1 Effect of Loading Rate and Creep
In no material can fracture happen instantly. Cracks take a finite time to form and to propagate over a finite distance. The reason is that the process of bond ruptures proceeds at a certain finite rate. The basic physical theory describing the process is the rate process theory, in which the rate of bond ruptures is determined by the activation energy, U. The probability (or frequency) of bond rupture depends on the microstress level at the crack tip, which in turn is determined by either the stress intensity factor, K j , or by the energy release rate, G. Based on these physical observations, the following approximate relation ensues (Evans, 1974):
a = M K j /K u T e - W (7.1)
in which a = velocity of crack tip propagation, T — absolute temperature, R = universal gas constant, and i/c, n = empirical constants. Roughly, n ~ 30, while vc can have very different values. According to Eq. 7.1, the relationship between log a and log i f / should be linear. But this is true only approximately. Experiments indicate a mildly nonlinear relationship between log Ki and the loading rate, but no clear information exists with regard to a.