Data-driven reduced order models for effective yield strength and partitioning of strain in multiphase materials

Abstract There is a critical need for the development and verification of practically useful multiscale modeling strategies for simulating the mechanical response of multiphase metallic materials with heterogeneous microstructures. In this contribution, we present data-driven reduced order models for effective yield strength and strain partitioning in such microstructures. These models are built employing the recently developed framework of Materials Knowledge Systems that employ 2-point spatial correlations (or 2-point statistics) for the quantification of the heterostructures and principal component analyses for their low-dimensional representation. The models are calibrated to a large collection of finite element (FE) results obtained for a diverse range of microstructures with various sizes, shapes, and volume fractions of the phases. The performance of the models is evaluated by comparing the predictions of yield strength and strain partitioning in two-phase materials with the corresponding predictions from a classical self-consistent model as well as results of full-field FE simulations. The reduced-order models developed in this work show an excellent combination of accuracy and computational efficiency, and therefore present an important advance towards computationally efficient microstructure-sensitive multiscale modeling frameworks.

[1]  K. Lee,et al.  Observation of the TWIP + TRIP Plasticity-Enhancement Mechanism in Al-Added 6 Wt Pct Medium Mn Steel , 2015, Metallurgical and Materials Transactions A.

[2]  Hyoung-Seop Kim,et al.  Micromechanical finite element analysis of strain partitioning in multiphase medium manganese TWIP+TRIP steel , 2016 .

[3]  S. Kalidindi,et al.  Extracting single-crystal elastic constants from polycrystalline samples using spherical nanoindentation and orientation measurements , 2014 .

[4]  David T. Fullwood,et al.  A new spectral framework for establishing localization relationships for elastic behavior of composites and their calibration to finite-element models , 2008 .

[5]  A. Misra,et al.  Room-temperature deformation behavior of directionally solidified multiphase Ni-Fe-Al alloys , 1997 .

[6]  Surya R. Kalidindi,et al.  Structure–property linkages using a data science approach: Application to a non-metallic inclusion/steel composite system , 2015 .

[7]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[8]  Helmut J. Böhm,et al.  A Short Introduction to Continuum Micromechanics , 2004 .

[9]  Parijat Deshpande,et al.  Exploration of data science techniques to predict fatigue strength of steel from composition and processing parameters , 2014, Integrating Materials and Manufacturing Innovation.

[10]  S. Kalidindi,et al.  Finite approximations to the second-order properties closure in single phase polycrystals , 2005 .

[11]  A. Gokhale,et al.  Constraints on microstructural two-point correlation functions , 2005 .

[12]  Yuksel C. Yabansu,et al.  Understanding and visualizing microstructure and microstructure variance as a stochastic process , 2011 .

[13]  Andrew Gillman,et al.  Computing overall elastic constants of polydisperse particulate composites from microtomographic data , 2011 .

[14]  S. Kalidindi,et al.  Crystal plasticity simulations using discrete Fourier transforms , 2009 .

[15]  S. Kalidindi,et al.  High throughput exploration of process-property linkages in Al-6061 using instrumented spherical microindentation and microstructurally graded samples , 2016, Integrating Materials and Manufacturing Innovation.

[16]  Surya R. Kalidindi,et al.  Microstructure Informatics Using Higher-Order Statistics and Efficient Data-Mining Protocols , 2011 .

[17]  S. Ahzi,et al.  A self consistent approach of the large deformation polycrystal viscoplasticity , 1987 .

[18]  Y. Murayama,et al.  High temperature strength, fracture toughness and oxidation resistance of Nb–Si–Al–Ti multiphase alloys , 2002 .

[19]  J. Michel,et al.  Effective properties of composite materials with periodic microstructure : a computational approach , 1999 .

[20]  Surya R. Kalidindi,et al.  Application of data science tools to quantify and distinguish between structures and models in molecular dynamics datasets , 2015, Nanotechnology.

[21]  A. Rollett,et al.  Modeling the viscoplastic micromechanical response of two-phase materials using Fast Fourier Transforms , 2011 .

[22]  Javier Segurado,et al.  A numerical approximation to the elastic properties of sphere-reinforced composites , 2002 .

[23]  Johannes Hötzer,et al.  Analytics for microstructure datasets produced by phase-field simulations , 2016 .

[24]  Ricardo A. Lebensohn,et al.  A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals : application to zirconium alloys , 1993 .

[25]  A. Reuss,et al.  Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle . , 1929 .

[26]  Timothy G. Trucano,et al.  Verification and Validation in Computational Fluid Dynamics , 2002 .

