Transport-Controlled Crack Growth

Substituting the mass of the gas molecule, in terms of its gram molecular weight, and Avogadro s number, Va and F are given as follows  

The functional dependence for transport-controlled crack growth is obtained simplify by equating the rate of consumption of the gas by reactions with the newly created crack surface and the rate of supply of gas by Knudsen flow along the crack. The rate consumption is equal to the rate at which new crack surface sites (atoms) are created, and is given by  

NoU (2 B) (number of surface sites created per unit time) 

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From the surface chemistry studies, it is seen that the titanium-water vapor surface reaction rate is very fast. The reaction rate constant kc at room temperature is of the order of 10 Pa s and supports the transport controlled for crack growth. (Although there is a slower additional reaction, its contribution to crack growth appears to be small, and no further consideration was given to it.) Conformance of the data to the model for transport controlled crack growth is shown in Fig. 9.13 at two AK levels and two heat treatment conditions. 

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 ... 

A contributing, if not controlling, mechanism for crack growth rate may be transport of corrosive reactants to the crack tip and/or corrosion products from the tip. This transport may be bulk flow of the environment into the crack as it advances or it may be diffusion of species such as Cl-, H+, and 02. 

Studies of environment-enhanced crack growth in gaseous environments have shown that crack growth may be controlled by (i) the rate of transport of the environment (along the crack) to the crack tip, (ii) the rate of surface reactions with the newly created crack surfaces to evolve hydrogen, or (iii) the rate of diffusion of hydrogen into the process zone ahead of the crack tip. In this simplified, chemical-based model, the competition between transport and surface reaction is considered. 

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) ... 

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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