A review of simulation and experiment research on cutting mechanism and cutting force in nanocutting process

Abstract

Nanocutting is a method of direct machining in nanomanufacturing field, and it is an important ultraprecision machining method. Nanocutting technology adopts single-point diamond cutting and nanoprobe scratching methods to make the machining accuracy of parts reach the nanometric scale. It is the method with the highest machining accuracy at present, so it is widely used in the processing of precision components. At the same time, nanocutting technology can be used to process nanostructures and provide processing methods for basic research in condensed matter physics. This paper summarized the cutting mechanism and cutting force in the nanocutting process, including the mechanism of nanocutting and brittle–ductile transition. The influence of RTS, temperature, wear and subsurface phase transformation on cutting performance is also discussed. At the same time, the characteristics of cutting force and friction coefficient during the cutting process are reviewed. After that, the simulation and experiment research of the nanocutting process are analyzed. At the end of the paper, the challenges and prospects of nanocutting technology are proposed and summarized.

1 Introduction

The manufacturing industry has gradually shifted from macroscopic manufacturing to microscopic manufacturing, especially nanomanufacturing [1,2,3]. Nanomanufacturing technology is a technology with material removal depth at the atomic level, and it is an ultraprecision machining method and has a wide range of applications in various fields such as aviation, energy, optics and electronics, which shows highly important practical value [4,5,6,7]. The applications of nanomanufacturing technology are listed in Table 1.

Table 1 Applications, methods and accuracy of nanomanufacturing technology

Nanomanufacturing technology can be used in two manufacturing processes. One is to manufacture nanostructures, and the other is to manufacture surface of parts with nanoscale precision [18]. Figure 1 shows the nanostructures used for communication [19,20,21].

Fig. 1

Nanomanufacturing examples [8, 19, 22]

In the nanomanufacturing process of nanostructures, the use of scanning probe microscope (SPM) to machine the surface of the workpiece is a common method. The scanning probe microscope realizes the manufacture of nanostructures by moving the probe in three coordinate directions, as shown in Fig. 2 [9].

Fig. 2

(Color online) (a) Machining patterns by cutting at varying pitches. (b) Very dense spiral cuts [9]

At the same time, ultraprecision machining tools adopting the method of single-point diamond turning can also achieve nanomachining accuracy. In 1962, Union Cardie of the United States developed an ultraprecision hemispherical surface processing equipment, which can process aluminum alloy hemispherical surfaces with a diameter of 101.6 mm to a mirror effect, with a processing shape accuracy of 0.6um and a surface roughness of 25 nm, which is also the first time for mankind to achieve nanoprocessing accuracy in the cutting process. Later in the 1970s, Moore Company, Pneumo Company and Dutch Phillips Company in America also developed ultraprecision machine tools with a machining surface accuracy of 10 nm successfully, as shown in Fig. 3 [10, 23, 24, 28].

Fig. 3

Ultraprecision grinding: (a) ultra-precision grinding system, (b) and (c) workpiece surface morphology after ultra-precision grinding [23]

2 Cutting mechanism

The research on nanocutting mechanism is the theoretical basis for realizing nanocutting. In the nanocutting process, not all materials within the cutting thickness range are removed. When the ratio of the cutting thickness to the cutting edge radius is less than the critical value, no chips will be generated during the cutting process, as shown in Fig. 4. The use of plastic cutting for brittle materials is also an important research direction of nanocutting mechanism. Through the nanocutting method, the processing of brittle materials can be realized. The reason is that in the cutting process of brittle materials, when the cutting thickness reaches nanometric level, the cutting mode will change from brittle mode to plastic mode, so as to realize the plastic processing of brittle materials. In this process, the most important thing is to determine the critical depth of cut in order to realize the brittle–plastic transformation of material processing [11]. The results of researches on the nanocutting mechanism are summarized in Table 2.

Fig. 4

Stagnation point denoted by “S” in nanocutting. The stagnation point is where the split flow of material occurs (left). For an extreme small cutting depth (right), there is no chip formation [19]

Table 2 Cutting mechanism in nanocutting process

In the nanocutting process, the ratio of cutting depth to cutting edge radius can be defined as the relative sharpness of the tool RTS, and RTS = h₀/r_e, where h₀ represents the cutting depth and r_e represents the cutting edge radius. The cutting model with the same RTS and different cutting edge radius is shown in Fig. 5. It can be found that when the RTS is the same, the reduction in the cutting edge radius leads to the reduction in the cutting depth. At the same time, during the cutting process, the plastic deformation flow is formed in the area of the workpiece near the rake face of the tool, which becomes the primary deformation zone (PDZ). By increasing the depth of cut, when the RTS is unchanged, the PDZ area will also increase and will lead to an increase in internal defects of the workpiece [37, 38].

Fig. 5

The effect of tool edge radius on the machined surface at the same RTS and tool advancement, but at (a) higher uncut chip thickness and (b) lower uncut chip thickness [30]

In the processing of brittle materials, in order to obtain the critical cutting depth of brittle–plastic transition, taper cutting experiments are often used to obtain this critical value. In the taper cutting experiment, as the cutting depth increases, the cutting surface gradually becomes rough and generates a lot of chips. The surface cutting process begins to change to brittle cutting mode, and the cutting depth from plastic cutting to brittle cutting is the critical depth of cut for brittle–plastic transition, as shown in Fig. 6 [19].

