OOF And Beyond: 2D Plasticity and 3D Microstructure-based Modeling
A. Ayyar1 and N. Chawla2
1Department of Mechanical and Aerospace Engineering2School of Materials
Fulton School of EngineeringArizona State University
Tempe, AZ 85287-6006 USA
OOF Workshop - June, 200111:00 Myriad Uses Craig Carter, M.I.T. 11:30 Discussion 11:45 3-D Meshing
Panos Charalambides, Univ. of Maryland Baltimore County 12:15 Discussion 12:30 - 13:45 Lunch - NIST cafeteria Thursday Afternoon - PROJECT SESSION A session for OOF users and potential users, discussing what they have done and/or what they would like to do. 13:45 OOF Research at Ford Research Lab
Alex Bogicevic, Ford Research Lab 14:00 Thermal Conductivity Simulations for TBC'sJim Ruud, GE CRD 14:20 Microstructure-Properties Correlation for Thermal Spray TBC's
Matthias Oechsner, Siemens Westinghouse Power Corporation 14:30 Overview of OOF Research at ORNL
Chun-Hway Hsueh, Oak Ridge Nat'l Lab 14:40 Discussion 15:00 OOF Research in Polymers
Martin Chiang, Polymers, NIST 15:15 Piezoelectricity and Beyond
Edwin Garcia, M.I.T. 15:35 OIM-2-OOF code
Venkata Vedula, Sandia National Labs 15:45 Discussion 15:55 Break 16:10 Residual Stresses in Ceramics
Yi Fang, Univ. of Houston 16:25 Microcracking in Alumina/Aluminum Titanate
Susan Galal Yousef, TU-Darmstadt 16:35 16:35 ThermomechanicalThermomechanical stresses in composites stresses in composites
NikNik Chawla, Arizona State Univ. Chawla, Arizona State Univ. 16:50 Marcelling Effects on Layered Composite Deformation
Venkata Vedula, UTRC 16:55 Discussion 17:10 Zebulon: Object-Oriented, Finite Element Software for Material
Behavior Development, Alan C. Mueller, Northwest Numerics, Inc. 17:20 Elle: Microstructure Modelling of Geological Materials
Lynn Evans, Monash University 17:25 Thermal Degradation of Marble
Thomas Weiss, Georg August Universität17:45 Discussion 18:00 to Dinner
Modeling efforts at ASU
2D ModelingElasticOOF
OOF in Education
2D ModelingElastic-plastic
ABAQUS2D Crack growth modeling
ElasticFRANC2D/L
3D VisualizationSerial Sectioning
ImageJ, RasterVect, SurfDriver, Mimics
3D ModelingElastic-plastic
ABAQUS
3D Crack growth modelingElastic
FRANC3D
Modeling at multi-length scales
0 20 40 60 80 100 120
0
20
40
60disp = 16.7950
µm50 µm
Microstructure-based Modeling
Continuum-based Modeling
Dislocation-based Modeling
Atomistic Modeling
Decreasing Length scale
Microstructure of extruded particle reinforced aluminum
2080/SiC/10pF(600)
2080/SiC/20pF(600)
2080/SiC/30pF(600)
LongitudinalTransverse
Short Transverse
Extrusion Axis
100 µm 100 µm
Applications of MMCs
Cylinder Liners
N. Chawla and K.K. Chawla, Metal Matrix Composites, (2006), Springer.
MMC replaced gr/epoxy FEGV in PW 4XXX engines
Power conductors
MMC Spikes for Track and Field Cleats
Approaches to numerical modeling of composites
Courtesy of A. Drake, St. Gobain Corp.
2D Microstructure Model
3D Microstructure Model
MicrostructureConventional
approach
2D Unit Cell Model
3D Unit Cell Model
Microstructure-based approach
Modeling the effect of second phase morphology on Young’s Modulus Esphere,L = 1.00
Eneedle,L = 1.01
Esphere,T = 1.00
Eneedle,T = 1.02Chawla et al., J. Mater. Sci. – Mater. Elect., (2004).
10 µm
450 MPa
0 MPa
-20 MPa
2D Microstructure-based finite element analysisElastic analysis
Ux = 0 Ux = 0.2% Strain
Y
X
σx
Chawla et al., Mater. Charac., (2003).
