Calibration of Weibull stress parameters using fracture toughness data

Abstract

The Weibull stress model for cleavage fracture of ferritic steels requires calibration of two micromechanics parameters $(m,\sigma _u )$. Notched tensile bars, often used for such calibrations at lower-shelf temperatures, do not fracture in the transition region without extensive plasticity and prior ductile tearing. However, deep-notch bend and compact tension specimens tested in the transition region can provide toughness values under essentially small-scale yielding (SSY) conditions to support Weibull stress calibrations. We show analytically, and demonstrate numerically, that a nonuniqueness arises in the calibrated values, i.e., many pairs of $(m,\sigma _u )$ provide equally good correlation of critical Weibull stress values with the distribution of measured (SSY) fracture toughness values. This work proposes a new calibration scheme to find $(m,\sigma _u )$ which uses toughness values measured under both low and high constraint conditions at the crack front. The new procedure reveals a strong sensitivity to m and provides the necessary micromechanical values to conduct defect assessments of flawed structural components operating at or near the calibration temperature in the transition region. Results of a parameter study illustrate the expected values of m for a typical range of material flow properties and toughness levels. A specific calibration is carried out for a mild structural steel (ASTM A36).