Application of damage mechanics in percussive drilling modelling

Abstract

A stationary-periodic quasi-static model of rock percussive deep drilling is introduced. First, an auxiliary problem of stationary indentation of a rigid indentor is considered. The rock is modelled by an in¯nite elastic medium with damage-induced material softening. The stationarity of the problem allows to reduce the damage history in a material point to the damage distribution down in space. The bore-hole is a semi-in¯nite cylinder with a curvilinear bottom. It is assumed the indentation is produced by a stationary motion of the rupture front at which an appropriate rock strength condition is violated. The bore-hole boundary is not known in advance and consists of four parts: a free of traction non-rupturing part, a contact non-rupturing part, a free of traction part of the rupture front, and a contact part of the rupture front. Thus the problem is formulated as a non-local non-linear free-boundary contact problem and algorithms of its numerical solution are discussed. The problem solution provides axial force necessary for the drill bit progression through the rock. Then the stationary-periodic percussive drilling problem is reduced to the stationary problem on the rupture progression stage of the cycle and to the classical contact problem on the reverse and progression-before-rupture stages of the cycle. As a result, this provides a nonlinear progression-force diagram.