The impact of various crack geometrical parameters on stress field over tip under different mixed loading conditions and inclination angles

摘要

Mixed mode fracturing behaviors in brittle materials are ubiquitous occurring in practicing engineering. Especially for rocks, tensile-shear loadings are one type of basic factors inducing failures. This paper presented analytical and numerical solutions to investigate the variations of stress field over crack front vicinity under different complex loading conditions and geometrical parameters. An analytical solution for crack under mixed loadings and various geometrical parameters (i.e. inclination angle alpha and shape parameter m of crack) was proposed, which also considers shear loadings both applying on internal boundary (i.e. crack surface) and external boundary (i.e. distance far away crack). The analytical solution for the model by complex potential method has been suggested. Numerical simulations have been carried out to verify the analytical solution of stress distribution adjacent to crack tip, in which the analytical solutions show good agreement with the numerical results. Three dimensionless loading coefficients () were defined to reflect the magnitudes of biaxial loading, external shearing and internal shearing, respectively. The characteristics of stress distribution, shearing effects and initiation stress were studied deeply under different with various alpha, m, and the effects of varied conditions on stress magnitude variations have been discussed. According to the solution, we derived the explicit expressions of stress intensity factor (SIF) under different loading situations. Considering the effects of various crack inclination angles and shear loadings, the variations of normalized SIF ratio 2/pi arctan(K-I/K-II) with various conditions also have been discussed. In conclusion, loadings and geometrical variations both have strongly effects on stress distributions around the tip, and the influences have the relationship with different situations.