Application of the Weibull Methodology to a Shallow-Flaw Cruciform Bend Specimen Tested Under Biaxial Loading Conditions

This paper describes the application of the Weibull methodology to the analysis of a shallow-flaw cruciform bend specimen tested under biaxial loading conditions. The cruciform bend fracture mechanics specimen was developed at Oak Ridge National Laboratory (ORNL) to introduce a far-field, out-of-plane biaxial bending stress component in the test section that approximates the nonlinear stresses resulting from pressurized-thermal-shock or pressure-temperature loading of a nuclear reactor pressure vessel (RPV). Tests with the cruciform specimen demonstrated that biaxial loading can have a pronounced effect on shallow-flaw fracture toughness in the lower transition temperature region for an RPV material. High-constraint deep-flaw compact tension C(T) and low-constraint shallow-flaw cruciform fracture toughness data were used to assess the ability of the Weibull methodology to predict the observed effects of biaxial loading on shallow-flaw fracture toughness. A new hydrostatic stress criterion along with five equivalent-stress criteria from the literature were selected to serve as candidate kernels in the integral formulation of the Weibull stress. Among these candidates, the hydrostatic stress criterion, derived from the first invariant of the Cauchy stress tensor, was determined to have the required sensitivity to multiaxial-loading states. In addition, a new calibration technique developed by researchers at the University of Illinois for determining the necessary Weibull parameters is applied to the C(T) and cruciform data. A three-parameter Weibull model based on the hydrostatic stress criterion is shown to predict the experimentally observed biaxial effect on cleavage fracture toughness by providing a scaling mechanism between uniaxial and biaxial loading states. In summary, the conclusions that can be drawn from this study are as follows: (1) With respect to its effect on fracture toughness, the biaxial effect is a constraint effect. (2) A Weibull statistical fracture model has been successfully calibrated with uniaxial toughness data obtained from a conventional high-constraint C(T) specimen and a uniaxially loaded shallow-flaw cruciform that is effectively equivalent to a conventional shallow-flaw SE(B) specimen. (3) The calibrated fracture model was able to successfully predict the intermediate constraint-loss effects associated with two levels of biaxial loading. (4) These preliminary results at a single test temperature offer encouragement that complex multiaxial loading effects on transition region fracture toughness can be predicted with statistical fracture models developed using data obtained from conventional specimens. (5) Future work is required to investigate these effects at other temperatures within the transition region.