[27]  G. Lütjering.  Influence of processing on microstructure and mechanical properties of (α+β) titanium alloys , 1998 .

[28]  R. Hill.  A self-consistent mechanics of composite materials , 1965 .

[29]  D. Fullwood,et al.  Delineation of the space of 2-point correlations in a composite material system , 2008 .

[30]  D. Fullwood,et al.  Microstructure reconstructions from 2-point statistics using phase-recovery algorithms , 2008 .

[31]  Marc G. D. Geers,et al.  A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials , 2017, J. Comput. Phys..

[32]  A. Misra,et al.  Room-temperature deformation behavior of directionally solidified multiphase Ni−Fe−Al alloys , 1997 .

[33]  M. Groeber,et al.  DREAM.3D: A Digital Representation Environment for the Analysis of Microstructure in 3D , 2014, Integrating Materials and Manufacturing Innovation.

[34]  J. Segurado,et al.  Multiscale modeling of plasticity based on embedding the viscoplastic self-consistent formulation in implicit finite elements , 2012 .

[35]  D. Parks,et al.  A self-consistent model of isotropic viscoplastic behavior in multiphase materials , 1991 .

[36]  E. Kröner.  Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls , 1958 .

[37]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[38]  Surya R. Kalidindi,et al.  Representation and calibration of elastic localization kernels for a broad class of cubic polycrystals , 2015 .

[39]  J. Segurado,et al.  Multiscale Modeling of Composite Materials: a Roadmap Towards Virtual Testing , 2011, Advanced materials.

[40]  J. Segurado,et al.  Micromechanics of particle-reinforced elasto-viscoplastic composites : Finite element simulations versus affine homogenization , 2007 .

[41]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[42]  A. Molinari,et al.  A STATISTICAL FORMULATION OF VISCOPLASTIC BEHAVIOR IN HETEROGENEOUS POLYCRYSTALS , 1989 .

[43]  I. Beyerlein,et al.  A dislocation density based crystal plasticity finite element model: Application to a two-phase polycrystalline HCP/BCC composites , 2014 .

[44]  Pedro Ponte Castañeda.  Second-order homogenization estimates for nonlinear composites incorporating field fluctuations: I—theory , 2002 .

[45]  E. Werner,et al.  A new view on transformation induced plasticity (TRIP) , 2000 .

[46]  S. Torquato,et al.  Microstructure of two‐phase random media. IV. Expected surface area of a dispersion of penetrable spheres and its characteristic function , 1984 .

[47]  Surya R. Kalidindi,et al.  Calibrated localization relationships for elastic response of polycrystalline aggregates , 2014 .

[48]  Surya R. Kalidindi,et al.  Versatile algorithms for the computation of 2-point spatial correlations in quantifying material structure , 2016, Integrating Materials and Manufacturing Innovation.

[49]  Surya R. Kalidindi,et al.  A data-driven approach to establishing microstructure–property relationships in porous transport layers of polymer electrolyte fuel cells , 2014 .

[50]  E. Kröner.  Bounds for effective elastic moduli of disordered materials , 1977 .

[51]  Salvatore Torquato,et al.  Effective stiffness tensor of composite media—I. Exact series expansions , 1997 .

[52]  Javier Segurado,et al.  Computational micromechanics of composites: The effect of particle spatial distribution , 2006 .

[53]  B. Budiansky.  On the elastic moduli of some heterogeneous materials , 1965 .

[54]  C. Tomé.  Self-consistent polycrystal models: a directional compliance criterion to describe grain interactions , 1999 .

[55]  Yuksel C. Yabansu,et al.  Extraction of reduced-order process-structure linkages from phase-field simulations , 2017 .

[57]  Pedro Ponte Castañeda.  Exact second-order estimates for the effective mechanical properties of nonlinear composite materials , 1996 .

[58]  S. Ahzi,et al.  Modeling of two-phase random composite materials by finite element, Mori–Tanaka and strong contrast methods , 2013 .

[59]  Somnath Ghosh,et al.  Multiple scale analysis of heterogeneous elastic structures using homogenization theory and voronoi cell finite element method , 1995 .

[60]  Surya R. Kalidindi,et al.  Hierarchical Materials Informatics: Novel Analytics for Materials Data , 2015 .

[61]  Surya R. Kalidindi,et al.  A new framework for computationally efficient structure–structure evolution linkages to facilitate high-fidelity scale bridging in multi-scale materials models , 2011 .

[62]  G. Milton.  The Theory of Composites , 2002 .

[63]  Y. Benveniste,et al.  A new approach to the application of Mori-Tanaka's theory in composite materials , 1987 .

