Self-Organization in Metal Plasticity: An ILG Update

In a 1987 article of the last author dedicated to the memory of a pioneer of classical plasticity Aris Philips of Yale, the last author outlined three examples of self-organization during plastic deformation in metals: persistent slip bands (PSBs), shear bands (SBs) and Portevin Le Chatelier (PLC) bands. All three have been observed and analyzed experimentally for a long time, but there was no theory to capture their spatial characteristics and evolution in the process of deformation. By introducing the Laplacian of dislocation density and strain in the standard constitutive equations used for these phenomena, corresponding mathematical models and nonlinear partial differential equations (PDEs) for the governing variable were generated, the solution of which provided for the first time estimates for the wavelengths of the ladder structure of PSBs in Cu single crystals, the thickness of stationary SBs in metals and the spacing of traveling PLC bands in Al-Mg alloys. The present article builds upon the 1987 results of the aforementioned three examples of self-organization in plasticity within a unifying internal length gradient (ILG) framework and expands them in 2 major ways by: (i) introducing the effect of stochasticity and (ii) capturing statistical characteristics when PDEs are absent for the description of experimental observations. The discussion focuses on metallic systems, but the modeling approaches can be used for interpreting experimental observations in a variety of materials.