Microstructure-Sensitive Uncertainty Quantification for Crystal Plasticity Finite Element Constitutive Models Using Stochastic Collocation Methods

Tran, Anh; Wildey, Tim; Lim, Hojun

doi:10.3389/fmats.2022.915254

Microstructure-Sensitive Uncertainty Quantification for Crystal Plasticity Finite Element Constitutive Models Using Stochastic Collocation Methods

Journal Article · Tue Sep 27 00:00:00 EDT 2022 · Frontiers in Materials

DOI:https://doi.org/10.3389/fmats.2022.915254· OSTI ID:1894600

Tran, Anh ^[1]; Wildey, Tim ^[1]; Lim, Hojun ^[1]

Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Uncertainty quantification (UQ) plays a major role in verification and validation for computational engineering models and simulations, and establishes trust in the predictive capability of computational models. In the materials science and engineering context, where the process-structure-property-performance linkage is well known to be the only road mapping from manufacturing to engineering performance, numerous integrated computational materials engineering (ICME) models have been developed across a wide spectrum of length-scales and time-scales to relieve the burden of resource-intensive experiments. Within the structure-property linkage, crystal plasticity finite element method (CPFEM) models have been widely used since they are one of a few ICME toolboxes that allows numerical predictions, providing the bridge from microstructure to materials properties and performances. Several constitutive models have been proposed in the last few decades to capture the mechanics and plasticity behavior of materials. While some UQ studies have been performed, the robustness and uncertainty of these constitutive models have not been rigorously established. In this work, we apply a stochastic collocation (SC) method, which is mathematically rigorous and has been widely used in the field of UQ, to quantify the uncertainty of three most commonly used constitutive models in CPFEM, namely phenomenological models (with and without twinning), and dislocation-density-based constitutive models, for three different types of crystal structures, namely face-centered cubic (fcc) copper (Cu), body-centered cubic (bcc) tungsten (W), and hexagonal close packing (hcp) magnesium (Mg). Our numerical results not only quantify the uncertainty of these constitutive models in stress-strain curve, but also analyze the global sensitivity of the underlying constitutive parameters with respect to the initial yield behavior, which may be helpful for robust constitutive model calibration works in the future.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003525

OSTI ID:: 1894600

Report Number(s):: SAND2022-8086J; 707350

Journal Information:: Frontiers in Materials, Journal Name: Frontiers in Materials Vol. 9; ISSN 2296-8016

Publisher:: Frontiers Research FoundationCopyright Statement

Country of Publication:: United States

Language:: English

References (62)

