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Recent Advances in Micro/Nano-cutting: Effect of Tool Edge and Material
Properties
Article in Nanomanufacturing and Metrology · February 2018
DOI: 10.1007/s41871-018-0005-z
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https://doi.org/10.1007/s41871-018-0005-z
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REVIEW PAPERS
Recent Advances in Micro/Nano-cutting: Effect of Tool Edge
and Material Properties
Fengzhou Fang1,3 • Feifei Xu1,2
Received: 7 October 2017 / Revised: 9 January 2018 / Accepted: 13 January 2018
International Society for Nanomanufacturing and Tianjin University and Springer Nature 2018
Abstract
Micro- and nano-machining technology has been applied in industry to generate high-precision parts with micro/nanometric accuracy or feature size in the recent decades. Cutting is one of the most powerful manufacturing processes, and the
material removal mechanism is urgently demanded by the industry to understand and improve the micro/nano-machining
process efficiently at a low cost. This paper presents the recent advances in cutting mechanism and its applicability for
predicting the surface generation and chip formation, especially when material is removed in micro- and nanoscale. In
addition to the industry-concerned performance parameters, fundamental physical parameters such as stresses, strains,
temperatures, phase transformation, minimum uncut chip thickness and size effects are discussed in this paper for the indepth understanding of the micro/nano-cutting process.
Keywords Micro/nano-cutting Material removal mechanism Tool edge Size effect Surface generation
1 Introduction
1.1 Definition of Micro/Nano-cutting
In micro-machining, micro indicates the range from 1 to
999 lm [1]. It means the feature size or machining accuracy of the products is ‘very small’ and not easy to fabricate. In definition of micro-cutting, it has to be
distinguished from the traditional macro-cutting where the
materials are seen as continuous and the individual grains
in materials are averaged and ignored. In micro-cutting, the
uncut chip thickness (UCT) is in microscale and always
& Fengzhou Fang
fzfang@gmail.com
Feifei Xu
yuanfei1116@163.com
1
State Key Laboratory of Precision Measuring Technology &
Instruments, Centre of MicroNano Manufacturing
Technology, Tianjin University, Tianjin 300072, China
2
Institute of Mechanical Manufacturing Technology, China
Academy of Engineering Physics,
Mianyang 621900, Sichuan, China
3
School of Mechanical and Materials Engineering, MNMTDublin, University College Dublin, Dublin, Ireland
smaller than the average size of the material grains. The
micro-cutting process has to take grain size and its distribution in materials into consideration. Simoneau et al. [2]
defined the micro-cutting as the point where the UCT is
less than the average grain size of the smallest grain type.
Similar to the grain size, the tool edge is usually ignored in
macro-cutting process. But it should be considered in
micro-cutting process. Therefore, the micro-cutting could
be defined in two aspects. One is the definition based on the
accuracy or feature size to be attained, such as cutting parts
with micro-metric accuracy or making products with
micro-metric feature size. Another is based on the differences from the macro-cutting; for example the UCT is in
microscale and less than the average grain size of the
smallest grain type, or the effect of the tool edge which is
in microscale could not be ignored.
Nano-cutting could be defined in the same way as the
micro-cutting. Therefore, the nano-cutting is generating
parts with nano-metric accuracy or making products with
nano-metric feature size. Another definition is that the UCT
of the nano-cutting process is in nanoscale and less than the
average grain size of the smallest grain type. The effect of
the tool edge which is in nanoscale too could not be
ignored.
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Nanomanufacturing and Metrology
1.2 Significance of Micro/Nano-cutting
With the development of manufacturing technology in the
recent decades, the cutting process including turning, milling still takes a large portion of machining processes. Due
to the continuous progress in machine tools and cutting
tools, the machining accuracy and feature size have
approached micro- and nano-metric scale. In this scale,
problems same as those in conventional cutting process,
like the stresses, strains, strain rates, temperatures, chip
formations, should be re-considered to optimize the cutting
parameters (feed, cutting speed, depth of cut, etc.), cutting
tool geometry parameters (tool materials, rake angle,
clearance angle, nose radius, edge shape, etc.) and coolant
or lubricant type (cryogenic cooling, high-pressure coolant
jet along the flank face or the rake face, etc.). Therefore,
the cutting mechanism in micro- and nano-metric scale
should be deeply understood and models for predicting the
performance and surface generation in micro/nano-cutting
processing should be established.
However, in micro/nano-cutting, the tool edge shape,
the size effect of materials which is almost ignored in
conventional cutting process plays an important role in
cutting mechanism. In this paper, recent advances about the
influence of tool edge shape and material properties on
micro/nano-cutting process are presented.
Mallock identified the shearing mechanism [10], which
might be the first work in which a shear theory was suggested. In the 1930s, Piispanen, one of the great pioneers
exploring the physics of cutting, introduced the so-called
card model [11]. His work stated that the material removal
process of metal is similar to the cutting of a deck of
stacked cards and the cards are inclined at an angle that
matches the shear plane angle. However, it was the work of
Ernst et al. [12] and Merchant [13, 14] in the 1940s that
made the shear plane model more recognized. Their work
has been seen as a milestone of the research of cutting
mechanism and is used as a basis for analyzing various
machining processes.
The well-known Merchant’s cutting model is shown in
Fig. 1. The relationship between the cutting force and other
parameters can be derived based on the model. The relationship of the shear angle u with the tool rake angle a and
the friction angle b deduced by the principle of minimum
required cutting energy is written as
a b
u ¼ 45 þ 2 2
The models mentioned above are always analyzed based on
some assumptions, which is systematically presented by
Shaw [11]:
(1)
2 Investigation Approaches
(2)
The ultra-precision machine tool which is a powerful tool
in realizing the machining of freeform surfaces [3] and
micro/nano-structural elements [4] is also an effective tool
in investigating the micro/nano-cutting process by applying
particular methods, such as the tapper cutting [5], orthogonal cutting [6] and so on. Besides that, a self-developed
cutting device which could be integrated to scanning
electron microscope (SEM) could be used to realize the
online observation of cutting process [7]. The AFM is an
instrument which could be used to imitate the cutting
process and identify the machinability of the workpiece
materials before cutting process [8, 9]. To fundamentally
understand the cutting process, analytical method and
numerical method are often employed and discussed in this
section.
(3)
(4)
(5)
(6)
The tool is perfectly sharp and straight, cuts
perpendicular to the direction of motion and has a
width greater than that of the workpiece;
The shear surface is a plane extending upward from
the cutting edge;
The cutting edge generates a plane surface, constant
depth of cut;
The workpiece moves relative to the tool with
uniform velocity;
The chip does not flow to either side;
A continuous chip is produced without built-up edge;
2.1 Analytical Method
Cutting mechanism has attracted much attention of many
researchers over decades. Various models have been proposed to improve the description of the cutting mechanism.
In principle, material is removed in shearing. In 1881,
Fig. 1 Schematic illustration of conventional cutting model [12]
123
ð1Þ
Nanomanufacturing and Metrology
(7)
There is no contact between the workpiece and the
clearance surface of the tool.
Slip-line field method is an effective analytical method
to study the cutting process and was used by Lee and
Shaffer [15] in 1951 to develop a cutting model. After that,
many slip-line models have been proposed. In 1977, the
parallel-sided shear zone theory proposed by Oxley et al.
[16] is an important progress in modeling cutting process,
as shown in Fig. 2. Oxley’s study considered the dependence of material flow stress upon strain, strain rate and
temperature and obtained the shear angle and other quantities of interest, which is the unique feature of Oxley’s
machining theory. In 2001, Fang et al. [17] developed a
universal slip-line model and it is further extended by
taking into consideration the effects of strain rates, temperatures [18] and the tool edge radius [19, 20].
2.2 Numerical Method
Compared to the analytic method, numerical method could
give a result more straight forward. Finite element method
(FEM) is a powerful numerical method which has a great
capacity in helping people to understand the fundamental
cutting mechanism [21]. The reliability of the FEM simulation depends on the mechanical and thermo-physical
parameters input to the model. Therefore, the characteristic
parameters of the materials at the strain of 100–700%,
strain rates up to 106 S1 , temperature up to 1400 C,
pressures near 2–3 GPa need to be obtained based on different experiments [21]. Generally, the material properties
used in cutting model are homogeneous and isotropic.
However, in micro/nano-cutting process, the UCT is
smaller than the grain size or the material which is actually
multiphase. The anisotropy or the non-homogeneity of the
material properties should be taken into consideration.
Abouridouane et al. [22, 23] described the thermo-mechanical behavior of the ferrite and pearlite phase of the
carbon steel by different constitutive model, and the results
are verified experimentally regarding chip formation and
Fig. 2 Model of chip formation used in Oxley’s analysis for
conventional machining [16]
processing forces. For anisotropic materials, such as the
single-crystal material, a crystal plasticity theory was
developed to help investigating the anisotropic plastic
deformation considering the crystal orientation and activated slip systems [24]. The crystal plasticity theory has
been implemented in FEM to study the micro-compression
[25] and micro-cutting [26, 27] behaviors of single-crystal
materials. In FEM simulations, the meshing strategy is an
important factor in influencing the simulation results.
Niesłony et al. [28] investigated the meshing strategies of
the cutting tools considering the tool edge radius and found
that the accurate representation of the tool micro-geometry
would influence the simulation results. Smoothed particle
hydrodynamic (SPH) simulation which is a mesh-free
technique has been coupled with the FEM to investigate the
micro-machining of FCC materials [29].
