Relation between Stochastic failure location and strength in brittle materials

Statistical characteristics of failure location and their relation to strength in brittle materials are studied. One-dimensional rod and bending of a beam under arbitrary distributed loads are studied as examples. The analysis is based on the weakest link approach, and is not confined to specific strength distributions (such as Weibull, Gaussian, etc.). It is found that the statistical moments of the failure location (average, variance, etc.) are directly related to the area moments (centroid, inertia, etc.) of a simple function of the stress field. Therefore, important information related to material strength can be experimentally obtained based on measuring failure locations. Such experiments do not require the measurement of stresses, strains, or displacements, and are very attractive for MEMS/NEMS applications. The approach is general and can be applied to other types of testing specimens.