boundary ought to be drawn to isolate the system
one wishes to analyze and the simplifying assumptions that will be considered.
This section is intended to provide a review of the literature of computer modeling
of the macroscopic phenomena of solidification.
The mathematical modeling of some of the macroscopic as well as the
microscopic phenomena present in solidification is discussed by Dantzig [7],
Overfelt [ 8] and Upadhya [9]. Fig. 2.11 depicts the different types of analyses
that can be performed as well as the outputs and results they may provide. Fig.
2.12 shows the typical areas that a comprehensive solidification modeling system
may consist of.
2
c
s
c
e
lin
o
.4.1 Fluid
Filling
asting proc
queeze cas
oupled with
nough to h
nes. Also,
f filling repr
Fig. 2.12
flow mode
g of the mo
cesses. Fo
sting and sa
h the heat t
inder prope
the temper
resent the i
2 Typical stag
ling
ld by the m
r slow filling
and casting
ransfer, sin
er filling of t
rature profil
nitial condit
35
es in a comp
molten meta
g processes
g, modeling
nce heat los
the mold, le
le of the liqu
tion for a su
5
rehensive sol
l usually re
s such as lo
g of the fluid
sses during
eading to co
uid casting
ubsequent
lidification mo
epresents th
ow pressur
d flow must
filling migh
old shuts an
and the mo
solidificatio
odel [10]
he first step
re die castin
be done
ht be large
nd/or weld
old at the e
on analysis,
p in
ng,
end
,
36
thus the accuracy of the solidification analysis is dictated to some extend by the
accuracy of the thermal conditions obtained at the end of the filling analysis.
Since most metals can be represented as incompressible Newtonian fluids, their
flow is governed by the Continuity and Navier-Stokes equations [7]
0 Eq. 2.1
Eq. 2.2
where:
is the density
is the velocity vector
is time
is pressure
is viscosity
is the body force
Besides proper predictions of velocities and pressure profiles in the liquid,
the filling of the mold is an important feature that can be included in the fluid flow
analysis. To properly model the advancement of the interface between the liquid
molten metal and the air in the mold cavity, Eq. 2.2 must be augmented to
describe the movement of the free surface. To model this situation, the majority
37
of the fluid flow software uses the volume-of-fluid method (VOF), which uses a
filling function which is advected with the fluid satisfying the equation [7]
· 0
Eq. 2.3
The value of within a given computational cell is associated with the
state of the cell: when =1 the cell is full, when =0, it is empty, and cells where
0 < < 1 contain the interface [7].
The other important part of the filling analysis is the heat transfer. Since
conduction is metals can be properly represented by Fourier’s law, the energy
transport equation is described by the heat conduction equation
· ·
Eq. 2.4
where:
is the specific heat
is the temperature
is the thermal conductivity
is the internal heat generation
The advective term · in Eq. 2.4 couples the energy transport equation
to the velocity field. To model the “phase change” of the liquid metal, the term
38
in Eq. 2.4 is used to represent the evolution of the latent heat in the liquid. One
of the expressions that can be used is
Eq. 2.5
where:
is the latent heat
is the fraction of solid
The evolution of the fraction of solids for a particular alloy must be
determined so that its mathematical representation can be used in Eq. 2.5. An
easier way to model the release of the latent heat is the so called “specific heat
method”. The release of the latent heat produces an increase in the internal
energy or enthalpy of the liquid, and since the specific heat and the enthalpy for
an alloy are related by
… … … … … … … … … …
1 ∆ … … … .
∆ … … … … … … …
Thus, knowing the evolution of the enthalpy from measurements, one can
backwards compute the specific heat in the region between the liquidus and
solidus, preserving the area under the curve as illustrated by Fig. 2.13. This
m
b
2
th
ty
la
re
fi
method prod
e easily im
.4.2 Stres
The m
he fluid flow
ype of analy
arge numbe
esults obtai
nal dimens
duces a pie
plemented
Fig. 2
ss modeling
modeling of
w problem.
ysis is that
er of compu
ined from a
sions in cas
ece-wise co
in the ener
2.13 Relations
g
f stresses in
One of the
the govern
utational iss
a stress mod
tings as we
39
ontinuous fu
rgy transpo
ship between
n castings r
e main reas
ing phenom
sues. Howe
del can be
ell as to imp
9
unction for t
rt equation
specific heat
represents
ons for the
mena are ve
ever, when
used to pre
prove mold
the specific
.
and enthalpy
a greater c
greater dif
ery comple
properly so
edict residu
design to m
c heat that c
y [11]
challenge th
fficulty in th
x and pose
olved the
ual stresses
match casti
can
han
is
e a
s and
ng
40
shrinkage to the so called pattern maker allowance, mostly regarded as an
empirical factor. This topic has been an active research area in many casting
processes for more than a decade and the underlying theory behind this
modeling work has been outlined in a series of papers [11-16].
Stress modeling is a thermo-mechanical analysis that involves solving the
equilibrium, constitutive and compatibility equations, which relate force to stress,
stress to strain, and strain to displacement, respectively. The equilibrium
equations can be represented by
∆ ∆ Eq. 2.6
where
∆ ∆ , ∆ , ∆ , ∆ , ∆ , ∆
∆ ∆ , ∆ , ∆
The compatibility equations that relate strain to displacements can be
represented by
∆ ∆ Eq. 2.7
where
∆ ∆ , ∆ , ∆ , ∆ , ∆ , ∆
∆ ∆ , ∆ , ∆
41
The matrix representation of the differential operators is written in the
matrix as
0 0
0 0
0 0
0
0
0
The constitutive equations that relate stress to strain can be represented
by
∆ ∆ Eq. 2.8
where the matrix contains the elastic constants, which are a function of only
two material properties ( , Young’s modulus, and , Poisson’s ratio) for isotropic
materials
42
As stated in Eq. 2.8, only elastic strains are responsible for stress
development in castings. This just confirms the experimental results of different
stress-strain curves at different temperatures such as those shown in Fig. 2.3,
since plastic strains are easily accommodated by plastic deformation of the
casting, whereas elastic strains produce elastic stresses which represent the
residual stresses with which the casting is left after is taken out of the mold, or in
some instances at room temperature.
As already mentioned, the stress modeling problem is a thermo-
mechanical one. The temperature differences between the casting and the mold
that are present when the casting is cooling inside the mold are the source of
volumetric contractions that happen in the casting. Since most castings are
comprised of intricate shapes of different volume-to-surface-area ratios which
usually cool at different rates and which interact with the mold walls in many
different ways, the volumetric shrinkage induced by the cooling of the casting is
usually restrained by either, other sections of the casting or by the mold walls.
This restraining effect causes the development of strains that lead to casting
distortion or the development residual stresses during the later stages of cooling.
It should be mentioned that thermal strains by themselves do not cause any
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43
stresses, they just promote a “thermal load” or a “mismatch” that are eventually
translated into elastic or plastic strains.
As far as modeling of casting stresses is concerned, thermal strains are
the main source of elastic and plastic strains. The stress model is usually
composed of a thermal and a mechanical model. Since the conduction in most
metals can be accurately represented by Fourier’s law, the thermal model
involves solving the energy equation (Eq. 2.4) without the advective term.
The stress model can be solved in a sequential or a coupled manner. The
thermal model can be solved first and its results can be “loaded” into the
mechanical one. On the other hand, both models can be solved in a coupled
manner, solving for the temperature field first and the displacement field second,
and then back checking whether the produced displacement field affected in any
way the thermal field. Coupled models are usually employed when the
development of a gap due to shrinkage of the casting affects the heat transfer
rate between the casting and the mold. This phenomenon can affect the thermal
field in the casting because the formation of the gap reduces the heat transfer
coefficient at the casting/mold interface, which retards cooling of the casting and
produces higher ejection temperatures that may lead to larger distortions.
2.5 Finite element method in solidification modeling
Because of the many challenges that the modeling of macroscopic
phenomena of solidification involves, the topic has attracted the attention of
many researchers throughout the world. Finite elements have been widely
44
accepted for solving the governing equations previously presented. The
formulation and solution of the governing equations by finite elements has been
presented in a wide variety of publications [10-13, 17-24].
Dantzig [12] presents the formulation and solution technique for modeling
the development of the thermal stresses in castings. A detailed description of the
treatment of the different strains present during the cooling of a casting is
presented with enough emphasis on the constitutive relations that govern each
type of deformation. The formulation presented treats the problem as a thermal-
mechanical one, thus no account is given to the effects of the thermally coupled
fluid flow effects on the stress development in the casting. Lewis et al [11]
discuss the finite element algorithms to model the solidification of a metal from
the mold filling stage to the final cooling of the casting. The proposed formulation
considers the thermally coupled fluid flow and mechanical conditions that govern
the whole solidification problem. Considerable attention is given to the way the
latent heat release at the solid-liquid interface takes place. A free surface
tracking method is implemented in the formulation so the position of the fluid front
can be predicted in the mold filling stage. Trovant et al [17] present a numerical
algorithm to model the shrinkage of a metal while it undergoes solidification.
Latent heat release, fluid front tracking as well as other fluid flow conditions are
taken into account in this work. Seetharamu et al [10] discuss the thermal stress
generation problem in castings and the formulation of a thermally coupled elasto-
viscoplastic model is presented. The proposed model results are validated
mainly with experimental results for large steel ingots. A numerical scheme that
45
uses shell elements to represent the casting is presented by Hetu et al [18] to
simulate the filling of thin-walled die castings. Owing to their very thin design, the
filling analysis of die castings is simulated using the also known 2.5D approach,
in which a thickness is given to the shell elements, reducing the numerical
complexity and running times usually faced with full three dimensional meshes.
A numerical scheme to treat three dimensional meshes for casting processes
such as sand casting is also presented. A free surface tracking method is also
implemented to accurately predict the advancement of the fluid front during mold
filling stage. The formulation of an elastic-viscoplastic stress model is also
discussed. The formulation of a very sophisticated coupled thermoplastic model
is presented by Agelet et al [19]. The model considers temperature dependent
material properties. Latent heat effects are also incorporated into the formulation
through a free energy function. Plastic response of the material has been
modeled using a temperature dependent model that takes into account nonlinear
hardening due to plastic deformation and thermal linear softening.
Implementation of gap dependent thermal conditions is also considered in the
formulation. A very original formulation of a thermal-mechanical model with
considerations for microstructure evolution in aluminum alloys is presented by
Celentano [20]. This original work presents several important relevant
contributions such as: the unified formulation to describe the liquid, mushy and
solid phases present during solidification, gap dependent thermal conditions, the
effect of volumetric expansions due to phase transformations, the possibility to
capture large geometric distortions especially at high temperatures and the
46
influence of the coupled dendritic/eutectic microstructure formation on the
temperature dependent constitutive laws.
Of special consideration is the work presented by Bellet et al [21-22]. The
proposed work discusses a very comprehensive formulation of a fully coupled
thermo-mechanical model that uses an elastic-viscoplastic material formulation to
describe the casting. The proposed formulation is justified on the basis of the
importance of the gap-dependent heat transfer conditions present at the
casting/mold interface. A unified temperature dependent elastic-viscoplastic
formulation to describe the material behavior in the liquid, mushy and solid states
is presented, so that the solidification of the liquid metal can be accurately
described throughout the whole cooling process. An important contribution of
this work is the incorporation of contact conditions between the casting and the
mold even though the mold is considered a rigid body. This important feature
allows the modeling of stress development due to contact restraints imposed by
the mold during solid-to-solid shrinkage. The proposed formulation has been
implemented in the finite element code THERCAST targeted for solidification
analyses. A recent enhancement to the code was made by incorporating an
Arbitrary Lagrangian Eulerian (ALE) method as described in [23]. The added
capabilities allow the tracking of the free surface of the fluid front in a filling
analysis with better resolution than the to the commonly used VOF method for
Reynold’s number on the order of 103 to 104. The ALE scheme is also used for
handling convection effects due to density gradients induced in the remaining
47
liquid pool at the end of filling. The implications of the proposed formulation are
explained in large detail therein.
The formulation of a model that accounts for fluid-solid thermal-
mechanical interactions is presented by Cruchaga et al [24]. A coupled multi-
physics model for the analysis of solidification processes is presented. The
proposed formulation has been developed to accurately describe the material
description during the liquid, mushy and solid phases that occur during the filling,
solidification and cooling of the casting. The important contribution of this
formulation is that it is aimed at being able to describe the influence of fluid
motion on the temperature field and casting/mold evolutions when advective
effects caused by the liquid pool are taken into account. An additional
contribution sought is to be able to study the effect of non-uniform initial
temperature fields in the solidification and cooling stages. This modeling feature
enables to suppress the commonly used assumption of uniform temperature
distribution at the end of filling, which might be invalid for slow filling processes
such as sand and permanent mold casting. As noted by the authors, the
consideration of buoyancy effects and phase change during the whole process
couples the fluid phase motion with the thermal and mechanical responses
through the fluid velocity, temperature field and gap formation [24].
2.6 Computer modeling of casting and die distortion in die casting
Because of the high cost involved in building a die, computer modeling
has emerged as a useful tool in helping designers to predict potential operational
48
problems in dies. The field of computer modeling in die casting has being an
active research area for more than two decades. Early computer models have
focused on predicting thermal profiles as well as fluid patterns. These models
have been widely popular and the area has become relatively mature. However,
because of its complexity the subject of part and die distortion in die casting has
been explored for more than a decade only. This section provides a review of
the literature that has been published in this field.
2.6.1 Die distortion modeling
Die casting die distortion modeling has been analyzed in a series of
publications [25-34]. Barone et al [25] proposed a modeling technique that
accounts for the clamping, temperature and pressure loads using the boundary
element method. The proposed scheme is particularly unique, in the sense that
the thermal load resulting from the continuous injection and cooling of molten
metal that causes the die to elastically distort, has been characterized to affect
only the region of the die near the cavity. It is claimed that the effects of this
thermal load are concentrated near this region, and based on that the boundary
element method is used. The proposed modeling approach considers structural
elements such as inserts, dies, and platens. Machine toggle and tie bars are
incorporated by additional representation of their stiffness. The results obtained
for an automotive transmission case claimed to correlate well with experimental
evidence.
Another modeling approach based on the boundary element method is
proposed by Milroy et al [26]. The model attempts to predict elastic deformations
49
at the cavity surface that result from thermal expansion and cavity pressure
effects. Clamping force effects are not incorporated on the model, but instead
the die is anchored at the corners. It is claimed that based on the model
predictions, dimensional changes that compensate for the thermal expansion on
the cavity can be proposed, so the cavity dimensions come to be correct during
operational conditions and flashing problems can be eliminated.
A normalized approach designed to predict thermal stress in a die casting
die is proposed by Dour [27]. The model represents the die casting die as a slab,
which is subjected to a heat flux load on one face, while the other face is kept
isolated. The model is rather simple and its results clearly do not reflect the
effects of important mechanical loads.
The bulk of the literature as far as die distortion is concerned is presented
in references [28-34]. These publications emerged as a result of the
investigations performed at the Center for Die Casting at The Ohio State
University. The main purpose of the research was to: a) assess and characterize
the important loads that contribute to the deformation of the die, b) provide
design guidelines to machine and die builders in order to minimize and/or
attenuate die deflection, parting plane separation, excessive machine distortion
that may result from unbalanced tie bar loading, etc, c) provide guidelines to
practitioners to assess the influence of machine and die interaction in the final
distortion of die casting parts. Several research cases have been performed and
their results have provided a clearer understanding of the important factors that
determine the deflection in die casting dies.
50
The results of the research work at The Ohio State University have
established the main causes of die deflection. It has been determined that die
deflections are caused by the mechanical and thermal loads experienced by the
dies during operation. Research findings have suggested that the majority of the
die distortion is caused by the uneven thermal profiles experienced by the die
during operation. These uneven thermal profiles are caused by the asymmetric
and irregular shapes normally used in casting design. Process control
parameters such as total cycle time, dwell time and cooling line configuration
have been proven to substantially affect the way thermal profiles develop in the
die. Clamping force effects have been also proven to be significant. Due to the
uneven thermal expansion of the die, once it is brought in contact during
clamping, an uneven sealing at the parting plane might be caused. The
described situation can give rise to spitting of molten metal outside the cavity.
Flashing problems might reduce the productivity of the casting process, since
post-processing operations may need to be incorporated to trim the extra
material. Another side effect of the described situation is the uneven loading of
the tie bars, thus tie bar breakage or severe wearing of bushings might be also
experienced. The intensification pressure used at the end of filling has also
being characterized as important in die deflection modeling. Research findings
suggest that this pressure load may affect cavity dimensions and also can
worsen flashing problems if uneven sealing of the parting plane is present.
51
2.6.2 Casting distortion modeling
The prediction of residual stresses and part distortion in die casting has
been analyzed by Ragab [35], Sequeria et al [36], and Caulk et al [37]. The first
two studies rely in the use of commercially available Computer Aided
Engineering (CAE) packages, the first one based on a finite element formulation
using Abaqus, whereas the second one uses the finite difference based code
tailored for casting analyzes MAGMASoft. Caulk et al [37] present a formulation
that employs a combination of boundary element and finite element methods. A
description of the procedures followed in each case study is presented.
The understanding of phenomena governing die deflection modeling in the
Center for Die Casting brought up the issue of incorporating the possibility of
modeling casting distortion. The case study presented by Ragab [35] was aimed
at predicting the distortion and residual stresses in a ribbed plate. The modeling
stages were as follows. At the start of the simulation, the casting was placed in
contact with the undeformed die. Subsequently, the clamping, thermal and
pressure loads were applied all instantaneously. After these loads were applied,
the casting was allawed to cool inside the die. The cooling of the casting to room
temperature was also simulated, taking the displacements, temperatures and
stresses at the point of ejection as the initial conditions for this analysis. A
sensitivity analysis in which several parameters such as: material constitutive
model, gap dependency of heat transfer coefficient was also performed to test
their impact on the final distortion results. Dimensional results of selected
features of the casting from the simulation model were compared against
52
experimental results. A fair amount of disagreement was found between the
experimental results and the simulation predictions, having the greatest
difference for casting features across the parting plane. Three main factors were
identified as the main source of disagreement. The first one was the inability of
the casting solid elements to follow the distorted shape of the die as the
clamping, thermal and pressure loads were applied, leading to inaccuracies in
the initial shape of the casting as well as to some contact stresses induced in the
casting from contact with the die walls. The second factor was the modeling
inaccuracy in representing the intensification pressure load. This load, which is
in actuality transferred by the liquid casting to the cavity walls, was modeled as a
boundary condition applied at the cavity surface. In doing this, the casting and
the cavity wall were not placed in tight contact at the beginning of the cooling
period, thus initial contact conditions of the casting features with those of the die
were not properly represented. A side effect of the intensification pressure used
in die casting is the fact that the phase change of the liquid metal takes place
under the action of high pressures. This condition means that a hydrostatic
compressive stress of state should be applied to the solidifying liquid elements,
translating into initial plastic deformation of the weak metal, producing high
distortions. This complex phenomenon was also not modeled. The lack of
material properties that can describe the mechanical behavior of the material at
high temperatures, especially near the solidus, was the third factor that was
identified as contributor for the differences between the modeling and the
experimental results.
53
The distortion of an aluminum outboard housing was modeled by Sequeria
et al [36]. The modeling work was done using the module MAGMAstress
included in the commercial casting software MAGMASoft. The procedure to
predict residual stresses and distortions in MAGMA is carried out in two stages.
