Davim J. Paulo (editor). Machining. Fundamentals and Recent Advances

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140 A. Pramanik et al.

Figure 5.11(a) shows that the longitudinal (parallel to the axis of the machined

bar) residual stress on the machined non-reinforced alloy surface is tensile for the

whole range of feeds considered but that it is compressive for the MMC. The

magnitude of the tensile residual stress (10–140 MPa) is much larger than the

compressive one (0–16 MPa). The residual stress of the non-reinforced alloy is

low at low feed, but with increasing feed, it increases at a very high rate. After

a certain feed, this rate decreases and very little further increase in residual stress

is noted. For the MMC, the compressive residual stress decreases and moves to-

wards neutral at a low rate with increasing feed. The transverse (perpendicular to

the axis of the machined bar) residual stress (Figure 5.11(b)) for the non-

reinforced alloy shows a similar trend to the longitudinal one. The transverse re-

sidual stress for the MMC is nearly neutral and does not vary significantly with

feed (Figure 5.11(b)).

Figure 5.12(a) shows that the residual stress (longitudinal) is tensile (10−100

MPa) in machined surface of the non-reinforced alloy and compressive (3–12

MPa) in that of the MMC for the considered range of speeds. The longitudinal

residual stress for non-reinforced alloy is low at lower cutting speed and increases

at a high rate with increasing speed before reaching a constant value. The influ-

ence of speed on longitudinal residual stress on the MMC surface is negligible.

The transverse residual stress in the non-reinforced alloy is also tensile and in-

creases at an almost constant rate increasing speed (Figure 5.12(b)). Similar to the

longitudinal residual stress, the transverse residual stress for the MMC does not

vary significantly with the variation of speed for the range considered.

From the above discussion it is clear that the residual stress in the machined

non-reinforced alloy surface is tensile but that it is compressive in the MMC for

all the conditions considered. Capello [54] divided the mechanisms of residual

stress generation into three categories: mechanical (plastic deformation), thermal

(thermal plastic flow) and physical (specific-volume variation). Tensile residual

stresses are caused by thermal effects and compressive stresses by mechanical

effects related to the machining operation. The relatively small compressive stress

Figure 5.11. Effect of feed on residual stress at a speed of 400 m/min and a depth of cut of

1 mm: (a) longitudinal and (b) transverse

Machining of Particulate-Reinforced Metal Matrix Composites 141

measured on the MMC surface indicates marginally higher influence of the me-

chanical factor compared to the thermal factor. On the other hand, thermal effects

play a prominent role over mechanical effects in residual stress generation when

the reinforced particles are absent. The influence of the thermal factor for the non-

reinforced alloy increases with increasing feed/speed.

For the MMC, based on the machining and indentation investigations [16,

19],

it appears that three factors are mainly responsible for excessive mechanical de-

formation on the machined surface that take over the thermal effects: (a) restric-

tion of matrix flow due to the presence of particles, (b) indentation of particles on

the machined surface and (c) high compression of matrix in between particles and

the tool. At low feed, these factors become very prominent. Increased percentage

of particle fracture/debonding forces (as will be discussed in Section 5.2.6) indi-

cates higher tool–particle interactions at low feed. However, with increasing feed,

the indentation effects of particles as well as the tool–particle interaction decrease

for the same length of machined workpiece. Additionally, the effects of tempera-

ture increase with increasing feed. Thus high compressive residual stress values at

low feed and lower stress values at higher feed can be expected.

The influence of temperature is comparatively small at low cutting speed but

increases its influence with increasing speed [46]. The influence of mechanical

factors also increases due to increasing strain rate. With varying speed, it appears

that mechanical and thermal effects balance out, resulting in a negligible compres-

sive residual stress on the machined MMC surface.

