Thick Yield Surface: An Approach to the Processing of Computer Experiments on Poly Crystalline Deformation

"The main idea of the report is that the yield surface can be presented as thick, ""foamed surface"" with dimensionality exceeding two. By other words, perhaps, the yield surface is fractal, i.e. it belongs to the class of geometric objects with fractional dimensionality. Apparently, fractal structure of the yield surface is determined by the fractal structure of natural materials. ""Cloud of internal stresses"" term is introduced to describe the stress distribution in representative volume element. Its plastic flow is determined by the interaction of this cloud with the thick yield surface. Thick yield surface and internal stress cloud concepts allow to determine an additional correlation between micro mechanical models of polycrystals and phenomenological theory of plasticity.1. IntroductionClassical plastic flow models are not satisfying the modem requirements. There are two main directions in their development. The first, mathematical, is connected with the development of the general theory of rheological relationships; the second, physical, is connected with the development of the representative volume element (RVE) models which are based on specific ideas about deformation mechanisms. Within the framework of the first direction, the macroscopic experimental data is formalized; the second approach deals with the generalization of physical research results for the different scale levels that are involved in plastic deformation.These approaches have advantages and disadvantages. In phenomenological theories, the advantages are the mathematical simplicity and laconic formulation of constitutive relations, which allows using them in practical calculations. However, the mathematical models of this class can not be considered as general, they are useful only for the description of limited range of deforming processes. On the other hand, physical theories that are based on the description of real plastic deformation mechanisms are very explanatory and predictive, but they lack mathematical simplicity. The above circumstances lead us to the necessity of compromise that can be found in determining the constitutive relations for RVE, which structure and parameters would bear the information about rnicrolevel and mesolevel phenomena. In this synthesis direction, the fundamental role belongs to [1,2], etc."