Transport-Controlled Fatigue Crack Growth

For highly reactive gases/active surfaces (e.g., water vapor/aluminum), the rate of reaction of the environment with the newly created crack surfaces at the crack tip is limited by the rate of transport of gases by molecular (Knudsen) flow to the crack tip. The extent of reaction with the newly created crack surface, or surface coverage 9 is proportional to the rate of arrival of the gas and the time for reaction as described in Chapter 8 namely, 

In Eqn. (9.4), F is the volumetric flow rate, po is the external pressure of the deleterious gas, S is the surface area (both sides) of the crack increment, No is the density of surface sites (or number of metal atoms per unit area), k is Boltzmann s constant, and ris the absolute temperature. Note that, because of the transport by molecular (Knudsen) flow along the crack, the gas pressure at the crack tip would be orders of magnitude less than po. 

By defining the fractional surface coverage 0 as 0 = (Po/f)/iPo/f)s, and sub stituting it into Eqn. (9.3), The functional dependence on vapor pressure and fre quency becomes  

2 Surface/Electrochemical Reaction-Controlled Fatigue Crack Growth 

Similar to the case of sustained loading, it is assumed that the surface reaction(s) that control crack growth follow first-order kinetics. As such the surface coverage 9 of a deleterious gas is given by  

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Pao, P. S., Gao, M., and Wei, R. P., Critical Assessment of the Model for Transport-Controlled Fatigue Crack Growth, in Basic Questions in Fatigue, ASTM STP 925, Vol. II, American Society for Testing and Materials, Philadelphia, PA (1988), 182-195. 

This behavior is generally characterized by a plateau region, which prevails over a definite threshold It i usually referred to as stress CF as SCC systems usually exhibit this behavior, and the most common theory assumes that the crack growth rate is because of the addition of SCC and pure fatigue crack advance. This type of synergistic effect is observed in systems not sensitive to SCC such as ferritic stainless in seawater under cathode polarization. It is often associated with HE. It is possible that the plateau behavior is because of the control of crack growth rate by nonmechanical processes such as transport processes (73). 

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