Shear on the Flow Surface of Metallic Crystals

The present article addresses the following question: How is it that shears are so common in the plastic deformation of metallic alloys? An answer is sought in a geometric description of the shear flow when the deformation is produced by slip systems gliding according to the Schmid law. Such flows are represented schematically by what is called “simple shear” and a kinematic study is done of the way these shears can be produced by the joint activity of various slip systems. This implies specific conditions on the glide rates, which can be known analytically thanks to adequate parametrizations. All the possible shears have been calculated in the case of cubic metals deforming with identical critical resolved shear stresses (Bishop and Hill polyhedron). Three dimensional representations are given in the space of the Bunge angles associated with the principal directions of the shears. A special attention has been given to the number of slip systems involved. Most of the shears are not far from some combination of two or three systems. This is quantified by defining the misorientation $ω$ between a shear taken at random and the set of shears produced by the glide on two or three octahedral slip systems. It is found that in most cases, $ω<15deg$⁠. The maximum value of $ω$ (30.5 deg) is found for the orientations called Cube and U in rolled metals.