During the first stage the die quasi steady-state temperature profile is obtained
by simulating a repeated number of thermal cycles. Once this quasi steady-state
profile is reached, the casting is added to the analysis and the cooling period of
the casting cycle is simulated. It is worth mentioning that this analysis is purely
thermal; thus, no account for any deformations and stresses due to contact
interactions between the casting and the die is being taken. At the end of this
step, the casting final temperature profile is extracted and is taken as the initial
condition for the second stage. This part of the analysis consists in performing a
thermal-mechanical analysis on the casting under free convection thermal
conditions. The results of this part produce the distorted pattern that results from
the cooling of the casting to room temperature. Typical outputs from this kind of
simulation are displacements and residual stresses. As far as the case study is
concerned, it was stated that the numerical displacement predictions obtained
from the analysis correlate well with experimental measurements. However, the
modeling procedure just described does not take into account any deformation of
the die that results from thermal and mechanical loads present during normal
operation, thus any dimensional changes in the cavity resulting from such loads
are not accounted for. Furthermore, residual stresses and distortion of the
casting that results from hindered shrinkage by the die walls is also not being
54
considered, since the modeling procedure does not model contact between the
solid bodies. Phase change under pressurized conditions is likely to be also not
incorporated, thus one more source of inaccuracy is present as well. Based on
the above mentioned factors, it is doubtful that the reported simulation results
could correlate well with the experimental measurements.
The modeling procedure described in [25] for modeling of die distortion is
part of the numerical scheme used by Caulk et al [37] to model distortion and
residual stresses in die casting parts. The procedure followed can be described
in two stages. In the first stage a die distortion analysis is performed in order to
obtain the deformed operating conditions of the die. Modeling of die distortion is
obtained by considering the thermal load that results from the continuous
injection and solidification of the casting inside the die, the clamping load, and
the intensification pressure. The casting is not incorporated in this stage of the
model. It is assumed that the casting ejects with the same shape as the
deformed die cavity. It is claimed that because the yield stress of the casting is
so low while inside the die, most of the deviatoric stresses are insignificant. The
second stage consists of a thermo-mechanical model that represents the cooling
of the casting after ejection. It is assumed that the casting responds elastically
as it cools outside the die. It is worth mentioning that the casting is modeled
using linear shell elements, and the analysis is solved using a finite element
formulation.
55
2.7 Casting distortion studies
A series of research projects aimed at determining the variability of casting
dimensions in regard to process variables and casting geometric features were
done in Professor’s Voigt group at the Pennsylvania State University [2, 38-39].
The studies done covered three casting processes, die casting [2], sand casting
[38] and investment casting [39]. The major goal in all these studies was to
predict, by using statistical methods, the pattern allowance that should be applied
to the mold based on different casting geometric features. The projects
consisted in performing a statistical dimensional analysis of a series of casting
geometric features, the results of which provided a measure of the dimensional
variability of the feature in regard to different process variables as well as its own
geometric shape.
As far as the die casting study is concerned [2], several important
conclusions were drawn that are worth mentioning. A major conclusion of this
study was the fact that current dimensional tolerance standards in die casting do
not represent the actual capabilities of the process. Underestimation of
tolerances for small features and overestimation of tolerances for large features
figured among the most common practices in industry. The study also concluded
that casting geometry variables and process variables significantly affect the
dimensional stability of die casting features. The following variables were
identified as major sources of dimensional variability: casting feature length, shot
weight, feature restraint, hold time, and die locking force. The degree of restraint
imposed by a core or a die wall was also identified as a contributor in this regard.
56
Numerical predictions of dimensional changes in steel castings using
MAGMASoft were conducted by Professor Beckermann’s group [40]. The goal
of the study was to assess the capabilities of MAGMA to predict pattern
allowance factors for steel sand castings by comparing the results of the
computer models with measurements done by Professor’s Voigt group at the
Pennsylvania State University. The geometries analyzed corresponded to one of
those analyzed by Peters [38] and a shovel adapter produced by an industrial
partner. A thermal-mechanical analysis of the solidification of each sand casting
was done and the results were compared with experimental measurements. This
case study concluded that for features that undergo unrestrained shrinkage, the
results provided by the computer model showed fairly good agreement with the
experimental ones. However, large disagreement was reported for features that
experienced partial or complete restraint during shrinkage. Among the possible
reasons identified were the inability of MAGMA to incorporate the mold material
in the stress analysis, leading to inaccurate modeling of phenomenon such as
gap formation and/or development of stresses and deformations in castings due
to contact interactions between the casting and the mold. Another reason was
the inaccurate modeling of irreversible sand expansion experienced by some
types of sand when a certain temperature range is reached.
The results of an industrial study performed by Honda engineers were
presented in [41]. The goal of this project was to determine the most significant
process variables that dictate the dimensional stability of die castings. A
statistical analysis of casting geometric features was done in order to assess the
57
influence of process variables such as: melting temperature, die filling velocity,
water quenching temperature, spraying time and holding time. The study
concluded that holding time was the most significant factor that affects the
dimensional variability of die castings. It was stated that all other factors had a
minor effect in this regard.
A study of the effects of process control parameters on casting
dimensional variability for die casting was done by Osborne [42]. The research
study focused on determining the effect of process parameters on across parting
plane dimensions and in dimensions within the ejector die. The selected factors
were: injection velocity, dwell time, cycle time, cooling line, spray time and metal
temperature. To assess the effects of these process variables two die designs
were selected. For across parting plane dimensions a flat plate, the parting
plane of which was placed in the middle of the plate thickness, was selected.
The plate thickness and its flatness were chosen as response variables. To
study dimensions within the ejector die, a flat plate with four ribs protruding into
the ejector die was selected. The three distances formed between the four ribs
were chosen as response variables for this case. A fractional factorial design
was used as a guide to conduct the experiments. Analysis of variance results
showed that the gate velocity, cooling line and the cycle time have a significant
effect on the plate thickness. Flatness measurements showed no significant
dependence on any of the selected factors. Statistical results showed that
dimensions within the ejector die are significantly affected by the dwell time only,
no other factor showed any significant effect on the analyzed features.
58
Computer models have also been recently used for the prediction of
tooling allowance factors for investment casting [43]. Investment casting
represents a more challenging case due to the complexity of the many physical
phenomena involved in producing a final casting. Production of the wax pattern,
shell, dewaxing, and final casting all add more complexity to the already difficult
task of predicting tooling shrinkage factors. In essence, two different molds are
used before a casting is actually produced, and thus tooling factors for each mold
have to be accurately predicted before a dimensionally sound casting is
obtained. The study only considered the die-wax and shell-alloy systems, and
ignored the shell-wax system. It was stated that because the fused silica shell
experiences null deformation before the casting is poured, this part of the
process could actually be ignored in the analysis.
The die-wax model was developed using Abaqus. A visco-elastic
constitutive model was used to characterize the wax, the properties of which had
been previously determined by the authors. An eight-node thermally coupled
brick hybrid element able to carry hydrostatic pressure was used to represent the
wax. The reported results for the die-wax system showed fairly large
disagreement between the computer model and the experimental data.
Shrinkage factors for the computer model were 2.5 times larger than the
measured ones. Regarding the shell-alloy system, limited modeling details were
given in the report. The model consisted in predicting the deformation of an
aluminum A356 casting. It was claimed that good agreement was found between
59
the computer model predictions and the experimental measurements; however,
numerical results were not reported.
2.8 Summary
Castings distort and develop residual stresses mainly due to the effect of
two restraints. One source of restraint is the mold walls that prevent the casting
from freely shrinking while cooling inside the mold. The other set of restraints is
developed due to the differential thermal cooling of different regions of the
casting. This differential thermal cooling is the result of the irregularity of the
different shapes that make up a casting.
Analyzing casting distortion for any casting process represents a
challenging endeavor due to the complex interplay of the many physical
phenomena involved. From a macroscopic point of view, it involves solving the
fluid flow, heat transfer and stress equations in a coupled manner. It is the stress
aspects of the analysis that represent the greater challenge due to complex
nonlinearities in material behavior and contact conditions during solidification and
cooling.
Finite elements have emerged as a reliable tool for solving the complex
set of nonlinear equations afore mentioned. The wide variety of the different
techniques developed is based on different sets of simplifying assumptions to
make the problem solvable. The insights provided by this numerical analysis
toolset have helped product designers and tool builders produce better castings.
60
In die casting finite elements and finite difference techniques have been
employed to solve the complex problem of casting distortion. The problem has
been mainly formulated as thermal-mechanical, without accounting for the fluid
flow aspects due to the fast filling times characteristic of the process. The
developed methodologies differ from each other based on the different
assumptions taken and also based on the limitations of the formulation used.
61
3 CHAPTER 3
MODELING METHODOLOGY
3.1 Introduction
This chapter describes the modeling approach taken to predict the
distortion of the casting. Because die casting is a forming process that relies on
the use of a rather stiff metallic die to shape the final product, deformations on
tooling shape cavity become significantly important when trying to predict final
product dimensions. Therefore, the analysis and prediction of final casting shape
must include the prediction of the die cavity shape at operating conditions.
This chapter is divided into two main parts: methodology for modeling die
distortion and the methodology for modeling part distortion. The first part
describes in detail all the modeling steps followed to predict the operating die
conditions, thermal and mechanical. The second part uses the predictions given
by the die distortion model and incorporates the casting into the analysis in order
to predict the shape of the casting while it cools inside the die and after ejection.
A detailed description of each of these two sections is provided in the following
pages.
62
3.2 Die distortion modeling
Modeling of die distortion has been an active research area at the Center
for Die Casting at The Ohio State University. The results of the studies done
have been published in a series of papers [28-34]. As a result of the early
research findings it was determined that the main causes of the elastic
deflections experienced by the die are: the clamping force developed by the tie
bar stretching, the uneven thermal profile of the die that results from the
continuous injection and cooling of material cycle after cycle and the
intensification pressure applied to increase material feeding and reduce pore size
across the casting volume. It has been found that the result of the interaction of
all these static loads leads to uneven elastic deflections of the die that have
proved to affect its performance as well as the cavity dimensions. The
description of the model and the approach followed to model the mentioned
loads is provided in the following paragraphs.
Modeling of die distortion requires the inclusion of the die and machine
elements. In this research project the model was built based on a Buhler SC-250
ton cold chamber die casting machine available at Ohio State. The model
included the die, ejector support block, ejector and cover platens. Tie bars were
not included due to the procedure used to model the clamping force which is
described later. Fig. 3.1 shows the described model.
h
th
Beca
alf of the m
he nodes ly
use of the l
model was u
ying at the s
Fig. 3.1 M
left-to-right
used. A sym
symmetry p
63
Machine mode
symmetry
mmetric bo
plane, const
3
el finite eleme
of the mach
undary con
training the
ent mesh
hine and th
ndition was
eir motion in
he casting, o
specified o
n the directi
only
on all
ion
64
normal to that plane. In order to simulate the resting of the cover platen on the
machine foundation and of the ejector platen on the rails, the motion in the
vertical direction of some nodes on these surfaces was restrainted. The contact
interaction among all the structural elements was specified as small sliding,
having a coulomb friction coefficient of 0.1.
3.2.1 Clamping force modeling
Modeling of clamping force required a particular procedure. To model the
effects of clamping force a pressure load was applied on both platens as shown
in Fig. 3.2. Fig. 3.3 shows the areas where the pressure was applied. The
region at the back of the ejector platen was selected as the area where the
toggle pads act, whereas the area in the cover platen represents the regions
where the reaction from the tie bar locking nuts is developed. The application of
both pressure loads was done during the same step. The clamping force
magnitude was equally divided between the top and bottom regions on each side
of the machine, and thus, any unbalance due to die location was not accounted
for. The unbalanced between the top and bottom tie bars has been estimated to
be about 8%, and it is thought to be negligible [44].
The procedure described was followed in order to arrest an observed
semi-rigid body motion that resulted from tie bar stretching when tie bars were
included in preliminary models. The observed motion caused divergence when
contact was being established between the casting and the die surfaces. A more
detailed description of this situation will be provided when the procedure to model
the cooling of the casting inside the die is described in the following sections.
66
Fig. 3.3 Location of clamping pressure on platens
Modeling clamping force as a constant pressure load may cause
suboptimal machine deflection patterns. The assumption of equal load between
the top and the bottom might be reflected in a platen distortion patterns that may
not represent the machine characteristics and die sealing at the parting plane
adequately. In reality, when the die is moved down the bottom tie bars take up
more load and greater contact pressure magnitudes are obtained at the bottom
67
of the parting plane. The assumption of equal load therefore, may be expected
to alter this profile, possibly affecting die opening magnitudes when the pressure
load is applied. Additionally, tie bar load redistribution due to the effects of
intensification pressure cannot be account for, since the pressure magnitude is
kept constant throughout the analysis. The inability to account for this load
redistribution may lead to slightly different platen distortion patterns that could
possibly change across parting plane dimensions.
3.2.2 Thermal load modeling
The thermal load represents the uneven thermal profile that develops in
the die as a result of the continuous injection and cooling of fresh metal cycle
after cycle. Thus, in order to model this load a series of cycles simulating the
different thermal conditions experienced by the die had to be modeled in a
transient thermal analysis. The thermal model included the casting, die and
cover platen.
A series of twenty thermal cycles were run in order to develop the die
quasi steady-state thermal profile. A description of the boundary conditions
specified on each of the different stages in each of the cycles is presented in
Table 3.1. All the structural elements are assumed to start at a room
temperature of 30 ºC in the first cycle. The liquid metal is assumed to be injected
in each cycle at a uniform temperature of 600 ºC. The heat transfer coefficient
between the casting and the die, as well as all of the structural elements was
kept constant and with a magnitude of 5000 W/m2-K. Although this coefficient is
time and temperature dependent for the case of casting/die interaction,
68
simulation results have proved to be rather insensitive to these effects. This
might be attributed to the finite capacity of the die to extract heat because of the
drop of its thermal conductivity as its temperature rises. Additionally, as the
liquid metal releases its latent heat during solidification, the surface temperature
of the die rises and in some regions may be equal to the casting temperature,
which limits the amount of heat flux through the interface.
69
Stage Boundary conditions
Die is closed
• Contact between the casting/die is disabled
• Contact between the die halves is enabled
• Free convection on exposed surfaces of die
• Free convection on the die cavity surface
• Free convection on exposed surface of cover platen
Dwell time • Contact between casting/die is enabled
• Free convection on die cavity surface is disabled
Die is open
• Casting/die contact on the cover side is disabled
• Contact between the die halves is disabled
• Free convection on exposed surfaces on the die
• Free convection on exposed surface on the casting
Casting is ejected • Casting/die contact on the ejector side is disabled
• Free convection on exposed surfaces on the die
Spray • Forced convection on the die cavity
• Free convection on remaining surfaces of the die
Idle • Free convection on exposed surfaces on the die
Table 3.1 Boundary conditions applied on the simulated thermal cycles
70
Table 3.2 to Table 3.4 show the physical and thermal material properties
used in the analysis for each of the different materials. The die was assigned H-
13 material properties, whereas the cover platen was characterized using the
steel 4140 material properties. The casting material was aluminum A380.0,
having the typical material properties found in the die casting literature.
Property Magnitude
Density 7820 kg/m3
Coefficient of thermal expansion 1.7x10-5
Thermal conductivity 29 W/m2-K
Specific heat
23 °C 458.8 J/kg-K
200 °C 518.5 J/kg-K
400 °C 587.7 J/kg-K
600 °C 726.2 J/kg-K
700 °C 905.4 J/kg-K
760 °C 1151.1 J/kg-K
800 °C 885 J/kg-K
850 °C 792.7 J/kg-K
900 °C 747.9 J/kg-K
1000 °C 733 J/kg-K
Table 3.2 Physical properties for H-13 tool steel
71
Property Magnitude
Density 7820 kg/m3
Coefficient of thermal expansion 1.7x10-5
Thermal conductivity 40 W/m2-K
Specific heat
150 °C 473 J/kg-K
200 °C 473 J/kg-K
350 °C 520 J/kg-K
400 °C 520 J/kg-K
550 °C 561 J/kg-K
600 °C 561 J/kg-K
Table 3.3 Physical properties for a typical 4140 steel alloy
Property Magnitude
Specific heat 419 J/kg-K
Latent heat 120000 J/kg
Liquidus temperature 580 C
Solidus temperature 538 C
Density 2700 kg/m3
Table 3.4 Physical properties for aluminum A380.0 die casting alloy
72
3.2.3 Intensification pressure modeling
The intensification pressure was modeled as a constant pressure load. It
was applied on all the die cavity surfaces where the pressurized liquid casting
would act upon the die. Even though the intensification pressure is time and
space dependent, modeling it in a dynamic analysis would make the running time
extensively long, making the analysis rather impractical for the scope of this
research work. Additionally, the uncertainty in the spatial and temporal variation
of the pressure may make the analysis rather inconclusive.
The die distortion model is assembled in a single Abaqus input file. The
nodes and element sets of all the structural components are all listed in the input
file. Material properties are defined and assigned to each of the different
components. In addition to the listed thermal and physical properties shown in
Table 3.2 to Table 3.4 typical magnitudes for Young’s Modulus and Poisson’s
ratio for steel are included in the material properties as well.
The loads as well as the boundary conditions are defined in the different
steps of the analysis. For the die distortion model, a static analysis is performed
and the described loads are sequentially applied in three different steps. The
first step applies the clamping force. The application of the thermal load is done
during the second step by specifying the nodal temperatures at the point of
injection as predicted by the transient thermal analysis. Lastly, in the third step
the cavity pressure is applied.
73
3.3 Modeling of part distortion
The modeling of part distortion was divided into three different models.
The first model determines the initial casting shape after the metal has filled the
die cavity. The second model simulates the cooling of the casting inside the die.
The third model simulates the cooling of the casting after ejection. The models
are run in the described sequence and the results provided by each model are
subsequently used by the following one. A detailed description of the modeling
procedure used in each case is provided in the following sections.
Fig. 3.4 shows the casting used for this research project. The geometry of
the casting was designed for a process control study done by Osborne [ 42] as
part of his research work. All of the casting ribs are formed in the ejector half,
with the cover contributing only to form the back of the plate. The design of this
casting was done in order to use the distance between the ribs as a measure for
in-cavity distortion, whereas the depth of the ribs was used to provide a measure
for across parting plane distortion.
3
st
th
d
.3.1 Mode
The p
tep towards
he die expe
ifferent pro
eling the tra
predictions
s the mode
eriences ela
ocess loads
Fig. 3
acking of ca
obtained by
eling of cast
astic deflect
. These de
74
3.4 Casting fin
avity distorti
y the die di
ting distortio
tions result
eflections ca
4
nite element m
ion
stortion mo
on. As has
ing from the
ause small
mesh
odel represe
s been alrea
e combined
but importa
ent the first
ady describ
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ant
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the
75
dimensional changes in the die cavity, changes that must be captured since they
represent the initial shape the liquid casting acquires at the end of the filling.
In order to know what the initial casting shape is prior to the onset of
cooling, an accurate description of the deformed die cavity shape must be
obtained first. Ragab [ 35] experimented tracking the distorted die shape by tying
the casting surfaces to the die cavity surfaces. The model included the casting,
die, platens, ejector support block. All parts in the model were discretized using
solid brick finite elements. It was reported that because the casting was
represented by solid elements, limitations in the element deformations prevented
it from accurately tracking the die shape as the different loads were applied.
