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TECHNICAL PAPERS

# Toughness and Oblique Metalcutting

[+] Author and Article Information
A. G. Atkins

J. Manuf. Sci. Eng 128(3), 775-786 (Nov 08, 2005) (12 pages) doi:10.1115/1.2164506 History: Received January 19, 2005; Revised November 08, 2005

## Abstract

The implications of whether new surfaces in cutting are formed just by plastic flow past the tool or by some fracturelike separation process involving significant surface work, are discussed. Oblique metalcutting is investigated using the ideas contained in a new algebraic model for the orthogonal machining of metals (Atkins, A. G., 2003, “Modeling Metalcutting Using Modern Ductile Fracture Mechanics: Quantitative Explanations for Some Longstanding Problems  ,” Int. J. Mech. Sci., 45, pp. 373–396) in which significant surface work (ductile fracture toughnesses) is incorporated. The model is able to predict explicit material-dependent primary shear plane angles $ϕ$ and provides explanations for a variety of well-known effects in cutting, such as the reduction of $ϕ$ at small uncut chip thicknesses; the quasilinear plots of cutting force versus depth of cut; the existence of a positive force intercept in such plots; why, in the size-effect regime of machining, anomalously high values of yield stress are determined; and why finite element method simulations of cutting have to employ a “separation criterion” at the tool tip. Predictions from the new analysis for oblique cutting (including an investigation of Stabler’s rule for the relation between the chip flow velocity angle $ηC$ and the angle of blade inclination $i$) compare consistently and favorably with experimental results.

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## Figures

Figure 1

Piispanen’s “deck of cards” model for cutting with a single shear plane. Plastic slip in plane strain along a finite-width primary shear band is impossible under constant volume unless a gap occurs in the region of XY. Otherwise ZWV is an increase in plastic volume (adapted from Cook (1)).

Figure 2

(a) Permanent skewing of chip in oblique cutting into a helix as opposed to into a spiral in orthogonal cutting. Rake angle αn=10deg, depth of cut 0.13mm; material steel (from Shaw (3)); (b) chip formation in oblique cutting showing the three velocity components, namely, the workpiece approach velocity VW, the shear velocity VS in the shear plane, and the chip velocity VC in the plane of the tool face (from Amarego and Brown (28)); and (c) the resultant force Fres has components FP parallel with the velocity approach vector VW; FQ perpendicular to the finished work surface; and FR perpendicular to the other two. FP is the “power” force, FQ is the “thrust” force, and FR is the “radial” force which are the forces usually measured by a dynamometer. ηC is the chip velocity angle; ηC′ is the angle of inclination of the friction force F to the normal to the cutting edge in the rake face; ηS is the shear flow angle; and ηS′ is the angle of inclination of the shear force FS to the normal to the cutting edge in the shear plane (from Amarego and Brown (28)).

Figure 3

Experimental results given in (19) for (a)FP, (b)FQ, and (c)FR versus depth of cut for 1008 cold drawn steel; w=0.126in.(3.24mm) and αn=20deg for all. Inclination angles in experiments are i=10deg, 20deg, 30deg, and 40deg. Full lines are predictions of new theory employing β≈0.8 radians or 46deg, R≈300lb∕in.2(54kJ∕m2), and τy≈56,000psi(390MPa). Although there is separation between the plots for FP and FQ at all obliquities, the differences are not marked within the range of obliquities employed experimentally. At tool obliquities greater than those employed in the experiments, the predicted FP and FQ force components separate out, with FQ changing sign. FR versus t0 is always different for all obliquities.

Figure 4

The full lines show the variation of (a) the theoretical normalized power force FP∕Rw, (b) thrust force FQ∕Rw, and (c) radial force FR∕Rw with angle of obliquity at different Z=(R∕τyt0) for constant tool rake angle αn=20deg and friction angle β=46deg. For i<0.7rad(>40deg), FP∕Rw and FQ∕Rw are essentially constant, but thereafter FP∕Rw is predicted to decrease slightly, and FQ∕Rw to decrease more and change sign at i> about 70deg. Over all angles of obliquity, FR∕Rw increases throughout. Experimental data for a 20deg rake angle tool at inclination angles of i=10deg, 20deg, 30deg, and 40deg are given by the open circles (t0=0.008in.) and open triangles (t0=0.004in.). The dashed lines are for a frictionless 20deg rake angle tool and Z=1. From the Z loci and the known depths of cut, the data and theory correspond to R∕τy≈5×10−3in.(1.4×10−5m).

Figure 5

(a) Theoretical variation of chip velocity angle ηC with tool rake angle αn for two tool obliquity angles (i=40deg and 20deg) and two values of Z (10 and 1). (b) A “Stabler” plot of ηC versus i for various αn. Full lines are present theory, points are the Brown and Amarego results (19).

Figure 6

Predictions for the shear flow angle ηS(a) as it depends on i at different αn and different Z; and (b) as it depends on αn at different i and different Z (αn has only minor influence in these plots, the main influence is from Z)

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