Copyright by Dongwoo Kim 2012 · PDF filePrediction of Microstructure Evolution of...

Copyright

by

Dongwoo Kim

2012

The Dissertation Committee for Dongwoo Kimcertifies that this is the approved version of the following dissertation:

Prediction of Microstructure Evolution of

Heat-Affected Zone in Gas Metal Arc Welding of Steels

Committee:

Eric M. Taleff, Supervisor

Joseph J. Beaman, Supervisor

David L. Bourell

Aloysius K. Mok

Desiderio Kovar



by

Dongwoo Kim, B.S.; M.S.

DISSERTATION

Presented to the Faculty of the Graduate School of

The University of Texas at Austin

in Partial Fulfillment

of the Requirements

for the Degree of

DOCTOR OF PHILOSOPHY

THE UNIVERSITY OF TEXAS AT AUSTIN

August 2012

Dedicated to my family for their constant love and encouragement.

Acknowledgments

I am sincerely grateful for the support and advice provided by my

supervisors, Dr. Joseph J. Beaman and Dr. Eric M. Taleff. Dr. Beaman

has given me his patience, support, and enduring confidence throughout my

work at Austin. Dr. Taleff has provided his immense breadth and depth of

Materials Science & Engineering, which has been strongly influential in my

research and education.

I would like to thank Dr. David L. Bourell, Dr. Aloysius K. Mok,

and Dr. Desiderio Kovar for guiding my work as members of my dissertation

committee.

I would like to acknowledge my colleagues for their help and contribu-

tions to this research as well as their friendship. From the Beaman Group I

would like to thank Vikram Devaraj, Felipe Lopez, Cameron Booth, and Zheng

Li. From the Taleff Group I would like to thank Dr. Trevor Watt, Alexander

Carpenter, Jakub Jodlowski, and Aravindha Antoniswamy. I would also like

to thank Dr. Sanjiv Shah for the help he gave regarding welding experimental

procedures.

Finally, I acknowledge the love and support of my wife, Guckju, and

my sons, Yeojun and Yeosan. I could never have achieved this work without

the encouragement of my family.

v



Publication No.

Dongwoo Kim, Ph.D.

The University of Texas at Austin, 2012

Supervisors: Eric M. TaleffJoseph J. Beaman

The heat-affected zone (HAZ) is the most common region of weld

failures. The weld failures are directly related to the microstructure.

Microstructure control of the HAZ is crucial to weld quality and prevention of

weld failures. However, publications on modeling the development of the HAZ

are relatively limited. Moreover, no efforts have been made to predict the HAZ

microstructures in real-time. The primary goal of this research is to present a

methodology to enable real-time predictions of microstructure evolution in the

HAZ and its mechanical properties. This goal was achieved by an approach

based on materials science principles and real-time sensing techniques. In this

study, the entire welding process was divided into a series of sub-processes.

Real-time multiple measurements from multiple sensors were incorporated

into the sub-processes. This resulted in an integrated welding system upon

which the predictions for the final HAZ microstructure are based. As part

vi

of the integrated system, the microstructural model was used to predict the

TTT curves, volume fractions of the decomposition products, and hardness

numbers of the heat-affected zones of steel alloys. Actual welds were performed

under two different sets of conditions, and the resulting experimental data

were compared with predictions made using the microstructural model. The

predicted and experimental microstructure and hardness are found to be in

good agreement, indicating that the microstructural model can be used in

real applications. This research can act as an important component of future

research to enable physics-based flexible control of welding.

vii

Table of Contents

Acknowledgments v

Abstract vi

List of Tables xi

List of Figures xii

Chapter 1. Introduction 1

1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . 4

1.3 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

1.4 Dissertation Outline . . . . . . . . . . . . . . . . . . . . . . . . 17

Chapter 2. Experimental Setup 20

2.1 Travel Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.2 Welding Power Supply and Welding Gun . . . . . . . . . . . . 20

2.3 Experimental Conditions . . . . . . . . . . . . . . . . . . . . . 22

2.4 Data Acquisition System . . . . . . . . . . . . . . . . . . . . . 25

2.4.1 Infrared (IR) Sensing . . . . . . . . . . . . . . . . . . . 25

2.4.2 Measurements of Current, Voltage, and Temperature . . 26

Chapter 3. Three-dimensional Heat Transfer during GMAW 28

3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2 Welding Heat Source . . . . . . . . . . . . . . . . . . . . . . . 29

3.2.1 Real-time IR Sensing of Thermal Distribution and BeadWidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.2.2 Measurement of Power Input . . . . . . . . . . . . . . . 37

3.2.3 Gaussian Surface Flux Distribution . . . . . . . . . . . . 39

viii

3.3 Heat Transfer in the Base Metal . . . . . . . . . . . . . . . . . 41

3.3.1 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . 41

3.3.2 Heat Equation . . . . . . . . . . . . . . . . . . . . . . . 42

3.3.3 Boundary Conditions . . . . . . . . . . . . . . . . . . . 44

3.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

Chapter 4. Microstructural Model 57

4.1 Kinetic Equations for Phase Transformation . . . . . . . . . . 57

4.2 Base Material Dependent Properties . . . . . . . . . . . . . . . 60

4.2.1 Solidus and Liquidus Lines . . . . . . . . . . . . . . . . 60

4.2.2 Precipitate Dissolution Temperature . . . . . . . . . . . 60

4.2.3 Transformation Temperatures . . . . . . . . . . . . . . . 62

4.3 Austenite Formation . . . . . . . . . . . . . . . . . . . . . . . 65

4.3.1 Initialization of Ferrite and Pearlite . . . . . . . . . . . 65

4.3.2 Ferrite and Austenite Formation . . . . . . . . . . . . . 66

4.4 Grain Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.5 Carbon Segregation . . . . . . . . . . . . . . . . . . . . . . . . 69

4.6 Austenite Decomposition . . . . . . . . . . . . . . . . . . . . . 71

4.7 Hardness Calculation of the HAZ . . . . . . . . . . . . . . . . 77

Chapter 5. Comparison of Predicted and Experimental Results 80

5.1 Evaluation of the Microstructure Model with ExperimentalTTT Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . 81

5.1.1 Prediction of TTT Diagrams . . . . . . . . . . . . . . . 81

5.1.2 Comparison of Predicted and Experimental TTT Diagrams 83

5.1.3 Root Mean Square Error (RMSE) Analysis . . . . . . . 90

5.2 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . 98

5.2.1 Weld Characteristics . . . . . . . . . . . . . . . . . . . . 98

5.2.2 Hardness Measurements of the HAZ . . . . . . . . . . . 102

5.2.3 Microstructures of the HAZ . . . . . . . . . . . . . . . . 110

5.3 Experimental Validation of Model Predictions . . . . . . . . . 118

5.3.1 Prediction of Transient Microstructure and Hardness . . 118

ix

5.3.2 Comparison of Predicted and Experimental Hardness . . 128

5.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Chapter 6. Future Work 141

6.1 A Reduced Order Model for 3D Heat Transfer and Fluid Flow 141

6.2 The Kinetics of Austenite Decomposition . . . . . . . . . . . . 142

6.3 Physics-based Flexible Control . . . . . . . . . . . . . . . . . . 142

Bibliography 145

Vita 153

x

List of Tables

2.1 Heat Treatments of Steels Studied (wt%) . . . . . . . . . . . . 23

2.2 Nominal Chemical Compositions of Steels Studied (wt%) . . 23

2.3 Experimental Welding Conditions . . . . . . . . . . . . . . . . 24

2.4 Main Specifications of the IR Camera . . . . . . . . . . . . . . 26

3.1 Data Used for the Calculation of Temperature Fields . . . . . 45

3.2 Comparison between Predicted Values of the Penetration Depthand Bead Width with Those Obtained from Experiments . . . 49

4.1 Solubility Products for Carbides in Austenite . . . . . . . . . . 62

5.1 Adjustment Factors . . . . . . . . . . . . . . . . . . . . . . . . 92

5.2 Hardness Measurements of AISI 1018 Steel (condition A) . . . 107



xi

List of Figures

1.1 A schematic diagram of the various sub-zones of the HAZindicated on the Fe-Fe3C equilibrium diagram (Source: KennethEasterling, Introduction to the Physical Metallurgy of Welding,2nd edition, 1992). . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2 CCT diagram for AISI 4130 steel containing 0.30% C, 0.64%Mn, 1.0% Cr, and 0.24% Mo (Source: Basic Principles andDesign Guidelines for Heat Treating of Steel, Metals HandbookDesk Edition). . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.3 Schematic diagram of GMAW. . . . . . . . . . . . . . . . . . . 12

1.4 Chain of sub-processes. . . . . . . . . . . . . . . . . . . . . . . 14

2.1 Welding test station: A, Workpiece; B, Welding gun; C, Steppermotor; D, IR camera. . . . . . . . . . . . . . . . . . . . . . . . 21

2.2 Relationship between wire feed rate and resistor voltage. . . . 22

3.1 3D IR signal distribution on the surface of the base metal. . . 33

3.2 Front panel of the LabVIEW virtual instrument. . . . . . . . . 34

3.3 Linescans for different times and locations. . . . . . . . . . . . 35

3.4 IR Images at different times. . . . . . . . . . . . . . . . . . . . 36

3.5 Measurements of voltage, current, and power. . . . . . . . . . 38

3.6 Gaussian circular heat flux. . . . . . . . . . . . . . . . . . . . 40

3.7 Schematic of Cartesian coordinate system. . . . . . . . . . . . 43

3.8 Three-dimensional surface temperature distribution in the Kelvinscale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.9 Surface temperature distribution shown as isotherms in theKelvin scale. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.10 Comparison between measured and calculated linescans: x =3.0 mm from the arc center (y = 161 pixel). . . . . . . . . . . 52

3.11 Comparison between measured and calculated linescans: x =3.3 mm from the arc center (y = 162 pixel). . . . . . . . . . . 53

3.12 Calculated weld pool shape. . . . . . . . . . . . . . . . . . . . 54

xii

3.13 Comparison between calculated and experimental weld poolcross-sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.14 Time-temperature histories at 10 locations in the HAZ. . . . . 55

4.1 (a) The Fe-C phase diagram identifying critical temperatures.(b) Temperature history identifying regions that are consideredin the microstructural model. . . . . . . . . . . . . . . . . . . 63

4.2 Temperature history showing transformation regions . . . . . . 76

5.1 TTT diagram for AISI 3140 steel. [From H. Boyer (editor),Atlas of Isothermal Transition and Cooling TransformationDiagrams, American Society for Metals, 1977, p. 99.] . . . . . 85

5.2 Comparison between predicted and experimental TTT diagramfor AISI 3140 steel before modification. . . . . . . . . . . . . . 86




5.6 Logarithm of the RMSE vs. adjustment factor for AISI 3140steel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5.7 Comparison between predicted and experimental TTT diagramfor AISI 3140 steel after modification. . . . . . . . . . . . . . . 94




5.11 Welded specimen. . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.12 Transverse sections (condition A). . . . . . . . . . . . . . . . . 100

5.13 Transverse sections (condition B). . . . . . . . . . . . . . . . . 101

5.14 Vickers indenters on transverse section of 1018 steel (magnifi-cation 50×, condition A). . . . . . . . . . . . . . . . . . . . . 104


xiii


5.17 HAZ microstructure of 1018 steel (magnification 500×, condi-tion A, 45◦ direction). Continued. . . . . . . . . . . . . . . . . 112



5.20 Microstructure evolution for 1018 steel at location 1 (condition A).119









5.29 HAZ hardness distribution for 1018 steel (condition A, 45◦ di-rection). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130






5.35 HAZ hardness and peak temperature as a function of distancefrom fusion zone for 1018 steel (condition A, 45◦ direction). . . 136



xiv

Chapter 1

Introduction

1.1 Overview

Welding is an important and basic joining process. Within the entire

metal fabrication industry, arc welding is the third largest job category, behind

assembly and machining [1]. The gas metal arc welding (GMAW) process is a

relatively complex process, but is widely used in industry because of the speed

at which joints can be made and the reliability of these joints in service. The

chemical, oil, aerospace, shipbuilding construction and other industries rely

heavily on reliable welds. Because welding operations appear relatively simple

to perform, it is easy to forget the complexity of the chemical and metallurgical

reactions that take place when the weld is deposited. Microstructure control

is crucial to weld quality and prevention of weld failures. The development of

techniques to more effectively control microstructure created during welding

will have a significant positive impact on product cost and quality.

Many fabricated components and structures are welded. Invariably, the

weld joint is the most critical region from a performance perspective. Fatigue

cracking is by far the most common failure mechanism in welded joints, and

unstable fracture is perhaps the most dramatic, occurring without warning and

1

often leading to catastrophic consequences [2]. The heat-affected zone (HAZ)

is the region of base metal which has its microstructure and properties altered

by welding. The HAZ has complex metallurgical reactions that can degrade

the HAZ mechanical properties. Despite their small size, brittle regions within

the HAZ can have a strong influence on failure by brittle fracture. The HAZ is

the most common region of weld failures directly related to the microstructure.

The main objective of this research is to provide a physics-based capability to

predict the final weld microstructure and properties of the HAZ produced

during welding, a capability intended to enable future physics-based control

technologies for welding.

Considerable effort documented in the literature has been put into

numerical modeling of the welding process. The main focus of prior inves-

tigation was on heat transfer and fluid flow in the weld pool. Comprehensive

modeling and simulation of fundamental transport phenomena may provide a

detailed understanding of the weld pool geometry [3–6]. But, it is difficult to

predict HAZ microstructures accurately because of the complexity of the local

time-temperature histories and the general nonlinearity of the kinetics of the

metallurgical reactions. Publications on modeling the development of the HAZ

are relatively limited. Moreover, no efforts have been made to predict the HAZ

microstructures in real-time. This work proposes a methodology for predicting

the microstructure evolution of the HAZ and its mechanical properties in real-

time to achieve a major improvement in the quality of welded products. This

objective is achieved by an approach based on materials science principles and

2

real-time sensing techniques.

Real-time sensing is required for predicting microstructure evolution in

GMAW. Infrared (IR) sensing is adapted in this research because GMAW is

essentially a thermal process. IR sensing measures the thermal profile on the

surface of a workpiece. This thermal profile provides fundamental information

to any model of heat transfer and microstructure evolution. A microstructural

model describes metallurgical reactions that determine how the microstructure

develops during welding, including austenite grain size and transformation

products in the HAZ. The mechanical properties of metals are sensitive to

their microstructure. By controlling the microstructure, one can have the

properties to provide the best service. As a measure of mechanical properties,

the hardness of the HAZ is a very good indicator of its susceptibility to

cracks and other problems. The local phase fraction of various microstructure

components is utilized to calculate the hardness.

This research can act as an important component of future research to

enable physics-based flexible control of welding. Enabling of that technology

will ultimately require development of a physics-based control algorithm

that can accommodate a variety of changes in welding conditions, such as

substitution of materials, varying process speeds, varying product geometries,

etc., without extensive new testing [7]. This research will play a role in realizing

this type of control, in particular seeking microscale defect-free products.