The methodology used in this research work relies in the use of a shell
mesh to track the distortions in the cavity. The same structural components for
the die distortion model are used in this model. The application of the three
different process loads is sequentially done as described before. In order to
avoid having a solid casting tracking the cavity distortions, a shell mesh is used
instead. The shell mesh is built using the surface elements of the casting mesh,
sharing the same nodes as the casting surface elements. By sharing the same
nodes, the displacements obtained from the shell mesh can be readily mapped
onto the casting mesh surface.
The dimensional changes in the cavity are tracked by tying the shell mesh
to the die cavity mesh. Tying the shell to the die cavity provides a description of
the distorted die cavity shape after the application of the already mentioned static
loads. After the die has been distorted, the predicted displacements of the shell
76
mesh can be applied to the casting mesh, providing a casting shape that
matches that of the deformed die cavity. The underlying assumption in this
procedure is that the distortions in the cavity are small enough that they can be
mapped only to the casting surface without affecting its interior structure.
Fig. 3.5 shows the shell mesh used for this model. With a three-
dimensional mesh of the casting, the shell mesh can be readily obtained using
the meshing capabilities of any pre-processor. For this model, a shell thickness
of 0.0254mm was specified. To avoid any modeling limitations due to rigidity on
the shell, the Young’s Modulus of the shell material was specified to be three
orders of magnitude smaller than that of regular steel.
The model is run as a static analysis. As has been already described,
clamping, thermal and pressure load are sequentially applied in three different
steps. At the end of the analysis, the displacement predictions from the shell are
extracted and used in the following model. The description for modeling the
cooling of casting inside the die is provided in the next section.
3
th
ej
d
b
.3.2 Mode
Mode
he casting t
jector supp
imensional
y the shell
eling the co
eling the co
to the die d
port block a
casting me
mesh.
F
oling of cas
oling of the
istortion mo
nd the cast
esh are mo
77
ig. 3.5 Shell e
sting inside
e casting ins
odel. This
ting. The in
odified using
7
element mesh
the die
side the die
model inco
nitial nodal
g the displa
h
e requires th
orporates th
coordinates
acement pre
he addition
e die, plate
s of the thre
edictions gi
of
ens,
ee-
iven
78
The analysis is run as fully-coupled thermal-mechanical in two different
steps. During the first step the contact between the casting and the die is
disabled and the whole structure is elastically deformed by applying the same
clamping, thermal and pressure loads as in the preceding shell model. The
objective is to reproduce the die cavity deflections that were obtained in the shell
model, but now in a fully-coupled thermal-mechanical model. In the second step,
once the structure has already been deformed and the casting shape comes into
perfect contact with the distorted cavity shape, the contact between the casting
and the die is enabled and the casting is left to cool for a specified dwell time.
Based on the procedure just described, it can be noticed that the modeling
of the intensification pressure required a decoupling between the casting and the
die at the contact surfaces. The intensification pressure is modeled as a
pressure load on the faces of the die cavity surface elements, where in actuality
comes from the loading action of the casting onto the die. This decoupling
means that the pressurized conditions under which the casting cools inside the
die are not present, and as such, the contact conditions are not being properly
represented. This pressurization represents also an initial hydrostatic state of
stress which may lead to initial plastic strains at the early stages of cooling and
possibly to elastic strains at the later stages when the casting has acquired
enough strength. This modeling limitation is currently faced by the lack of finite
elements that are able to carry hydrostatic pressure and develop multi-phase
behavior depending on their temperature. Although Abaqus does list a “hybrid”
element in its element library possessing the characteristics just described,
79
preliminary tests performed confirmed the inability to transfer the hydrostatic
pressure uniformly throughout the casting volume. It was also observed that the
deformations induced due to thermal loads behaved unrealistically.
Another modeling item that deserves a more detailed explanation is the
clamping force modeling procedure. As it is well known, the clamping force is
developed due to tie bar stretching. As the tie bars stretch there usually is some
quasi-rigid body motion created along the clamping direction. During the course
of this research work a model that included the tie bars was initially used. As
already described, the displacements obtained by the shell mesh are used to
provide a description of the distorted cavity, a distortion that is then mapped to
the three-dimensional casting mesh using the shell nodal displacements.
However, in the fully-coupled thermal-mechanical model that simulates the
cooling of casting in the die, convergence problems were faced because of the
inability of the contact algorithm in Abaqus to properly establish contact between
the casting and the die cavity surfaces. This modeling difficulty was experienced
in spite of the fact that there was a perfect match between the casting and the die
cavity surfaces at the point at which the contact between the surfaces was
enabled.
The source of the divergence was found to be the rigid body motion of the
structure prior to the establishment of contact between the casting and the die.
Abaqus/Standard, which uses an implicit algorithm to solve for the equilibrium
equations, has limited capabilities if such contact conditions are present during
80
the analysis. This solver requires that all contacting surfaces meet at the
beginning of the analysis in order to establish contact properly.
3.3.3 Modeling cooling of casting post-ejection
Modeling the cooling of the casting after ejection required a model with the
casting being the only component. As the previous case, the model is defined as
a fully-coupled thermal-mechanical analysis. The predicted nodal displacements,
nodal temperatures and stresses provided by the previous analysis are used as
initial conditions in this model. The initial coordinates of the casting are modified
by adding the displacements at ejection to the casting starting coordinates. In
order to guarantee mechanical equilibrium, a series of weak spring elements are
used to restraint the casting motion in all three directions. The stiffness of the
springs is set to be 10N/m to avoid any artificial loading onto the casting. A
convective boundary condition of 20W/m2-K is applied to the casting surface to
simulate the heat transfer conditions between the casting and the surrounding
air. The analysis is run for sufficient time to guarantee the casting temperature
reaches that of the environment.
3.4 Constitutive model for the casting material
The casting was represented using an elastic-plastic constitutive model.
The constitutive model describes the mechanical behavior of the casting material
and should include appropriate representations over the range of temperatures
relevant for the analysis. For this analysis, temperature dependent elastic
81
properties and temperature and strain rate dependent plastic properties were
used.
The elastic properties included the definition of the Young’s Modulus and
Poisson’s ratio over a range of temperatures. Fig. 3.6 shows the temperature
dependency of pure aluminum, AA1201 and AA3104. As can be noticed from
the curves, Young’s modulus for aluminum alloys is independent of the alloy
chemistry. The results shown confirm the understanding that Young’s Modulus is
an intrinsic material property that is a function of the strength of the atomic
bonding. The results of Fig. 3.6 were used to specify the elastic properties for
the casting alloy used in this study.
82
Fig. 3.6 Temperature dependence of Young’s Modulus [45 ].
The plastic behavior of the die casting alloy was experimentally
determined as part of this research work. A series of tensile tests at different
combinations of temperatures and strain rates were conducted and the results
were used as input data in the finite element model. The details of this
experimental research project are presented in Chapter 4.
83
3.4.1 Finite element selection for casting
The casting was represented by using reduced integration finite elements
with temperature and displacement degrees of freedom. Reduced integration
was employed because volumetric locking was observed in some regions of the
casting when fully integrated finite elements were used. Volumetric locking is a
numerical phenomenon characteristic of plastic analysis that rely on
approximating the incompressibility of the material response by making the
Poisson’s ratio close to ½. This incompressibility response brings the constraint
of no change in volume into the finite elements that must be satisfied in addition
to meeting the displacement field that results from the kinematics of the problem
being analyzed. These constraints must be satisfied at all integrations points in
the finite elements. Since the fully integrated coupled thermal-mechanical finite
elements in Abaqus (C3D8T) use 2 integration points along each direction (a
total of 8 per element), the constraints cannot be met and the element is said to
“lock”. Reduced integrated elements use one lesser integration point along each
direction facilitating meeting the mentioned constraints.
3.5 Modeling die distortion using Fluid-Structure-Interaction (FSI) in ADINA
The distorted die cavity at the end of filling represents the initial shape
conditions for the casting at the onset of solidification. This distorted die cavity
shape results from the effects of mainly three process loads, clamping,
temperature and intensification pressure. Accurate predictions of casting final
dimensions require modeling the distorted die cavity shape adequately, since the
84
elastic deflections experienced produced dimensional changes in the die cavity
that affect the casting dimensions.
In die distortion models the intensification pressure effects have been
traditionally represented by using a constant pressure boundary condition applied
to the die cavity surface. Ideally, the intensification pressure should be the result
of the loading action of the pressurized casting acting onto the die cavity
surfaces. However, this hydrostatic loading cannot be modeled because
continuum solid elements lack a hydrostatic pressure degree of freedom and are
rendered inadequate for these purposes.
The latest developments in finite element modeling algorithms allow
modeling the interaction of fluid and structural elements. These modeling
capabilities represent the state-of-the-art in finite element codes and were initially
adopted for modeling casting and die distortion. The finite element package
ADINA was selected because it allows multi-physics modeling in one single
integrated code.
The adoption of this modeling technique was thought to augment casting
and die distortion modeling efforts due to the following. First, since the casting
could be represented using liquid elements that possess a pressure degree of
freedom, modeling intensification pressure effects could be readily done by
applying a pressure load to the biscuit and letting the casting fluid elements load
the deformable die. Second, the distorted die cavity shape at the end of filling
could be readily obtained from the distorted casting mesh because the fluid-
structure-interaction algorithm requires the liquid elements to always follow the
85
distorted shape. Therefore, the initial casting shape at the onset of solidification
could be readily obtained from the distorted fluid mesh.
3.5.1 Fluid Structure Interaction (FSI) Model
The model was divided into two domains, namely the solid and the liquid
domains. The solid domain was comprised of the structural elements which
included the inserts, die, ejector support block, ejector and cover platens and tie
bars. The liquid domain was on the other hand comprised of only the casting. In
the structural elements the usual boundary conditions applied to die distortion
models were considered. Contact between all the deformable bodies was
incorporated as well. In the fluid domain, the casting was represented with liquid
elements, which have pressure and velocity degrees of freedom. A fluid-
structure-interaction boundary condition was specified for all the surfaces in both
the casting and the die where they were expected to interact. Clamping and
thermal force was simulated by applying a pressure load on the ejector platen.
Thermal load was modeled by prescribing a temperature load on the inserts and
die. Intensification pressure was modeled by normal surface traction load on the
biscuit region of the casting. The loads were applied sequentially in a total of
three steps.
The displacements on the casting mesh were extracted at the end of the
analysis. Fig. 3.7 shows the predictions given by the FSI model. These results
show that the cavity distortion is not negligible and the predicted displacement
magnitudes emphasize the importance of incorporating the contributions of the
die deflections in casting distortion analyses.
86
Fig. 3.7 FSI cavity displacement predictions
This displacement field represented the distorted cavity shape at the end
of filling and was considered as the initial casting shape for a subsequent
thermal-mechanical solidification/cooling model. The same mesh for all the
different components used in the FSI model was used in a fully coupled thermal-
mechanical model. The model was comprised of the same structural
components as before with the addition of the casting. The final coordinates of
87
the casting in the FSI model were taken as the initial coordinates for the thermal-
mechanical model.
Since modeling casting solidification/cooling must consider the interaction
between the casting and the die, the deformed state predicted in the FSI model
had to be reproduced using the same loading conditions. Clamping and thermal
loads were modeled as described, whereas the intensification pressure was now
modeled as a pressure load applied to the die cavity surfaces. Contact between
the casting and the die was not enabled until the deformation was reproduced. It
is worth mentioning that during this model all the finite elements used to
represent all the components had temperature and displacements degrees of
freedom. The model was run in Abaqus, using the C3D8T coupled temperature-
displacement three dimensional elements.
While running this model convergence difficulties were experienced.
Examination of the results showed a mismatch between the casting shape and
die cavity surfaces after the initial loading was applied. The semi-rigid body
motion due to tie bar stretching after clamping was identified as the source of
divergence in the thermal-mechanical model. The displacement predictions after
clamping between the FSI and the thermal-mechanical model differed by as
much as 0.07mm and this difference was large enough to prevent proper
establishment of contact.
It was conjectured that the different contact algorithms used by each code
produced different displacements. Since coupled thermal-mechanical models
can be analyzed in ADINA it was decided to set up the solidification model and
88
run it all in ADINA. The same loading and boundary conditions as described
before were reproduced in an ADINA thermal-mechanical model. The results
showed that the displacement predictions of the thermal-mechanical model were
different when compared with the FSI predictions. The magnitude of these
differences was close to 0.07mm as well. These differences in displacement
predictions within ADINA prevented further modeling efforts using the code and it
was abandoned.
89
4 CHAPTER 4
DETERMINATION OF CASTING ALLOY CONSTITUTIVE
MODEL
4.1 Introduction
Physical and mechanical material properties are a fundamental piece of
information needed in computer modeling. The accuracy in the properties
magnitude and their dependencies on different material characteristics determine
to a large degree the predictions given by the computer models. Different kinds
of properties are needed depending on the type of analysis being performed. For
instance, thermal analyses require physical and thermo-physical properties such
as thermal conductivity, density, specific heat and latent heat. Depending on the
type of analysis, mechanical finite element models usually require properties
such as Young’s Modulus and Poison’s ratio. If the material deformation is
expected to exceed the elastic range, definition of the plastic behavior must be
part of the material properties as well.
As outlined by Ludwig [46], casting distortion computer models require a
particular set of thermal and mechanical material properties. On one hand,
90
the thermal properties are needed because they are used to compute the
evolution of temperatures in the casting as it solidifies and cools. On the other
hand, the mechanical properties are needed because they are used to predict
the strains and stresses in the casting as it cools and develops strength. The
accuracy in the magnitudes of the required properties and the adequate
expression of their dependencies on physical quantities such as temperature, or
on material characteristics such as strain rate, determine the accuracy of the
predictions given by the computer models.
Currently, the lack of high temperature mechanical properties for die
casting alloys is limiting the advancement of casting distortion computer models
in the die casting industry. The thermal properties are thermo-physical and
physical properties for which well-known procedures are available and have been
widely determined already. At the present time, computer codes have been
developed that can compute theses properties using thermo-dynamical principles
as presented by Saunders et al [47], Miettinen [48] and Miettinen et al [49].
These codes have been readily incorporated in casting CAE packages such as
ProCAST [50]. However, the mechanical properties at high temperatures are not
available and their determination remains open. The need is justified because it
can help increase the productivity of the industry by providing tools to predict
machine tooling allowances that can produce castings within tolerances at the
first shot, eliminating the high cost trial and error procedure. High-temperature
mechanical properties can also be used to predict casting residual stresses and
91
give product designers a valuable input to their designs before a single casting is
produced.
This chapter describes the activities done to determine the elevated
temperature mechanical properties for the die casting aluminum alloy A380.0.
First, a background regarding the finite element procedures used to predict
distortion and stresses in castings is provided. This section highlights the
importance and relevance of the use of accurate mechanical material properties
from a computational point of view. Next, a literature review of the available
high-temperature mechanical properties for some casting alloys and the testing
methods used for their determination is presented. The procedures followed to
obtain the elevated temperature mechanical properties for the die casting
aluminum alloy A380.0 are presented next. The section describes the selected
specimen, machine, testing temperatures and methodology. The results of the
tensile tests performed to the material are presented in the following section.
4.2 Background
Finite element analyses are mathematical models aimed at representing
the performance of a given isolated natural system. The mathematical
expressions represent the differential equations that mathematically describe the
nature of the physical phenomenon under study. As discussed in Chapter 2
section 2.4.2, the set of mathematical differential equations get assembled in an
algebraic form that for a mechanical system lead to the following three sets of
equations: mechanical equilibrium equations that relate forces and stresses,
92
compatibility equations that relate strains to displacements and finally the
constitutive equations that relate stresses to strains. It is in the last set of
equations that material properties are used to map the strains to stresses using
the elasticity and/or plasticity matrices. This chapter presents the finite element
procedures followed to compute the stresses in a typical casting analysis.
As was described in Chapter 2 section 2.4.2 elastic strains are responsible
for residual stresses in castings. However, it has been stated by Thomas [13]
that the expansions and contractions due to temperature change and phase
transformations, plasticity and creep contribute to generation of small but
important elastic strains. Therefore, the total increment strain vector is
composed of the elastic, thermal and inelastic strain components
∆ ∆ ∆ ∆ Eq. 4.1
where:
∆ is the incremental elastic strain
∆ is the incremental thermal strain
∆ is the incremental inelastic strain
As presented by Ludwig [46], viscoplasticity occurs when the comparison
stress in the casting material reaches the yield stress, which is temperature
dependent . Usually, the von Mises criterion is employed as the
comparison stress for the analysis, given the following flow condition
93
0,0,
with
12
12
12 3
The visco-plastic flow model can be expressed in different mathematical
models. Abaqus offers among many others the Johnson-Cook hardening model,
Drucker-Prager model and Hyperbolic-sine law model. Assuming a Power-law
model as shown in [46], the inelastic incremental strain rate can be expressed as
∆∆
Eq. 4.2
with
where
is the hardening exponent
The incremental thermal strain is expressed as:
∆ ∆ 1,1,1,0,0,0
94
where
is the thermal expansion coefficient
With the expressions for the elastic, thermal and inelastic incremental
strains available, the generalized constitutive equation can be expressed as
follows [46]
∆ · ∆ ∆ ∆ Eq. 4.3
∆
0,
∆,
With ∆ being a fictive stress that accounts for the temperature
dependence of the yield stress .
The plasticity matrix is defined as
( )
( )⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
⋅⎟⎟⎠
⎞⎜⎜⎝
⎛⎥⎦
⎤⎢⎣
⎡+
+
⎥⎦
⎤⎢⎣
⎡+
==
2'6
2'6
2'5
2'5
2'6
2'4
2'5
2'4
2'4
2'6
2'3
2'5
2'3
2'4
2'3
2'3
2'6
2'2
2'5
2'2
2'4
2'2
2'3
2'2
2'2
2'6
2'1
2'5
2'1
2'4
2'1
2'3
2'1
2'2
2'1
2'1
2_
2
123
129
σσσσσσσσσσσσσσσσσσσσσσσσσσσσσσσσσσσσ
σγ
γ
KKKKK
M
M
M
M
En
E
Dplastic
with
95
( ) 3/3211'1 σσσσσ ++−=
( ) 3/3212'2 σσσσσ ++−=
( ) 3/3213'3 σσσσσ ++−=
As can be seen from Eq. 4.2 the incremental inelastic strain component
depends on the material properties. The strain hardening exponent and the
yield stress are both a function of temperature. Therefore, in order to compute
accurately the contribution of the inelastic strain, the temperature dependence
the plastic material properties must be defined in the casting constitutive model.
The accuracy on the material properties will determine the accuracy of the total
strain, which in turn will determine the accuracy of the stress predictions as has
been shown above.
4.3 Literature review
This section presents a review of the available relevant literature regarding
elevated temperature material properties of some casting alloys. The section is
divided into three parts. Part one introduces some of the available mechanical
properties of die casting alloys. The second part describes the different tests
performed by several researchers in determining some of the mechanical
properties of a variety of aluminum casting alloys. Lastly, the third one presents
the high-temperature tensile test results obtained using a Gleeble machine for a
variety of direct chill casting alloys done by several research groups.
