A STATISTICAL APPROACH FOR FRACTURE OF BRITTLE MATERIALS BASED ON THECHAIN-OF-BUNDLES MODEL

An analytical method for the assessment of failure probability of brit tle materials exhibiting progressive cracking prior to cleavage fractu re is presented. The underlying fracture mechanism is based on the ass umption that instability of a critical flaw no longer lends to failure and causes redistribution of the local stresses. The fracture process progresses by consecutive unstable propagation of the surviving flaws lip to total failure. A limiting distribution far the fracture stress , which is identical with the first asymptotic distribution of smalles t values, is derived on the basis of a chain-of-bundles probability mo del. Numerical procedures for calculating the parameters of the limiti ng distribution are also described Due to the nature of the resulting distribution the method employs the maximum likelihood estimation of p arameters combined with a finite element solution to the crack-tip fie lds. An application of the present model to analyze the effect of notc h depth on fracture toughness values obtained from single-edge notch b end (SENB) specimens is also included.