Advertisement

Nanomanufacturing and Metrology

, Volume 2, Issue 3, pp 177–185 | Cite as

Study on Diamond Cutting of Ion Implanted Tungsten Carbide With and Without Ultrasonic Vibration

  • Jinshi Wang
  • Fengzhou FangEmail author
  • Guangpeng Yan
  • Yuebin Guo
Original Articles
  • 140 Downloads

Abstract

Tungsten carbide (WC) is an outstanding mold material used in precision engineering. In the manufacturing of high-quality surface with nanometric roughness, ultraprecision diamond cutting is always employed. As a typical difficult-to-cut brittle material, however, WC leads to significant tool wear during the process. For the WC that contains cobalt as a binder, this classical problem has been traditionally mitigated by ultrasonic-assisted cutting. While for a binderless WC, experimental work has shown that ultrasonic vibration may aggravate tool wear and deteriorate surface integrity. Therefore, surface modification of binderless WC by ion implantation is investigated in this paper. Material lattice structure, mechanical properties and nanometric cutting process of normal and implanted WC are experimentally investigated. Molecular dynamics simulation is conducted to understand the processes from atomic-scale. Deformation mechanism, stress field and cutting forces are analyzed. The results reveal that after ion implantation, the surface layer of WC becomes amorphous and softer, which significantly improves the chip formation and the machinability at nanoscale.

Keywords

Nanometric cutting Surface modification Ultrasonic vibration Brittle material 

1 Introduction

Sintered tungsten carbide with high hardness and wear resistance is a widely used industrial material. Currently, WC components are mainly produced by grinding [1]. In contrast, diamond cutting is more powerful in the ultraprecision machining of freeform optics and microstructures [2]. However, it is very difficult to cut WC due to its hard and brittle nature, which causes severe tool wear and poor surface integrity. Many efforts have been exerted to overcome these problems by the use of ultrasonic vibration-assisted cutting (UVAC), a technique for the machining of steel, brittle materials and functional surfaces [3]. For example, effects of cutting parameters such as cutting speed and nose radius have been studied, and many researches have shown an obvious improvement in machinability by UVAC [4, 5, 6].

On the other hand, cutting on binderless tungsten carbide (BL-WC) has not been well understood. Unlike the classical WC with a binder material of cobalt or nickel, BL-WC has either a small binder phase, or the WC grains are united by a nonmetallic material. As a result, it becomes harder and more wear-resistant, which is preferred for applications such as precision glass molding, but also makes the machining process more challenging. For example, a systematic study [7] on the influences of its material properties and process parameters showed that BL-WC is more prone to fracture than WC with a binder phase of Co or Ni. The recommended instantaneous uncut chip thickness is merely 4 nm to achieve a high-quality surface in the ductile mode. This low rate of material removal would require a long machining time. There have also been reports on the disadvantages of ultrasonic vibration in the machining of other brittle materials. For the superhard alumina crystal, tool wear is more serious in UVAC [8]. Surface integrity is also reported to become worse in the ultrasonic grinding of glass ceramic [9]. These results imply that vibration may have a negative influence on the machining process. Intuitively, there are two potential risks in the use of UVAC on a superhard material such as BL-WC. First, the high-frequency impact between the tool tip and the workpiece could break the tool edge. Second, the small amount of material removed in each vibration cycle requires a low cutting speed, which would increase the actual cutting distance and accelerate tool wear. Therefore, it is necessary to explore a new approach to further reduce the tool wear and improve the machined surface integrity. In addition, numerical simulation is also important to understand the mechanism of vibration-assisted cutting. For example, the finite element method was used to study the vibration-assisted micro-milling of magnesium alloy [10]. By contrast, molecular dynamics (MD) is more suitable for simulating nanometric cutting with a strong size effect [11]. MD has been employed to study the vibration cutting of brittle material such as monocrystalline silicon [12, 13] at atomic scale, but cutting on WC with a polycrystalline structure is rarely reported.