Fig. 6

Taper cutting [26] and the groves on GaF₂ single crystal [27]. The ductile–brittle transition is denoted by the onset of surface cracks as the cutting depth exceeds the critical value [19]

Nanoscratch experiment is also a kind of method of taper cutting. In the process of nanoscratch, the cutting depth is also increasing with the increase in normal load and cutting displacement, and the whole cutting process is divided into four stages. At the beginning, it is the elastic stage, followed by the elastic–plastic stage, plastic stage and brittle stage, and once it enters the brittle stage, the cutting force decreases because the material is removed in a brittle way, as shown in Fig. 7 [31].

Fig. 7

Scheme of different modes of removing a brittle material with increasing normal load and cutting depth: elastic (1) and elastoplastic (2) deformations, plastic (3) and brittle (4) removal of the material [31]

In the processing of soft and brittle materials, such as KDP crystals, plastic cutting of brittle materials can be achieved by reducing the cutting depth to a few nanometers. However, for this ultraprecision machining method, there are still shortcomings of low cutting efficiency. At the same time, through the study of some difficult-to-machine materials such as ceramics, it is found that when the heat-assisted process is used, the processing difficulty can be significantly reduced. However, there are few studies on the plastic processing of KDP crystals using thermally assisted processes. Therefore, it is necessary to study the processing methods of soft and brittle materials such as KDP. Through the scratch test on the KDP crystal at 23 °C and 170 °C, it can be found that during the process of scratching the KDP crystal at 23 °C, a lot of debris is generated around the scratch, and the scratch is relatively rough. In the process of scratching the 170 °C KDP crystal, there is less debris around the scratch and the scratch is relatively smooth, as shown in Figs. 8, 9, 10. Through further analysis, it can be found that the critical brittle–plastic transition cutting depth (3.61um) of KDP crystal at 170 °C is 8.6 times of that at 23 °C (0.42um). This further verifies the positive influence of temperature on the plastic cutting of KDP crystals and provides experiment guidance for the study of crack-free surface processing of KDP crystals [29].

Fig. 8

(a) Schematics of nanotests at varying temperatures; (b) close snapshot of the experimental system (NanoTest); (c) schematic of heating arrangement of NanoTest; (d) diagrams of nanoindentation and scratch tests at different temperatures [29]

Fig. 9

The residual groove morphologies of varied-depth scratches at different temperatures [29]

Fig. 10

The scratch surface morphologies processed at elevated temperature (e.g., 170 °C) (a); (I–V) are the magnified images showing the representative morphology features [29]

Ultraprecision machining can realize the removal of nanomaterials [54], but when the cutting depth drops to a few atoms, it is difficult to achieve by experimental methods, and the use of molecular dynamics simulation methods becomes feasible. Molecular dynamics method can simulate the cutting characteristics of different cutting conditions, cutting edge radius and cutting material when the cutting depth is a few atoms. It is the most effective simulation method for studying nanocutting process so far [32,33,34]. Through the molecular dynamics simulation of the nanocutting process, the cutting stress during the cutting process can be obtained. The calculation formula of von Mises stress in nanocutting process is:

$${\sigma }_{vonmises}=\sqrt{\frac{{({\sigma }_{x}-{\sigma }_{y})}^{2}+{({\sigma }_{x}-{\sigma }_{y})}^{2}+{({\sigma }_{x}-{\sigma }_{y})}^{2}+6({\tau }_{{}_{xy}}^{2}+{\tau }_{{}_{xz}}^{2}+{\tau }_{{}_{yz}}^{2})}{2}}.$$

The calculation formula of hydrostatic pressure is:

$${\sigma }_{hydrostatic}=\frac{{\sigma }_{1}-{\sigma }_{3}}{2}$$

Among them, ${\sigma }_{x},{\sigma }_{y},{\sigma }_{z},{\tau }_{xy},{\tau }_{xz}$ and ${\tau }_{yz}$ are the six-direction stresses of a single atom and ${\sigma }_{1}$ and ${\sigma }_{3}$ are the main stresses. The equivalent von Mises stress and hydrostatic pressure of workpiece during nanocutting process are shown in Figs. 11 and 12, respectively [44].

Fig. 11

a Dislocation distribution and b von Mises stress distribution in the subsurface of the nanocutting model [44]

Fig. 12

Distribution of a high coordination atoms and five-coordination structure and b hydrostatic stress distribution [44]

The use of molecular dynamics simulation methods to study the mechanism of nanocutting is also an important direction. The use of the method can directly characterize the various physical and chemical interactions between the tool and the workpiece in the nanocutting process and can increase the simulation types of tools and the forms of the cutting process, such as the simulation of grinding wheels and milling tools as well as bevel cutting process. Through the molecular dynamics simulation, the cutting force and subsurface deformation as well as phase change of the workpiece during the cutting process can be obtained. At the same time, in the process of using molecular dynamics simulation, improving the simulation scale is also an important topic. At present, the use of parallel calculation method can effectively improve the simulation scale and speed. The applications of molecular dynamics simulation method for the investigation of nanocutting mechanism are shown in Table 3 [37, 47,48,49].