Molecular dynamics (MD) simulation is another useful
approach in investigating the material removal mechanism
in nanoscale. MD simulation was first applied by Lawrence
Livermore National Laboratory (LLNL) and Precision
Engineering Department at Osaka University to investigate
the cutting process [11]. In 1990s, Shimada et al. [30, 31]
conducted a series of investigations on the mechanism of
nano-cutting of single crystals by MD simulation. The
Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) [32] is a public-domain computer code
used to simulate the cutting process. And the simulation
results could be visualized and analyzed by Visual
Molecular Dynamics (VMD) [33] and Open Visualization
Tool (OVITO) [34]. The microstructural or dislocation
evolution of the workpiece could be analyzed based on
common neighbor analysis (CNA) [35], dislocation
extraction algorithm (DXA) [36] and the displacement
vectors module in OVITO.
The accuracy of the potential function used in MD
simulation determines the reliability of the simulation
results [37]. Lennard–Jones (LJ), Morse and embeddedatom method (EAM) potentials were employed to investigate the effect of interaction potential on the MD simulation of nano-cutting by Oluwajobi et al. [38]. The results
showed that the EAM potential is most suitable in the three
potentials, because it describes the metallic bond better.
Morse potential is usually used to depict the interaction
between the atoms of cutting tool and workpiece materials.
Goel et al. [37] thought it is not robust enough to describe
covalent bond interactions between silicon and diamond.
Therefore, the analytical bond order potential (ABOP)
proposed by Erhart and Albe [39] is used to describe the
interaction within and between the diamond tool and silicon. Tersoff potential [40, 41] is usually applied in investigating the brittle materials, such as the silicon and
germanium. However, it is failed to simulate the brittle
fracture in nano-cutting [42]. It is because the Tersoff
123
Nanomanufacturing and Metrology
potential is a short-ranged potential which could not
describe the transition events, such as the bond dissociation, accurately [43]. Stillinger–Weber potential is applied
by Zhang et al. [44] to investigate the phase transformations and dislocation activated in single-crystal silicon. In
nano-cutting of silicon carbide (SiC), the Vashishta
potential [45] which could reproduce the brittle fracture
and the fracture toughness accurately [46], is applied by
Xiao et al. [47] on a self-developed GPU-accelerated MD
codes to simulate the fracture in cutting process.
However, the MD simulation is usually used in nanoscale system, due to the limitation of the computational
power. The FEM model could be used in a larger scale, but
microstructure evolution in plastic deformation could not
be displayed. Multiscale simulation has been developed to
bridge the gap between the MD and FEM simulation. It
was applied by Son [48] and Pen [49] et al. to simulate the
nano-cutting of single-crystal copper. Based on the development of the numerical method, the micro/nano-cutting
mechanism would be fully revealed in the future.
3 Advances in Investigating Cutting
Mechanism
3.1 Influence of Tool Edge
The cutting tool edge has a significant influence on the
cutting force, stress, temperature and other fundamental
physical parameters. Especially when it is comparable to
the UCT, the effect of the tool edge is non-ignorable and
making a larger part of the workpiece materials under the
plowing or extrusion of the tool whose effective rake angle
is mainly negative. It changes the material flow, the chip
formation, and the stagnation point or the dead metal zone
in front of the tool edge. Therefore, the generated surface
quality would be influenced by the cutting tool edge due to
the side flow, recovery and so on. In this section, the
influences of the tool edge on the cutting mechanism
mentioned above, including the characterization of the
edge, are displayed and discussed.
The effect of tool edge radius on cutting process was early
mentioned by Chien [56], Albrecht [57] and Masuko [58].
After that, many researches have been conducted to
investigate the effect of the tool edge on the cutting force,
temperature, chip formation, etc. However, the characterization of the tool edge is almost depending on individual
researchers, measurement uncertainty and fitting algorithm.
These factors would cause discrepancies in describing the
tool edge with tool edge radius. Therefore, a common
understanding for the influence of tool edge on cutting
process is inhibited by the poor detected consistency.
Besides that, there is no international standard to characterize the micro-geometry of tool edges, although the
macro-geometry of the cutting tool is internationally
standardized [59]. It becomes indispensable to draft a
standard and characterize the shape of tool edge based on
it.
Wyen and Wegener [60] have proposed a new algorithm
to increase the repeatability in characterizing the cutting
edge radius by making the choice of fitting area user
independent. As shown in Fig. 3, the first step is to generate straight lines for the rake and flank face by least
squares fitting of the initial given data. Then, the fitted
straight lines cross at the virtual tool tip pc and the wedge
angle b is obtained. The intersection point pint of the wedge
angle bisector and tool edge profile is the point where a
circle needs to intersect and is tangent with the fitted
straight lines. The tangent points determine the upper fitting limit for refitting the rake and flank face lines. The
fitting of the lines is repeated until the distance between the
tangent point and the foregoing tangent point approximates
zero. Therefore, the two tangent points determine the limit
of fitting area for fitting the tool edge with a cycle. The tool
edge radius rb is calculated by a least squares fitting using
all points within the micro-geometry limit.
For the cutting edge which is not a symmetrical circle,
only tool edge radius cannot describe the shape of cutting
edge precisely. Therefore, Wyen et al. [59] develop a
3.1.1 Characterization of Tool Edge
Tool edge which was usually neglected in conventional
macro machining process, such as the shear plane model
proposed by Merchant [50], has become an important
parameter in influencing the cutting process [51–54]. The
shape of the cutting edge is defined as the transition
between the rake face and the flank face of a cutting wedge
[55]. Generally, the shape of the tool edge is simply considered as rounded and characterized by an edge radius rb .
Fig. 3 Proposed method for characterizing rounded tool edge [59, 60]
123
Nanomanufacturing and Metrology
method in characterizing the asymmetry of cutting edges.
As shown in Fig. 4, a line is drawn through the intersection
point pint perpendicular to the wedge angle bisector and
intersects with the fitted rake and flank face lines. The
distances from the intersection points to the profile of
cutting edge in the direction parallel to the wedge angle
bisector are Dc and Da . The ratio of them indicates the
asymmetry S(S ¼ Dc Da ).
Denkena et al. [61] proposed the form-factor method
(also referred to as K-factor method) to characterize the
shape of tool edge, especially when the cutting edge is
asymmetrical, as shown in Fig. 5. Four parameters Sa, Sc,
Dr, and u were introduced. and the average cutting edge
rounding S and the form-factor K (Kappa) were deduced to,
respectively, specify the dimension and shape of the
rounding at the cutting edge. The ratio K ¼ 1 indicates a
symmetrically rounded cutting edge. When the ratio is
below or above 1, the shape of the cutting edges is in
waterfall or trumpet style, respectively. The distance Dr
indicates the flatness of tool edge. The smaller the Dr value
is, the sharper the cutting edge is. Yussefian et al. [62]
proposed a method to identify the cutting edge by the
adaptive placement of the knots that minimizes the residual
error from fitting the B-spline to the tool profile data.
Subsequent to edge identification, the edge is modeled by
parametric quadratics. And four parameters are derived to
characterize the cutting edge which is symmetrical or
asymmetrical.
Fig. 4 Asymmetry determination of a rounded cutting edge [59]
However, too many parameters may inhibit their applications in practice. In 2012, Denkena et al. [63] proposed a
new parameter called as normalized plowing zone
A0a ¼ Aa =la . Aa is the area between the cutting edge profile
and the workpiece bordered with stagnation point and the
contact point in flank face side. la is the corresponding
contact length of the cutting edge profile between these two
points. The influence of the parameter on the tool wear,
burr formation and residual stress has been investigated. In
2017, Xu et al. [64] considered the tool edge radius rb
could be fitted only using the cutting edge profile between
stagnation point and the contact point mentioned above.
Because of the process force, the surface integrity is mainly
influenced by the tool edge profile under the stagnation
point [63]. The influence of the newly proposed radius rb
on the stagnation region, chip formation, subsurface damage, and cutting forces has been investigated and found that
it could be used to characterize the cutting performance of
a cutting tool, and reduce discrepancies in describing the
tool edge, especially when it is asymmetrical [64]. Comparing the method to that proposed by Denkena et al. [63],
the normalized plowing zone is in linear relationship with
the new proposed tool edge radius, if taking the profile in
the flank face side as a circle.
In nano-cutting process, diamond cutting tools are usually employed to generate parts with nano-metric precision
and finish. The tool edge radius can be down to 10–100 nm
which is smaller than those of the tungsten carbide or
PCBN inserts, due to the unique material properties of
single-crystal diamond and reliable tool edge preparation
processes [65, 66]. Therefore, how to accurately measure
the shape of diamond tool edge and to analyze the effect of
the tool edge shape on micro/nano-cutting process become
a significant issue. Optical microscope and scanning electron microscope (SEM) can be used to monitor the diamond tool edge [67, 68]. But they both failed in measuring
the shape of the diamond cutting tool edge precisely. The
SEM image is basically a 2D projection of a 3D object.
Therefore, additional efforts should be done, such as the
combination of electron-beam-induced deposition (EBID)
with SEM by Shi et al. [69]. With this method, quantitative
characterization of diamond tool edge radius and wear land
length for new and worn diamond tools can be derived
from analysis of the EBID-SEM images. But the detailed
information of the diamond tool edge shape cannot be
measured with this method. Atomic force microscope
(AFM) is an effective method in measuring the shape of
diamond tool edge for its nano-metric vertical and lateral
resolution. The copied profile of a diamond cutting tool
edge which is formed by indenting the tool cutting edge
into the surface of copper has been measured by AFM [70].
