Three-dimensional elastic-plastic finite-element analyses of constraint variations in cracked bodies

Abstract

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 elastic-perfectly plastic material under monotonie 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 α g 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 α g were found to be nearly independent of crack length and were related to the stress-intensity factor for a given thickness. Using the global constraint factors, crack-tip-opening displacements calculated from a modified Dugdale model compared well with the finite-element results from small- to large-scale yielding conditions for both thin and thick bodies. An application of the global constraint factor concept to model fatigue-crack growth under aircraft spectrum loading is presented.