96
4.3.1 Die casting alloys
The microstructures and mechanical properties of a wide variety of
common die casting alloys were determined in a comprehensive research project
done at Worcester’s Polythecnic Institute Materials Processing Institute [51]. The
results of the study were intended to be used by product designers to provide
them with more accurate tools while selecting die casting materials. A total of 26
different alloys were tested. Tensile test and mechanical test specimens were
produced following required ASTM standards. The tensile tests were performed
at room temperature, 100 ºC and 200 ºC. Axial extensometers were used for
both, the room temperature and the higher temperature cases. For the higher
temperature cases, the specimens were heated using a heating chamber,
monitoring the specimen’s temperature using thermocouples attached to the
specimen’s length. A total of 35 specimens were tested at room temperature,
while a total of 5 were tested for the higher temperature conditions. The machine
test velocity for both all the temperature conditions was 0.05in/min. A series of
tensile tests were generated using the recorded data for all the tested alloys.
The results can be seen in the cited report.
The creep behavior of three aluminum die casting alloys was determined
by Jaglinski et al [52]. The selected aluminum alloys were B-390 (Al-17%Si-
4%Cu-0.5%Mg), eutectic Al-Si alloy (Al-13%Si-3%Cu-0.2%Mg) and Al-17%Si-
0.2%Cu-0.5%Mg alloy. The objective of the study was to provide product
designers with creep material data for engine design, as many of these
components work under high temperatures and creep and relaxation might be
97
observed during engine operation. As-cast tensile test specimens were used to
perform the creep tests. Constant creep load uniaxial tests were done using a
dead weight lever frame, where strain was measured using axial extensometers
securely attached to the specimen’s gage section. The testing temperatures
were 220 ºC, 260 ºC and 280 ºC. The results obtained are shown in Fig. 4.1.
From the results it was observed that the eutectic alloy experienced larger strains
to failure and longer rupture times than the other two tests alloys.
98
Fig. 4.1 Creep properties for die casting aluminum alloy A380.0 [52]
4.3.2 Aluminum casting alloys
Singer et al [53] conducted an experimental work to determine the
mechanical properties of a variety of hypoeutectic Al-Si alloys below and in the
solidus temperatures. The purpose of the study was to provide experimental
data that would assist in explaining the phenomenon of hot-shortness. A total of
99
ten different alloys were tested, including super-purity aluminum. The selected
specimen design varied depending on whether the temperature was below or
above the solidus. Fig. 4.2 shows the two designs used. The specimens were
heated using a resistance tube furnace that slid on the testing apparatus,
providing uniform heating throughout the specimen’s length. Fig. 4.3 and Fig. 4.4
show the results obtained. The experimental results showed that the tensile
strength of the tested Al-Si alloys decreases gradually as the temperature
increases above 400 ºC, reaching finite magnitudes at the solidus temperature.
As can be seen from the figures below, the slope of the strength-temperature
curves increases as the silicon content increases. The results showed that the
reduction in area and elongation remained high for all the tested alloys up to the
solidus temperature. At the solidus temperature however, the elongation and
reduction in area decreased to zero and the maximum strength reached a very
low magnitude.
100
a)
b)
Fig. 4.2 Testing devices used for determining flow stress a) below 300 ºC and b) above 300 ºC [53]
102
Fig. 4.4 Flow stress for Al-Si alloys at temperatures above the solidus [53]
Kim et al [54] performed a numerical analysis on the deformation and
shrinkage of small rectangular castings. The dimensions of the castings were
50x24, 100x24 and 150x24mm. A really simple two dimensional analysis,
assuming four-folded symmetry of the casting was done. Four-node quadratic
elements were used to represent the castings. A useful piece of information
103
encountered in the article is the temperature-dependent behavior for the Yield
Strength and Young’s Modulus for the selected casting material shown in Fig.
4.5. The material under study corresponded to an Al-7%Si-0.3%Mg alloy. It is
not clear from the results obtained whether the computer model results
correlated well with experimental observations.
Fig. 4.5 Material properties for an Al-7%Si-0.3%Mg alloy [54]
The mechanical behavior of various Al-Cu alloys at solidifying and just-
solidified temperature conditions was determined by Wisniewski et al [55]. The
goal of the study was to develop an adequate fracture criterion to predict hot
104
tearing for Al-Cu solidifying alloys. The percentage Cu content was varied from
2.5 to 7.5%. Rectangular bars 13x51mm were tested at strain rates that ranged
from 1x10-5 to 1x10-1 s-1. The specimens were mounted onto a fixture in an
Instron machine. A quartz lamp furnace was used to heat the specimens at the
required temperatures. The tests were carried at constant extension rates. Load
and extension magnitudes during testing were recorded and the obtained data
were converted to stress and strain respectively. The obtained results show that,
at all strain rates, the maximum stress decreased as the Cu content was
increased. Also, it was found that the maximum strength decreased sharply as
the liquid fraction increased.
The mechanical behavior of an Al-4.5%Cu-Mg-Ti alloy in the mushy zone
was determined in an experimental study conducted by Vicente-Hernandez et al
[56]. The main objective was to determine an adequate testing procedure to
determine the visco-plastic mechanical behavior of aluminum alloys in the mushy
zone in order to provide solidification computer models with reliable material data
for gap formation predictions. The developed test consisted in the pushing of a
needle at a constant rate into a solidifying ingot. The cooling conditions in the
mold were controlled carefully to obtain vertical isotherms. The described test
provided records of applied force versus needle displacement at different
temperatures. The Norton-Hoff power law model describing the strain-rate
dependency of the mechanical behavior was then fitted using the experimental
data. The fitted model was used in a thermal-mechanical analysis of a solidifying
ingot aimed at predicting gap formation. The results showed a remarkable match
105
between the measured displacements and the displacements predicted by the
simulation. It was claimed that the lack of accurate material data, especially
visco-plastic mechanical behavior, in the mushy zone can limit to a great extend
the validity of computer models in predicting air gap formations, heat transfer
conditions and thermal stresses in solidification analyses.
4.3.3 Gleeble testing
Computer modeling of residual stresses and deformations in castings has
gained popularity across casting industries because the general understanding of
the governing phenomena and the computer algorithms have progressed
considerably. However, a lacking piece of information in all computer models is
the mechanical behavior of alloys at the cooling conditions dictated by the
casting process being modeled. The Direct Chilling (DC) casting process has
received increased attention from the modeling community and as a result, the
determination of material properties for typical DC aluminum alloys has been
done over the past years. A common denominator across all studies conducted
is the use of Gleeble testing for performing elevated-temperature tensile tests at
various strain rates characteristic of the DC process. A review of some of some
of the studies published is provided in the following paragraphs.
Van Haaften et al [57] conducted an experimental study to determine the
mechanical properties of AA1050, 113104 and AA5182 DC aluminum casting
alloys. The objective was to obtain a Power law model using the experimental
data that can be used in computer models to predict thermal stresses and
deformation in DC ingots. A series of tensile tests at different temperatures and
106
strain rates were performed using a Gleeble 1500 and a Gleeble 3500. The
specimens were machined from as-cast rolling slabs. Non-cylindrical specimens
10mm in diameter and 95mm long, with a reduced 8mm diameter at the center
were used for the testing. The selected temperatures ranged from room
temperature to the solidus temperature, whereas the strain rates ranged from
1x10-5 to 1x10-1 s-1. It is stated that most of the experiments were conducted in a
stroke controlled mode, using the load controlled mode for the highest
temperature cases. From the described procedures, it is not clear however how
the constant strain rates were achieved, just the obtained range as mentioned
above was stated. Three replications were done for all the testing cases. The
obtained data was fitted to the extended Ludwik power law and to the Garofalo’s
hyperbolic-sine models.
Using a Gleeble machine the flow stress at steady-state creep conditions
for AA3103 aluminum alloy was determined by Farup et al [58]. The goal of the
experimental study was to obtain the parameters of the Garofalo’s model for use
in DC thermal-mechanical finite element models. Non-cylindrical specimens
being 10mm in diameter, 90mm long and a reduced 8mm diameter at the
specimen’s center were used. The temperatures ranged from 325 ºC to 550 ºC,
whereas the strain rates varied from 1x10-6 to 1x10-2 s-1. In order to achieve
steady state creep conditions at the intended strain rates in the range of 1x10-2 to
1x10-4 s-1a constant jaw velocity was used, whereas for the smallest strain rates
1x10-5 to 1x10-6 s-1a constant force was used instead. The obtained results
showed a marked scattered in the data. It was stated that differences in
107
specimens’ circularity measured at the specimen’s center were as high as 50 to
80%, causing an uncertainty of ±30% in the steady state strain rate.
Furthermore, noise in the load cell readings at the low stress levels was identified
as another source of error in the measurements. The obtained results were
successfully used to determine the parameters of the Garofalo’s equation.
The mechanical properties under compression, tension and cyclical
compression for AA582 DC aluminum alloy were determined by Alhassan-Abu et
al [59]. The objective was to determine the parameters of the Garofalo’s
equation for use in computer modeling of thermal-mechanical stress in DC
ingots. The tests were carried out using a Gleeble 1500 machine. The
temperatures ranged from 250 ºC to 500 ºC, whereas strain rates varied from
1x10-5 to 1x10-1 s-1. For the tensile tests the specimens had a gauge length of
27mm and a gauge diameter of 5mm. It is stated that the intended strain rates
were achieved using constant displacement rates, yielding mean strain rates in
the above mentioned range. The results obtained were used to determine the
parameter of the Garofalo’s hyperbolic-sine model. It was concluded that the
fitted Garofalo’s model predicted accurately the mechanical behavior of the
material for temperatures above 350 ºC, whereas it failed to predict the strain
hardening behavior at the lower temperatures.
Tensile tests were conducted to determine the effects of strain rate and
thermal history on the constitutive behavior of an Al-Mg AA5182 DC alloy [60]. A
Gleeble 3500 thermo-mechanical simulator was used to conduct the
experiments. The thermal histories included as-cast, heated and homogenized
108
conditions. The strain rates ranged from1x10-4 to 1x10-3 s-1. The selected
specimen shape and testing procedures were the same as in [57]. The results
obtained suggested that the constitutive behavior is independent of the thermal
history. The fitted Garofalo’s equation was able to accurately predict the
mechanical behavior of the alloy in the tested conditions.
4.4 Determination of aluminum A380.0 mechanical properties
This section describes the procedures followed for the determination of
the elevated temperature mechanical properties for A380.0 aluminum alloy. A
detailed description of all the steps followed for carrying out the project is
provided. Issues such as machine and specimen selection, the selected design
of experiments matrix, production and preparation of specimens and testing
methodology are presented in the following paragraphs.
4.4.1 Machine and specimen selection
The Gleeble machine was selected to carry out the elevated temperature
tensile tests. The decision was taken based on the information found in the
literature and presented in the previous section. As was reported in the cited
articles, the Gleeble thermo-mechanical simulator can readily perform tensile
tests at the required temperatures and strain rates. The reliability of the control
system in controlling temperature, jaw velocity and loading force made the
Gleeble an excellent choice for the project. Currently, a Gleeble 3800 and a
109
Gleeble 1500 are available at The Ohio State University at the Welding
Engineering and Material’s Science Engineering departments respectively.
The Gleeble system is a high-strain-rate, high temperature testing
machine where a solid specimen is held horizontally by water cooled grips,
through which electric current is introduced to resistance heat the test specimen
[61]. Fig. 4.6 shows the schematic of a typical Gleeble test. Specimen
temperature is monitored by a thermocouple that is welded to the specimen’s
surface. The temperature of the specimen is controlled by a function generator
using the readings provided by the thermocouple. The direct-resistance heating
system of the Gleeble machine can heat specimens at rates of up to 10,000 ºC/s.
Due to this capability, this machine can perform hot tensile tests several times
faster than conventional methods. Radial strain measurements are readily done
by attaching a dilatometer that monitors the reduction in area as the specimen is
being tensioned.
110
Fig. 4.6 Schematic of a typical Gleeble test [57]
Gleeble machines are commonly used for thermo-mechanical physical
modeling of a wide variety of processes. Applications range from phase
transformation analyses where heat treatment conditions ought to be controlled
really accurately, plastic deformation of materials at high strain rates such as
high velocity forging, friction stir welding where material is subjected to a
torsional state of stress at high temperatures, etc. The different machine models
provide different capabilities in the maximum developed force, torque, maximum
and minimum jaw velocities, etc. The 3800 model available at the Welding
Engineering facilities was designed for high velocity and high force applications,
whereas the 1500 model was designed for small forces and slow velocity
applications. A key differentiator between these two models is the valve that
controls the flow rate of oil to displace the jaws, determining the minimum and
111
maximum attainable speeds. The 1500 model with a 60GPM control valve was
selected because of its capabilities in displacing the jaws at velocities that would
generate the smallest strain rates in the order of 1x10-5 and 1x10-6 s-1
characteristic of the cooling conditions in die castings.
The specimen design shown in Fig. 4.7 was selected based on the shapes
described in the articles cited in section 4.3.3. The common denominator in
those designs was the use of a cylindrical specimen with a reduced diameter at
the center. The reduction in area was purposely done in order to guarantee that
the maximum strained region is at the specimen’s center. Additionally, as
reported by Walsh et al [62], quadratic temperature profiles are typical of a
Gleeble test, where the maximum temperature is located at the specimen’s
center and the water cooled grips define the lowest temperature points. Thus,
the quadratic temperature profile together with the reduction in area guarantees
that the region of failure is located at the specimen’s center, eliminating the need
of a gage length.
112
Fig. 4.7 Schematic of the test bar used for tensile tests
The radial strain at this region can be readily obtained by placing a
dilatometer that monitors the reduction in area as shown in Fig. 4.6.
Eq. 4.4 shows how the radial strains are computed
2
Eq. 4.4
where
is the current diameter
is the starting diameter
113
The radial strains can be converted to longitudinal strains as expressed in
Eq. 4.5
Eq. 4.5
where
is the Poisson’s ration
The stresses can be readily computed by dividing the applied force by the
reduced cross-sectional area as shown
Eq. 4.6
where
is the applied force
is the reduced cross-sectional area
A couple of assumptions are used behind the computation of the
longitudinal strains and stresses. One is the assumption of a homogeneous
temperature distribution. The other assumption is a homogenous cross-sectional
shape throughout the specimen’s length. Both assumptions generate non-
uniform flow stresses along the specimen’s length, leading to inaccuracies in the
computed stresses and strain rates. This was recognized by Farup et al [63]
where they investigated the effects of those in-homogeneities in the computed
114
strain fields. An axis-symmetric model representing the specimen in their tests
was modeled in Abaqus. The obtained visco-plastic properties from the
experiments were assigned to the material. Three conditions were studied: one
represents the same temperature and shape in-homogeneities as in the
experiments, another one assumes a non-cylindrical specimen but with a uniform
longitudinal temperature profile and the last one assumes a cylindrical specimen
with the parabolic temperature profile characteristic of their tests. The obtained
results showed that the variation in the visco-plastic strain rate along the radius
varies as much as 12.5%, with a maximum at the center. It was recognized that
the major source of variation was the parabolic temperature profile, contributing
more than the non-cylindrical shape to the observed radial differences. It can
therefore be expected that the obtained strain-rates in the experiments carry an
error of at least 12.5% due to the above mentioned in-homogeneities.
4.4.2 Design of experiments matrix
A design of experiments was proposed where the specimen temperature
and strain rate were the design variables. The selected temperatures ranged
from 25 ºC to 500 ºC having ten different levels. The strain rates were
determined by analyzing the cooling conditions on the casting following the
expression
Eq. 4.7
where
115
is the strain rate
α is the coefficient of thermal expansion
is the cooling rate
Cooling rates from a computational thermal analysis of different regions of
a solidifying casting were extracted and Eq. 4.7 was used to calculate the strain
rates. The obtained results produced strain rates that ranged from 1x10-2 to
1x10-6 s-1. Given the results obtained, five different levels for the strain rate were
selected. Because of the different levels obtained for the two design variables, a
Hexagonal design was selected [64]. Table 4.1 shows the design matrix.
116
Run Temperature (C) Strain rate (s-1)
1 500 3.16E-04
2 486 2.26E-03
3 444 1.28E-02
4 381 4.62E-02
5 304 9.16E-02
6 221 9.16E-02
7 144 4.63E-02
8 81 1.28E-02
9 39 2.27E-03
10 25 3.17E-04
11 25 3.17E-04
12 39 4.42E-05
13 81 7.83E-06
14 144 2.16E-06
15 221 1.09E-06
16 304 1.09E-06
17 381 2.16E-06
18 444 7.80E-06
19 486 4.40E-05
20 263 3.16E-04
Table 4.1 Experimental array for tensile tests
117
4.4.3 Specimen production and preparation
Specimen were produced using an existing insert available at The Ohio
State University. The insert design allowed the production of two specimen per
shot. A photograph of the insert used for the production of the specimen is
shown in Appendix A. The production was carried out continuously during one
shift at Empire Die Casting Co., Inc. located in Macedonia, Ohio. A total of 800
specimen were die cast with an average cycle time of 40s and a shot weight of
0.5kg. The information regarding alloy chemistry and cycle time parameters
used for production is presented in Appendix B.
After production, specimen were trimmed. Runners, biscuit and any
excessive flash were manually removed. The runner and biscuit were removed
using a rubber hammer, while the flash was removed using a vertical band saw.
Radiographs were taken on all specimen to guarantee that only the best
would be tested. The specimen were x-rayed at Ultra Labs Inc., located in
Cleveland, Ohio. The radiographs showed that the majority of the specimens
had shrinkage porosity at the grip ends, while very little porosity was detected at
the reduced cross-sectional area. Out of the 800 specimen produced 370 were
selected for testing.
The selected specimen were machine-threaded using a threading die.
The specific thread used was ½-20. The finer pitch was selected to maximize
the number of threads engaged during testing to avoid stripping the threads. The
machine-threading was also done to guarantee proper alignment between the
axes produced by the threads on both grip ends.
118
After threading the specimen were polished. Polishing was done using a
rotating brush, with the main intention of removing residual flash at the parting
plane. A smooth surface finish was obtained after polishing was completed.
4.4.4 Testing methodology
As can be seen in Table 4.1, the 20 cases required different combinations
of temperatures and strain rates. Two different approaches, namely constant jaw
velocity and constant force, were used to perform the tests and they were
developed based on the way the required strain rates were achieved. A
description of the procedures followed on each of the approaches is provided in
the following paragraphs.
The strain rate is a mechanical behavior material characteristic that
provides a measure of the rate of strengthening or softening of the material under
a given set of loading conditions. This rate of strengthening or softening may or
may not be constant depending on the way the material responds as the plastic
deformation is taking place. Constant strain rates at temperatures below
creeping are usually achieved by loading the material under a constant rate of
displacement and can be readily computed by using the following expression
Eq. 4.8
where
is the jaw velocity
is the deformed length
119
Because most aluminum alloys start creeping at temperatures around 300
ºC, all the test cases at temperatures below 300 ºC were conducted under
constant jaw velocities. As can be seen from Eq. 4.8 the magnitude of the strain
rate is proportional to the magnitude of the jaw velocity. A detailed description of
the correlations obtained between applied jaw velocity and achieved strain rate
will be provided in the next section.
For temperatures above 300 ºC, the tests were conducted by applying a
constant force. Under steady state creep conditions, the constant force is
translated into a constant stress because the rate of elongation remains
constant. That constant rate of elongation is a guarantee that the strain rate
remains constant throughout the test. A detailed description of the obtained
correlations between the applied force and achieved strain rate for the different
temperatures above 300 ºC is provided in section 4.4.4.2
4.4.4.1 Velocity controlled
A series of room temperature tests were performed to determine the
correlation between the jaw velocity and the obtained radial strain rate measured
at the specimen’s center. The jaw velocity was varied progressively by orders of
magnitude and the strain was measured by a dilatometer and recorded by the
Gleeble’s data acquisition system. With the time history of the recorded strain,
MATLAB’s curve fitting toolbox was used to filter the data and to compute the
first derivative.