3

1.2 Research Objectives

The main objectives of this research are as follows.

1. Implement sensing techniques that provide data from which three-

dimensional (3D) thermal information can be extracted in real-time.

2. Provide prediction of microstructure evolution in the HAZ.

1.3 Methodology

The energy of fusion welding causes a thermal cycle that drives

microstructural changes in the HAZ. The HAZ can be divided into a number

of sub-zones. Figure 1.1 shows the various sub-zones that can form in the HAZ

of a carbon steel containing 0.15 wt% C. Each sub-zone refers to a different

type of microstructure and, more important, each structural type is likely to

possess different mechanical properties. The HAZ ranges from the solid-liquid

transition zone on its inner edge to the unaffected base metal on its outer edge.

In order to obtain a reasonable understanding of the HAZ, it is necessary to

consider how the microstructure of the base metal reacts to a complete thermal

cycle. During heating, the microstructure in the HAZ can be partially or fully

austenitized as temperature goes above the lower critical temperature (A1) or

the upper critical temperature (A3), respectively. On cooling, the austenite

decomposes to its daughter products. Ferrite, pearlite, and bainite are formed

by nucleation and growth, while martensite is formed by a diffusionless shear

transformation.

4

solidified weld

grain growth zone

recrystallized zone

partially transformed zone

tempered zone

Liquid

Liquid + γ

γ

α + Fe3C

γ + Fe3C

solid-liquid transition zone

unaffected base

material

heat affected zone

Tem

p, ºC

Pea

k T

em

pera

ture

, T

p

Fe Wt % C

A3

A1

Figure 1.1: A schematic diagram of the various sub-zones of the HAZindicated on the Fe-Fe3C equilibrium diagram (Source: Kenneth Easterling,Introduction to the Physical Metallurgy of Welding, 2nd edition, 1992).

In this study, steel is mainly considered because of its technical

importance and complex behavior due to phase transformations. However,

the principles established for the HAZ microstructural changes in steels

may readily be applied to other materials. Because the microstructure

and mechanical properties of the sub-zones vary based on the chemical

composition of steels, three different types of steel are investigated: AISI

1018, AISI 4130, and AISI 4140 steels. AISI 1018 is often used for structural

and automotive applications. AISI 1018 is a low-carbon steel that has

5

the best weldability among these three steels. It may be relatively easy

to predict the HAZ microstructure of this steel. AISI 4130 and AISI

4140 are chromium-molybdenum steel because of their alloying elements.

Chromium and molybdenum provide steels with good fatigue, abrasion, and

impact resistance. However, these alloying elements result in more complex

phase transformations during welding. AISI 4130 is very similar to 4140,

but has lower carbon content, providing it with better weldability and

formability. AISI 4140 has the poorest weldability and the most difficulties

when predicting the HAZ microstructure because of its highest carbon-

equivalent (Cequiv). These different types of steel are tested under two different

sets of experimental conditions. The HAZ microstructure and hardness are

investigated at several locations from the fusion zone to the unaffected base

metal. The resulting experimental data are compared with predictions made

from the microstructural model. The prediction scope and limitations of the

microstructural model are studied. The weldability is assessed in terms of

the HAZ microstructure and the weld characteristics such as the penetration

depth and bead width.

It is useful to briefly consider formation of the various microstructures

of three main sub-zones in the HAZ.

• Grain growth zone

This zone is subjected to a peak temperature just above precipitate dis-

solution temperature, thus allowing austenite grains to grow. Austenite

6

grains are assumed to be pinned by carbide/nitride precipitates until

their dissolution. Austenite grain growth begins after the dissolution of

precipitates. Grain growth continues until the A3 temperature is reached

during cooling. At this time, austenite starts decomposing into ferrite

initially, but may form pearlite or bainite upon further cooling below

the A1 temperature. Finally, if austenite is still present upon reaching

the martensite start temperature, that austenite may transform into

martensite. These proportions of products can vary widely depending

on the cooling rate, austenite grain size, alloy content, and other factors.

In particular, high cooling rate encourages formation of martensite in

high carbon-equivalent steels.

• Recrystallized zone

This zone corresponds to a peak temperature between the A3 and

precipitate dissolution temperatures, assumed to be above the A3, thus

allowing austenite grains to form but not grow significantly. As peak

temperature goes above the A3, the remaining ferrite matrix transforms

to austenite. Carbide/nitride precipitates may not be fully dissolved at

this temperature. This does not allow the newly formed austenite grains

to grow significantly. Therefore, the austenite decomposition on cooling

tends to produce a fine grained ferrite–pearlite structure, depending on

welding energy input, plate thickness, and other factors. Nonequilibrium

products that require fast cooling rates, such as bainite and martensite,

are less like to form in this region than in the grain growth region.

7

• Partially transformed zone

This zone corresponds to a peak temperature between the A1 to A3

temperatues. Pearlite colonies transform to austenite and may begin

consuming ferrite upon heating to above the A1. The austenite decom-

poses into fine grains of pearlite and ferrite during cooling. The prior

ferrite microstructure may be essentially unaffected. Nonequilibrium

products that require fast cooling rates are least likely to form in this

region.

There are two main types of transformation diagram that represent

transformation kinetics for steels: time-temperature transformation (TTT)

and continuous cooling transformation (CCT) diagrams. Figure 1.2 shows

the TTT and CCT diagrams of AISI 4130 steel, along with lines of different

rates of cooling. Dashed lines represent the TTT diagram that measures

the transformation rate at a constant temperature, while solid lines represent

the CCT diagram that measures the extent of transformation as a function

of time for a continuous decreasing temperature. As shown in Figure 1.2,

the CCT diagram can be slightly shifted to lower temperatures and longer

times compared to the TTT diagram. For engineering applications, the CCT

diagram is more useful than the TTT diagram. However, the number and

accuracy of the CCT diagrams currently available are limited compared to

the TTT diagrams because the construction of a single CCT diagram is very

time consuming. Therefore, in this study, a series of experimental TTT

8

Time, s

Te

mp

era

ture

, ºC

A B C

Figure 1.2: CCT diagram for AISI 4130 steel containing 0.30% C, 0.64% Mn,1.0% Cr, and 0.24% Mo (Source: Basic Principles and Design Guidelines forHeat Treating of Steel, Metals Handbook Desk Edition).

diagrams are used for comparison with predicted TTT diagrams to evaluate

the prediction capability of the microstructure model.

Cooling rate affects the decomposition products of austenite. Figure 1.2

describes the relation between the cooling rate and the resulting transforma-

tion products. The highest cooling rate, shown by curve A, leads to formation

of bainite and martensite. As the cooling rate reduces, shown by curve B,

other transformation products are formed; these include ferrite, bainite and

martensite. The slowest cooling rate, shown by curve C, produces ferrite

and pearlite. Bainite and martensite are hard and brittle. A coarse-grained

prior austenite structure with hard and brittle decomposition products reduces

fracture toughness and fatigue resistance. This research addresses methods

9

for preventing microstructures prone to fatigue and fracture in the HAZ by

identifying and controlling the microstructures produced.

Three basic approaches to predict HAZ properties have been proposed

in the literature [8–15]. One group of researchers attempted to predict the

hardness distribution through the HAZ without directly taking into account

the phases present in the microstructure [8, 9]. This method is based on

the hypothesis that the unknown hardness at some point in the HAZ can

be predicted by matching that point with either a cooling rate at some

temperature, or cooling time between two temperatures, on a sample piece

of the same steel previously tested under known conditions. There is no direct

calculation of metallurgical reaction rates in this approach, and the effects of

prior austenite grain size and peak temperature achieved are not considered.

Another approach to HAZ microstructure prediction was proposed by

Ashby and Easterling et al. [10, 11]. The prior austenite grain size and final

amount of martensite can be predicted from a plot of cooling time (time to cool

from 800 to 500 ◦C) and peak temperature. Transformation rates for ferrite,

pearlite, bainite and martensite are then calculated by using cooling rates

predicted by a modified version of Rosenthal’s analytical equation [16]. The

austenite grain growth calculation is based on a simplified kinetic equation.

In their analysis, they also proposed a relation for precipitate dissolution

temperature that takes into account the retarding effect of nitrides and

nonferrous carbides on grain growth. A drawback of this approach is the

weakness of the Rosenthal equation, which has a known error resulting from

10

the point heat source assumption used to derive the analytical solution. The

calculation procedure used to estimate the austenite decomposition products

is also quite approximate.

A third set of workers modified Kirkaldy’s hardenability algorithm [12]

to predict the microstructure of the HAZ [13–15]. This approach accounts for

the effect of austenite grain growth on the HAZ microstructure. The algorithm

was coupled with a three dimensional (3D) finite element heat transfer program

developed by Goldak et al. [17] to predict the transient microstructure of the

HAZ. This coupled program provided a powerful tool for welding process

selection. However, the general application of this model for a real-time

control system is limited because it uses not only a well-known heat input

but also a thermal history calculated off-line. It is the purpose of this research

to demonstrate that this basic algorithm, when combined with real-time IR

sensing data, can provide a real-time prediction of the HAZ microstructures

and is, thus, a promising tool for a much stronger physics-based real-time

control system.

Modeling of the GMAW process requires synthesis of knowledge from

various disciplines [18]. It is inherently a multi-physics problem. Previous weld

process modeling focused on individual physical processes. These include a

dynamic model for current and arc length [19], a real-time model of electrode

extension [20–22], heat source models [17, 23, 24], models for heat transfer

and fluid flow in the weld pool [3–6], and models for solidification and phase

transformations [12, 13]. The primary limitation of these methods is that

11

Sub-process 1

Contact tip to workpiece (CT)

Ls

Rs

Contact tube

ElectrodeWire feed rate (S)

Current (I)

Weld speed (R)

Open-circuit

Voltage ( )Voc

Workpece

Weld pool

+

−

Arc

Electrodeextension ( )ls

Sub-process 2

Sub-process 3

Sub-process 1

Figure 1.3: Schematic diagram of GMAW.

the individual processes are considered in isolation, when they are in fact

interrelated. Consequently, the welding process and process variables are

rarely all well optimized. In this research, individual models are integrated,

and the HAZ microstructure is predicted based on the integrated welding

system.

Figure 1.3 shows a schematic diagram of the GMAW process, including

an electric power supply. As shown, the welding process may be considered

as several sub-processes in an electric circuit. Each sub-process has its own

inputs and outputs, which are intermediate variables for the whole. The

initial inputs, which are the inputs of sub-process 1, should be manipulated

to achieve the desired final outputs, which are the outputs of sub-process 3.

12

Although manipulation of the inputs is easy, the effects on the final outputs

take several steps to realize. Each sub-process should be monitored to integrate

the entire welding process as a complex and uncertain dynamic system. A

possible solution to produce the desired final outputs may be to monitor the

intermediate variables which are close to the output of each sub-process.

Figure 1.4 illustrates the chain of sub-processes, from the setting of the

welding power to the final qualitative assessment of the weld. Sub-process 1

represents the dynamics of the power supply and droplet transfer, in which

the heat and mass transferred from electrode tip to workpiece are determined.

Sub-process 1 has four inputs: open-circuit voltage, distance from contact tip

to workpiece, wire feed rate, and weld speed. These inputs are adjusted to

achieve the desired final outputs.

Sub-process 2 may be represented by a heat source model. This

model estimates a distribution of power density in space, and thus describes

a prescribed heat source on the surface of the workpiece. An electric arc

heat source has complex physical behaviors that are not yet completely

understood. The core idea of the power source model is to adequately

represent these complex physics with a simplified model, such as the normal

circular model [25] or the double ellipsoidal model [17]. This requires

approximations and calibration procedures, which have been typically done

off-line by trial and error. For example, geometrical parameters of the above

two models are estimated from the results of repeated weld experiments and

off-line simulations. In this research, real-time approximations are presented.

13

Open-circuit voltage

Contact tip to workpiece

Wire feed speed

Weld speed

Sub-process 1

Power supply model

Heat input to workpiece

Sub-process 2

Heat source model

3D heat source configuration

Sub-process 3

Heat transfer model

Microstructure model

Weld pool geometry

Microstructure

Mechanical property

Weldability assessment

Sensing

Thermal profile

Composition

Initial microstructure

Sensing

Current, voltage

Figure 1.4: Chain of sub-processes.

14

Commercial IR sensing equipment is used for real-time monitoring of the

thermal profile on the workpiece surface. IR sensing can provide a two-

dimensional (2D) image of the IR emission on the surface of the workpiece and

a line scan profile across the weld pool. The IR sensing data are analogous

to the heat source parameters, and this analogy is applied to estimate shape

and size of the heat source configuration. The outputs of sub-process 1 and

the phenomenological data acquired by IR sensing will be incorporated into

the heat source model and then used to determine a three-dimensional (3D)

distribution of specific heat flux in real-time. The 3D heat source model

provides the necessary inputs for sub-process 3 in real-time.

Sub-process 3 will be represented by two models. One is a macroscale

model at the process scale, and the other is a microscale model for prediction

of microstructure evolution in the HAZ. The macroscale model represents

heat transfer for the workpiece. Comprehensive modeling and simulation

of transport phenomena may provide detailed insight for the weld pool

geometry and the thermal history of the HAZ [3–6]. However, such expensive

calculations make it prohibitively difficult to seek a real-time control solution

by this method because of highly complex and nonlinear equations. In this

study, fundamentals of heat transfer in the workpiece are simulated off-

line. This simulation produces temperature-time histories throughout the

fusion and heat-affected zone, weld bead width, and depth of penetration.

The resulting temperature history in the HAZ is a necessary input to

the microstructure model. Simulation predictions of the bead width and

15

penetration are compared with experimental measurements.

The microstructure model for sub-process 3 describes metallurgical

reactions in the HAZ. Cycles of rapid heating and cooling induce solid

state transformations in the HAZ during welding. Mechanical properties of

welded steel depend on prior austenite grain size and transformation products

created in the HAZ. To predict the final weld microstructure and hardness

of the HAZ, the hardenability algorithms by Kirkaldy and co-workers are

utilized [12–14, 26]. Input data to this model include chemical composition

and initial microstructure of the base metal and the thermal history of the

HAZ. The outputs for a steel workpiece are the fraction of ferrite, pearlite,

austenite, bainite, martensite, and the prior austenite grain size. The

algorithm for metallurgical kinetics is divided into two distinct parts. The

first algorithm part deals with the calculations of various critical temperatures

and constants. These includes the lower and upper critical temperatures,

precipitate dissolution temperature, bainite start temperature, martensite

start temperature, and liquidus and solidus lines, which are functions of

carbon and alloy content of the base steel. The second algorithm part must

predict microstructures produced by arbitrary thermal histories. The reaction

kinetics required include austenitization, austenite grain growth, and austenite

decomposition during cooling. The microstructure model is validated by

comparing predicted time-temperature transformation (TTT) diagrams with

experimental TTT diagrams. Since most steels used in welded structures

are low-alloy hypoeutectoid steels, the microstructure model is applied to

16

these steels, which contain microstructures of ferrite and pearlite at room

temperature. The chemical composition of the base metal is important because

of its influence on the response of the base metal to the thermal cycle during

welding. In this research, the prediction capability of the microstructure model

is evaluated for three different grades of steel.

