Hoop stress intensity factor and crack-kinking in anisotropic brittle solids

To analyze crack-kinking in an infinite, homogeneous, anisotropic, linearly elastic plane containing a central main crack, two stress intensity factors are defined. These are associated with the hoop and shear stress components at the tip of the main crack. When the hoop stress intensity factor (HSIF or K-omega omega) is maximum, then the shear stress intensity factor (SSIF or K-r omega) is zero. These stress intensity factors (SIF's) are alternatives to the commonly used Modes I and II stress intensity factors (K-I and K-II which uncouple for isotropic but not for anisotropic solids. Moreover, Modes I and II stress intensity factors defined at the tip of a vanishingly small kink emanating from the tip of an existing main crack (K-I((k)) and K-II((k))) are calculated by using the method that models a kink as a continuous distribution of edge dislocations. Then, the relation of HSIF (SSIF) to K-I((k)) (K-II((k))) is examined in details for various combination of relevant parameters, i.e., for different material properties, material symmetry orientations, and loadings. It is observed that for small kink angles (to the first order in the kink angle, e.g., for less than 8 degrees) HSIF (SSIF) equals K-I((k))) (K-II((k))) to within less than 1%; this holds for much larger kink angles when the material is isotropic. As a result of this observation, for small kink angles, all field quantities al the tip of a vanishingly small kink can be obtained from the fields that exist at the tip of the initial main crack prior to kinking, i.e., to the first order in the kink angle, the Modes I and II stress intensity factors at the tip of a vanishingly small kink (just after kinking) respectively equal HSIF and SSIF (just before kinking). On the other hand, depending on loading and material anisotropy, K-I((k))) (K-II((k))) at the tip of a vanishingly small kink can deviate from HSIF (SSIF) by several hundred percent, for large kink angles. Furthermore, the K-based fracture criteria for anisotropic solids are examined in some detail. It is shown that, even for small kink angles, the study of the variation of the SIF's with the kink angle requires the corresponding complete nonlinear equation, as linearization with respect to the kink angle may produce extraneous and seemingly peculiar results.