The Portevin-Le Chatelier effect. Its prediction and place in gradient thermodynamics

Summary

Here we treat theoretically the Portevin-Le Chatelier effect, whereby the stress is a staircase function of strain. The deformation is continous, except at discrete values of stress (metastable stress states), where it occurs spontaneously and discontinuously. The theory is in the context of gradient thermodynamics of internal variables. It is shown that the prediction of the effect lies in the solution of an eigen-value problem and that metastable stress states arediscrete eigenvalues of the solution of a second order partial differential equation. A comparison with experiments in the literature shows that the predicted stress eigen-states are very close to the observed metastable stress states in torsion and simple tension.