5.2.3.3 Hardness

Similar to monolithic metal, microhardness of the surface/subsurface of machined

MMC increases beyond the bulk hardness due to the plastic deformation, causing

an increase in dislocation density that is controlled by particle size and volume

fraction, and machining parameters [49]. The microhardness is higher near the

machined surface layer and decreases with the depth of machined sub-surface due

to a decrease in the work hardening of the matrix material beneath the surface

Figure 5.12. Effect of speed on residual stress at a feed of 0.1 mm/rev and depth of cut of 1

mm: (a) longitudinal and (b) transverse

142 A. Pramanik et al.

layer. The microhardness beneath the machined surface increases with increasing

particle size and volume fraction. The initial matrix hardness greatly influences

the extent of sub-surface damage. The lower the matrix microhardness, the deeper

the plastic deformation zone beneath the machined layer will be [57]. The overall

increase of hardness of machined MMC surface is more marked for composites

reinforced by fine particles [28].

5.2.4 Shear and Friction Angles

Shear and friction angles are associated with machining forces, efficiency of metal

removal process, surface roughness and tool wear. Generally a ductile material

will have a low shear angle and a brittle material will have a large shear angle

[23]. This parameter can be determined using the chip thickness ratio, which is

a measure of plastic deformation in metal cutting. The relation to calculate the

shear angle

is:

−

⎞

⎛

⎟

⎜

−

⎝

⎠

rcos

tan

rsin

(5.2)

where r

is chip thickness ratio (defined as the cut thickness divided by the chip

thickness) and γ is the tool rake angle.

The friction angle controls the temperature generation at the tool–chip interface

and hence crater wear. This parameter can be derived from the associated cutting

and thrust forces using the equation:

−

⎞

⎛

⎟

⎜

−

⎝

⎠

cc tc

Ftan

tan

Ftan

(5.3)

where β is the mean friction angle and F

and F

are the chip formation forces in

the cutting and thrust directions, respectively. A higher friction angle will result in

the generation of a higher temperature at the tool chip–interface and hence high

tool wear. The applicability of Equations (5.2) and (5.3) for MMC machining was

considered in [57,

58].

Figure 5.13(a) shows the effect of reinforced particles on the shear angle with

the variation of feed. The shear angle increases with the increase of feed for both

workpiece materials. Initially its rate of increase is very high and the shear angle

for the MMC is higher than that for the non-reinforced alloy. After a certain feed it

becomes higher for the non-reinforced alloy. Then the variation of shear angle

with feed reduces for both materials. According to Equation (5.2) a higher shear

angle means a lower chip thickness or higher chip thickness ratio (r

). During

machining, the chip undergoes complete deformation across its thickness in the

primary shear zone, but in the secondary shear zone deformation is restricted to

the tool–chip interface region. Therefore, with increasing cut thickness the thick-

ness of the secondary deformation of chips reduces compared to the total chip

thickness. This causes inhomogeneous deformation of chips and the generation of

well-broken C-shaped chips for the MMC.

Machining of Particulate-Reinforced Metal Matrix Composites 143

The effect of reinforced particles on friction angle with the variation of feed is

presented in Figure 5.13(b). The friction angle curves have a hyperbolic shape for

the MMC and non-reinforced alloy. Initially the friction angle for the non-

reinforced alloy is little higher than that for the MMC and they start to decrease at

a high rate with increasing feed. Above a certain feed the friction angle for the

non-reinforced alloy becomes lower than that for the MMC. With a further in-

crease of feed this angle continues to decrease at a reduced rate for both materials.

The variation of shear angle with speed due to presence and absence of parti-

cles is depicted in Figure 5.14(a). Shear angles for the non-reinforced alloy are

higher than those for the MMC over the range of speeds considered in this investi-

gation. For the non-reinforced alloy, the shear angle initially decreases with in-

creasing cutting speed, then it starts to increase at a small rate with further in-

creases of speed. This reflects the initial increase of force with speed and then

decrease after certain speed. The shear angle for the MMC continuously increases

with the increase of speed at a low rate.

Figure 5.14(b) shows the effect of particles on the friction angle with variations

of the cutting speed. Unlike the shear angles, friction angles for the MMC are

Figure 5.13. Effect of feed on shear and friction angles at a speed of 400 m/min and a

depth of cut of 1 mm: (a) shear angle and (b) friction angle

Figure 5.14. Effect of speed on shear and friction angles at a feed of 0.1 mm/rev and

a depth of cut of 1 mm: (a) shear angle and (b) friction angle

144 A. Pramanik et al.

higher than those for the non-reinforced alloy over the whole range of speeds

considered. At low speed, a comparatively low friction angle is noted for the non-

reinforced alloy, but it increases rapidly with increasing speed and reaches a con-

stant value with further increases of speed. A small increase of friction angle for

the MMC is noted with increasing speed.

