Chip formation in the machining of hardened steel

Chip Formation in the Machining of Hardened Steel
M. C. Shaw (1). A. Vyas, Arizona State University, Tempe, Arizona/USA
Received on January 4,1993
Abstract
With the avai1abilit.y o f polycrystalllne cubic boron nitride (PCBN) i t i s possible t o
machine vend hard gears, etc. at speeds of (60-150 m/min = 200-500 fpm). When
this i s done using PCBN tools i n face milling, Chip formation i s of a cyclic saw
toothed type. This type of chip formation i s reviewed i n relation t o other types of
cylic and noncyclic chip formation. The root cause o f high frequency, saw toothed
chip formation i s found to be periodic gross Shear fracture extending from the
free surface of the chip toward the tool t.ip and not adiabatic shear as commonly
believed.
Keywords: Cutting, Cubic boron nitride (CBN), Chip formation
Introduction
With the appearance of superhard cutting tool materials i t
i s possible t o machine work materials such as case carburized
gears a f t e r heat treatment rather than by grinding (Hodgson and
Trendler,1901; Schwarzhofer and Kaelin, 1986; Koenig et al,
1990) In the course of a general study of this possibility some
very interesting cyclic chips have been obtained i n the practical
cutting speed range s i m i l a r t o ones described i n the literature
when machining materials of lower hardness at very high speeds.
In order t o optimize such machining operations, i t i s important t o
understand the chip forming mechanics of these cyclic chips i n
fundamental terms.
Before discusssing experimental results
obtained when face m i l l i n g case carburized steel specimens w i t h
polycrystalline cubic boron nitride (PCBN) tools, i t i s useful to
review cyclic chip formation from a broad point of Vie’w

Cyclic Chip Formation

Within a short time a f t e r Merchant (1941, 1945) published
his world famous model of continuous chip formation (Fig. la), i t
was suggested by several authors that a l l chips do not behave i n
accordance w i t h this model. I f the work i s relatively s o f t and not
prestrain hardened, chip formation w i l l involve a pieshaped zone
(Fig. lb) and an even more extensive shear zone i f the radius a t the
tool t i p (p) i s large relative to the undeformed chip thickness a
(Fig. Ic).

Fig. I . Chip formation for -flow- type chips
a ) concentrated shear model f o r
Precoldworked softmaterial.
b! Pie shaped shear zone for soft.
annealed material
c) More extensive shear zone w i t h
subsurface plastic f l o w f o r tool
w i t h rounded t i p

a
.::

continuously across the w i d t h of the chip but are separated by
regions undergoing subfracture plastic flow. These microcracks
are subsequently rewelded w i t h further deformation. Evidence f o r
this i s the fact that the mean shear stress-on the shear plane
increases w i t h normal stress (Merchant, 1945) which would not be
the case l f only plsstic f l o w were involved. Further evidence i s
the presence of the ends of localized microfracture planes on the
back of a “flow !ype” chip IFig.2). Since there i s no evidence of
microfracture on the side surface of a continuous “flow” type

chip, i t has been generally incorrectly assumed that no fracture i s
involved.
One of the f i r s t papers concerning cyclic Chip formation
where the chip i s continuous but i s alternately thick and thin and
rnOVeS in a stick-slip fashion up the face of the tool was described
by Bickel (1954) a t the ClRP General Assembly of that year.
Bickel used a high frequency flash lamp t o produce a series of
pictures showing the development of what i s generally referred to
as a wavy chip !Fig. 3). This was the sit.uation f o r a relatively
s o f t material machined at relatively high but practical cutting
speeds f o r the HSS and carbide tools then i n use. As the chip was
fot-med, the shear angle gradually decreased w i t h the chip
stationary on the tool face u n t i l the component of force along the
tool face was sufficient t o cause the chip t o move up the tool face
as the shear angle increased. This was followed by the chip again
Coming to rest and’a repetition of the cycle 01 variation In shear
angle, forces and chip thickness. With this type of chip there was
no gross fract.ure (i.e fracture where t.he plane of fracture
extends clear across the ‘width of the chip) and when viewed from
the side, i t had the same appearance as a continuous “flow” type
chip except that there were signs of greater and less strain having
taken place I n the thin and thick chip vicinities respectively
(Fig.3). Similar cyclic chips were described by Eugene (1957) a
short time after Bickel. Albrecht !I9621 has presented a
discussion of wavy chip formation that involves the Cycllc
variation of shear angle but no gross fracture.

b1

rn

It. was also soon discovered that a great deal o f cutting
involved cyclic chip formation. The rnechanics of this type of chip
formation has been thoroughly viewed by Komanduri and Brown
(198 1) and some important observations concerning this topic
have been published by Nakayania (1974, 1988). Those interested
i n cyclic chip formation w i l l find these three papers a valuable
starting point. Only observs:ions that tixtend the concepts
presented i n these papers or s h i f t the emphasis w i l l be presented
here.

