oof and beyond: 2d plasticity and 3d microstructure-based modeling · 2020. 9. 10. · oof and...

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: nchawla@asu.eduwww.eas.asu.edu/~cme/cme-faculty/chawla