Computer aided simulation and experimental studies of chip flow and tool wear in the turning of low alloy steels by cemented carbide tools

1. Wew, 139 (1990) 235-260 235
COMPUTER-AIDED SIMULATION AND EXPERIMENTAL
STUDIES OF CHIP FLOW AND TOOL WEAR IN THE
TURNING OF LOW ALLOY STEELS BY CEMENTED
CARBIDE TOOLS*
T. H. C. CHILD.9and K. MAEKAWA’
Department qf Mechanical Engineering University c$L.eeds, Leeds LS2 9JT (U.K.)
A finite element modelling @‘EM) analysis of chip flow has been developed
on a CAD (computer-aided design) computer and used to aid studies of the
wear of cemented carbide tools turning an aluminium-deoxidized and an
ahuninium-deoxidized, calcium-treated resulphurized low alloy steel. The latter
steel formed a Ca-Mn-S deposit on the tool rake face and, at a given feed
and speed, machined with 20% lower tool forces and 60-fold less crater
wear than the former. Subsidiary tests showed both steels to have the same
mechanical properties but that the Ca-Mn-S deposit reduced chip-tool
friction; input of these data to the FEM analysis resulted in lower predicted
cutting forces and temperatures for the deposit-forming steel. The temperature
calculations, with a thermal activation wear model, indicate provisionally
that the crater-wear-reducing properties of the deposit were multiplicatively
20-fold due to its effect as a diffusion barrier and three-fold due to lower
temperatures.
1. Introduction
This paper has two purposes: to report on the development of an
elastic-plastic and thermal finite element analysis of chip flow and stresses,
tool temperatures and wear in metal turning; and to report experiments on
the machinability of low alloy steels that have been used both to test the
analysis and to gain a more quantitative insight into the steelmaking factors
that affect machinability. The analysis needs further refinement, particularly
in its tool force prediction capacity, but has been helpful in tool temperature
and wear prediction.
*Paper presented at The Instituteof Metals 1st InternationalConference on the Behaviour
of Materials in Machining, Stratford-upon-Avon,U.K., November S-10, 1988.
‘Present address: Department of Mechanical Engineering, lbaraki University, Japan.
Elsevier Sequoiw’Printed in The Netherlands

2. 236
Slip-line field plasticity analyses of metal machining, in which the variation
of a metal’s yield stress with flow is neglected, conclude that in any machining
circumstances there are ranges of allowable values of chip thickness and
tool force and hence temperature [l-4]; such analyses cannot give unique
predictions of chip formation or therefore of tool wear.
In practice, unique predictions of machining parameters have been
achieved by including yield stress dependence on flow in the analysis and
by coupling the chip-tool friction to the flow, for example requiring it to
depend locally on the chip shear flow stress or on contact pressure. The
first studies in this area were by Oxley and coworkers [5, 61, but their
analytical method required a number of averaging approximations to be
made. Subsequent advances have been made by numerical, finite element,
analysis.
Large strains, strain rates and temperatures make machining a diflicult
subject for numerical analysis, and any analysis is only as good as its
mechanical property and friction assumptions. There have been demonstrations
of finite element modelling (FEN) solutions of machining problems which
have used simplified material or friction models [ 7, 81, but the major detailed
study has been by Usui and his group [9 I; the present paper is based on
their work. A programme previously written for a supercomputer IlO] has
been simplified and pre- and postprocessors added for interactive use on a
CAD (computer-~ded design) computer. The principles are summarized in
Section 2.
Differences in non-metallic inclusion content and form are well known
to be the source of major differences in machinability between differently
produced steels. Inclusions can have at least four separate effects on tool
wear: (1) lubrication of the tool rake face by deposits formed from the
inclusions can cause lower tool forces and temperatures; (2) these deposits
can also act directly as a protective barrier between the tool and the sliding
chip or work material; (3) other inclusions can be abrasive to the tool; (4)
others again can embrittle the work material to weaken its resistance to chip
formation. Calcium treatment of ~~~-deo~~ed steels, to convert
abrasive ahunina to softer inclusions which also form beneficial deposits on
mixed cemented carbide and TiN-coated tools, has been one steelmaking
development for reduced tool wear [ 11-131. Another has been inclusion
control by resulphurization [ 14, 151. Both approaches have come together
in the commercial development of ahuninium-deoxidized, calcium-treated and
slightly resulphurized semi-free-cutting low alloy steels [ 16, 171. However,
although it is qualitatively clear that reduced abrasion, lower cutting forces
and temperatures and a barrier effect all play a part in reducing tool wear
by these steels, there is no quantitative model for assessing the relative
importance of these factors nor for predicting tool wear dependence on
cutting speed and feed.