Stresses are inherently based on local microstructure characteristics – Elastic analysis
Particle free region,82 MPa
Clustered region,120 MPa
50 µm50 µm
300 MPa
-20 MPaσxx (0.1% applied strain)
0
50
100
150
200
250
0 5 10 15 20Position ( m)µ
Matrix
Matrix
Particle
Chawla et al., Mater. Charac., (2003).
2D Microstructure-based modeling Results of tensile anisotropy
Microstructure based FEA was able to predict anisotropy in normalized Young’s modulus
1.1
1.2
1.3
1.4
1.5
10 15 20 25 30
Nor
mal
ized
You
ng’s
Mod
ulus
Ec/E
m(G
Pa)
Volume Percentage of SiC
Longitudinal
Transverse
Thermal stress distribution200 MPa
-200 MPa
50 µm 50 µm
10 vol.% SiC 30 vol.% SiC
Chawla et al., Mater. Charac., (2003).
with increasing SiCvolume fraction
50 µm
F280with decreasing SiC
particle size
50 µm
F1000
100 MPa
-100 MPa
Particle reinforced metal matrix composites
100 µm Extrusion Axis
Ganesh and Chawla, Metall. Mater. Trans. (2004)
2080/SiC/10p
Elastic regime
microplasticity
Maximum work hardening rate
global plasticityComposite fracture
Stre
ss
Strain
σpl, onset of damage
N. Chawla, C. Andres, J.W. Jones, J.E. Allison, Metall. Mater. Trans. (1998)
0
100
200
300
400
500
600
700
0 0.01 0.02 0.03 0.04 0.05
True
Stre
ss (M
Pa)
True Strain
30%20%
10%
0%
2080 Al/SiCp-T8
Variation of clustering in Al/SiC/15p
A. Ayyar and N. Chawla, Comp. Sci. Tech., 66 (2006) Processing by R. J. Fields, NIST
• Clustering was controlled by processing composites with varying Al:SiC particle size ratio
– Blended, pressed and sintered
• Increasing the Al:SiC particle size ratio resulted in a greater degree of SiC clustering
Clustered distributionHomogenous distribution
20 µm
Ratio = 6.6mDAl µ3350 = mDSiC µ550 =mDAl µ750 =
20 µm
mDSiC µ550 =Ratio = 1.4
Incorporating actual microstructure into FEM
Segmented Image
Original SEM Image
Vector Image
100 µm
100 µm
100 µm10 µm
Meshed Microstructure
SiC Particle Al Alloy 2080-T6
100 µm
ImageJ
RasterVect
Abaqus, HyperMesh
Effect of SiC particle clustering on local strain stateElastic – plastic analysis
Ratio = 1.4, COV = 0.38 Ratio = 6.6, COV = 0.61
Ux = 0 Ux = 0
Need for 3D modeling
Courtesy of A. Drake, St. Gobain Corp.
2D Microstructure Model
3D Microstructure Model
Microstructure Microstructure-based approach
2D analysis is either plane stress or plane strain
SiC particles have complex geometry
SiC particles modeled as “discs”in 2D analysis
Serial sectioning concept
Two-dimensional (2D) in plane viewof the object Stack of series of 2D images with a
given distance between the images
Reconstruction of 3Dmodel from series of2D images
3D Object
Serial sectioning process flow chart
N. Chawla, V.V. Ganesh, B. Wunsch, Scripta Mater. (2004).
Material preparation
Indentation offiducial marks
Polishing
Imaging
Imagesegmentation
3D Reconstruction3D Visualizationof SiC particles
3D Microstructureof the composite
Extrusion axis.
