The thick yield surface: idea and approach for investigating its structure

The hypothesis presented in the present work is that the yield surface can be presented as a thick 'foamed surface' with dimensionality exceeding two, that is the yield surface is of a fractal nature. A micromechanical model of a polycrystal based on cellular automata (the cellular model) is proposed to investigate the yield surface structure. A polycrystal representative volume is modelled as a population of interconnected units which, in turn, can consist of lower-scale-level units. Simple units, which do not have an internal structure, are deformed by sliding along the various allowed sliding systems. To consider the stress distribution within the limits of the components, the approach of a self-consistent field is used. The rotation of units and moment stresses connected with it are taken into account. The results of computer experiments show that the number of known plastic deformation effects can be adequately described by the proposed cellular model. The 'thick yield surface' concept allows the additional correlation between micromechanical models of polycrystals and phenomenological theory of plasticity to be determined.