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.

1.
Cook
,
N. H.
,
Finnie
,
I.
, and
Shaw
,
M. C.
, 1954, “
Discontinuous Chip Formation
,”
Trans. ASME
0097-6822,
76
, pp.
153
162
.
2.
Astakov
,
V. P.
, 1999,
Metal Cutting Mechanics
,
CRC Press
, Boca Raton, FL.
3.
Shaw
,
M. C.
, 1984,
Metal Cutting Principles
,
Clarendon Press
, Oxford.
4.
Merchant
,
M. E.
, 1944, “
Basic Mechanics of the Metal Cutting Process
,”
J. Appl. Mech.
0021-8936,
11
, pp.
A168
A175
.
5.
Oxley
,
P. B. L.
, 1989,
Mechanics of Machining: An Analytical Approach to Assessing Machinability
,
Ellis Horwood
,
Chichester
.
6.
Adibi-Sedeh
,
A. H.
, and
Madhavan
,
V.
, 2002, “
Effect of Some Modifications to Oxley’s Machining Theory and the Applicability of Different Material Models
,”
Mach. Sci. Technol.
1091-0344,
6
, pp.
379
395
.
7.
Fang
,
N.
, and
Jawahir
,
I. S.
, 2002, “
Analytical Predictions and Experimental Validation of Cutting Force Ratio, Chip Thickness, and Chip Back-Flow Angle in Restricted Contact Machining Using the Universal Slip-Line Model
,”
Int. J. Mach. Tools Manuf.
0890-6955,
42
, pp.
681
694
.
8.
Rosenhain
,
W.
, and
Sturney
,
A. C.
, 1925, “
Report on the Flow and Rupture of Metals During Cutting
,”
Proc. Inst. Mech. Eng.
0020-3483,
1
, pp.
194
219
.
9.
Atkins
,
A. G.
, 1974, “
Fracture Toughness and Cutting
,”
Int. J. Prod. Res.
0020-7543,
12
, pp.
263
274
.
10.
Atkins
,
A. G.
, 1974, “
A Dimensional Analysis for Machining to include Fracture Toughness
,”
Proc NAMRC-II Madison
,
SME
,
Dearborn, MI
, pp.
398
407
.
11.
Reuleux
,
F.
, 1900, “
Uber den Taylor Whitescen Werkzeugsthal
,”
Verein zur Berforderung des Gewerbefleissen in Preussen Sitzungsberichte
,
79
, pp.
179
189
.
12.
Kendall
,
K.
, 2001,
Molecular Adhesion and its Applications
,
Kluwer/Plenum
,
NY
.
13.
Griffith
,
A. A.
, 1921, “
The Phenomena of Rupture and Flow in Solids
,”
Philos. Trans. R. Soc. London, Ser. A
0962-8428,
221
, pp.
163
198
.
14.
Atkins
,
A. G.
, and
Mai
,
Y-W
, 1984/88,
Elastic and Plastic Fracture
,
Ellis Horwood
,
Chichester, UK
.
15.
Trent
,
E. M.
, 1991,
Metal Cutting
, 3rd ed,
Butterworth-Heinemann
,
London
, p.
34
.
16.
Atkins
,
A. G.
, 2003, “
Modeling Metalcutting Using Modern Ductile Fracture Mechanics: Quantitative Explanations for Some Longstanding Problems
,”
Int. J. Mech. Sci.
0020-7403,
45
, pp.
373
396
.
17.
Atkins
,
A. G.
, 2004, “
Rosenhain and Sturney Revisited: The ‘Tear’ Chip in Cutting Reinterpreted in Terms of Modern Ductile Fracture Mechanics
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
0954-4062,
218
, pp.
1181
1194
.
18.
Thomsen
,
E. G.
Yang
,
C. T.
, and
Kobayashi
,
S.
, 1965,
Mechanics of Plastic Deformation in Metal Processing
,
Macmillan
,
New York
.
19.
Brown
,
R. H.
, and
Amarego
,
E. J.
, 1964, “
Oblique Machining with a Single Cutting Edge
,”
Int. J. Mach. Tool Des. Res.
0020-7357,
4
, pp.
9
25
.
20.
Finnie
,
I.
