Strength variability in brittle materials with stabilizing and destabilizing resistance fields

Abstract

Variability in the fracture strength of materials with flaws which experience various stabilizing and destabilizing fields during their extension to failure is examined. Two cases are considered: (a) when the flaws are subjected to a residual surface stress, and (b) when the resistance to crack extension increases with crack length (R- or T-curve behavior). In the analysis, the crack size distribution is treated as continuous. By invoking the equilibrium and instability criteria for fracture, and by describing the physical stabilizing and destabilizing fields in terms of the appropriate stress intensity factors, the forms of the strength distributions are obtained. General forms for the crack size distribution are assumed and fundamental statistical descriptors, mean and standard deviation, are used to characterize the strength and variability. The results of the analysis are insensitive to the crack size distribution assumed and indicate that the variability in the cases studied is not necessarily a monotonic function of the microstructural variables. Directions for altering the microstructure of materials in order to obtain optimum strength and variability characteristics are discussed. © 1993.