Linking atomistic, kinetic Monte Carlo and crystal plasticity simulations of single-crystal tungsten strength: Linking atomistic, kinetic Monte Carlo and crystal plasticity simulations of single-crystal tungsten strength Cereceda, David; Diehl, Martin; Roters, Franz GAMM-Mitteilungen, Vol. 38, Issue 2 https://doi.org/10.1002/gamm.201510012	journal	September 2015
Explicit Cost Bounds of Algorithms for Multivariate Tensor Product Problems Wasilkowski, G. W.; Wozniakowski, H. Journal of Complexity, Vol. 11, Issue 1 https://doi.org/10.1006/jcom.1995.1001	journal	March 1995
The Curse of Dimension and a Universal Method For Numerical Integration Novak, Erich; Ritter, Klaus Multivariate Approximation and Splines https://doi.org/10.1007/978-3-0348-8871-4_15	book	January 1997
aphBO-2GP-3B: a budgeted asynchronous parallel multi-acquisition functions for constrained Bayesian optimization on high-performing computing architecture Tran, Anh; Eldred, Mike; Wildey, Tim Structural and Multidisciplinary Optimization, Vol. 65, Issue 4 https://doi.org/10.1007/s00158-021-03102-y	journal	April 2022
Convergence of quasi-optimal sparse-grid approximation of Hilbert-space-valued functions: application to random elliptic PDEs Nobile, F.; Tamellini, L.; Tempone, R. Numerische Mathematik, Vol. 134, Issue 2 https://doi.org/10.1007/s00211-015-0773-y	journal	October 2015
High dimensional integration of smooth functions over cubes Novak, Erich; Ritter, Klaus Numerische Mathematik, Vol. 75, Issue 1 https://doi.org/10.1007/s002110050231	journal	November 1996
Simple Cubature Formulas with High Polynomial Exactness Novak, Erich; Ritter, Klaus Constructive Approximation, Vol. 15, Issue 4 https://doi.org/10.1007/s003659900119	journal	October 1999
DIC Challenge: Developing Images and Guidelines for Evaluating Accuracy and Resolution of 2D Analyses Reu, P. L.; Toussaint, E.; Jones, E. Experimental Mechanics, Vol. 58, Issue 7 https://doi.org/10.1007/s11340-017-0349-0	journal	December 2017
Quantifying the Uncertainty of Critical Resolved Shear Stress Values Derived from Nano-Indentation in Hexagonal Ti Alloys Zhao, Z.; Ruiz, M. R.; Lu, J. Experimental Mechanics, Vol. 62, Issue 5 https://doi.org/10.1007/s11340-021-00813-7	journal	January 2022
Simulation-assisted materials design for the concurrent design of materials and products McDowell, David L. JOM, Vol. 59, Issue 9 https://doi.org/10.1007/s11837-007-0111-7	journal	September 2007
Vision for Data and Informatics in the Future Materials Innovation Ecosystem Kalidindi, Surya R.; Medford, Andrew J.; McDowell, David L. JOM, Vol. 68, Issue 8 https://doi.org/10.1007/s11837-016-2036-5	journal	August 2016
Identifying Structure–Property Relationships Through DREAM.3D Representative Volume Elements and DAMASK Crystal Plasticity Simulations: An Integrated Computational Materials Engineering Approach Diehl, Martin; Groeber, Michael; Haase, Christian JOM, Vol. 69, Issue 5 https://doi.org/10.1007/s11837-017-2303-0	journal	March 2017
Gaussian-Process-Driven Adaptive Sampling for Reduced-Order Modeling of Texture Effects in Polycrystalline Alpha-Ti Tallman, Aaron E.; Stopka, Krzysztof S.; Swiler, Laura P. JOM, Vol. 71, Issue 8 https://doi.org/10.1007/s11837-019-03553-1	journal	June 2019
Parametrically Homogenized Constitutive Models (PHCMs) for Multi-scale Predictions of Fatigue Crack Nucleation in Titanium Alloys Ozturk, Deniz; Kotha, Shravan; Pilchak, Adam L. JOM, Vol. 71, Issue 8 https://doi.org/10.1007/s11837-019-03554-0	journal	June 2019
Machine Learning-Aided Parametrically Homogenized Crystal Plasticity Model (PHCPM) for Single Crystal Ni-Based Superalloys Weber, George; Pinz, Maxwell; Ghosh, Somnath JOM, Vol. 72, Issue 12 https://doi.org/10.1007/s11837-020-04344-9	journal	September 2020
Solving Stochastic Inverse Problems for Property–Structure Linkages Using Data-Consistent Inversion and Machine Learning Tran, Anh; Wildey, Tim JOM, Vol. 73, Issue 1 https://doi.org/10.1007/s11837-020-04432-w	journal	November 2020
Application-Specific Computational Materials Design via Multiscale Modeling and the Inductive Design Exploration Method (IDEM) Ellis, Brett D.; McDowell, David L. Integrating Materials and Manufacturing Innovation, Vol. 6, Issue 1 https://doi.org/10.1007/s40192-017-0086-3	journal	March 2017
