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Paris’ law is a crack growth equation that gives the rate of growth of a fatigue crack [3]. The stress intensity factor K characterizes the load around a crack tip and the rate of crack growth is experimentally shown to be a function of the range of the stress intensity ΔK experienced in a loading cycle (shown in Figure 1.7). The Paris’ equation describing this is

Figure 1.7 Illustration of Paris Law.

(1.43)

where a is the crack length and dadN is the fatigue crack growth for a load cycle N. The material coefficients C and m are obtained experimentally and their values depend on environment, temperature, and stress ratio. The stress intensity factor range has been found to correlate with the rate of crack growth in a variety of different conditions, which is the difference between the maximum and minimum stress intensity factors in a load cycle, defined as

(1.44)