Three-dimensional elastic-plastic (small-strain) finite-element analyses were used to study the stresses, deformations, and constraint variations around a straight-through crack in finite-thickness plates for an elastlc-perfectly plastic material under monotonic and cyclic loading.Middle-crack tension specimens were analyzed for thicknesses ranging from 1.25 to 20 mm with various crack lengths. Three local constraint parameters, related to the normal, tangential, and hydrostatic stresses, showed similar variations along the crack front for a given thickness and applied stress level. Numerical analyses indicated that cyclic stress history and crack growth reduced the local constraint parameters in the interior of a plate, especially at high applied stress levels. A global constraint factor ag was defined to simulate three-dimensional effects in two-dimensional crack analyses. The global constraint factor was calculated as an average through-the-thickness value over the crack-front plastic region.Values of eg were found to be nearly independent of crack length and were related to the stress-intensity factor for a given thickness.
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.
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.
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