Fig. 4.8 shows the strain-time and strain rate-time plots for a case where
the jaw velocity was 0.001mm/s. The top figure shows that the radial strain came
120
to be in the order of 1x10-3 mm/mm, while the strain rate was about 1x10-6 s-1.
The fact that the strain rate is 3 orders of magnitude smaller can be explained by
the order of magnitude of the time scale, which is about 1x103 s. The strain rate
results were plotted in a histogram and the results are shown in Fig. 4.9. The
histogram clearly depicts that the radial strain rates at the specimen’s center
were all in the order of 1x10-6 s-1.
Fig. 4.10 shows the results obtained for a jaw velocity of 1mm/s. As can
be seen from the top plot the radial strain remained in the same order of
magnitude as in the previous case, whereas the time scale was reduced by 3
orders of magnitude. This resulted in an average radial strain rate in the order of
1x10-3 s-1 as shown by the histogram in Fig. 4.11. From the observed trends it
can be expected that a higher jaw velocity would cause even shorter failure
times, resulting in higher radial strain rates.
The results for a jaw velocity of 100mm/s are shown in Fig. 4.12. This jaw
velocity magnitude caused failure times to be in the order of 1x10-3 s, generating
radial strain rates in the order of 1x101 s-1 as shown in the histogram in Fig. 4.13.
As can be noticed from the results shown, there exists a clear correlation
between the jaw velocity and the achieved radial strain rates. A series of more
tests with various jaw velocities were done and the results were processed as
described before. From the log-log scatter plot shown in Fig. 4.14, a linear
correlation between the jaw velocity and the achieved radial strain rate can be
observed. Although the correlation plot shown in Fig. 4.14 was generated using
the results of room temperature tests, this correlation was found to be valid and
121
vary only slightly for temperatures up to 260 ºC. Therefore, the obtained plot was
used as a basis to carry out all the test cases where the specimen’s temperature
was under 300 ºC.
4
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rocedure.
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Thus, it was
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Under a co
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Fig. 4.14 Stra
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12
ain rate vs. ja
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28
w velocity co
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ensile tests
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129
and constant forces and obtain a correlation between the applied constant force
and the achieved radial strain rate. The procedure followed to obtain such
correlation plots is presented using some sample results for a particular set of
temperature conditions.
Fig. 4.15 shows the strain-time plot for a tensile test carried out at 381 ºC
under a constant force of 1KN. The figure clearly shows a linear behavior of the
radial strain, depicting the steady state creep. A linear polynomial was fit to the
linear portion of the curve and the obtained slope was taken as the radial strain
rate. For this test, a strain rate of 1x10-6 s-1 was obtained.
The results for a test performed at the same temperature but under a
1.5KN constant force are presented in Fig. 4.16. The curve shows a slightly
different behavior as compared with the previous one, but a large linear portion
can still be seen. After fitting a linear polynomial to the linear portion of the curve
a radial strain rate of 1x10-4 s-1 was obtained.
Fig. 4.17 shows the results of a test done using a constant force of 2.0KN
and at the same 381 ºC temperature. The obtained results show a similar trend
of the strain-time curve as in the previous case, but with a time to failure
reduction of about an order of magnitude. Taking the linear portion of the curve
from 65 to 85s, the slope of a linear polynomial fitted came to be about 1x10-3 s-1.
From the results presented thus far a correlation between the applied
force and the achieved radial strain rate can be observed. It can be noticed that
at a given specimen’s temperature, the higher the applied force the smaller the
obtained radial strain rate. Based on this, a series of correlation plots were
130
generated for the temperatures at and above 300 ºC. At those temperature
levels, the constant force was varied and the radial strain rates were computed
as described before. The obtained correlation plots are shown in Fig. 4.18 to Fig.
4.22.
Fig. 4.15 Strain vs. time curve for a 1.0KN force at 381 ºC
133
Fig. 4.18 Strain rate force vs. force correlation plot at 300 ºC
1.00E‐06
1.00E‐05
1.00E‐04
1.00E‐03
1.00E‐02
1.00E‐01
1.00E+00
2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7
Strain ra
te (1
/s)
Force (KN)
Correlation between Force and Strain Rate at 300 C
134
Fig. 4.19 Strain rate force vs. force correlation plot at 381 ºC
1.00E‐06
1.00E‐05
1.00E‐04
1.00E‐03
1.00E‐02
1.00E‐01
1.00E+00
0.5 1 1.5 2 2.5 3 3.5 4
Strain ra
te (1
/s)
Force (KN)
Correlation between Force and Strain Rate at 381 C
135
Fig. 4.20 Strain rate force vs. force correlation plot at 445 ºC
1.00E‐06
1.00E‐05
1.00E‐04
1.00E‐03
1.00E‐02
1.00E‐01
1.00E+00
0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6
Strain ra
te (1
/s)
Force (KN)
Correlation between Force and Strain Rate at 445 C
136
Fig. 4.21 Strain rate force vs. force correlation plot at 485 ºC
1.00E‐06
1.00E‐05
1.00E‐04
1.00E‐03
1.00E‐02
1.00E‐01
0.5 0.6 0.7 0.8 0.9 1 1.1
Strain ra
te (1
/s)
Force (KN)
Correlation between Force and Strain Rate at 485 C
137
Fig. 4.22 Strain rate force vs. force correlation plot at 500 ºC
4.4.4.3 Results
The tensile tests were carried out using the correlation plots shown in the
previous section. Five replications were performed for each of the twenty
different cases. All one hundred tests were randomized to minimize the effect of
the many sources of error. The details of the randomization of the runs can be
found in Appendix C. Selection of the specimens for each test was done
randomly as well to minimize the effect of specimen quality on the results. The
tests were completed in the period from May 10 to June 8, 2007, five months
1.00E‐07
1.00E‐06
1.00E‐05
1.00E‐04
1.00E‐03
1.00E‐02
1.00E‐01
1.00E+00
0.5 0.6 0.7 0.8 0.9 1 1.1
Strain ra
te (1
/s)
Force (KN)
Correlation between Force and Strain Rate at 500 C
138
after they were produced. Fig. 4.23 to Fig. 4.42 show the true Stress vs. true
strain curves for each of the twenty runs.
Fig. 4.23 Stress vs. strain curves at 500 ºC and 1x10-4 s-1 strain rate
157
Fig. 4.42 Stress vs. strain curves at 263 ºC and 1x10-4 s-1 strain rate
For Run 18 as shown in Fig. 4.40 only three replications were done. This
was due to the fact the first two replications were carried out using a greater
force, while for the last three a smaller force was used. At the completion of the
one hundred runs it was decided to re-run the first two replications. The
dilatometer could not be borrowed again and the tests were not completed.
Because five replications were done for each of the twenty runs, the mean
was selected to represent the five different sets of data. The mean was
158
computed by averaging the five different stress magnitudes strain-wise. Fig. 4.43
and Fig. 4.44 show the computed average curves for the cases with
temperatures below 300 ºC and above 300 ºC respectively.
159
Fig. 4.43 Stress vs strain curves for temperatures below 300 ºC
Fig.
4.4
3 S
tress
vs
stra
in c
urve
s fo
r tem
pera
ture
s be
low
300
ºC
160
Fig. 4.44 Stress vs strain curves for temperatures above 300 ºC
Fig.
4.4
4 S
tress
vs
stra
in c
urve
s fo
r tem
pera
ture
s ab
ove
300
ºC
161
The mechanical properties shown in the figures above had to be
processed for use in computer models. In Abaqus, the elastic and plastic
properties need to be defined in separate tables. The elastic properties must be
defined as a table of Young’s Modulus and Poisson’s ration at different
temperatures. These properties were extracted from Fig. 3.6 as mentioned. The
plastic properties must be defined as tables of Yield Stress, plastic strain as a
function of temperature for each of the different strain rates. Since the obtained
material properties include the elastic and plastic behavior, the elastic part was
removed for defining the required tables. Fig. 4.45 to Fig. 4.49 show final curves
used for the computer models.
Fig. 4.45 Simulation material properties for strain rate of 1x10-6 s-1
0.00E+00
5.00E+07
1.00E+08
1.50E+08
2.00E+08
2.50E+08
3.00E+08
0 0.02 0.04 0.06 0.08 0.1 0.12
Yield Stress (P
a)
Plastic strain
Simulation material properties for strain rate of 1x10‐6 s‐1
81 C
144 C
220 C
304 C
381 C
444 C
162
Fig. 4.46 Simulation material properties for strain rate of 1x10-5 s-1
Fig. 4.47 Simulation material properties for strain rate of 1x10-4 s-1
0.00E+00
5.00E+07
1.00E+08
1.50E+08
2.00E+08
2.50E+08
3.00E+08
0 0.01 0.02 0.03 0.04 0.05 0.06
Yield Stress (P
a)
Plastic strain
Simulation material properties for strain rate of 1x10‐5 s‐1
39 C
486 C
0.00E+00
5.00E+07
1.00E+08
1.50E+08
2.00E+08
2.50E+08
3.00E+08
3.50E+08
0 0.02 0.04 0.06 0.08 0.1 0.12
Yield Stress (P
a)
Plastic strain
Simulation material properties for strain rate of 1x10‐4 s‐1
25 C
263 C
500 C
163
Fig. 4.48 Simulation material properties for strain rate of 1x10-3 s-1
Fig. 4.49 Simulation material properties for strain rate of 1x10-2 s-1
0.00E+00
5.00E+07
1.00E+08
1.50E+08
2.00E+08
2.50E+08
3.00E+08
0 0.01 0.02 0.03 0.04 0.05 0.06
Yield Stress (P
a)
Plastic strain
Simulation material properties for strain rate of 1x10‐3 s‐1
39 C
486 C
0.00E+00
5.00E+07
1.00E+08
1.50E+08
2.00E+08
2.50E+08
3.00E+08
0 0.02 0.04 0.06 0.08 0.1 0.12
Yield Stress (P
a)
Plastic strain
Simulation material properties for strain rate of 1x10‐2 s‐1
81 C
144 C
221 C
304 C
381 C
444 C
164
4.5 Summary
Material properties are one of the most important pieces of information
when building a finite element model. The constitutive equations that relate
stress to strain are a function of the material constitutive model used. If the
constitutive model used does not represent adequately the response of the
analyzed part, the stress and force predictions will be highly questionable.
The lack of mechanical properties at temperatures relevant for
solidification analysis was the motivation to carry out a project to determine the
constitutive model for the die casting alloy being used in this research project.
Test bars were die cast and specimens were qualitatively selected based
radiography results. A series of stress-strain curves at different combinations of
temperature and strain rate were obtained. Five replications were done at each
combination of temperature and strain rates in order to obtain statistical
significance. The tests were carried out using displacement and force control
modes in a Gleeble thermal-mechanical simulator. The displacement control
mode was used for temperatures below creep (about 300 ºC), whereas the force
control model was used for temperature above creep. Calibration curves for both
modes of control were developed to carry out the tests.
The results obtained showed the large dependency of the flow stress on
both, temperature and strain rate. Temperature and strain rate effects on flow
stress showed a more marked effect at temperatures greater than 150 ºC.
Perfect plasticity was obtained at temperatures about 220 ºC. The obtained
trends suggested that strain rate has a greater impact on flow stress at
165
temperature above 300 ºC. For instance, a reduction of 4 orders of magnitude
on strain rate at 381 ºC caused the flow stress to be reduced by two-thirds. The
obtained experimental curves were summarized in a series of tables that were
used as input data to the simulation models.
166
5 CHAPTER 5
RESULTS
5.1 Introduction
This chapter presents the results of a dimensional analysis performed on
a research casting. Experimental measurements taken on actual production
castings are compared against computer model predictions. The comparisons
are made using the results of a Design of Experiments (DOE) used to assess the
effects of process parameters on final casting distortion. Computer models
simulating the same process conditions as the DOE were prepared and the
results were used to test the adequacy of the computer model predictions for in-
cavity and across parting plane dimensions.
The chapter is divided into four sections. The first section presents the
results of the statistical analysis performed using the measurements taken on
experimental castings. The results of computer models simulating the same
combination of process conditions as in the DOE are presented in the second
section. In this section comparisons between the two sets of results are
presented as well. The third section is devoted to the analysis of the adequacy
167
of different sets of modeling assumptions used for part distortion modeling in die
casting. Lastly, an analysis of the residual stress predictions given by the
computer models is presented in the fourth section
5.2 Part distortion experiments
A design of experiments was done with the objective of determining the
effects of typical process parameters on final casting distortion. The parameters
selected were intensification pressure and dwell time. These two factors have
been commonly used to explain part distortion behavior in actual production
castings. Dwell time is a control parameter typically used for controlling casting
dimensions. It is a common belief among die casters that leaving the casting in
the die longer produces castings with less distortion. Intensification pressure on
the other hand has been commonly linked to across parting plane dimensional
issues in castings, having a direct correlation with the pressure magnitude. The
practical relevance and the simplicity of adjusting them during production was a
key factor in selecting these two factors for this experimental set up.
Three levels for each factor were selected, making a total of nine different
runs. Table 5.1 shows the matrix design. The casting selected for this study is
shown in Fig. 5.1 and corresponds to the ribbed plate shown in Chapter 3. This
casting is formed using a simple open-close die, with the ribs all formed within
the ejector side, whereas the ribs height is formed between the ejector and cover
sides. Fig. 5.2 shows the casting dimensions. The dimensions shown represent
the room temperature cavity dimensions without considering any shrinkage
fa
th
w
d
actor. Beca
he ribs were
whereas the
istortion.
ause the rib
e selected a
e ribs heigh
bs are forme
as features
t was selec
16
ed within th
s that chara
cted to char
Fig. 5.1 Sele
68
he ejector s
acterize the
racterize th
cted casting
side, the dis
in-cavity d
e across pa
stance betw
istortion,
arting plane
ween
e
c
w
e
b
ru
p
Fig. 5an
The c
onditions u
was decided
arlier and 2
ars represe
un tests wit
ressure at
5.2 Casting dind 1º draft on
combination
sed for pro
d to test the
2 seconds l
ents the up
th half mach
the lowest
imensions in walls formed
n of process
oducing the
e effect of d
ater. The n
per limit the
hine injectio
pressure le
16
millimeters (2d by the insert
s paramete
casting in t
dwell time b
nominal inte
e machine c
on capacity
evel.
69
2º draft on intet and die shoe
ers of run 5
the previou
y ejecting t
ensification
can provide
y and nearly
erior walls fore, see Appen
represents
us research
the casting
n pressure l
e; thus, it w
y no intensi
rmed by the inndix E)
s the nomin
studies. It
2 seconds
evel of 680
was decided
ification
nsert
nal
t
0
d to
170
Run Pressure (bars) Time (s)
1 170 11
2 170 7
3 170 9
4 340 11
5 680 9
6 680 7
7 340 9
8 340 7
9 680 11
Table 5.1 Matrix design for experimental DOE
The different runs were randomized and were run in the order listed on
Table 5.1. A series of castings were initially produced using the parameters of
run 1 to get the die to a quasi-steady thermal state. Batches of 30 castings were
produced for each of the different 9 runs. Although 30 castings were produced
for each run, only the last 20 were used for the dimensional analysis to allow the
die to reach quasi-steady thermal state after the change in process conditions.
During production a series of process parameters were recorded. Actual
cycle times were taken because a rather high variability was introduced due to
the difficulty in controlling spraying time, machine dwell time, closing time and
ladling time. Actual casting weights with and without runner and biscuit were
171
recorded as well because of the inconsistency in pouring volume during the
experiments. The furnace temperature was also observed to vary during the
experiments and it was therefore decided to record it.
5.2.1 Dimensional measurements on production castings
The scope of this research required precise, accurate and repeatable
measurements on the production castings. A Coordinate Measurement Machine
(CMM) was selected to perform the measurements. Additionally, a fixture was
designed and built to secure the castings properly during the measurements.
The fixture was designed considering the 3-2-1 fixturing principle, establishing
this way the coordinate system relative to which all measurements were
expressed consistently. Fig. 5.3 shows the six gauging locations on the casting
that were contacted by the fixture.
s
c
b
h
a
d
5
th
The C
eries of poi
asting featu
etween the
eight was u
For th
long each o
imensions
.4. The five
he points at
CMM meas
ints on the
ures used t
e ribs were
used to stud
he in-cavity
of the fins w
were recor
e points we
t the middle
surements c
different ca
o character
used to stu
dy the acro
Fig. 5
y dimension
width. The
rded at a dis
ere equally
e. Five indi
17
consisted in
asting featu
rize the dist
udy the in-c
oss-parting
.4 Selected c
ns the coord
coordinate
stance 25m
spaced alo
ividual dista
73
n recording
res. Fig. 5
tortion. As
avity dimen
plane dime
casting dimen
dinates of 5
s of all the
mm from the
ong the widt
ances were
the coordin
.4 shows th
mentioned
nsions, whe
ensions.
sions
5 points wer
points for t
e bottom as
th, always l
e computed
nates of a
he selected
d, the distan
ereas the rib
re recorded
the in-cavity
s shown in
locating on
using the
d
nces
bs
d
y
Fig.
e of
174
coordinates of each of the five pairs of points. The final distance between the
ribs was taken as the average of those computed distances.
Coordinates at the top surface of each of the ribs were recorded to
determine the across-parting plane dimensions. As for the in-cavity dimensions,
five points were sampled along the fins width. Rib # 1 was discarded from the
measurements because of excessive flashing. The recorded coordinate along
the ribs height was used to determine the across-parting plane distance for each
fin. The final distance was taken as the average of five different coordinates.
5.2.2 Statistical analysis
An Analysis of Variance (ANOVA) was performed using the obtained
CMM measurements. The intensification pressure and dwell time were specified
as the main factors during the analysis. The additional recorded data for total
cycle time, shot weight, casting weight and furnace temperature was treated
considering these parameters as blocking factors.
A General Linear Model was selected to perform the statistical analysis in
MINITAB. The two main factors and the additional recorded data were all
included in the model. The furnace temperature, cycle time, shot weight and
casting weight were treated as random factors in the model. It was assumed that
the interactions between the random factors were not statistically significant and
only their main effects were considered. Eq. 5.1 shows the model form used for
this analysis as specified in MINITAB.
Eq. 5.1
175
where
corresponds to the analyzed distance
represents the effects of the intensification pressure
represents the effects of the dwell time
represents the effects of the interaction between pressure and dwell
time
represents the effects of the furnace temperature
represents the effects of the cycle time
represents the effects of the shot weight
represents the effects of the casting weight
represents the error term
The ANOVA table, main effect plots, interaction plots and box plots were
requested as outputs for the statistical analysis. The results of this analysis are
presented next for the in-cavity and across parting plane dimensions.
5.2.3 In-cavity dimensions
Table 5.2 to Table 5.4 show the ANOVA results for three selected
distances. As can be seen, for all three distances the intensification pressure,
dwell time and their interaction are all statistically significant. Regarding the
blocking factors, shot weight and casting weight are significant for D1 and D2,
whereas for D3 only the shot weight turned out to be significant. Total cycle time
and the furnace temperature did not have a statistically significant effect on the
final casting dimensions as shown in the ANOVA tables.
