Functional Weibull-based models of steel fracture toughness for structural risk analysis: estimation and selection

A key input component of numerous reliability studies of industrial components or structures, steel fracture toughness is usually considered as a random process because of its natural variability. Moreover, toughness presents a high sensitivity to temperature which also plays a fundamental role, as an environmental forcing, in such studies. Therefore a particular attention has to be paid to the assessment of its stochastic functional modelling, conducted by a statistical analysis of indirect measures. While a Weibull shape arising from statistical physics is recognized as one of the most relevant approach to represent local variability, the selection of functional parameters requires an accurate methodology of fracture toughness modelling. This article provides such a methodology, that solves inconsistencies in former data treatments. The innovation consists in three improvements: (a) the thickness correction of the steel specimen is included throughout the calculation and not performed a priori; (b) nonstandard but informative data are included in the assessment as censored data; (c) a chi-square test is developed to assess the model quality relatively to fracture toughness data, indexed by temperature. Illustrated by the exploration of a database feed by several European manufacturers, this complete methodology is implemented in a dedicated software tool.