Astakhov V. Tribology of Metal Cutting

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Generalized Model of Chip Formation 27

small plastic deformation allowed by the ductility of even very brittle materials, the

formed crack opens and the partially formed chip comes into contact with the tool rake

face (Phase 5). Since then, the partially formed chip serves as a cantilever beam loaded

by the compressive force and the bending moment, as shown in Fig. 1.15. As a result,

combined stress acts at the chip root which serves as the chip-cantilever support. When

this combined stress reaches a certain limit, fracture of the chip-cantilever takes place

at its root (support) (Phase 6). As such, the separate, almost rectangular chip elements

are produced (Phase 7) as observed in the cutting of brittle work materials using cutting

tools with positive rake angles [84,29]. This chip is common in the automotive industry

in the machining of slip yokes made of ductile cast iron. This chip type may be referred

to as the regularly broken chip.

The second case in the machining of brittle work materials takes place when the compo-

nents of the cutting system are so arranged that the resultant force R does not intersect

the conditional axis of the partially formed chip, as shown in Fig. 1.17(a). As such,

no bending moment can arise due to the interaction of the tool rake face and the partially

formed chip. As a result, there is no bending stress in the root of the chip-cantilever so

that the ﬁnal fracture of this chip (and thus the layer is removed) takes place only due

to the compressive stress imposed by the penetration force P. The chip formed consists

of irregularly shaped fragments of the work material and dust which are the same as

in the fracture of the work material under compression (Fig. 1.17(b)). This dust is the

well-known nuisance of machine shops dealing with machining of cast irons. Figure 1.18

presents a system consideration of the model shown in Fig. 1.17(a). Phase 1 illustrates

the initial stage when the tool is forced by the penetration force P into the workpiece.

As a result, the compression stress grows in the workpiece starting from the ﬁrst contact

point. Further advance of the cutting tool leads to the development of crack network

pre-rupture evolution (Phase 2), which eventually leads to the compression-type fracture

of the layer being removed (Phase 3). Further advance of the cutting tool (Phase 4)

(a) (b)

Conditional axis of the partially

formed chip

Fig. 1.17. Resultant force R does not intersect the conditional axis of the partially formed chip

(a) that results in common fracture of a brittle material under compression (b) (after Astakhov [18]).

28 Tribology of Metal Cutting

System Time

Fig. 1.18. System consideration of the model shown in Fig. 1.17(a).

leads to the bulk rupture of the layer being removed and the formation of the chip in the

form of irregularly shaped pieces of the work material and dust (Phases 5 and 6). Then

a new cycle of chip formation begins (Phase 7) which repeats itself in two stages (Phase

8 is the same as Phase 4). The chip produced in this process can be referred to as the

irregularly broken chip.

The two cases discussed in the machining of brittle materials can be related to work

materials of low ductility (elongation is ≤2%). Many real work materials used in every-

day practice are not so brittle. For example, malleable cast irons exhibit elongation from

1 to 10%, spheroid graphite cast irons – from 3 to 15%, ductile cast iron – minimum.

10%, lead bronzes – from 5 to 15%, etc. Therefore, these materials exhibit appreciable

plastic deformation before fracture. Figure 1.19 shows system consideration of the model

of chip formation for such materials. As shown, the surface of the maximum combined

stress (compressive and bending stresses) is located at a certain angle to the direction of

tool penetration. Although the fracture of chip fragments takes place along this surface,

this fracture is not purely brittle because the layer being removed deforms plastically

prior to this fracture. The chip formed in this process can be referred to as the deformed

fragmentary chip.

This model can be considered as a transitional model between the discussed model of

chip formation in the machining of brittle materials and that of ductile materials discussed

further although it should possibly be attributed to the machining of brittle materials. This

is because the crack originates at the tool cutting edge (as it is clearly shown in Fig. 1.19)

and then runs to the workpiece free surface. However, it is necessary to mention that

transition in the mechanics and physics of chip formation from brittle to ductile zone is

itself continuous by nature while any model is discrete. Therefore, one should clearly

Generalized Model of Chip Formation 29

(b)(a)

(c)

(d)

Fig. 1.19. Quick-stop micrographs of partially formed chip. Workpiece material: lead bronze;

orthogonal cutting on a shaper; cutting conditions: cutting speed 35 m/min, uncut chip thickness

2.2 mm, dry cutting; cutting tool material: P10; Tool geometry: rake angle – 15

◦

, ﬂank angle – 8

◦

(after Astakhov [18]).

realize that no single model could satisfy the properties of work materials used today.