Accurate prediction of the mechanical properties of steels depends

first on the ability to predict microstructure from chemistry and processing

variables and, second, on the ability to relate microstructure to mechanical

properties. The hardness of the HAZ is related to tensile strength and indicates

any embrittlement. It has been observed that an upper limit on hardness is

necessary to avoid HAZ cracking. For low alloy steels, a hardness over 350 VPN

in the HAZ indicates susceptibility to cracking. Hardness in the HAZ can be

calculated from the predicted microstructure using the rule of mixtures. When

the volume fractions of ferrite, pearlite, austenite, bainite, and martensite are

known, the rule of mixtures was shown to accurately predict the hardness [10].

1.4 Dissertation Outline

This work comprises six chapters. Chapter 1 states the motivation

behind this work, the research objectives, and methodology. The methodology

used in this work describes the manner in which a series of sub-process models

are integrated and the manner in which the HAZ microstructure is predicted

based on the integrated model.

Chapter 2 describes the experimental setup. This setup consists of

17

a travel mechanism, a welding power supply and gun, and a data acquisition

system. These components are used for adjusting the welding process variables

and measuring the intermediate variables.

Chapter 3 presents the real-time extraction of a 3D heat source and

the consequent heat transfer in the base metal. The integrated physics-based

model is validated through experiments. The experimental and calculated

results are compared with regards to the surface temperatures, penetration

depth, and bead width.

Chapter 4 presents the theory of the microstructural model. All kinetic

equations and principles of microstructural modeling are discussed along with

key programming considerations.

Chapter 5 presents the major results of microstructural predictions.

The predicted TTT diagrams are compared with the experimental TTT

diagrams to evaluate the prediction capability of the microstructural model.

Actual welds are produced, and the microstructure of these welds is charac-

terized. Microscopy and Vickers hardness tests are used for characterizing

the microstructure across the HAZ of the welds. The hardness is measured

at various locations within the HAZ. The resulting experimental data are

compared with predictions made from the microstructural model. The

prediction scope and limitations of the microstructural model are discussed.

Chapter 6 presents a summary and suggestions for potential future

work. It presents an approach for developing a physics-based flexible control

18

system that integrates multiple physics-based models and monitors multiple

measurements of a welding process.

19

Chapter 2

Experimental Setup

2.1 Travel Mechanism

Figure 2.1 shows the welding test station, which provides easy adjust-

ment of welding process variables such as the travel speed and the contact tip-

to-workpiece distance. Backlund built the welding test station with guidelines

for future design evolution [27]. Relative motion between the workpiece and

the arc is achieved by keeping the torch stationary and moving the workpiece

at the desired travel speed. A stepper motor manufactured by Stober Drives

Inc. is used for achieving the desired travel speed and linearity in the travel

path. The motor is controlled using LabVIEW software with a NI PCI-7340

motion controller.

2.2 Welding Power Supply and Welding Gun

A Miller XMT 350 MPA power supply and a Miller Spoolmatic 15A

welding gun are used for the GMAW experiments. The Miller XMT 350

MPA is a constant-voltage welding machine that has automatic arc length

control, known as self-regulating. The electrode and the shielding gas are

simultaneously fed to the workpiece through the Miller Spoolmatic 15A

20

Figure 2.1: Welding test station: A, Workpiece; B, Welding gun; C, Steppermotor; D, IR camera.

welding gun. The shielding gas protects the welding area from atmospheric

gases such as nitrogen and oxygen, which may cause fusion defects, porosity,

and weld metal embrittlement.

A Miller WC-24 Weld Control is required to establish a connection

between the welding power supply and welding gun. Measuring the wire

feed rate required modification of the welding gun. To adjust the wire feed

rate, the welding gun controls the speed of its own built-in DC motor with a

potentiometer. The potentiometer regulates the motor input voltage, which

determines the motor speed, and thus, the wire feed rate. Figure 2.2 shows

the relationship between the voltage at both ends of a resistive element of the

potentiometer and the wire feed rate measured with a Millermatic 251 machine.

21

0 1 2 3 4 50

100

200

300

400

500

600

700

800

Voltage (V)

Wire

feed

rat

e (in

/min

)

y = −155.19x + 799.17

Real dataLinear fitting

Figure 2.2: Relationship between wire feed rate and resistor voltage.

To display the wire feed rate data, a virtual instrument using LabVIEW

software was made by using the linear relationship shown in Figure 2.2.

2.3 Experimental Conditions

In this work, single-pass bead-on-plate welds were made along the

center of each steel plate. Three different types of steel were used for evaluating

the prediction capability of the microstructural model. AISI 1018 is a plain

carbon steel with a good weldability. AISI 4130 and AISI 4140 are types

of chromium-molybdenum steel. Among these types of steel, AISI 4140 has

the poorest weldability and the greatest amount of carbon and other alloying

elements. Heat treatment and chemical composition of the test materials are

22

presented in Tables 2.1 and 2.2. The base metal had a thickness of 0.635 cm

(1/4 in) and a width of 5.08 (2 in) for each set of alloy specimens. A grinder and

a commercial solvent were used for preparing the surface of the metal before

welding. The surface of the metals was cleaned with a commercial solvent to

remove grease, oil, or dirt. The grinder removed surface oxides. Welding was

carried out under two experimental conditions, A and B. Table 2.3 lists the

experimental welding conditions used in this work.

Table 2.1: Heat Treatments of Steels Studied (wt%)

Treatment Hardness (HV)

AISI 1018 Cold drawn, quenched and tempered 192AISI 4130 Annealed at 865 ◦C 164AISI 4140 Oil quenched, fine grained, tempered at 650 ◦C 240

Table 2.2: Nominal Chemical Compositions of Steels Studied (wt%)

C Mn Si Cr Mo S P

AISI 1018 0.18 0.75 0.03 0.02AISI 4130 0.28 0.40 0.20 0.80 0.15 0.02 0.02AISI 4140 0.38 0.75 0.15 0.80 0.15 0.02 0.02

23

Table 2.3: Experimental Welding Conditions

Welding speed 25 in/minWire feed rate 350 in/min (condition A),

300 in/min (condition B)Contact tip-to-workpiece distance 0.55 inPower supply operating mode Constant voltageOpen-circuit voltage 24 VTorch angle 0 degreeShielding gas composition 75% Ar, 25% CO2

Shielding gas flow rate 25 CFHElectrode ER 70S-6 carbon steelElectrode diameter 0.030 in (condition A),

0.035 in (condition B)Weldment thickness 0.25 in

24

2.4 Data Acquisition System

2.4.1 Infrared (IR) Sensing

A FLIR A320G infrared camera measured and imaged the surface

temperature distribution of the base metal. The most important parameter to

set correctly is the emissivity, which is a measure of the amount of radiation

emitted from the base metal, relative to that from a perfect blackbody of

the same temperature. Generally metallic materials have emissivities that

depend on surface condition and temperature [28]. One way to determine the

emissivity experimentally is by comparing the IR temperature measurements

of the metal with simultaneous temperature measurements obtained using

a thermocouple. The difference in the temperature readings is due to the

emissivity, which is set on the IR camera before sensing. In this work, a

thermocouple is used for adjusting the emissivity.

The IR camera is attached to the welding test station as shown in

Figure 2.1. The distance and skewed angle between the base metal and

the front lens of the camera are 9.25 in and 33 ◦, respectively. Table 2.4

lists the main specifications of the IR camera. The IR camera is connected

to the computer through an Ethernet cable. LabVIEW virtual instruments

generate true temperature images from 16-bit raw images acquired from the IR

camera. The IR camera can generate 76,800 (320×240) accurate temperature

measurements in every image. A raw pixel image is measured and recorded at

a sampling interval of 0.05 s. A LabVIEW virtual instrument is also used to

analyze the temperatures of the imaged base metal.

25

Table 2.4: Main Specifications of the IR Camera

Detector type Uncooled microbolometerSpectral range 7.5∼13.0 µmResolution 320×240 pixelSampling frequency Up to 60 HzDigital data streaming Gigabit EthernetTemperature −20 ◦C to 120 ◦C

0 ◦C to 500 ◦C300 ◦C to 2000 ◦C

Accuracy ±2 ◦C or ±2 of reading

2.4.2 Measurements of Current, Voltage, and Temperature

A Model HHM72 current probe manufactured by Omega Engineering

Inc. is used for DC current sensing. Two different hook-shaped jaws of the

current probe are hooked onto the welding cable connected to the positive

weld output terminal of the welding machine. The display and recording

of the varying current during welding are achieved by using a LabVIEW

virtual instrument and National Instruments (NI) hardware. The output of

the current probe is connected to a NI SCC-FT01 module inside a NI SC-2345

connector block. The connector block carries the signals of the current probe

to the NI PCI-6229 data acquisition board that is installed in the workstation

computer.

The voltage between the positive and negative weld output terminals

represents the open-circuit voltage. The two terminals are connected to a NI

SCC-FT01 module inside a NI SC-2345 connector block. The connector block

26

carries the signals to the NI PCI-6229 data acquisition board. A LabVIEW

virtual instrument is used for displaying and recording the voltage during

welding.

A K-type thermocouple is used for measuring the temperature at a

point on the surface of the base metal. The thermocouple consists of two

different conductors that produce a voltage, proportional to a temperature

difference. These signals are connected to a NI SCC-TC02 module inside a NI

SC-2345 connector block. The connection block carries the signals to the NI

PCI-6229 data acquisition board. A LabVIEW virtual instrument is used for

displaying and recording the temperatures during welding.

27

Chapter 3

Three-dimensional Heat Transfer during

GMAW

3.1 Introduction

A good weld is identified by its weld pool geometry and microstructure.

Heat transfer modeling is used to predict the weld pool size and temperature

history. The temperature history is a necessary input for predicting the final

microstructure of the weld material. Many investigators have studied the

heat transfer and fluid flow during GMAW [3–6]. Their investigations have

provided detailed insight into the weld pool geometry and the thermal history

of the HAZ. However, these investigations assumed that the heat input is

well-known. In fact, a comprehensive approach to controlling the quality of

the weld requires real-time monitoring of the heat source by using sensors and

real-time control of the heat input to the workpiece by regulating the welding

variables such as the travel speed, wire feed rate, etc. Therefore, the use of

the well-known heat input in the heat transfer model limits the application of

the heat transfer model in real-time control of the welding process, even if the

model could be implemented in real-time.

Methods for the real-time monitoring of the welding heat source and

28

for the use of the monitoring results in the heat transfer model have not been

developed for many reasons, such as the complexity of the welding process

and lack of reliable sensors. In the present work, real-time measurements are

incorporated into the heat source model, which is then used to determine a

three-dimensional (3D) distribution of the specific heat flux in real-time. The

3D heat source model is in turn integrated into the heat transfer model. This

chapter explains how this integrated system can predict the weld pool size and

thermal history with a reliable degree of precision.

3.2 Welding Heat Source

Physics-based modeling of the welding heat source has not been well

studied because of the complex nature of energy transport from the contact tip

to the workpiece. In this research, the shape and power density distribution of

the heat source are determined on the basis of real-time IR sensing and power

measurements in a welding circuit.

3.2.1 Real-time IR Sensing of Thermal Distribution and BeadWidth

Many investigators have used IR sensing techniques for weld process

monitoring. IR sensing can provide the 2D temperature distribution on

the surface of the workpiece and a linescan profile across the weld [29–31].

Many studies have used these IR data to directly estimate important weld

characteristics such as the bead width, penetration depth, and cooling rate.

29

In this study, IR data is used to configure the heat source model. The output of

the heat source model provides the required input to the heat transfer model,

which calculates the weld characteristics.

The emissivity of a metallic material depends on the surface and

temperature of the material. The liquid-phase emissivity is higher than

the solid-phase emissivity [28]. The IR camera used in this study, FLIR

A320G, has a high accuracy with ±2 ◦C of reading, but the measurable

range of temperature is limited to 2000 ◦C. Moreover, the IR camera cannot

exactly sense the IR emission from the high temperature zone. It leads

to an underestimation of the IR signal emitted from the hot weld surface

and the molten weld pool. Thus, online estimation of the emissivity factor

for a specific pixel is difficult. It makes online temperature measurement

of the IR camera limited. A constant emissivity of 1 was assigned to all

pixels during welding. Despite the limitation of the IR camera, the IR

sensing provides an overall thermal picture of the workpiece being welded.

This determines the spatial distribution of thermal energy emitted from the

surface of the workpiece. Emissivity correction was achieved by using two

distinctively different temperatures: the solidus temperature at the bead

boundary and the temperature measured by a thermocouple during welding.

The thermocouple measures the temperature at 10 mm from the longitudinal

center of the workpiece, which corresponds to the temperature around 115 ◦C.

The temperature distributions obtained by the two-point calibration were

compared with the simulation results.

30

Figure 3.1 shows the 3D IR signal distribution on the surface of the

base metal. It can be seen that it is difficult to configure the 3D IR signal

distribution in the weld pool region because of the limited measurement

capability of the IR camera. On the other hand, the 3D IR signal distribution

on the solid phase base metal can be measured accurately, and it may be

described by a two-variable exponential function.

Since the IR image shows a skewed view, both visual information and

corresponding quantitative measurements of the IR signal are necessary for

analyzing the IR image. Figure 3.2 shows an IR image in the front panel

of the LabVIEW virtual instrument (VI). The skewed IR image and the

corresponding measurements of the IR signal can be made to overlap. In

Figure 3.2, the weld bead edge can be observed clearly, whereas the 2D weld

pool boundary cannot be easily recognized. Image analysis shows that the

maximum change in the signal occurs at both edges of the weld bead, regardless

of the distance from electrode in the negative x-direction. This significant

change occurs because of the difference in emissivity between the liquid phase

electrode deposited on the workpiece and the solid phase workpiece.

Figure 3.3 shows a series of linescans at different times and locations.

The locations are indicated in terms of pixels. The pixel length is converted

into millimeters using the LabVIEW VI. A magnetic field is generated around

the electric arc. A moving workpiece and non-uniform current flow during

welding can result in the magnetic field having an unbalanced configuration.

This uneven magnetic flux can in turn cause the arc to move during welding.

31

The series of plots in Figure 3.3 indicates this phenomenon at different times

and locations. In Figures 3.3 (a) and (c), the arc appears to be relatively

stable, while in Figure 3.3 (b), the arc appears to be slightly unstable. The

arc behavior may be further explained by considering the current measurement

in the next section.

