A Probabilistic Model of Brittle Crack Formation.
Interim rept. Apr 86-Mar 87,
CASE-WESTERN RESERVE UNIV CLEVELAND OH
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Probability of a brittle crack formation in an elastic solid with fluctuating strength is considered. A set omega of all possible crack trajectories reflecting the fluctuation of the strength field is introduced. The probability PX that crack penetration depth exceeds X is expressed as a functional integral over omega of a conditional probability of the same event taking place along a particular path. Various techniques are considered to evaluate the integral. Under rather non-restrictive assumptions we reduce the integral to solving a diffusion type equation. Here a new characteristic of fracture process, crack diffusion coefficient, is introduced. Then an illustrative example is considered where the integration is reduced to solving an ordinary differential equation.