Fig. 2. Back (free) surface of ‘flow’
type chip showing ends of
rnicrorfracture planes

Fig. 3. Wavy chip

A l l types of metal cutting involves fracture. Even the
forma?ion o f continuous (so-called f l o w type) chips (Fig la)
involves extensive localized microfractures that do not extend

Annals of the ClRP Vol. 42/1/1993

29


A I I other cyclic Chip tormation involves periodic gross
fracture that extends clear across the width of the Chip Periodic
gross fracture may begin at the tool t i p or at !he free back surface
of the chip The f i r s t type which leads t o relatively small

drsconnected segments i s generally termed discontinuous chip
formation
Discontinuous Chip Formation
Figure 4 shows cyclic chip formatjun where gross fracture
originates periodically from the tool t i p (A). The numbers under
the sketches are motion picture frame numbers. The l a s t sketch
on the l e f t i s a composite showing how a single chip segment i s
formed. I n this case, the chip does not slide over the tool face as
i t is. formed but r o l l s down upon t.he tool face as the center of the
chip i s extruded upward. When frame 40 i s reached, the free
surface of the chip i s tangential t o the t.ool face and tool face
f r i c t i o n i s essentially zero at the tool tip.

same f o r a reasonably homogeneous work mat.erial
Figure 6
shows the situation when the fracture curve extends below the
line of tool t i p travel. This i s then a source of surface roughness
for discontinuous chip formation and the finished surface w i l l
consist of alternale unburnished (dull) and burnished (shiny)
regions when the finished surface i s viewed from above (Fig. 6b).
cast iron and unleaded 70130 or 60/40 brasses are materials that
tend t o give discontinuous chips that are easily disposed of. It i s
found that the stick-slig freauency of segment formation i s
influenced i n a minor way by the stiffness of the tool-work
machine tool system.

Saw T o o t h Chip F o r m a t i o n
Still another type of cyclic Chip i s obtained w i t h cold
worked 60/40 brass Figure 7a shows a Chip root f o r such a
material while Figure 7b i s a diagrammatic interpretation In t h i s

case, perlodic gross fracture occurs at the free surface where
normal stress on the shear plane i s zero and runs clear across the
surface t o the tool t i p In Figure 7a. a new crack i s l u s t about t o
occur and run t o the tool tip. Nakayama (1988) has given good
reasons why FG i s parallel t o the resultant force (R) on the tool.

Fig. 4. Cyclic chip formation f o r Beta brass(after Cook et al; 1954)

Figure 5 shows the elastic stress pattern when a
concentrated horizontal force P is acting at the tool point (tool
face f r i c t i o n essentially zero). OF i s a line of constant shear
stress direction and since the magnitude of the shear stress
rncreases as point 0 i s approached, OG o r a related line curving
upward from 0 and t o the left should be the fracture surface f o r
discontinuous chip formation. The importance of tool face f r i c t i o n
being essentially zero when a new crack forms at. 0 i s that tool
face f r i c t i o n a t 0 would give r i s e t o a compressive stress there
that would tend t o prevent crack i n i t i a t i o n a t A i n Figure 4 . The
condition that determines when a new gross crack forms at. A i s
when the shear stress a t A i s high enough and the normal stress i s
l o w enough consistent w i t h the shear strength of the material at
A to cause fracture.

P

Fig. 5. Elastic stress pattern f o r cutting force P and zero tool face
f r l c t i o n force at t l p of Sharp t o o l l a f t e r Marlelloti, 1941)

Fig 6 Situation when crack running from A t o E ext.endS below
path 01 cutting edge A-C

a) side view b) top view showing crack region (gray)
and burniqhed cut region (shiny)
Eased on the foregoing sequence of events leading to
discontinuous chip formation i t IS t o be expected, as observed,
that the size and shape o f each segment will be auuroxlmately the