Even though the welding arc is not constantly symmetric, these

linescans show that the maximum rate of the signal change occurs at the

weld bead boundary. In Figures 3.3 (a), (b), and (c), each linescan shows

almost the same distance between the two points where the positive maximum

and negative maximum of the first derivative of the IR signal occur. Theses

distances were compared with experimental measurements of the weld bead

width at the corresponding positions. The comparison clearly showed that this

measuring technique can always detect the bead width with sufficient accuracy,

less than 0.1 mm. Further, from Figure 3.3, it can be observed that the signal

distribution is normal outside the weld bead.

Figure 3.4 shows a series of 2D thermal images in the form of isotherms

at different times. From this figure, it can be observed that inner isotherms just

below the torch are circular, while outer isotherms are double elliptical. The

inference that may be drawn from this observation is that the heat source itself

is circular and the temperature distribution on the surface of the workpiece is

double elliptical because of the moving heat source. From Figures 3.1–3.4, it

can be said that IR sensing confirms that in 3D configuration, the heat source

distribution is circular Gaussian and the temperature distribution is elliptical

32

Gaussian under the conditions considered in this study.

Figure 3.1: 3D IR signal distribution on the surface of the base metal.

33

Figure 3.2: Front panel of the LabVIEW virtual instrument.

34

0 50 100 150 200 250 3000

200

400

600

800

1000

1200

1400

1600

1800

2000

y (pixel)

IR s

igna

l

165 pixel166 pixel167 pixel

(a) t = 7 s

0 50 100 150 200 250 3000

200

400

600

800

1000

1200

1400

1600

1800

2000

y (pixel)

IR s

igna

l


(b) t = 10 s

0 50 100 150 200 250 3000

200

400

600

800

1000

1200

1400

1600

1800

2000

y (pixel)

IR s

igna

l


(c) t = 13.5 s

Figure 3.3: Linescans for different times and locations.

35

(a) t = 1.5 s (b) t = 4 s

(c) t = 6 s (d) t = 9 s

(e) t = 11 s (f) t = 13 s

Figure 3.4: IR Images at different times.

36

3.2.2 Measurement of Power Input

Despite IR sensing providing the shape information on the heat source,

accurate 3D temperature measurements on the surface of the base metal are

limited. Moreover, in this study, power measurement is more desirable than

temperature measurement for determining the instantaneous amount of energy

input into a weld. The heat source model corresponds to sub-process 2 in

Figure 1.4, which is a process intermediate between sub-process 1 and sub-

process 3. The output of sub-process 1 and the input of sub-process 3 have

the unit of power.

Figure 3.5 shows measurements of the voltage, current, and resulting

power during welding. It can be observed that measurements are not constant

even if the power system supplies a constant power. This result is consistent

with the fact that the welding arc could not be perfectly stable, stated in

the preceding section, and the measurements may be corrupted by noise. A

process for removing noise from actual measurements may be required. The

use of a model-based filtering technique is an excellent way to obtain minimum

error estimates of the actual measurements. However, it requires knowledge

of system and measurement dynamics. In this study, as the simplest noise

reduction method, the mean value of the power was regarded as the steady-

state magnitude of the power.

37

0 5 10 15 20 25−20

0

20

40

60

Time (s)

Vol

tage

(V

)

0 5 10 15 20 25−100

0

100

200

300

400

Time (s)

Cur

rent

(A

)

0 5 10 15 20 25

0

5000

10000

15000

Time (s)

Pow

er (

W)

PowerMean value

Figure 3.5: Measurements of voltage, current, and power.

38

3.2.3 Gaussian Surface Flux Distribution

Pavelic et al. [25] proposed a heat source model that can determine the

distribution and amount of the heat flux on the surface of the base metal. In

this model, the heat flux distribution was assumed to be circular normal. It

was shown through IR sensing that the shape of the heat source was circular

normal. It is therefore reasonable to adapt this model for this study. The

Gaussian surface flux distribution is given by,

q(r) = q(0)e−C r2 (3.1)

where q(r) is the surface flux at radius r in W/m2, r is the radial distance

from the center of the heat source in m, q(0) is the maximum flux at the

center of the heat source in W/m2, and C is the concentration coefficient in

m−2. Figure 3.6 shows the 3D Gaussian surface flux distribution.

Equation (3.1) can be integrated as,∫ ∞

0

q(r)2πrdr =

∫ ∞

0

q(0)e−C r22πrdr =q(0)π

C= ηV I (3.2)

where η is the heat source efficiency, V is the voltage, and I is the current.

In Equation (3.2), the unknown variables q(0) and C should be determined

to configure the 3D heat source in real-time. IR sensing showed that a

significant temperature change occurs across the bead width boundary. From

this observation, it can be assumed that the effective arc power is limited

within the bead width boundary and that the value of q(r) at the weld bead

39

Figure 3.6: Gaussian circular heat flux.

40

boundary is equal to 10% of the maximum value of the heat flux. Then,

q(rB) = q(0)e−C rB2

= 0.1q(0) (3.3)

where rB is half of the bead width. From Equations (3.2) and (3.3),

C =2.30

r 2B

(3.4)

q(0) =CηV I

π(3.5)

The concentration coefficient C is inversely proportional to the square of half

of the weld bead width. The maximum heat flux at the center, q(0), is

proportional to the effective arc power. Once both C and q(0) are determined

through real-time multiple measurements and by using Equations (3.4) and

(3.5), the Gaussian heat flux can be configured in real-time.

3.3 Heat Transfer in the Base Metal

3.3.1 Assumptions

In order to simplify the mathematical model, the following assumptions

were made.

1. The welding process is a steady state, i.e., the heat input, travel speed,

wire feed rate, etc., are steady with regard to time.

2. The only mode of heat transfer in the base metal is conduction. Fluid

flow in the metal is negligible. The base metal is isotropic, homogeneous,

and solid at all times.

41

3. No phase changes occur during welding. Physical properties such as

the thermal conductivity, density, and specific heat are constant with

temperature. Weld pool size is determined by the location of liquidus

line.

4. The mass input, that is, the addition of the filler metal, can be ignored,

and any effect of the mass input on the heat input to the base metal is

negligibly small.

5. The base metal is symmetric along the weld centerline, and thus, it is

sufficient to construct and analyze only half of the base metal.

6. The plasma arc deposited on the top surface of the workpiece is the only

heat source. Electrical energy generation due to resistance heating when

an electrical current is passed through the workpiece is neglected.

3.3.2 Heat Equation

The 3D x–y–z coordinate system is shown in Figure 3.7. The small

circle on the top surface of the base metal indicates the area where the welding

arc is deposited. The origin of the Cartesian coordinate system is at the

center of the circle. Thus, during welding, the coordinate system is fixed at

the stationary center of the heat source and the base metal travels along the

x-axis.

For the translational motion of the workpiece, the above assumptions

42

Figure 3.7: Schematic of Cartesian coordinate system.

can be used to simplify the heat equation into the following form:

∇ · (k∇T ) +Q = ρCPu · ∇T (3.6)

where k is the thermal conductivity in W/m ·K, T is the absolute temperature,

Q is the heat source in W/m3, ρ is the density in kg/m3, CP is the specific

heat capacity at constant pressure in J/kg ·K, and u is the velocity vector in

m/s.

The first term on the left-hand side of Equation (3.6) represents the

conductive heat transfer in the base metal. The second term on the left-hand

side, Q, is the heat input per unit volume to the workpiece from the welding

arc and is determined by using Equation (3.1). The term on the right-hand

side of Equation (3.6) is the convective term, which accounts for the spatial

redistribution of heat because of the movement of the workpiece.

43

3.3.3 Boundary Conditions

The top and bottom surfaces of the steel plate lose heat owing to natural

convection and surface-to-ambient radiation:

qt = ht(T0 − T ) + εσ(T 4amb − T 4) (3.7)

qb = hb(T0 − T ) + εσ(T 4amb − T 4) (3.8)

where ht and hb are the heat transfer coefficients for natural convection, T0

is the associated reference temperature, ε is the surface emissivity, σ is the

Stefan-Boltzman constant, and Tamb is the ambient air temperature. The

front surface has a preset temperature, which is denoted by T0:

T = T0 (3.9)

The rear surface is an outlet boundary where convective heat transfer is

dominant since the heat equation has the convective term:

qr = hr(T0 − T ) (3.10)

The side surface has a well insulated boundary with no heat flux across the

boundary:

qs = 0 (3.11)

3.4 Results

The heat source model was incorporated into the heat transfer model.

The heat transfer model was implemented with the finite element analysis

44

software, COMSOL Multiphysics. Free triangular meshes were generated to

discretize a continuous domain into a set of discrete sub-domain consisting of

4860 elements. The temperature distribution on the surface of the workpiece,

the size and shape of the weld pool, and the temperature histories were

calculated for AISI 1018 steel. The data used for the calculation of the heat

transfer are presented in Table 3.1.

Table 3.1: Data Used for the Calculation of Temperature Fields

Property/Parameter Value

Heat transfer rate to workpiece, Q (W) 4183Heat source efficiency, η 0.80Effective radius of the heat region, rH (mm) 3.7466Concentration coefficient, C (m−2) 4.916× 105

Welding speed, u (mm/s) 10.583Convection heat transfer coefficient, ht (W/m2 ·K) 12.25Convection heat transfer coefficient, hb (W/m2 ·K) 6.25Surface emissivity, ε 0.3Reference temperature, T0 (K) 300Ambient temperature, Tamb (K) 300Solidus temperature, TS (K) 1723Thermal conductivity, k (W/m ·K) 51.9Density, ρ (kg/m3) 7870Specific heat, CP (J/kg ·K) 486

The simulation results were compared with two types of experimental

measurements: IR sensing data, which indicate the temperature fields on the

surface of the workpiece, and the characteristics of actual welds, such as the

size and shape of the weld pool. The experimental results used in the study

45

were obtained under the experimental conditions presented in Table 2.3 of

Chapter 2. The figures presented in this section correspond to the results for

AISI 1018 steel under the experimental condition A. As mentioned previously,

because the measurable temperature range of the IR camera was limited to

below 2000 ◦C, the temperature distribution of only the solid phase region was

compared.

Figure 3.8 shows the calculated 3D temperature distribution on the

surface of the workpiece. The temperature gradient in front of the heat

source is higher than that behind the heat source. Figure 3.9 displays the

surface temperature distribution as a colored set of isothermal lines. In

Figures 3.8 and 3.9, it can be seen that the temperature fields have an elliptical

Gaussian distribution. The calculated temperature distribution in Figure 3.8

is analogous to the distribution determined from IR sensing data presented in

Figure 3.1, except for the liquid phase region. The calculated isothermal lines

in Figure 3.9 are also analogous to the isotherms obtained from IR sensing

data presented in Figure 3.4.

Figures 3.10 and 3.11 compare the measured linescans with the calcu-

lated linescans at two distances from the arc centerline. These linescans were

obtained for the same time instant as that of the linescans in Figure 3.3 (c).

Figures 3.10 (a) and 3.11 (a) compare the raw IR signal with the calculated

temperature, while Figures 3.10 (b) and 3.11 (b) compare the calibrated IR

temperature with the calculated temperature. The raw IR signals were

converted to the temperatures based on the two-point calibration and thermal

46

energy distribution observed by the IR sensing. The two-point calibration

was achieved by using the solidus temperature at the bead boundary and

the temperature measurement of a thermocouple during welding. The IR

sensing showed that the IR signal distribution is normal outside the weld

bead. In Figures 3.10 (b) and 3.11 (b), the difference between the measured

and calculated temperature distributions may be explained by two effects.

First, a small value of the concentration coefficient C increased the width of

the heat source. C is related to the source width; a larger value of C, a

more concentrated source. A slightly larger value of C could provide a good

comparison, but it resulted in somewhat worse predictions of the weld pool

size. Second, the simplified model, which only considers the heat transfer

by conduction in the base metal, was used. The molten metal transfer plays

an important role in arc stability and the weld pool shape, providing the

heat and momentum to the weld pool [32]. The consideration of this metal

transfer mechanism would lead to a better comparison of the experimental and

predicted temperature distribution on the surface of the base metal.

Figure 3.12 shows the predicted shape of the weld pool. The weld pool

surface was determined by using the liquidus temperature. The predicted

shape of the weld pool may be represented by a combination of two different

ellipsoids: the front half of the weld pool is the quadrant of one ellipsoid, and

the rear half is the quadrant of the other ellipsoid. This double ellipsoidal

shape is consistent with the movement of the base metal during welding. The

penetration depth was determined to be 3.3 mm in the negative x–direction

47

from the origin of the coordinate system. In this figure, the top surface of the

cylinder indicates the area where the heat flux is distributed. A similar finding

has been reported in a previous study [33].

Figure 3.13 shows a comparison between the calculated and experimen-

tal cross-section of the weld pool. The predicted penetration depth is slightly

larger than the experimental value, while the predicted bead width is slightly

smaller than the experimental value. In addition, the fusion zone boundary

of the actual weld pool is different from that of the predicted weld pool. It

is thought that fluid flow in the weld pool affects the shape of the weld pool.

The significant convection may be driven by a combination of the surface

tension, electromagnetic, and buoyancy forces [4, 34]. However, these forces

were neglected in this study. Table 3.2 compares the penetration depth and

bead width predicted by the FEM model with those obtain from experiments;

it can be seen that errors amount to less than 10%. Despite the existence of

differences between the predicted and the corresponding experimental results,

Figure 3.13 and Table 3.2 show that both are in reasonable agreement.

Figure 3.14 shows the predicted temperature histories at 10 locations in

the HAZ from the fusion zone to the unaffected base metal. The locations were

chosen at intervals of 0.005 in (0.127 mm) starting at the solidus line. In the

computer simulation, the workpiece began to move from x = 10 mm (t = 0 s)

ahead of the welding arc and passed through the center of the welding arc

located at x = 0 mm (t = 0.95 s). Time-temperature histories were obtained

48

Table 3.2: Comparison between Predicted Values of the Penetration Depthand Bead Width with Those Obtained from Experiments

ExperimentalWeld pool size

Experimental Predictedcondition values (mm) values (mm)

AWidth 7.27± 0.10 6.62Depth 2.05± 0.08 2.41

BWidth 7.88± 0.06 7.70Depth 2.73± 0.06 2.77

from the steady state temperature distribution by converting distance to time;

the welding speed was used for this conversion. The results show that the

peak temperatures occur behind the welding arc, but vary with the location.

Each location witnessed initial preheating and a rapid increase in temperature

during heating. As the transport mechanism moved the workpiece away from

the heat source, each location witnessed comparatively slower cooling. This

behavior is very similar to the temperature distribution on the metal surface,

which is shown in Figure 3.8 (b).

49

(a) Front view

(b) Side view

Figure 3.8: Three-dimensional surface temperature distribution in the Kelvinscale.

50

Figure 3.9: Surface temperature distribution shown as isotherms in the Kelvinscale.

