Three-Dimensional Stress Field Near the Crack Front of a Thin Elastic Plate

Abstract

Based on very detailed full-field finite element analysis of the near tip region of a thin isotropic elastic plate, the three-dimensional stress state in the vicinity of a through-crack front is characterized. The computed stress field reveals strong three-dimensional effects within a radial distance of about one-half thickness from the crack-tip. Further away from the tip, through-thickess variation of field quantities decreases and, at the radial distance of approximately 1.5 times the thickness, in-plane stresses merge with the dominant two-dimensional plane stress solutions. These “two-dimensional-three-dimensional” transition distances are essentially independent of the material Poisson’s ratio, yet the amplitude of variation is greatly affected by its value. The influence of Poisson’s ratio is clearly illustrated by local J along the crack front, which shows much higher variation through the thickness for nearly incompressible solids. At points very close to the crack front, relative magnitudes of out-of-plane strain components become very small, and asymptotic plane strain conditions prevail locally. On the mid-plane of the plate, the crack tip field converges to that given by the local plane strain stress intensity factor solution within a radial distance from the tip of less than 0.5 percent of thickness. In addition, it is found that the field near the intersection of crack front and free surface may be characterized by the corner singularity of a quarter infinite crack in a half space. The size of this domain is inferred from the gradient of local stress intensity factor with respect to distance from the free surface, and it appears that the corner singularity region extends up to a spherical radius of about 3 percent of plate thickness away from the intersection. Also the amplitude of the corner singularity field is described by a corner stress intensity factor, and its magnitude is determined for thin plates of various Poisson’s ratios.