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TECHNICAL PAPERS

# Dissolution Profile of Tool Material Into Chip Lattice

[+] Author and Article Information
Tim K. Wong

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824

Patrick Kwon

Department of Mechanical Engineering, Michigan State University, East Lansing, MI 48824pkwon@egr.msu.edu

The flux condition of Cook and Nayak is a forerunner of the one considered in this work. Here, we incorporate the notion of solubility to the boundary condition, and also consider vacancies and interstitials with the chip’s bulk.

That $Xs$ has a zero-flux condition at the tool-chip interface reflects the neglect of the mass diffusivity of substitutional impurities.

This assumption reflects the belief that the rise in system temperature is almost entirely due to plastic deformation and friction. In other words, molecular mass transfer from the tool does not significantly affect the background temperature. For a given distance, the steady state for thermal diffusion is established much faster than the steady state for mass diffusion, which gives the physical problem a natural division in time scale. In fact, the thermal diffusivity of a material is typically orders of magnitude larger than the mass diffusivities of impurities moving through the material. The system temperature can be significantly increased by drastic changes in the tool geometry due to wear, but this temperature increase is not due to mass-transfer coupling, but rather to changes in the cutting forces because of a change in tool geometry.

The wiggles in $Xi$ near the origin reflect the difficulty with which the coarse mesh tries to resolve a sudden increase. Fortunately, these wiggles do not pose a significant problem in the convergence of numerical solutions, but they do affect accuracy. The tradeoff in mesh coarseness is necessary, as relaxation runs (later) cost well over $8h$ to run on a computer with a $1.2GHz$ processor. The issue of wiggles will be re-visited in Appendix .

The uniformity of $kfwd$ implies uniformity in reaction rates given a uniform driving force; however, because a low value of $DV$ preserves the vacancy-depletion zone near the contact interface, there are no renewed, Frank-Turnbull reactions during relaxation for a short distance into the depth of the chip (Figs.  67). Hence, the rise of the $Xs$ hump is not significantly altered during post-machining relaxation.

Spatial dependence of mass diffusivity is due to the background temperature and pressure fields (28). The sharp drops in mass diffusivities near the origin correspond to the ferrite-to-austenite transition point, which, at an estimated tool-chip interface pressure of $0.33e9Pa$, is approximately $718°C$. Table-lookup values are taken from Elliot et al. (32) as Arrhenius functions of the absolute temperature. Constant values of mass diffusivities are adopted in the simulation for a practical reason: A sharp drop in diffusivity requires mesh refinement for resolution and numerical stability, especially in the presence of strong advection. Physically, however, most tool wear occurs downstream of the cutting edge (which correlates directly with the boundary supply of interstitials in Fig. 4) where the mass diffusivity is almost constant (Fig. 8), hence the use of constants.

J. Manuf. Sci. Eng 128(4), 928-937 (Mar 07, 2006) (10 pages) doi:10.1115/1.2280680 History: Received June 02, 2005; Revised March 07, 2006

## 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 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.

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## Figures

Figure 1

Schematic of the Frank-Turnbull reaction

Figure 2

Variation of temperatures away from the average

Figure 3

Mesh used in the first-order, species-transfer problem

Figure 4

(a)–(c) Sample XV, Xi, and Xs distributions, respectively. (d) Schematic of the chip-flow and chip-depth directions with a “see-thru” tool.

Figure 5

A check of Kramer’s hypothesis that dissolution wear is bounded by solubility for the (a) 2.5m∕s and (b) 4m∕s cutting speeds

Figure 6

(a) Matching experimental W-concentration profiles using only steady-state W distributions from the model; (b) the relaxation run

Figure 7

(a) Steady-state and relaxation solution for tungsten impurity at x=1.8mm for tungsten impurity at a 2.5m∕s cutting speed; (b) the relaxed Xs distribution at 4.7 milliseconds

Figure 8

(a) and (b) A comparison of available values of diffusivities versus actual values used in simlations for (a) 2.5m∕s cutting speed, (b) 4m∕s cutting speed

Figure 9

(a) and (b) XV and Xi distributions using table-lookup values of Fig. 8

Figure 10

(a) Surface dissolution rate constant of Eq. 6 with and without smoothing; (b) magnified image of (a)

Figure 11

(a) and (b) Steady-state Xi distributions (a) before smoothing; (b) after smoothing

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