Table 3 Nanocutting mechanism investigated by using molecular dynamics

The application of molecular dynamics to simulate nanocutting process is an effective method to study the nanocutting process, but the scale of molecular dynamics simulation method has certain limits [51,52,53]. Usually, the model scale to study the interaction characteristics between materials is below 100 nm. The multiscale simulation method effectively solves this problem. Through the combination of molecular dynamics simulation method and finite element simulation method, a method based on quasi-continuous medium is proposed. In the quasi-continuous medium-based method, molecular dynamics simulation is used to model the key area, while finite element simulation is used to model the rest, so that the establishment and simulation of large-scale models can be realized, and then, large-scale models can be established and simulated. During the cutting process, the characteristics of cutting surface roughness, cutting force, residual stress and temperature are accurately simulated, as shown in Figs. 13 and 14 [5, 55,56,57,58,59,60,61, 72, 75].

Fig. 13

Multiscale model for nanometric cutting of single-crystal aluminum [56]

Fig. 14

The atom snapshot with motion of the tool: a at the 20th time step; b at the 43rd time step [56]

Due to the anisotropy of crystalline materials, the crystal orientation has a great influence on the surface generation of the workpiece during nanocutting process [74]. Based on the slip theory, Liu [62] et al. proposed a theoretical model to analyze the influence of crystal orientation on arbitrary crystals in nanocutting process. A series of molecular dynamics (MD) simulations of nanocutting under various crystal orientations have been carried out to investigate the surface generation mechanism of the single-crystal material, as shown in Fig. 15. The simulation results show that the cutting direction determined the shape of material accumulation and the propagation direction of subsurface defects, and the width of the tool and the thickness of uncut chip determined the range of accumulation and subsurface defects [62].

Fig. 15

The slip direction and corresponding slip planes of (a) S1, (b) S2, (c) S3, (d) S4, (e) S5 [62]

Compared with traditional cutting methods, ultrasonic vibration cutting (UVC) has received more and more attention from researchers due to its advantages such as low cutting force, high cutting stability, low tool wear and good machining quality [63].

3 Tool wear

With the development of diamond cutting technology, brittle materials such as silicon and germanium can be removed by plastic cutting, but diamond tools wear fast during the machining process. Therefore, it is necessary to study the wear mechanism of the tools in the nanocutting process. Researchers have studied the wear of diamond tools with diamond cutting workpieces with different crystal orientations and found that when the rake face crystal orientation is (110), the thrust force of the tool is smaller, so the diamond tool is more wear resistant and has a longer tool life when the rake face crystal orientation is (110). Bouwelen [64] showed that as the cutting time increases, the temperature of the contact surface between the workpiece and the tool increases, and tool wear is due to the phase transition of subsurface of workpiece from the diamond (sp3) structure to the graphite (sp2) structure. Zhao [65] studied the wear of the diamond tip in AFM, analyzed the friction and wear behavior of the AFM diamond tip in the process of cutting oxygen-free copper, aluminum alloy and single-crystal silicon and analyzed the surface roughness of the processed workpiece. It is found that the use of oxygen-free or low-oxygen cutting fluids during the cutting process of copper, the use of lubricants when cutting aluminum and the use of smaller feed rates and depths when cutting single-crystal silicon while ensuring low temperature and low oxygen are all effective to reduce tool wear during the cutting process [66, 67].

In the nanocutting process, according to the machining difficulty, the materials can be divided into easy-to-machine materials and difficult-to-machine materials. Common easy-to-machine materials include aluminum, copper alloy, silver and gold, and difficult-to-machine materials include silicon, silicon carbide, germanium, selenide and other materials, as shown in Fig. 16. In the process of cutting easy-to-machine materials, the tool wear is small, and the processing stroke can reach several hundred kilometers without obvious wear. In the process of cutting difficult-to-machine materials, the tool wears a lot, even when the machining stroke reaches 1 km, the tool has already experienced serious wear. At the same time, tool life is also related to tool wear. When cutting easy-to-machine materials, the service life is longer, and when cutting difficult-to-machine materials, the service life is shorter, as shown in Fig. 17 [68].

Fig. 16

Classification of easy-to-cut and difficult-to-cut materials for diamond tools in UPDM [22, 69]

Fig. 17

Schematic map of diamond tool life for different workpiece materials [68]

In the nanocutting process, according to the wear geometry and location, diamond wear can be divided into flank wear, notch wear, groove wear, tool tip wear and crack wear, among which flank wear and notch wear are two more serious wear phenomena, as shown in Fig. 18 [68].

Fig. 18

SEM pictures of worn diamond tools [68]

By studying the nanocutting process of single-crystal copper-containing Be element, it can be found that during the cutting process, C atoms move from the diamond tool to the middle of Be atoms, but no C atoms move from the diamond tool to the middle of Cu atoms. It shows that the C element and the Be element have a chemical reaction and forms Be₂C, which intensifies the wear of the diamond tool, as shown in Fig. 19 [70, 82].

Fig. 19

Carbide formation on workpiece surface during nanocutting of CuBe [70]

In the nanocutting process, the use of nanocutting fluid can significantly improve the wear performance of the tool and provide high performance in terms of surface roughness, cutting temperature and chip morphology, as shown in Fig. 20 [71, 77, 78].

Fig. 20

Optical microscope images of tool wear examined with different zoom ratios: a) Dry, d) VGO + nAg + DW [71]

The tool wear has also strong relationship with the temperature between the tool and workpiece[76]. Cheng et al. [73] discussed the influence of temperature on the wear of tool in nano cutting process and verified the phenomenon by AFM cutting experiment. Through the comparison of cutting forces and tool wear condition, it was found that the  basic wear mechanism of diamond tool is thermochemical wear.

