A Probabilistic Model of Brittle Crack Formation.
Abstract
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 P(X) 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1987
- Accession Number
- ADA184423
Entities
People
- Abdelsamie Moet
- Alexander Chudnovsky
- Boris Kunin
Organizations
- Case Western Reserve University