176
Source DF Seq SS Adj SS Adj MS F P
Pressure 2 2.46975 0.34399 0.17199 35.25 0
Dwell time 2 0.73519 0.38066 0.19033 39.00 0
Pressure*Dwell time 4 0.49068 0.30921 0.07730 15.84 0
Furnace temp 1 0.01079 0.01662 0.01662 3.41 0.067
Cycle time 2 0.00763 0.01446 0.00723 1.48 0.230
Shot weight 4 0.21162 0.15678 0.03920 8.03 0
Casting weight 2 0.06845 0.06845 0.03422 7.01 0.001
Error 162 0.79051 0.79051 0.00488
Total 179 4.78642
Table 5.2 ANOVA results for distance D1
177
Source DF Seq SS Adj SS Adj MS F P
Pressure 2 0.02224 0.001695 0.000847 3.27 0.040
Dwell time 2 0.159563 0.097493 0.048747 188.38 0
Pressure*Dwell time 4 0.08093 0.052938 0.013234 51.14 0
Furnace temp 1 0.000375 0.000028 0.000028 0.11 0.742
Cycle time 2 0.006029 0.000835 0.000417 1.61 0.202
Shot weight 4 0.04748 0.044191 0.011048 42.69 0
Casting weight 2 0.004126 0.004126 0.002063 7.97 0
Error 162 0.041923 0.041923 0.000259
Total 179 0.362680
Table 5.3 ANOVA results for distance D2
178
Source DF Seq SS Adj SS Adj MS F P
Pressure 2 0.0647878 0.020 0.010 14.42 0
Dwell time 2 0.0245811 0.0125068 0.006253 9 0
Pressure*Dwell time 4 0.0402822 0.0405695 0.010142 14.6 0
Furnace temp 1 0.0001343 0.0000318 0.0000318 0.05 0.831
Cycle time 2 0.006718 0.0019448 0.0009724 1.40 0.25
Shot weight 4 0.0248597 0.0224419 0.0056105 8.08 0
Casting weight 2 0.001697 0.0016978 0.0008489 1.22 0.297
Error 162 0.1125 0.1125 0.0006945
Total 179 0.275561
Table 5.4 ANOVA results for distance D3
Fig. 5.5 shows the main effect plots obtained from the statistical analysis.
To facilitate interpretation of distortion results the experimental measurements
have been normalized against the nominal distance at room temperature. The Y
axis scale shows this normalized magnitude multiplied by 100. The closest the
magnitude is to 100, the lesser the distortion.
The observed pressure trends seem to suggest that for all distances, the
greater the intensification pressure the bigger the distortion. It is conjectured that
as the pressure is increased the ribs thickness increases, coupled with more die
warpage leading to a greater reduction in the selected in-cavity distances. On
the other hand, the dwell time curves show rather inconsistent trends, suggesting
179
only for D2 that the longer the casting remains in the die the smaller the
distortion. For D1 and D3 the middle dwell time level produces the smallest
distortion. A possible explanation for this behavior is the fact that the distance
D2 is formed in the middle section of the insert where there is more mass
distribution and a hot spot is developed, leaving the warpage of the casting on
that region more sensitive to the dwell time. As the casting warps it is
conjectured that the distance between the fins that form D2 gets reduced more
than D1 or D3.
Fig. 5.5 Experimental main effect plots for in-cavity dimensions
180
Fig. 5.6 shows the obtained interaction plots. The lowest intensification
pressure level curves show consistent behavior for distances D1 and D3,
suggesting only for D2 that the longer the dwell time the smaller the distortion. At
this lowest pressure level, the middle dwell time level produces the smallest
distortion for distances D1 and D3. The middle level pressure curves on the
other hand show that for D1 and D2 the longer the dwell time the smaller the
distortion, whereas for D3 the pressure curve has a maximum at 9s dwell time
rather than a minimum as in the previous set of pressure results. The highest
pressure level curves show a consistent trend for D1, D2 and D3, suggesting a
minimum at the 9s dwell time.
The rather high inconsistency in the interaction plot results seems to
indicate that distortion is a more complex phenomena than what would be
expected, being a complex interplay of physical phenomena such as residual
stresses and temperature at ejection. On one hand it might be possible to have
more distortion on a casting that gets ejected after a longer dwell time just
because of the higher residual stress built-up even though the ejection
temperatures are lower. On the other hand it might be possible to produce more
distortion on a casting ejected sooner as a result of the combination of higher
ejection temperatures and very low residual stresses. Therefore, although the
trends depicted in Fig. 5.6 may not be generalized, they do bring the attention to
the fact that distortion is far more dependent on the interaction of process control
parameters than on the individual action of them. Moreover, it can be expected
that different features or dimensions on castings respond differently to the
181
process parameters. Thus, adjusting process parameters might bring some
dimensions within tolerances while it may cause others to fall out of tolerances.
Fig. 5.6 Experimental interaction plots for in-cavity dimensions
The box plots for these measurements are shown in Fig. 5.7. As can be
seen, the spread of the data is rather large in some cases especially for distance
D3, but overall the means can be distinguished somewhat clearly. The spread of
182
the data might be attributed to the lack of accurate control in total cycle time and
pour volume during the casting session.
Fig. 5.7 Box plots for in-cavity dimensions
5.2.4 Across parting plane dimensions
Because across parting plane dimensions are typically reported to be
harder to control, it was decided to analyze some of these features on this
183
casting. These dimensional features are typically more sensitive to variations in
intensification pressure magnitudes and slides positioning; thus, it was thought
that the DOE used for this study could provide some insights into the
dependency of these features to the proposed design variables.
The ANOVA results for these dimensions are presented in Table 5.5 to
Table 5.7 for the three different distances. The statistical results show that for H2
and H4, the pressure, dwell time and their interaction are all statistically
significant, whereas for H3 only the pressure and the interaction term are
significant. Regarding the blocking factors, only the shot weight and casting
weight resulted to be statistically significant as seen in the tables.
The ANOVA results for the across parting plane dimensions came in good
agreement with the in-cavity dimensions results. Both sets of results show that
the design variables, intensification pressure and dwell time, and their interaction
term resulted to be statistically significant for all but H3 dimension. It is worth
mentioning that although the ANOVA results show that the design variables have
a statistically significant effect on the dimensions studied, the practical effect may
or may not be significant enough and the dimensional changes may be
considered all within the expected variability of the process.
184
Source DF Seq SS Adj SS Adj MS F P
Pressure 2 7.67 0.96983 0.48491 45.25 0
Dwell time 2 0.09110 0.21502 0.10751 10.03 0
Pressure*Dwell time
4 3.70939 1.27241 0.3181 29.68 0
Furnace temp 1 0.00283 0.00090 0.00090 0.08 0.773
Cycle time 2 0.01951 0.06119 0.03059 2.85 0.060
Shot weight 4 0.25488 0.16029 0.04007 3.74 0.006
Casting weight 2 0.31945 0.31945 0.15972 14.90 0
Error 162 1.73607 1.73607 0.01072
Total 179 13.808
Table 5.5 ANOVA results for distance H2
185
Source DF Seq SS Adj SS Adj MS F P
Pressure 2 3.42595 0.47073 0.23536 29.80 0
Dwell time 2 0.02434 0.02398 0.01199 1.52 0.222
Pressure*Dwell time
4 1.51288 0.43658 0.10914 13.82 0
Furnace temp 1 0.00815 0.00628 0.00628 0.80 0.374
Cycle time 2 0.00649 0.01968 0.00984 1.25 0.290
Shot weight 4 0.28381 0.15766 0.03942 4.99 0.001
Casting weight 2 0.33147 0.33147 0.16574 20.98 0
Error 162 1.27954 1.27954 0.00790
Total 179 6.87262
Table 5.6 ANOVA results for distance H3
186
Source DF Seq SS Adj SS Adj MS F P
Pressure 2 3.78156 0.78919 0.3936 34.05 0
Dwell time 2 0.00883 0.10098 0.05049 4.36 0.014
Pressure*Dwell time
4 1.35853 0.48737 0.12184 10.51 0
Furnace temp 1 0.00030 0.00117 0.00117 0.1 0.751
Cycle time 2 0.03882 0.01100 0.00550 0.47 0.623
Shot weight 4 0.69171 0.43277 0.10819 9.34 0
Casting weight 2 0.41198 0.41198 0.20599 17.77 0
Error 162 1.87746 1.87746 0.01159
Total 179 8.16198
Table 5.7 ANOVA results for distance H4
Fig. 5.8 shows the main effect plots for selected across parting plane
distances. Only for H2 do the plots show that the higher the intensification
pressure the larger the distance. The data seems to suggest that only for this
case, does the common belief that the higher pressure the larger the across
parting plane distance may hold. For distances H3 and H4, the highest pressure
level produced a smaller distance than the middle pressure level as shown in the
plots. The dwell time main effect plots depict a rather consistent trend for all
three distances, suggesting that the 9s dwell time produces the longest ribs.
187
Fig. 5.8 Experimental main effect plots for across parting plane dimensions
The interaction plots for the across parting plane dimensions are
presented in Fig. 5.9. The obtained trends clearly show the effects of the
intensification pressure on the across parting plane dimensional behavior. The
pressure plots also show the rather consistent behavior across all the analyzed
distances.
At the lowest pressure level, where almost no intensification pressure was
used, minimal distortion was obtained at a dwell time of 9 seconds. This
behavior was reversed at the highest intensification pressure level, suggesting
188
that distortion is the maximum at the 9 seconds dwell time. When intensification
pressure is used at the middle level, the results show that the longer the dwell
time the greater the obtained shrinkage.
The interaction results show the intricate interrelation of the effects of the
intensification pressure and dwell time on the across parting plane dimensions.
These trends reinforced the claim that in-cavity and across parting plane casting
distortion is far greater the result of a complex interplay of residual stresses and
temperature profiles and it becomes rather difficult to isolate the effects of these
two process variables when their interaction effects drive casting distortion to
such a large extent. Only at one pressure level did the results suggest that the
longer the dwell time the greater the shrinkage.
The interaction plots may also indicate that pressure gradients within the
solidifying casting played some role in across parting plane dimensions. This
claim can be supported by looking at the Y scale of the interaction plot for
distance H4, which shows magnitudes closer to 100, indicating that the distance
at this location is larger. Smaller distances at locations far from the gate might
have been obtained due to premature solidification before the intensification
pressure took effect.
189
Fig. 5.9 Experimental interaction plots for across parting plane dimensions
The box plots for the across parting plane measurements are shown in
Fig. 5.10. Even though a large amount of outliers can be seen, some general
trends can be observed from the data. For a fixed dwell time level, the
intensification pressure follows an upward trend across all three distances. By
the same token, at the same pressure level, the dwell time curves follow similar
trends for the three distances. Three main trends can be noticed resembling the
observed behaviors shown in Fig. 5.9.
190
Fig. 5.10 Box plots for across parting plane dimensions
5.3 Computer model predictions
5.3.1 Model preparation
Computer models simulating the process conditions listed in Table 5.1
were prepared following the modeling methodology described in Chapter 3. The
three modeling stages were followed to predict the final casting distortion for
each of the 9 different experimental runs.
191
Individual thermal models for each of the three different dwell times were
prepared in order to account for the differences in die thermal profiles resulting
from the different cycle times. The obtained thermal results were used to
simulate the thermal load during the first two modeling stages. The three
different intensification pressure levels used in the DOE were modeled by
applying three different pressure loads correspondingly.
The fully-coupled thermal-mechanical models were run to completion
using 64-bit Windows-based work stations. The running time for the computer
models varied based on the simulated dwell time, taking 15, 19 and 21 days for
the 7, 9 and 11 seconds simulated dwell time respectively. The running times
were rather long because the maximum step size was controlled not to exceed
0.010 seconds. This restriction in step size was imposed by design in order to
avoid numerical errors in the stress field due to large temperature differences
within steps.
5.3.2 Distance calculations
5.3.2.1 Coordinate transformation
The distortion predictions given by the computer models were analyzed
taken the CMM measurements as the basis for the analysis. A coordinate
transformation was required in order to express the final distorted nodal
coordinates of the casting relative to the same coordinate system defined by the
fixture used in the experimental measurements. The coordinate system
established by the fixture during the measurements was mathematically
constructed using the final distorted coordinates of six nodes in the casting
lo
c
c
d
ocated the c
ontacted by
oordinates.
Three
istorted coo
closest to th
y the fixture
.
Fig. 5.11 S
e datum pla
ordinates o
he same ga
e. Fig. 5.11
Sampling orde
anes were m
of those six
19
auging poin
1 shows the
er of casting n
mathematic
sampled no
92
nts were the
e sampling
nodes for coo
cally constru
odes. The
e actual cas
order of the
ordinate trans
ucted using
normal of t
stings were
e nodal
sformation
g the final
the first dat
e
tum
193
plane was obtained using the coordinates of the nodes 1, 2 and 3 and was
computed as follows
where
corresponds to the normal of the first datum plane
, 1 … 3 corresponds to the , , nodal coordinates of the sampled
nodes
With the first’s plane normal known, the complete plane equation for the
first datum plane was obtained by using the coordinates of node 1 and solving
the following dot product
,
The normal of the second datum plane was obtained by using the
coordinates of the nodes 4 and 5, and the normal of the first datum plane by
solving the following cross product
where
corresponds to the normal of the first datum plane
194
, 4,5 corresponds to the , , nodal coordinates of the sampled
nodes
With the second’s plane normal known, the complete plane equation for
the second datum plane was obtained by using the nodal coordinates of node 4
and solving the following dot product
,
The third’s datum plane normal was determined to be the cross product of
the normals of the first and second datum planes
The complete plane equation for the third datum plane was obtained by
using the coordinates of node 6 and solving the following dot product
,
Knowing the parameters of the plane equation for the three datum planes,
the origin was readily determined by solving the following linear system of
equations
195
where
, , correspond to the , , coordinates of the origin
, , , 1 … 3 correspond to the parameters of the plane’s normal
Expressing the distorted nodal coordinates in the coordinate system
determined by the datum planes consisted in performing an affine transformation.
An affine transformation is a map between two vector spaces and consists of a
linear transformation and a translation. The fixture basis determined by its datum
planes were expressed as vectors in the computer model coordinate system as
defined by the three computed normal vectors
The order of these basis vectors is defined by the original orientation of
the coordinate system used in the computer models. The last computer normal
corresponds to the axis, the second computed normal corresponds to the
axis and the first computed normal corresponds to the axis.
The orientation of the basis in the fixture coordinate system was not
coincident with the orientation of the basis in the computer model. The axis in
the fixture basis corresponded to the negative axis in the computer model
basis, the axis corresponded to the axis, respectively, while both axes were
oriented in the same direction. The rotation matrix R shown below was used to
orient the fixture basis properly
196
0 1 01 0 00 0 1
The affine transformation of coordinates may be done either way, from the
fixture coordinate system to the computer model coordinate system or viceversa.
Considering expressing the CMM experimental readings in terms the computer
model coordinate system, the following affine transformation may be used
1 0 1 1
where
corresponds to a vector of ( , , ) coordinates expressed in terms of
the computer model coordinate system
corresponds to a vector of ( , , ) coordinates expressed in terms of
the fixture coordinate system
, , is the vector containing the coordinates of the origin
Since the objective is the transformation of computer model results in
terms of the fixture coordinate system, the following transformation was used
1 0 1 1
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5.3.2.2 Distance calculation
The in-cavity and across parting plane distances were computed using the
same procedures as the CMM measurements. The nodal coordinates of points
located the closest to the same locations of the sampled points during the CMM
measurements were selected to compute the distances. Since a symmetric
model was used in the simulations only three nodes were sampled along the
casting width. The nodes were chosen to be equally spaced as in the CMM
measurements with the middle point always located at the symmetry plane.
As in the CMM measurements, for the in-cavity dimensions the nodes
were selected on opposing sides of the ribs forming the corresponding distance.
For each of the in-cavity dimensions three pairs of nodal coordinates were
selected and the individual distance between each pair of nodes was computed.
The final in-cavity dimension was taken to be the average of the three individual
distances.
As in the CMM measurements, the coordinate along the ribs height was
used to estimate the across-parting plane dimension for each rib. For each
across parting plane dimension, three individual coordinates corresponding to the
three selected nodes along the ribs width were used and the final distance was
taken to be the average of those three coordinates. The dimensions H2, H3 and
H4 used in the experimental measurements were considered in this analysis as
well.
198
5.3.3 In cavity dimensions
Fig. 5.12 shows the main effect plots obtained using the computer model
predictions. As for the experimental result plots, all computer model results are
expressed as a ratio of the final predicted dimension to the nominal dimension,
expressed in percentage. On the one hand, the pressure and dwell times curves
for distances D2 and D3 show the same trends all suggesting that maximum
distortion is obtained at the middle level for each factor. On the other hand, the
results for distance D1 are different. The pressure curve in this case shows a
downward trend indicating that the higher the intensification pressure the greater
the distortion, whereas the dwell time curve suggests that the longer the dwell
time the lesser the distortion.
As far as trends are concerned, computer model results show a rather
considerable disagreement when compared to the experimental results. The
main effect results come in good agreement only for distance D1 for the
intensification pressure factor and in somewhat close agreement for distance D3
for the dwell time factor. All other plots show opposite trends.
199
Fig. 5.12 Simulation main effect plots for in-cavity dimensions
Fig. 5.13 shows the interaction plots using the simulation results. In most
cases the interaction plots show different behaviors across the three different
distances, depicting more repeatability for distances D2 and D3. The plots
showed that at the lowest pressure curve, lesser distortion was obtained at a
dwell time of 9 seconds for distance D1, whereas it was the opposite for
distances D2 and D3. The same trends were obtained at the middle pressure
level. At the highest pressure level, the pressure curves for distances D1 and D2
200
suggested that the higher the intensification pressure the lesser the distortion,
whereas for distance D3 a minimum was observed at the middle dwell time level.
As with the main effect plots, the interaction plots using the computer
model results came in noticeable disagreement with the experimental results.
The two sets of results showed good agreement only for distances D1 and D3 at
the highest pressure level. The results for the remaining plots differed notably.
Fig. 5.13 Simulation interaction plots for in-cavity dimensions
201
5.3.4 Across parting plane dimensions
Fig. 5.14 shows the main effect plots for the across parting plane
dimensions. The main effect pressure plots show similar trends for distances H3
and H4, depicting a minimum at the middle level. Only for distance H2 do the
pressure curve follow an upward trend, suggesting the higher the intensification
pressure the smaller the across parting plane distortion. The main effect
pressure plot for distance H2 shows a good correlation with the experimental
case, following the same trend. On the other hand, the plots for distances H3
and H4 follow reversed trends when compared with the experimental results.
The computer model dwell time main effect plots show rather expected
trends. For two of the three analyzed dimensions, the plots suggest that the
longer the dwell time the greater the distortion. These trends might be somewhat
expected since leaving the casting in longer contact with the die would potentially
lead to greater across parting plane shrinkage. The general trends of these
results do not correlate well with the experimental trends; however, the physical
interpretation of the computer model results agrees better with field observations.
202
Fig. 5.14 Simulation main effect plots for across parting plane dimensions
Fig. 5.15 shows the interaction plots obtained from the computer models
results. The obtained plots show somewhat consistent trends for distances H3
and H4 only. For these two distances, the lowest and mid pressure level plots
follow a downward trend suggesting the longer the dwell time the greater the
shrinkage. At the highest pressure, maximum shrinkage was obtained at the
middle level dwell time. On the contrary, reversed behaviors were obtained for
distance H2. This subset of results show reversed trends for all pressure levels
when compared to the results for distances H3 and H4.
