Abstract
A severe obstacle for the routine use of crystal plasticity models is the effort associated with determining their constitutive parameters. Obtaining these parameters usually requires time-consuming micromechanical tests that allow probing of individual grains. In this study, a novel, computationally efficient, and fully automated approach is introduced which allows the identification of constitutive parameters from macroscopic tests. The approach presented here uses the response surface methodology together with a genetic algorithm to determine an optimal set of parameters. It is especially suited for complex models with a large number of parameters. The proposed approach also helps to develop a quantitative and thorough understanding of the relative influence of the different constitutive parameters and their interactions. Such general insights into parameter relations in complex models can be used to improve constitutive laws and reduce redundancy in parameter sets. The merits of the methodology are demonstrated on the examples of a dislocation-density-based crystal plasticity model for bcc steel, a phenomenological crystal plasticity model for fcc copper, and a phenomenological crystal plasticity model incorporating twinning deformation for hcp magnesium. The approach proposed is, however, model-independent and can be also used to identify parameters of, for instance, fatigue, creep and damage models. The method has been implemented into the Düsseldorf Advanced Material Simulation Kit (DAMASK) and is available as free and open-source software. The capability of translating complex material response into a micromechanical digital twin is an essential precondition for the ongoing digitalization of material property prediction, quality control of semi-finished parts, material response in manufacturing and the long-term behavior of products and materials when in service.
Highlights
Crystal plasticity (CP) models cast the extensive knowledge gained from experimental and theoretical studies of single crystal deformation and dislocation physics into anisotropic elastic-plastic mean-field continuum approximations applicable to a wide range of scenarios from small-scale micromechanical up to engineering time and length scales (Roters et al, 2010)
The methodology developed in this study is demonstrated by determining the constitutive parameters of three widely used crystal plasticity models: a phenomenological model (Hutchinson, 1976), a dislocation-density-based model (Ma and Roters, 2004) and a phenomenological model incorporating defor mation twinning (Kalidindi, 1998), all implemented in the Düsseldorf Advanced Material Simulation Kit (DAMASK) package (Roters et al, 2019)
The spectral solver implemented in DAMASK (Eisenlohr et al, 2013; Roters et al, 2019; Shanthraj et al, 2015) is used to conduct the CP simulations using these three constitutive laws
Summary
Crystal plasticity (CP) models cast the extensive knowledge gained from experimental and theoretical studies of single crystal deformation and dislocation physics into anisotropic elastic-plastic mean-field continuum approximations applicable to a wide range of scenarios from small-scale micromechanical up to engineering time and length scales (Roters et al, 2010). Because of the substantial experimental efforts associated with such “virtual single crystal” experiments, it is instead preferable to identify CP constitutive parameters from macroscopic stress–strain data obtained from standard tensile or compression testing Such procedures would catalyze wider use of advanced CP models in the industrial practice where access to small scale experiments for parameter identification is limited and/or too costly. The stress response at different loading conditions is approximated using relationships defined between the adjustable material parameters and the stress response This allows to perform more than 106 evaluations of the constitutive response in approximately the same time as needed for one CP simulation with a fairly complex dislocation-density-based constitutive model used in this study. The methodology developed in this study is demonstrated by determining the constitutive parameters of three widely used crystal plasticity models: a phenomenological model (Hutchinson, 1976), a dislocation-density-based model (Ma and Roters, 2004) and a phenomenological model incorporating defor mation twinning (Kalidindi, 1998), all implemented in the DAMASK package (Roters et al, 2019)
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