A statistical approach to the rupture of brittle materials
Abstract
Since initial defects are the main cause of the failure of structures made of brittle materials, the scope of this paper is to take these defects into account in the evaluation of the failure probability of a structure. Using the weakest link theory assumption and modeling the failure probability of a single link, a general relationship between the statistical distribution of defects and the failure probability is obtained. After determining the size of the critical defect, some correlations between the defect distribution and the Weibull's parameters are deduced from either Linear Fracture Mechanics or Continuum Damage Mechanics. The effect of the statistical distribution of defects within the material is computed and studied with respect to the distribution itself, the loaded volume of the structure and the heterogeneity of the stress field.
 Publication:

European Journal of Mechanics Solids
 Pub Date:
 1992
 Bibcode:
 1992EJMS...11..753H
 Keywords:

 Brittle Materials;
 Failure Analysis;
 Fracture Strength;
 Statistical Distributions;
 Ceramics;
 Cumulative Damage;
 Linear Equations