And the elastic spring-back effect has been compensated
Fig. 5 Form-factor method for cutting edge characterization [55, 61]
123
Nanomanufacturing and Metrology
by Li et al. [71]. When the diamond tool edge is directly
measured by AFM, it is difficult to align AFM tip with tool
edge due to the low depth-of-field and poor resolution of
the optical microscope in conventional AFM, especially
when the diamond tool nose radius is in micro-metric scale.
Gao et al. [72, 73] combined an AFM with an optical
sensor for alignment of the AFM probe tip with the diamond tool edge in submicrometer range more easily. A 3D
edge profile measured by the instrument is shown in
Fig. 6a, and from the sectional profiles of the tool edges,
the tool edge could be evaluated, as shown in Fig. 6b.
Actually, the evaluation of the diamond tool edge radius
has the same problems mentioned by Bassett et al. [74]
which is the measurement inaccuracy caused by different
operators and algorithms. In 2010, Shimizu et al. detailedly
introduced the method of characterizing the diamond tool
edge with AFM, taking into consideration the influence of
the shape of AFM probe. And the methods how to handle
the data of the cutting edge profile are proposed. Diamond
tools edge with nose radius of 0.2 mm and 1.5 lm were
measured with good repeatability [75]. The characterization method proposed in [64] may be a simple and effective
method to describe the tool edge with feature size of several tens of nanometers, but more investigations based on
experimental and theoretical analyses should be done to
verify the hypothesis.
An international measurement standard of diamond tool
needs to be established, and a relationship of the diamond
tool edge shape with the cutting quality should be investigated and understood by the researchers and engineers to
choose and fabricate a perfect tool for different applications. Therefore, the influences of the tool edge on the
cutting mechanism are discussed in the following sections.
3.1.2 Influence on Cutting Force
More and more difficult-to-machine materials which have
unique material properties are emerging and widely used in
the current industry. The shape of the tool edge becomes
one of the major factors in influencing the cutting process
Fig. 6 a 3D edge profile
measurement result of diamond
cutting tool, b sectional profiles
of the tool edges [72]
123
[52, 54, 76, 77]. In nano-cutting process, it is important to
study machining this type of materials, such as hard and
brittle materials by using a diamond tool with special
chamfer in the tool edge [78]. A large number of researches
have to be considered to investigate the cutting force, stress
and temperature distribution with the change of cutting tool
edge, in order to optimize the shape of cutting edge for
micro/nano-cutting of different materials.
According to the experiment results, the cutting force as
well as the feed force generally increases with the increment of cutting edge radius [79, 80]. The feed forces are
more sensitive to a change in cutting edge radius than
cutting forces [60]. Same results were obtained by the finite
element simulations, not only in the micro-cutting process
but also in the nano-cutting process [81, 82]. The plowing
force which directly acts on the cutting edge is also
determined and separated from the total force in order to
better understand the cutting process, as shown in Fig. 7
[57, 60]. Same as the cutting force, the plowing force in the
cutting direction is less sensitive to the change of cutting
edge radius than the force in the feed direction. Both of
them increase linearly with the increment of the edge
radius. When the cutting tool edge is characterized by the
form-factor method mentioned in the last section, the
process forces are mostly affected by the edge segment on
the flank face, Sa , whereas the impact of the segment on the
rake face, Sc , is negligible [55].
In nano-cutting process, the edge radius of the tool
causes a nonlinear variation in the cutting forces when the
ratio of UCT to the tool edge radius t ½rb \1 (½rb indicates the tool edge radius remains constant, and in this
reference ½rb ¼10–60 nm) [83]. When the ratio
t ½rb 1, the cutting force exhibits an approximately
linear relationship with the UCT. This phenomenon is the
size effect caused by the tool edge radius in cutting process
and is described as the specific cutting energy increases
rapidly and nonlinearly as the ratio t rb decreases. It is also
found in Ref. [70, 84–87]. The specific cutting energy is the
ratio of the cutting force to the product of UCT and cut
Nanomanufacturing and Metrology
in following sections. Lucca et al. [90] performed experiments to study the effect of tool edge geometry (rake angle,
tool edge radius) on the cutting forces and specific energy
with UCT changing from 20 to 10 nm. They found that at
small UCT, the effective rake angle rather than the nominal
rake angle determines the direction of the resultant force.
3.1.3 Influence on Stress
Fig. 7 Separation of active force Fa into plowing force FPl and chip
forming force FCh and into components in feed and cutting direction
[60]
width in orthogonal cutting [88]. Similar results were
obtained by Ranganath et al. [89] while cutting gray cast
iron in micro-metric scale, with the tool edge radius change
from 15 to 72 lm in orthogonal cutting experiments. As
shown in Fig. 8, the cutting force and feed force coefficients which are similar to the specific cutting energy
increase nonlinearly with the decrease in the ratio t=rb
(begins at the ratio t rb 1 for cutting force coefficient
and 2 for feed force coefficient). Further discussion of the
size effect caused by the materials’ size effect is displayed
Fig. 8 a Cutting force coefficient versus t=rb ratio for different edge
radii. b Feed force coefficient versus t=rb ratio for different edge radii
[89]
The force action on the cutting tool relates the stress distribution at the tool edge which would affect the performance of the cutting tools [91]. The unit forces, such as
unit tangential force and unit normal force acting on the
contour of the cutting edge, are investigated with tool edge
radius range from 4 to 40 lm [92]. The minimum UCT and
the unstable region are identified by the distribution of the
unit forces in the tool edge. Özel [52] investigates the stress
distribution in four different tool edge shape, including
uniform chamfer, uniform waterfall hone, uniform hone
and variable hone inserts. And results show that the most
favorable stress distribution is obtained with variable hone
micro-geometry insert.
Besides that, the tool edge also influence the stress
distribution in the workpiece materials under/ahead of tool
edges. When the tool edge radius is negligible, the primary
shear zone could be simply seen as a shear plane, which
has been assumed by Ernst et al. [12] and Merchant
[13, 14] in the 1940s to build the shearing cutting model.
But when the ratio of UCT to tool edge radius t rb
decreases to a certain value, the shear zone and the von
Mises stress distribution become more extensive and
extend to the area under the cutting tool edge [84, 93]. As
shown in Fig. 9, the plastic deformation behavior for
t=rb ¼ 1 and 3 is similar to that of conventional shearing
model. When the ratio t=rb reduced below 1, the materials
undergo severe plastic deformation and the size and
thickness of it increase due to the merger of the primary
and secondary deformation zone [93]. Similar results were
obtained by Yan et al. while cutting silicon in ductile-zone
with the tool edge radius change from 50 to 500 nm using
FEM method [82]. With the increase in cutting tool edge,
the primary shear region becomes further deeper and
broader forming a large triangular high-stress region
beneath/ahead of the tool. With the increase in edge radius,
the maximum stress decreases slightly, but is still maintained at a high level.
In 1998, Fang et al. [94] propose that the hydrostatic
pressure under the tool edge is beneficial to cutting brittle
materials in ductile region. It is proved that the area of the
hydrostatic pressure zone extends with the increase in
cutting tool edge radius by finite element modeling of the
silicon [82]. Similar results were obtained by molecular
123
Nanomanufacturing and Metrology
Fig. 9 von Mises effective
stress distributions at the
different ratios t=rb [93]. a
t=rb ¼ 1; b t=rb ¼ 3; c
t=rb ¼ 0:6; and d t=rb ¼ 0:2625
dynamic simulation of copper with the ratio t=rb change
from ! to 0.23, as shown in Fig. 10. The hydrostatic
pressure tends to cause an increase in critical UCT of brittle
materials which is identified by experiments [95]. It seems
that a larger tool edge radius causes a bigger critical UCT
under which the brittle material is removed in ductile
mode. But there is an upper bound of tool edge radius when
cutting brittle materials like silicon whose upper bound
value is between 700 and 800 nm [96]. The upper bound of
tool edge radius is explained by the increase in tensile
stress which borders upon the interface of plastic and
elastic deformation zones, when the tool cutting edge
radius increases. Based on the tensile stress distribution,
the critical conditions for the crack initiation have been
determined by Li et al. [97]. The stress distribution in the
material is also influenced by itself. The magnitude of
concentrated stresses under the tool edge is much higher
for silicon compared with copper [98].
The distribution of stress rxx which is in the cutting
plane at the cutting direction is investigated by Xiao et al.
[47] using molecular dynamic simulation, as shown in
Fig. 10 Hydrostatic stress
distributions at a t=rb ¼ 1; b
t=rb ¼ 1; c t=rb ¼ 0:46; and d
t=rb ¼ 0:23 [99]
123
Fig. 11. The results show that compressive stress exists in a
region near the cutting edge and with the tensile tress
around the compressive zone. The maximum tensile stress
tends to increase with the increment of UCT which would
lead to fractures under the larger UCT. The formation and
propagation of the cracks would be discussed detailedly in
the section of surface generation.
3.1.4 Influence on Cutting Temperature
Cutting temperature has been a research topic for a long
period of time [100]. The temperature measurement
methods in material removal processes have been reviewed
by Davies et al. [101]. Generally, the cutting temperature is
the energy dissipated by the materials deformation and
friction at the interface between cutting tool and workpiece
[102]. The shape of the tool edge has a significant influence
on the cutting force and stress distribution in the tool and
workpiece, especially in the micro/nano-cutting process
when the ratio t=rb reduced to a certain value. Meanwhile,
the tool edge shape affects the temperature distribution in
Nanomanufacturing and Metrology
Fig. 11 Distribution of stress
rxx in the cutting zone [47].
a 40 nm, b 35 nm, c 30 nm,
d 25 nm, e 20 nm, f 10 nm
the tool/workpiece contact zone. In the traditional orthogonal cutting process where the tool edge radius is ignored,
the heat is generated in the primary, secondary and tertiary
deformation zone [103], due to the plastic work done at the
shear plane and the friction work done on the tool/chip and
tool/workpiece interface zone. The heat generated in the
secondary zone is the main factor to rise the temperature of
cutting tool. The primary zone also influences the temperature distribution in the cutting tool by transferring the
heat to the chip and then through the interface zone to the
tool rake face. Therefore, the temperature distribution on
the tool rake face is influenced by the generated heat in the
primary and secondary zones [104].