3. 237
Earlier studies on the wear of cemented carbide tools used to turn steels
which did not form rake face deposits have established that at high cutting
speeds crater wear is, and flank wear may be, thermally activated. Depth
wear per unit time (dwldt) or per unit sliding distance (dwldl) has been
proposed to depend on temperature T and also on contact stress a, [ 18-211:
or
(lb)
It is diflicult to distinguish experimentally between these forms because of
the dominance of the temperature term and also because of the diiliculty
of determining temperature.
In this paper, flank and crater wear rates are reported for a steel-cutting
grade of carbide turning two low alloy steels, and temperatures are calculated
by the finite element analysis. The data are reduced to the form of eqn.
(lb); the activation energies Q are found to be the same for each steel but
the coefficients A are found to differ, and this is discussed in terms of the
steels’ inclusion contents,
2. The finite element machining simulation
The analysis applies to steady state orthogonal machining. An initial
guess is required of the shape of a chip: most simply the guess may be a
straight chip defined entirely by its shear plane angle, the feed and the tool
rake angle; or it could be the result of a previous analysis. The chip is
supposed to be preformed on the surface of the work material and to be
stress free. Calculation proceeds by incrementally displacing the workpiece
towards the tool so that a load develops between the chip and tool. A plastic
state develops in the chip formation zone and it is checked whether the
consequent plastic flow is consistent with the assumed chip shape. If it is
not, the assumed shape is systematically and automatically altered and the
calculation repeated. The cycle continues until the assumed and calculated
flows converge.
The CAD implementation includes a preprocessor which generates from
a primitive mesh (F’ig. l(a)) the ilnite element mesh of an initial guess (F’ig.
l(b)). After a successful calculation a postprocessor constructs graphical
output, e.g. chip and tool temperature contours (F’ig. l(c)). Further details
have been published previously [221.

4. 238
Fig. 1. (a) Finite element preprocessor primitive me& (b) hMal guess mesh and (cl exmph
of postprocessar temperaturecontouroutput.
The work material is assumed to obey the Prandti--Reuse flow rules and
the van M&es yield eriteriort f23, 241. The element stifhess equations are
formal&ted for large strain increments in an updated hgra@an approach,
~clu~ element shape change and rot&on terms [2Sf but exchIing
relax&ion of over-constraint of ~~ornp~~ib~~ [26f. The steady state

5. 239
temperature distribution in the chip and tool is obtained by solving the
thermal diffusion equation in its variational form [271, which has been used
previously in metal-cutting analyses [28, 291.
2.2. Flow stress and j+iction characteristics
Good physical property data are essential inputs to the analysis.
In the analysis, following ref. 9, the unisxial yield stress u of the work
material is assumed to vary with strain, strain rate and temperature according
to
a=B (lo+)? (2)
where the coefficients B, M and N vary with temperature and are obtained
from experiments. The strain path dependence [9] of the yield stress is
ignored.
Friction conditions between chip and tool vary from heavily loaded near
the cutting edge to lightly loaded where the chip leaves the tool. The friction
stress 7 is empirically related to the shear flow stress k of the chip material
by PI
7= k [1 - exp {- (pq$c)} (3)
As the normal stress a, tends to zero, AT,, tends to p and p is seen to be
a friction coefficient, but as a,, becomes greater than k, 7 saturates at k.
3. Experimental procedure
Hot forged bars, nominally 100 mm in diameter, from two casts of a
low alloy steel, grades BS970 708M40 and 708M40 MAXIM*, were provided
by British Steel plc, heat treated by oil quenching to 960 “C, followed by
air cooling from 600 “C. Their compositions and hardnesses are recorded
in Table 1. The calcium-treated and resulphurized steel is seen to be the
MAXIM grade.
These were turned on a lathe without coolant by cemented carbide tools
(8% Co, 75% WC, 17% (Ti-Ta-W)C, Sandvik Grade S2). In alI cases the
tool end and side clearance angles were 6”, the approach angle was 14” and
the nose radius was 0.25 mm. Three side rake angles (O’, 6” and 12”) and
two feed and depth of cut combinations (0.125 mm rev-‘, 1.25 mm and
0.254 mm rev”, 2 mm) were tested. In the iirst instance the cutting speed
was varied from 150 to 300 m min-‘, but it was later raised to 450 m min-’
for the MAXIM steel.
Tool cutting and thrust forces were measured in an initial set of short
tests, before tool wear developed, using a Kistler piezoelectric force platform.
Swarf was also collected, chip thickness measured and shear plane angle
*MAXIMis a registered trade name of United Engineering Steels.