In this work, both ultrasonic vibration and ion implantation are employed to investigate their effects on the diamond cutting of BL-WC. Ion implantation is a surface modification method that softens the material and reduces its brittleness [14], which has been successfully applied to the nanometric cutting of single crystals including silicon, germanium and silicon carbide [15, 16]. Nitrogen ion implantation has also been employed to increase the mechanical strength and wear resistance of WC [17], but in that application, WC was used as a cutting tool material rather than a workpiece. Whether ion implantation can facilitate the cutting of WC is not yet known and is the topic addressed in this paper. The experimental results in Sects. 4.1 and 4.2 show that after ion implantation, amorphization occurs in the surface layer and the hardness is reduced. Chips with shear bands are also observed in the cutting test of implanted WC, which indicates a significant improvement in the machinability. In Sect. 4.3, the MD simulation results of the nanometric cutting of polycrystalline/implanted WC with and without vibration are presented to reveal the underlying mechanisms.

2 Experimental Investigation

The BL-WC material used in this work is the RCCFN type (Nippon Tungsten Co., Ltd.) whose components include WC, TiC and TaC. The average grain size is 0.6 μm. Gold ion implantation with 7 MeV energy and 6.4 × 1014 cm−2 dose, which forms a modified layer with 1 μm theoretical thickness, is conducted by a tandem electrostatic accelerator at room temperature. The beam scan area is 1 cm2, and the current is maintained at ~ 100 nA during the implantation. Nanoindentation and selected area electron diffraction (SAD) are used to study the modification of the mechanical strength and the material lattice. Using a Berkovich tip, the maximum indentation depth and strain rate are 0.3 μm and 0.05 s−1, respectively. A cross-sectional sample with 44 nm thickness is prepared by focused ion beam (FIB) for the SAD. The influence on machinability is investigated by taper grooving test using a single crystalline diamond tool with 0.5 mm nose radius, 0°rake angle and 150 mm/min cutting speed. The chip of implanted WC is analyzed using a scanning electron microscope (SEM) to study the material removal process.

Four groups of 2-m cutting tests are conducted to compare the effects of ion implantation and ultrasonic vibration using an ultraprecision lathe (Moore, Nanotech 250). As shown in Fig. 1, the workpiece rotates with the spindle and moves in the x direction (feed). The diamond tool moves in the z direction, which determines the cutting depth. As a result, the tool path relative to the workpiece is a spiral line and the screw pitch is determined by the rotation and feed speeds. At the same time, the tool vibrates along an elliptical locus at an ultrasonic frequency of 93 kHz, which is realized by an extra ILSONIC module produced by INNOLITE Co., Ltd. The major and minor axes of this ellipse lie in the cutting (y) and depth-of-cut (z) directions, respectively, with amplitudes Ac and At. In elliptical ultrasonic vibration-assisted cutting (EUVAC) on brittle material, there are two critical thicknesses that characterize the material removal in each spindle revolution and tool vibration cycle. The tm1 is the maximum undeformed chip thickness that is always used in the conventional diamond turning process [18]. It is determined by the tool nose radius (Rnose), cutting depth (D) and feed per revolution (f), as shown in Fig. 2a and formula (1). The tm2 is another special thickness that indicates how much material is removed in one vibration period, as shown in Fig. 2b, which is approximated as the product of the cutting speed (vcut) and the vibration period (Tvib) as the frequency is high enough (formula (2)). For a brittle material, a smooth surface can be realized only when material is removed at nanometric scale. In this study, therefore, the tm1 is 100 nm in all the test groups. The tm2 is 190 nm and 250 nm when cutting the normal and implanted WC, respectively. The detailed parameters are listed in Table 1.
Fig. 1

Experimental setup for diamond cutting test (x feed direction, y cutting direction, z depth-of-cut direction)

Fig. 2

Illustration of material removal in EUVAC (x feed direction, y cutting direction, z depth-of-cut direction). a The ‘O1’ is the center of the round cutting edge (solid arc), which moves to ‘O2’ after the workpiece completes one rotation; the cutting edge is the dashed arc then. b The tool advances a distance of tm2 in one vibration period

Table 1

Details of diamond cutting test

Parameters

Values

Single crystalline diamond tool

Nose radius: 0.468 mm

Rake angle: − 30°

Clearance angle: 15°

Cutting depth

0.8 μm

Cutting distance

2 m

Cutting speed

18 mm/s (for normal WC)

23 mm/s (for implanted WC)

Ultrasonic frequency

92.9 kHz

Amplitude in cutting direction (Ac)

Approx. 1–2 μm (peak to valley)1

Amplitude in thrust direction (At)

