Applicability of the classical fracture mechanics criteria to predict the crack propagation path in rock under compression

Abstract

A higher order displacement discontinuity method (HDDM) with quadratic elements is used in this study to evaluate the validity of classical fracture criteria in order to predict crack propagation path under mixed mode loading I–II in the case of a crack in an infinite body. Crack propagation path is predicted here by defining three stress states, uniaxial tensile stress (UTS), uniaxial compressive stress (UCS) and biaxial compressive stress (BCS). Comparing with experimental results, it was found that by increasing the crack inclination angle, the length of crack propagation path increases and the slope of this path decreases. For BCS state, G-criterion almost loses the validity and can be replaced with σ-criterion. S-criterion is strongly dependent on Poisson’s ratio and it is recommended to study fracture under brittle and ductile behaviour. Due to the complexity of crack tip element equations, the effect of this element on the results has been studied in detail and it was found that by considering the mid-point of the last element as a reference point to evaluate displacement discontinuities (D_s and D_n), there is no need to use special crack tip element. This procedure facilitates the modelling and shortens the solution.

Keywords:

• Classical fracture criteria
• propagation path
• crack path length
• mixed mode loading
• displacement discontinuity method