2D frictional crack initiation and propagation analysis using the numerical manifold method

Abstract

By using both a physical mesh and a mathematical mesh to formulate a physical problem, the numerical manifold method (NMM) can lead to a very simple meshing task, which allows a direct capture of the discontinuities across the crack surfaces. In this study, verification of the stress intensity factor ahead of flaw tips is first performed to demonstrate that the NMM is capable of analyzing crack problems with a high degree of accuracy. Based on the contact technique of the NMM and the incorporation of the Mohr-Coulomb crack initiation criterion, the effects of the friction and cohesion on the crack growth from a closed flaw (crack) under compression are investigated. The NMM can not only accurately predict the pure tensile or pure shear crack growth, but also satisfactorily predict the development of mixed shear-tensile crack types. The crack type is strongly influenced by the ratio of the compressive strength (σc) to the tensile strength (σt) of the material. When the σc/σt ratio is between 5 and 7, the mixed type of cracks will typically develop. However within this range of σc/σt ratio, the lateral confining stress, the friction angle between the flaw surfaces and the inclination angle of the flaw may also significantly affect the crack type developed. Large and small flaw inclinations favor the development of oblique-type cracks and coplanar-type cracks respectively. The secondary cracks are not necessarily shear cracks but can also be tensile cracks. This study thus demonstrates the advantages and strong potential of the NMM in dealing with continuous- discontinuous problems. Copyright 2012 ARMA, American Rock Mechanics Association.