Two complementary methodologies are described to quantify the effects of crack-tip stress triaxiality (constraint) on the macroscopic measures of elastic-plastic fracture toughness, J and Crack-Tip Opening Displacement (CTOD). In the continuum mechanics methodology, two parameters, J and Q, suffice to characterize the full range of near-tip environments at the onset of fracture. J sets the size scale of the zone of high stresses and large deformations while Q scales the near-tip stress level relative to a high triaxiality reference stress state. Full-field finite element calculations show that the J-Q field dominates over physically significant size scales, i.e., it describes the environment in which brittle and ductile failure mechanisms are active. The material's fracture resistance is characterized by a toughness locus, Jc(Q), which defines the sequence of J-Q values at fracture determined by experiment from high constraint conditions (Q =0) to low constraint conditions (Q < 0). Contents Section No.

Fracture in the ductile-brittle transition region of ferritic steels is complicated by scatter, produced by local sampling effects, and specimen geometry dependence, which results from relaxation in crack tip constraint. Scatter and constraint are interrelated in that each influences the magnitude of the other. This article summarizes recent research on fracture in the transition region and presents a unified framework for addressing size effects and scatter. A stress volume model for quantifying constraint effects is described briefly, and a comparison between theory and experiment is presented. This model has been applied only to stationary cracks in plane strain, but methods to account for ductile crack growth and three-dimensional effects are described. The inadequacies of the weakest link model for cleavage fracture are discussed, and an improved statistical model is introduced. This new model considers the probability of propagation and arrest of cleavage microcracks. A number of recommendations for analyzing cleavage fracture toughness data are presented. Transition region data for a given material should be viewed as a statistical distribution rather than a single value. However, these data should be corrected for constraint effects and ductile crack growth before applying statistical analysis. One of several statistical distributions may be applied to cleavage data; each of the proposed distribution functions has advantages and disadvantages. One of the unknowns in transition region fracture is the threshold toughness of the material, that is, the absolute lower bound.

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This investigation examines the ability of an elastic T-stress analysis coupled with a modified boundary layer (MBL) solution to predict stresses ahead of a crack tip in a variety of planar geometries. The approximate stresses are used as input to estimate the effective driving force for cleavage fracture (J0) using the micromechanically based approach introduced by Dodds and Anderson. Finite-element analyses for a wide variety of planar-cracked geometries are conducted that have elastic biaxiality parameters (β) ranging from -0.99 (very low constraint) to +2.96 (very high constraint). The magnitude and sign of β indicate the rate at which crack-tip constraint changes with increasing applied load. All results pertain to a moderately strain-hardening material (strain-hardening exponent (n) of 10). These analyses suggest that β is an effective indicator of both the accuracy of T-MBL estimates of J0 and of applicability limits on evolving fracture analysis methods (that is, T-MBL, J-Q, and J/J0). Specifically, when ∣β∣ &gt;0.4 these analyses show that the T-MBL approximation of J0 is accurate to within 25% of a detailed finite-element analysis. As “structural-type” configurations, that is, shallow cracks in tension, generally have ∣β∣ &gt;0.4, it appears that only an elastic analysis may be needed to determine reasonably accurate J0 values for structural conditions.

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