Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications

F. Roters^a,*, P. Eisenlohr^a, L. Hantcherli^a, D. D. Tjahjanto^a, T. R. Bieler^b , D. Raabe^a

^aMax-Planck-Institut für Eisenforschung, Düsseldorf, Germany
^bChemical Engineering and Materials Science, Michigan State University, East Lansing MI, USA

Abstract This article reviews continuum-based variational formulations for describing the elastic–plastic deformation of anisotropic heterogeneous crystalline matter. These approaches, commonly referred to as crystal plasticity finite element models, are important both for basic microstructure-based mechanical predictions as well as for engineering design and performance simulations involving anisotropic media.

Besides the discussion of the constitutive laws, kinematics, homogenization schemes, and multiscale approaches behind these methods we also present some examples including in particular comparisons of the predictions with experiments. The applications stem from such diverse fields as orientation stability, microbeam bending, single-and bicrystal deformation, nanoindentation, recrystallization, multiphase steel (TRIP) deformation, and damage prediction for the microscopic and mesoscopic scales and multiscale predictions of rolling textures, cup drawing, Lankfort (r) values, and stamping simulations for the macroscopic scale.

The elastic–plastic deformation of crystalline aggregates depends on the direction of loading, i.e. crystals are mechanically anisotropic. This phenomenon is due to the anisotropy of the elastic tensor and to the orientation dependence of the activation of the crystallographic deformation mechanisms (dislocations, twins, martensitic transformations). A consequence of crystalline anisotropy is that the associated mechanical phenomena such as shape change, crystallographic texture, strength, strain hardening, deformationinduced surface roughening, and damage are also orientation dependent. This is not a trivial statement as it implies that mechanical parameters of crystalline matter are tensor quantities.