ABSTRACT

Fragmentation mechanism in sphere indentation was explored numerically using the discrete element code PFC3D®. The fracturing sequences were analyzed in a face-centered cubic (FCC) crystal structure and a randomly generated particle assembly with material properties similar to those of hard rocks such as granite. In the crystal structure, development of the Hertzian cone crack and the damaged zone underneath the indenter was followed by nucleation of a full penny-shaped median crack. In the randomly generated sample, the Hertzian cone crack was no longer evident. Half penny-shaped radial cracks instead of the median crack formed. Depending on the state from which unloading of the indenter started, a deep saucer-shaped lateral crack may initiate and propagate in both the crystal structure and the random packing. Locations of the lateral crack initiation were observed to be at the side instead of the base of the damaged zone. The tensile stress field developed near the free surface during the unloading stage was responsible for the formation of the lateral cracks.

1. INTRODUCTION

Fragmentation mechanism in sphere indentation was explored numerically in this paper using the discrete element code PFC3D® .The fracturing sequences were analyzed in a face-centered cubic (FCC) crystal structure and a randomly generated particle assembly with material properties similar to those of hard rocks such as granite. Special attention has been paid to investigate the effect of unloading on the fracture mechanics of the lateral cracks. Indentation fracture mechanics has been extensively studied since Hertz in 1880s, in particular for materials such as glasses, metals and ceramics [3-9]. While the fracturing mechanisms of the Hertzian cone crack and the radial and median cracks are well established, in studies focusing on material testing, lateral cracks have been usually regarded as secondary and received little attention [9]. Development of lateral cracks is nevertheless the main mechanism of material removal in mechanical excavation in rocks. Fundamental understanding of how lateral cracks initiate and propagate is therefore critical to improving the drilling efficiency and bit design. Lawn and Swain [6] observed the development of lateral cracks in the unloading stage of Knoop and Vickers indentation tests in soda-lime glass. Based on the Boussinesq stress field for a point load, they described the following idealized sequence of events for indentation in brittle materials with a sharp indenter, i.e., a tool of wedge, conical or pyramidal shape. When the indenter gets into contact with the surface, irreversible deformation around the contact point is first produced. As the indentation load exceeds a threshold, a median crack initiates below the contact point at the elastoplastic boundary and propagates downward stably. When the indenter is removed, the median crack first closes, but may grow sideways to reach the surface and become a half penny-shaped crack on complete unloading. The residual stress field due to mismatch in strain recovery in the plastic zone and the surrounding elastic matrix may lead to development of the lateral cracks. The lateral cracks may initiate beneath the plastic zone and propagate towards the free surface.

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