3-DIMENSIONAL SLIGHTLY NONPLANAR CRACKS

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, T(xx), T(xz), T(zz), 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 lambda(x) and lambda(z) is determined as T(xx) + T(zz)g<0 where g is negative, with a very small magnitude,for 0<lambda(x)/lambda(z)<1/square-root 3 and positive for 1/square-root 3<lambda(x)/lambda(z)<infinity; this suggests that when T(xx)=0, a compressive stress T(zz) may cause crack deflection with large wavelengths parallel to the crack front and a tensile stress T(zz) may cause deflection with small wavelengths parallel to the front. For comparable T-stress values, it is shown that a negative T(xx) always enhances the stability of a mode 1 planar crack and a negative T(zz) ensures the stability of a mode 1 crack against perturbations parallel to the crack front. The shear component T(xz), 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.