30

Fig. 7. a) Optical Photomicrograph o f partially formed continuous
chip of60/40 cold worked brass (rolled to 60% reduction
i n area before cutting). Rake angle = -150; undeformed
chip thickness
O.16mm (.0063in), cutting speed =
0.075 m min-1(2.95 ipm) (Nakayama, Toyama Universit-y)
b) diagrammatic representaion of a)
As soon as a crack runs from B t o A i n Figure 7b. material
i s displaced f r o m cross hatched region 1 1.0 2 w i t h further advance
of the tool. This forces the block of material A B W outward t o i t s
rinal position EFGD w i t h essen!ially no deformation except f o r
that associated w i t h f r i c t i o n sliding along AB, DG and the tool
face AH. In the case o f Figure 7, f r i c t i o n on the tool face is
relatively low and the resultant force on !he tool i s approximately
horizontal and the fracture angle 4 i s 45O. The fact that the
direction o f the cold worked f l o w lines i n Figure 7aremains
unchanged i n the uncut material and i n the bulk of the chip i s
consistent w i t h the foregoing mechanism (Nakayama 1988).
The work done i n t h i s type of chip formation w i l l involve
frictional sliding resistance along planes AB and 0 6 and tool face
AH plus a relatively small amirunt o f extrusion related energy
associated w i t h the displacement of material from 1 t o 2 (Fig. 7b)

.A new fracture plane w i l l develop when the total sliding
distance i s sufficient t o again produce the fracture stress a t the
free surface. The dotted planes 8'A' etc are subsequent fracture
planes which w i l l be uniformly spaced f o r a homogeneous work
material. It should be noted that i n Figs. 7 the sliding that
occurs i s l i k e that of a f r i c t i o n slider w i t h essentially zero
subsurface plastic flow.

Fig.8 Optical photomicrographs of Coninuirus titanium chips
a) st low cut.ting speed of 25 mm/min ( 1 ipm)
b) a t relatively high cutting speed o f 53 m/min (175 fpm)
c i diagrammatic interpretation of b) (after Shaw etal, 1954)


Figure 8a shows a titanium chip produced at low speed
where a saw toothed chip i s produced due t o shear fracture
surfaces running periodically i r o m the free surface t o the tool t i p
i n the manner of Figure 7. Here the major expenditure of energy i s
again involved i n overcoming sliding f r i c t i o n along the tool face
and fracture surfaces. L i t t l e evidence of plastic f l o w i s evident.
w i t h i n the segments. Figure 8 b shows the chip produced from the
same material but. a t a more normal cutting speed 153 m/min (175
fpm)]. Several differences between 8a and 8b are evident:
0

There i s considerable secondary deformation along the
tool face i n Figure 8b but not i n 8a
The secondary deformation along the tool face i s
very inhomogenenus i n Figure 8b
There i s evidence of considerable subsurface deformation

along the fracture surfaces i n Figure 8b

C o m p o s i t e Chip F o r m a t i o n
Figure 8c shows a diagrammatic interpretation of Figure
8b. I n this case, gross fracture extends only part way to the tool
tip. The gross fracture crack w i l l be stopped at a point where the
compressive stress on the shear plane reaches a ralue sufficiently
high t o stop the crack. This rneans that the layer below the
stopped crack must be removed by the flow type cutting
mechanism while the upper part involves sliding frictional
resistance. Deformation in the secondary shear zone along the
tool face i s very inhomogeneous. There i s evidence of unusually
large plastic strain i n the secondary shear zone along extensions
of the gross shear cracks (indicated by dots in Figure 8c). This
suggests that weakening associated w i t h the generation of
noncontinuous microcracks along the dotted crack extensions
shown in Figure 8c i s responsible for the concentrated shear bands
i n the secondary shear zone
The shear bands eviden! i n Figure Rb l i e along the shear
fracture planes and are evident when materials having l o w
thermal properties (conductivity and volume specific heat) are cut
at relatively high speeds. A t high speeds of sliding, considerable
thermal energy develops and w i t h l o w thermal properties, this
results i n thermal softening and considerable subsurface f l o w
along the sliding f r i c t i o n (fracture) surfaces. These concentrated
shear bands are frequently referred t o as being due t o adiabatic
shear. While this i s true enough regarding the end result,
adiabatic shear i s not the root cause of this type o f cyclic Chip
formation but merely evidence of the presence of high thermal
energy due t o high speed sliding along already formed periodic