The friction and wear properties of different tool materials have also been studied [80]. Kuai [79] found that the wear resistance of tool of WC-7Co is significantly better than that of WC-10Co, so the appropriate tool material is a key factor for the tool to have excellent cutting performance. The test of tool wear during nanomachining has also been carried out at different levels. Singh [81] used an interferometer to collect the cutting edge wear image of the tool and measure the profile, which provided experimental support for minimizing tool wear and optimizing machining conditions, as shown in Fig. 21.

Fig. 21

(a) Measurement of new tool, (b) measurement of worn out tool after 30 cycles [81, 82]

4 Subsurface damage

Molecular dynamics simulation method is also an effective method in the study of the subsurface damage mechanism of the workpiece during the nanocutting process. Through molecular dynamics simulation of the single-crystal silicon cutting process, it can be found that during the cutting process, the subsurface has undergone a phase change of Si-I → Si-II → a-Si, and dislocations are generated at the same time, as shown in Fig. 20 [89]. The molecular dynamics simulation method can be also used to simulate the subsurface crystal morphology [90, 91]. By comparing the subsurface crystal morphology at different cutting depths, it can be found that as the cutting depth increases, the subsurface defects of the cut workpiece increase significantly. When the cutting depth is 0.7 nm, the defect thickness is about 1 nm; when the cutting depth is 1.5 nm, the defect thickness is about 2.5 nm; when the cutting depth is 2.1 nm, the defect thickness is about 4 nm. At the same time, as the cutting depth increases, the subsurface crystal structure also changes to a certain extent. When the cutting depth is less than 1.5 nm, the ratio of HCP and BCC atoms is basically stable. When the cutting depth increases to 2.1 nm, as the cutting distance increases, the ratio of HCP atoms increases, as shown in Fig. 22 [83,84,85,86,87,88]. Zhang [97] studied the nanocutting process of single-crystal copper at different cutting speeds and cutting depths through molecular dynamics simulation and found that at the same cutting speed, the cutting depth had a significant impact on the type of crystal structure on the subsurface [98, 99].

Fig. 22

MD simulation of the sc-Si nanometric cutting process. (a) The snapshot of the cutting process with the temperature in the contact region of 300 K; (b) the snapshot of the cutting process with the temperature in the contact region of 700 K. High-pressure Si-II phase is present in (a), and a metastable phase Si-IV is visible in (b) [89]

During the nanocutting process, not only phase transition appears, but also dislocations occur at the subsurface [58, 60, 63,64,65]. And the types of dislocations are different under different cutting depths, as shown in Fig. 23. When the cutting depth was 0.7 nm, the type of dislocation was Shockley dislocation. With the increase in cutting depth, Shockley dislocation gradually transformed into Stair-rod dislocation, and finally, Hirth dislocation appeared [83].

Fig. 23

Subsurface crystal structures under different cutting depths. (a) 0.73 nm, (b) 1.5 nm, (c) 2.1 nm [83]

By simulating the cutting process, the distribution of different crystal structure types during the cutting process can be obtained, and it can be found that the HCP crystal structure accounts for the largest proportion during the cutting process. At the same time, it can be found that dislocations continue to increase and eventually form grain boundaries in the cutting process, as shown in Fig. 24 [93, 94].

Fig. 24

CNA images of the transformation process between dislocations and grain boundaries [93]

Brittle materials are easy to produce crack and damage during ultraprecision machining, which has an adverse effect on the performance of cutting materials. Therefore, it is necessary to conduct in-depth research on the crack generation mechanism of brittle materials. Chen [95] carried out molecular dynamics simulation of nanocutting process on brittle gallium arsenide, studied the crack generation mechanism of gallium arsenide under different cutting parameters and found that in the process of high-speed nanocutting, the damage in the subsurface of gallium arsenide is mainly changed from dislocation to phase transformation and amorphization, and there is a high value of tensile concentration stress, which leads to the formation of crack, as shown in Fig. 25.

Fig. 25

The crack formation process in model with tool radius of 76 nm colored with the coordination number and tensile stress, when the cutting distance is (a, d) 30 nm, (b, e) 42 nm, (c, f) 54 nm [95]

To study the subsurface damage in the nanocutting process, the RDF (radial distribution function) can also be used to characterize the subsurface crystal structure changes. The RDF represents the particle density which is the function of the distance from the reference atom, and its value is the ratio of the regional density to the global density of the particles in the periodic boundary box. The regional density is the ratio of the particle number of spherical shell to the volume of the spherical shell, and the global density is the ratio of the total number of particles in the box to the volume of the box. By selecting Si–C, Si–Si/C–C, Si–C in SiC and Si–Si atom pairs in polycrystalline SiC, the RDF of SiC subsurface during nanocutting can be obtained, as shown in Fig. 26. It can be found that during the cutting process, the RDF peaks of the atom pairs are reduced, indicating that the atoms inside the subsurface crystal have migrated and the crystal structure has changed during the cutting process. And it can be found that the amorphous structure appears in the chip and the subsurface of the cutting surface, but there is no amorphous structure inside the workpiece, indicating that the amorphous state is formed on the cutting subsurface during the cutting process, as shown in Fig. 27 [97].

