Multi-scale rheological model for discontinuous phenomena in materials under deformation conditions

A study of possibilities given by the developed Cellular Automata–Finite Element (CAFE) multi-scale model for prediction of the initiation and propagation of micro-shear bands and shear bands in metallic materials subjected to plastic deformation is described in the paper. Particular emphasis in defining the criterion for initiation of micro-shear and shear bands, as well as in defining the transition rules for the cellular automata, is put on accounting for the physical aspects of those phenomena occurring in two different scales in the material. The proposed approach led to the creation of the real multi-scale model of strain localization. This model predicts material behavior in various thermo-mechanical processes. Selected examples of applications of the developed model to simulations of metal forming processes, which involve strain localization, are presented in the paper. An approach based on the Smoothed Particle Hydrodynamic, which allows to overcome difficulties with remeshing in the traditional CAFE method, is presented in the paper as well. In this approach remeshing becomes possible and mesh distortion, which limits application of the CAFE method to simple deformation processes, is eliminated.

Possibilities to include in numerical simulation stochastic and discontinuous phenomena occurring in material

Simulation of materials processing has to face new difficulties regarding proper description of various discontinuous and stochastic phenomena occurring in materials. Commonly used rheological models based on differential equations treat material as continuum and are unable to describe properly several important phenomena. That is the reason for ongoing search for alternative models, which can account for non-continuous structure of the materials and for the fact, that various phenomena in the materials occur in different scales from nano to mezo. Accounting for the stochastic character of some phenomena is an additional challenge. One of the solutions may be the coupled Cellular Automata (CA) – Finite Element (FE) multi scale model. A detailed discussion about the advantages given by the developed multi scale CAFE model for strain localization phenomena in contrast to capabilities provided by the conventional FE approaches is a subject of this work. Results obtained from the CAFE model are supported by the experimental observations showing influence of many discontinuities existing in the real material on macroscopic response. An immense capabilities of the CAFE approach in comparison to limitations of the FE method for modeling of real material behavior is are shown this work as well.