DTIC ADA585657: Stochastic Multiscale Modeling of Polycrystalline Materials

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STOCHASTIC MULTISCALE MODELING OF
POLYCRYSTALLINE MATERIALS
ADissertation
PresentedtotheFacultyoftheGraduateSchool
ofCornellUniversity
inPartialFulfillmentoftheRequirementsfortheDegreeof
DoctorofPhilosophy
by
BinWen
January2013
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Stochastic Multiscale Modeling of Polycrystalline Materials
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STOCHASTICMULTISCALEMODELINGOFPOLYCRYSTALLINE
MATERIALS
BinWen,Ph.D.
CornellUniversity2013
Mechanical properties of engineering materials are sensitive to the underly-
ing random microstructure. Quantification of mechanical property variabil-
ity induced by microstructure variation is essential for the prediction of ex-
treme properties and microstructure-sensitive design of materials. Recent ad-
vances in high throughput characterization of polycrystalline microstructures
have resulted in huge data sets of microstructural descriptors and image snap-
shots. Toutilizetheselargescaleexperimentaldataforcomputingtheresulting
variability of macroscopic properties, appropriate mathematical representation
of microstructures is needed. By exploring the space containing all admissi-
ble microstructures that are statistically similar to the available data, one can
estimate the distribution/envelope of possible properties by employing effi-
cient stochastic simulation methodologies along with robust physics-based de-
terministic simulators. The focus of this thesis is on the construction of low-
dimensional representations of random microstructures and the development
of efficient physics-based simulators for polycrystalline materials. By adopt-
ing appropriate stochastic methods, such as Monte Carlo and Adaptive Sparse
GridCollocationmethods,thevariabilityofmicrostructure-sensitiveproperties
ofpolycrystallinematerialsisinvestigated.
Theprimaryoutcomesofthisthesisinclude:
•
Developmentofdata-drivenreduced-orderrepresentationsofmicrostruc-
turevariationstoconstructtheadmissiblespaceofrandompolycrystalline
microstructures.
•
Development of accurate and efficient physics-based simulators for the
estimationofmaterialpropertiesbasedonmesoscalemicrostructures.
•
Investigating property variability of polycrystalline materials using effi-
cient stochastic simulation methods in combination with the above two
developments.
Theuncertaintyquantificationframeworkdevelopedinthisworkintegrates
informationscienceandmaterialsscience,andprovidesanewoutlooktomulti-
scale materials modeling accounting for microstructure and process uncertain-
ties. Predictive materials modeling will accelerate the development of new ma-
terialsandprocessesforcriticalapplicationsinindustry.
BIOGRAPHICALSKETCH
The author was born in the city of Shenyang, Liaoning Province, China, in
November, 1983. After completing his high school education from Shenyang
No. 120 Middle School, the author was admitted into the department of Aero-
nautical Science and Engineering at Beijing University of Aeronautics and As-
tronautics (BUAA) in 2002, from where he received his Bachelor’s degree in
June, 2006, and the Master’s degree in June, 2008. In August 2008, the author
enteredthedoctoralprogramattheSibleySchoolofMechanicalandAerospace
Engineering, Cornell University, and was awarded another Master’s degree in
January2011.
iii
ThisthesisisdedicatedtomyparentsGuipuWenandXiaojieAnfortheir
constantsupportandencouragementtowardsacademicpursuitsduringmy
schoolyears.
iv
ACKNOWLEDGEMENTS
I would like to express my most sincere gratitude to my advisor, Professor
Nicholas Zabaras, for his constant support, motivation and guidance over the
lastfouryears. Hisinvaluablehelpandcarecovernotonlytheacademicwork,
but also the life beyond lab. I would also like to thank Professors Christopher
Earls and Derek Warner for serving on my special committee and for their en-
couragementandsuggestionsduringthecourseofthiswork. Theirkindlyhelps
areprecioustome.
This research was supported by the Computational Mathematics program
of AFOSR (grant F49620-00-1-0373), the Materials Design and Surface Engi-
neering program of the NSF (award CMMI-0757824), the Mechanical Behav-
ior of Materials program Army Research Office (proposal to Cornell University
No. W911NF0710519),theComputationalMathematicsprogramofNSF(award
DMS- 0809062) and an OSD/AFOSR MURI09 award to Cornell University on
uncertainty quantification. This research used resources of the National En-
ergy Research Scientific Computing Center, supported by the Office of Science
of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.
Additional computing resources were provided by the NSF through TeraGrid
resources provided by NCSA under grant number TG-DMS090007. I would
like to thank the Sibley School of Mechanical and Aerospace Engineering for
having supported me through a teaching assistantship for part of my study at
Cornell. The computing codes were developed based on open source scientific
computation libraries including PETSc, GSL, and FFTW. The academic license
that allowed for these developments is appreciated. Finally, I would like to
thank fellow MPDC members and other friends for their support during my
daysatCornell.
