Predicting how crack tip residual stresses influence brittle fracture

A probability distribution model, based on the local approach to fracture, has been developed and used for estimating cleavage fracture following prior loading (or warm pre-stressing) in two ferritic steels. Although there are many experimental studies it is not clear from these studies whether the generation of local residual stress and/or crack tip blunting as a result of prior loading contribute to the enhancement in toughness. We first identify the Weibull parameters required to match the experimental scatter in lower shelf toughness of the candidate steels. Second we use these parameters in finite element simulations of prior loading on the upper shelf followed by unloading and cooling to lower shelf temperatures to determine the probability of failure. The predictions are consistent with experimental scatter in toughness following WPS and provide a means of determining the relative importance of the crack tip residual stresses and crack tip blunting. We demonstrate that for our steels the crack tip residual stress is the pivotal feature in improving the fracture toughness following WPS. The paper finally discusses these results in the context of the non-uniqueness and the sensitivity of the Weibull parameters. key words: local approach, brittle fracture, failure probability, warm pre-stressing, residual stress NOMENCLATURE a Crack length, mm a/W crack/ligament ratio,-i order number of specific specimen (i=1,.., N) m Weibull exponent,-N total number of specimens (sample size