5.2.5 Relation Between Shear and Friction Angles

As noted earlier the shear angle

is associated with the geometry of chip forma-

tion and hence cutting forces, etc. The theoretical relations obtained for

by Mer-

chant [60] and Lee and Shaffer [61] are:

βγ

⎧

−−

⎪

⎨

⎪

−−

⎪

⎩

( ) Merchant

( ) Lee and Shaffer

(5.4)

where

and

are the friction and rake angles, respectively.

However, the experimental results obtained by investigators such as Kobayashi

and Thomson [62] and Pugh [63] for a wide range of (monolithic) work materials

and cutting conditions show that the following relation is more appropriate for

βγ

=− −BC( ) (5.5)

where B and C are constants that depend on the work material.

Figures 5.15(a and b) show the experimental values of

plotted against

−() for the MMC and aluminium alloy. The linear regression lines for the

data are also shown in the figures. It can be seen that the experimental results fall

y = -0.4245x + 35.777

= 0.617

0 1020304050607080

β-γ (degree)

Ø (degree)

(a)

y = -0.6311x + 46.638

= 0.716

0 10203040506070

β-γ (degree)

Ø (degree)

(b)

Figure 5.15.

versus (

–

) relationship: (a) for the MMC; (b) for the aluminium alloy

Machining of Particulate-Reinforced Metal Matrix Composites 145

close to the lines represented by Equations (5.6) and (5.7) for the MMC and alu-

minium alloy, respectively.

φβγ

=− −()

for MMC (5.6)

φβγ

=− −() for aluminium alloy (5.7)

It can be seen that, similar to the case of cutting monolithic materials discussed

above, there also exists a linear relationship between

and (β – γ) even for the MMC.

In the case of the non-reinforced alloy, the relationship is similar to Merchant’s equa-

tion (Equation (5.4)). The notable difference is that the value of B (Equation (5.5)) for

the MMC is not identical to that for the matrix material (Equations (5.6) and (5.7)).

5.2.6 Forces

The measured cutting and thrust forces at different feeds are presented in Fig-

ure 5.16. It can be seen that cutting force for the non-reinforced aluminium alloy is

slightly larger than that for the MMC (Figure 5.16(a)). For the two materials, the

experimental cutting forces increase more or less linearly with the increase in feed

and the rate of increase is almost similar. Thrust forces increase at a lower rate

than the cutting forces (Figure 5.16 (b)). At lower feeds, the thrust force for the

non-reinforced alloy is higher than that for MMC, but above a certain feed the

opposite trend is noticed. At this stage, a similar rate of increase of forces is noted

for the two materials. Thrust forces are higher than cutting forces at lower feeds

(below 0.1 mm/rev) but the opposite is observed at higher feeds.

Figures 5.17(a, b) present the variation of cutting and thrust forces with cutting

speed for the MMC and aluminium alloy. In the case of the MMC, the speed does

not influence the two forces significantly. For the non-reinforced alloy, both forces

are lower than those of the MMC at low cutting speed but with increasing speed

the forces increase and at a certain point are higher than those of the MMC. With

Figure 5.16. Variation of forces with feed at a speed of 400 m/min and a depth of cut of

1 mm: (a) cutting force and (b) thrust force

146 A. Pramanik et al.

further increases of the speed, the forces start to decrease (due to thermal

softening) and at a certain point again become lower than those of the MMC. The

cutting forces are higher than the thrust forces for both materials at all cutting

speeds considered in this investigation.