Akbar et al. [105] investigated the temperature distribution in the cutting tool influenced by the heat fraction
transferred into the tool. The results show that lower part of
the heat transferred to the tool decreasing the temperature
in it hence prolongs the tool life. Therefore, conditions
should be chosen to remove the larger part of heat by the
chip, such as using a coated tool [106] or a high cutting
speed. The temperature distribution on the rake face of
sharp cutting tool (tool edge radius 2 lm) has been
detected by IR-CCD camera, as shown in Fig. 12a, when
cutting the steel SS2541 with UCT of 0.1 mm. The measured maximum temperature point is on the rake face with
distance 0.15 mm from the cutting edge [80]. It is compared with a round edge tool (tool edge radius 25 lm) in
the cutting process, as shown in Fig. 12b, and found only a
small increase in maximum temperature (* 10–15 C) on
the rake face. The increase in the temperature could be
accounted for the increased the secondary shear zone
thickness in the chip as well as the tool–chip contact length
due to the tool edge radius. Thus, it could be deduced that
less effect acts on the temperature distributions of tool rake
faces, when the ratio ½t=rb (½t indicates the UCT remains
constant) decreases from 50 to 4.
Actually, it is still difficult for the IR-CCD camera to
detect the temperature distribution in the tool edge radius
ranging from several tens of nanometers to several tens of
micrometer. Therefore, the simulation methods are used to
predict the temperature in the tool edge. Karpat et al. [107]
analyze the temperature distribution in different tool edges
using the finite-element simulations. Results show that the
rake face temperature distributions are more evenly in
waterfall hone tools than honed tools. And the lowest tool
tip temperature is obtained in waterfall hone tool with Sa :
Sc ¼ 30 : 60 lm for 175 m/min cutting speed and 150 lm
UCT, and Sa : Sc ¼ 20 : 40 lm for 125 m/min cutting
speed and 100 lm UCT [107]. Özel further considered the
smaller UCT in the tool tip and designs a tool with variable
hone edge to reduce the ratio t=rb in the tool tip [52]. The
smallest hot zone is found to be on the variable honed
insert which also has a smallest maximum temperature of
about 626 C.
Denkena et al. develop a setup for temperature measurement in cutting tool with a graded-index-multimode
fiber optic to collect and guide the electromagnetic IR
radiation to the IR detectors of the pyrometer [53]. From
the temperature gradient determined in the wedge, the
segment in the rake face Sc has no significant influence on
the isotherms for the tool with the same Sa ¼ 100 lm. And
waterfall hones with bigger Sa lead to higher thermal load
of the wedge [74]. With increase in Sa , the maximum
123
Nanomanufacturing and Metrology
Fig. 12 Effect of tool edge
micro-geometry on tool
isotherms a sharp tool, b round
tool [80]
temperature shifts from the rake face to the flank face [55].
Similar results were obtained by Yan et al. in nano-cutting
of silicon with the tool edge radius increase from 50 to
1000 nm [82]. The ratio ½t=rb ([t] stays constant at
100 nm) decreased from 2 to 0.2, the high-temperature
region in front of the too rake face shrinks while that under
the tool flank face grows gradually. At the ratio
½t=rb ¼ 0:5, the temperature rise at the flank face side has
become higher than that at the rake face side. When the
ratio ½t=rb ¼ 0:2, temperature rise only takes place at the
flank face side. The temperature increase at flank face
causes a severe wear between the tool and the elastic
recovered workpiece materials and finally affects the generated surface quality [82]. It is identical to the molecular
dynamic simulation of the diamond cutting of silicon; the
number of atoms at the tool flank face showing an increase
in temperature is larger than that at the rake face, especially
at the place where the silicon atoms try to recover elastically [37]. Cai et al. [108] investigate the temperature in
three different zones and find that the temperature near the
arc part of the cutting tool edge is larger than that under the
flank face of the tool and the zone far from the machined
surface. The temperature in the tool edge or the flank face
tends to accelerate the formation rate of silicon carbide and
hence increase the wear of diamond tools. The wear
mechanism has been identified by the experiments [109].
The distribution of temperature on the sharp diamond tool
has been investigated by Yan et al. [110] and found a hightemperature region forms at the center of the chip. This
phenomenon would further soften the workpiece material
causing the adhesion on the rake face of the cutting tool,
which could be optimized by two-step cutting process.
The diamond turning of micro/nano-structures with
multitip diamond tool shows a powerful capacity for
improving the production efficiency, suppressing the tool
wear and increasing the machining area with one diamond
tool. The temperature in the tool tips has been investigated
by Tong et al. [111], as shown in Fig. 13. The results show
that the inner sides of the tool tips are higher than other
123
sides, which would cause a severer wear in the inner side of
the multitip diamond tool.
3.1.5 Influence on Chip Formation and Minimum UCT
Generally, the material is removed by shearing which is
first identified by Mallock [10] and the model is built by
Merchant et al. [12–14]. In the shearing model, the tool
edge is simplified as sharp. With the development of
manufacturing technology, the machining accuracy and
feature size have approached micro/nano-metric scale. In
this scale, the UCT becomes comparable to the cutting tool
edge radius. Therefore, the chip formation and the minimum UCT would be influenced by the tool edge.
Similar to the stress distribution in the cutting zone with
a round cutting edge, the shear plane would extend to a
shearing zone in front of the cutting edge [11, 112]. Woon
et al. [112] systematically investigate the effect of tool
edge radius on the chip formation behavior of micro-machining. And the results show that the primary deformation
zone expands with the shrinkage of secondary deformation
zone following the reduction in total tool–chip contact
length, when the ratio ½t=rb decreases from 2 to 1. Further
reducing the ratio ½t=rb to 0.4, the secondary deformation
zone akin to merge with the larger and thicker primary
deformation zone. When the ratio ½t=rb is 0.2, the secondary deformation zone disappeared or absolutely merged
with the primary deformation zone [112].
In 1989, Moriwaki and Okuda [66] performed diamond
cutting experiments on copper with UCT changing from 3
to 2.5 nm and found that the material removal mechanism
experiences a transition from cutting to plowing. In nanocutting process, Fang et al. [5, 94, 113] investigated the
influence of the tool edge radius on nano-cutting mechanism by both molecular dynamics analysis and experimental study. The results showed that the atoms are
extruded in front of the cutting tool, when the UCT is 1 nm
and edge radius is 5 nm. A new nano-metric cutting model
that material removal at the nanoscale is on extrusion
Nanomanufacturing and Metrology
Fig. 13 Temperature
distribution of tool tips at a
cutting distance of 17 nm;
a single tip tool (first pass and
second pass); b multitip tool
[111]
mechanism was proposed by Fang et al. [5, 88, 94, 113], as
shown in Fig. 14.
Woon et al. [114] found that in micro-cutting process
the chip formation mechanism also transforms from
shearing to an extrusion-like behavior, at a critical combination of UCT and tool edge [114]. Simoneau et al. [2]
investigated the influence of tool edge radius on the chip
formation by cutting medium carbon steels with TiNcoated tungsten carbide tools whose cutting edge radius is
measured to be 8 to 10 lm. Result shows that the continuous chips are generated when the UCT is larger than or
equal to the tool edge radius, as shown in Fig. 15a–c.
While the UCT decreases, a transition from shearing to
quasi-shear-extrusion chip occurred as shown in Fig. 15d–
f.
Fig. 15 Chip cross sections in different t/rb [2]. a t=rb ¼ 10, b
t=rb ¼ 5, c t=rb ¼ 1, d t=rb ¼ 0:4, e t=rb ¼ 0:3, f t=rb ¼ 0:2
Fig. 14 Schematic illustration of nanoscale cutting model [5]
When the tool edge cannot be ignored, there is a
threshold below which the chip formation cannot form
stably or just no chip formation. Kim et al. [115] observed
plowing under a certain UCT indicating existence of a
threshold. The threshold is defined by Ikawa et al. [116] as
the minimum uncut thickness that can be removed stably
from workpiece surface with a cutting edge under perfect
123
Nanomanufacturing and Metrology
performance. And the minimum UCT is thought to determine the extreme accuracy attainable under specific cutting
conditions, tool and workpiece, etc. The minimum UCT is
also defined as the threshold whether a chip is formed or
not [115, 117, 118]. Liu et al. [119] take orthogonal cutting, turning and milling process into consideration and
define the minimum UCT. The minimum UCT strongly
relates to the material separation mechanisms in front of
the tool edge. Two major approaches have been proposed
to analyze the material separation mechanism [55, 107].
Both will be discussed in the following.
