An Effect of Plastic Anisotropy on the Strain Rate Intensity Factor

Abstract

The strain rate intensity factor in the theory of rigid perfectly plastic isotropic materials is the coefficient of the principal singular term in a series expansion of the equivalent strain rate in the vicinity of maximum friction surfaces. This coefficient can be used to predict the evolution of material properties in a narrow layer in the vicinity of surfaces where the friction stress is high. Usually, conventional evolution equations are not compatible with the plasticity equations near maximum friction surfaces. It is therefore of interest to extend the theories based on the strain rate intensity factor to more general models than the rigid perfectly plastic isotropic solids. The present paper deals with plane strain deformation of rigid plastic anisotropic material. It is shown by means of a simple analytic solution that the velocity field is singular in the vicinity of maximum friction surfaces. Thus the strain rate intensity factor can be introduced for such materials. An effect of plastic anisotropy on its value is demonstrated. In addition, it is shown that rigid plastic solutions for anisotropic materials can exhibit various types of singularity in the vicinity of maximum friction surfaces, in contrast to isotropic materials where one type only is possible. Nevertheless, in most cases the type of singularity is same for isotropic and anisotropic materials.