Consistent modeling of the coupling between crystallographic slip and martensitic phase transformation for mechanically induced loadings

• Published in: International journal for numerical methods in engineering 2022-07, Vol.123 (14), p.3179-3236
• Main Authors: Carvalho, Miguel Vieira, Bortoli, Daniel, Andrade Pires, Francisco M.
• Format: Article
• Language: English
• Subjects: Asymptotic methods; consistent linearisation; Constitutive equations; Constitutive relationships; crystal plasticity; Crystallography; Deformation mechanisms; Evolution; finite element method; Incompressibility; Kinematics; Martensite; martensitic transformation; Martensitic transformations; Mathematical models; numerical integration techniques; Phase transitions; Plastic flow; Plastic properties; Polycrystals; Slip; viscoplastic regularization
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.6962

A computational framework is proposed to model anisotropic metallic polycrystals subjected to mechanically induced loadings. It enables the simulation of crystal‐plasticity‐like phenomena at finite strains. The unified framework of thermodynamically consistent constitutive equations is formulated such that it couples the crystallographic slip and martensitic transformation theories. The constitutive description for the slip plasticity evolution incorporates an anisotropic hyperelastic law with self and latent‐hardening. The mechanically induced martensite formation kinematics is based on the crystallographic theory of martensitic transformations. The complete set of highly coupled equations is expressed in a single system of equations and solved by a monolithic solution procedure. It is based on the Newton–Raphson methodology and incorporates the complete linearisation leading to asymptotic quadratic rates of convergence. The quasi‐static discretized evolution equations are integrated with a fully implicit scheme, except for the critical resolved slip stresses, which employ the generalized midpoint rule. The plastic flow is integrated with an implicit exponential integrator to exactly preserve the plastic incompressibility. Viscous regularizations for both deformation mechanisms are pursued to overcome numerical difficulties and model the behavior over a wide range of strain‐rate sensitivities. Numerical examples are presented to demonstrate the efficiency and predictive capability of the methodology.