Surface Reaction and Diffusion-Controlled Crack Growth

2 Surface Reaction and Diffusion-Controlled Crack Growth 

If the rate of transport of gases along the crack were sufficiently fast, then crack growth would be controlled (rate limited) by the rate of surface reactions with the newly created crack surface. Assuming, for simplicity, that the reactions follow first-order kinetics, the rate of increase in the fractional surface coverage 6 is given by Eqn. (8.15)  

The functional dependence of crack growth rate on pressure and temperature (for a monotonic gas) is deduced from the foregoing relationship as follows  

More generally, for diatomic gases, such as hydrogen, the following form for surface reaction control is used  

If the transport and surface reaction processes are rapid i.e., not rate limiting), then crack growth would be controlled by the rate of diffusion of the embritthng species into the fracture process zone ahead of the crack tip. For diffusion-controlled crack growth, therefore, the rate equation assumes the following form  

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