C. Ruggieri et al., A STATISTICAL APPROACH FOR FRACTURE OF BRITTLE MATERIALS BASED ON THECHAIN-OF-BUNDLES MODEL, Journal of applied mechanics, 62(2), 1995, pp. 320-328
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.