51

−20 −10 0 10 200

500

1000

1500

2000

2500

3000

3500

4000

Distance from y−aixs (mm)

IR s

igna

l

FEM simulationIR measurement

(a) Comparison between IR signal and calculated temperature

−20 −10 0 10 200

500

1000

1500

2000

2500

3000

3500

4000


Cal

ibra

ted

Tem

pera

ture

(K

)


(b) Comparison between calibrated IR temperature and calculated temperature

Figure 3.10: Comparison between measured and calculated linescans:x = 3.0 mm from the arc center (y = 161 pixel).

52

−20 −10 0 10 200

500

1000

1500

2000

2500

3000

3500


IR s

igna

l


(a) Comparison between IR signal and calculated temperature

−20 −10 0 10 200

500

1000

1500

2000

2500

3000

3500


Cal

ibra

ted

Tem

pera

ture

(K

)


(b) Comparison between calibrated IR temperature and calculated temperature

Figure 3.11: Comparison between measured and calculated linescans:x = 3.3 mm from the arc center (y = 162 pixel).

53

Figure 3.12: Calculated weld pool shape.

7.27 mm 6.62 mm

2.41 mm2.05 mm

Solidus line

Figure 3.13: Comparison between calculated and experimental weld pool cross-sections.

54

HAZ

①②③④⑤⑥⑦⑧⑨⑩

Base metal

FZ

0 1 2 3 4 5 60

200

400

600

800

1000

1200

1400

1600

Time (s)

Te

mp

era

ture

(°C

)

①

⑩

Figure 3.14: Time-temperature histories at 10 locations in the HAZ.

55

3.5 Conclusions

A combination of real-time measurements, a heat source model, and a

heat transfer model has been used to predict the weld characteristics and the

temperature history of the HAZ. The main conclusions in this chapter are as

follows:

1. The recording and analysis of the IR image using LabVIEW virtual

instruments showed that the lateral width of the weld pool could be

measured with a high accuracy through IR sensing.

2. IR sensing showed that the heat flux distribution was circular normal

and the temperature distribution was elliptical normal for the welding

process considered in this study.

3. Real-time multiple measurements from multiple sensors were incorpo-

rated into the heat source model. This configured the 3D Gaussian heat

flux in real-time, determining the variables of the heat source model.

4. The heat source model was coupled with the heat transfer model. This

coupled system can be used to predict the penetration depth and bead

width of the weld pool and the time-temperature history of the HAZ.

5. General features of the predicted temperature fields were consistent with

experimental results obtained from IR sensing and an actual weld.

56

Chapter 4

Microstructural Model

In this chapter the theoretical background for microstructural modeling

is presented. Kirkaldy et al. [12, 35] presented an algorithm for predicting

the microstructure and hardenability of low alloy steels. This algorithm is

based on kinetic equations that describe the approximate isothermal phase

transformation and rigorous thermodynamics. Watt et al. [14, 15] showed that

Kirkaldy’s evolution equations can be used to predict the phase fractions, grain

sizes, and heat-affected-zone (HAZ) hardness for single pass welds. Oddy et

al. [13] further extended this algorithm to account for partial austenitization,

carbon segregation and arbitrary thermal histories, including reheating. The

microstructure model described in this chapter is based on the approach by

Oddy et al. The implementation in a computer program is discussed in relation

to this theory.

4.1 Kinetic Equations for Phase Transformation

Zener [36] and Hillert [37] made important contributions to the study of

steel thermodynamics and phase transformations. They reported fundamental

principles regarding the decomposition of austenite and the effect of alloying

57

elements. Based on the equations developed by Zener and Hillert, Kirkaldy [12,

26] presented a general formula describing the TTT curve, which calculates

the time τ required to transform X fraction of austenite at temperature T :

τ(X,T ) =1

α(G)D∆T q

∫ X

0

dX

X2(1−X)/3(1−X)2X/3(4.1)

where α(G) = β2(G−1)/2, β is an empirical coefficient, G is the American

Society for Testing and Materials (ASTM) grain size, D is an effective diffusion

coefficient, ∆T is the undercooling given as (A3 − T ), and q is an exponent

that depends on the effective diffusion mechanism. The exponents in the

denominator of the integrand take into account the rate at which the interface

area between the austenite and the decomposition product changes.

For alloyed steels, the effective diffusion coefficient can be approximated

by the series resistance relation [38],

1

D=

1

DC

+n∑

i=2

kiCi

Di

(4.2)

where DC is the diffusion coefficient of carbon in austenite, Di is the diffusion

coefficient of element i, Ci is the concentrations of element i, and ki is a

coefficient of element i that is obtained by fitting experimental data. The

summation is over the alloying elements.

Kirkaldy et al. fitted the prediction of Equation (4.1) to data

from the Atlas of Isothermal Transformation and Cooling Transformation

Diagrams [39], an extensive collection of experimental data, and presented the

58

coefficients of the integral in Equation (4.1) for ferrite, pearlite, and bainite,

as respectively given by Equations (4.3), (4.4), and (4.5):

τF=

59.6Mn + 1.45Ni + 67.7Cr + 244Mo

2(G−1)/2∆T 3 exp(−23500

RT

) I (4.3)

τP=

1.79 + 5.42(Cr +Mo + 4MoNi)

2(G−1)/2∆T 3DP

I (4.4)

τB=

(2.34 + 10.1C + 3.8Cr + 19Mo)10−4Z

2(G−1)/2∆T 2 exp(−27500

RT

) I (4.5)

where chemical compositions are expressed in wt%, R is the gas constant

in cal/mol ·K, I in Equations (4.3)–(4.5) are the volume fraction integrals

as shown on the right-hand side of Equation (4.1), and Z in Equation (4.5)

accounts for the slow termination of the bainite reaction and is given as,

Z = exp[X2 (1.9C + 2.5Mn + 0.9Ni + 1.7Cr + 4Mo− 2.6)

](4.6)

The undercooling ∆T is given as (A3 − T ), (A1 − T ), and (BS − T ) for the

ferrite, pearlite, and bainite reactions, respectively. The effective diffusion

coefficient DP in Equation (4.4) is determined by Equation (4.2) as,

1

DP

=1

exp(−27500

RT

) +0.01Cr + 0.52Mo

exp(−37000

RT

) (4.7)

Unlike ferrite, pearlite, and bainite, martensite forms by a sudden shear process

in the austenite lattice, which is a diffusionless phase transformation. The

Koistinen-Marburger equation is considered to give the best representation of

the martensite transformation [40]:

XM = 1− exp [−k(MS − T )] (4.8)

59

where XM is the volume fraction of martensite, k is the kinetic parameter,

and Ms is the martensite start temperature.

4.2 Base Material Dependent Properties

4.2.1 Solidus and Liquidus Lines

The solidus is the temperature at which the material begins to melt.

The liquidus is the temperature at which all constituents of the material (such

as an alloy) are transformed into liquid state. At temperatures between the

solidus and the liquidus, the material simultaneously consists of solid and

liquid phases. For low alloy steels, the solidus TS and liquidus TL lines are

given by [41],

TL = 1530.0− 80.581C (4.9)

TS = 1527.0− 181.356C (4.10)

where C is the carbon content of the steel in wt% and the solidus and liquidus

temperatures are in ◦C.

4.2.2 Precipitate Dissolution Temperature

Fine particle dispersions created from the alloying elements retard

austenite grain growth. The more stable the particles are, the more effectively

grain growth is retarded to higher temperatures. The steels studied in this

work are AISI 1018, AISI 4130, and AISI 4140. AISI 4130 and AISI 4140

are low alloy steels containing chromium (Cr) and molybdenum (Mo) as

60

strengthening agents. The grain-pinning precipitates that form from these

additions are chromium carbide (Cr23C6) and molybdenum carbide (Mo2C).

The general approach to evaluate precipitation is based on reactions

between a substitutional element and an interstitial element (C or N) in

austenite to form a compound XaYb:

aX + bY = XaYb (4.11)

where a and b are stoichiometry constants, X is the concentration of the

substitutional alloying element (carbide former, e.g., Cr or Mo) in austenite,

and Y is the concentration of the non-metal interstitial element (C) in

austenite. The equilibrium solubility product K is given by,

K = [X]a[Y ]b (4.12)

where the product is expressed in wt%. The temperature dependence of the

solubility is given by,

log [X]a[Y ]b = A− B

T(4.13)

where A and B are constants that may be estimated from free energy data or

determined experimentally, and T is the temperature in K.

Equation (4.13) can be inverted to calculate the precipitate dissolution

temperature Td at which the carbide dissolves completely, given sufficient time

to reach equilibrium [10, 11]. In computer simulation, it is assumed that the

precipitates dissolve immediately as the temperature increases above Td.

Td =B

A− log[Xa][Y b](4.14)

61

The values of A and B for carbides (Cr23C6, Mo2C) in austenite are given in

Table 4.1. The calculated Td for nominal AISI 4130 and 4140 compositions

are 910.4 ◦C and 925.6 ◦C, respectively.

Table 4.1: Solubility Products for Carbides in Austenite

Compound Metal Non-metal A B

Cr23C6 Cr C 5.9 7375Mo2C Mo C 5.0 7375

4.2.3 Transformation Temperatures

The transformation temperatures are often referred to as critical

temperatures. There are four transformation temperatures of interest in the

microstructural model: upper critical temperature A3, lower critical temper-

ature A1, bainite start temperature Bs, and martensite start temperature

Ms. This set of transformation temperatures and the precipitate dissolution

temperature divide the HAZ thermal history into eight distinct regions, as

shown in Figure 4.1.

The transformations that occur at A1, A3, and Bs are diffusion

controlled. The critical temperatures are sensitive to chemical composition,

heating rate, and cooling rate. Rapid heating allows less time for diffusion

and tends to increase the critical temperature. Likewise, rapid cooling tends

to lower the critical temperature.

Generally, the critical temperatures for a given steel are determined

62

Bs

A1

A3

Td

Tp

Ms

5

4

6

7

8

3

1

2Tem

per

ature

(ºC

)

Austenite (γ)

Composition (wt% C) Time (s)

Ferrite (α)α + Fe3C

γ + L

L

(a) (b)

Figure 4.1: (a) The Fe-C phase diagram identifying critical temperatures.(b) Temperature history identifying regions that are considered in themicrostructural model.

experimentally. However, empirical formulas that predict the effects of alloying

elements on the critical temperatures have been developed by regression

analysis of large amounts of experimental data.

When the temperature of the material exceeds A1, it is assumed that all

pearlite transforms immediately to austenite. This is the transition for region

1 to 2 in Figure 4.1(b). Between A1 and A3, region 2 in Figure 4.1(b), the

material is a mixture of ferrite and austenite. The upper critical temperature

63

A3 is given by [42],

A3(◦C) = 910− 203

√C− 15.2Ni + 44.7Si + 104V + 31.5Mo + 13.1W

− [30Mn + 11Cr + 20Cu− 700P− 400Al− 120As− 400Ti] (4.15)

where the compositions of the alloying elements are in wt%. The low critical

temperature A1 is similarly given by [43],

A1(◦C) = 723− 10.7Mn− 16.9Ni + 29.1Si + 16.9Cr + 290As + 6.38W (4.16)

In the recrystallized zone, between A3 and Td, region 3 in Figure 4.1(b),

austenite grains are pinned by precipitates and their growth is delayed until

the precipitates dissolve completely. As the temperature increases above

Td, the austenite grain growth begins immediately and continues until the

temperature decreases below A3. The grain growth zone corresponds to region

4 in Figure 4.1(b).

If the weld cools rapidly enough to bypass ferrite (A3) and pearlite (A1)

formation, through regions 4, 5 & 6 in Figure 4.1(b), and the temperature

decreases below Bs, the austenite begins to decompose to bainite. The bainite

start temperature Bs is given by [12],

Bs(◦C) = 656− 58C− 35Mn− 75Si− 15Ni− 34Cr− 41Mo (4.17)

On even more rapid cooling of the weld, austenite in the HAZ may bypass the

bainite transformation and decompose into martensite below Ms, region 8 in

Figure 4.1(b). The martensite start temperature Ms is given by [12],

Ms(◦C) = 561− 474C− 33Mn− 17Ni− 17Cr− 21Mo (4.18)

64

4.3 Austenite Formation

4.3.1 Initialization of Ferrite and Pearlite

The steel is assumed to be initially at room temperature (20 ◦C) and to

remain in equilibrium during heating. In region 1 in Figure 4.1(b), the steel is

a mixture of ferrite and pearlite. The volume fractions of ferrite and pearlite

are given by the lever law,

XF =C− Ceut

Cα − Ceut

(4.19)

XP = 1−XF (4.20)

whereXF is the volume fraction of ferrite, XP is the volume fraction of pearlite,

C is the carbon content of steel, Ceut is the carbon content of the eutectoid,

and Cα is the carbon content of ferrite. The carbon content of the eutectoid

is obtained by rearranging Equation (4.15),

Ceut =[ϕ1 − ϕ2 − A1]

2

2032(4.21a)

ϕ1 = 910− 15.2Ni + 44.7Si + 104V + 31.5Mo + 13.1W (4.21b)

ϕ2 = 30Mn + 11Cr + 20Cu− 700P− 400Al− 120As− 400Ti (4.21c)

The carbon content of ferrite below A1 is given by an empirical relation that

assumes a linear decrease from the eutectoid value to zero at room temperature

(20 ◦C) [44].

Cα =T − 20.0

A1 − 20.0(0.105− 115.3× 10−6 × A1) (4.22)

65

4.3.2 Ferrite and Austenite Formation

Austenite is formed from pearlite colonies as the temperature in the

HAZ rises above A1. Homogeneous austenite formation is assumed in region 2

of Figure 4.1. The steel in this region is a mixture of ferrite and austenite.

Under equilibrium, the volume fraction of austenite and ferrite is given by the

lever law,

XF =C− Cγ

Cα − Cγ

(4.23)

XA = 1−XF (4.24)

where XF is the volume fraction of austenite, XA is the volume fraction of

austenite, and Cγ is the carbon content of the austenite. The carbon content

of austenite is obtained from Equation (4.15),

Cγ =[ϕ1 − ϕ2 − T ]2

2032(4.25a)

ϕ1 = 910− 15.2Ni + 44.7Si + 104V + 31.5Mo + 13.1W (4.25b)

ϕ2 = 30Mn + 11Cr + 20Cu− 700P− 400Al− 120As− 400Ti (4.25c)

The carbon content of ferrite above A1 is given by,

Cα = 0.105− 115.3× 10−6 × T (4.26)

As the temperature increases, the ferrite fraction decreases in accor-

dance with the lever law. Above A3, the steel is completely austenite, as shown

in Figure 4.1 (region 3) except for any undissolved precipitates. Austenite

formation requires carbide decomposition, from pearlite, and carbon diffusion.

