Phenomenological theory of the Portevin‐Le Chatelier effect

Starting from the observation that the serrations appearing in the Portevin‐Le Chatelier effect are produced by hopping deformation bands a set of three autonomous equations is derived for the phenomenological variables load, band velocity and deformation profile. Approximate solutions for the three quantities are given and it is shown that a negative strain rate sensitivity is only sufficient, but not necessary for the appearance of serrations. The treatment of the bands as solitary waves is based on the existence of a mechanical equation of state, using the total dislocation density as structure parameter. A discussion of this approach reveals that a full description of the Portevin‐Le Chatelier effect is not possible on the basis of a single structure parameter.