In fact, a set of models should be developed consisting of a number of different models

each suitable in some range of properties of the work and tool materials and cutting

conditions. As new work and tool materials are introduced, this set should be updated

with new models accounting for new mechanics and the physical process with respect

to the cutting process.

1.5.2 Ductile work materials

When considering ductile work materials, different distinctive models are developed

depending on the properties of the work material, contact conditions at the tool–chip

interface and tool geometry [25]. The basic case of chip formation in cutting ductile

materials takes place when no seizure occurs at the tool–chip interface and this is the

most common case in the cutting of most engineering materials. At the initial stage

of chip formation, an elastoplastic zone forms in front of the cutting edge due to the

stress concentration, which is due to the pure compression of the layer to be removed.

30 Tribology of Metal Cutting

Chip

Tool

(a) (b)

Fig. 1.20. The interaction between the tool rake face and the partially formed chip: (a) partially

formed chip-cantilever subjected to the penetration force P from the tool rake face, (b) two

components of the penetration force P, (c) maximum plastic deformation in the bending occurs

in the vicinity of the cantilever’s free surface and (d) deformation takes place along the line of

maximum combined stress 1-1.

As a result, the plastic deformation of this layer takes place by pure shearing during

this stage. As the tool advances further, the plastically deformed part of the layer being

removed gradually comes into close contact with the tool rake face. When full contact is

achieved, this part serves as a cantilever and subjected to the penetration force P from

the tool rake face, as shown in Fig. 1.20(a).

This penetration force can be resolved into two components namely, compressive force Q,

acting along the direction of the conditional axis of the partially formed chip, and bending

force S, acting along the transverse direction, as shown in Fig. 1.20(b). Therefore, the

partially formed chip can be considered as a cantilever beam subjected to the mutual

action of the compressive force Q and bending moment M

(

= SL

)

. When it happens,

the state of stress in the chip root (the cantilever support) becomes complex because it

includes a combination of the bending and compressive stresses. As such, the slip-line

ﬁeld in the deformation of such a cantilever can be thought of as the superposition of

the slip-line ﬁeld due to bending and that due to compression.

Generalized Model of Chip Formation 31

The known studies of slip-line deformation ﬁelds of cantilevers with curved contours

[30,85] show that the maximum plastic deformation in the bending occurs in the vicinity

of the cantilever’s free surface adjacent to its clamped side. Figure 1.20(c) shows the

intensity of this deformation by the corresponding slip lines. As it is well known [30,85],

the plastic deformation under compression is the result of successive shear deformation

taking place along the direction of the maximum shear stress. As such, this direction is

oriented at the angle of 45–90

◦

depending on the ductility of the material.

When these two slip-line ﬁelds are superimposed, the deformation process of the partially

formed chip shifts from pure shearing to complex shearing. As such, the surface of

the maximum combined stress becomes curved (as shown by its trace 1–1) and the

maximum deformation occurs at both the ends of this surface, as shown in Fig. 1.20(d).

The discussed state of stress can be easily veriﬁed by a simple FEA and by observation

of grain structure of a partially formed chip [25] and by the experimental results obtained

by Zorev [29].

Figure 1.21 presents a system consideration of the model shown in Fig. 1.20(d). Phase 1

shows the initial stage. When the tool is in contact with the workpiece, the application of

the penetration force P leads to the formation of deformation zone ahead of the cutting

edge. The workpiece ﬁrst deforms elastically and then plastically. As a result, a certain

elastoplastic zone forms ahead of the tool that allows the tool to advance further into

the workpiece so that a part of the layer being removed comes in close contact with

the tool rake face (Phase 2). When full contact is achieved, the state of stress ahead

of the tool becomes complex including a combination of the bending and compressive

stresses. The dimensions of the deformation zone and the maximum stress increase with

penetration force P. When the combined stress in this zone reaches the limit (for a

given work material), a sliding surface forms in the direction of the maximum combined

stress (Phase 3). This instant may be considered as the beginning of chip formation.

System Time

123

456

System Time

Fig. 1.21. System consideration of the model shown in Fig. 1.20(d).

32 Tribology of Metal Cutting

As soon as the sliding surface forms, all the chip-cantilever material starts to slide

along this surface and thus along the rake face (Phase 4). Upon sliding, the resistance

to tool penetration decreases, leading to a decrease in the dimensions of the plastic

part of the deformation zone. However, the structure of the work material, which has

been deformed plastically and now returns to the elastic state, is different from that

of the original material. Its appearance corresponds to the structure of the cold-worked

material. Experimental studies [25,29,86–88] showed that the hardness of this material

is much higher than that of the original material. The results of the experimental study

using a computer-triggered, quick-stop device proved that this material spreads over the

tool–chip interface by the moving chip that constitutes the well known chip contact layer

(Phase 5), which is now believed to be formed due to the severe friction conditions in the

so-called secondary deformation zone [29]. The sliding of the chip fragment continues

until the force acting on this fragment from the tool reduces, because a new portion

of the work material is entering into contact with the tool rake face. This new portion

attracts a part of the penetration force P. As a result, the stress along the sliding surface

diminishes, becoming less than the limiting stress that ceases the sliding. A new fragment

of the chip starts to form (Phase 6).

The chip formed in this way is referred to as the continuous fragmentary chip. It has a saw-

toothed free side and a non-uniform strength along its length. The shear strength of the

fragments is much greater than that of fragment connections. Therefore, obstruction-type

chip breaker works well to break this chip type into manageable-size pieces convenient

for proper chip disposal.

Comparison of the predicted and actual chip structures shows that they are identical

(Fig. 1.22). Increasing the cutting speed leads to signiﬁcant reduction in the “average

pitch” between two successive “teeth” on the chip free surface and to further distinction

between the chip fragments and their connectors. Such a chip is known as the shear

localized chip.

Fig. 1.22. Structure of the continuous fragmentary chip: (a) prediction and (b) experiment.

Generalized Model of Chip Formation 33

It is worthwhile to notice an essential fact that stems from the considerations of this

model. The chip formation process is cyclic so that the resistance to the tool penetration

into the workpiece varies within each cycle of chip formation and is thus time dependent.

Therefore, it should be expected that the bending moment and thus the bending stress in

the deformation zone should vary over this cycle. Naturally, the cycles in chip formation

are not exactly the same due to the variations in the crystalline structure of the work

material (dislocation density varies over the volume of the workpiece), presence of

inclusions, residual stresses from the previous manufacturing operations and many other

factors. What does not change is the sequence “loading-fracture” found in any cycle. This

cyclic nature of the chip formation process determines the inherent dynamic nature of the

metal cutting process. Depending upon the variations in the magnitude of the penetration

and other forces, which are components of the resultant cutting force, the performance

of the machining system (which includes the cutting system, ﬁxture, machine, etc.)

is affected in different ways. Naturally, the response of the components of the machining

system would depend on the static and dynamic stiffness and rigidity of the whole

machining system. Due to great variety of work materials, cutting tools, machining

regimes, conﬁgurations of the workpiece and many other factors, the magnitude and

its variation (including frequency), point of application, and direction of the resultant

cutting force vary within a very broad range. In the author’s opinion, misunderstanding

of the above-described interactions of the components of the machining system led to the

interpretation of the cutting force as having a stochastic nature (for example [89–91]). If

it would be so, the whole cutting process should be considered as stochastic and thus its

prediction cannot be made on the basis of its theoretical analysis.

1.5.3 Highly ductile work materials

Bearing in mind the presence and signiﬁcance of the bending stresses in the deforma-

tion zone [25], we are now ready to consider the known difﬁculties in the cutting of

highly ductile materials. It is well known that increasing the ductility of the work mate-

rial lowers its machinability. By this, it is meant that both the cutting temperature and

power per unit volume of metal removed will increase [92]. This conclusion, however,

stems from the practice of metal cutting rather than from the known theories of chip

formation. As discussed above, the known model recognizes simple shearing as the only

cause for chip formation and thus cannot explain why machining of a work material with

lower shear strength requires more energy than that with a much higher shear strength.

To understand the phenomenon, a special experiment was carried out [87]. Two

specimens – the ﬁrst made of AISI steel 1045 (yield strength σ

= 525 MPa, ultimate

strength σ

UTS

= 585 MPa, elongation at break δ = 10%), the second made of much more

ductile steel AISI 302 (σ

= 250 MPa, σ

UTS

= 610 MPa, δ = 67%) were machined

using the same cutting regime (cutting speed was 90 m/min; feed – 0.12 mm/rev; depth

of cut – 1.5 mm; no cutting ﬂuid, a P10 carbide cutter with rake angle of −8

◦

In the experiment, the chip compression ratio, ζ was measured and the deformed struc-

ture of the chip produced was analyzed. For the ﬁrst specimen, it was found that

= 1.87, while for the second ζ

= 5.22. As shown in Chapter 2, the degree of

plastic deformation and thus the energy required by the cutting system in the machin-

ing of steel AISI 302 is much greater than that in the machining of AISI steel 1045.

34 Tribology of Metal Cutting

(b)(a)

WorkpieceTool Tool Workpiece

(c)

Fig. 1.23. Chip formation in the machining of a ductile material: (a) chip compression ratio ξ = 2,

(b) chip compression ratio ξ = 5 and (c) typical chip structure in the cutting of a highly ductile

material (×200).

Moreover, it was also found in this test that the temperature of the chip is almost 200%

higher in the machining of steel AISI 302.

While the reason for higher plastic deformation in the machining of highly ductile work

materials will be analyzed later, the changes in the chip deformed structure with increas-

ing ductility of the work material can be explained as follows. Figure 1.23(a) shows

the model of chip formation in the machining of a ductile material where the chip

compression ratio ξ = 2, while Fig. 1.23(b) shows the model of chip formation in the

machining of a highly ductile material where the chip compression ratio ξ = 5. In both

the models, the right-hand coordinate system is set as follows:

The x axis coincides with the direction of the sliding plane (approximation of the surface

of the maximum combined stress) in the current chip formation cycle.

The y axis is perpendicular to x axis, as shown in Figs. 1.23(a) and (b).

The z axis (not shown) is perpendicular to the x and y axes.

Because it was found experimentally that in metal cutting the change in the volume in

the chip plastic deformation is negligibly small [12,25,29], the following expression for

Generalized Model of Chip Formation 35

strains is valid

+ε

= 0, (1.20)

where ε

,ε

and ε

are the true strains along the corresponding coordinates.

Referring to Figs. 1.23(a) and (b), consider a volume of the work material located between

the two successive sliding planes (shown as hatched area in Figs. 1.23(a) and (b)). The

plastic deformation of this volume can be represented by corresponding strains as

= ln

,ε

= ln

,ε

= ln

, (1.21)

where, x

and x

are the dimensions of the discussed volume along the

corresponding coordinates before and after deformation, respectively.

It is known [25] that, when properly measured, the chip width is practically equal to the

width of cut, which yields z

= z

, thus ε

= 0. Accounting for this result, substituting

Eq. (1.20) into Eq. (1.21) and ignoring signs, one can obtain

= ln

= 0or

(1.22)

A very important conclusion immediately follows from Eq. (1.22): increasing chip

thickness x

(i.e. the chip compression ratio ζ) leads to the directly proportional reduc-

tion of distance y

between the two successive sliding planes, increasing the number

of sliding planes per unit length of the chip. To support this conclusion, Fig. 1.23(c)

shows a micrograph of the chip structure formed in the cutting of the second specimen.

In this micrograph, a great number of traces of the sliding planes, one closely followed

by another, can be observed that makes its appearance quite similar to the continuous

chip (Section 1.5.5). However, the conditions of chip formation considered show that

this chip is still a continuous fragmentary chip with a very small distance between two

successive fragments. Naturally, the breakability of this kind of the chip deteriorates

with increasing ductility of the work material. A similar picture can be observed in the

micrograph of the quick-stop section through copper chip presented by Trent and Write

(Fig. 4.27 in [62]).

As the number of sliding planes per unit length of the chip increases, heat generation

due to the relative sliding of chip fragments increases proportionally. This explains the

much higher temperatures in the machining of highly ductile materials. Quite often, the

chip formed has a cherry-red color due to its high temperature.

It is necessary to mention, however, that transition in the mechanics and physics of

chip formation from ductile to highly ductile zone is itself continuous by nature while

any model is discrete. At a certain point, when ductility of the work material becomes

great enough to develop high temperatures at the tool–chip interface, periodic and then

permanent seizure can occur.

36 Tribology of Metal Cutting

1.5.4 Model of chip formation when periodic seizure occurs at the tool–chip interface

Seizure as a phenomenon in metal cutting was probably ﬁrst introduced and described by

Zorev [29], although Zorev did not study this phenomenon thoroughly. The reason for

that is simple: not many work materials having the properties which lead to seizure as well

as the corresponding machining regimes, were used in the 1960s. Trent has presented the

evidence for seizure in his articles and books for more than 20 years and his results are

summarized in his book [93]. However, in his article [63] Trent complained that though

appreciation of the condition of seizure at the tool–chip interface is fundamental to the

understanding of the whole process of metal cutting, it has not been recognized by most

engineers or by tribologists. In the excellent Wear – A Celebration Volume (1984), the

hypothesis of seizure in metal cutting was dismissed in two paragraphs by J.M. Challen

and P.L.B. Oxley as a phenomenon which “is not ruled out for certain conditions.”

This is a strange reason because many phenomena in metal cutting occur only under

certain conditions. In the author’s opinion, the concept of seizure is not accepted by

other researchers simply because the tribology of seizure is not discussed thoroughly

and thus understood. For example, Trent and Write associated seizure with the built-up

edge (p. 41 in [62]) and thus its inﬂuence on chip formation and tool wear at relatively

high cutting speeds, although it is a well-established fact [29] that no built-up edge can

occur at this speed range. In other words, it is not sufﬁcient to point out the existence of

a phenomenon and present purely experimental evidences of its occurrence. Rather, the

physical conditions of its occurrence and its inﬂuence on the process outcomes should

be clearly established. Unfortunately, this is not the case with seizure and thus available

books on metal cutting do not mention this term [11,43,44,55].

This situation may be explained by the fact that Trent was concerned mainly with the

metallographic aspect of the problem and did not correlate it with the other important

mechanical and physical phenomena occurring at the tool–chip interface during the chip

formation of different work materials. In his book [93], Trent ﬁrst presented the single-

shear plane model of chip formation and then discussed the evidence of seizure which

has little correlation with this model. It appears that the lack of the model of chip

formation under conditions of seizure causes the situation discussed. Therefore, it was

found necessary to clarify the place of seizure in chip formation.

Seizure, having adhesion nature, ceases a normal chip sliding over the tool face because

of the continuous contact in both the hills and valleys of the tool–chip contact surface.

For seizure to occur, a high contact temperature is the prime condition. As explained

above, in the cutting of highly ductile work materials the energy consumption per unit

volume of the removed material is high, and when it is combined with the low thermo-

conductivity of the work material, high temperatures develop at the tool–chip interface

which might lead to seizure.

Figure 1.24 presents a model of chip formation when seizure occurs at the tool–chip

interface [83,87]. In this model, it is assumed that the temperature and contact pressure

at the tool–chip interface have reached a level when seizure occurs so that the force

required for the sliding of the chip over the tool rake face (the tool–chip interface ab)

becomes greater than that required for the plastic deformation of the layer being removed

ahead of the partially formed chip. Surface ac separates the motionless chip and the