To study the influence of tool–particle interactions on force generation, force

signals from dynamometer were investigated. Force signals at different cutting

conditions for the MMC and the non-reinforced alloy during cutting are presented

in Figure 5.18. No significant influence of these interactions on the force signals is

noted, as the signals are similar for the MMC and non-reinforced alloy. This may

be due to smaller interparticle distance in the MMC. It is estimated that for an

MMC with 20 vol% (uniformly distributed spherical particles) of reinforcement

(size 12 μm) the interparticle distance is approximately 4.5 μm. At the lowest

cutting speed used (100 m/min) the cutting tool will travel this distance in only

0.0027 s and it seems that the data acquisition system is not fast enough to detect

individual tool–particle interactions. In addition, at a depth of cut of 1 mm, since

the length of the active cutting edge is over 1 mm and particles are more or less

uniformly distributed in the MMC, continuous tool–particle interactions will occur

along the cutting edge. Hence, the effect of individual tool–particle interaction on

the force signal is not likely to be distinguishable.

From this discussion, it is clear that the strength of MMC did not vary signifi-

cantly with feed and speed compared to that of corresponding matrix material.

However, the strength of the MMC was lower than that of the matrix material

because of the possible cracks generated during deformation. Chip breakability

was found to improve due to the presence of the reinforcement particles in the

MMC. Short chips were formed under almost all conditions. Both the longitudinal

and transverse residual stresses on the matrix surface were tensile and increased

with increasing speed and feed. On the other hand, the presence of the reinforce-

ment particles induced compressive residual stresses on the machined MMC sur-

face due to their interaction with the cutting tool. The surface roughness of the

MMC was controlled by particle fracture and/or pull out at low feeds, but at higher

feeds it was controlled by the feed. On the other hand, the surface roughness of the

matrix material was mainly controlled by the feed. The variations of the shear and

friction angles with feed for the MMC were similar to those for the matrix mate-

Figure 5.17. Variation of forces with speed at a feed of 0.1 mm/rev and a depth of cut of

1 mm: (a) cutting forces and (b) thrust forces

Machining of Particulate-Reinforced Metal Matrix Composites 147

rial, i.e., with increasing feed, the shear angle increased and the friction angle

decreased though the rate of variation depended on the feed. However, the influ-

ence of speed on the shear and friction angles was less marked for both materials.

For the MMC, the shear and friction angles increased very little with increasing

speed. On the other hand, for the aluminium alloy, initially the shear angle de-

creased and the friction angle increased at low speed, but after a certain speed, the

shear angle increased and the friction angle remained constant with further in-

creases of speed. The relationship between

and (β – γ) for the matrix material,

i.e.,

B – C (β – γ), still holds for the MMC. The value of C is 1/2 for both mate-

rials and the values of B are π/5 and π/4 for the MMC and matrix material, respec-

tively.

5.3 Modelling

5.3.1 Forces

A few models are available for cutting force prediction for MMCs. These models

are now considered.

100

120

01234

Time (Sec)

Forces (N)

Cutting-MMC Cutting-Aluminium

Thrus t-M MC Thrust- Aluminium

110

130

150

170

190

01234

Time (Sec)

Forces (N)

Cutting-MMC Cutting-Aluminium

Thrust-MMC Thrust-Aluminium

(a) (b)

100

120

140

01234

Time (Sec)

Forces (N)

Cutting-MMC Cutting-Aluminium

Thrust-MMC Thrust- Aluminium

100

105

110

115

120

125

01234

Time (Sec)

Forces (N )

Cutting-MMC Cutting-Aluminium

Thrust- MMC Thrust- Aluminium

Figure 5.18. Force signals at different cutting conditions during machining of MMC and

aluminium alloy at a depth of cut of 1 mm: (a) feed 0.025 mm/rev and speed 400 m/min;

(b) feed 0.4 mm/rev and speed 400 m/min; (c) speed 100 m/min and feed 0.1 mm/rev; (d)

speed 800 m/min and feed 0.1 mm/rev

148 A. Pramanik et al.

Kishawy et al. [45] developed an energy-based analytical force model to pre-

dict force in the cutting direction for orthogonal cutting of an MMC using a ce-

ramic tool at low cutting speed. The total specific energy for deformation was

estimated from the energy consumed in the primary and secondary shear zones

(which depended on the matrix matrial) and the energy due to debonding/fracture

of the particles (which depended on the MMC properties). Only the force in the

cutting direction was calculated form the total energy consumed in machining.