Uncertainty Quantification and Propagation in Computational Materials Science and Simulation-Assisted Materials Design Honarmandi, Pejman; Arróyave, Raymundo Integrating Materials and Manufacturing Innovation, Vol. 9, Issue 1 https://doi.org/10.1007/s40192-020-00168-2	journal	January 2020
Uncertainty Quantified Parametrically Homogenized Constitutive Models for Microstructure-Integrated Structural Simulations Kotha, Shravan; Ozturk, Deniz; Smarslok, Benjamin Integrating Materials and Manufacturing Innovation, Vol. 9, Issue 4 https://doi.org/10.1007/s40192-020-00187-z	journal	September 2020
Kinetics of flow and strain-hardening Mecking, H.; Kocks, U. F. Acta Metallurgica, Vol. 29, Issue 11 https://doi.org/10.1016/0001-6160(81)90112-7	journal	November 1981
Validating a polycrystal model for the elastoplastic response of magnesium alloy AZ31 using in situ neutron diffraction Agnew, S.; Brown, D.; Tome, C. Acta Materialia, Vol. 54, Issue 18 https://doi.org/10.1016/j.actamat.2006.06.020	journal	October 2006
Atomistically informed crystal plasticity model for body-centered cubic iron Koester, Aenne; Ma, Anxin; Hartmaier, Alexander Acta Materialia, Vol. 60, Issue 9 https://doi.org/10.1016/j.actamat.2012.03.053	journal	May 2012
In situ observation of collective grain-scale mechanics in Mg and Mg–rare earth alloys Wang, F.; Sandlöbes, S.; Diehl, M. Acta Materialia, Vol. 80 https://doi.org/10.1016/j.actamat.2014.07.048	journal	November 2014
Key computational modeling issues in Integrated Computational Materials Engineering Panchal, Jitesh H.; Kalidindi, Surya R.; McDowell, David L. Computer-Aided Design, Vol. 45, Issue 1 https://doi.org/10.1016/j.cad.2012.06.006	journal	January 2013
pBO-2GP-3B: A batch parallel known/unknown constrained Bayesian optimization with feasibility classification and its applications in computational fluid dynamics Tran, Anh; Sun, Jing; Furlan, John M. Computer Methods in Applied Mechanics and Engineering, Vol. 347 https://doi.org/10.1016/j.cma.2018.12.033	journal	April 2019
Uncertainty propagation in reduced order models based on crystal plasticity Tallman, Aaron E.; Swiler, Laura P.; Wang, Yan Computer Methods in Applied Mechanics and Engineering, Vol. 365 https://doi.org/10.1016/j.cma.2020.113009	journal	June 2020
DAMASK – The Düsseldorf Advanced Material Simulation Kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale Roters, F.; Diehl, M.; Shanthraj, P. Computational Materials Science, Vol. 158 https://doi.org/10.1016/j.commatsci.2018.04.030	journal	February 2019
Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index Saltelli, Andrea; Annoni, Paola; Azzini, Ivano Computer Physics Communications, Vol. 181, Issue 2 https://doi.org/10.1016/j.cpc.2009.09.018	journal	February 2010
A dataset of synthetic hexagonal close packed 3D polycrystalline microstructures, grain-wise microstructural descriptors and grain averaged stress fields under uniaxial tensile deformation for two sets of constitutive parameters Mangal, Ankita; Holm, Elizabeth A. Data in Brief, Vol. 21 https://doi.org/10.1016/j.dib.2018.10.172	journal	December 2018
Thermally-activated non-Schmid glide of screw dislocations in W using atomistically-informed kinetic Monte Carlo simulations Stukowski, Alexander; Cereceda, David; Swinburne, Thomas D. International Journal of Plasticity, Vol. 65 https://doi.org/10.1016/j.ijplas.2014.08.015	journal	February 2015
Unraveling the temperature dependence of the yield strength in single-crystal tungsten using atomistically-informed crystal plasticity calculations Cereceda, David; Diehl, Martin; Roters, Franz International Journal of Plasticity, Vol. 78 https://doi.org/10.1016/j.ijplas.2015.09.002	journal	March 2016
Parametrically homogenized constitutive models (PHCMs) from micromechanical crystal plasticity FE simulations: Part II: Thermo-elasto-plastic model with experimental validation for titanium alloys Kotha, Shravan; Ozturk, Deniz; Ghosh, Somnath International Journal of Plasticity, Vol. 120 https://doi.org/10.1016/j.ijplas.2019.05.007	journal	September 2019