The first approach is based on the existence of a stagnation point on the tool round edge, below which the
material flows under the tool to form the machined surface
and above which the material flows up along the tool face
to form chip [120]. Fang [19, 20] comprehensively defines
the tool edge roundness by four variables. Stagnation point
is one of the four variables, and the others are tool edge
radius, tool–chip frictional shear stress above or below the
stagnation point on the tool edge. As shown in Fig. 16a is
the material flow around the tool edge with a radius of rb
and a UCT of h. A stagnation point S is assumed on the tool
edge locating at a stagnation angle hs . At this point, the
effective negative rake angle ce ¼ p=2 hs determines the
separation height hs ¼ rb ð1 cosðhs ÞÞ. With the decrease
in the UCT, the separation height tends to equal the UCT
which is the minimum UCT, hm (hm ¼ rb ð1 cosðhc ÞÞ, hc
is the corresponding critical stagnation angle, and the
corresponding
critical
effective
rake
angle
cec ¼ p=2 hs ¼ arcsin 1 hm =rb ).
Lai et al. [120] applied 3D molecular dynamics to
investigate the effective rake angle of the stagnation region
which is almost a point. The relationship between the
minimum UCT and tool edge radius has been found. One
of the simulation snapshots is shown in Fig. 17. The
effective rake angle of stagnation point is approximately
constant with the same depth of cut and different tool edge
radii. The separation height is almost in proportion to UCT
and increases with it when cutting using the same tool edge
radius. The critical effective rake angle deduced at the
point where separation height equals the UCT is between
Fig. 16 Cutting with an edge
radius tool, a stagnation point,
b stagnation zone
123
Fig. 17 Stagnation region on the 3D simulation snapshot [120]
- 65 to - 70. Different molecular dynamics simulation
results obtained by Hosseini et al. [99] showed that the
stagnation angle was approximately constant with the
variation of the ratio t=½rb (the tool edge radius ½rb remains constant at 4.9 nm) from 0.22 to 0.59, except the
ratio t=½rb 0:15. This indicates that UCT has no obvious
effect on stagnation angle. Therefore, the change of the
separation height hs with the UCT is always neglected. The
separation height is approximately equal to the minimum
UCT hm , which has been used by Yuan et al. [117] to
investigate the effect of diamond tool sharpness on minimum UCT. The deduced minimum UCT is
0
1
B
C
Fy þ lFx
ffiC
hm ¼ r b B
@1 rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
A
Fx2 þ Fy2 ð1 þ l2 Þ
ð2Þ
where Fx and Fy are the horizontal and vertical forces
acting on the stagnation point S. According to the equation,
if the tool edge radius rb is known, the minimum UCT is
determined by the ratio Fy =Fx and the friction coefficient l.
The minimum UCT is estimated to be 20–40% of the
cutting edge radius [117].
Son et al. [121] took the friction coefficient between the
tool and the workpiece into consideration and deduced the
equation of minimum UCT:
hm ¼ rb ð1 cosðp=4 b=2ÞÞ
ð3Þ
where b is the friction coefficient angle (b ¼ tanðlÞ).
According to the equation, an increase in the friction
Nanomanufacturing and Metrology
coefficient could reduce the minimum UCT [122]. Malekian et al. [118] investigated the minimum UCT using the
minimum energy approach and infinite shear strain method.
Results showed that the stagnation point locates at the
place where the critical angle (hc ) approximates the friction
coefficient angle b. Therefore, the critical effective rake
angle cec ¼ b p=2 could be seen as the key factor in
determining the minimum UCT, following the equation:
hm ¼ rb ð1 cosðbÞÞ
ð4Þ
According to the equation, the minimum UCT increases
with the increment of the friction angle or the friction
coefficient.
Lai et al. [123] simulated orthogonal cutting of copper
and found that the minimum UCT is 0:25rb when the
cutting edge radius is 2 lm and the rake angle is 10.
Woon et al. [124] investigated the effects of tool edge
radius on flow stagnation phenomenon using Lagrangian–
Eulerian FE modeling approach. They found that the
material separations could be attributed to the counterbalance of shear contact components and it is insensitive to
UCT. The stagnation angle in their model is 58:5 0:5
with the UCT of 2 to 20 lm and cutting speed of 100 m/
min. Jin et al. [125] proposed a slip-line model for microcutting considering the effect of tool edge radius. The
model based on the existence of stagnation point on the
tool edge and the stagnation angle is calculated by the finite
element model.
The minimum UCT has a significant influence on the
generated surface roughness. Weule et al. [51] proposed
the relationship of the minimum UCT with surface
roughness. It is responsible for the generated sawtooth-like
surface profile. Wang et al. [126] applied this relationship
and deduced an equation about surface roughness and
minimum UCT. The minimum UCT obtained by experiments
based
on
the
proposed
equation
is
hm ¼ ð0:28 0:33Þrb . The material flow in front of the
asymmetrical tool edge which is characterized by the formfactor method has been investigated by quick-stop experiments and the FEM [55, 127]. For rounded cutting edges
with K [ 1, extensive workpiece material deformation
occurs. This effect decreases by shifting the form factor to
K \ 1. Based on simulation results, the point of material
separation locates at effective rake angle cec ¼ 46 2 .
Therefore, the minimum UCT is determined by the tool
edge shape and the effective rake angle.
The second approach is based on the existence of a
stagnation region in front of the tool edge like a
stable build-up edge (BUE) or a dead material zone (DMZ)
which changes the flow of workpiece material. As shown in
Fig. 16b, the stagnation-zone tip S is where the workpiece
material starts to split into two parts. The formation of
stagnation zone or dead metal zone is determined by the
tool edge shape, cutting speed, material and frictional
properties between the tool and workpiece materials [129].
One of the extreme conditions is to cut materials with a
large negative rake angle which could be used for simulating grinding process or helping analyzing the chip formation under low ratio t=rb [128]. As shown in Fig. 18b,
when cutting with - 60 rake angle, a stagnation region
like a triangle dead metal appeared at the tool tip. It could
be seen as a stable built-up edge which influences the
shearing process making the formation of serrated chips.
Figure 18a is the finite element modeling (FEM) of the
chip formation which is similar to the experimentally
obtained serrated chips [128]. Asymmetrically designed
chamfers in cutting tool edge also change the material flow
by causing a stagnation zone. The size and the shape of the
stagnation zone are determined by the designed chamfers
[55, 127]. Similar results were obtained by Chen et al.
[130] in cutting AISI H13 hot work die steel with PCBN
tool. He found a small part of the workpiece material
adjacent to the cutting edge with no relative velocity
between the tool and workpiece. This phenomenon indicates the existence of stagnation region [131]. The position
of the generated stagnation region on tool edge obtained by
FEM is same as the experimental results obtain by Ng
[132].
When cutting with a sharp tool, the stagnation region at
the tool tip is small and unstable [99]. Similar results were
obtained by finite element modeling. For sharp tool, the
size of stagnation region is small and the shape changes
during cutting [133]. When cutting with rounded tool
edges, the stagnation zone forms at the beginning of cutting
and its shape becomes stable when steady-state cutting is
reached [99]. The finite element modeling results show that
the shape of stagnation region is almost triangular and the
size of it increases linearly with tool edge radius. As shown
in Fig. 19, the distance from the stagnation-zone tip S to
Fig. 18 Chip formation with stagnation region in rake angle of - 60
[128]
123
Nanomanufacturing and Metrology
Fig. 19 Total velocity distribution during steady-state cutting [133]. a
rb ¼ 50 lm, b rb ¼ 100 lm
the machined surface which could be seen as the separation
height hs increased with edge radius. And its distance to
rake face ts always stays constant [133]. Kountanya et al.
[129, 134] experimentally investigated the formation of
dead metal cap ahead of the rounded tool edge. A real-time
visual picture of the dead metal cap was obtained in cutting
cartridge brass with the ratio t=rb ¼ 0:73 (the edge radius
rb is 220 lm) and the cutting speed of 7.8 mm/s. However,
dead metal cap was not formed when cutting zinc.
Kim et al. [135] investigated the formation of build-up
edge with the variation of the ratio t=½rb (½rb = 6 nm)
from 0.1 to 0.9. When the ratio t=rb is 0.1, no chip was
formed. And when the ratio t=rb is 0.2, the material tended
to pile up ahead of the tool. As the ratio increased above
0.4, the piled-up material developed into chips, and the
transition from plowing regime to cutting regime happens.
Build-up edges were always formed in a triangular shape
ahead of the round tool edge in the cutting regime
according to the molecular dynamic simulations. Liu et al.
[136] proposed a slip-line field model which takes into
consideration dead metal cap formed in front of the cutting
edge to solve minimum UCT and cutting temperature
iteratively. With an initial value of the normalized minimum UCT (kn ) which is defined as the ratio of the minimum UCT to edge radius, the cutting temperatures are
calculated by the slip-line model and used to compute the
yield strength (r) of the work hardened material and the
shear strength (sa ) of the adhesive junction. The normalized minimum UCT is recalculated by Kragelskii–Drujuanov equation as
sa
kn ¼ 0:5 ð5Þ
r
The calculation is continued until the computed and
initial value is smaller than the preset tolerance. The model
is experimentally validated with micro-end milling tests on
1040 steel. In the tests, the minimum UCT is obtained by
measuring the sudden surface height change on the
machined sidewall. Results showed that the slip-line model
predictions match the experimental results well. The
123
minimum UCT is ð0:2 0:45Þrb which increases with
cutting edge radius and the cutting speed when machining
1040 steel.
When cutting using an asymmetrically rounded tool
edge which is characterized by the form-factor method, the
influence of Sc on the stagnation region is negligible,
whereas the influence of Sa is significant. Therefore, for
tool edge of large K, the material separation point is located
nearly at the end of the flank face which makes the
effective UCT approximately the same as the UCT.
