On the relationship between the Cottrell–Stokes law and the Haasen plot

The Cottrell–Stokes (CS) law requires that the ratio between the flow stress at two temperatures and same material structure (the CS ratio) is a function of the two temperatures involved and is independent of strain. This holds in many pure single and polycrystalline metals and provides fundamental insight into the nature of thermally activated plastic flow. The standard method for testing the validity of the law in given material system is to monitor the dependence of the strain rate sensitivity coefficient S on the applied stress, i.e. the Haasen plot. It is conjectured in the literature that if the Haasen plot is a straight line passing through the origin, the Cottrell–Stokes law holds. In this article we study this conjecture using a model of thermally activated dislocation motion across arrays of obstacles. It is shown that multiple types of Haasen plots may be obtained at constant CS ratio, i.e. when the CS law is imposed at all times. Hence, the validity of the CS law cannot be determined exclusively based on the Haasen plot. As a corollary it is shown that S is a convex function of the flow stress.