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.

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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

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Civil Engineering
  • Coefficients
  • Crack Propagation
  • Crack Tips
  • Cracks
  • Differential Equations
  • Diffusion Coefficient
  • Energy
  • Equations
  • Mechanics
  • Potential Energy
  • Probabilistic Models
  • Probability
  • Statistical Analysis
  • Structural Engineering
  • Test And Evaluation
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Materials Science (Mechanical Engineering).