Estimating the crush zone size under a cutting tool in coal

Abstract

As part of an effort to understand the mechanics of fine fragment formation in coal, which is important in studies of respirable dust due to mining, fracture toughness measurements and the strain energy density (SED) theory were applied to calculate the crush zone size under a cutting tool in coal. This zone is the major source of fine fragments in the 1 to 10 µm size range. The model used in these calculations is a boundary element program containing a failure criterion based on the SED theory. The boundary element program calculates linear elastic stresses at numerous points in the coal material ahead of a cutting bit. These stresses are then input to a subroutine called critical flaw length and orientation (CFLO) which uses the SED theory to determine the CFLO for a small crack at the boundary element stress computation point. The extent of crushing is based on earlier postulates about the role of inherent flaws in a fragmentation process. To form 1 to 10 µm fragments requires firstly a local stress strong enough to activate flaws with a characteristic length less than 1 to 10 µm and secondly, a flaw density sufficient to provide an average spacing between flaws also on the order of 1 to 10 µm. The locus of active 10 µm flaws represents the maximum possible extent of fine fragmentation in the 10 µm or less size range assuming that a sufficient inherent flaw density exists. The approach offers a first order approximation to the extent of crushing under a tool tip. The size and shape of the crush zone volume is affected by the attack angle and geometry of the tool.