Crystal Plasticity Elastic-Plastic Rate-Independent Numerical Analyses of Pollycrystalline Materials

Abstract

Macroscopic analyses of plastic forming processes give only the overall description of the problem without the consideration of mechanisms of plastic deformation and the microstructure evolution. For the consideration of these processes, numerical simulations within crystal plasticity include the change of texture, anisotropy, and strain hardening of the material are used. In this paper, a crystal plasticity rate-independent model proposed by Anand and Kothari is applied for numerical analyses of polycrystalline materials. The slip was considered as the main mechanism of the plastic deformation. Basic constitutive equations of crystal plasticity for large deformation theories are presented. The selected results of elastic-plastic problems obtained using both macro- and micro- scales software for the explicit and implicit integration are featured here. The heterogeneous distribution of strain and stress in different grains are obtained, which is associated with the various crystal orientation. The crystal plasticity modelling of materials subject to plastic deformation involves not only the information about the change of a material’s shape in a macro-scale, but also describes the phenomena occurring in material in a micro-scale.

Explicit and Implicit Integration of Constitutive Equations of Chaboche Isotropic-Kinematic Hardening Material Model

“…It is worth noting that, in Abaqus software the user material procedure is defined in the corotational framework which rotates with the material. Procedure written for a small strains can be also applied for a large strains analysis, because of some additional computations made by Abaqus for calculated stress increments in order to make them objective [28]. A very good agreement in stress and strain distributions is obtained which proves that the user material procedure is written correctly.…”

“…The advantage of using the user material procedure is the easy access to all material data and user parameters in each ) stress (Eq. 40-41) [28]. where: 𝝈̇ is stress rate tensor in a corotational frame, 𝝈 is Cauchy stress tensor, 𝑾 is spin tensor which comprises both the deformation and the rotation and 𝛀 is the angular velocity tensor resulting from a rigid body rotation.…”