6. TGBLE1
Chemicalanalysisandhardnessofthesteels
MaterialElement(wt.%)*NV30@Pa)
N
%
cSiMOPSGrMONiALcuSnCa
708M400.360.210.770.020.040.940.150.220.030.240.02<0.00052.65kO.l
708M400.410.320.850.010.091.110.210.080.0250.090.010.00462.7OkO.l
MAXIM
*Balance:iron.

7. 241
calculated. Shear stresses on the primary shear plane were calculated from
the forces and shear plane angles.
Flank wear land length and crater shape were measured in tests of total
cut distance up to 1.8 km, at cut distance increments initially of 75 m and
later of 150 or 300 m. Flank wear land lengths were converted to flank
wear depths, from a knowledge of the side clearance angle, prior to expressing
flank wear rate as wear depth per unit sliding (or cut) distance. Crater shape
was measured by a surface profilometer at the midpoint of the depth of cut.
Crater wear rate was expressed as maximum depth wear rate per unit sliding
distance; in this case sliding distance was the distance that the chip slid
over the tool, which is less than the cut distance since the chip speed was
less than the cutting speed.
Tool rake face deposits were studied by scanning electron microscopy
(SEM) using backscattered electron images and energy dispersive X-ray
analysis.
Subsidiary measurements were performed to establish the steels’ me-
chanical and friction characteristics. High strain rate compression testing,
using a Hopkinson bar apparatus, was carried out on cylindrical samples
machined from the steels, initially 10 mm Iong and 6 mm in diameter. Strains
up to 1.0 were achieved by repeated impacts each of strain increment 0.05,
at strain rates from 200 to 2000 s’ and at temperatures up to 700 “C.
Rapid heating was achieved by an ~duc~on coil round the sample and rapid
cooling by quenching in water. Earlier work [30] has demonstrated that with
this equipment, strains up to a level of 1.0 can be achieved at the higher
temperatures before thermally controlled microstructural alterations start to
affect the flow stress signi6cantly. The equipment is thus relevant to metal
machining in which room temperature microstructures pass through the
straining and heating cycle in fractions of a millisecond.
Friction between the chip and tool was studied in a special machining
test, using a split tool dynamometer [9), at a cutting speed of 100 m min-‘,
a feed of 0.2 mm rev-’ and with a 0” rake angle tool. Measurement of the
variation of force over the rake face of the tool enabled the normal and
friction stress distributions to be calculated.
4. Results
Table 2 summarizes the measured initial cutting and thrust forces, F,
and FT,the chip shear plane angles $ and calculated primary shear plane
shear stresses k, and the steady state crater and flank wear rates.
In any cutting condition the cutting force of the MAXIM steel was about
20% less than, the thrust force about 40% less than, the chip thickness
about 10% less than but the primary shear plane shear stress about the
same as that of the 708M40 steel. The lower forces and thinner chips of
the MAXIM steel are not due to lower flow stress.