Parametrically homogenized constitutive models (PHCMs) from micromechanical crystal plasticity FE simulations, part I: Sensitivity analysis and parameter identification for Titanium alloys Kotha, Shravan; Ozturk, Deniz; Ghosh, Somnath International Journal of Plasticity, Vol. 120 https://doi.org/10.1016/j.ijplas.2019.05.008	journal	September 2019
Investigating mesh sensitivity and polycrystalline RVEs in crystal plasticity finite element simulations Lim, Hojun; Battaile, Corbett C.; Bishop, Joseph E. International Journal of Plasticity, Vol. 121 https://doi.org/10.1016/j.ijplas.2019.06.001	journal	October 2019
An efficient and robust approach to determine material parameters of crystal plasticity constitutive laws from macro-scale stress–strain curves Sedighiani, K.; Diehl, M.; Traka, K. International Journal of Plasticity, Vol. 134 https://doi.org/10.1016/j.ijplas.2020.102779	journal	November 2020
Roles of texture and latent hardening on plastic anisotropy of face-centered-cubic materials during multi-axial loading Pham, M. S.; Creuziger, A.; Iadicola, M. Journal of the Mechanics and Physics of Solids, Vol. 99 https://doi.org/10.1016/j.jmps.2016.08.011	journal	February 2017
Two-way multi-scaling for predicting fatigue crack nucleation in titanium alloys using parametrically homogenized constitutive models Ozturk, Deniz; Kotha, Shravan; Pilchak, Adam L. Journal of the Mechanics and Physics of Solids, Vol. 128 https://doi.org/10.1016/j.jmps.2019.04.009	journal	July 2019
Estimating mechanical properties from spherical indentation using Bayesian approaches Fernandez-Zelaia, Patxi; Roshan Joseph, V.; Kalidindi, Surya R. Materials & Design, Vol. 147 https://doi.org/10.1016/j.matdes.2018.03.037	journal	June 2018
Determination and analysis of the constitutive parameters of temperature-dependent dislocation-density-based crystal plasticity models Sedighiani, Karo; Traka, Konstantina; Roters, Franz Mechanics of Materials, Vol. 164 https://doi.org/10.1016/j.mechmat.2021.104117	journal	January 2022
Global sensitivity analysis using polynomial chaos expansions Sudret, Bruno Reliability Engineering & System Safety, Vol. 93, Issue 7 https://doi.org/10.1016/j.ress.2007.04.002	journal	July 2008
Polynomial chaos expansion for sensitivity analysis Crestaux, Thierry; Le Maıˆtre, Olivier; Martinez, Jean-Marc Reliability Engineering & System Safety, Vol. 94, Issue 7 https://doi.org/10.1016/j.ress.2008.10.008	journal	July 2009
Sensitivity analysis techniques applied to a system of hyperbolic conservation laws Weirs, V. Gregory; Kamm, James R.; Swiler, Laura P. Reliability Engineering & System Safety, Vol. 107 https://doi.org/10.1016/j.ress.2011.12.008	journal	November 2012
Incorporation of deformation twinning in crystal plasticity models Kalidindi, Surya R. Journal of the Mechanics and Physics of Solids, Vol. 46, Issue 2 https://doi.org/10.1016/s0022-5096(97)00051-3	journal	February 1998
Using texture components in crystal plasticity finite element simulations Raabe, Dierk; Roters, Franz International Journal of Plasticity, Vol. 20, Issue 3 https://doi.org/10.1016/s0749-6419(03)00092-5	journal	March 2004
Theory of orientation gradients in plastically strained crystals Raabe, D.; Zhao, Z.; Park, S. -J Acta Materialia, Vol. 50, Issue 2 https://doi.org/10.1016/s1359-6454(01)00323-8	journal	January 2002
Uncertainty-quantified parametrically homogenized constitutive models (UQ-PHCMs) for dual-phase α/β titanium alloys Kotha, Shravan; Ozturk, Deniz; Ghosh, Somnath npj Computational Materials, Vol. 6, Issue 1 https://doi.org/10.1038/s41524-020-00379-3	journal	August 2020
Perspective: Materials informatics and big data: Realization of the “fourth paradigm” of science in materials science Agrawal, Ankit; Choudhary, Alok APL Materials, Vol. 4, Issue 5 https://doi.org/10.1063/1.4946894	journal	April 2016
An inductive design exploration method for hierarchical systems design under uncertainty Choi, Hae-Jin; Mcdowell, David L.; Allen, Janet K. Engineering Optimization, Vol. 40, Issue 4 https://doi.org/10.1080/03052150701742201	journal	April 2008
Texture and anisotropy Wenk, H-R; Houtte, P. Van Reports on Progress in Physics, Vol. 67, Issue 8 https://doi.org/10.1088/0034-4885/67/8/r02	journal	July 2004