Approx. 0.5 μm (peak to valley)1

Cooling

Mist

Test 1

Normal WC, CC2

tm1: 100 nm

Test 2

Implanted WC, CC

tm1: 100 nm

Test 3

Normal WC, EUVAC

tm1: 100 nm, tm2: 190 nm

Test 4

Implanted WC, EUVAC

tm1: 100 nm, tm2: 250 nm

1The amplitudes are calculated values

2CC: conventional cutting without ultrasonic vibration

$$ t_{m1} = R_{\text{nose}} - \sqrt {R_{\text{nose}}^{2} + f^{2} - 2f\sqrt {2R_{\text{nose}} D - D^{2} } } $$
(1)
$$ t_{m2} = v_{\text{cut}} T_{\text{vib}} $$
(2)

3 Molecular Dynamics Analysis

The MD method is used to study the influences of vibration and implantation on the nanometric cutting, and the model is shown in Fig. 3. A polycrystalline WC workpiece containing 20 grains and 253,438 atoms is generated by 3D-Voronoi tessellation using Atomsk [19]. Each grain comprises the hexagonal close-packed (HCP) lattice and a random orientation. The workpiece scale is 60 × 30 × 1.5 nm. Thirty tungsten particles with 25 keV energy are implanted into the polycrystalline WC model to mimic the surface modification. The diamond tool is set as a rigid body to reduce the simulation time, and different edge radii (10 and 30 nm) are considered to study the influence of edge blunt, which always occurs in the cutting of hard material. The rake and clearance angles are 0° and 12°, and the cutting depth and speed are 10 nm and 40 m/s, respectively. In the simulation of vibration cutting, the tool also vibrates at 11 GHz along an ellipse with 8 nm major axis (in y direction) and 4 nm minor axis (in z direction). An analytic bond-order potential is used to describe the interaction between the W–W, C–C and W–C pairs [20], and periodic boundary condition is used in x dimension. The MD simulation and outcome data analysis are conducted by Lammps and Ovito [21, 22]. Table 2 lists details of the simulation parameters.
Fig. 3

Nanometric cutting model of polycrystalline WC

Table 2

Details of molecular dynamics simulation

Parameters

Values

Workpiece material

Polycrystalline and implanted WC

Workpiece size

60 nm × 30 nm × 1.5 nm

Potential function

Bond-order potential

Implantation particle

Tungsten

Implantation energy

25 keV

Tool material

Diamond (rigid body)

Rake and clearance angles

0° and 12°

Edge radius

10 nm, 30 nm

Cutting depth

10 nm

Cutting speed

40 m/s

Tool vibration frequency

11 GHz

Major and minor axes of ellipse

8 nm and 4 nm

Environment temperature

293 K

Time step

2.0 fs for nanometric cutting

0.1 fs for ion implantation

Periodic boundary condition

x dimension

4 Results and Discussion

4.1 Surface Modification

Figure 4a is the modification of the material lattice. The SAD of the normal WC exhibits a shows point matrix which indicates a crystalline grain phase. After ion implantation, grain boundaries still exist, but amorphization has occured in the grains because there are rings in the SAD pattern. In addition, some spots also exist. Therefore, the implanted surface is a mixture of crystalline and amorphous phases. Changes in the crystal lattice lead to an obvious decrease in material strength. Nanoindentation shows that the averaged hardness and Young’s modulus are reduced from 28.6 to 19.9 GPa and from 715.8 to 535.3 GPa, respectively (Fig. 4b). (The Young’s modulus of normal WC from nanoindentation is similar to the theoretical value of 710 GPa [20], which shows a good performance of the potential function we used.) In the taper grooving test, the surface of normal WC is full of cracks, even when the cutting depth is extremely small. In contrast, both the size and density of the cracks are significantly reduced after implantation (Fig. 4c). Furthermore, curled chips are found only on the surface of the implanted WC (Fig. 4d). To observe the inner details, FIB is used again to slice the chip. Firstly, the chip shape is resulted from a large plastic deformation process. This does not occur during the cutting of normal WC, where material is removed through brittle fracture. Secondly, the features on two sides of the chip are very different. On the newly formed surface, there are numerous imbricate structures. During chip deformation, this surface is stretched and bears a tensile stress. As a result, fractures occur at smaller scale. These fractures should originate from material imperfections such as grain boundaries and implantation defects. In contrast, shear bands occur on the other side evolving from the free surface before the cutting. This serrated morphology is characteristic of hard-alloy cutting [23] and is caused by periodic adiabatic shear deformation. Unlike brittle fracture, shear is a chip formation mechanism of highly localized plastic deformation [24]. Therefore, these results verify the improvement in the machinability of WC by ion implantation.
Fig. 4

