Diffusion-Controlled Fatigue Crack Growth

If the transport and surface reaction processes are fast not rate limiting), then crack growth would be controlled by the rate of diffusion of the embrittling species into the fracture process zone ahead of the crack tip. The functional dependence for diffusion-controlled crack growth, therefore, assumes the following form  

The exponent m in Eqn. (9.11) is typically assumed to be equal to 1/2 for diatomic gases, such as hydrogen but the number m is used here to recognize the possible existence of intermediate states in the dissociation from their molecular to atomic form. The factor 2 in the exponential term again recognizes the dissociation of diatomic gases, such as hydrogen (H2), into atomic form. 

Note that the functional dependence of fatigue crack growth response can be quite different between the different material-environment systems. These differences arise from differences in reactivity, mechanisms, kinetics, etc., and must be characterized carefully. 

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