On the Portevin-Le Chatelier effect: theoretical modeling and numerical results

A new model is presented for a physically-consistent description of plastic material instabilities referred to as Portevin–Le Chatelier (PLC) effect, namely the oscillatory plastic flow that may be observed in metallic alloys subjected to load-or displacement-controlled plastic deformation in a certain range of strain, strain rate and temperature. The model is conceived to describe the kinetics of Dynamic Strain Ageing (DSA), that is the dynamic interaction between mobile dislocations and diffusing solute atoms which is known to be the primary mechanism inducing the PLC effect. The model is coupled in time and (one-dimensional) space and introduces two intrinsic time scales in the evolution equations and a characteristic length scale through a diffusion-like term with spatial second-order gradient. Approximate analytical solutions are first derived for the boundaries ofthe PLC range and for the strain localization characteristics defining the kinematics of PLC deformation bands. Numerical results are then obtained through Finite Differences solutions of the space–time coupled equations: a considerable wealth of features is discovered, including the appearance of various PLC band types depending on the applied strain rate. Phenomenological characteristics (i.e. stress–strain curves) are presented together with the corresponding space–time patterns of strain localization. The obtained results are in agreement with the analytical solutions developed here and with the available experimental observations on the PLC effect.