Crack propagation and coalescence in brittle materials under compression

Abstract

Two particular cases concerning crack propagation and coalescence in brittle materials have been modeled by using the rock failure process analysis code, RFPA^2D, and the results have been validated by reported experimental observations. Firstly, axial compression of numerical samples containing a number of large, pre-existing flaws and a row of suitably oriented smaller flaws are simulated. It has been confirmed that under axial compression, wing-cracks nucleate at the tips of the pre-existing flaws, grow with increasing compression, and become parallel to the direction of the maximum far-field compression. However, coalescence of the wing-cracks may be in either tensile mode or shear mode, or a combination of both modes. The numerical results show qualitatively a reasonably good agreement with reported experimental observations for samples with similar flaw arrangements. The numerical results demonstrate that, with a confining pressure, the crack growth is stable and stops at some finite crack length; whereas a lateral tensile stress even with a small value will result in an unstable crack growth after a certain crack length is attained. Secondly, failure mode in a sample containing inhomogeneities on grain scale has also been simulated. The results show that the failure mode strongly depends on the mechanical and geometric properties of the grains and inclusions.

Introduction

Numerous experimental1, 2, 3, 4, 5, 6, 7, 8and theoretical3, 6, 9, 10, 11efforts have been devoted to the understanding of the crack initiation, propagation, and coalescence of pre-existing flaws in brittle materials. Uniaxial compression experiments with a rock-like model material containing double flaws conducted by Reyes and Einstein[6]showed that pre-existing non-persistent flaws coalesce in two different modes: (1) if the pre-existing flaws overlap, the coalescence occurs through interconnection of the developing wing cracks; (2) if the pre-existing flaws do not overlap, coalescence occurs through secondary cracks. Further experimental work on this topic has been carried out by Bobet and Einstein[7], and Shen et al.[8]. Experiments with samples containing multiple pre-existing flaws were carried out by Nemat-Nasser and Horii[3]. It was shown that for a certain overall orientation of the flaws the growth of the out-of-plane cracks may become unstable, leading to possible macroscopic faulting.

Although fracture mechanics provides a fundamental basis in understanding crack behavior, the use of fracture mechanics to describe the propagation and coalescence of multiple cracks in geomaterials is arduous. As a matter of fact, much of the theoretical study of fracture is focused on an individual crack. Although this approach is most successful when fracture occurs by the propagation of a single crack, for rock mechanics or civil engineering and geophysical problems, the analysis of material failure modes characterized by multiple cracking events can be treated through different approaches. Several numerical models have emerged as useful tools to simulate failure by multiple cracking events and to study the general behaviors of brittle fractures3, 6, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18. For example, by combining a smeared crack/damage mechanics approach with a strain-based failure criterion, coalescence through secondary cracks was analyzed by Reyes and Einstein[6]. Similar work was performed by Shen and Stephansson[10]by using the DDM (discontinuous deformation method) model with a modified G-criterion. In the work of Nemat-Nasser and Horri[3], a closed form solution was obtained for a regular set of flaws, assuming that the pre-existing straight flaws are closed and the trajectory of the branching crack is straight. Later on they improved their model to consider the possible curved branching path[4]. Zaitsev and Wittmann[16]have published a paper on crack propagation in the specimen with a compressive load but without consideration of the interaction among the distributed cracks. Within the framework of BEM and DDM, crack propagation, interaction and coalescence, and the size effects on strength for brittle specimen have been studied by Carpinteri et al.[17]. A damage mechanics model has been used by Han and Swoboda[18]to simulate a set of flaws distributed regularly with the same orientation.

In the present paper, two particular cases concerning crack propagation, interaction and coalescence in brittle materials are studied with a numerical tool called the rock failure process analysis code, RFPA^2D, developed recently by Tang[19]. The purpose of this approach is to accentuate the fundamentally different mechanisms which may be involved in failure either in tension or shear mode, depending on the confinement conditions. Motivated by the observations of the model experiments conducted by Horii and Nemat-Nasser[4], numerical model samples containing pre-existing multiple flaws similar to the setup in their experiments have been adopted. The flaws may be pre-existing cracks, or some irregular inhomogeneities such as weak inclusions. From the mathematical point of view, this represents a rather difficult problem in numerical modeling, which has not been dealt with before. The second simulated case deals with failure mode in a sample containing inhomogeneities on a grain scale. The simulations shown in this paper seem to demonstrate that RFPA^2D is a powerful numerical technique for solving this kind of problem, which involves crack initiation, propagation, interaction and coalescence in brittle materials with pre-existing flaws or other inhomogeneities. However, more work has to be done for a general conclusion.