Elastoplastic materials with martensitic phase transition and twinning at finite strains: Numerical solution with the finite element method

Abstract

A new quasistatic problem formulation and finite element (FE) algorithm for martensitic phase transition (PT) and twinning in elastoplastic materials at large strains, based on a recently proposed thermomechanical approach [1–2] are presented. The instantaneous occurrence of PT in some region based on thermodynamics, without introduction of volume fraction and prescribing the kinetic equations for it, is considered. Stress history dependence during the transformation process is a characteristic feature of the PT criterion. The deformation model is based on the multiplicative decomposition of the total deformation gradient into elastic, transformation and plastic parts and the generalization of Prandtl-Reuss equations to the case of large strains and PT. The case of small elastic, but large plastic and transformation strains is assumed. For numerical simulation of PT the ‘inverse’ problem is considered, i.e. the position and size of the PT region (nucleus) are prescribed in advance, and then the condition for PT is defined from the PT criterion. Such an approach includes a finite element solution of the elastoplastic problem with the prescribed transformation deformation gradient and the changing elastoplastic properties in the transforming region during PT. The usage of the current configuration and the true Cauchy stresses along with assumptions of small elastic strains and zero modified plastic spin allows us to use—with small modifications—the radial return algorithm and the consistent elastoplastic moduli for the case of small strains. Some modifications of the iterative algorithm related to the numerical integration of constitutive equations along with the radial return algorithm are suggested in order to improve the accuracy of solutions for large increments of external load (such modifications can be used for any elastoplastic problem without phase transition as well). The model problems of nucleation at shear-band intersection and appearance of a single martensitic plate and a single twin are solved and analyzed.