fracture surfaces.
The cyclic formation of these fracture
surfaces i s the actual cause of the instability and not adiabatic
shear as suggested by Shaw et al (1954). Saw tooth chips are
obtained w i t h (Fig. 8b) and without (Fig. 8a! the presence of
adiabatic shear
When a titanium rrlloy i s cut at extremelu low speed (-0.001
rn/min = 0.004 fpm) continuous chips of the type shown i n Figlire 4
w i t h individual segments welded together are obtained !Komanduri
and Turkovich, 1981) In this case, periodic fracture begins at the
tool tip. However, a t more practical speeds but as l o w as
25 mm/min [ I ipm]) chip format.ion i s as shown i n Figure 8 w i t h
periodic lractiure st-arting at the free surface as suggested by
Nakayams ( 1 988)
Kornanduri and tiis associates have obtained turning chips
very s i m i l a r to that of Figure 8b when cutting materials having
l o w thermal properties a t very high speeds Figures 9a and 9b are
two examples. Figure 9a is a saw toothed chip produced when
machining AlSl 4340 steel of moderate hardness (% = 325
Kg/mm*) at a high speed 250 m/min (800 fpmi This i s seen to be
similar t o Figure 8b except. !hat. the very high speed of sliding
along the extensions of the gross fracture surfaces !dots i n Fig.
8c) and along the tool face results i n what appears t o be melting
as indicated by the whit.e [unet-ched ) bends. i n Figure 9a. Figlure
9a shows periodic melting at points A, 6, C, etc. along the ton1
face. As Komanduri has suggested, the speed of the chip
luctuates periodically and w i l l have i t s maximum velocity j u s t
a f t e r gross fracture occurs. This appears t o correspond t o the

regions of greatest depth o i melting where the r a t e of heat.

g e n m t i o n will be B maximum. A t higher cutting speeds than that
pertaining i n Figure 9a an w e n thicker white layer was evident
along the tool face
Figure 9b shows a saw toothed chip produced when turning a
nickel base tlirbine alloy at what i s 8 high speed f o r this material.
The chip of Figure 9b i s very s i m i l a r t.o !.hose o f Figures 8b and 9a
From Figure 9c i t i s evident that when periodic gross cracks
do not penetrate a l l the way t o the t.ool tip, two t-ypes of chip
formrjtion are superimposed - that COrreSpOnding to Figure 7b
where sliding f r i c t i o n i s predominant and that corresponding t o
very nonhomogeneous f l o w type chip iormat.ion w i t h extensive
secondary shew flow along the tool face
Lindberg and Lindstrom (1983) studied saw toothed chip
formation of A l S l 1035 steel and found that. saw toothed chips
were not formed even at very high speeds if the undeforrned chip
thickness (feed) had a low value. For examDle, saw toothed chips
were formed at a frequency of about 14000 Hertz at a cutting
Speed of 150 m/min (490 fpm), a feed of 0.315 mmirev (0.012
ipr)and a depth of cut of 2 rnm (0.080 in) but continuous chips
were formed at the same speed and depth of cut when the feed was
reduced to 0.100 mm/rev (0.004 ipr). Since the highest natural
frequency of any of the components of the tool-work-machine tool
systern i s only about 1000 Hz, i t follows that the stiffness o f the
System shoulU have no influence on the frequency of segment
formation. This has been found t o be so for a l l cases of saw tooth
chip formation (Komanduri et 81, 1982).
nelting
This Is not the f i r s t t i m e what i s believed to be a molten
layer has been observed i n metal cutting. Schaller (1962) in
studying the machining of specially deoxidized steels having a

low tendency t o cause cratering o f carbide tools at high cutting
speeds has observed a nonetching white layer along the tool face
(Fig. 10) This appears t o be a material that has melted and then
cooled so rapidly that an unresolvable grain size o r none at a l l
(amorphous) develops In this case relatively low melting ternary
(Si$-AI,O,-CuO
inclusions spread over the tool face and act as
a diffusion barrier.

Fig. 4 U p t i i a l photomicrographs of continuous saw toothed chips
produced when machining d i f f i c u l t materials a! high speel
a) AlSl 4340 steel (Hg = 325 z HRC = 34) turned w i t h
AI,O,/Ti
ceramic tool at cutting speed of 250
m/min !800fprn), feed of O.Smm/rev.(O.O I8 ipr),depth
of clut of 3.75 mm (0.1Soin), rake angle of - 5O. no
cutting fluid (after Kornanduri et al, 1982)
b!

