Critical grain size microcracking

To estimate the critical grain size above which spontaneous microcracking would occur, the various energy terms have to be considered. For the sake of simplicity, the grains are assumed to be cubes with grain size d in which case the total energy of the system is " ... 

Pits that reach a critical depth can act as crack initiation sites if they lead to a higher local stress intensity. The crack initiation time in this case corresponds to the incubation time of pits of a critical size. Alternatively, precipitation reactions at the grain boundaries can render an alloy sensitive to intergranular corrosion. The preferentially corroded grain boundary then serves as initiation site of a crack. Inclusions, preexisting microcracks, or other structural defects are also likely crack initiation sites. The crack initiation time, in this case, is defined as the time required for a crack to reach a detectable size. Crack initiation may also be the result of hydrogen formed by a corrosion reaction that may cause embrittlement of the metal or of successive ruptures of a passive film or tarnish layer, but these mechanisms are more important for the propagation than the initiation of cracks. Because of the multitude of possible crack initiation mechanisms, and because of the statistical nature of the phenomenon, it is not possible to predict the crack initiation time from first principles. 

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