On the kinematics of Portevin–Le Chatelier deformation bands: theoretical modeling and numerical results

A model is presented for the description of the Portevin-Le Chatelier (PLC) effect, namely the oscillatory plastic yielding that may be observed in metal alloy specimens for certain ranges of the applied stress/strain rates and testing temperatures. The phenomenological model is based on the underlying microstructural Dynamic Strain Ageing (DSA), i.e. the dynamic interaction between mobile dislocations and diffusing solute atoms. Both time and space couplings are taken into account. Focus is made on Type A PLC instabilities, that is single PLC bands that nucleate and propagate smoothly throughout the tensile specimen as solitary plastic waves. The kinematics of these PLC bands is first studied analytically, based on some simplifying assumptions, and then validated numerically by a Finite Differences integration of the model equations. The characteristics of the PLC bands, that is band speed, band width and band plastic strain are filtered out automatically from the space-time fields of plastic activity. The band parameters exhibit very good matching with the theoretical results and order-of-magnitude agreement with the experimental observation of the PLC effect.