Solution t-reated and aged lnconel 718 (y=300 s
4 3 ) nickel based turbine alloy turned w i t h
A1,0, /TIC ceramic tool at cut.ting speed of 92 m i m i n
(300 fpm), feed of O.2Omm (0.008 ipr), dept.h of cut of
2.5 mm (0.100 in!, rake angle, -5O. no c.utt.ing fluid
(after Komanduri and Schroeder, 1’3861

31


DeSalvo and Shaw (1969) have investigated the possibilities

of hydrodynamic action w i t h such a situation and have shown that.
what at first glance appears to be a f i l m that i s inclined i n the
wrong direction f o r positive hydrodynamic pressure development
w i l l actually give positive pressure. This becomes clear by
reference t o Figure I 1 Figure I la shows the classical slider
bearing w i t h a stationary inclined pad and an extensive member
moving w i t h a velocity V to the l e f t while Figure 1 l b shows the
chip moving parallel t o the stationary tool. Figure 1 ICi s the
kinematic equivalent of Ilb which is seen t o be identical t o Ila.

These chips are seen t o h a w t.he same appearance as those
of I'igure 9 including the following:

0

0

0

periodic gross cracks extending part way from free
slurface of chip t.o tool t.ip
very Iit-tle evidence of plastic f l o w i n t.he "teeth' of the
chip
heavy plastic f l o w i n ?he region of the chip below the
extent of gross cracks and along the tool face
white unetched layers along ?he too! face and gross
frac!ure surfaces

Fig. 10.Formation of layer on tool face when turning specially
deoxidized steel at high speed (after Schaller, 1962)

Venuvinod e t a l (1983) have also found a structureless
w h i t e layer when using an externally driven rotary tool to turn
m i l d steel. The presence of such a f i l m led to l o w force levels
which were attributed to hydrodynamic action. No such f l u i d
f i l m s were
found f o r materials having higher thermal
conductivity (Cu, Al, brass).
The unetched white layers i n Figure 9 represent a third case
i n metal cutting where molten layers appear t o be involved. No
legitimate evidence of melting i n grinding exists even though the
specific energy in fine grinding i s more than an order o f
magnitude greater than that f o r metal cutting (Shaw, (1984).
A t cutting speeds even higher than those f o r Figures 9a and
9b. the chips are no longer continuous (Komanduri e l al, 1982) but
consist of individual segments. This i s apparently due t o melting
of a continuous layer separating individual segments.

Fig. 12 a) Optical photomicrograph of continuous saw toothed chip
produced when face m i l l i n g case carburized steel (61
kl at cutting speed of 500 fpm (152 m/min), feed of
0.0 10 i p r (0.25 mm/rev), depth of cut 0.010 i n (0.25
mm), rake angle of - 7,and using no cutting fluid.
b) Scanning electron micrograph o f portion of a) at 5x the
magnification.
Chips produced a t other feeds and speeds were s i m i l a r t o
those of Figiure 12 The material i n the white layer along the tool
face in Figure 128 i s seen t o be essentially wihout structure This

a)

6)

Fig 1 1 a) Classical hydrodynamic slider bearing w i t h f l u i d layer
decreasing i n thickness i n direction of motion
b) Inclined 'fluid' layer between stationary tool and solid
chip surface moving parallel t o tool face
c) kinematic equivalent of b) which i s the same as a)

was even found t o be the case in SEN micrographs of the white
layer at 3500~.

Figure 8c holds equally w e l l f o r Figures 9, 8b and 12. When
the gross cracks extend only part way t o the tool t i p there are t w o
shear angles Q:

9, = the gross fracture plane shear angle (459)

Milling H a r d Case C a r b u r i z e d Steel
0

When case carburized A l S l 8620 steel (b= 61 and 0.050 i n
case depth ~ 1 . 2 5mm) is subjected t o a plane m i l l i n g operation
under the following conditions, saw-toothed chips very s i m i l a r t o
those in Figure 3 are obtained (Fig. 12):
Cutting speed: 500, 200 fpm (152, 6 1 m/min)
Depth of cut: 0.010, 0.005 i n (0 25, 0.13 mm)
Feed: 0.0 10, 0.005 i p r (0.25, 0.13 mm/rev)
Rake angle: -7
Tool: Five PCBN inserts each 0.500 x 0.188 i n (12.5 x
4.80mm), 0.031 i n (0.78mm) nose radius, 3 i n

cutter diameter (76mm). 80"x100" diamond
shaped inserts w i t h 100' corner used.

32

+2

= the plastic defomation shear angle for the f l o w type
chip formation region

( @ 2 < Q,).

