On singular stress at the crack tip of a thick plate under in-plane loading

By superposition of three asymptotic solutions, which collectively satisfy all the equilibrium and compatibility equations as well as boundary conditions, the three-dimensional crack tip stresses of a thick plate with a through-the-thickness cut are shown to be of square root singularity throughout the thickness. The near tip deformation is shown to be plane strain with stress intensity factor changing in the thickness direction. All components of the singular stresses vanish on plate surfaces. The profile of the stress intensity factor in the thickness direction cannot be determined by the asymptotic analysis alone.