8. TMLE2iz
Experimentalresultsofforces,chipthicknessandtoolwearrate
RakeFeedSpeed7osM40708M40L%fAXlMDepthwear/slidingdistance(pmkm-‘)
angle(mmrev-‘)(mmid)
@f-s)PCFT(PkFcFTrb708Lu40~~~~40MAxiM
CN)(N)(da)(MW(N>(N>(de&&‘a)
craterFlankc-r-Flank
00.12515043530525718357155297371310.5
22542527427740370174327515210.5
30041726030740357164327321308.42.83.5
60.12510005.8
1201512.1
1504162592672733915231701
2264122583072933916232702549.503.0
3003972373072033314234704
120.1251504152592672731111835701136.303.8
2254152703071631111736687369.1
30037619431728320124376889613.2
00.2544504515.8
60.25415011075063070596227732702423.7
225109853831684900292356541959.53.42.9
300113556733701924270346894688.37.2
37591626334679225.9
450988294347205115.7
120.25415010344033170087824639665
22510063563370788821236699
30010063783469686923038669

9. 243
0 0.4 0.8 1.2 1.6
CUT OISTANCE.km
.
/ I.
/. A0a-0 ,
100 200 300 400
CUTTING SPEED, m imln
Fig. 2. Crater (A) and flank (m) depth wear increase with cut distance for 708M40; a=6”,
f=0.125 mm, U-225 m mix?.
Fig. 3. Crater depth wear rate increase with cutting speed for 708M40 MAXIM (0) and 708M40
(0); a= 6”, f= 0.254 mm.
0&-100
CUTTING SPEED m/mfn
Fig. 4. Flank depth wear rate increase with cutting speed for 708M40 MAXIM (0) and 708M40
(0); for all rake angles and feeds.
Figure 2 shows the typical linear increase of maximum crater depth
with cut distance and the initial nmning-in of flank wear depth.
The crater wear rate when turning the MAXIM steel was only large at
a feed of 0.254 mm rev-’ and cutting speeds greater than 300 m mini. In
these conditions the 708M40 steel caused rapid tool failure. There are
therefore few direct comparisons of crater wear rate in Table 2 but, as shown
in Fig. 3, at a feed of 0.254 mm rev-’ the 708M40 steel showed a 60-fold
greater wear rate than the MAXIM grade at speeds of 225 and 300 m min-‘.
The flank wear rate of the 708M40 steel was also greater than that of
the MAXIMgrade, but a dependence on speed and feed was scarcely noticeable.
Figure 4 shows flank wear rates plotted against cutting speed without
identification of rake angle or feed. The MAXIM flank wear rate is about

10. 244
half that of the other steel except at the highest cutting speed of 450 m
&-? when a jump occurred in its wear rate.
Figure 5 shows backscattered SEM images of rake face deposits formed
on the tools, typical af all feeds and speeds. The lower magniiication images
show the cutting edge horizontal at the top and the full contact length
between chip and tool: a shorter contact length is seen for the MAXIM than
for the 708M40 steei. The deposit from the MAXIM grade is also seen to
be thin: cemented carbide can be seen through it as the light material; the
deposit co&&ted calcium, manganese and suiphur but no ahuninium.The
deposit from the 7OSM40 steel was mainly iron.
Figure6 shows representative results from the Hopkinsun bar tests. The
flow stresses of the two steels were almost ~~t~~~le from one another.
Mean estimates of B, M and N in equation (2) are (with temperatures 8 in
“C and crin GPa1
Fig. 5 SEM images of tool rake faces used to turn (a), (c) 7OSM40 MAXIM and (b), fd)
708M4~ steels; a= 6”, f- 0.254 mm, U= 225 m mi&.

11. 245
with strain and temperature at a strain rate of 1000 s-';solid
symbols, 708M40;opensymbols,708M40 MAXIM.
* on
La)
0 0.L 0.8 1.2
(a) DISTANCE FROM CUTTING EDGE, mm @I
0.8
DISTANCE FROM CUTTING EDGE, mm
Fig.7.Contactstresseson therakefacefor(a)708M40 and (b)708M40 MAXIM; a=OO,
j=O.2 mm, U=lOO m mirP.
B=l.W exp(-0.00188)+0.38 exp(-O.OOOOl(&-445)2}
+0.16 exp{-0.0002(0-570)2}
M= 0.017 +0.0000686
N=0.135 e~(-0.0012e)+O.O7 e~(-0.00002(~-465~}
(4)
The complexity of I3 copes with the blue-brittle peak in flow stress at around
550 “C in Fig. 6.
Figure 7 shows the variations of normal and friction contact stresses
over the tool rake face obtained from the split tool tests. For the 708M40
steel the friction stress in the lightly loaded region at the end of the contact
was greater than the normal stress, but for the 708M40 MAXIM steel it was
less. Figure 8 plots friction stress against normal stress: the low load gradients
give p= 1.3 for the 708M40 and 0.75 for the MAXIM steel. The saturated
value of friction stress of the MAXIM steel is 0.86 times that of the 708M40,

