Dissolution Profile of Tool Material Into Chip Lattice

Abstract

The dissolution hypothesis of tool wear is rearticulated as a boundary condition for the transfer of tool components to the chip’s bulk via diffusion. In this setting, dissolution wear is defined more generally as the combined events of tool decomposition at the interface and the subsequent mass transfer of decomposed elements into the chip region. Chemical equilibrium is invoked for the distribution of tool species at the tool-chip interface. Under a linear-diffusion hypothesis, one would expect an exponentially decaying concentration profile of tool species in the chip. However, a humped concentration profile has been found experimentally by Subramanian et al. in 1993. In this paper, the Frank-Turnbull mechanism is proposed to explain the humped concentration profile of tool constituents into the chip. This mechanism is defined by the interaction between interstitial impurities and vacancies to form substitutional impurities, and it introduces a quadratic nonlinearity in the advection-diffusion-reaction equations. The present approach is semi-empirical in that, while the interstitial- and substitutional impurity distributions are solved from the equations, the vacancy distribution is constructed so that the final substitutional-impurity distribution agrees with the observed data. The present interpretation of the Frank-Turnbull mechanism in the wear process is illustrated by finite-element simulations.