An Approximate Technique for Predicting Size Effects on Cleavage Fracture Toughness (Jc) Using the Elastic T Stress

Abstract

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∣ >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∣ >0.4, it appears that only an elastic analysis may be needed to determine reasonably accurate J0 values for structural conditions.

Numerical investigation of 3-D constraint effects on brittle fracture in SE(B) and C(T) specimens

“…The interaction of crack-tip plastic zones with nearby traction-free surfaces and with global plastic zones affects strongly the near-tip stresses which control the onset of cleavage fracture. Stresses relax below the values determined uniquely by the J-integral [471 for the high constraint condition of small-scale yielding (SSY) [23] which exists early in the loading. This loss of a unique relationship between the crack-tip stresses and J , coupled with an absolute thickness effect due to random metallurgical variations and microstructural flaws along the crack front, underlies the specimen geometry, loading mode and size effect in tests to measure cleavage fracture toughness in the DBT region (see Wallin…”

Transient elastic‐plastic‐creep crack‐tip stress fields under load‐controlled loading

“…However, it has been shown that the use of the HRR field to define the Q ‐parameter can give a slight difference in the asymptotic behaviour under SSY . Accordingly, an alternative definition using the T ‐stress is often used: where the subscript “ T = 0” refers to the stress value correspond to the field for T = 0.…”

Using torsional bar testing to determine fracture toughness

“…Kirk et al 7 . show the effect of finite size on opening mode stress, σ yy , near the crack tip at a constant normalized distance R = r /( J / σ 0 ) ahead of the crack as…”

“…The J ‐integral value near the crack tip was evaluated under incremental loading, using a non‐linear analysis method based on the small‐strain criterion. The size effect on opening mode stress near the crack tip at a constant normalized distance R , R = r /( J / σ 0 ), leading ahead of the crack can be investigated approximately with the Kirk–Dodds–Andersons formula 7 . For illustrative purposes, σ 0 is set to equal the yield stress, 441 MPa.…”