203
When compared to the experimental results, relatively good agreement
was observed. For distances H3 and H4, both the experimental and computer
model results follow similar trends for the middle and highest pressure level
curves. For these two distances at the lowest pressure, the results do not
correlated well. The largest differences were observed for distance H2, where
for all pressure levels the computer models followed reversed trends when
compared to the experimental plots. A more detailed comparison of the results is
presented in the next section.
Fig. 5.15 Simulation interaction plots for across parting plane dimensions
204
5.4 Comparison of experimental and computer model results
Simulation results for in-cavity and across parting plane dimensions were
compared against the experimental measurements. Because computer models
generate only one numerical result for each distance, a single numerical
experimental value had to be selected for comparisons purposes. It was decided
to use the median of each run and compare it with the simulation results. The
results for each run are expressed as a ratio of the difference between the
experimental and computer model predictions to the experimental distance,
expressed in percentage. The following equation was used for computing the
results
100
Eq. 5.2
Fig. 5.16 shows the results obtained for the in-cavity dimensions. The
results showed that in most cases computer models over-predicted the change in
dimensions, resulting in smaller distances when compared to experimental
results. The largest differences were consistently obtained for distance D2,
reaching a difference of up to 0.5% in run 7. Computer model and experimental
predictions came in closer agreement for distances D1 and D3, with differences
averaging 0.14% and 0.15%, respectively. On average, the differences between
both sets of results across all distances were about 0.2%.
Over prediction of casting warpage by the computer models might be a
likely explanation for the consistent under estimation given by the computer
205
models. It is conjectured that the weak resistance of casting to bending loading
is the artifact result of the linear reduced integration elements used to represent
it. Linear reduced integration elements are prone to hourglassing and tend to be
too flexible under bending loads, leading to greater than expected warpage on
the casting.
Fig. 5.16 Comparison of results for in-cavity dimensions
The results obtained for the across parting plane dimensions are shown in
Fig. 5.17. In general, the difference between the computer model predictions
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Differen
ce (%
)
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In‐cavity dimensions
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D2
D3
206
and the experimental measurements were larger than for the in-cavity
dimensions. The differences were as large as 1.7%, which might be considered
rather noticeable. The results showed that in most cases the differences were
larger for distance H4, located the closest to the gate. Except for one case, the
results showed that the obtained differences for distances H2 and H3 were
smaller than 0.5%, averaging 0.03% and 0.20% across all runs respectively.
These results may also show that the computer model is able to predict across
parting plane dimensions within acceptable levels for some locations and may
argue that the inability to predict in other locations might be attributed to an
inadequate modeling assumption such as a boundary condition.
Fig. 5.17 Comparisons of results for across parting plane dimensions
‐1.50
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ce (%
)
Run
Across parting plane dimensions
H2
H3
H4
207
A likely explanation to help describing the observed differences in
distortion predictions for across parting plane dimensions might be obtained by
looking at Fig. 5.18 and Fig. 5.19. Fig. 5.18 shows the different across parting
plane dimensions obtained for all the experimental cases. Distance H2 is the
farthest from the gate, whereas distance H4 is at the gate. From this plot it can
be seen that the across parting plane dimensions near the gate are larger. This
might be explained due to the vertical off-center positioning of the die, whose
geometric center is located 76.2mm (3in) down relative to the geometric center of
the platen. Additionally, the center of pressure of the cavity is located 10mm
(0.4in) down, relative to the geometric center of the die. This off-center
positioning of the die and cavity translates into an off-center loading during
operation and causes the die to open up at the bottom, leading to larger across
parting plane dimensions near the gate. Additionally, since the casting is gated
from the bottom, solidification progresses from the top-down and any premature
solidification of the top regions before the intensification pressure takes effect
would concentrate this pressure loading near the gate, contributing to lager
across parting plane dimensions.
208
Fig. 5.18 Distribution of across parting plane experimental dimensions
Fig. 5.19 shows the across parting plane dimensions obtained from the
computer model results. These results predicted different trends when compared
to the experimental results, suggesting larger dimensions far from the gate. This
might be explained due to the way the clamping force was modeled. In this
research work clamping force was modeled by applying a constant pressure load
at the back of the ejector and cover platens. The load was assumed to be of
equal magnitudes at the top and bottom and no account for load imbalance due
to off-center positioning of the die was taken. Moreover, having a constant
pressure load prevents from capturing any load redistribution that takes place
after the intensification pressure is applied. The limitations of this approach may
29.7
29.8
29.9
30.0
30.1
30.2
30.3
30.4
1 2 3 4 5 6 7 8 9
Distance (m
m)
Run
Ribs dimensions using experimental results
H2
H3
H4
209
cause the machine to behave too stiff preventing any cavity enlargement,
especially across parting plane, leading to smaller dimensions.
Additionally, the observed differences may also be due to the inability to
model the intensification pressure adequately. As described, the intensification
pressure is the result of the loading action of the pressurized casting acting on
the die. These pressurized solidification conditions may guarantee a tight
contact between the casting and the die at all times, preventing the casting from
freely shrinking across the parting plane. Because the solid elements used to
represent the casting cannot carry a hydrostatic pressure, the described
solidification conditions cannot be modeled. In this modeling work the
intensification pressure is modeled as a pressure load acting on the die cavity
surface and a de-coupling at the casting/die interface exists that allows the
casting to shrink freely across the parting plane. This modeling limitation may
also lead to smaller across parting plane dimensions, especially at locations
where the intensification pressure effects are larger, particularly near the gate.
210
Fig. 5.19 Distribution of across parting plane simulation dimensions
5.5 Testing the adequacy of part distortion modeling assumptions
Because of the high degree of complexity commonly found in nature, the
use of mathematical models for simulating a particular system always requires
the use of assumptions to be able to solve the given problem. Developing
computer models in die casting has always represented a real challenge
because of the many interrelated physical phenomena that take place during the
process of making a casting. Currently, all of the available codes used for part
distortion modeling in die casting rely on a set of assumptions limiting to varying
degrees the accuracy of the numerical predictions.
29.429.529.629.729.829.930
30.130.230.3
1 2 3 4 5 6 7 8 9
Distance (m
m)
Run
Ribs dimensions using simulation results
H2
H3
H4
211
It was decided to investigate the adequacy of the different sets of
modeling assumptions most commonly found. Computer models were generated
to reproduce the different sets of assumptions taken. Table 5.8 shows six
different sets of modeling assumptions analyzed. Case 1 represents the
methodology presented in this dissertation work. Case 2 was designed to
investigate the effect of having an elastic constitutive model representing the
casting and represents the same set of assumptions as Case 1, but the casting
constitutive model was taken to be purely elastic. Case 3 was designed to
investigate the contributions of the elastic deflections of the tooling in casting final
dimensions. In this case the elastic deflections of the die are not accounted for
and the casting is assumed to be ejected with the same shape as the room
temperature cavity and only having a characteristic ejection thermal profile.
In case 4 the casting is assumed to be ejected with the same shape as the
operating cavity at the point of ejection and with a characteristic thermal profile.
Case 5 represents the same set of assumptions as case 1, but the casting is
assumed to be ejected stress-free. This case was designed to investigate the
effect of the residual stress predictions at ejection obtained in this research work
in casting final dimensions. Case 6 represents a slight variation of case 4 in
which the casting is represented using an elastic constitutive model. This case
was designed to investigate the validity of assuming an elastic model for the
casting after ejection.
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Case Modeling assumptions
1
• Elastic deflections of die • Contact interactions casting/die • Casting is ejected with the predicted shape, stress and thermal profile • Elastic-perfectly-plastic constitutive model
2
• Elastic deflections of die • Contact interactions casting/die • Casting is ejected with the predicted shape, stress and thermal profile • Elastic constitutive model
3 • Casting shape matches room temperature cavity shape • Casting ejected stress-free and with predicted thermal profile • Elastic-perfectly-plastic constitutive model
4 • Casting shape matches distorted cavity shape • Casting ejected stress-free and with predicted thermal profile • Elastic-perfectly-plastic constitutive model
5
• Elastic deflections of die • Contact interactions casting/die • Casting is ejected stress-free, with the predicted shape and thermal
profile • Elastic-perfectly-plastic constitutive model
6 • Casting shape matches distorted cavity shape • Casting ejected stress-free and with predicted thermal profile • Elastic constitutive model
Table 5.8 Proposed sets of modeling assumptions
The computer models were prepared using the described modeling
assumptions and the combination of process conditions of run 5 from the DOE as
shown in Table 5.1. This run was selected because it represents the nominal
combination of process conditions designed to produce the casting under study.
The numerical predictions of the computer models were compared against the
213
experimental data obtained for run 5. As with the previous analysis, the median
of the experimental results was taken as the single numerical value to be used
for comparing the experimental data with the computer model predictions.
The computer model results were expressed in the fixture coordinate
system using the same affine transformation as described in section 5.3.2.1. Fig.
5.20 shows the results obtained for the in-cavity dimensions. The results show
that the best predictions were obtained in case 4, where the casting is assumed
to be ejected stress-free and with the same shape as the distorted die cavity at
the point of injection. Under these set of assumptions, assuming an elastic
model for the casting material yields results as good as assuming an elastic-
plastic model. The predictions for case 1, which uses the methodology proposed
in this research work, were substantially improved when the residual stresses at
ejection are not accounted for. This observation shows the effect the residual
stresses at ejection can have in driving the casting distortion after ejection.
The results showed that the worst predictions were obtained when an
elastic constitutive model is used to represent the casting throughout the
analysis. These results clearly show that the use of an elastic model is not
adequate for modeling casting distortion. The second worst predictions were
obtained when the elastic deflections of the die are not accounted for. These
results show the significant contributions of the die deflections in the in-cavity
casting dimensions and suggest the die and machine elements must be included
in the analysis.
214
Fig. 5.20 Comparisons of results for in-cavity dimensions predicted by the different sets of modeling assumptions
Fig. 5.21 shows the results obtained for the across parting plane
dimensions. The predictions for these distances followed a different pattern as
the in-cavity dimensions, and the set of modeling assumptions that were not able
to provide good predictions previously resulted to be reasonably good for across
parting plane dimensions. A clear example of this situation can be seen from the
across parting plane predictions given by case 2, which uses an elastic model for
the casting. The predictions given by this case were the closest to the
experimental results for all distances, showing differences of 0.07 and 0.11% for
distances H2 and H3, respectively. The results of case 3 also showed the close
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Differen
ce (%
)
Case
In‐cavity dimensions
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D2
D3
215
agreement obtained for the across parting plane distances, where before they
were a poor predictor for in-cavity dimensions.
In consistency with the results of Fig. 5.17, the obtained data also shows
that all cases over estimate the shrinkage of distance H4. This observation
seems to suggest that the modeling methodology relies on an assumption that
consistently affects the across parting plane dimensions near the gate. As was
mentioned before, the overly stiff behavior of the machine might be attributed to
the constant pressure used to model the clamping force effects. Additionally, the
inability to model the intensification pressure adequately may lead to smaller
dimensions as well.
Fig. 5.21 Comparison of results for across parting plane dimensions predicted by the different sets of modeling assumptions
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ce (%
)
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Across parting plane dimensions
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216
5.6 Stress results
The ability to predict the deformation and residual stresses in a casting is
of vital importance for casting design and performance. It is well known that the
distribution and magnitude of the stresses on a casting can severely limit its
function. Moreover, the residual stresses can have a significant impact on the
casting final dimensions if their magnitudes and distributions are such that
twisting and warping result from the state of stress. Because of their importance,
it was decided to study the behavior of the stress evolution on the castings using
the computer model results.
To analyze the behavior of the residual stresses on the casting, a series of
points of interest were selected and their stress, strain and temperature profiles
were studied. The plots were generated from the simulation results of run 5,
corresponding to a 9s dwell time and an intensification pressure of 680bars as
listed in Table 5.1. Although the magnitudes of the stresses and strains vary
depending on the process conditions used to produce the casting, run 5 was
selected because it represents the nominal process conditions designed to
produce the casting under study.
Fig. 5.22 shows the selected locations for this analysis. The points were
all located at the casting symmetry plane. The von Mises, maximum principal,
medium principal and minimum principal stresses were all extracted from the
finite element’s centroid at the locations shown. The cooling profile of the
selected elements is plotted along with the stresses to help interpreting the
results.
217
To gain more insight into the stress behavior, the maximum principal,
medium principal and minimum principal strains at the centroid of the selected
elements were plotted as well. It was decided to analyze the strains because
they may provide more indication into the nature of the cooling conditions the
casting experiences, since thermal strains as such do not cause stresses,
stresses develop only if the shrinkage is constrained either due to a die wall or
due to differential thermal cooling of different regions of the casting.
Fig. 5.22 Analyzed stress locations at the symmetry plane
Fig. 5.23 to Fig. 5.26 show the stress and temperature profiles at the
selected regions. The results depict a rather consistent trend at these locations,
suggesting a stress built-up while the casting cools in the die followed by stress
relaxation after ejection. The stress built-up may be explained by the fairly rigid
constrained cooling conditions the casting experiences while it remains in the die.
218
At ejection, when this restraint is removed and the casting is free to shrink, some
degree of relaxation takes place as reflected by the observed sudden drop in the
stress plots.
The stress plots suggest that the degree of relaxation after ejection varies
depending on location. Locations 1 and 2 show that after ejection the stresses
relax and remain low for the rest of the cooling time. On the other hand, the
stress plots for locations 3 and 4 suggest that although relaxation takes place
after ejection, the stresses build up after ejection. A likely explanation for this
behavior might be the fact that these locations are situated near a hot spot and
deformation might be still taking place, leading to an increase of the stresses at
these regions. These results also show that the magnitudes of the computer
model stress predictions are within an expected range. At the selected locations,
the stress results vary between 30 to 60 MPa, considered within acceptable
levels.
222
Fig. 5.26 Stress and temperature profiles at location 4
A useful piece of information regarding the stress behavior in the casting
can be obtained by looking at the strain profiles. As mentioned, the stresses on
a casting develop due to the constrained shrinkage conditions that can be
developed due to differential thermal cooling between different regions of the
casting and also due to contact between the casting and the die walls. Thus,
looking at the strains can provide insights into the nature of the cooling conditions
223
because the thermal strains just provide a “thermal load” or mismatch that is
mapped into stresses if some restrainting is experienced.
Fig. 5.27 to Fig. 5.30 show the profiles for the maximum, medium and
minimum principal strains at the same locations shown in Fig. 5.22. In
agreement with the stress plots, the strain curves show that strains are indeed
developed while the casting cools in the die. The development of these strains
might be due to plastic behavior of the rather weak casting, unable to resist the
restraint of the stiff die walls. The weak behavior of the casting at these
temperatures can be well explained by looking at material properties of the
casting shown in Fig. 4.43 and Fig. 4.44. These curves show that casting yields
under perfect plasticity at the temperature range observed while cooling in the
die and is therefore rather weak to resist any constrained shrinkage.
After ejection, the strain plots show a rather interesting trend. When the
casting is ejected, the strains experienced a sudden increase, followed by an
asymptotic downward trend while the casting cools to room temperature. The
sudden rise in magnitude might be explained by the stress relaxation taking
place, since at this point the casting can shrink freely potentially causing a rise in
the thermal strains that are accommodated as plastic stresses leading to
relaxation. The downward asymptotic trend may correspond to the ability of the
casting to shrink freely as it cools to room temperature.
227
Fig. 5.30 Strain profiles at location 4
5.7 Summary
The statistical analysis done using the CMM measurements predicted that
the pressure, dwell time and their interaction were all statistically significant for
both, the in-cavity and across parting plane dimensions. The interaction plots for
the in-cavity distances showed the degree to which complex relationship
between the ejection temperature profile and the residual stresses at ejection can
drive the dimensional behavior of the casting. The across parting plane
228
interaction plots showed more consistent trends across all three distances.
These results also suggested larger dimensions for distances near the gate.
Computer model interaction predictions correlated well with only a few
experimental cases. The dimensional predictions for in-cavity dimensions
showed close agreement with the experimental results, with differences
averaging 0.18% across all analyzed distances. On the other hand, the
predictions for across parting plane dimensions showed larger differences,
especially for the dimensions near the gate. The observed differences in results
for the distance at the gate were as large as 1.79%. However, the results for the
other two dimensions were much closer to the experimental measurements with
differences averaging 0.03% and 0.20%, respectively.
It is conjectured that the larger differences in results for across parting
plane dimensions might be attributed to modeling aspects. The constant
pressure load used to model clamping force effects is thought to cause an overly
stiff behavior of the machine, leading to smaller deflections and potentially to
smaller across parting plane dimensions. Additionally, the inability to model
pressurized solidification for the casting prevents from having a tight contact
between the casting and the die, which may also lead to a larger shrinkage
across parting plane.
The results obtained from testing the adequacy of different sets of
modeling assumptions yielded different trends for in-cavity and across parting
plane dimensions. On the one hand, for in-cavity dimensions the best results
were obtained when the casting is assumed to be ejected stress-free and with
229
the same shape of distorted die cavity shape at ejection. The use of an elastic or
an elastic-plastic model for the casting material did not have any impact on the
results. The worst predictions were obtained when an elastic model is used for
the casting material. On the other hand, for across parting plane dimensions the
best predictions were given when the casting material is assumed to be elastic.
Nonetheless, in all cases the shrinkage for across parting plane dimensions were
over predicted.
The analysis of the stress profiles provided insights into the evolution of
the stresses during the whole cooling period. A stress built-up was observed
while the casting cools in the die, followed by a stress relaxation at the point of
ejection. The obtained plots suggested that the evolution of the stresses after
ejection is location dependent, showing some degree of stress built-up for
regions undergoing distortion after ejection. The analysis of the strain plots
correlated well with the observed stress profiles, clearly depicting the built-up and
relaxation that take place in the casting as it cools.
230
6 CHAPTER 6
CONCLUSIONS
6.1 Introduction
The motivation for this research work was the need to develop a computer
modeling methodology to predict final dimensions and residual stresses in a die
casting. The difficulty of the problem consisted in accounting for the elastic
deflections experienced by the die, which bring about dimensional changes in the
cavity during operation. Thus, a methodology aimed at predicting final casting
dimensions must account for these dimensional changes, since the initial casting
shape at the end of filling is determined by the distorted die cavity.
Accounting for the dimensional changes taking place in the die cavity
requires tracking its distortion during the loading. Clamping, temperature and
intensification pressure are the main static loads considered when modeling die
distortion. The machine components must be included in the model to properly
simulate the loading conditions. The main complexity lies in how the cavity
distortions are tracked, since the method for tracking the distortion must be
accurate to within tenths of a millimeter to be of any use.
231
Additionally, stresses in a casting have a significant impact in driving its
distortion and the casting material must be accurately represented in the model.
This requires accurate temperature and strain rate dependent constitutive
models for representing the casting material, since the mapping of the strains to
stresses relies on the assumed constitutive model.
A modeling methodology for predicting final dimensions and residual
stresses in a die casting was developed using Abaqus, a commercially available
FEA package. The material properties needed to represent the casting material
were determined as part of this research work as well. The predicted dimensions
given by the model were in relatively close agreement with experimental
measurements. The methodology over predicts shrinkage for across parting
plane dimensions located near the gate.