Extrusion axis
Sample
Serial sectioning process – Region of interest
Region of interest
Vickers indentations (fiducial marks)
Al matrix
SiC particles
50 µm
1 µm between sections
3D reconstruction and visualization
2D serial sections stacked on top of each other
Contour added around the particle in each sections
A surfacing process connects the contours to generate 3D object
12
34
5
6
7
8
9
3D Object
Wire frame view Full texture view
3D Microstructure visualization - 2080/SiC/20p
10 µm
Incorporating 3D model into FEM analysis
•The particles are imported into HyperMesh® and the matrix geometry is created. •The model is then meshed and exported to ABAQUS for analysis
21 µm65 µm
55 µ
m
70 Particles Meshed Model
10 node Tetrahedral elements
Effect of model size (Thickness)
40 µm 3 µm
30 µ
m
55 µ
m
20 µm65 µm
40 µ
m
40 µm40 µm
3 µm Model 20 µm Model
40 µm Model0.19410SiC
0.3374Al
Poisson’s RatioElastic Modulus (GPa)Material
Ux = 0
Loading Axis
VY = 0
Strain Strain
Stre
ss
Stre
ss
SiCAl 2080
Effect of model size
0
100
200
300
400
500
600
0 0.005 0.01 0.015 0.02
0 15 30 45400
420
440
460
480
500
107.840 µm
107.520 µm
1073 µm
E (GPa)Model3 µm Model
40 µm Model
20 µm Model
Stre
ss (M
Pa)
Strain (mm/mm)
0.2%
YS
(MP
a)
Model Thickness (µm)
20 µm model was chosen as the representative volume
Microstructure variability
65 µm 20 µm
55 µ
m
70 µm 20 µm
60 µ
m
Region 1 Region 2
Simulation was carried out on two models created from different regions to validate the approach
Microstructure variability
0
100
200
300
400
500
600
0 0.005 0.01 0.015 0.02
Strain (mm/mm)
107.5Region 2
107Region 1
E (GPa)Model
Region 1
Region 2
Effect of simplifying particle geometry
N. Chawla, R.S. Sidhu, and V.V. Ganesh, Acta Mater., (2006).N. Chawla and K.K. Chawla, J. Mater. Sci. – 40th Ann. (1966-2006), (2006).
EllipsoidsMicrostructure
89128
87323
No. of Elements
253D Ellipsoidal
HoursModel
263D Microstructure
Comparison of microstructure-based model with conventional models and experiment
0
100
200
300
400
500
600
0 0.005 0.01 0.015 0.02
Strain (mm/mm)
Stre
ss (M
Pa)
Microstructure
Experiment Spherical
Ellipsoidal
N. Chawla, R.S. Sidhu, and V.V. Ganesh, Acta Mater., (2006).N. Chawla and K.K. Chawla, J. Mater. Sci. – 40th Ann. (1966-2006), (2006).
http://neutrons.ornl.gov/
Experimental verification of internal strain/stress by neutron diffraction
Monochrometer: 1.452, 1.731, 1.886, 2.275 Å
Detector Angel: 30-150o
Detection System: 7 Position-Sensitive Detectors
Detector Resolution: 1.8 mm
Measurement of internal strains during tensile test
Incident CollimatorDetector
Tensile Sample
Neutron Diffraction for Longitudinal Internal Strain Measurement
Diffraction Peak: Al (311), SiC (116)
Monochrometer: 1.729567 Å
Gauge Volume: 5×5×5 mm
Displacement Control Rate: 0.0005 mm/s
Displacement Step Size: 0.02 mm
Diffraction Acquisition Time: Al-8 minutes, SiC-4 minutes
Incident beam
Al (331)
SiC (116)
0
100
200
300
400
500
0 0.01 0.02 0.03 0.04 0.05
Global Strain
Global Stress-Strain Curve
Internal Stress
Pure 2080 Al
0
200
400
600
800
1000
1200
1400
0 0.01 0.02 0.03 0.04 0.05
Global Strain
Global Stress-Strain Curve
SiC Internal Stress
Al Matrix Internal Stress
2080Al-20vol.% SiC
0
200
400
600
800
1000
1200
1400
0 0.005 0.01 0.015 0.02 0.025 0.03
Global Strain
Global Stress-Strain Curve
SiC Internal Stress
Al Internal Stress
2080Al-30 vol.% SiC
Comparison of global stress and internal stress during tensile testing
Internal stress of Al matrix and SiCparticle was measured by neutron diffraction.
Strains were calculated by changes in lattice spacing during tensile testing.