66

In actual welds, true equilibrium is rarely achieved on heating because of

limited carbon diffusion in a short thermal cycle. To account for this effect,

Oddy et al. [13] introduced a transient, heterogeneous austenite formation

term based on superheating kinetics into the microstructure model. Even

if their effort provided more accurate predictions of austenite formation,

this improvement to the microstructure model had little effect on the final

microstructure predicted. Thus, superheating kinetics for austenite formation

is not taken into consideration in this study.

4.4 Grain Growth

Austenite grain growth in the HAZ occurs most readily above the

equilibrium dissolution temperature of carbides and nitrides [45]. It is

assumed that the carbide/nitride precipitates pin the austenite grains until

the precipitate dissolution temperature is reached and that the precipitates

all dissolve in a narrow temperature band. The austenite grain growth then

continues up to the peak temperature of the thermal cycle. On cooling, the

austenite grains still grow until the temperature decreases to the upper critical

temperature A3 because the carbide/nitride precipitates cannot reform during

this cooling period.

The classical grain growth equation is given by [14],

dg

dt=

k

2gexp

(− Q

RT

)(4.27)

where g is the grain size in µm, k is the grain growth constant in µm2/s, Q

67

is the activation energy for grain growth in cal/mole, R is the universal gas

constant in cal/mole ·K, T is the temperature in K, and t is the time in s.

Equation (4.27) assumes that grain growth is diffusion controlled and

that the driving force is the grain-boundary energy. Equation (4.27) does

not consider the nucleation process. Considering both nucleation and growth

kinetics may give a more accurate prediction of grain size. However, this

requires detailed experimental data for an individual steel and is beyond the

scope of this study.

The initial grain size is assumed to be approximately 5 to 10 µm

for the steels considered in this study. The activation energy for austenite

grain growth depends on the type of boundary-pinning precipitates and is

determined by the following equations [11].

Q

RTm

= 12 for TiC (4.28)

Q

RTm

= 13 for Cr23C6 (4.29)

Q

RTm

= 19 for Mo2C (4.30)

where Tm is the melting temperature. The equation required to calculate the

activation energy for the plain carbon steel (AISI 1018) does not exist. Because

the chemical composition of Ti-microalloyed steels is similar to that of AISI

1018 steel, the value for TiC is used in calculating the activation energy for

austenite grain growth in AISI 1018 steel.

The grain growth constant assumed is k = 1.26× 1012 µm2/s. In fact,

the grain growth constant is a physical parameter that depends on the type of

68

boundary-pinning precipitate. Khoral [46] calculated this value based on Ion’s

experimental results [47] for Ti-microalloyed steel. This value is not based on

extensive experimental data. However, available literature indicates that it

provides useful predictions [13, 15]. Even if this equation does not prove as

accurate for the steels used in this work, it is adopted for all simulation for

the practical reason that it likely provides a better prediction than not taking

austenite grain growth into account at all, which is the only alternative.

4.5 Carbon Segregation

In this work, carbon segregation refers to the non-uniformity of carbon

content in the HAZ microstructure. The carbon content more strongly

influences the transformation kinetics of alloy steels than do any other alloying

elements. The carbon content determines the critical temperatures, as shown

in Equations (4.15), (4.17), and (4.18). These equations show that an increase

in the carbon content leads to a decrease in the critical temperatures.

Any point in the HAZ undergoes its own thermal cycle and has its own

peak temperature during welding. The carbon content of the austenite can

differ from the bulk value of the alloy during the thermal cycle. On heating,

austenite begins to form with a carbon content corresponding to the eutectoid

value. As the temperature increases, the carbon content of the austenite

decreases according to Equation (4.25). When the temperature reaches the

upper critical temperature A3, homogeneous austenite with low carbon content

is assumed to form.

69

Austenite is the parent phase of all decomposition products: ferrite,

pearlite, bainite, and martensite. In the HAZ, austenite can transform to

any of the listed microstructures on cooling. The decomposition process of

austenite is complicated by two factors. One is that the decomposition starts at

the critical temperature, which varies with the carbon content of the remaining

austenite. The other is that the carbon content of the decomposition products

formed differs from that of the parent austenite.

Homogeneous austenite transforms to ferrite if it is cooled to below

A3. It is assumed that the carbon content of the ferrite produced is at the

maximum solid solubility of carbon in ferrite at A1. This assumption slightly

overestimates the actual carbon content of the ferrite. However, it does not

cause a significant error. As ferrite forms, it rejects carbon into the austenite.

Thus, the remaining austenite has a higher carbon content than the bulk value.

The bulk carbon content remains constant even though the carbon content

locally partitions. When ferrite forms, the carbon content in the remaining

austenite can be calculated by [13],

Ct+∆tγ =

X tAC

tγ +∆XACα

X t+∆tA

(4.31)

where the superscript t+∆t denotes the updated state and the superscript t

denotes the current state. Below A1, pearlite is assumed to form with carbon

content equal to the eutectoid value. Thus, as pearlite forms, it has a higher

carbon content than the remaining austenite. When pearlite forms, the carbon

70

content in the remaining austenite can be calculated by,

Ct+∆tγ =

X tAC

tγ +∆XACeut

X t+∆tA

(4.32)

Ferrite and pearlite are assumed to continue to form at about the same time

below A1 until bainite begins to form. In simulation, both Equations (4.31)

and (4.32) are consecutively computed for one time step.

Bainite and martensite are assumed to form with the carbon content of

the currently remaining austenite. Their carbon contents may vary with the

critical temperature and the fraction transformed to ferrite and pearlite. In

general, as the carbon content of the austenite increases, the hardness of the

decomposition products produced increases.

4.6 Austenite Decomposition

Based on Kirkaldy’s equations [12, 35, 38] given by Equations (4.3)–

(4.5), Watt et al. [14, 15, 44] presented a set of ordinary differential equations

(ODEs) that describe the kinetics of austenite decomposition. The set of ODEs

for austenite decomposition to ferrite, pearlite, and bainite can be obtained

by differentiating Equations (4.3)–(4.5):

71

dXF

dt=

2(G−1)

2 (∆T )3 exp(−23500

RT

)59.6Mn + 1.45Ni + 67.7Cr + 24.4Mo

XF

2(1−XF )

3 (1−XF )2XF

3 (4.33)

dXP

dt=

2(G−1)

2 (∆T )3DP

1.79 + 5.42(Cr +Mo + 4MoNi)XP

2(1−XP )

3 (1−XP )2XP

3 (4.34)

dXB

dt=

2(G−1)

2 (∆T )2 exp(−27500

RT

)10−4(2.34 + 10.1C + 3.8Cr + 19Mo)Z

XB

2(1−XB)

3 (1−XB)2XB

3 (4.35)

where the effective diffusion coefficient DP in Equation (4.34) is obtained by,

1

DP

=1

exp(−27500

RT

) +0.01Cr + 0.52Mo

exp(−37000

RT

) (4.36)

and Z in Equation (4.35) represents the slow transformation rate and is given

by,

Z = exp[XB

2 (1.9C + 2.5Mn + 0.9Ni + 1.7Cr + 4Mo− 2.6)]

or (4.37a)

Z = 1 for (1.9C + 2.5Mn + 0.9Ni + 1.7Cr + 4Mo− 2.6) < 0 (4.37b)

These equations describe the austenite decomposition rates into the product

phases. The ferrite, pearlite, and bainite formation rates are computed

indirectly. The volume fraction relation between the decomposed austenite

and the newly formed phase can be given by,

XA +Xi = 1 (4.38)

where the subscript i denotes any of the product phases, namely, ferrite,

pearlite, and bainite. The austenite is consumed in producing the product

phases during continuous cooling. The austenite phase fraction participating

72

in the current reaction is decreased. Furthermore, austenite decomposition

may stop at an equilibrium fraction. Equation (4.38) is modified to account

for these facts:

XA −XeqA +Xi = 1−Xeq

A −Xpre (4.39)

where XeqA is the austenite equilibrium volume fraction and Xpre is the

previously decomposed austenite volume fraction. Both XeqA and Xpre are

updated at every time step. Equation (4.39) is divided by (1 − XeqA − Xpre),

resulting in a normalized expression,

XA −XeqA

1−XeqA −Xpre

+Xi

1−XeqA −Xpre

= 1 (4.40)

Equation (4.40) can then be written as,

XA +X i = 1 (4.41)

which is the same form as Equation (4.38). Using the normalized variables

described above, Equations (4.3)–(4.5) describe the normalized reaction rates.

The volume fraction of newly formed phase Xi is also obtained from the

normalized fraction relation.

In the austenite/ferrite and austenite/pearlite reactions, the austenite

equilibrium volume fraction XeqA is calculated by the lever law at each time

step. For the ferrite formation reaction,

XeqA/F =

Ctγ − Cα

Cγ − Cα

X tA for T > A1 (4.42a)

XeqA/F =

Ctγ − Cα

Ceut − Cα

X tA for T < A1 (4.42b)

73

where Ctγ is the carbon content in the remaining austenite, which is updated

according to Equations (4.31) and (4.32), and Cγ is the carbon content of

the austenite phase boundary in a phase diagram, which is calculated by

Equation(4.25). In Equation (4.42a), XeqA/F is the austenite fraction that

remains after the reaction is complete. In Equation (4.42b), XeqA/F is the

austenite fraction that decomposes to pearlite. For the pearlite formation

reaction,

XeqA/P =

Ceut − Ctγ

Ceut − Cα

X tA (4.43)

which is the austenite fraction that decomposes to ferrite.

Martensite is formed by the rapid cooling of austenite that traps carbon

atoms because they do not have time to partition by diffusion and, thus, form

other decomposition products. Because no diffusion occurs, the martensite

has the same carbon composition as the austenite from which it is formed.

The Koistinen-Marburger equation [40] can be used to compute the volume

fraction of martensite produced by austenite decomposition to martensite.

This equation is described again for convenience,

XM = 1− exp [−k(MS − T )] (4.44)

Using the volume fraction relation in Equation (4.38), the austenite fraction

is given by,

XA = exp [−k(MS − T )] (4.45)

74

An incremental equation for the austenite fraction ∆XA can be derived in

terms of the current and the next time step,

∆XA = X t+∆tA −X t

A

= X tA

(ek∆Tn − 1

)(4.46)

where ∆Tn = T t+∆t − T t. The parameter k is 0.011 ◦C−1 for most steels, but

does depend on the alloy composition, especially the carbon content. The

carbon dependence may be important when carbon segregation is considered.

It can be estimated based on limited experimental data as [48],

k =4.61

97.1C + 161(4.47)

The volume fraction of newly formed martensite XM is also obtained by using

the volume fraction relation in Equation (4.38).

Figure 4.2 shows the temperature history obtained from the heat

transfer model presented in Chapter 3. Emphasizing the main transformation

kinetics in each region, the temperature history is divided into eight distinct

regions: (1) initialization of ferrite and pearlite, (2) austenite formation, (3)

precipitate dissolution, (4) austenite grain growth, (5) austenite decomposition

to ferrite, (6) austenite decomposition to pearlite, (7) austenite decomposition

to bainite, and (8) austenite decomposition to martensite.

As the HAZ temperature decreases below A3, ferrite begins to form

at the grain boundaries of austenite. As the temperature decreases below

A1, pearlite begins to form. In addition to BS, bainite formation requires the

75

0 2 4 6 8 10 12 140

500

1000

1500

Time (s)

Tem

pera

ture

(°C

)

4

A3

Td

Bs

A1

5

6

3

A3

78

2

1Ms

Tp

A1

Figure 4.2: Temperature history showing transformation regions

computation of a bainite transition temperature BT . BT is the temperature at

which the formation rate of bainite exceeds those of both ferrite and pearlite.

Equations (4.3)–(4.5) can be used to determine the rate coefficients of ferrite,

pearlite, and bainite at temperatures below BS. The rate coefficient depends

on the undercooling, austenite grain size, and alloy composition at a particular

temperature. Ferrite and pearlite continue to form until the temperature

decreases below BT or until their volume fractions reach the equilibrium

value. Bainite starts to form as the temperature decreases below BT , which

serves as the actual bainite start temperature. Bainite formation stops as the

76

temperature decreases below the martensite start temperature. Martensite

forms if the temperature decreases below MS and if austenite is available for

decomposition. In this study, martensite formation is assumed to stop if the

temperature decreases below the martensite finish temperature MF , or if the

cooling time after welding reaches 1 min. It is assumed that MF is room

temperature (20 ◦C).

4.7 Hardness Calculation of the HAZ

Maynier et al. [49] proposed a general formula for predicting the

hardness of low alloy steels as a function of their phase composition. It

requires calculating the hardness of the constituent martensite, bainite, and

ferrite-pearlite. For mixed structures, the total hardness H is calculated by a

summation rule over volume fractions,

H = HMXM +HBXB +HFPXAFP (4.48)

where the hardness is in Vickers Pyramid Number (VPN); HM , HB, and

HAFP are the Vickers hardness of martensite, bainite, and austenite-ferrite-

pearlite mixture, respectively; XM , XB, and XAFP are the volume fractions of

martensite, bainite, and austenite-ferrite-pearlite, respectively.

The VPNs of HM , HB, and HAFP are calculated using the relations

provided by Maynier et al. [49]. Their expressions in terms of alloying element

77

wt% are,

HM = 127 + 949C + 27Si + 11Mn + 8Ni + 16Cr + 21 log Vr (4.49)

HB = −323 + 185C + 330Si + 153Mn + 65Ni + 144Cr + 191Mo

+ log Vr(89 + 53C− 55Si− 22Mn− 10Ni− 20Cr− 33Mo) (4.50)

HAFP = 42 + 223C + 53Si + 30Mn + 12.6Ni + 7Cr + 19Mo

+ log Vr(10− 19Si + 4Ni + 8Cr + 130V) (4.51)

where Vr is the cooling rate at 700 ◦C in ◦C/h, which can be given in terms of

seconds as,

Vr =

(800− 500

∆t8−5

)3600 (4.52)

where ∆t8−5 is the time required for cooling from 800 ◦C to 500 ◦C. For many

weldable steels, this defines the temperature range within which austenite

decomposes by solid state transformations. Equations (4.49)–(4.51) are valid

within,

0.1 wt% < C < 0.5 wt%

Si < 1.0 wt%

Mn < 2.0 wt%

Ni < 4.0 wt%

Mo < 1.0 wt%

(Mn + Ni +Mo) < 5.0 wt%

Cr < 3.0 wt%

V < 0.2 wt%

Cu < 0.5 wt%

0.01 wt% < Al < 0.05 wt%

78

The effects of microalloying elements (Nb, Ti, Zr and B) are not taken into

account. Using all these relations, the variation of hardness in the HAZ can

be determined from predictions of the transformed microstructure.

79

Chapter 5

Comparison of Predicted and Experimental

Results

In this chapter the predictions of the microstructural model are

compared with experimental results. The microstructural model can be used to

calculate the TTT diagram as well as the volume fractions of the decomposition

products for low alloy steels. To evaluate the prediction capability of the

microstructural model, a series of TTT diagrams was produced and compared

with the experimental TTT diagrams. Adjustment factors based on root mean

square error (RMSE) analysis were introduced to the microstructural model

to obtain a better fit to the TTT curve.