Fig. 26

RDF of SiC substrates before after nanoabrasion [97]

Fig. 27

The structural transformation of SiC substrates after abrasion [97]

In the research of subsurface damage mechanism in nanocutting process [100,101,102, 131], Raman spectroscopy is a fast non-destructive testing method used to characterize the structure of materials. Raman spectroscopy can detect the phase transition of the crystal from crystalline to amorphous during the nanocutting process, and at the same time, it can detect the residual stress during the nanocutting process. In the polycrystalline germanium cutting process, Raman spectroscopy is used to characterize the deformation and damage of the subsurface during the cutting process. When a tool with a rake angle of -30° is cutting along the (100) direction of the polycrystalline germanium surface, the Raman spectrum Ge-I bands of the machined surface with different cutting depths are shown in Fig. 28. It can be found that the Raman spectrum peak at 300 cm⁻¹ decreases with the increase in the cutting depth, indicating that the crystal defects increase with the increase in the cutting depth. At the same time, it can be found that when the cutting depth is less than 131 nm, there is almost no Raman spectrum peak shift, while when the cutting depth is between 131 and 169 nm, a certain Raman spectrum peak shift will occur, indicating that the amorphous germanium is formed in the subsurface, as shown in Fig. 29 [104].

Fig. 28

Raman spectra of the machined surfaces with different UCTs after taper cutting (θ:-30°, cutting orientation: 001(100)) [104]

Fig. 29

Comparison between the Raman spectra of the machined and unmachined surfaces of germanium. The residual stresses calculated based on the shift in the Ge-I peak are shown above the Raman spectra (θ:-30°, cutting orientation: 001(100)) [104]

Raman spectroscopy can also be used to measure the subsurface residual stress of the workpiece during the cutting process. For example, the subsurface stress can be obtained by performing Raman spectroscopy on the subsurface during the SiC cutting process, as shown in Fig. 30 [105].

Fig. 30

Residual stress analysis [105]

To study the subsurface physical change mechanism of the workpiece, nano-FTIR spectroscopy can be used for detection and analysis. Nano-FTIR spectroscopy is a kind of infrared near-field spectroscopy based on Fourier transform, which can be used to perform spectral analysis on the surface of materials and display surface changes, as shown in Fig. 31 [106].

Fig. 31

Subsurface nano-FTIR spectroscopy experiments on well-defined multilayer samples. a Schematics of the experiment and PMMA/PS test sample, including the topography line profile of a d₂ = 85-nm-thick PS layer covering the t₂ = 59.4-nm-thick PMMA layer on Si. b Reference nano-FTIR phase spectra recorded on thick PMMA and PS layers. c Subsurface nano-FTIR phase spectra of PMMA at different depths d₂ below PS (average of 50 spectra (80 spectra for d₂ ≥ 85 nm), 30-s acquisition time per interferogram, × 128 zero filling, 17 cm⁻¹ spectral resolution). Black arrows in c indicate the spectral peak shift [106]

5 Cutting force

The cutting force in the nanocutting process is an important property to characterize the nanocutting process [103, 115, 117, 119,120,121]. In the nanocutting process of SiC, the lower value of the cutting force represents that the cutting mode is likely to be brittle cutting, and the higher value represents that the cutting mode is likely to be plastic cutting. So the cutting force amplitude can also be used to determine whether the cutting process is plastic cutting or brittle cutting, as shown in Fig. 32 [107,108,109,110,111, 122, 123]. The tools used for the cutting force detection are summarized in Table 4.

Fig. 32

Cutting force and acoustic emission data to distinguish brittle-regime with ductile-regime machining [107]

Table 4 Tools used in measurement of cutting force by molecular dynamics and experiments

By studying the change in cutting force during the nanocutting process [124, 127, 128, 150], the cutting force in x and y directions at different cutting depths and the formation mechanism of cracks during the cutting process can be acquired, as shown in Fig. 33. The dotted and solid line in Fig. 34 represents the cutting force in x and y directions at a cutting depth of 4 nm, as shown in Fig. 33. In the process of nanocutting of lutetium oxide, when the cutting stroke is before 45 nm, the cutting force presents a tendency of increasing first and then fluctuating steadily. When the cutting stroke is at 47 nm-50 nm, the cutting force begins to drop sharply, and at this time, it can also be found that there is a crack inside the workpiece. Therefore, the change in cutting force can also show the existence of internal cracks in the workpiece during the cutting process [113].

Fig. 33

Curve of cutting force in different models (cutting speed = 500 m/s): Models 1–4 refer to cutting depth 1 nm, 2 nm, 3 nm and 4 nm, respectively [113]

Fig. 34

Crack formation process in Model 4 (cutting speed = 500 m/s, cutting depth = 4 nm): (a) Before steady stage. (b) Steady stage. (c) Before crack initiation. (d) Crack initiation. (e) Crack extends. (f) Further extension [113]

In the nanocutting process, cutting force measurement has always been an important issue. By establishing the relationship between the cutting force, the normal force and the material removal rate, a model for predicting the cutting force during the nanoscratch process was obtained. Finally, it is found that the predicted results are in good agreement with the experimental results, as shown in Fig. 35 [116].

Fig. 35

(a) Calculated material removal rate during machining cycles. (b) Predicted and measured lateral force. (c) Predicted and measured normal force [116]

In the ultraprecision cutting process, due to workpiece installation errors, the cutting surface of the workpiece will be tilted, which requires a lot of time to adjust the workpiece and the tool. In another case, because the processed surface is a curved surface, it is necessary to know the curved surface information in advance before designing the processing path, and the design process is complicated. In order to solve the above problems, an adaptive processing method was proposed, which can automatically design the processing path according to the shape of the processed surface, therefore achieving high-efficiency ultraprecision processing. The adaptive processing method can adopt the combination of AFM and ultraprecision machine tools to achieve constant cutting force during processing, but this method has the disadvantage of low processing accuracy. By adopting a cutting force control system based on a flexible drive mechanism, high-precision adaptive machining can be realized. By controlling the expected loading force, a relatively stable cutting depth can be obtained. It can be found that when the applied loading force is 12mN, 18mN, 24mN, 30mN, 45mN, 60mN and 90 mN, the average cutting depth is 59 nm, 83 nm, 112 nm, 139.7 nm, 179.2 nm, 228.6 nm and 309.5 nm, respectively, as shown in Fig. 36. The shape of the processed curved surface is shown in Fig. 37 [114].