0
200
400
600
800
1000
1200
1400
0 0.01 0.02 0.03 0.04 0.05
Global Strain
Global Stress-Strain Curve
SiC Internal Stress
Al Matrix Internal Stress
2080Al-20vol.% SiC FEM
FEM
FEM
Comparison of microstructure-based FEM predictions of stress/strain partitioning with neutron diffraction measurements
• FRANC2D/L* was used to model crack growth• Crack path was not known in advance, hence re-meshing method
was used• Fracture calculations using Linear Elastic Fracture Mechanics (LEFM)
principles– Stress Intensity Factors that govern the fracture process were calculated
using Modified crack closure method– Max. Circumferential Tensile Stress theory was used to determine the
crack propagation direction
*Mark James and Daniel Swenson, (1998), http://www.mne.ksu.edu/~franc2d/
Modeling crack growth in particle reinforced composites
50 µm
Al/SiCp system
Aluminum alloy
Silicon Carbide particles
Numerical model description
σ
0v =y0=xu
Al Alloy 2080-T6E=74GPaν=0.330
SiC ParticleE=410GPa ν=0.190
“Average” Composite2080/SiC/15p – T6E=98GPa ν=0.309
• Plane stress
• Elements = 18,000; Nodes = 47,000
20µm
Embedded cell
A. Ayyar and N. Chawla, Comp. Sci. Tech., 66 (2006)
20 µm
Ratio = 6.6mDAl µ3350 = mDSiC µ550 =
Simulated crack paths in models with clustered particle distribution
Crack growth direction
A. Ayyar and N. Chawla, Comp. Sci. Tech., 66 (2006)
Embedded cells
Fatigue crack growth mechanisms at Low/High R-RatioBefore Crack Growth After Crack Growth
R = 0.8
20 µm 20 µmCrack growth is observed through the SiC particles.
Before Crack Growth After Crack Growth
R = 0.1
20 µm 20 µmCrack growth is observed around the SiC particles.
Ganesh and Chawla, (2004)
Motivation for modeling reinforcement particle fracture• Reinforcement particles do not posses infinite strength.• Regions around a crack-tip are at a high stress state. How does this
high stress influence the load bearing capabilities of the particle?• When particles fracture, how do they influence the crack path and the
crack-tip driving force?
SiC ParticleNon-linear interface
10 µmAl Alloy
Particle fracture
Normal displacement (units)
Nor
mal
stre
ss (M
Pa)
20µm
Crack propagation with particle fractureCrack growth direction
20µm
No particle fracture
Particles have fractured
9650
1250
1100
950
800
600
450
300
150
1
0.3
MPa
Von Mises stress contours at applied stress of 48 MPa
Particle is stillbearing load
Particle has fractured
Von Mises stress contours for varying loads
20µm
Crack growth direction
Applied stress of 48 MPa
Applied stress of 7 MPa
Applied stress of 14 MPa
20µm
20µm
No particle fracture
Particles have fractured
9650
1250
1100
950
800
600
450
300
150
1
0.3
MPa
Influence of particle fracture on crack trajectory
Crack growth direction
Fractured particles attract the crack
Particles deflect the crack Applied stress of 7 MPa
Applied stress of 48 MPa
5 µm
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
1.10
0 20 40 60 80 100 120
Projected crack length, a (µm)
Normalized SIF vs. crack length
)()(
cpkAlSiCk
I
I
Crack growth direction
Shielding
Anti-shielding
Particle fracture influences the crack-tip driving force
Applied stressof 7 MPa
Applied stress of 48 MPa
10 µm
10 µm
Applied stress of 14 MPa
0.70
0.75
0.80
0.85
0.90
0.95
1.00
1.05
1.10
70 75 80 85 90
No particle fracture
Shielding
Anti-shielding
Ongoing research
• Modeling particle (SiC) fracture in 3D models• Clustering analysis in 3D• Modeling crack growth in 3D
http://www.cfg.cornell.edu/index.htm
Acknowledgments
• Postdocs: X. Deng (Kennametal) and J.J. Williams
• Graduate Students: R. Saha, B. Wunsch (MIT), and V.V. Ganesh (Intel)
• Office of Naval Research (ONR)– N00014-01-1-0694 (Program Manager: A.K. Vasudevan)
• High Temperature Materials Laboratory User Program (ORNL)
• M. James and D. Swenson, "FRANC2D/L: A Crack Propagation Simulator for Plane Layered Structures," available from http://www.mne.ksu.edu/~franc2d/.
E-mail: [email protected]/~cme/cme-faculty/chawla
