Strength/size effect for anisotropic brittle materials under a random stress state

A simple analytical method for predicting the strength/size effect is propo sed for anisotropic brittle materials under 2- or 3-D random stress states. Statistical characteristics of the stress state (mean values and all possi ble correlations) along with statistical characteristics of random strength properties are assumed to be known and are used as initial data. The aniso tropy of the random strength response is also taken into account. The metho d is a generalization of a previously proposed approach allowing one to pre dict the probability of failure or reliability by means of an exact analyti cal solution. The new method is developed for ideally brittle materials and accounts for the size effect and non-uniformity of the random stress state , when all statistical parameters of loading are functions of the coordinat es. Examples are provided to illustrate the use of the method and to show e ffects of size, variability of strength properties, and variability of load ing for typical composites. Although the method is proposed for anisotropic composite materials, it may also be used for brittle isotropic materials ( glass, ceramic, etc.). (C) 1999 Elsevier Science Ltd. All rights reserved.