A SIMPLE PHENOMENOLOGICAL MODEL OF THE STRESS RELAXATION IN SLOWLY EVOLVING 3D POLYCRYSTALLINE MATERIALS

摘要

The phenomenon of propagation of a stress field through complex 3d polycrystalline materials along the grain boundaries performing very slow random motion is studied. After applying the Hall-Petch coupling relation it turns out that the relaxation process proceeds in time anomalously. As a consequence, a fractional evolution equation of order one half for the relaxation function is postulated and its solutions are presented. Inter pretations of the process in terms of the diffusion on a comb-like structure (antipersistent Random Walk with d(w) = 4) and/or the generalized Gauss-Kolmogorov (in) homogeneous turbulence scenario with the Hurst exponent of H = 1/4 are proposed. [References: 62]