A persistent modal plastic model for instabilities in Al-Mg alloys with 1D application

Several alloys are subjected to plastic instabilities that are due to the interaction between dislocations and solutes. Among them, Luders bands and the Portevin-Le Chatelier (PLC) effect are of particular interest as they complicate the industrial use of many commercial alloys. They involve a repeated softening that results in mesh sensitivity and a bad conditioning during simulations. Existing models recreate qualitative features such as strain localization, possible bands propagation and oscillating flow curves. Yet they struggle to quantitatively match the kinematics of strain bands, such as their apparent velocity or the strain jump they carry. This issue impacts metal forming processes optimization, where prediction is critical in order to control plastic instabilities. In this paper, a framework called modal plasticity is proposed as a way to embed an internal length in the problem formulation. A model dedicated to describing the PLC effect is then derived with the purpose to provide an explicit description of the kinetics of localization bands. A 1D implementation is proposed and illustrated on several test cases. The developed framework provides a simple way to handle instabilities and describes different types of PLC manifestations.