Distinct Element Modeling of Rock Cutting under Hydrostatic Pressure

Distinct element method was used to model a rock material and sim ulate orthogonal machining of this material. A rock specimen was created to approxi mate Carthage marble, the rock material used in this study. A methodology was developed to apply a hydrostati c pressure to the rock specimen during the simulation. Comparison between machining with and wit hout hydrostatic pressure was presented. It was found that the application of a hydrosta tic pressure enhances plastic deformation during material removal. Longer chips are formed and cutti ng force increases with pressure. The distinct element method is shown to be an effective tool in m deling of rock cutting and can provide insights on the tool-rock interactions. Introduction The development of polycrystalline diamond compacts (PDC) as cutting el ements in the early 1970s represented a significant advance in rock drilling technology. The use of PDC cutters allows rocks to be sheared instead of being crushed, resulting in high penetration rate in drilling. However, their use is restricted to excavating relatively soft rocks due to the brittl eness of the PDC cutters. Since their development, PDC bits have been a subject of extensive research. Many exper im ntal investigations have contributed to a better understanding for the rock-tool interaction, tool wear mechanisms, and thermal aspects during cutting using a PDC cutter [1-7]. Since ex p riments are most times costly to run and it is difficult to directly observe the material removal process, numerical tools have been developed to model rock cutting. Numerical simulations have been performed to elucidate rock-tool inter action during rock cutting. Two approaches are generally used to model rocks depending on how the damag is represented: either indirectly via constitutive relations or directly by forma tion and tracking of a large number of discrete cracks. Many studies have been reported to model rock materials by the continuum approach. Boone at al. [8] applied the strength of materials approach to predict crack init iat on and used LEFM for propagation of cracks of known length. Finite element method (FEM) was applied to model rock structures with discrete cracks. Wang and Lhenhoff [9] studied bit pene ration into rock using FEM. A similar FEM technique was also used by Zeuch et al. [10] to model the cutting problem. Korinets et al. [11] used another FEM based code (DIANA) to simulate rock breakag with a spherical/flat-bottomed indenter and disc roller cutter. A modified e xpansion cavity model was implemented by Tan et al. [12] in a boundary elements method (BEM) code together with a fracture model to simulate the formation of fractures under the action of single and mult iple indenters. All of these models modeled rock as a homogenous material. More recently, Kou et al. [13] modeled the machining of inhomogeneous rocks using RFPA , a FEM package which has the capability to model inhomogeneous rocks. Although brittle fracture at large depths of cut wa s effectively simulated, the ductile flow at small depths of cut could not be revealed with the FE M method. Rock cutting is associated with two different mechanisms of material removal: the shear induced yielding and the tensile induced cracking. Parameters such as depth of cut and speed det ermine which mechanism is the dominant cutting mechanism. Since traditional FEM packages have di fficulty treating the two mechanisms simultaneously, a different approach is needed to model these types of mat rials. The distinct element method (DEM) developed by Cundall and Hart [14] provi des a direct Key Engineering Materials Online: 2003-09-15 ISSN: 1662-9795, Vol. 250, pp 110-117 doi:10.4028/www.scientific. net/KEM.250. 110 © 2003 Trans Tech Publications Ltd, Switzerland All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of Trans Tech Publications Ltd, www.scientific. net. (Semanticscholar.org-13/03/20,20:10:19) Key Engineering Materials Vols. 111 approach to treat this problem. Unlike traditional numerical methods bas ed on continuum theories, which are shown to be limited in dealing with the two failure modes at the same time, discrete element method can model damage and brittle fracture simultaneously, which occ urs as a result of particle separation and sliding at microscale. It idealizes a material as collection of arbitrarily sized particles bonded together and utilizes the breakage of the bonds to represent damage . Huan [15] modeled rock samples using DEM and conducted simulations of rock cutting on the rock specimens. It was foun d that material removal is realized by a ductile flow of the par ticles at small depths of cut while large fractures are formed at larger depths of cut. More recently, Le i and Prasad [16] used the same method to study rock cutting under hydrostatic pressure with a simple contact bond model. The purpose of this study is to gain a deeper understanding of rock cutting process und r external pressure through the use of distinct element method. It is a well-obs rved fact that a rock behaves differently with application of an external hydrostatic pressure. D illing of hard rock under the surface of the earth is almost always done under the pressure of drilling m ud. Since this drilling mud is always in contact with the rock surface being cut, the rock is effectively drilled under a hydr ostatic pressure. Therefore, it is very important to understand how confining pressure (use d interchangeably with hydrostatic pressure in this paper) affects tool-rock interactions during cutting. The insights from this study are expected to assist in developing better PDC bits for under ground drilling applications. In the following sections, a rock specimen is first generated with an as sembly of circular particles to approximate Carthage marble. Then a methodology to apply hydrostatic pr essure is developed. Finally, rock cutting simulation is conducted under different conditions of exter nal p essure and tool rake angle and compared with experimental results. Modeling of Rock Specimen Particle Flow Code. PFC is the two-dimensional particle flow code used in this study that models the movement and interaction of circular particles by DEM [17]. The interaction between any two circular particles is governed by the constitutive model defined at the contact. The constitutive model consists of a stiffness model, a slip model and a bonding model, which cont rols the deformation, separation and movement of the particles. The contact stiffness model relates the contact force and relat ive displacement in the normal and shear directions. The stiffness model is described by the force-dis placement law as given in Eqs.1 and 2: i n n n i n U k F = . (1) s i s s i U k F ∆ − = ∆ . (2) where n i F is the normal contact force, k n is the normal stiffness, U n is the normal displacement, n i is the i th component of the unit normal vector, s i F ∆ is the incremental shear force, k s is the shear stiffness, and si U ∆ is the incremental shear displacement. The slip model describes a frictional behavior between contact entit ies and allows slip to occur by limiting the shear force. The slip model is defined by a dimensionle ss friction coefficient, μ, at the contact. The contact is checked for slip conditions by calculating the maximum allowable shear contact force given by Eq.3. Slip is allowed when the total shear forc e ex eeds the maximum shear contact force, max F in Eq.3: n i s max F F μ = . (3) The parallel bond model is used to define the norma l and shear contact bond strength. A parallel Key Engineering Materials Vol. 250 111