A semi-infinite higher-order displacement discontinuity method and its application to the quasistatic analysis of radial cracks produced by blasting

Abstract

We introduced a higher-order indirect boundary element method in a traction-free half-plane known as semi-infinite displacement discontinuity method. The method is modified to use the linear elastic fracture mechanics principles for radial crack analysis in brittle materials like rocks. In this numerical method there is no need to discretize the traction-free boundary of the half-plane into higher-order elements thus decreasing the number of elements without affecting the accuracy of the solution to the desired problems. The use of higher-order elements increases the accuracy so that it is possible to discretize both the boundary of the body and radial cracks by the same higher-order elements, therefore there may be no need to use the more complicated hybrid methods. A special crack tip element is added for each crack tip to increase the accuracy of displacement discontinuities near the crack ends due to their singularities. Based on the brittle behavior of most rocks, linear elastic fracture mechanics principles have been used to find the fracture mechanics parameters (mode-I and mode-II mixed mode stress intensity factors) of radial cracks occurring in common blasting operations. Arbitrary fracture criteria can be implemented in this code, but here a simple maximum tangential stress criterion is used to predict the angle of deviation (initiation) of radial cracks. Although this code is specially designed to include the traction-free half-plane problems, it is somewhat comprehensive so that any number of radial cracks with any length in the finite, infinite and semi-infinite planes can be treated easily. The validity of the method is proved by solving simple examples and some previously solved problems in the literature.