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TABLEOFCONTENTS
BiographicalSketch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
TableofContents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
ListofTables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii
ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
1 INTRODUCTION 1
2 UNCERTAINTY QUANTIFICATION AT A SINGLE MATERIAL
POINT 11
2.1 Investigating mechanical response variability of single-phase
polycrystallinemicrostructures . . . . . . . . . . . . . . . . . . . . 12
2.1.1 Modelreductiontheory . . . . . . . . . . . . . . . . . . . . 12
2.1.2 Microstructurerepresentationandreconstructionmethod-
ology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.1.3 Texturemodeling . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1.4 Sparsegridcollocation . . . . . . . . . . . . . . . . . . . . . 30
2.1.5 Deterministicsolver . . . . . . . . . . . . . . . . . . . . . . 32
2.1.6 Numericalexamples . . . . . . . . . . . . . . . . . . . . . . 34
2.1.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
2.2 Investigating variability of fatigue indicator parameters of two-
phasenickel-basedsuperalloymicrostructures . . . . . . . . . . . 50
2.2.1 Constructionofmicrostructurestochasticinputmodel . . 50
2.2.2 Polynomial chaos expansion of stochastic reduced-order
model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
2.2.3 Thepre-imageprobleminKPCA . . . . . . . . . . . . . . . 63
2.2.4 Two-phasecrystalplasticityconstitutivemodel . . . . . . 66
2.2.5 Numericalexamples . . . . . . . . . . . . . . . . . . . . . . 72
2.2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3 UNCERTAINTY QUANTIFICATION OF MULTISCALE DEFORMA-
TIONPROCESS 104
3.1 Microstructurerepresentation . . . . . . . . . . . . . . . . . . . . . 105
3.2 Bi-orthogonalKarhunen-Loe`vedecomposition . . . . . . . . . . . 107
3.3 Themultiscaledeterministicsolverandinputdataset . . . . . . . 113
3.3.1 Themultiscaledeterministicsolver . . . . . . . . . . . . . . 114
3.3.2 Initialsamplegeneration . . . . . . . . . . . . . . . . . . . 116
3.4 Numericalexamples . . . . . . . . . . . . . . . . . . . . . . . . . . 120
3.4.1 Constructionandvalidationofthereduced-ordermodel . 121
3.4.2 Stochasticmultiscaleforgingsimulation . . . . . . . . . . . 127
3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
vi
4 AN EFFICIENT IMAGE-BASED METHOD FOR MODELING THE
ELASTO-VISCOPLASTIC BEHAVIOR OF REALISTIC POLYCRYS-
TALLINEMICROSTRUCTURES 136
4.1 Crystalelasto-viscoplasticfastFouriertransformsimulator . . . . 137
4.1.1 Solutionofcrystalelasticboundaryvalueproblems . . . . 138
4.1.2 Solutionofcrystalvisco-plasticboundaryvalueproblems 142
4.1.3 Solution of crystal elasto-viscoplastic boundary value
problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4.1.4 CEPFFTalgorithm . . . . . . . . . . . . . . . . . . . . . . . 146
4.1.5 Anintegratedformulation . . . . . . . . . . . . . . . . . . . 148
4.2 Microstructuremodel . . . . . . . . . . . . . . . . . . . . . . . . . . 150
4.2.1 Discretization . . . . . . . . . . . . . . . . . . . . . . . . . . 151
4.2.2 Gridandtextureupdate . . . . . . . . . . . . . . . . . . . . 153
4.3 Numericalexamples . . . . . . . . . . . . . . . . . . . . . . . . . . 157
4.3.1 Basic formulation versus the augmented Lagrangian for-
mulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
4.3.2 Crystal elasto-viscoplastic FFT simulations for polycrys-
tallinemicrostructures . . . . . . . . . . . . . . . . . . . . . 163
4.3.3 InvestigationoffatigueindicatorparametersofIN100 . . 173
4.3.4 Computationalefficiency . . . . . . . . . . . . . . . . . . . 179
4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
5 CONCLUSIONANDSUGGESTIONSFORFUTURERESEARCH 184
5.1 Multiscalemodelingofsuperalloysystems . . . . . . . . . . . . . 185
5.2 Uncertainty quantification with realistic polycrystalline mi-
crostructures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
5.3 Advanced methodologies for uncertainty analysis, property pre-
dictionandmaterialdesign . . . . . . . . . . . . . . . . . . . . . . 188
Bibliography 190
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