On the computational treatment of fully coupled crystal plasticity slip and martensitic transformation constitutive models at finite strains

Abstract

In this article, four numerical techniques are formulated to improve the reliability and numerical efficiency of stress update algorithms of crystal-plasticity-like phenomena at finite strains. The resulting algorithmic setting is especially relevant for structural analyses of polycrystals and the multiscale evaluation of anisotropic microstructures in metallic materials. These techniques are exemplified with a constitutive model, which couples crystallographic slip and martensitic transformation deformation mechanisms with a viscous regularization. The model is characterized by a set of highly coupled equations expressed in a single system and solved by a monolithic solution procedure. The first technique employs a sub-stepping procedure to generate a better initial guess for the Newton-Raphson scheme used in the iterative solution of the equilibrium problem at the Gauss quadrature point. Then, a logarithmic discretization of the exponential parameter of the viscoplastic law is proposed to approximate the target value of the exponential parameter incrementally in the return mapping algorithm. A strategy to remove the strain-rate dependence and reduce the necessary viscoplastic parameters is also presented to help with the stiff equations that arise in the rate-independent limit. Finally, an efficient strategy is suggested to complete the transformation process when the full martensitic transformation is approached. These techniques can be easily used in any combination and dramatically improve the model's efficiency by enabling more significant incremental steps to be used within the monolithic solution procedure. A thorough assessment of their impact is shown in a series of ablation studies.

Mechanisms of Component Degradation and Multi-Scale Strategies for Predicting Composite Durability: Present and Future Perspectives

“…This method has been the focus of extensive research since the late 1990s, and is essentially based on the nested solution of two boundary value problems, one at each scale [227], in a strategy commonly referred to as FE 2 . It has been utilised to solve problems related to fracture and damage mechanics [236,237], contact mechanics [238,239], mechanically-induced phase transformations [240,241], and even heat conduction [242], among others.…”