This model has several weaknesses. Firstly, the energy in the secondary deforma-

tion zone was taken to be one-third of that in the primary deformation zone. This

assumption was based on the results obtained for (monolithic) steel work materials

which may not be applicable to MMCs. Secondly, the width of crack and, initial

and final crack lengths of ceramic particles were 1 μm, 1 μm and the circumfer-

ence of a particle respectively. However, no information was given to justify these

assumptions. Thirdly, the model was only verified at low cutting speed (60 m/min)

because of the use of ceramic tools in their tests. In addition, energy due to

ploughing was not considered.

Pramanik et al. [29] developed a mechanics model for predicting the forces of

cutting particle reinforced MMCs based on material removal mechanism. The

force generation mechanism was considered to be due to three factors: (a) chip

formation, (b) ploughing and (c) particle fracture/debonding. The chip formation

force was obtained by using Merchant’s analysis but those due to matrix plough-

ing deformation and particle fracture were formulated, respectively, with the aid of

the slip-line field theory of plasticity and the Griffith theory of fracture. This

model is now discussed.

As noted earlier, there are similarities in the chip formation mechanism of

MMCs to that of monolithic materials such as aluminium or steel. It should be

noted that, during machining, shearing occurs in a zone rather than on a plane.

However, at higher cutting speeds, the thickness of the shear zone reduces and

hence it can be approximated by a shear plane [22]. Due to the simplicity of the

shear plane models and relatively high cutting speeds normally used when ma-

chining MMCs with PCD tools, Pramanik et al. [29] selected Merchant’s analysis

[60] to determine the chip formation forces. In Merchant’s analysis, the chip is

considered as a separate body in equilibrium under the action of two equal, oppos-

ing forces: the force which the tool exerts on the back surface of the chip and that

which the workpiece exerts on the base of the chip at the shear plane (AB in Fig-

ure 5.19). Thus the force components acting on the tool in the direction of cutting,

, and that in the direction of feed (thrust), F

, were determined using the equa-

tions given below [60]:

βγ

φφβγ

βγ

φφβγ

−

⎫

⎪

+−

⎪

⎬

−

⎪

+−

⎭

cc s c

tc s c

cos( )

sin cos( )

sin( )

sin cos( )

(5.8)

The theory is limited to orthogonal cutting with plane face tools having a single straight

cutting edge.

Machining of Particulate-Reinforced Metal Matrix Composites 149

where A

is the cross-sectional area of cut, τ

is the shear strength of MMC, β is the

mean friction angle, γ is the tool rake angle and

is the shear angle, which is

given by Equation (5.2). The shear angle,

, and the mean friction angle, β, are

shown to depend on machining conditions, workpiece material, etc.

Since the particle fracture was considered separately in this model, only the

matrix metal was assumed to be subjected to ploughing. In order to determine the

force components due to metal matrix ploughing, the equations given in [64],

which are based on a slip-line field model for a rigid wedge sliding on a half-space

and for orthogonal cutting, were used. With the above model, the ploughing force

components acting on the tool in the direction of cutting, F

, and that in the direc-

tion of feed, F

, were determined as

242

πγ

ππγ

⎫

⎞

⎛

⎜⎟

⎪

⎝⎪

⎠

⎬

⎞

⎡⎤⎛

⎪

=+ +

⎜⎟

⎢⎥

⎪

⎣⎦⎝

⎠

⎭

cp sm n

tp sm n

Flrtan

F lr tan

(5.9)

where l is the active cutting edge length, r

is the cutting edge radius and τ

is the

shear strength of the matrix material.

Noting that the width of cut is the active cutting edge length which encompasses

straight and round parts of the cutting edge involved in cutting, l is given by

()

−

−−

⎡

⎤

⎡⎤

⎞

⎛

⎣

⎦

=+ +

⎢⎥

⎜⎟

⎝

⎠

⎣⎦

ar cos

lr sin

rsin

(5.10)

where r

is the tool nose radius, κ

is the approach angle, f is the feed and a is the

depth of cut.

Figure 5.19. Machining process of MMC (from Pramanik et al. [29])

Cutting direction

Machined surface

Cutting tool

Matrix material

Ceramic particles

D C