Fig. 36

(b) The cutting depths at different reference forces for the copper [114]

Fig. 37

The three-dimensional fabrication of the (a) sine-shaped microstructure and (b) microstructure array on copper surface [114]

6 Friction and friction coefficient

When the diamond tool is cutting the surface of the workpiece, a certain amount of friction and wear will occur between the tool and the workpiece. When the friction and wear reach a certain level, the machining accuracy of the tool is reduced, and the tool needs to be replaced for the next cutting. Therefore, it is a very necessary problem to study the friction phenomenon and mechanism in the cutting process. The coefficient of friction during the cutting process can be obtained by calculating the ratio of the cutting force to the loading force during the cutting process, as shown in Figs. 38 and 39 [34, 125, 126, 129, 130, 133,134,135].

Fig. 38

SEM micrographs showing scratch wear track for different loads and scratch passes [125]

Fig. 39

Effect of the load and the number of passes on the material removal parameter (fab) [125]

The material machinability can also be judged by the friction force and the friction coefficient. Islam [84] found that the friction coefficient was large when the material was removed by grinding, while the friction coefficient was small when it was removed by cutting, which shows that efficient removal of material can be more easily achieved by cutting, as shown in Fig. 40. At the same time, it can also be found that as the cutting depth increases, the friction coefficient also increases. Finally, it was found that the friction coefficients of different materials were not the same. For example, the friction coefficient of Cu is about 0.5, but it is about 0.4 for Ni.

Fig. 40

The friction coefficient with respect to the depth of cut for different tool geometries and different materials [128]

The accurate determination of the friction coefficient during nanoscratch is a valuable research problem in the field of nanofriction [134, 136]. Carreon [132] simulated the actual working condition of the nanoindenter by considering the spherical shape, used the established analytical formula for the analysis of friction coefficient, then compared with the experiment results and found that the description of the friction coefficient is more accurate by considering the spherical shape of the nanoindenter, as shown in Fig. 41 [137].

Fig. 41

Plowing friction coefficient curve of CaF2 using PAVER model. Experiments (solid orange and blue), Lafaye et al. model ($\omega$ = 0, dashed green), PAVER model (${f}_{A}$ = 1.067; 240 nm) (red dot dashed), PAVER model (${f}_{A}$ = 0.996; 480 nm) (purple dotted). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.) [132]

7 Nanocutting experiment

Nanocutting experiments can be implemented in ultraprecision machine tools and nanoscratch instrument. In the nanoscratch test, a nanoscratch tester is used for the scratch test, as shown in Fig. 42 [138, 142,143,144,145, 148, 149]. The facilities used in the nanocutting experiments are shown in Table 5.

Fig. 42

Experimental setup and taper scratch schematic diagram [138]

Table 5 Facilities used in the validation of nanocutting experiments

By conducting nanoscratch experiments on copper alloys, it is possible to obtain the nanoscratch morphology of copper alloys under different phases, as well as the relationship between the scratch depth and the scratch displacement, as shown in Table 6 and Fig. 43 [151]. Among them, the maximum loading force is 10uN, 20uN, 30uN and 40uN, respectively.

Table 6 Profiles obtained along the length of each groove [139]

Fig. 43

Scratch tests conducted to determine the minimum chip thickness and the elastic recovery of the (a) α phase and (b) β phase [139]

Nanocutting can be used to realize the manufacture of nanostructures. By using the AFM diamond probe to scratch on the surface of the silicon-based workpiece and apply a certain vertical load while scratching, the manufacture of nanodots, linear nanostructures, nanobosses and nanocharacters can be realized [116, 140], as shown in Figs. 44 and 45. This nanocutting method does not need to apply voltage to the AFM probe, so it is a very promising nanofabrication method suitable for the manufacturing process of electrical insulators such as quartz and glass in future.

Fig. 44

(a) Friction-induced nanodots on Si(100) by line scratch with D = 10 nm, N = 100 and Fn = 10 μN; (b) surface isolated mesa by scanning scratch with N = 15 and Fn = 85 μN; (c) nanoline array by line scratch with N = 100 and Fn = 45, 55, 85 and 135 μN, respectively; (d) nanowords of “TRI” by line scratch with N = 50 and Fn = 50 μN [30]

Fig. 45

Comparison of hillocks on different materials created by N = 200 and Fn = 50 μN. (a) Si(100), (b) monocrystalline quartz and (c) glass [140]

Through the nanoscratch experiment, the material removal mechanism can be studied when the cutting depth is more than ten nanometers. By selecting GaAs as the nanoscratch experiment object, and selecting the loading force of 27μN, 30μN and 33μN for the scratch test, the scratch depths of 9.2 nm, 11 nm and 17 nm were obtained. It is found that when the depth of the scratch is less than 11 nm, the material is removed by extrusion, and when the depth of the scratch is greater than 11 nm, the material is removed by cutting. Therefore, when the cutting mechanism is extrusion, only burrs are formed in the cutting process, and when the cutting mechanism is cutting, chips are formed, as shown in Figs. 46 and 47 [141, 151,152,153,154,155,156,157,158,159].

