A Statistical Approach for Fracture of Brittle Materials Based on the Chain-of-Bundles Model

Abstract

An analytical method for the assessment of failure probability of brittle materials exhibiting progressive cracking prior to cleavage fracture is presented. The underlying fracture mechanism is based on the assumption that instability of a critical flaw no longer leads to failure and causes redistribution of the local stresses. The fracture process progresses by consecutive unstable propagation of the surviving flaws up to total failure. A limiting distribution for the fracture stress, which is identical with the first asymptotic distribution of smallest values, is derived on the basis of a chain-of-bundles probability model. Numerical procedures for calculating the parameters of the limiting distribution are also described. Due to the nature of the resulting distribution, the method employs the maximum likelihood estimation of parameters combined with a finite element solution to the crack-tip fields. An application of the present model to analyze the effect of notch depth on fracture toughness values obtained from single-edge notch bend (SENB) specimens is also included.