Variations of a global constraint factor in cracked bodies under tension and bending loads

Elastic-plastic finite-element analyses were used to calculate stresses and displacements around a crack in finite-thickness plates for an elastic-perfectly plastic material. Middle- and edge-crack specimens were analyzed under tension and bending loads. Specimens were 1.25 to 20 mm thick with various widths and crack lengths. A global constraint factor alpha(sub g), an averaged normal-stress to flow-stress ratio over the plastic region, was defined to simulate three-dimensional (3D) effects in two-dimensional (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.