However, while machining with a tool edge of small K, the
height of the material separation point approaches the
magnitude of Sc [137]. Further investigation shows that a
stagnation zone forms in front of tool edges with K [ 1 and
in the case of tool edges with K \ 1 a stagnation zone
cannot be clearly recognized [55, 74]. However, in nanocutting of single-crystal silicon, the stagnation zone forms
in both kinds of the tool edge which is investigated by MD
simulations [64]. Besides that, the size and the position of
the stagnation region are also determined by the crystallographic orientation of the workpiece material [138].
In nano-cutting of aluminum, the stagnation region
forms in front of tool edge, as shown in Fig. 20 [139]. The
sharp tool edge with a negative rake face entraps a large
number of atoms forming a large stagnation region at its
edge, especially at its side. However, when cutting the
material by a sharp tool edge with a positive rake angle,
almost no atoms are entrapped and no stagnation region
forms at the tool edge, as shown in Fig. 20c–d. The shape
of the stagnation region could be approximated to an arc
with the center locating at the center of tool nose, and its
radius is denoted as Rs . The separation height or the stagnation height is calculated according to the equation
Rn Rs . The separation height of the tool edge with large
edge radius is larger than that of small tool edge radius, as
shown in Fig. 20a–b.
With the size of the stagnation zone increases, it tends to
work as a build-up edge, which sticks to the cutting edge or
the rake face forming a new cutting edge. The hardness of
the build-up edge is measured by Kummel et al. [140], and
the results show that its hardness is two to three times
higher than the hardness of the initial workpiece material.
The grain size of the build-up edge is refined from the
microscale to nanoscale. The size of the build-up edge is
changed with the cutting parameters; for example, the area
and height of build-up edge decrease with increasing cutting speed from 50 to 100 m/min [140]. The decreasing
build-up edge with the increase in speed can be explained
by the higher temperature in the cutting zone [141]. The
increase in material hardness results in a decrease in the
formation of build-up edge [142]. The build-up edge in
front of the tool edge tends to reduce the cutting forces due
Nanomanufacturing and Metrology
Fig. 20 Stagnation region on the cutting tool edges [139]. a rb ¼ 5 nm; c ¼ 0 , {100} \011[, b rb ¼ 2:5 nm; c ¼ 0 , {100} \001[ c
rb ¼ 0 nm; c ¼ 15 , {111\} \1–10[ d rb ¼ 0 nm; c ¼ 15 {111} \1–10[
to the generated higher rake angle and sharper tool edge
[143]. But during the cutting process, the variation of the
build-up edge geometry and its aperiodic separation from
the cutting tool would degenerate the machined surface
quality [144]. Meanwhile, the separation of the build-up
edge from the tool edge could lead to the damage of the
tool decreasing the tool life [145]. However, in certain
conditions, such as the low cutting speed (50 m/min), the
formation of build-up edge also has the potential to protect
the tool against the flank wear and crater wear, which has
been observed by Kummel et al. [140]. They further stabilized the build-up edge in front of the tool edge by texturing the rake face with dimples [146]. With the
stable build-up edge, the wear of the flank face and the
corner radius are suppressed.
In this section, the influence of the tool edge on the
minimum UCT and chip formation has been discussed. The
minimum UCT is an important factor in determining the
material removal mechanism. Xu et al. [138] presented that
the material is removed by shearing mechanism when the
UCT is comparably larger than the minimum UCT. When
the UCT is similar or smaller than the minimum UCT, the
material is removed in extruding mechanism. For further
decreasing the UCT, rubbing happens and no material is
removed. More discussions about the influence of material
deformation mechanisms on the surface generation will be
displayed in the next section.
3.1.6 Influence on Surface Generation
In addition to the industry-concerned performance parameters, fundamental physical parameters such as stresses,
strains, temperatures, phase transformation and minimum
UCT have been discussed for the in-depth understanding of
surface generation in cutting process. The influence of tool
geometries, especially the cutting tool edge, on the generated surface would be discussed in this section. The
generated surface affected by the material properties in
cutting process will be introduced in the next section.
In cutting process, the generated surface is determined
by the feed rate and tool nose radius if assuming that the
workpiece material is removed ideally and the machined
surface texture is the replication of tool nose profile. The
theoretical peak-to-valley roughness is formulated as
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Rth ¼ Rn R2n ðf =2Þ2 f 2 =8Rn , where Rn is tool nose
radius and f is feed rate [11]. However, it always deviates
from its ideal value due to many factors, such as material
properties of workpiece [147, 148] and cutting tool
geometry [96, 149–152]. Wu et al. [153] experimentally
investigated the influence of the ratio t=½rb (½rb stays
constant at 8 lm) on surface roughness and found that the
deviation from the theoretical value increases with the
decrease in the ratio t=½rb . They thought that the size
effect-induced stress nonlinear increase causes the increase
in material side flow and then the increase in surface
roughness. The minimum surface roughness is achieved
near the minimum UCT which is estimated to be
ð0:2 0:3Þrb . The deviation from the theoretical value has
also been investigated by Childs et al. [154, 155]. They
thought the feature of the cutting tool that determined the
machined surface roughness changed from the tool nose
radius to the tool edge radius, as the feed was reduced in
turning process. Woon et al. [114] found that the generated
123
Nanomanufacturing and Metrology
surface quality is deteriorated by further decreasing the
ratio t=½rb (½rb stays constant at 10 lm) to 0.05, where the
discontinuous chips were produced. In the finish hard
turning of AISI 52100 steel, Thiele et al. [79] found that
cutting edge with small edge radius results in lower average surface roughness values than that with large edge
radius. The effect of the cutting edge radius on the surface
roughness decreased with an increase in workpiece hardness. In diamond cutting of silicon, Fang et al. [70] found
that large tool edge radius increases the machined surface
roughness. Similar results were found by Yuan et al. [117]
in diamond cutting of aluminum alloys. Ng et al. [83]
investigated surface roughness in diamond cutting of aluminum 2075-T6 and found that the generated surface at an
UCT smaller than the tool edge radius is rougher than that
with larger UCT.
The phenomenon that the cutting-induced surface
roughness always deviates from the theoretical value could
be partly attributed to the effect of the cutting tool edge
[156]. The elastic recovery and the side flow of materials
are two factors affected by tool edge and further influence
the surface roughness. The combined effect of elastic
recovery and side flow which causes greater and deeper
marks on machined surface was referred as the swelling
effect by Cheung et al. [157]. Sata et al. [158] found that
there was no swelling for brass when compared with the
roughness obtained in cutting of medium carbon steel.
Therefore, greater swelling would generate on the
machined surface of the softer material. Cheung [157] and
Kong et al. [159] thought the amount of recovery which is
determined by the forces on the clearance face and Young’
modulus of the workpiece material would cause a wavy
machined surface. Schaal et al. experimentally investigate
the influence of cutting edge radius on elastic recovery in
metal cutting. Results showed that the elastic recovery for
the sharp tool is lower than for the blunt tool and the
variation of elastic recovery is in coherence with the
change of surface roughness [160]. To predict the surface
roughness in single point diamond turning, Zong et al.
[156] introduced an additional term to the roughness formulation proposed by Grezesik [161]. It is formulated as
f2
hm
Rn h m
H
0
Rth ¼
1þ
þ
ð6Þ
þ k1 rb k2
E
8Rn
2
2
where H and E are the Vickers hardness and Young’s
modulus. k1 relates to the tool nose radius and rake angle,
and k2 relates to the maximal UCT and tool edge radius. He
et al. [162] considered the contribution of the elastic
recovery to the machined surface roughness individually.
Based on the prediction method proposed by them, the
contribution of material recovery to Al6061 is
0:9162hm ¼ 0:3207rb .
123
The side flow is the plastic deformation of workpiece
material at a direction opposite to the feed direction in
cutting process [163]. It is a result of the interactions
between cutting tool and workpiece material [164]. Kishawy et al. [152] proposed two mechanisms to describe the
formation of material side flow. The first one is the squeeze
between the machined surface and the tool flank face,
especially when the UCT is smaller than the minimum
UCT. The second one is that the trailing edge notch
induced high temperature and pressure makes the material
be pressed aside. They further investigated the formation of
side flow by 3D thermo elasto-viscoplastic finite element
method and found that more side flow is generated with
higher nose radius and lower feed [165]. Cheung and Lee
[166] found that the machined surface roughness increased
with an increase in tool nose radius at large radius but
decreased at small radius. This phenomenon may be partly
caused by the side flow. Ge et al. [167] found that the
severe worn tool edge caused the severe swell of the
material in the machined surface due to the side flow. Lai
et al. [168] found that the side flow increases the height of
the tool marks left on the machined surface and therefore
influences the machined surface roughness of germanium.
The side flow of material has been taken into account to
predict
the
machined
surface
roughness
[156, 162, 164, 169]. In 2006, Liu et al. [164] established a
relationship between the roughness due to side flow Rp and
the rheological factor x, which is formulated as
Rp ¼ k1 ln x þ k2
ð7Þ
E cot h
ry e
ð8Þ
x¼
ry is the average flow stress and e is defined as the ration of
the average flow stress with and without strain gradient
strengthening. E is the Young’s modulus. k1 and k2 are two
coefficients needed to be calibrated via actual cutting tests.
In 2014, Zong et al. [156] introduced a scale coefficient
k3 relating to the side flow to the surface roughness prediction formulation. In determining the value of the coefficient k3 , the feed rate and tool nose radius are considered.
