Abstract. An existing model of slow crack growth in brittle composites is extended to the case of cyclic loading. The mode of crack growth being modeled consists of a sequence of jumps of random magnitude with random arrest durations between the jumps. Both the jumps and the arrest durations are governed by their respective non-homogeneous Poisson processes, one in space coordinate, the other one in the number of cycles N. A PDE is derived for the transition probability of the random process that represents crack tip location as a function of N. A Paris Law type relation is derived. A numerical illustration is considered.

Received: October 24, 2012

AMS Subject Classification: 74R10, 60K35

Key Words and Phrases: brittle fracture, stochastic Crack growth, Paris law

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DOI: 10.12732/ijpam.v84i3.3 How to cite this paper?
Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2013
Volume: 84
Issue: 3

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