Fig. 46

(a,c,e) Typical AFM images and (b,d,f) cross sections of nanochannels fabricated using normal load of 27 μN, 30 μN and 33 μN, respectively [141]

Fig. 47

SEM images of the machined nanochannels for different normal loads: (a) 27 μN, (b) 30 μN, (c) 33 μN [141]

At the same time, in the GaAs nanoscratch experiment, the subsurface properties can be studied. As one of the direct machining methods, the machining method based on the AFM tip inevitably leads to the subsurface damage of the sample due to the contact between the tip and the workpiece, and the subsurface defects have a decisive influence on the performance of GaAs-based devices [160]. Therefore, good subsurface quality is very important for the application of GaAs-based devices. However, the subsurface damage mechanism of GaAs in the nanoscratch process has not been fully understood. Observation of the GaAs subsurface after nanoscratch by transmission electron microscope (TEM) shows that defects, dislocations and amorphous structures are generated on the GaAs subsurface during the scratching process, which causes the damage of the subsurface, as shown in Fig. 48 [141].

Fig. 48

(a)-(d) HRTEM images of regions 1, 2, 3 and 4 marked in Fig. 10(a). Stacking faults can be observed in (a), (c) and (d). Furthermore, (b) and (d) show nanocrystallines and amorphized layers, respectively [141]

In the nanocutting experiment research, the ultraprecision lathe (Moore Nanotech 350) can be used to carry out the nanometric taper cutting experiment. In the taper cutting experiment of the ultraprecision lathe, the cutting depth was gradually increased from 0 to 100 nm, and the taper was kept at 0.02°. In the experiment, taper cutting experiments with cutting depths of 10 nm and 24 nm were carried out, and the subsurface crystal morphology during the cutting process was obtained, as shown in Fig. 49. It can be found that as the cutting depth increases, the thickness of the subsurface amorphous layer decreases from 5-8 nm to 3-5 nm. And when the cutting depth is 10 nm, there is no crystal deformation under the amorphous layer. Finally, cracks were also found on the cutting subsurface, which also reflects the brittle nature of SiC [161, 162].

Fig. 49

TEM observations of the (a), (b) amorphous layer, (c), (d) linear deformation zone and (e), (f) nanometric crack in the subsurface. The white spots in the high angle annular dark field image (f) are silicon atoms [161]

In the nanoscratch experiment, Raman spectroscopy can be used to test the subsurface damage mechanism during the scratching process and to characterize the phase transition process. In the unstressed state, the peak of the Raman spectrum of the workpiece subsurface reaches nearly 10,000, but it decreases slightly during plastic cutting, and the peak is 9188, indicating that the workpiece subsurface has a certain elastic deformation during the plastic cutting process, but it does not produce amorphous structure and there is no phase change. During the brittle–plastic transition cutting process, the peak value dropped sharply to about 1000, indicating that the subsurface of the workpiece had an amorphous structure during the brittle–plastic transition cutting process. In brittle cutting, the peak value is only about 150, indicating that a large amount of amorphous structure is produced on the subsurface of the workpiece during brittle cutting, as shown in Fig. 50 [163, 174].

Fig. 50

Raman spectra of: (a) original surface, (b) ductile regime, (c) DBT regime, and (d) brittle regime in the varied-load scratch tests [163]

8 Challenges and prospects

The research of nanocutting is carried out from two aspects, namely ultraprecision machine tool processing and nanoprobe processing [164,165,166, 185,186,187, 190,191,192]. The use of AFM probes for nanocutting is also a very effective nanoscale processing method [46, 170]. The use of AFM probes for processing has the characteristics of low cost, flexible control and high precision, as shown in Fig. 51. The fabrication of micro–nanotrenches and 3D micro–nanostructures can be achieved by AFM probes. At the same time, by integrating chemical, thermal, electrical and magnetic effects in the tip of the AFM probe, the AFM processing efficiency can be further increased [171, 173,174,175,176,177,178,179,180,181,182, 184, 188, 189, 193, 194, 200].

Fig. 51

Schematic of the AFM tip-based nanomechanical machining system. (b) Schematic of the conventional cutting system. K1 is the elastic constant of the AFM cantilever. K2 is the equivalent elastic constant of the tool system. Ks is the equivalent elastic constant of the support of the machine tools [171]

The traditional AFM scratching process has the problems of low processing efficiency and low material removal rate. Wang [167] proposed a nanomilling method based on AFM tip to improve processing efficiency and material removal rate and conduct nano-channel processing on single-crystal silicon to study its processing mechanism. The wear rate of ultra nanocrystalline diamond (UNCD) atomic force microscope (AFM) tips in AFM applications is significantly lower than that of silicon and silicon nitride tips, so they have great potential for effective use in tip-based nanomanufacturing processes, as shown in Fig. 52 [168, 183, 195].

Fig. 52

AFM images obtained at different stages of Test 1 conducted on the silicon samples: (a) 3D AFM image of the unworn nanotool, (b) 3D AFM image of the nanotool after a total nanomilling distance of 24 mm, (c) cross-sectional AFM data from section A–A at different stages of the experiment and (d) cross-sectional AFM data from section B–B at different stages of the experiment [168]

Recently, a new type of field emission scanning probe lithography system (FE-SPL) has been developed, which uses probes that can perform field emission. There is a certain voltage between the tip of the system and the substrate. Due to the localized effect of the tip of the electric field, when the tip of the tip is close enough to the substrate, only a very low voltage can be applied to achieve the Flower–Nordheim field emission and achieve the effect of the pattern exposure, as shown in Figs. 53 and 54 [169, 196,197,198,199, 201,202,203].