In 2015, He et al. [169] thought the side flow is one of the
uncertain components determining the surface roughness
which is predicted empirically by a radial basis function
(RBF) neural network. In 2016, a new prediction model
was proposed by them [162]. The side flow-induced
increment of surface roughness is formulated as
w ¼ kd kt kf hmin bD , where bD is the effective cutting width,
hmin is the minimum UCT, kd is a scale coefficient determined by the material properties of workpiece, and kt and
kf are two variable coefficients relating to the tool nose
radius and feed rate, respectively. The minimum UCT hmin
used in their study is 0:35rb , and the scale coefficient
Nanomanufacturing and Metrology
determined by the material properties is 0.001 lm-1.
However, the tool edge radius or the anisotropy of the
material which determines the minimum UCT and the side
flow lack direct consideration in predicting the machined
surface roughness. The side flow effect on the surface
generation or the surface roughness should be investigated
deeply.
The material deformation mechanism in cutting process
is one of the most important factors in influencing the
surface generation, especially the side flow and the
recovery which is determined by the deformation mechanism. Zhang et al. [170] reviewed the surface roughness
formation in ultra-precision machining and thought that the
larger tool edge radius would lead to higher plowing phenomenon causing an increase in surface roughness. In
orthogonal cutting of aluminum, Xu et al. [138] found that
small minimum UCT accompanied with small recovery
height and contact length between the flank face and
workpiece material caused a better surface quality. The
surface quality gets worse when the UCT is similar to the
minimum for the cutting direction of {100} \001[ and
{100}\011[, due to the extruding removal mechanism
taking place at the cutting condition. Xu et al. [139] found
the side flow effect on surface generation in nano-cutting of
aluminum as shown in Fig. 21. A larger part of the side
flow material and residual material are at or under the
stagnation region which is characterized by stagnation
radius Rs . Then, in the cutting process, they are extruded by
the tool edge to form the side flow. The position, shape and
size of the stagnation region which are determined by the
material properties and tool edge geometry would influence
the side flow of nano-cutting process. Small tool edge
radius and positive rake angle which could suppress the
formation of stagnation region or enlarge the stagnation
radius Rs (decrease the separation height Rn Rs ) would
decrease the size of side flow [139].
The side flow of the material, on the other hand, would
result in Poisson burr which would deteriorate the
machined surface quality in cutting process [171]. The
increase in tool edge radius which increases the size of side
flow would encourage the formation of the Poisson burr
and enlarge the size of it [172]. Fang and Liu [173] found
Fig. 21 Atoms tend to form the
side flow region (yellow) and
residual region (blue), a before
and b after nano-cutting [139]
that the formation of burrs could be suppressed by
decreasing the UCT. To minimize the burrs in cutting
process, the UCT should be comprehensively matched with
the cutting tool edge radius [171].
In this section, the influence of the tool edge on the
surface generation has been discussed. However, the surface generation could also be affected by the material
properties which would be discussed in the next section.
3.2 Influence of Material Properties
The material properties, such as the crystallographic orientation [138, 148, 174], grain size [175], grain boundary
[147, 176, 177], or hard particles [178–180] of or in
workpiece material, have important effects on the cutting
process. Therefore, in this section, the influence of the
material properties would be discussed in three aspects: the
influence of ductile materials, the influence of brittle
materials and the influence of the defects, such as grain
size, grain boundary and hard particle, on the micro/nanocutting process.
3.2.1 Influence of Ductile Materials
In micro/nano-cutting process, the material is removed
under the scale which is usually smaller than the material
grain size [181]. Therefore, the size effect of materials
could not be neglected [88, 182]. The size effects of the
material have been studied by many researchers. Volkert
et al. [183] and Lee et al. [184] investigated the mechanical
properties of Au columns with a diameter changing from
100 nm to 8 lm. The results that the yield stress and
apparent strain hardening rate increased with a decrease in
column diameter were found under the uniaxial compression experiments. Similar results were found in niobium
single crystals [185] and even amorphous metals
[186, 187]. Abad et al. investigated temperature-dependent
size effects on the strength of [111]—oriented tantalum and
[100]—oriented tungsten pillars by elevated temperature
compression tests [188]. Kaira et al. [189] investigated the
microscale deformation behavior of bicrystal boundaries in
pure tin by the micropillar compression tests and found that
Rn-r
Rn-r
Rn
Rs
Rn
PV
A-A
Side flow
(a)
Rs
Workpiece
(b)
Residual
region
Side flow
region C-C
Workpiece
B-B
PV’
123
Nanomanufacturing and Metrology
the random angle grain boundaries in the micropillar act as
barriers to the dislocation glide causing the strengthening
mechanism. Shan et al. [190] found the annealing of
micropillar through mechanical deformation due to the
exhaustion of dislocations making the dislocation density
fall to zero. The size effects of material in micro/nanoscale
would appear in micro/nano-cutting process, partly causing
a rapid and nonlinear increase in specific cutting energy,
especially at the nano-metric UCT [83, 191]. Lai et al.
[192] found the increase in the specific cutting energy with
a decrease in UCT in investigating the nano-cutting by
three-dimensional MD simulations. Xu et al. [138] found
that the size effects of materials make different plastic
carriers, such as the twin, stacking faults and dislocations,
generate on the plastic deformation zone of different cutting directions, as shown in Fig. 22. And the processing
forces would be influenced by the size effect and anisotropy of materials. Therefore, when decreasing the UCT,
the effect of cutting direction which is actually the effect of
crystallographic orientation or anisotropy of the materials
on the cutting process becomes non-ignorable, whether the
workpiece is single or polycrystalline material
[138, 181, 193].
In 1994, Yuan et al. [181] experimentally investigated
the influence of crystallographic orientations on the cutting
force and generated surface roughness. They found that the
fluctuation in the cutting force is responsible for the variation of the machined surface roughness. Lee et al. [194]
found different surface roughness is obtained at different
crystal planes. They thought that the anisotropy of materials which would cause the anisotropy of Young’s modulus and different amount of recovery caused the difference
on generated surface roughness. The best surface roughness is obtained on aluminum {100} planes by To et al.
[195]. The shear angle and shear stress were also determined by the crystallographic orientations, but they are less
Chip
Frank partial
dislocations
Cutting
direction
Chip
Diamond
tool
ISF
sensitive to the changes of cutting conditions [196]. The
side flow which is another important factor in deteriorating
the generated surface roughness would be influenced by the
anisotropy of materials. It has been investigated by Xu
et al. [139] and found that the side flow could be suppressed by optimizing the cutting directions. Small side
flow is formed at the cutting direction of {100}\011[,
{110}\001[ and {110}\1–10[, whose stagnation height
is smaller than that of others. The stagnation height, to a
certain extent, is corresponding with the minimum UCT
and the minimum depth of material removal. The effect of
the crystal orientation on minimum depth of material
removal has been investigated by Zhu et al. [197]. Similar
to the effect of crystallographic orientation on side flow in
cutting process, the formation of burrs is also affected by
the anisotropy of materials. Wu et al. [172] found that the
maximum burrs are formed on the {111} planes of copper
and the minimum burrs are formed on {100} planes of
copper.
3.2.2 Influence of Brittle Materials
The subsurface deformation for the brittle materials, such
as the silicon and germanium, is also influenced by the
crystallographic orientation, and the best cutting directions
which lead to the thinnest thickness of deformed layer are
obtained [174, 198]. The machining-induced phase transformation and residual stress could be investigated by
micro-Raman spectroscopy [199, 200]. Yan experimentally
investigated the influence of the cutting direction on surface deformation and the critical UCT of single-crystal
silicon [201]. The results showed that the cutting direction
of {100}\128–3090[ had the largest critical UCT which
meant the best ductile machinability. And the machininginduced amorphization layer at this cutting direction is the
thinnest compared to the other cutting directions. For KDP
Twin bondary
Chip
Cutting direction
ESF
Diamond tool
TB
Perfect
dislocations
Twin boundary
Other
dislocations
(a)
Shockley partial
dislocations
Stair-rod
dislocations
Shockleypartial
dislocations
Workpiece
(b)
ISF
Flankpartial
dislocations
Fig. 22 Snapshots of the microstructure evolution at cutting direction of a {100}\011[, b {110}\001[ [138]
123
Workpiece
Nanomanufacturing and Metrology
crystal, the critical UCT has been investigated under the
cutting of {100}, doubler and tripler planes of KDP. The
maximum critical UCTs were obtained at different cutting
planes [202]. Zong et al. [203] proposed a predictive model
for the calculation of critical UCT taking the compression
force and micro-friction force into consideration. Cai et al.
[204] simulated the crack initiation in the nano-cutting of
silicon by MD. They found that cracks may be initialized
due to a peak deformation zone in front of cutting tool
edge. Xiao et al. [47] investigated the crack initiation and
propagation in nano-cutting of silicon carbide with different UCT by MD simulations, as shown in Fig. 23. The
crack propagation direction is determined by the UCT.
Shallow craters would form on the machined surface when
the crack propagates parallel to the cutting direction.
Otherwise, steeper crater would be formed if the crack
propagates downward the subsurface. Fang et al. [7] realized ductile cutting of silicon in a developed cutting device
under the online SEM observation and found that the cutting velocity would influence the brittle-ductile transition.
One nm surface roughness (Ra) on single-crystal silicon
has been achieved by optimizing the cutting process
[5, 70]. Li et al. [205] realized the ductile cutting of germanium by fast tool servo (FTS) ultra-precision turning.
Near-rotational freeform surface with nano-metric surface
roughness has been achieved efficiently. Microlens arrays
of single-crystal silicon have also been machined in ductile
region by slow tool servo (STS) ultra-precision turning
[206].
