Coupling of the Weibull stress model and macroscale models to predict cleavage fracture

Abstract

This study couples the ASTM E1921 procedure to characterize the ductile-to-brittle toughness of ferritic steels in terms of K J c (or J c) values with the Weibull stress model, i.e., the “local approach” for fracture at the microscale. The E1921 procedures assume that uniform, small-scale yielding (SSY) conditions exist at fracture along the full crack-front, which supports the use of a simple thickness scaling relationship to adjust experimental toughness values to an equivalent 1T size. For smaller specimens tested at temperatures in the mid-to-upper transition, plasticity induced constraint loss (crack-front triaxiality) frequently invalidates the simple scaling relationship. The non-dimensional functions, g( M= bσ 0/ J), derived from application of the Weibull stress approach for a specific specimen and material, describes the evolution of constraint loss effects on the fracture toughness relative to a plane-strain, SSY reference condition. The g-functions vary with parameters of the Weibull stress model, material flow properties, and specimen geometry, but not with the absolute specimen size. By combining the g-functions and a Weibull stress-based expression for the cumulative probability, a new procedure is proposed that adjusts (scales) measured toughness values simultaneously for both thickness and constraint loss directly within the existing E1921 framework. Monte Carlo simulations are used with the new approach to estimate the effects of constraint loss on the E1921 reference temperature, T 0, for a range of specimen types, sizes and material properties.The paper concludes with an application of the new g-function approach in the E1921 framework for fracture tests performed on an A36 structural steel to correct the data sets for constraint loss and to estimate constraint loss effects on the T 0 value.