, 1963, “
A Comparison of Stress Strain Behaviour in Cutting with that in Other Material Tests
,”
Proceedings International Production Engineering Research Conference
,
Pittsburgh, PA
,
ASME
,
New York
, pp.
76
82
.
21.
Atkins
,
A. G.
,
Rowe
,
G. W.
, and
Johnson
,
W.
, 1983, “
Shear Strain and Strain Rates in Kinematically-Admissible Velocity Fields
,”
Int J Mech Eng Education
,
10
, pp.
265
278
.
22.
Atkins
,
A. G.
, 1997, “
Fracture Mechanics and Metalforming: Damage Mechanics and the Local Approach of Yesterday and Today
,”
Fracture Research in Retrospect: G Irwin Festschrift
,
H. P.
Rossmanith
, ed.,
Rotterdam
,
Balkem
a, pp.
327
338
.
23.
Atkins
,
A. G.
, 1980, “
On Cropping and Related Processes
,”
Int. J. Mech. Sci.
0020-7403,
22
, pp.
215
231
.
24.
Atkins
,
A. G.
, 1981, “
Surfaces Produced by Guillotining
,”
Phil Mag (David Tabor Festschrift)
,
43
, p.
627
.
25.
Atkins
,
A. G.
, 2000, “
Ductile Shear Fracture Mechanics
,”
Key Eng. Mater.
1013-9826,
177–180
, pp.
59
68
.
26.
McClintock
,
F. A.
, 2002, “
Slip Line Field Fracture Mechanics: A New Regime of Fracture Mechanics
,” in
Fatigue and Fracture Mechanics
,
W. G.
Reuter
and
R. S.
Piascik
, eds.,
American Society for Metals
,
Metals Park, OH
.
27.
Stabler
,
G. V.
, 1951, “
The Fundamental Geometry of Cutting Tools
,”
Proc. Inst. Mech. Eng.
0020-3483,
165
, pp.
14
26
.
28.
Amarego
,
E. J.
, and
Brown
,
R. H.
, 1969,
The Machining of Metals
,
Prentice-Hall
,
Englewood Cliffs
, New Jersey.
29.
Shaw
,
M. C.
,
Cook
,
N. H.
, and
Smith
,
P. A.
, 1952, “
The Mechanics of Three-Dimensional Cutting Operations
,”
Trans. ASME
0097-6822,
74
, pp.
1055
1064
.
30.
Kopalinsky
,
E. M.
, and
Oxley
,
P. L. B.
, 1984, “
Size Effects in Metal Removal Processes
,”
Conf. 3rd on Mechanical Properties at High Rates of Strain
(Inst. Physics Conf. Series No. 70),
Oxford Univeristy
, pp.
389
396
.
31.
Atkins
,
A. G.
, 2005, “
Toughness and Cutting: A New Way of Simultaneously Determining Ductile Fracture Toughness and Strength at Intermediate and High Strain Rates
,” J. G. Williams Festschrift, ed.,
Eng. Fract. Mech.
0013-7944,
72
, pp.
849
860
.
32.
Felbeck
,
D. K.
, and
Atkins
,
A. G.
, 1996,
Strength and Fracture of Engineering Solids
, 2nd ed.,
Prentice Hall
,
Upper Saddle River
, NJ.
33.
Shaw
,
M. C.
,
Smith
,
P. A.
, and
Cook
,
N. H.
, 1952, “
The Rotary Cutting Tool
,”
Trans. ASME
0097-6822,
74
, pp.
1065
1076
.
34.
Kronenburg
,
M.
, 1954,
Grundzuge der Zerspanunglehre
, 2nd ed.,
Springer-verlag
,
Berlin
.
35.
Atkins
,
A. G.
,
Xu
,
X.
, and
Jeronimidis
,
G.
, 2004, “
Cutting, by Pressing and Slicing, of Thin Floppy Slices of Materials Illustrated by Experiments on Cheddar Cheese and Salami
,”
J. Mater. Sci.
0022-2461,
39
, pp.
2761
2766
.
36.
Atkins
,
A. G.
, 2005, “
Optimum Blade Configurations for the Cutting of Soft Solids
,”
Proc ESIS TC-4
, submitted to Engr Fract Mech.
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