12. I I I t
0 100 200 300
CUTTING SPEED , m/h
Fig. 8. Variation of friction stress with normal stress on the rake face for 708M40 (0) and
708M40 MAXIM (0).
Fig. 9. Tool forces and maximumrake face temperaturesfor 708M40 (a) and 708M40 MAXIM
(0) with n=6”,f=O.f25 mm, d=1.25 mm: ---, FEM calculations; -, experiment.
suggesting a modified form of equation for the MAXIM steel:
r=0.86 k {l-exp(-l.l6pa,/k)) (3a)
4.3. Finite element calculutim
Equation (Z), with coefficients from eqn. (4), and eqn. (3) or (3a) were
input to the Gnite element programme. Calculated tool forces and maximum
rake face temperatures for 6” rake angle tools, a feed of 0.125 mm rev-’
and a depth of cut of 1.25 mm are presented in Fig. 9; the forces obtained
experimentahy are included for comparison. The programme correctly predicts
lower forces and temperatures for the 708M40 MAXIM than for the 708M40
steel. However, the predicted cutting forces are twice as large as measured.
Although the predicted thrust forces are at the same level as the measured
forces, the predicted differences between the 708M40 and 708M40 MAXIM
steels are less than those measured. The predicted temperature differences
of about 80 “C have not been tested experimentally.
Measured maximum crater depth wear rates have been paired with
calculated maximum rake face temperatures, and flank wear rates have been
paired with calculated cutting edge temperatures to test the validity of eqn.
l(b). The data are presented in F’ig. 10. At high temperatures (Z’> 1070 K
for 708M40 and T> 1170 K for 708M40 MAXIM) the wear is thermally
activated: a value of & of 40 + 2 kcal mol-’ may be deduced for both steels.
At lower temperatures the wear depends only slightly on temperature. The
data for the two steels are displaced signScantly from one another: at
high temperatures A (eqn. l(b)) is 140 X 10’ @rn km-’ for 708M40 and

13. 247
TEMPERATURE, Y
1200 1000 800 600
’ 0’ I 1
‘.
100
0
- b
t 0
E
t 0%
_--/
E ‘O , =>.-r-._-?a
0
0 m
G
G 00 m-p -a
1
6 8 10 12
1IT, IO-“'K-l
F'ig.10. Crater ($0) and flank (H, Cl) depth wear rate variations with temperature for 708M40
(0, II) and 708M40 UAXIM (0, Cl).
6.3 X lo-? pm km-’ for 708M40 MAXIM. At lower tempers the wear
rate of the 708M40 steel is three times that of the 708M40 MAXIM steel:
this ratio differs from the two times quoted in the context of F’ig. 4. It is
seen in Fig. 10 that the higher flank wear rates of the MAXIM steel that led
to the two times factor of Fig. 4 belong to the high temperature part of the
wear characteristic.
5;.Discussion
The turning tests con&m earlier work [16] that the calcium-treated and
resulphurized MAXIM grade of i’OSM40 steel machines with lower forces
than the untreated 708M40 steel; the Hopkinson bar tests confirm that the
two steels have the same yield properties. The lower forces come not from
lower yield stresses but from a thin lubricating layer of Ca-Mn-S that is
deposited on the rake face when turning the MAXIM steel.
The friction properties of the layer have been measured directly. Near
the cutting edge the layer’s presence limits the friction stress to 0.86 of the
shear yield stress of the chip mate&& 0.86 agrees well with other indirect
assessments of the friction factor of free-machining steels (41. In the region
where the chip leaves the tool the layer is associated with a friction coefficient
of 0.75, compared with 1.3 for the untreated steel.

