ABSTRACT

Apart from the most commonly observed tensile wing cracks, horsetail cracks curving in a direction different from that of the tensile wing cracks are also observed initiated from the flaw tips. In the past, due to the convenience of analytical and numerical analyses, these two types of cracks were usually not differentiated. This paper examined the cracking processes of these two crack types, by using the non-linear dynamics hydrocode. The numerical study focused on the new cracks initiated from a pre-existing inclined flaw embedded in a rectangular specimen. The cracking model was based on the incorporation of the cumulative damage failure criterion and the Drucker-Prager strength model. The numerical results verified that tensile crack opening occurred along the tensile wing crack trajectory both in the elements adjacent to the pre-existing flaw and far away from the pre-existing flaw. In contrast, the horsetail crack was associated with a short shear crack segment adjacent to the flaw tip. Its remaining crack trajectory, which gradually curved towards the loading direction, was tensile in nature.

1. INTRODUCTION

Various crack types have been reported to initiate from a pre-existing flaw in rock specimens under compression. In addition to the most commonly observed tensile wing cracks, horsetail cracks [1] curving in a direction different from that of the tensile wing cracks are also observed initiated from the flaw tips in the field studies (figure 1) and in the laboratory experimental studies, e.g. [2 – 4].

Since the trajectories of tensile wing crack and horsetail crack both have a curvilinear shape, they were often not differentiated and given a common name of “wing cracks” [5]. For the convenience of analytical and numerical studies in modeling crack initiation and propagation, notably in the sliding wing crack model, both types of crack trajectory are typically modeled in the same way as straight lines initiating from the flaw tips, and being aligned with the external loading direction [6]. Although there are models [7, 8] taking into account of the crack initiation angle of the tip cracks, they are based on the consideration of mode I stress intensity factor KI, assuming that the initiation of tip cracks is due to tensile opening mode.

There have been attempts to differentiate these two crack types based on their temporal cracking sequence [2, 9, 10], i.e. primary cracks vs secondary cracks, which were however not supplemented by an in-depth investigation of the underlying mechanics. As it will be shown in this paper by the numerical modeling technique, the underlying mechanisms of the formation of these two crack types are found to be different. A proper differentiation of these two crack trajectories is thus necessary.

2. METHODOLOGY

In the present study, numerical analyses were performed by the dynamic analysis software AUTODYN, which incorporates the static damping technique to the timedependent loading in order to achieve a quasi-static loading condition. This non-linear dynamics hydrocode was used to model the crack initiation and propagation processes for rock specimens containing a single preexisting flaw.

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