Also, i n Figure Eic, p i s the spacing of successive gross fracture
planes on the work surface and pc i s the corresponding spacing on
the chip (p>p,). The cutting r a t i o for such a composite model
w i l l be
r = pJp
(1)

As Nakayama !I3881 has shown, the resultant force on the tool
face i s as shown in Figures 8a and 9 and the included angle at the
t i p of each "tooth" should be 4S0 as indicated in Figure 9


C o n c l u d i n g Remarks
Considerably more information may be extracted by
examination of a saw tooth chip than from a cant-inuous f l o w type
LhiP but t o consider t h i s would carry the present, diSclJSsion too
f a r ailellj The main objective of t h i s paper was t o demonstrate
!hat Saw tooth chips are obtained no! onlq when

a highly cold wYorked b r i t t l e material i s machined even a t
l o w Speeds [Fig. 7 f o r brass)
a a d i f f i c u l t t o machine material w i t h

low thermal
properties (k, pc) i s niachirted over a wide range of
speeds (Fig. 8, Ti) and Fig. 9b (Ni base alloy
a a somewhat d i f f i c u l t to machine material and moderate
hardness i s machined at very high Speed (Fig.98,
AlSl 4340 steel)
but also when
0 a very nard b i t t l e material i s machined at relatively l o w
speed (Fig. 12 - case caburized hard steel)
A second objective was t o show the relationship of saw
tooth chip formation t o other modes of cyclic chip lormation as
well as t o f l o w type Chips. A l l types o f chip formation involve
fracture as w e l l as plastic flow. The f l o w type chip involves
localized microfracture and rewelding i n conjunction w i t h plastic
f l o w &haw et al, 1991). I t i s important t o keep this i n mind
when attempting analytical simulation of any chip forming
process. Use of the Von Mises f l o w criterion i s inadequate as a
constitutive relation even f o r f l o w type chip formation and i s
particularly inadequate f o r cyclic Chips, since i t does not take the
important fracture aspect i n t o account.
An important result i s that what appears t o be a liquid layer
of chip rnaterial i s formed along the tool face when a very hard
b r i t t l e material such as hardened case carburized steel i s
macnineu at ordinary speeds. This means that the contact area
between Chip and tool w i l l be 100% of the apparent area of
contact. This coupled w i t h the very high temperature involved

(M.P. of work material) greatly increases the likelihood of crater
wear on the tool face. Polycrystalline CBN i s w e l l suited t o the
machining of superhard work materials because of i t s hardness,
chemical stability i n contact wit.h high tmperature iron and i t s
outstanding thermal properties

Komaridut-1, R ; Schroe0er.T A.; Hayra, J., von Turkovich, 8..F.; and
Florn, D.G 119823 On the Ca+astrophic Shear Instability i n
High Speed Machining of an AlSl 4330 St.eel, J. Ena. Ind
(Trans.ASME) 104- I2 1 - I 3 I
Komandluri, R.; Flom, 0 G.,and Lee, m !1'?851 Highlights of DARPA
Advanced M a m n i n g Research Program, J. Eno. f o r InU.
(Trans ASME). 107. 325-335
Komanduri, R. and Schroeder, T.A. (19863 On Shear Instability i n
machining a Nickle-Iron Base Superalloy
J. Ena. for Ind. (Trans. ASME) 108. 93- I 00
Lindberg, B. and Llndstrorn, R. (19833, Measruements of the
Segmentation Frequency i n the Chip Formation Process,
Annals of CIRP.32/1, 17-20
Martelotti,M.E. (1941) An Analysis of the Milling Procss
TRANS ASME,63.8,677
Merchant, M. E. (1945). Mechanics of the Metal Cutting Process
J. ADD^. Phus. 16.267(a) 318(b)
Nakayama, K. (1974) The Formation of Saw-tooth Chip, &
ylternat. Conf.. on Produc., Tokyo, 572-577
Nakayama, K. (1988) Machining Characteistics of Hard Materials,
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Schaller, E. (1962) Beitrag zur Untersuchung Yon Spannungen und
dynamischen Vorgangen i n der Grenzschicht zwischen
Wergzeug und Span bei der StahlZerSDannUng m i t

Hartrnetallwerkzeugen. QEna.. Dissertation. T.H. Aachen
Schwerzhofer, R.P. and Kaelin, A. (1986) Finish Cuting of Case
Hardened Gears, Annals of CIRP.35/1. 45-50
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Shaw, M.C. (1984) Slurface Melting in Grinding Operations? Annals
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Shaw, M.C.; Janakiram, M. and vyas. A (199 1 ) The Role of Fracture
i n Metal Cutting Chip Formaion, Proc. NSF Grantees CON. on
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