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Elasticfactor eg, an averaged-normal-stress-to-flow-stress ratio over the plastic region, was defined to simulate three-dimensional (3D) effects in twodimensional (2D) models. For crack lengths and uncracked ligament lengths greater than four times the thickness, the global constraint factor was found to be nearly a unique function of a normalized stress-intensity factor (related to plastic-zone-size-to-thickness ratio) from small-to large-scale yielding conditions for various specimen types and thickness.For crack-length-to-thickness ratios less than four, the global constraint factor was specimen type, crack length and thickness dependent. Using a 2D strip-yield model and the global constraint factors, plastic-zone sizes and crack-tip displacements agreed reasonably well with the 3D analyses.For a thin sheet aluminum alloy, the critical crack-tip-opening angle during stable tearing was found to be independent of specimen type and crack length for crack-length-to-thickness ratios greater than 4.

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An experimental study of crack tip opening displacement (CTOD) for Mode I/Mode II stable crack growth in thin sheet 2024-T3 aluminum has been conducted. To perform the experiments, an Arcan specimen and fixture was modified so that (1) slippage in the grips was eliminated, (2) large rotations of the fixture components were achievable and (3) bending stresses were minimized. Defining Θ to be the angle between the Mode I loading direction (perpendicular to the crack line) and the direction of applied loading, experimental results indicate that (a) for large amounts of crack extension, a ≥ 10 mm, the value of CTOD at 1 mm behind the crack tip appears to approach a constant value of 0.1 mm for all modes of loading, (b) the direction of crack extension varied with applied mixed mode loading, (c) Mode I crack extension is predominant for 0° ≤ Θ ≤ 60°, (d) Mode II crack extension is predominant for 75° ≤ θ ≤ 90° and (e) a transition zone exists for angles θ near 75°.

Fracture tests were conducted on 76.2mm wide, 2.3mm thick middle crack tension (M(T)) specimens machined from 2024-T3 aluminum sheet. The specimens were tested in the T-L orientation and comparisons were made to similar tests conducted in the L-T orientation. Measurement of critical crack tip opening angle (CTOA), applied stress, and crack front shape were made as a function of crack extension. A two-dimensional, elastic-plastic finite element analysis was used to simulate the fracture behavior for both orientations. The results indicate that the T-L orientation had a 10% lower stress at fracture than similar tests conducted in the L-T orientation. Correspondingly, the critical CTOA in the T-L tests reached a constant value of 4.7° after 2–3mm of crack extension and the L-T tests reached a value of 6°. The fracture surface of the T-L specimens were observed to remain flat, while those of the L-T specimens transitioned to a 45° slant fracture after about 2–3mm of crack extension. The tunneling behavior of the two orientations also differed; the T-L specimens reached a deeply tunneled stabilized crack front shape, while the L-T specimens were observed to have only a small amount of tunneling once the crack began to grow on the 45° slant. The two-dimensional, elastic-plastic finite element analysis was able to simulate the fracture behavior for both the T-L and L-T orientations.

A small strain theory, three-dimensional elastic-plastic finite element analysis was used to simulate fracture in thin sheet 2024-T3 aluminum alloy in the T-L orientation. Both straight and tunneled cracks were modeled. The tunneled crack front shapes as a function of applied stress were obtained from the fracture surface of tested specimens. The stable crack growth behavior was measured at the spec&en surface as a function of applied stress. The fracture simulation modeled the crack tunneling and extension as a function of applied stress. The results indicated that the global constraint factor, ag, initially dropped during stable crack growth. After peak applied stress was achieved, ag began to increase slightly. The effect of crack front shape on ag was small, but the crack front shape did greatly influence the local constraint and through-thickness crack-tip opening angle (CTOA) behavior. The surface values of CTOA for the tunneled crack front model agreed well with experimental measurements, showing the same initial decrease from high values during the initial 3mrn of crack growth at the specimen's surface. At the same time, the interior CTOA values increased from low angles. After the initial stable tearing region, the CTOA was constant through the thickness. The three-dimensional analysis appears to confirm the potential of CTOA as a two-dimensional fracture criterion. NOMENCLATURE