7.1. Influence of Loading Rate on Size Effect

Strictly speaking, fracture is always a time dependent phenomenon. In polymers, strong time dependence of fracture growth is caused primarily by viscoelasticity of the material (see the works of Williams and others beginning with the 1960s). In rocks and ceramics, the time dependence of fracture is caused almost exclusively by the time dependence of the bond ruptures that cause fracture. In other materials such as concrete, both sources of time dependence are very important (Ba ant and Gettu 1992, Ba ant and Wu 1993; Ba ant and Li 1997; Li and Ba ant 1997). Both sources of time dependence have a significant but rather different influence on the scaling of fracture.

Consider first the rupture of an interatomic bond, which is a thermally activated process. The frequency of ruptures is given by the Maxwell-Boltzmann distribution, defining the frequency f of exceeding the strength of atomic bonds, f ? e ^{- ? / RT}, where T = absolute temperature, R = gas constant and ? = energy of the vibrating atom. When a stress is applied, the diagram of the potential energy surface of the interatomic bonds is skewed as sketched in Fig. 7.1a. This causes the activation barrier for bond breakages to be reduced from Q to a smaller value Q - c ?, and the activation barrier for bond restorations to be increased from Q to Q + c ?, where Q =...