However, to eliminate the formation of cracks in cutting
of brittle materials, the UCT is less than the critical UCT
which is a relatively small value and usually in nano-metric
scale. Therefore, the machining efficiency is relatively low
and the machined surface quality could not attain a
stable status due to the other factors in cutting process. To
improve the machinability of brittle materials, many
assistant methods, such as the ultrasonic elliptical vibration
assistant [207], laser beam assistant [208–210] and surface
modification methods [211–213], have been proposed.
Ultrasonic vibration-assisted cutting which is an effective method in diamond cutting of ferrous metals
[214–216] was also a method in improving the machinability of brittle materials [207]. The critical UCT was
improved significantly for the soda-lime glass (an amorphous material) by applying the ultrasonic vibration cutting. Based on the advantages of the ultrasonic vibrationassisted cutting process, ultra-precision cutting of glass can
be realized. This technology has been used in other hard
and brittle materials, such as the tungsten carbide [217].
Laser beam which has high directional characteristics
can be focused to a small point creating high power density. It is widely used in processing of materials [218], such
as cutting, welding, marking and sintering. Besides that, it
is also used in assisting the cutting of brittle materials, such
as the silicon [209] and sapphire [210]. In laser beamassisted cutting of silicon, the surface roughness was
improved and the radial spokes which are caused by the
crystallographic orientation effect can be eliminated [209].
The anisotropy effect of the single-crystal C-plane sapphire
on the ductile mode cutting was investigated in laser-assisted cutting technology [210]. The results showed that for
different cutting directions, the critical UCT was improved
by applying this technology.
Surface modification method is used to modify the
workpiece surface to be machinable by bringing different
physical or chemical characteristics and meanwhile not to
change the properties of original materials. In micro/nanocutting process, initial application of this approach is
incidental on the nickel. Arnold et al. [219] machined
nickel phosphorus alloy by diamond tool and observed that
tool wear was decreased with an increase in phosphorus
content. After that, Brinksmeier et al. [220] modified the
steel molds using plasma nitridation to reduce the wear of
diamond tool in cutting process. For brittle materials, such
as the machining of single-crystal silicon, Fang et al. [211]
proposed a novel method which is the ion implantation
surface modification method (NiIM), to enhance the
machining efficiency, improve the surface quality and
prolong the tool life in nano-cutting. After the ion
implantation, the critical UCT of the silicon is increased for
4 times or even higher. By using the modification process,
Fig. 23 Molecular dynamics snapshots at various UCT [47]. a 40 nm,
b 35 nm, c 30 nm, d 25 nm, e 20 nm, f 10 nm
Fig. 24 Mirror surfaces: a flat mirror and b freeform sinusoidal
mirror [211]
123
Nanomanufacturing and Metrology
flat mirrors and freeform sinusoidal mirrors were machined
with nano-metric surface finish, as shown in Fig. 24. The
same method of NiIM has been applied in cutting of singlecrystal silicon carbide [212] and germanium [213]. The
detailed mechanism about the influence of the surface
modification on nano-cutting of silicon has been discussed
by Wang et al. [221].
3.2.3 Influence of Grain Size, Grain Boundary and Hard
Particle
The grain size of the material accompanied with grain
boundary would affect the plastic deformation in cutting
process and further influence the generated surface quality.
In nano-cutting, both the regular Hall–Petch relation and
inverse Hall–Petch relation are found [175]. The regular
Hall–Petch relation in nano-cutting is due to the resistance
of the grain boundary to the dislocation movement. The
inverse Hall–Petch relation is caused by the grain boundary
diffusion and movement in nano-cutting [175]. At the grain
boundary, tears were found to generate when cutting Al–
Mg alloy [177]. The processing force would vary as the
tool passed the grain boundaries [182]. Simoneau et al.
[176] found that surface dimples occur at the hard to soft
grain boundaries but do not occur when cutting through
soft to hard grain boundaries. The dimples could be
reduced by sizing the grain structure appropriately to the
cutting parameters and specially the UCT. Surface treatment processes could be used to change the surface properties of materials and suppress the influence of the grain
boundary on the surface generation, such as the friction stir
process which has been applied by Tauhiduzzaman et al.
[147] on the polycrystalline aluminum surface before cutting process. The results showed that the large grain
boundaries were absent and the related defects disappeared
on the machined surface. The grain size would also influence the burr formation in cutting process. The materials
with small grain size are found to be beneficial to reduce
the size of the burrs [172].
Hard particle in workpiece also plays an important role
in plastic deformation and surface generation during cutting process. Ding et al. [179] found the formation of voids
on the machined surface caused by the hard particles in Al
RSA-905 and Al-6061. When the top layer of the machined
surface is removed, the hard particle could be found near
the voids. In cutting process, the hard particle could be
sheared and fractured. The vacation of the broken parts of
the hard particle causes the generation of the voids and
enlarges the voids as the loose particles are drawn along by
the cutting tool [180]. The formation of the voids could be
suppressed by making the hard particle be machined in
ductile mode, such as the reduction of UCT. Ultrasonic
vibration-assisted cutting was also found to be an effective
123
method to achieve a stable-state cutting performance, an
improved surface roughness and reduced burr size [222].
MD simulation has been used to investigate the influence
of pore and second-phase particles on the subsurface
damage and surface integrity in cutting process [178]. In
2017, Xu et al. [223] investigate the influence of the hard
particle on the surface generation, plastic deformation and
processing forces in nano-cutting of aluminum by MD
simulation. The results show that when the hard particle is
removed, only a small shallow pit is left on the machined
surface. Otherwise, it is pressed down to the subsurface of
the workpiece left larger and deeper pit on the generated
surface. Besides that, the hard particle in the workpiece
would increase the processing force when the cutting tool
edge or the plastic carriers interact with the hard particle. In
ultra-precision cutting of SiCp =Al composites, in which the
SiCp is the hard particle in a soft aluminum material, many
defects, such as pits, voids, microcracks, grooves, protuberances, matrix tearing and so on, are generated on the
machined surface [224]. Better surface quality could be
obtained when the SiCp particles are removed by pressed
into or cut through mechanism. Otherwise, when the SiCp
particles are pulled out or crushed in cutting process,
cracks and pits will form on the machined surface which
deteriorates the surface quality. The precipitates (Mg2 Si)
which generate at the isothermal heat treatment would
introduce scratch marks on the machined surface and
deteriorate the surface roughness in cutting or Al6061
[225].
4 Conclusions and Outlook
The recent advances about the influence of the tool edge
and material properties on micro/nano-cutting process are
reviewed. The material deformation mechanism, such as
shearing, extruding, and rubbing mechanisms, has been
presented in this paper to explain the plastic deformation
and surface generation phenomena in micro/nano-cutting
process. For distinguishing these material deformation
mechanisms, they are summarized as follows:
•
•
Shearing mechanism: With the UCT that is larger than
the minimum UCT, a shearing plane forms in front of
the tool edge and expands from the stagnation point or
the tip of stagnation region. The material flow direction
changes abruptly at the shearing plane. Materials above
the stagnation point or stagnation region would be
removed as a chip. The material below it would be
pressed and flow to the flank face of cutting tool
forming as machined surface.
Extruding mechanism: With the UCT that is less than
or similar as minimum UCT, the stagnation point or
Nanomanufacturing and Metrology
•
•
stagnation region does not form stably in front of tool
edge and no shearing plane expands, making the
material be extruded away from the cutting edge to
form as a chip. With a decrease in UCT, the cutting
process is combined with extrusion and rubbing
mechanisms, making the material be removed less
efficiently.
Rubbing mechanism: With decreasing the UCT to a
value much smaller than minimum UCT, the cutting
tool rubs along the workpiece surface and slightly
presses the surface down to the bottom of cutting tool
edge. The workpiece material experiences elastic–
plastic deformation due to the interaction with tool
edge and flank face, which, to some extent, affects the
generated surface roughness. In rubbing, no chip would
form, but the machined surface would be deteriorated.
Plowing mechanism: Plowing mechanism is the
appearance of the side flow processes. The side flow
is the workpiece material flow to the two sides of the
tool edge left the material on the machined or
unmachined surface. The material flows at the direction
opposite to the feed direction deteriorate the machined
surface roughness.
Based on the fundamental understanding of the material
deformation mechanism in micro/nano-cutting process,
more efforts should be made on the research field as
follows:
•
•
•
•
The design and fabrication of the cutting tool should be
optimized to meet the extreme requirement of the
micro/nano-cutting process.
The machinability of the workpiece material should be
improved by applied surface modification and other
assisted cutting technologies.
The prediction model of the micro/nano-cutting-induced surface should be further investigated by taking
the material properties and tool edge shape into
consideration.
Atomic and/or close-to-atomic scale manufacturing
(ACSM), such as atomic machining, should be taken
into account as the main future manufacturing technology [226].
Acknowledgements The authors thank the supports of Science
Challenge Project (No. TZ2018006), the National Natural Science
Foundation (Nos. 61635008 & 51320105009), the National Key
Research and Development Program (No. 2016YFB1102200), the
‘111’ project by the State Administration of Foreign Experts Affairs
and the Ministry of Education of China (No. B07014), and the Science Fondation Ireland (SFI) (No. 15/RP/B3208).
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Fang FZ (2015) Suggestions of strategic development of manufactuirng: ‘‘Manufacturing 3.0’’. People’s Daily, Beijing (in
Chinese)
Fengzhou Fang professor in
manufacturing, working in the
areas of micro/nano machining,
optical freeform manufacturing,
bio-medical
manufacturing,
ultra-precision manufacturing
and metrology.
123
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Feifei Xu engineer in manufacturing, working in the areas of
ultra-precision manufacturing
and micro/nano-cutting, including the surface generation,
modification, material removal,
plastic
deformation,
and
characterization.