Consistent modeling of the coupling between crystallographic slip and martensitic phase transformation for mechanically induced loadings. (25th March 2022)

• Record Type: Journal Article
• Authors: de Carvalho, Miguel Vieira; de Bortoli, Daniel; Andrade Pires, Francisco M.
• Is Part Of: International journal for numerical methods in engineering. Volume 123:Number 14(2022)
• Page Start: 3179
• Page End: 3236
• Publication Date: 2022-03-25
• Subjects: consistent linearisation -- crystal plasticity -- finite element method -- martensitic transformation -- numerical integration techniques -- viscoplastic regularization; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6962
• Languages: English
• ISSNs: 0029-5981

Abstract

Abstract: 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.