Shallow Flaws Under Biaxial Loading Conditions—Part II: Application of a Weibull Stress Analysis of the Cruciform Bend Specimen Using a Hydrostatic Stress Criterion1

Abstract

Oak Ridge, Tennessee USA Cruciform beam fracture mechanics specimens-have been developed in the Heavy Section Steel Technology (HSST) Program at Oak Ridge National Laboratory (ORNL) to introduce a prototypic, farfield, out-of-plane biaxial bending stress component in the test section that approximates the nonlinear biaxial stresses resulting from pressurized-thermal-shock or pressure-temperature loading of a nuclear reactor pressure vessel (RPV). Matrices of cruciform beam tests were developed to investigate and quantify the effects of temperature, biaxial loading, and specimen size on fracture initiation toughness of two-dimensional (constant depth), shallow, surface flaws. Tests were conducted under biaxial load ratios ranging from uniaxial to equibiaxial. These tests demonstrated that biaxial loading can have a pronounced effect on shallow-flaw fracture toughness in the lower transition temperature region for RPV materials. Two and threeparameter Weibull models have been calibrated using a new scheme (developed at the University of Illinois) that maps toughness data from test specimens with distinctly different levels of crack-tip constraint to a small scale yielding (SSY) Weibull stress space. These models, using the new hydrostatic stress criterion in place of the more commonly used maximum principal stress in the kernel of the 6, integral definition, have been shown to correlate the experimentally observed biaxial effect in cruciform specimens, thereby providing a scaling mechanism between uniaxial and biaxial loading states.

Reduction of measured toughness due to out‐of‐plane constraint in ductile fracture of aluminium alloy specimens

“…Although previous work has shown out‐of‐plane loading does not influence the in‐plane stresses, 26 it is conceivable that the specimen geometry is such that the out‐of‐plane loading influences the in‐plane constraint. If this were the case, the results of the biaxial tests could merely be due to variations in in‐plane constraint.…”

“…The mixed effect of low in‐plane and high out‐of‐plane constraint has received some attention, for example notable experiments were performed in the Oak Ridge National Laboratory 22–26 . The Oak Ridge National Laboratory work consisted of two sets of experiments on cleavage fracture of A533B steel.…”

“…It is clear then that there is uncertainty in the effectiveness of biaxial loading on shallow cracks to demonstrate an effect of out‐of‐plane loading. Some researchers believe they found an effect of biaxial loading 22–28 whereas others observed no change 29,30,32 . Because most of the experimental investigations were performed using FPB cruciform specimens in bending, shallow cracks had to be introduced in the specimens which led to a mixed effect of low in and high out‐of‐plane constraint.…”

Validation of constraint‐based methodology in structural integrity of ferritic steels for nuclear reactor pressure vessels

“…First, application of Eq. (12) shows that a shift in T 0 of −15 • C corresponds to an increase in effective mean toughness of K c mat /K mat = 1.23 measured at T = T 0 (K mat = 100.3 MPa √ m). Second, based on data presented in Ref.…”

“…The Weibull stress is conventionally derived from the distribution of maximum principal stress (σ 1 ) within the plastic zone ahead of the crack. Williams et al 12 have suggested that replacing σ 1 with the hydrostatic stress, σ H , to calculate the parameter Q H (i.e. Q → Q H , the so-called hydrostatic Qstress) provides an improved prediction of out-of-plane constraint effects on fracture toughness, i.e.…”