Results of surface modification on material properties and nanometric grooving. a Cross-sectional TEM image and SAD patterns. b Load–displacement curves of nanoindentation. c, d SEM observation of groove surface and chip morphology

4.2 Diamond Cutting

Figures 5 and 6 show the tool wear and machined surface of each test group (see Table 1). In the conventional cutting of normal WC (Test 1), a 3-μm-width wear land with microgrooves occurs on the flank face, which is caused by friction and scratching. Under elliptical vibration (Test 3), edge chipping is the major wear type. In contrast to frictional wear, which is a gradual process, chipping is more violent and is caused by high-frequency impact. Especially, when cutting superhard material, cleavage fracture of the diamond can be induced. The wear is reduced after surface modification. The tool edge maintains its integrity in the conventional cutting of implanted WC (Test 2). In the EUVAC (Test 4), the edge chipping also becomes lighter, and only a 1.2-μm-width wear land occurs on the flank face, which is much smaller than that in Test 1. In addition, some WC material adheres to the tool edge in the cutting without ultrasonic vibration (Tests 1 and 2). The reason is the high temperature caused by the friction between the chip and rake face, as well as the large plastic deformation in the cutting region. In EUVAC, temperature drops as the tool separates from the workpiece.
Fig. 5

SEM observation of tool edge wear

Fig. 6

Machined surface: a topology and b roughness evolution

In this work, mirror surface can be achieved only on the implanted WC. Detailed observation by atomic force microscope (Fig. 6a) shows that the surface topology is also influenced by grain boundaries, and the scrape marks imply the occurrence of tiny imperfections on the tool edge in the conventional cutting (Test 2). The grooves on the surface machined by EUVAC (Test 4) are caused by the flank wear shown in Fig. 5. Figure 6b is the evolutions of surface roughness in Tests 2 and 4. The data are obtained using a white light interferometer. In EUVAC, the machined surface becomes rougher after the initial 0.81 m cutting length, due to the deterioration of the tool flank face. In contrast, the roughness is more stable in the conventional cutting on implanted WC, which exhibits the lowest tool wear.

4.3 Mechanisms

In this section, results of the MD simulation are analyzed to gain a better understanding of the phenomena discussed above. In the conventional cutting of normal WC, there exist three kinds of grain deformation processes (Fig. 7a). First, a grain can be completely removed from the substrate, and the grain boundary then becomes a part of the shear band. Second, a grain can be segmented by the shear band, whereby only a portion is removed. As deformation along grain boundaries consumes less energy than bond breakage in grains, the first process is the major mechanism of chip formation. Third, the HCP lattice can change and undergo phase transformation. This always takes place in the subsurface near the tool. In vibration cutting, the process is intermittent and extra energy is transferred to the workpiece through high-frequency vibration. As a result, more in-grain deformations occur as shown in Fig. 7b. In addition, the angle between the cutting velocity and the tool rake face (α in Fig. 7c) periodically varies during vibration cutting. In some instances, the effective rake angle becomes much negative, which induces higher compressive stress. As a result, more amorphous structures occur in the chip.
Fig. 7

Chip formation in the a conventional and b vibration cutting of normal WC, c Comparison of chip morphologies (In this and the following figures, an ellipse with a red spot is provided in the vibration cutting simulation to indicate the current tool position in one cycle.)

Figure 8a is the hydrostatic and maximum shear stress fields in the conventional cutting of normal WC. A high-pressure (up to 13 GPa) region occurs in the vicinity of the cutting edge due to its round shape. Shear stress tends to concentrate in the grains with ordered lattice, and is lower at grain boundaries. The stresses are released once a piece of material is removed from the substrate along the shear band. Figure 8b shows the stress fields at different instants in a vibration cycle. During the cut-in process, the highest hydrostatic pressure increases to 44 GPa and the high-pressure region extends. While during the separation, the compressive region shrinks and tensile region increases. