Astakhov V. Tribology of Metal Cutting

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Generalized Model of Chip Formation 57

0.05

0.05 0.10 0.40 1.00 2.00 n, m/s

0.10

0.20

0.40

1.00

2.00

4.00

f, KHz

1018 steel

1045 steel

Cr-Ni-Mn Alloy

303 steel

Fig. 1.40. Effect of cutting speed on the frequency of chip formation (after Astakhov [18]).

min

= 0

min

= 0

max

(a)

(b)

Crack

Fig. 1.41. Model of chip formation of the segmental chip suggested by Nakayama: (a) system

consideration and (b) state of stress at point B.

58 Tribology of Metal Cutting

According to this model, the chip formation process is cyclic (periodic). The following

phases can be distinguished in this model:

• Phase 1 (Fig. 1.41(a)) illustrates the state when chip element 1 has almost completed

its formation and the formation of the next chip element 2 has just started (according

to the model, the formation of two-chip fragments takes place in each cycle).

The formation of chip element 2 begins with a further rise of the workpiece free

surface at point A.

• Phase 2 begins when segment AB becomes parallel to the direction of the cutting

force. Then, a shear crack is initiated at point B heading downward along the shear

plane to the cutting edge represented by point O. The state of the stress achieved at

this phase is shown in Fig. 1.41(b). The crack then develops until the crack-arresting

normal stress becomes high enough to cease crack propagation.

• Phase 3 begins when the chip element 2 starts to glide outward like a friction slider

along the cracked surface until the next crack is formed at point C.

• Phase 4 is the same as Phase 1. Chip element 2 has almost ﬁnished its formation

and the formation of the next chip element 3 has just started.

In the author’s opinion, the results obtained in Nakayama’s tests are rather methodological

than application oriented because:

• Chip formation processes at low and high (normal) cutting speeds are entirely

different for the same cutting regime, work material, tool material and geometry.

Zorev [29] conducted the comparison of chip formation at low (Chapter 2 in [29])

and high cutting speeds (Chapter 3 in [29]) and thus proved and concluded the above

theory. He demonstrated that a work material that readily cracks at very low cutting

speed (similar to that used in Nakayama’s tests) would not do so at a higher cutting

speed (for example, Figs. 38 and 139(a) in Zorev’s book [29]).

• The state of stress shown in Fig. 1.41(b) corresponds to pure compression. Because

the work material is assumed to be of highly cold-worked material (brittle), the

crack may not form in the direction of the maximum shear stress because the work

material has already exhausted its ability to deform plastically.

• The deformed chip structure presented by Nakayama does not support the model

discussed because there is no distortion of the grains along the direction of crack

formation. If, as suggested by the model, a crack formed at the workpiece free

surface does not run through the whole chip towards the cutting edge due to high

arresting stresses, only a part of the chip cross section slides as a glide and the other

part should be deformed plastically to a great extent. In the micrograph presented

by Nakayama, however, no traces of plastic deformation are observed.

The most essential ﬁndings made by Nakayama, about crack initiation at the free surface

of the partially formed chip was experimentally conﬁrmed by Kishawy and Elbestawi

[101] in their study of chip morphology when machining a hardened steel (in both orthog-

onal cutting on tubes and oblique cutting) at a cutting speed of ν = 160 m/min with a

metalloceramic tool TNG having a negative rake angle γ =−6

◦

. They also found that

this crack develops without noticeable deformation of the workpiece free surface, as was

Generalized Model of Chip Formation 59

suggested by Nakayama at low cutting speeds. The model of chip formation used by

Kishawy and Elbestawi [101] (Fig. 1.42), was developed by Elbestawi, Srivastawa and

El-Wardany, assuming that the compressive stresses in front of the cutting edge lead to

crack formation at the free surface owing to the brittleness of the work material [102].

According to this model, a crack initiates at the workpiece free surface (point B) without

any noticeable plastic deformation (raise of AB) and then propagates toward the tool.

However, the propagation ceases before this crack reaches the cutting edge (point C),

where severe plastic deformation exists due to the high compressive stress and temper-

ature originated from the cutting edge. The crack DC formed then serves as a sliding

plane for the fractured material enclosed between the tool rake face and this crack. This

part (region ABCD in Fig. 1.42(a)) of the layer being removed from segment 1 of the

chip shown in Fig. 1.42(b). Further tool advance leads to the extrusion of region CDO

into segment 2 of the chip formed (Fig. 1.42(b)).

However, the experimental part of study by Kishawy and Elbestawi [101] did not fully

support the model discussed. Particularly, the microhardness test showed the presence of

signiﬁcant plastic deformation in chip segment 1. At low cutting feeds, this deformation

is concentrated at the lower part of this segment, while the upper part is found to be

more deformed at high feeds. It cannot happen if the fracture and deformation of the

layer being removed take place according to the model shown in Fig. 1.42(a).

Analyzing segmental chip formation, one may conclude that it takes place in machining

under rather speciﬁc conditions when:

• Work material has special properties: hardened, heat treated, high strength – both

ultimate and yield (for example, titanium alloys), low thermal conductivity, etc.

• Uncut chip thickness is rather small and/or variable along the cutting edge. For

example, Vyas and Shaw [45] used round cutting edge in their hard turning tests.

Although the variable chip thickness causes different cutting conditions for different

sections perpendicular to the cutting edge, they constructed their model using the

plane strain assumption.

(a) (b)

−g

Segment 1

Segment 2

Upper part Lower part

Fig. 1.42. (a) Model of chip formation of the segmental chip suggested by Elbestawi, Srivastawa

and El-Wardany, and (b) chip fragment produced according to this model.

60 Tribology of Metal Cutting

• Cutting speed is very high for a given work material so the localized deformation

in chip formation is characterized by three sequential events [95,103]: elastic defor-

mation, plastic deformation (hardening and softening), and ﬁnally local failure and

shearing.

• Machining system is not dynamically stable [104].

A detailed analysis of the multiple publications on the subject allows the author to con-

clude that the segmental chips are often formed when machining difﬁcult-to-machine

materials at elevated cutting speeds, as shown in Fig. 1.28(d) and in Fig. 1.43. Low

thermal conductivity, small difference between the ultimate and yield strength, high

hardness enhance the formation of the elemental chip. However, the mechanism of its

formation is not different from that of the formation of the saw-toothed chip (Fig. 1.32).

Multiple studies conducted by Jawahir (for example, [13,14,82]) showed that the ele-

mental chip often formed as a part of the “normal” saw-toothed chip even for “usual”

work materials like AISI steel 1045 machined at cutting speed ν = 150 m/ min, cutting

feed f = 0.5mm/rev (Fig. 11 in [14]).

The segmental chip should not be mixed with unstable chip having similar appearance.

In the author’s opinion, the variation of the cutting force being the major and most

powerful source, causes and thus creates vibrations in the machining system, not vice

versa as concluded by Komanduri [104].

1.10 Applicability and Signiﬁcance of Chip Formation Models

The rapid progress in the development of cutting tool materials including coatings and

in the design, manufacturing and application of indexable cutting inserts having various

shapes of the rake surface brought signiﬁcant changes in the cutting processes over the

last 10 years. Moreover, wide use of specialized Computer Numerical Control (CNC) and

multi-axis high-precision machines having rigid structures changed the methodology of

tool design and application. As a result, one may wonder if the “classical” representation

of cutting process by models of chip formation suitable for orthogonal cutting is still of

any assistance to tool and process designers. In other words, a simple question is to be

answered: what useful information that can be obtained knowing and understanding the

different chip formation models?

To be able to answer this challenging question, one should know how to correlate a

real cutting process to that considered by orthogonal cutting models. To do that, cer-

tain strict deﬁnitions of the basic terms have to be clariﬁed. These are discussed in

Appendix A. Once these are clearly established, useful information about the contact

stresses, temperatures, energy partition in the cutting system and many other important

aspects of the cutting process can be obtained from such modeling. This information is

to be directly used in the cutting wedge design, engineering, and choice of tool materials

and coatings, selection of cutting ﬂuids, and methods of its proper application and the

determination of the stability of the cutting process. Moreover, this information is of

prime importance when one tries to correlate the input parameters of the cutting process

with its outputs as needed, quality of the machined parts including the machining residual

stresses, productivity, etc.

Generalized Model of Chip Formation 61

(a)

(b)

(c)

Zone A

Zone B

Fig. 1.43. Non-uniform deformation of chip fragments in machining work material 4

(Fig. 2.27(d)): (a) cutting speed ν = 150 m/min, heavily deformed part (Zone A) occupies approx-

imately 62% of the chip segment area. Its hardness is 756 HV, the hardness of the chip in Zone B

is 632 HV; (b) cutting speed ν = 300 m/min, heavily deformed part (Zone A) occupies approxi-

mately 40% of the chip segment area. Its hardness is 742 HV, the hardness of the chip in Zone B

is 640 HV; (c) cutting speed ν = 1500 m/min, heavily deformed part (Zone A) occupies approxi-

mately 33% of the chip segment area. Its hardness is 720 HV, the hardness of the chip in Zone B

is 618 HV (Courtesy of Prof. S. Ekinovi

c).

62 Tribology of Metal Cutting

Another important aspect is the reliable chip control, which is of great importance in auto-

mated machining. Knowing a particular chip type for a given set of machining conditions,

one should be able to select the optimum type of chipbreaking techniques to control the

shape and length of chip pieces suitable for transportation from the machining zone.

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