ABSTRACT
Chip formation in rock under a line load and in front of a drag bit cutter is numerically investigated. Analysis is accomplished by a special purpose interactive graphics finite element code, SICRAP, written for the simulation of mixed mode crack propagation under linear elastic fracture mechanics assumptions. The first study provides some interesting qualitative results, and in the second study, correlation with experimental tests on chip formation by drag bit cutter in Berea sandstone is found to be very satisfactory. This indicates that elastic analysis, coupled with fracture mechanics, is capable of modeling rock cutting.
INTRODUCTION
The parametric investigation of continuous mechanical excavation devices, e.g. disc cutters, used in tunnel boring machines, and drag bit cutters, has primarily relied on numerous expensive experimental studies. Due to the complexity of the problem, analytical studies have only complemented the experimental work. Few attempts have been made to analyze the problem by the finite element method. The process being one of crack formation and progagation [3], any numerical investigation must be capable of modeling: the stress singularities and the mixed mode crack propagation. To perform such an extensive and comprehensive study by the finite element method, an automatic remeshing algorithm is a must. To the best of the authors' knowledge, all the previous finite element analysis of rock cutting were based on a smeared crack approach coupled with non-linear analysis and non-fracture mechanics criteria for crack extension. The process of chip formation being really a fracture propagation problem it could best be approached using principles of fracture mechanics. This paper will present, for the first time to the authors' best knowledge, a comprehensive solution to the problem of discrete crack modeling of rock cutting using fracture mechanics concepts.
FINITE ELEMENT MODELING OF CRACK PROPAGATION
To address the difficulties associated with a crack propagation study, a finite element model must possess the following features: proper modeling of the r-l/2 stress singularity (assuming the process zone ahead of the crack tip is small, justifying the use of linear elastic fracture mechanics), accurate determination of the two stress intensity factors K1 and Kll , built-in mixed mode crack propagation criteria, joints elements to model crack closure, and automatic remeshing to accommodate crack nucleation/extension. To ascertain the stability and direction associated with a crack, the stress intensity factors must be known. The problem here is twofold: (a) to model the appropriate form of the singularity by special elements, and (b) to extract the stress intensity factors from the near-tip displacement field. The isoparametric quadratic singular element [1] is used to model the stress singularity, and the displacement correlation method is used to determine stress- intensity factors (SIF) from the nodal displacement of the singular elements. It has been argued that the accuracy with which the SIF are calculated, using the quarter point singular element, is dependent on 1/a (singular element length over crack length). To assess such dependency on l/a, and to propose a set of recommendations for the local meshing around the crack tip, an extensive parametric study was performed by the first author [7].
