Plane strain deformation by slip in FCC crystals

Abstract

Deformation studies of a metal or alloy single crystal under plane strain boundary conditions have proved valuable for providing information on the deformation behavior of such materials under multiaxial states of stress and strain. Examples include the initiation and propagation of cracks during brittle fracture and the development of deformation textures in metal forming operations. Restrictions imposed by plane strain boundary conditions on the values of global strain components and on active slip systems by the principle of maximum plastic work confine slip to subsets of physically possible crystallographic slip system (CSS). Such ensembles produce components of global strain that independently satisfy plane strain constraints. This leads to the definition of Pseudo Slip Systems (PSS) having basis vectors formed from the resultants of corresponding basis vectors in participating CSS. Nye’s State of Dislocation tensor applied at both macro- and micro-structural scales describes global and local lattice rotations resulting from the geometrically necessary dislocation (GND) content. Local Nye Tensors (LNT) for each active CSS are dyadic products of their Burgers vector and a Dislocation Density Vector (DDV) describing the GND population. This vector, lying in the slip plane, has a magnitude equal to that of the local GND, and a direction given by the character of the resultant population. The Global Nye Tensor (GNT), A, is the sum of LNTs for each active CSS and expresses in global specimen coordinates the resultant Burgers vector flux from all active CSS. We demonstrate these relationships by analyzing plane strain deformation in a Ni single crystal caused by wedge indentation along a 〈110〉 direction.