Previous researchers have compared their simulation results with

measurements made by Ion [10]. In this study, in contrast, actual welds

were performed under two different sets of conditions, and the microstructure

of these welds was characterized using microscopy and Vickers hardness

tests. The resulting experimental data were compared with predictions

made using the microstructural model. In particular, the predicted hardness

distributions were compared with the experimentally measured ones. Then,

the microstructure evolution was described in terms of the decomposition

80

products throughout the time-temperature history.

In this research, the predictions for the final HAZ microstructure are

based on the integrated welding system that includes real-time IR sensing, the

heat source model, and the heat transfer model as well as the microstructural

model. The scope of the predictions and the limitations of this integrated

system are discussed.

5.1 Evaluation of the Microstructure Model with Ex-perimental TTT Diagrams

5.1.1 Prediction of TTT Diagrams

The kinetic equations described in Chapter 4 are used to calculate the

TTT diagrams. The reaction coefficients in Equations (4.33)–(4.35) become

constant at a particular temperature. This simplifies the kinetic equations to

dXF

dt= RFXF

2(1−XF )

3 (1−XF )2XF

3 (5.1)

dXP

dt= RPXP

2(1−XP )

3 (1−XP )2XP

3 (5.2)

dXB

dt=

RB

ZXB

2(1−XB)

3 (1−XB)2XB

3 (5.3)

where RF , RP , and RB are the reaction coefficients for ferrite, pearlite,

and bainite, respectively. These coefficients can be calculated at a given

temperature and separated from Equations (5.1)–(5.3) for convenience before

integration. Then, the kinetic equations become still more simplified as

81

dXi

dt= f(Xi) (5.4)

which contains only a function of the volume fraction of the product phases.

The TTT diagram indicates when a specific transformation starts and finishes,

i.e., when Xi has the values of 0.001 (or 0.01) and 0.999 (or 0.99) for the start

and finish curves, respectively. Integration of Equation (5.4) provides the times

corresponding to the start and finish curves. For the ferrite reaction, the time

for Xi = 0.001 is 0.298 s and the time for Xi = 0.999 is 4.058 s. When the

reaction coefficients are included, the start time Ts and finish time Tf are given

by,

Ts =0.298

RF

(5.5)

Tf =4.058

RF

(5.6)

For the pearlite reaction, the start and finish times can be calculated similarly.

For the bainite reaction, the effect of Z, which is a nonlinear function of

composition and Xi, should be considered in Equation (5.4).

The reaction coefficients are determined by several factors, including

the prior austenite grain size, the alloy composition, and undercooling.

These coefficients were calculated with an interval of 5 ◦C from the upper

critical temperature A3 to room temperature. The temperature range of

each decomposition product was determined according to the transformation

82

temperatures, which can be calculated using the procedures described in

Chapter 4.

5.1.2 Comparison of Predicted and Experimental TTT Diagrams

The TTT diagrams were predicted for several types of steels: AISI

3140, 4130, 4140, and 1050. The ASM Atlas of Isothermal Transformation and

Cooling Transformation Diagrams [39] was used for comparison. Figure 5.1

shows the experimental TTT diagram for AISI 3140 steel from the ASM Atlas.

Figures 5.2–5.5 compare the predicted TTT diagrams with the experimental

TTT diagrams. It can be seen that the predicted TTT diagrams are

consistently shifted to shorter times. However, the overall distributions of

the predicted curves are in reasonable agreement with the experimental TTT

diagrams. The predicted diagram for the plain carbon steel is somewhat

better than that for the alloy steel. A significant discrepancy occurs in the

transformation finish times for the chromium-molybdenum alloy steels such as

AISI 4130 and 4140. The predicted finish times for these steels appear to be

much less than the experimental finish times. Kirkaldy et al. reported possible

defects in their model that may result from some of the model’s assumptions,

as follows [12]:

1. In the ferrite and pearlite regime, there may be deviations due to the

assumption of a single nucleation model that is independent of temper-

ature, because the actual nucleation mechanism at higher temperature

may be different from that at lower temperature.

83

2. In the bainite regime, there may be deviations due to the assumption of

unvarying steady-state growth, because the actual growth may slow at

longer times because of the presence of substitutional alloying elements.

There may also be an effect due to diffusionless shear in the formation

of lower bainite, while the model does not consider a distinction between

the upper and lower bainite.

To correct the significant errors in the predictions in the bainite regime,

Kirkaldy et al. introduced the Z factor shown in Equation (5.3), which

accounts for the very sluggish transformation of austenite to bainite. However,

this adjustment was not completely successful. The difference between the

predicted and experimental TTT curves may be mainly due to the use of a

single nucleation and closure model for all products and temperatures.

84

Figure 5.1: TTT diagram for AISI 3140 steel. [From H. Boyer (editor), Atlasof Isothermal Transition and Cooling Transformation Diagrams, AmericanSociety for Metals, 1977, p. 99.]

85

10−2

100

102

104

106

0

100

200

300

400

500

600

700

800

Time [log(s)]

Tem

pera

ture

(°C

)

FerritePearliteBainiteMartensiteReal data

Figure 5.2: Comparison between predicted and experimental TTT diagramfor AISI 3140 steel before modification.

86

10−2

100

102

104

106

0

100

200

300

400

500

600

700

800

Time [log(s)]

Tem

pera

ture

(°C

)



87

10−2

100

102

104

106

0

100

200

300

400

500

600

700

800

Time [log(s)]

Tem

pera

ture

(°C

)



88

10−2

100

102

104

106

0

100

200

300

400

500

600

700

800

Time [log(s)]

Tem

pera

ture

(°C

)



89

5.1.3 Root Mean Square Error (RMSE) Analysis

One way to judge how well the microstructural model predicts the

TTT diagram is to quantify the degree of deviation between the predicted and

experimental TTT curve. The most common measure of this deviation is the

square root of the mean square error (RMSE), which is given by,

s =

√√√√√ n∑i=1

(xP − xE)2

n− 1(5.7)

where xP is the predicted value at a particular temperature, xE is the

experimental value at the corresponding temperature, and n is the number

of data points taken from the experimental TTT curve. A smaller RMSE

value indicates a better prediction.

As shown in Figure 5.1, the TTT diagram consists of three thick curves:

the start curve for ferrite and bainite, the start curve for pearlite, and the

finish curve for pearlite and bainite. All these curves were compared with the

predicted TTT curves, and the RMSE values were calculated in all regions

except for near the transformation temperatures. The set of data representing

an experimental TTT diagram contains discrete points. These discrete data

are converted into a continuous form by linear interpolation, in which a straight

line fit is drawn between each pair of adjacent data points.

The adjustment factor necessary to minimize the RMSE between the

predicted and experimental TTT curves may provide a better comparison.

The use of this factor is equivalent to modifying the transformation rate of

90

Kirkaldy’s kinetic equation. Figures 5.2–5.5 indicate that the predicted curves

should be shifted to longer times, which means that the transformation rate

should be decreased. The reaction coefficients in Equations (5.1)–(5.3) were

divided by the adjustment factors. The simplified kinetic equations with the

adjustment factors can thus be written as,

dXF

dt=

RF

AF

XF

2(1−XF )

3 (1−XF )2XF

3 (5.8)

dXP

dt=

RP

AP

XP

2(1−XP )

3 (1−XP )2XP

3 (5.9)

dXB

dt=

RB

ZAB

XB

2(1−XB)

3 (1−XB)2XB

3 (5.10)

where AF , AP , and AB are the adjustment factors for ferrite, pearlite, and

bainite, respectively. A constant adjustment factor for each decomposition

product was used to minimize the RMSE, and thus three adjustment factors

were found for each TTT diagram. The same process to predict a TTT

diagram was repeated in the computer simulation while varying the adjustment

factor from 1 to 10 with an interval of 0.1.

Figure 5.6 shows the logarithm of the computed RMSE as a function

of the adjustment factor for AISI 3140 steel. The minimum value of the

RMSE was found for a different adjustment factor for each decomposition

product. Table 5.1 lists the calculated adjustment factors that minimize the

RMSE for AISI 3140, 1050, 4130, and 4140 steels. Figures 5.7–5.10 compare

the TTT diagrams predicted using the adjustment factors listed in Table 5.1

with the experimental TTT diagrams. For the plain carbon steel, the use

91

of adjustment factors to modify the transformation rate provided a better

prediction, shifting the predicted curve to longer times. However, for the

high alloy steel, the modification of the transformation rate using adjustment

factors provided a less satisfactory prediction. There is still a significant

discrepancy between the predicted and experimental finish curves. This is

because of the limitations of the model discussed previously. Comparison

of Figures 5.2–5.5 and Figures 5.7–5.10 demonstrates that this modification

may lead to an improvement in the microstructural model. However, the

adjustment factor is a kind of fuzzy factor and will not lead to intrinsic

improvement in the microstructural model. Better fundamental modeling

of the austenite decomposition based on the transformation kinetics may be

required to alleviate this discrepancy.

Table 5.1: Adjustment Factors

AISI 3140 AISI 1050 AISI 4130 AISI 4140

Ferrite 2.1 2.1 6.1 2.8Pearlite 2.1 3.2 1.0 1.4Bainite 4.9 3.4 5.1 3.0

92

1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4

Adjustment factor

Tim

e [lo

g(s)

]

FerritePearliteBainite

Figure 5.6: Logarithm of the RMSE vs. adjustment factor for AISI 3140 steel.

93

10−2

100

102

104

106

0

100

200

300

400

500

600

700

800

Time [log(s)]

Tem

pera

ture

(°C

)


Figure 5.7: Comparison between predicted and experimental TTT diagramfor AISI 3140 steel after modification.

94

10−2

100

102

104

106

0

100

200

300

400

500

600

700

800

Time [log(s)]

Tem

pera

ture

(°C

)



95

10−2

100

102

104

106

0

100

200

300

400

500

600

700

800

Time [log(s)]

Tem

pera

ture

(°C

)



96

10−2

100

102

104

106

0

100

200

300

400

500

600

700

800

Time [log(s)]

Tem

pera

ture

(°C

)



97

5.2 Experimental Results

5.2.1 Weld Characteristics

Figure 5.11 shows the bead-on-plate-welds for AISI 1018 steel. The

upper weld was made under experimental condition A (see Chapter 2) and

the lower weld was made under experimental condition B. For both welds,

weld bead can be clearly identified and its width is almost constant in weld

time and space, with the exception of both ends. The samples were cut to

investigate the weld characteristics, microstructure, and hardness. Specimen

preparation is crucial for the hardness test and optical microscopy, and the

specimen prepared should be truely representative of the weld samples. The

cut sample was mounted in non-conducting material. The surfaces of the

mounted samples were ground and polished to obtain a flat face with uniform

analysis conditions across the region of interest. Nital etching (5% nitric acid

and 95% ethanol) was used to reveal the microstructure of the carbon steels.

Figures 5.12 and 5.13 show the transverse sections for experimental

conditions A and B, respectively. In these figures, the fusion zone and the

HAZ were clearly identified, and thus the weld characteristics such as the bead

width and penetration depth can be measured exactly. The upper surface of

the HAZ has a symmetric bell-shape, while the lower surface of the HAZ is

hemispherical. The size of the HAZ was not uniform: the middle part is larger

than the top and bottom parts. The heat input per unit length for condition B

is higher than for condition A. Consequently, the penetration depth and bead

width for condition B were larger than those for condition A.

98

Figure 5.11: Welded specimen.

99

(a) AISI 1018 steel

(b) AISI 4130 steel

(c) AISI 4140 steel

Figure 5.12: Transverse sections (condition A).

100

(a) AISI 1018 steel

(b) AISI 4130 steel

(c) AISI 4140 steel

Figure 5.13: Transverse sections (condition B).

101

5.2.2 Hardness Measurements of the HAZ

A Wilson Tukon Hardness Tester (Model 2100) was used to measure

the HAZ hardness. Vickers micro-hardness tests were performed in which a

very small diamond indenter with pyramidal geometry was forced into the

surface of the specimen. The force was 0.5 kg, and the indentation time was

15 s. Careful measurements were made at equally spaced intervals of 0.005

in (0.127 mm) from the fusion zone to the unaffected base metal. In this

study, the measurement error was approximately within 5 VPN and may have

occurred while measuring the indent.

Because the size of the HAZ varies in different directions with respect to

the centerline of the heat flux, the hardness measurements were made in three

directions: 30 ◦, 45 ◦, and 90 ◦. These directions are defined in Figure 5.12 (a).

The hardness in the 30 ◦ direction is larger than that in the 45 ◦ direction,

which is larger than that in the 90 ◦ direction.

Figures 5.14–5.16 show series of Vickers indentations on the transverse

sections of AISI 1018, 4130, and 4140, respectively, in the 45 ◦ and 90 ◦

directions. The size of the resulting indentation is related to the hardness

number: the softer the material, the larger the indentation, and the lower

the hardness number. The variation of the indentation size is not significant

for AISI 1018 steel, as shown in Figure 5.14, indicating that the hardness

varied only within a narrow band. The variation of the indentation size

was moderate for AISI 4130 steel, as shown in Figure 5.15, indicating that

the hardness variation is moderate. In Figure 5.16, significant variation in

102

the indentation size can be observed for AISI 4140 steel, indicating that the

hardness varied significantly. Tables 5.2–5.4 list the Vickers hardness numbers

in three directions for the steels investigated under experimental condition A.

Figures 5.14–5.16 and Tables 5.2–5.4 show that the hardness has its peak value

in the grain growth zone, decreases gradually, and then remains steady in the

unaffected base metal.

103

(a) 90 ◦ direction

(b) 45 ◦ direction

Figure 5.14: Vickers indenters on transverse section of 1018 steel(magnification 50×, condition A).

104




105




106

Table 5.2: Hardness Measurements of AISI 1018 Steel (condition A)

Point 30 degree 45 degree 90 degree

1 238 242 2312 232 231 2203 213 213 2094 203 198 1995 204 198 1846 194 194 1997 195 194 1948 193 193 -9 189 193 -10 191 192 -11 191 - -12 190 - -13 194 - -14 191 - -15 190 - -

107



1 408 408 3932 438 435 3473 414 413 2554 417 372 2255 337 267 1736 282 255 1647 245 216 1648 226 194 -9 182 165 -10 172 161 -11 170 - -12 168 - -13 164 - -14 163 - -15 162 - -

108



1 541 558 5052 564 556 4993 561 564 4894 557 553 3815 562 504 3236 536 472 2867 526 398 2388 471 313 2389 389 250 -10 320 234 -11 262 - -12 263 - -13 256 - -14 249 - -15 244 - -

109

5.2.3 Microstructures of the HAZ

Figures 5.17–5.19 show a series of optical micrographs of various zones

in the HAZ for the steels investigated under experimental condition A. The

micrographs were taken right next to indentations shown in Figures 5.14–5.16.