[64]  J. Hudson.  Overall properties of heterogeneous material , 1991 .

[65]  B. Ganapathysubramanian,et al.  Microstructure taxonomy based on spatial correlations: Application to microstructure coarsening , 2016 .

[66]  A Tudor,et al.  Three-dimensional reconstruction of statistically optimal unit cells of polydisperse particulate composites from microtomography. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[67]  A. Çeçen,et al.  Development of high throughput assays for establishing process-structure-property linkages in multiphase polycrystalline metals: Application to dual-phase steels , 2017 .

[68]  H. Garmestani,et al.  Statistical continuum theory for inelastic behavior of a two-phase medium , 1998 .

[69]  Helmut J. Böhm,et al.  Mechanics of Microstructured Materials , 2004 .

[70]  S. Torquato,et al.  Random Heterogeneous Materials: Microstructure and Macroscopic Properties , 2005 .

[71]  J. Llorca,et al.  A self-consistent approach to the elasto-plastic behaviour of two-phase materials including damage , 2000 .

[72]  David T. Fullwood,et al.  Microstructure Sensitive Design for Performance Optimization , 2012 .

[73]  William Fuller Brown,et al.  Solid Mixture Permittivities , 1955 .

[74]  David T. Fullwood,et al.  A strong contrast homogenization formulation for multi-phase anisotropic materials , 2008 .

[75]  B. Schrefler,et al.  Multiscale Methods for Composites: A Review , 2009 .

[76]  M. Diehl,et al.  A spectral method solution to crystal elasto-viscoplasticity at finite strains , 2013 .

[77]  Surya R. Kalidindi,et al.  Multi-scale modeling of elastic response of three-dimensional voxel-based microstructure datasets using novel DFT-based knowledge systems , 2010 .

[78]  Salvatore Torquato,et al.  Microstructure of two‐phase random media. I. The n‐point probability functions , 1982 .

[79]  S. Kalidindi,et al.  Novel microstructure quantification framework for databasing, visualization, and analysis of microstructure data , 2013, Integrating Materials and Manufacturing Innovation.

[80]  M. Cherkaoui,et al.  Fundamentals of Micromechanics of Solids , 2006 .

[81]  P. Gilormini,et al.  Variational self-consistent estimates for cubic viscoplastic polycrystals : the effects of grain anisotropy and shape , 2001 .

[82]  Surya R. Kalidindi,et al.  Formulation and calibration of higher-order elastic localization relationships using the MKS approach , 2011 .

[83]  A. Molinari,et al.  Tuning a self consistent viscoplastic model by finite element results—I. Modeling , 1994 .

[84]  M. Knezevic,et al.  A dislocation density based elasto-plastic self-consistent model for the prediction of cyclic deformation: Application to AA6022-T4 , 2015 .

[85]  Ricardo A. Lebensohn,et al.  Integration of self-consistent polycrystal plasticity with dislocation density based hardening laws within an implicit finite element framework: Application to low-symmetry metals , 2013 .

[86]  Daniel B. Mark,et al.  TUTORIAL IN BIOSTATISTICS MULTIVARIABLE PROGNOSTIC MODELS: ISSUES IN DEVELOPING MODELS, EVALUATING ASSUMPTIONS AND ADEQUACY, AND MEASURING AND REDUCING ERRORS , 1996 .

[87]  W. E. Williams,et al.  Green's Functions , 1970, Nature.

[88]  A. Argon,et al.  Steady state power-law creep in heterogeneous alloys with coarse microstructures , 1979 .

[89]  David T. Fullwood,et al.  Elastic properties closures using second-order homogenization theories: Case studies in composites of two isotropic constituents , 2006 .

[90]  S. Torquato.  Random Heterogeneous Materials , 2002 .

[91]  David B. Brough,et al.  Microstructure-based knowledge systems for capturing process-structure evolution linkages. , 2017, Acta materialia.

[92]  C. Tasan,et al.  An Overview of Dual-Phase Steels: Advances in Microstructure-Oriented Processing and Micromechanically Guided Design , 2015 .

[93]  S. Nemat-Nasser,et al.  Micromechanics: Overall Properties of Heterogeneous Materials , 1993 .

[94]  Surya R. Kalidindi,et al.  PyMKS: Materials Knowledge System in Python , 2014 .

[95]  S. Torquato,et al.  New method to generate three-point bounds on effective properties of composites: Application to viscoelasticity , 1998 .

[96]  P. Gilormini,et al.  A finite element analysis of the inclusion problem for power law viscous materials , 1987 .