Weight function approach for stress analysis of the surface crack in a finite plate subjected to nonuniform stress fields

The effects of various nonuniform stress fields on the stress intensity factors for the semi-elliptic surface crack (three-dimensional problem) in a finite plate are determined using the weight function approach. The formulation satisfies the linear elastic fracture mechanics criteria and the principle of conservation of energy. Based on the knowledge of stress intensity solutions for the reference load/stress system, the expression for the crack opening displacement function for the surface crack is derived. Using the crack opening displacement function and the reference stress intensity factor, the three-dimensional weight functions and subsequently the stress intensity solutions for the surface crack subjected to nonuniform stress fields are derived. The formulation is then applied to determine the effects of linear, quadratic, cubic, and pure bending stress fields on the stress intensity factor for the surface crack in a finite plate. In the initial stage of the study a two-dimensional problem of an edge-crack emanating from the weld-toe in a T-joint is considered. The effect of parameters such as plate thickness, weld-toe radius, and weld-flank angle on the stress intensity factor for an edge-crack is studied. Finite element analyses of the welded T-joints are performed to study the effects of plate thickness, weld-toe radius and the weld-flank angle on the local stress distribution. The ratio of plate thickness to weld-toe radius ranging from 13.09 to 153.93, and the weld-flank angles of 30, 45, and 60 degrees are considered in the analyses. Based on the results from FEM analyses, a parametric equation for the local stress concentration factor and a polynomial expression for the local stress distribution across the plate thickness are derived using the method of least squares and the polynomial curve-fitting technique.