Location numbers are defined in Figure 5.14 (b). As described in Chapter 1,

the HAZ can be divided into several sub-zones based on its microstructure.

Three main sub-zones are clearly distinguishable in Figures 5.17–5.19: the

grain growth zone, the recrystallized zone, and the partially transformed zone.

The HAZ microstructure can be explained qualitatively on the basis of these

sub-zones. The width of the three main sub-zones varied slightly with the

Cequiv of the steels. Thus, the peak temperatures related to these sub-zones

depend on the Cequiv of the steels.

Figure 5.17 shows micrographs of AISI 1018 steel. In this figure, loca-

tions 1, 2, and 3 represent the grain growth zone, in which the Widmanstatten

ferrite plates grew from the grain boundaries. The white areas are light-etching

ferrite, and the gray areas are dark-etching bainite or pearlite. Locations 5

and 6 represent the recrystallized zone. In this zone, austenite does not have

sufficient time for grain growth to develop properly during heating, and the

grain size remains small. Therefore, during cooling, austenite decomposition

to ferrite tends to produce a fine grained ferrite-pearlite structure. Locations

7 and 8 represent the partially transformed zone, location 9 is the tempered

zone, and location 10 is the unaffected base material.

Figure 5.18 shows micrographs of AISI 4130 steel. In this figure,

110

locations 1 and 2 represent the grain growth zone, in which the higher

Cequiv, higher cooling rate, and larger grain size encouraged the formation

of martensite. Locations 3 and 4 still have martensitic microstructure, but

they have smaller grain sizes. Locations 5 and 6 represent the recrystallized

zone. In this zone, the lower cooling rate and the smaller grain size led to the

formation of pearlite and ferrite. Some bainite may also be present at the grain

boundaries. Location 7 represents the partially transformed zone, locations 8

and 9 are the tempered zone, and location 10 is the unaffected base material.

Figure 5.19 shows micrographs of AISI 4140 steel. In this figure,

locations 1, 2, and 3 represent the grain growth zone in which the higher

Cequiv, higher cooling rate, and larger grain size encouraged the formation of

martensite. In locations 4 and 5, the microstructure is essentially martensite

because of its higher Cequiv, and the grain size is somewhat larger than that of

AISI 4130 steel. Locations 6 and 7 represent the recrystallized zone, location

8 represents the partially transformed zone, and location 9 is the tempered

zone. Location 10 is the unaffected base material, which consists of light-

etching ferrite and dark-etching pearlite, as in the AISI 1018 and 4130 steels.

However, the volume fraction of pearlite is significantly higher than those of

the AISI 1018 and 4130 steels because of the higher carbon content.

111

(a) Location 1 (b) Location 2

(c) Location 3 (d) Location 4

(e) Location 5 (f) Location 6

Figure 5.17: HAZ microstructure of 1018 steel (magnification 500×,condition A, 45◦ direction). Continued.

112

(g) Location 7 (h) Location 8

(i) Location 9 (j) Location 10

Figure 5.17: HAZ microstructure of 1018 steel (magnification 500×,condition A, 45◦ direction).

113





114




115





116




117

5.3 Experimental Validation of Model Predictions

5.3.1 Prediction of Transient Microstructure and Hardness

When both the temperature history and the transformation kinetics

to the particular thermal process are known, the transient microstructure

and hardness at a specific point in the HAZ can be predicted. To predict

the transient microstructure at each time step, the microstructure model was

coupled with the heat transfer model that provides the temperature history.

At a given time step, the volume fraction of a specific decomposition phase and

the hardness can be determined anywhere in the HAZ. Figures 5.20–5.22 show

the microstructure evolution in terms of the various austenite decomposition

products and the consequent hardness evolution with time at locations 1, 3,

and 5 defined in Figure 5.17, respectively, for AISI 1018 steel. Figures 5.23–

5.25 show the microstructure evolution and the consequent hardness evolution

for AISI 4130 steel. Figures 5.26–5.28 show the microstructure evolution and

the consequent hardness evolution for AISI 4140 steel. All these figures can

be compared qualitatively with the micrographs shown in Figures 5.17–5.19.

118

0 5 10 15 20 25 30 350

0.2

0.4

0.6

0.8

1

1.2

1.4

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ed P

hase

Fra

ctio

ns

FerritePearliteBainiteMartensiteAustenite

(a) Microstructure evolution

0 5 10 15 20 25 30 350

50

100

150

200

250

300

350

400

Time (s)

Pre

dict

ed H

ardn

ess

(VP

N)

(b) Hardness evolution

Figure 5.20: Microstructure evolution for 1018 steel at location 1(condition A).

119

0 5 10 15 20 25 30 350

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0.6

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123

0 10 20 30 40 50 600

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0 10 20 30 40 50 600

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5.3.2 Comparison of Predicted and Experimental Hardness

Figures 5.29–5.31 compare the predicted and measured HAZ hardness

in the 45 ◦ direction for the steels investigated under experimental condition

A. Only small differences are visible between the predicted and measured

hardness for AISI 1018. For AISI 4130 and 4140 steels, the predictions

of the microstructural model are in good agreement with the experimental

measurements for the grain growth zone and the recrystallized zone. However,

the microstructure model overestimates the HAZ hardness for the tempered

zone and the unaffected base metal.

The difference may be explained by a combination of three factors.

First, the simplified heat transfer model overestimates the peak temperatures

of the tempered zone and the unaffected base metal. Second, the mi-

crostructural model assumes instantaneous, homogeneous austenite formation.

Homogeneous austenite is assumed to form from pearlite colonies as the

temperature rises above A1, and the steel is assumed to be completely austenite

above A3. As a result of these reasons, the microstructural model predicted

the austenite formation in the tempered zone and the unaffected base metal,

which should not have occurred. Lastly, the microstructural model is poorly

predict the finish times for pearlite and bainite, and the effect of these poor

predictions on the predicted hardness tends to increase as the carbon content

of the base metal increases. In particular, the microstructure model performs

poorly in predicting the austenite decomposition to pearlite or bainite for the

chromium-molybdenum alloy steels, as shown in the TTT predictions of these

128

steels. In the microstructural model, the austenite formed in the tempered

zone and the unaffected base metal during heating does not decompose to

pearlite sufficiently, then the remaining austenite transforms to bainite and

martensite as the temperature decreases, resulting in an increase in hardness.

Figures 5.32–5.34 compare the predicted and measured HAZ hardness

in the 30 ◦ direction for the steels investigated under experimental condition A.

Because of the irregular shape of the HAZ in the direction, the comparisons in

Figures 5.32–5.34 are slightly different from those shown in Figures 5.29–5.31:

the change in direction from 45 ◦ to 30 ◦ increases the error in the predicted

HAZ hardness.

Figures 5.35–5.37 show the relationship between the HAZ hardness

measurements and the calculated peak temperatures in the 45 ◦ direction for

the steels investigated under experimental condition A. These figures show that

the HAZ hardness is approximately proportional to the peak temperature, but

is sensitive to the carbon content of the base metal.

129

0 0.2 0.4 0.6 0.8 1 1.2 1.4150

200

250

300

350

Distance from FZ (mm)

Har

dnes

s (V

PN

)

MeasurementsPredictions

Figure 5.29: HAZ hardness distribution for 1018 steel (condition A,45◦ direction).

130

0 0.2 0.4 0.6 0.8 1 1.2 1.40

100

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0 0.2 0.4 0.6 0.8 1 1.2 1.4900

1000

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C)


0 0.2 0.4 0.6 0.8 1 1.2 1.4190

200

210

220

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240

250

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dnes

s (V

PN

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Peak temperatureHardness

Figure 5.35: HAZ hardness and peak temperature as a function of distancefrom fusion zone for 1018 steel (condition A, 45◦ direction).

136

0 0.2 0.4 0.6 0.8 1 1.2 1.4900

1000

1100

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0 0.2 0.4 0.6 0.8 1 1.2 1.4800

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138

5.4 Conclusions

In this study, the microstructure evolution in the HAZ was predicted

by using the integrated system that is a combination of multiple physics-

based models and multiple measurements. The scope of the prediction and

the limitations of the microstructural model were discussed in the context of

the experimental results. The predicted TTT diagrams were used to evaluate

the kinetic equations of Kirkaldy et al., which are the fundamental equations

for modeling the microstructural evolution in the HAZ. The comparison of the

predicted and experimental TTT diagrams showed that the microstructure

model works well but has inherent limitations that arise from the model’s

assumptions. Apparent discrepancies between the predicted and experimental

TTT curves may be due to the use of a single nucleation and closure model

for all temperatures in the pearlite and bainite regime.

An adjustment factor that effectively modifies the transformation rate

in Kirkaldy’s kinetic equation was introduced to minimize the RMSE between

the predicted and experimental TTT curves. The adjustment factor was

different for each product of austenite decomposition and for each type of

steel. This finding seems to indicate that the use of an adjustment factor

may be of limited utility, and a better fundamental model for the kinetics of

austenite decomposition may be required.

Actual welds were produced, and the experimental microstructural data

on these welds were compared with the results predicted by the microstructural

model. The predicted final microstructure was qualitatively compared with

139

micrographs of the various sub-zones in the HAZ. The predicted hardness

was quantitatively compared with the measured hardness in the HAZ. Despite

the discrepancy between the experimental and predicted hardnesses in the

partially transformed zones and tempered zones of high alloy steels, the

comparison showed that both the microstructure and hardness are in good

agreement, indicating that the microstructural model can be used in real

applications.

140

Chapter 6

Future Work

6.1 A Reduced Order Model for 3D Heat Transfer andFluid Flow

A basic requirement for accurate prediction of the weld microstructure

is to accurately predict the weld temperature history. In this study, a simplified

3D FEM model for steady state heat transfer was used for the predictions

of the weld characteristics and temperature history. The comparison results

in Chapter 2 indicated that better predictions can be achieved by a more

comprehensive modeling of transport phenomena, which considers the mass

transfer into the base metal and fluid flow and phase change in the weld

pool. However, expensive calculations make it difficult to seek a real-time

control solution by this method because of highly complex and nonlinear

equations. A reduced order model for 3D heat transfer and fluid flow should

be developed to overcome this limitation. The Beaman research group has

developed the reduced order model for vacuum arc remelting (VAR) of metal

alloys [50–52]. Techniques for reduced order modeling of VAR process will be

applied to GMAW process. In reduced order modeling, PDEs are rendered

into a set of coupled nonlinear ODEs to design model-based controller and

estimator. The reduced order model would describe the steady state and

141

transient characteristics of GMAW process.

6.2 The Kinetics of Austenite Decomposition

The austenite decomposition equations of Kirkaldy et al. have been

shown to be effective in predicting the transformation products. However, a

further investigation of bainite kinetics may lead to better results, improving

the prediction of finish time in bainite regime. Bainite is a non-lamellar ferrite-

cementite product of austenite decomposition. Two major morphologies of

bainite microstructures are upper bainite and lower bainite in view of the two

temperature ranges. Upper bainite is dependent on the diffusion-controlled

portioning of carbon between ferrite and cementite. Lower bainite could

be formed by a diffusionless shear because iron diffusion is restricted at the

relatively low temperatures. The use of distinct kinetic equations for the upper

and lower bainite may be required in the microstructural model.

6.3 Physics-based Flexible Control

The ultimate goal of this project is to develop physics-based flexible

control of welding. In physics-based flexible control, multiple physics-based

models and multiple measurements of a welding process are incorporated

into a control system [7]. In this study, the integrated system is a multiple-

input multiple-output (MIMO) system and has three sub-processes that are

combined with intermediate variables, which naturally results in a multi-sensor

system. Figure 1.4 in Chapter 1 presents a way to integrate the physics-based

142

models and the multi-sensor system. Inputs and state variables of sub-process

1 are directly related to control variables, which act to produce the desired

heat and mass inputs to the base metal. The effects of initial inputs on final

outputs take several steps to realize as shown in Figure 1.4. These inputs

and state variables are subject to constraints, which are derived from the

physical limitations and safety requirements of the welding system. Moreover,

the research seeks the real-time control algorithm that can handle changes

in manufacturing requirements such as substitution of materials and differing

product geometry. In these respects, this controller design may require more

effort relative to conventional control approaches. The state estimator design

is also a challenging problem, further complicated when the state variables are

subject to constraints.

A basic idea in control is inversion. If we have desired weld properties

for the system output, it is necessary to invert the relationship between input

and output to determine what input action is necessary. Inversion can be

achieved conveniently by the use of feedback mechanisms. It is important

to note that the reduced order process model for real-time control purpose

is applied. A major part of the future work deals with the issue of how to

determine the best feedback signal, so that the reduced order inverse solution

is achieved in a reliable and optimal fashion under the conditions as presented.

Model-based predictive control (MPC) may be a good choice to fulfill the above

requirements for the following reasons [53, 54].

1. For linear and nonlinear systems with input and state constraints,

143

MPC can provide constraint handling capability by using mathematical

programming, such as quadratic programming and semi-definite pro-

gramming.

2. MPC presents good tracking performance by utilizing the future refer-

ence signal for a finite horizon. In PID control, which has been most

widely used in industrial applications, only the current reference signal

is used. The PID control might be too short-sighted for the tracking

performance and thus has a lower performance than MPC.

3. MPC needs only finite future system parameters for the computation of

the current control. It can be an appropriate strategy for known time-

varying systems. Since MPC is computed repeatedly, it can adapt to

changes of future system parameters that can be known later, not at the

current time.

The absolute computation time of the reduced order model and the

physics-based flexible control algorithm may be not be fast enough to be

used as a real-time application for GMAW process. The model-base filter

may also increase computational cost. This problem will be overcome by

developing a new tool that can provide high speed computation and data

acquisition. The Computer Science and Engineering Department is developing

faster computational tools in parallel with this research.

144

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152

Vita

Dongwoo Kim was born in Incheon, South Korea on 21 November 1971,

the son of Giyeol Kim and Bokrye Park. He received the Bachelor of Science

in Earth Science at the Korea Military Academy, Seoul, South Korea in March

1996 and became an officer of the Korean Army. He served in the Korean Army

for six years, participating in various military operations as a signal officer. He

entered the graduate program in Aerospace Engineering at National Defense

Academy, Yokosuka, Japan in April 2003 and received the Master of Science

in March 2005. He worked as a national defense technology manager for a few

years for the Defense Acquisition Program Administration of South Korea. He

entered the doctoral program in Mechanical Engineering at the University of

Texas at Austin in August 2007.

Permanent address: Hwangchungpoguro 211-33, Guha-1ri,Naega-Myeon, Ganghwa-GunIncheon-Si, South Korea 417-892

This dissertation was typeset with LATEX† by the author.

†LATEX is a document preparation system developed by Leslie Lamport as a specialversion of Donald Knuth’s TEX Program.

153

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