Fig. 53

From classical electron beam lithography (EBL) toward a novel field-emission scanning probe lithography (FE-SPL) system with so-called active cantilever. These cantilevers are equipped with piezoresistive bending senor, a thermomechanical actuator and a sharp tip. In this manner, lithography and imaging are employed using the same cantilever [169]

Fig. 54

Donut-like features formed by a superimposed centered ablation of resist with surrounding crosslinking, measured after a wet development step. The spot exposure test array was imaged by SEM (a) and AFM (b). The donut features were induced by a single-spot exposure FE-SPL process (AFM topographic image and section graphs were not tip-convolution corrected). (c) AFM image showing a fragment of test 1.4-mm-long features exposed without interrupting of the exposure process [169]

Based on the research results and recent discoveries above, the research directions of nanocutting can be proceed from three aspects as following:

• (1) In the nanocutting process, the wear between the tool and the workpiece has a direct impact on the machining surface accuracy and tool life. Therefore, the friction mechanism in the nanocutting process also needs to be studied in depth. The tool is usually regarded as a rigid body in the simulation process, but in the actual process, the impact of tool wear on the machining process is also very significant, so the understanding of the friction and wear behavior and mechanism in the nanocutting process will be further deepened.

• (2) Nanoscale cutting by using AFM technology will be an important research direction in the field of nanocutting. However, it still has the problem of low cutting efficiency at the same time. Therefore, the development of high-speed AFM cutting technology is a very challenging direction.

• (3) Another direction of nanocutting technology development is the single-atom operation technology. In the single-atom operation method, STM is usually used to realize the movement of a single atom. However, using STM to move a single atom is inefficient, so it is necessary to develop STM technology for moving atoms in large scale by combining various technology from the fields of electricity, magnetism, heat and force.

• (4) At this time, the removal mechanism of atoms in atomic scale is still not well understood, which hinders the development of material removal technology in atomic scale. In future, it is necessary to increase the research of the relationship between potential and van der Waals force, electrostatic force and Lorentz force of atoms and to develop new atomic-scale processing technology from the aspect of releasing the interaction force between atoms.

9 Conclusions

The paper reviews cutting mechanism, tool wear mechanism, subsurface damage mechanism, cutting force, friction force, friction coefficient and nanocutting experiment in the nanocutting process and discusses all aspects from base theories and phenomena. In addition, the challenges and prospects of nanocutting technology are puts forward, and the views are summarized at the end. Meantime, it is believed that nanocutting technology still has certain shortcomings in terms of scale and efficiency. The conclusions are summarized as follows:

• (1) The nanomanufacturing technology has widespread influence on the applications of metamaterials, optics, mechanics, quantum devices, 2D materials, nanochannels and nanoconstrictions, which shows that nanomanufacturing is a basic and key technology for the development of other technologies.

• (2) The ratio of cutting depth to cutting edge radius (defined as the relative sharpness of the tool, RTS) is a key factor to realize nanocutting. And by increasing the depth of cut when the RTS is unchanged, the primary deformation zone (PDZ) area will also increase and will lead to an increase in internal defects of the workpiece.

• (3) The acquiring of critical cutting depth is decisive for the brittle–plastic transition in the processing of brittle materials, and by increasing the temperature of the cutting materials, the critical cutting depth can be increased, which leads to the reduction of processing difficulty for difficult-to-machine materials such as ceramics.

• (4) The materials can be classified to easy-to-cut and difficult-to-cut materials for diamond tools. And the tool wear can be explained from the aspect of chemical reaction. Also, the use of nanocutting fluid can significantly improve the wear performance of the tool. At last, the friction and wear properties of different tool materials are different, so it is important to choose the proper material for the tool.

• (5) In the nanocutting process, the subsurface damage is reflected in the form of dislocation, phase transformation, amorphization and crack, and with the cutting depth and cutting distance, increasing the subsurface damage also changed and increased. Then, the RDF (radial distribution function) can also be used to characterize the subsurface crystal structure changes.

• (6) The cutting force has significant influence on the surface quality of the machining workpieces, so in order to achieve high-efficiency ultraprecision processing, it is necessary to control the cutting force and keep it relatively stable.

• (7) The material machinability can be judged by the friction force and the friction coefficient. And the friction coefficient of the material can be acquired by experiment and established analytical formula.

• (8) The nanocutting experiments can be implemented in ultraprecision machine tools and nanoscratch instrument, and by the use of cutting force detector, transmission electron microscope (TEM), Raman spectroscopy, in which the cutting force, cutting morphology and subsurface phase change can be acquired.

• (9) The wear between the tool and the workpiece has a direct impact on the machining surface accuracy and tool life for ultraprecision machining method. So the research of enhancing the ability of wear resistance for the tool is expected to be further deepened. Also the development of high-speed AFM cutting technology is a very challenging direction. At last, it is necessary to develop STM technology for moving atoms in large scale by combining various technologies from the fields of electricity, magnetism, heat and force. From this aspect, the field emission scanning probe lithography system is a feasible method to solve the problem of current nanomanufacturing technology.