Prediction of single crystal instability in channel-die compression using Rice's criterion

Abstract

International audienceThis work concerns the behavior and instability of cold-deformed single crystals at large strains. The theoretical calculations integrate a phenomenological deformation model of the single crystal based on a polynomial approximation of the flow surface, within the limits of the homogeneous analysis of the deformation of the specimen. It is introduced in the context of three-dimensional kinematics, in which the strains and the gradients of the rate tensor are represented by higher triangular matrices. It accounts for the lattice rotation of the single crystals in the channel-die for several initial orientations representative of the rolling textures. The above formalism allows implementing Rice’s criterion of bifurcation into shear bands. It appears that the localization occurs for all crystallographic orientations, whether they rotate or not in the channel-die. The difference is in the earliness of the onset. The confrontation between theory and experience is presented using various results of the literature and data from the compression of single crystals in the authors’ laboratory. Although a variety of factors trigger instabilities, from the dislocation microstructure to the friction on the sample, Rice’s criterion proves efficient in predicting what happens within the grains. It accounts for the numerous shearing zones which can be spotted in the deformed metals