14. 248
The turningtests also confirm the lower tool wear rates caused by the
~I~ steel, Figure 10 shows that at tempera~es above 1120 K the wear
is theory activatedwith an activationenergyof 40 kcal mole-“: thisvalue
is in agreement with other studies IS]. Figure 10 also shows that at any
temperatureabove 1120 K the wear of the 70811140steel is 20 times that
of the MAXIMgrade: this is a measure of the effectivenessof the Ca-Mn-S
layer as a barrierto diffusionwear. However, Fig. 3 shows that at a given
feed and speed the wear of the ~0~~~~ steel is 60 times that of the ~~
grade. The 6U-fold factor is the product of the 20”fold factor due to the
barriereffect of the Ca-MnS layer and a three-foldfactor due to the Xower
temperaturewhen turningthe MAXIMgrade. ~ub~titut~~values of A and
Q in eqn. l(b) shows that the three-fold factor is eq~valent to a 100 “C
lower rn~~ rake face tempe~~e between tug the ~~ aJlzd
untreated7~SM4~ steels; 100 “C is typical of temperaturedifferences cal-
culated by the fYiniteelement analysis (Fig. 9f and also measured in other
work [15].
The relativeinfluence on high temperaturewear of the lubricatingand
barrierproperties of non-metallicinclusionsin steels can thusbe considered
qu~ti~~vely by means of eqn. (1). The p~i~~~ values, threefold and ZQ-
fold, deduced above depend, however, on the finite element turnpike
~~c~atio~. Some ~~e~~es with the finiteelementanalysis,considered
in the next subsection, mustmakethese quantitativeconchtsionsprovisional.
At ~rnpe~~es less than 1120 K the wear is not achy activated.
It is suggested thatthe lesser wear produced by the ~~ steel is due to
the absence of abrasive aluminainclusions f 161.
It has been demonstratedthat, startingfrom flow stressinformationand
friction characteristics,finiteelementpredictionsmay be made of machining
parametersusing a CAD computer fan Apollo II ma&tine).Figure 9 shows
guod agreement between predicted and measured thrust forces but poor
agreementbetweencuttingforces. Thisisrapport sincebettersternest
has been experienced previously in the analysisof an 18% Iv&steel [22].
Otheroutput from the programmeshows the force errors tu be due at least
inpartto excessivelylargecalculatedhy~os~~c stresses.Thisis arecognized
problem of el~tic-pl~tic finiteelement analyses:attemptsare to be made
to overcome this after the mannerof ref. 26. A furtherquestion to be faced
concerns the vahdity of applying mechanical property data obtained from
testing up to 700 “C and at strain rates up to 2000 s-’ to conditions in
which maximumtemperaturesand strainrates of 1100 “C and lo4 s-l are
calculated. Nevertheless,the present resuI&?are sufficientlypromising to
warrantfurther development, and these are planned.
It has been conGrmedthat ~~g~~~ ~~ low alloy steeIwhen turned
by ~~l-cu~g grade cemented carbide tools causes lower tool forces and

15. 249
much less crater and flanktool wear than does standard708M40 sted, and
that the two steels have the same yield proper&s.
Differences between the machinabihtyof the steela come from a thin
Ca-Mn-S layer that deposits on the rake face when turning the MAXIM
grade. This layer both lubricates the rake face contact to cause lower
temperaturesto be generatedand acts as a barrierto diffusionwear. Friction
properties of the layer have been measured directly. On the flank face the
lower abrasivenessof the MAXIMsteel brings benefits.
A finite element analysis of chip formation has been developed on a
CAD computer. It has given good predictions of tool thrustforces but has
been in error with respect to cutting forces. It needs more development
before it can be a reliable tool to aid mac~ab~~ studies.
Acknowledgments
This work was supported by the ACME Directorate of the SERC and
by British Steel plc. The Hopkinson bar and split tool friction tests were
ad~tion~y carried out at KitamiInstituteof Technology, Japan, under the
direction of Professor T. Kitagawa;we wish partiparticucucucucucucucto acknowledge his
help.
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