Three-Dimensional Slightly Nonplanar Cracks

Abstract

Abstract Three-dimensional slightly nonplanar cracks are studied via a perturbation method valid to the first-order accuracy in the deviation of the crack shape from a perfectly planar reference crack. The Bueckner-Rice crack-face weight functions are used in the perturbation analysis to establish a relationship, within first-order accuracy, between the apparent and local stress intensity factors for the nonplanar crack. Perturbation solutions for a cosine wavy crack with arbitrary wavelengths are used to examine the effects of three T-stress components, Txx, TXZ, TZZ, on the stability of a mode 1 planar crack in the x-z plane with front lying along the z-axis. A condition for the mode 1 crack to be stable against three-dimensional wavy perturbations of wavelengths λx and λz is determined as Txx + Tzzg < 0 where g is negative, with a very small magnitude, for 0<λx/λz<1/3 and positive for 1/3<λx/λz<∞; this suggests that when Txx = 0, a compressive stress Tzz may cause crack deflection with large wavelengths parallel to the crack front and a tensile stress Tzz may cause deflection with small wavelengths parallel to the front. For comparable T-stress values, it is shown that a negative Txx always enhances the stability of a mode 1 planar crack and a negative Tzz ensures the stability of a mode 1 crack against perturbations parallel to the crack front. The shear component Txz, while not affecting the mode 1 path stability, induces a mode 3 stress intensity factor once crack deflection occurs, and thus promotes the formation of en echelon-type cracking patterns.