Journal
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume 123, Issue 14, Pages 3179-3236Publisher
WILEY
DOI: 10.1002/nme.6962
Keywords
consistent linearisation; crystal plasticity; finite element method; martensitic transformation; numerical integration techniques; viscoplastic regularization
Funding
- Fundacao para a Ciencia e a Tecnologia (FCT) [SFRH/BD/130594/2017]
- Instituto de Ciencia e Inovacao em Engenharia Mecanica e Engenharia Industrial (INEGI)
- Fundação para a Ciência e a Tecnologia [SFRH/BD/130594/2017] Funding Source: FCT
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A computational framework is proposed to model anisotropic metallic polycrystals under mechanically induced loadings. The framework enables the simulation of crystal-plasticity-like phenomena at finite strains and couples the crystallographic slip and martensitic transformation theories. Numerical examples demonstrate the efficiency and predictive capability of the methodology.
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.
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