In the last decade, progress in brittle material technology (CC-composites, ceramics, ceramic composites, etc) made these so attractive for structural applications that one has to put up with their tendency to fail unpredictably, provided that one can predict with confidence probabilities of failure. The present paper addresses prediction of life-time scatter for brittle materials. In the paper, we model a commonly observed mode of slow crack growth in brittle materials, namely a Markovian stochastic pattern of a microscopic random jump, followed by a random waiting time, followed by a random jump, and so on. The waiting times are related, on physical grounds, to random energy barriers at the arrest points, whereas random magnitudes of the jumps are treated within the existing framework of Crack Diffusion Theory. This leads to a description of crack growth as a random process whose transition probability density satisfies a hyperbolic PDE. Relation to probabilistic life-time prediction is discussed and a simple illustrative example considered.
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January 1994
Review Articles
A Stochastic Model for Slow Crack Growth in Brittle Materials
Boris I. Kunin
Boris I. Kunin
Department of Mathematical Sciences, MDH 204, University of Alabama, Huntsville AL 35899
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Boris I. Kunin
Department of Mathematical Sciences, MDH 204, University of Alabama, Huntsville AL 35899
Appl. Mech. Rev. Jan 1994, 47(1S): S175-S183
Published Online: January 1, 1994
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Online:
April 29, 2009
Citation
Kunin, B. I. (January 1, 1994). "A Stochastic Model for Slow Crack Growth in Brittle Materials." ASME. Appl. Mech. Rev. January 1994; 47(1S): S175–S183. https://doi.org/10.1115/1.3122811
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