A simplified probabilistic model of the growth of creep cavitation

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Abstract
We present a simplified probabilistic model for the growth of creep cavitation based upon earlier work of Fariborz, Harlow and Delph. The model is cast in the form of a random differential equation, which is valid for times sufficiently short that the cavities do not cover an appreciable portion of the grain boundary. This equation is solved using a numerical technique due to Bellomo and Pistone in order to obtain the probability density function (p.d.f.) for the distribution of the cavity sizes as a function of time. In physical terms, this is equivalent to determining the normalized cavity size distribution as a function of time. The present model represents the first probabilistically-based model of creep cavity growth for which it has been possible to calculate the probability density function. The results are compared with experimentally measured cavity size distributions. They seem to be in good qualitative agreement with the data for the range of times for which the model is valid, as well as in reasonable quantative agreement in several aspects.