The influence of transition metal solutes on the dislocation core structure and values of the Peierls stress and barrier in tungsten Samolyuk, G. D.; Osetsky, Y. N.; Stoller, R. E. Journal of Physics: Condensed Matter, Vol. 25, Issue 2 https://doi.org/10.1088/0953-8984/25/2/025403	journal	November 2012
Assessment of interatomic potentials for atomistic analysis of static and dynamic properties of screw dislocations in W Cereceda, D.; Stukowski, A.; Gilbert, M. R. Journal of Physics: Condensed Matter, Vol. 25, Issue 8 https://doi.org/10.1088/0953-8984/25/8/085702	journal	January 2013
Quantifying uncertainty in the process-structure relationship for Al–Cu solidification Tran, Anh; Liu, Dehao; Tran, Hoang Modelling and Simulation in Materials Science and Engineering, Vol. 27, Issue 6 https://doi.org/10.1088/1361-651x/ab2690	journal	June 2019
Bounds and Self-Consistent Estimates for Creep of Polycrystalline Materials Hutchinson, J. W. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 348, Issue 1652 https://doi.org/10.1098/rspa.1976.0027	journal	February 1976
sMF-BO-2CoGP: A Sequential Multi-Fidelity Constrained Bayesian Optimization Framework for Design Applications Tran, Anh; Wildey, Tim; McCann, Scott Journal of Computing and Information Science in Engineering, Vol. 20, Issue 3 https://doi.org/10.1115/1.4046697	journal	April 2020
srMO-BO-3GP: A sequential regularized multi-objective Bayesian optimization for constrained design applications using an uncertain Pareto classifier Tran, Anh; Eldred, Michael S.; McCann, Scott Journal of Mechanical Design https://doi.org/10.1115/1.4052445	journal	September 2021
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data Babuška, Ivo; Nobile, Fabio; Tempone, Raúl SIAM Journal on Numerical Analysis, Vol. 45, Issue 3 https://doi.org/10.1137/050645142	journal	January 2007
A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data Nobile, F.; Tempone, R.; Webster, C. G. SIAM Journal on Numerical Analysis, Vol. 46, Issue 5 https://doi.org/10.1137/060663660	journal	January 2008
A Method for Constructing Local Monotone Piecewise Cubic Interpolants Fritsch, F. N.; Butland, J. SIAM Journal on Scientific and Statistical Computing, Vol. 5, Issue 2 https://doi.org/10.1137/0905021	journal	June 1984
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations Xiu, Dongbin; Karniadakis, George Em SIAM Journal on Scientific Computing, Vol. 24, Issue 2 https://doi.org/10.1137/s1064827501387826	journal	January 2002
Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics Najm, Habib N. Annual Review of Fluid Mechanics, Vol. 41, Issue 1 https://doi.org/10.1146/annurev.fluid.010908.165248	journal	January 2009
DREAM.3D: A Digital Representation Environment for the Analysis of Microstructure in 3D Groeber, Michael A.; Jackson, Michael A. Integrating Materials and Manufacturing Innovation, Vol. 3, Issue 1 https://doi.org/10.1186/2193-9772-3-5	journal	April 2014
Stochastic Design Optimization of Microstructures with Utilization of a Linear Solver Acar, Pınar; Srivastava, Siddhartha; Sundararaghavan, Veera AIAA Journal, Vol. 55, Issue 9 https://doi.org/10.2514/1.j056000	journal	September 2017

Similar Records

Multi-fidelity Uncertainty Quantification for Homogenization Problems in Structure-Property Relationships from Crystal Plasticity Finite Elements

Journal Article · Wed Oct 25 00:00:00 EDT 2023 · JOM. Journal of the Minerals, Metals & Materials Society · OSTI ID:2320353

An asynchronous parallel high-throughput model calibration framework for crystal plasticity finite element constitutive models

Journal Article · Wed Apr 12 00:00:00 EDT 2023 · Computational Mechanics · OSTI ID:2311555

Multi-fidelity microstructure-induced uncertainty quantification by advanced Monte Carlo methods

Journal Article · Tue Feb 07 23:00:00 EST 2023 · Materialia · OSTI ID:2311635

Related Subjects

36 MATERIALS SCIENCE
constitutive models
crystal plasticity finite element
polynomial chaos expansion
sparse grid
stochastic collocation
uncertainty quantification

Microstructure-Sensitive Uncertainty Quantification for Crystal Plasticity Finite Element Constitutive Models Using Stochastic Collocation Methods

Citation Formats

References (62)

Similar Records

Related Subjects