# Accession Number:

## ADA184423

# Title:

## A Probabilistic Model of Brittle Crack Formation.

# Descriptive Note:

## Interim rept. Apr 86-Mar 87,

# Corporate Author:

## CASE-WESTERN RESERVE UNIV CLEVELAND OH

# Personal Author(s):

# Report Date:

## 1987-06-01

# Pagination or Media Count:

## 30.0

# 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 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.

# Descriptors:

# Subject Categories:

- Mechanics