The method presented as part of this research work represents a starting
point towards developing accurate models for the study of dimensions in die
castings. Additionally, residual stress predictions can be obtained from the
results, providing a useful piece of information for casting design. The use of this
procedure may position casting designers and die builders in a better situation by
providing them with useful data available at their computer desks before any
casting is produced or any die is machined.
6.2 Research contributions
A computer model methodology to predict final casting dimensions and
residual stresses for the die casting process has been developed. The
232
procedure presented is able to account for the elastic deflections experienced by
the die. The die and machine components are part of the model and the main
process loads causing the elastic deflections of the die are modeled. The
method relies on using a shell mesh tied to the die cavity that tracks its distortion
during the application the clamping, temperature and intensification pressure
loads. Furthermore, accurate representation of the casting material was done by
using temperature and strain rate dependent mechanical properties determined
as part of this research work.
The computer model predictions were evaluated with experimental
measurements taken on production castings. Casting distortion characterized by
a set of in-cavity and across parting plane dimensions was determined for a
series of cases simulating different process conditions. The computer model
results were able to predict dimensions with close agreement, showing the
largest differences for the across parting plane dimensions near the gate.
6.3 Conclusions
6.3.1 Finite element modeling
The finite element methodology presented in this research work was the
end result of a series of modeling efforts done to develop a reliable method to
predict the distortion and residual stresses on a die casting. During the course of
this development a series of modeling difficulties were experienced, mainly
dealing with tracking the distortion of the die cavity. This section describes the
233
conclusions drawn from the challenges faced and the lessons learned while
overcoming such obstacles.
Tracking the distortion in the cavity was initially attempted by modeling the
interaction of fluid and solid elements in ADINA. The FSI model provided an
adequate way of describing the distorted die cavity shape, since the fluid casting
followed the cavity at all times. Moreover, the intensification pressure could be
modeled as load coming from the fluid casting, as supposed to be modeled as a
load acting onto the die. However, since liquid elements cannot turn into solids
modeling casting distortion required a coupled thermal-mechanical analysis,
which used the FSI predictions as initial conditions. Differences in displacement
predictions between the FSI and the thermal-mechanical model caused contact
divergence that were not resolved, eventually leading to abandoning this
modeling procedure.
Tracking of the distorted die cavity was successfully done by using a shell
mesh tied to the die cavity. The shell mesh was formed using the surface
elements of the three dimensional casting mesh, both meshes sharing the same
surface nodes. The shell was tied to the cavity and the die distortion was
modeled by applying the clamping, temperature and intensification pressure
loads in a static analysis. The displacement predictions given by the shell were
mapped onto the casting mesh, obtaining this way a description of the distorted
die cavity but now on a three dimensional mesh. The assumption behind this
methodology was that the distortions in the die are small enough that they can be
mapped only to the surface of the casting without affecting its interior structure.
234
Semi-rigid body motions were observed to cause contact divergence
during this modeling work. In Abaqus/Standard, divergence can be experienced
during the contact iterations if rigid body motions are experienced between
surfaces that are expected to come into contact. Modeling the effects of
clamping force produced semi-rigid body motion due to tie bar stretching and
difficulties were experienced when contact was being established between the
casting and die cavity surfaces at the onset of cooling. To overcome this
modeling issue, the tie bars were excluded from the model and the clamping
force effects were modeled by applying a pressure load on both platens. The
total force of equal magnitude on both sides suppressed any semi-rigid body
motion and allowed the contact between the casting and the die to be
established without any divergence issues. It is worth mentioning that this
modeling limitation might be overcome if Abaqus/Explicit is used to solve this
model since the contact formulations can readily accommodate rigid body
motions between contacting surfaces during the course of the analysis.
The use of reduced integration finite elements was required to represent
the casting in the computer models. Reduced integration elements were
employed because volumetric locking was observed when fully integrated
elements were used. Volumetric locking on fully integrated finite elements
results because modeling the incompressible material response characteristic of
plasticity adds kinematic constraints to an element, which for this case requires
the volume at the element’s integration point to remain constant. In some
circumstances, modeling this material response may over constrain the element,
235
causing an overly stiff behavior that locks it. Reduced integration elements use
fewer integration points that help satisfying the kinematic constraints more easily.
Modeling the hydrostatic pressure on the casting still remains as a
modeling opportunity for further research. The ability to have this degree of
freedom will allow modeling the pressurized solidification conditions in the
casting more adequately, since the hydrostatic state of stress represents the
initial conditions for the stress calculations. Having this modeling capability will
also provide a better representation of the interaction conditions between the
casting and the die, since the intensification pressure could be transferred from
the casting to the die removing de-coupling between them.
6.3.2 Determination of mechanical properties for casting material
The temperature and strain rate dependent mechanical properties for the
die casting alloy A380.0 were determined as part of this research work. This task
required the design of testing procedures, including the selection of testing
temperatures and strain rates, selection of machine, determination of machine
operational procedures, specimen selection, production and preparation. The
conclusions drawn from the different stages of this project are described in this
section.
An experimental design matrix was used to select the temperatures and
strain rates for conducting the tests. The temperatures were selected to span the
whole solidification range, while the selected strain rates were determined to be
characteristic of the cooling conditions in the die casting process. Temperatures
ranged from 25 ºC to 500 ºC, while the strain rates varied from 1x10-2 to 1x10-6 s-
236
1. Because the two design variables had different levels, an hexagonal design
was used for designing the matrix.
The selected specimen design used for the tensile tests corresponded to
the fatigue design recommended for die casting alloys. This design was selected
instead of the tensile test design because of space restrictions in the Gleeble
chamber. The production of the specimens was carried out by an industrial
partner using an existing tooling. Due to large porosity content found in the test
bars, 360 out of the 800 specimens produced were selected for the tests. It is
worth mentioning that the large porosity content found in the bars is the result of
the gating design in the insert.
The tensile tests were conducted in a Gleeble thermo-mechanical
simulator. This machine has been used extensively to determine the mechanical
properties for direct chill aluminum alloys and was selected for this project.
Preliminary tests were initially conducted using a Gleeble 3800. However,
limitations in the minimum displacement rates that can be achieved with this
model prevented from reaching the smallest strain rate magnitudes required in
this project. This displacement rate limitation resulted from the 200GPM
hydraulic valve installed in the machine model, allowing a minimum displacement
rate of 0.1mm/s. The tests were finally conducted in a Gleeble 1500, whose
60GPM hydraulic valve allowed achieving the smallest required strain rates.
Although the minimum strain rates were achieved, a 10-15GPM hydraulic valve
would have been recommended to guarantee accurate control of the machine
jaws.
237
Achieving the intended forces for the constant force tests posed some
difficulties during testing. Since the load cell installed in the Gleeble 1500 is
rated for 80KN, the applied forces for the tests fell within 1-4% of the load cell
output. The control system of the machine had difficulties interpreting the
readings appropriately due to excessive noise in the data. Although the tests
were carried out successfully, a smaller cell of about 10KN would have provided
a better feedback to the machine control system and allowed more accurate
controlled tests.
Among the twenty different runs carried out the tests performed at the
highest temperatures and smallest strain rates posed the biggest difficulties. The
smallest strain rates were difficult to achieve because they required small
displacement rates or small forces, which both were difficult to control for the
machine due to the reasons described above. At the highest temperatures,
another difficulty was faced due to surface oxidation of the test bars. This
oxidation repeatedly caused the thermocouple wires to detach from the surface
and the test had to be redone. A controlled testing environment using Argon had
to be employed to prevent surface oxidation and guarantee proper thermocouple
placement during the test.
From the results obtained, several conclusions can be drawn. At
temperatures below 100 ºC, the material did not exhibit strain rate dependency.
The flow stress was not observed to change under the tested strain rates. Strain
rate dependency was observed for temperatures above 145 ºC. Perfect plasticity
was obtained for temperatures above 220 ºC at strain rates ranging about 1x10-6
238
s-1. The yield strength of the material showed extremely high strain-rate
dependency for temperatures above 300 ºC, with magnitudes differing by as
much as 40MPa at a given temperature under different strain rates. An
interesting observation was noticed in which a higher flow stress was obtained at
486 ºC and a strain rate of 1x10-3 s-1 as compared with a case at 444 ºC and
1x10-6 s-1. This result shows the effect the strain rate can have on the flow
stress.
6.3.3 Design of Experiments
6.3.3.1 Experimental results
Several conclusions can be drawn from the statistical analysis done using
the results of the experimental measurements taken on production castings. The
ANOVA results showed that the pressure, dwell time and their interaction were
all statistically significant for both, in-cavity and across parting plane dimensions.
The obtained results strongly suggest that dimensional stability of castings is
tightly related to the interaction of these typical process control variables.
Generally speaking, the interaction plots for in-cavity dimensions did not
seem to suggest that longer dwell times lead to lesser distortion. On the
contrary, the plots showed the complex interplay of residual stresses and
temperature profiles at ejection and its impact in driving in-cavity dimensions.
The variability of the results across the three analyzed distances also showed
that different dimensions may respond differently to the process control variables.
This observation may argue that adjusting process control variables to bring one
239
dimension within tolerances may result in placing another dimension out of
tolerances. Therefore, care must be exercised when adjusting process variables.
The interaction plots for the across parting plane dimensions showed
more consistency than the in-cavity results across all distances. The pressure
plots at all levels followed similar trends and the obtained results suggested that
longer dwell times lead to greater shrinkage only when 340bars where used for
intensification pressure. On the other hand, when 170 or 680bars were used for
intensification pressure, the plots showed a minimum and a maximum at the 9s
dwell time, respectively. The experimental measurements showed that the
across parting plane dimensions were consistently larger near the gate. This
result may argue for the presence of pressure gradients within the casting and
may also suggest premature solidification in the casting before intensification
pressure takes effect.
6.3.3.2 Computer model results
To test the adequacy of the developed modeling methodology, computer
models simulating the same combination of process conditions as in the
experimental design were prepared. For all the simulated cases, the results
given by the computer models consistently over predicted the casting distortion
and the shrinkage across the parting plane.
The computer model predictions for in-cavity dimensions came in
relatively close agreement with the experimental results. The largest differences
were observed for only one distance, where the differences were as large as
0.5%. Nonetheless, it was observed that on average, the difference between the
240
computer model predictions and the experimental measurements for these in-
cavity distances was about 0.18%.
The predictions for the across parting plane dimensions showed a greater
discrepancy with the experimental results. The largest differences were
observed for the distance near the gate, where contrary to the experimental
measurements the computer model predicted smaller distances. The numerical
differences for this dimension were as large as 1.79%. However, the predictions
for the other two distances showed a closer agreement, averaging a difference of
0.12%.
As was mentioned, the differences between the computer model
predictions and the experimental measurements might be attributed to several
factors. For in-cavity dimensions, the consistent under prediction of the
dimensions might be explained by excessive casting warpage. Excessive
warpage in the casting might have been obtained due to the overly weak
behavior of the reduced integration elements used. These types of elements are
known to over-predict distortion under bending loads due to hourglassing, and a
minimum of four elements through the thickness must be used. For the casting
mesh only three elements through the thickness were used, which may have
potentially led to greater distortion.
For the across parting plane dimensions, clamping force modeling was
identified as one of the factors leading to smaller distances. Since clamping
force was modeled by applying equal pressure loads on the cover and ejector
platens, tie bar imbalance due to off center positioning of the die was not
241
accounted for. Moreover, this method is unable to accommodate any load
redistribution in the tie bars that may result when the intensification pressure is
applied. Thus, it is conjectured that modeling clamping force by using a constant
pressure load causes the machine to behave too stiff and may lead to smaller
across parting plane dimensions.
Additionally, the inability to model the intensification pressure adequately
may also lead to smaller across parting plane dimensions. It is conjectured that
the lack of pressurized solidification conditions in the casting allow it to freely
shrink away from the die, where in reality a tight contact exists due to the high
internal pressure present in the liquid metal. This situation may well explain the
largest differences between the computer model predictions and the
experimental results for the distance near the gate, where the intensification
pressure effects are larger.
6.3.4 Adequacy of different sets of modeling assumptions
As part of this research work, the adequacy of several sets of modeling
assumptions in predicting in-cavity and across parting plane dimensions was
evaluated. The results of this exercise provided valuable insights into the validity
of the existing modeling assumptions and exhibited their respective limitations.
For the in-cavity dimensions, the best predictions were obtained when the
casting was assumed to be ejected stress-free and with the same shape as the
distorted die cavity at the point of injection. Under these assumptions, using an
elastic or an elastic-plastic material model for the casting did not have any impact
in the final dimensions. The predictions of the modeling methodology developed
242
in this research work improved substantially when the residual stresses at
ejection were not accounted for. The worst predictions were obtained when the
casting material is assumed to be elastic throughout the analysis. Ignoring the
contributions of the elastic deflections of the die yielded the second worst
predictions
The across parting plane predictions followed different trends. Contrary to
the predictions for the in-cavity dimensions, the best across parting plane
predictions were observed when the casting material was assumed to be elastic.
Assuming the casting is ejected stress-free and with the same shape as the
distorted cavity predicted relatively good results as well. The predictions of the
proposed methodology developed in this research work did not improve when the
residual stresses at ejection were not accounted for.
6.3.5 Analysis of residual stress profiles
Because of the difficulty in measuring residual stresses in production
castings, the computer model results were used to analyze the evolution of
stresses at several locations within the casting. For different locations at the
parting plane, the stress profiles depicted a clear stress built-up while the casting
is in the die, followed by a stress relaxation at the point of ejection. The stress
built-up was explained by the restrainted shrinkage conditions in the die, while
the relaxation was explained by the ability of the casting to shrink freely after
ejection. The obtained plots showed that the stresses followed different trends
depending on the location and a built-up may be experienced at locations such
as a hot spot undergoing constrained shrinkage while cooling on air.
243
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252
APPENDIX B
TENSILE BARS MATERIAL CHEMICAL COMPOSITION AND DIE CASTING PROCESS CONTROL AND CYCLE PARAMETERS
256
Run order
Run Replication Temperature (ºC)
Strain rate (s-1)
Date Specimen #
1 12 1 39 1x10-5 5/10/07 410 2 8 1 81 1x10-2 5/10/07 29 3 6 1 221 1x10-2 5/10/07 677 4 2 1 486 1x10-3 5/10/07 686 5 2 2 486 1x10-3 5/10/07 326 6 3 1 444 1x10-2 5/10/07 435 7 2 3 486 1x10-3 5/10/07 468 8 4 1 381 1x10-2 5/10/07 480 9 10 1 25 1x10-4 5/25/07 99 10 18 1 444 1x10-6 5/10/07 829 11 18 2 444 1x10-6 5/11/07 88 12 15 1 221 1x10-6 5/11/07 541 13 16 1 304 1x10-6 5/26/07 835 14 2 4 486 1x10-3 5/26/07 795 15 1 1 500 1x10-4 5/26/07 239 16 4 2 381 1x10-2 5/26/07 346 17 16 2 304 1x10-6 5/26/07 24 18 16 3 304 1x10-6 5/26/07 574 19 19 1 486 1x10-6 5/26/07 90 20 13 1 81 1x10-6 5/29/07 257 21 8 2 81 1x10-2 5/29/07 399 22 12 2 39 1x10-5 5/29/07 717 23 5 1 304 1x10-2 5/29/07 84 24 14 1 144 1x10-6 5/30/07 366 25 7 1 144 1x10-2 5/30/07 403 26 11 1 25 1x10-4 5/30/07 106 27 16 4 304 1x10-6 5/30/07 135 28 10 2 25 1x10-4 5/30/07 641 29 19 2 486 1x10-5 5/30/07 240 30 9 1 39 1x10-3 5/31/07 747 31 1 2 500 1x10-4 5/31/07 286 32 11 2 25 1x10-4 5/31/07 316 33 13 2 81 1x10-6 6/1/07 799 34 6 2 221 1x10-2 5/31/07 96 35 17 1 381 1x10-6 5/31/07 405 36 5 2 304 1x10-2 5/31/07 177 37 12 3 39 1x10-5 5/31/07 264 38 12 4 39 1x10-5 5/31/07 381 39 20 1 263 1x10-4 5/31/07 56 40 1 3 500 1x10-4 5/31/07 712 41 2 5 486 1x10-3 5/31/07 791 42 17 2 381 1x10-6 6/2/07 628 43 1 4 500 1x10-4 5/31/07 485 44 18 3 444 1x10-6 6/1/07 127 45 17 3 381 1x10-6 6/3/07 646 46 4 3 381 1x10-2 6/1/07 37 47 17 4 381 1x10-6 6/5/07 285
Table C.1 Data collection for tensile tests
257
Table C.1 continued
48 3 2 444 1x10-2 6/1/07 651 49 10 3 25 1x10-4 6/1/07 472 50 1 5 500 1x10-4 6/1/07 154 51 14 2 144 1x10-6 6/4/07 31 52 20 2 263 1x10-4 6/5/07 335 53 7 2 144 1x10-2 6/5/07 381 54 18 4 444 1x10-6 6/5/07 689 55 7 3 144 1x10-2 6/5/07 206 56 5 3 304 1x10-2 6/5/07 33 57 14 3 144 1x10-6 6/6/07 383 58 19 3 486 1x10-5 6/5/07 741 59 4 4 381 1x10-2 6/5/07 521 60 19 4 486 1x10-5 6/5/07 191 61 9 2 39 1x10-3 6/5/07 256 62 6 3 221 1x10-2 6/5/07 513 63 13 3 81 1x10-6 6/6/07 656 64 11 3 25 1x10-4 6/5/07 267 65 19 5 486 1x10-5 6/5/07 59 66 3 3 444 1x10-2 6/5/07 408 67 9 3 39 1x10-3 6/5/07 364 68 8 3 81 1x10-2 6/5/07 698 69 20 3 263 1x10-4 6/5/07 2 70 17 5 381 1x10-6 6/7/07 483 71 20 4 263 1x10-4 6/5/07 247 72 4 5 381 1x10-2 6/7/07 761 73 5 4 304 1x10-2 6/7/07 58 74 11 4 25 1x10-4 6/7/07 620 75 10 4 25 1x10-4 6/7/07 30 76 11 5 25 1x10-4 6/7/07 535 77 6 4 221 1x10-2 6/7/07 130 78 10 5 25 1x10-4 6/7/07 786 79 6 5 221 1x10-2 6/7/07 694 80 14 4 144 1x10-6 6/7/07 831 81 18 5 444 1x10-6 6/7/07 710 82 12 5 39 1x10-5 6/9/07 280 83 15 2 221 1x10-6 6/7/07 258 84 15 3 221 1x10-6 6/8/07 503 85 9 4 39 1x10-3 6/8/07 753 86 7 4 144 1x10-2 6/8/07 464 87 14 5 144 1x10-6 6/9/07 484 88 15 4 221 1x10-6 6/10/07 697 89 8 4 81 1x10-2 6/8/07 283 90 3 4 444 1x10-2 6/8/07 740 91 20 5 263 1x10-4 6/9/07 349 92 13 4 81 1x10-6 6/11/07 255 93 9 5 39 1x10-3 6/8/07 265 94 13 5 81 1x10-6 6/11/07 104 95 5 5 304 1x10-2 6/8/07 23 96 8 5 81 1x10-2 6/8/07 757
258
Table C.1 continued
97 16 5 304 1x10-6 6/11/07 416 98 13 5 444 1x10-2 6/8/07 642 99 15 5 221 1x10-6 6/10/07 107 100 7 5 144 1x10-2 6/8/07 450