Finite-Element and Experimental Evaluation of the J-Integral for Short Cracks
Authors: Dodds RH , Read DT , Wellman GW 
Published: March 2009

Fitness-for-service assessments of critical metal structures such as piping systems, pressure vessels, and ships require accurate predictive methods for fracture of parts containing small flaws or short cracks. Flaw size, geometry, applied loads, fabrication, and material characteristics often combine to produce large-scale plastic zones inappropriate for evaluation by linear elastic fracture mechanics. The J-integral is widely advocated as a suitable parameter to characterize both material fracture toughness and the driving force in elastic-plastic fracture. Procedures have been proposed to measure the material fracture toughness, JIc, for standard test specimen geometries containing large crack lengths. However, there are no generally accepted methods to predict or experimentally measure the applied J-integral within a structural element containing a small crack (defined here by a crack length to remaining ligament ratio, a/W, &lt; 0.25).
This paper describes analytical studies conducted using the finite-element method (FEM) to predict applied J-integral values in single-edge-notch tensile panels (width/thickness ≈ 9) of HY-130 steel for crack lengths in the range 0.02 ≤ a/W ≤ 0.22. Nominal strain levels beyond yield are addressed specifically. Comparisons are made with preliminary experimental J-values obtained by integrating strain and displacement quantities measured along an instrumented contour. FEM plane stress predictions for applied J increasingly exceed experimentally measured values for decreasing crack lengths with large discrepancies observed at strain levels above nominal yield. The introduction of a small stiffened zone that provides partial through-thickness constraint around the crack tip, using a plane stress-plane strain overlay scheme, considerably reduces the disagreement. Near tip stiffening also improves results in the regime between elastic and fully plastic response and slightly elevates the predicted limit loads.
These computational results suggest a strong dependence of the applied J on partial through-thickness constraint near the tips of short cracks under conditions normally considered plane stress. The effect of near tip stiffening diminishes for crack lengths greater than the specimen thickness, but does reduce the small remaining discrepancy between FEM plane stress and experimental J-values for longer cracks. Both experimental and computational evidence imply the existence of a transition range of crack lengths in which the applied J begins to decrease significantly at strains above yield as the crack length approaches zero. Given the existence of a small flaw in a critical structural component, knowledge of this transition range behavior may prove essential for defect assessment. Two-dimensional FEM plane stress models do not predict this behavior unless augmented with the partial thickness constraint capability near the crack tip. The modeling scheme adopted in this study can be utilized without modification of standard elastoplastic analysis software and appears to minimize the necessity of expensive, three-dimensional nonlinear computations.