| Brittle failure by fracturing is studied, focusing on the mechanics of crack kinking in homogeneous, anisotropic solids. For plane problems, two stress intensity factors (SIF's) associated with the hoop and shear stress components at the crack tip are defined, which can be used to examine the crack growth process. For small kink angles HSIF and SSIF are almost equal to K;Alternative solution methods are examined. It is shown that the fracture problem can be formulated more efficiently when the crack-surface boundary conditions are expressed in terms of the resultant-forces instead of tractions. For the numerical solution (FEM), a crack-tip finite element is developed. This element incorporates Williams' crack-tip solution. The element is a polygon with its center at the crack tip. The effectiveness of this element is illustrated using several simple test problems.;For the inception of crack kinking, energy-release rate (G) is obtained by: (1) calculating (in terms of HSIF and SSIF) the work required to fully close the kink gap and restore the normal and shear stresses existed before kinking (G;To verify which criterion is suitable for anisotropic materials, some experiments are performed on notched single-crystal sapphire specimens. FEM is used to support the experimental results. The experimental observations are compared with the maximum-tensile stress and the maximum-G criteria. Several fracture measures are introduced. They correlate the fracture resistance of different cleavage planes and the local stress fields to the fracture path. The notched specimens tend to fracture where the tensile stress is maximum. The energy criterion failed to predict the fracture path for some of the specimens. |
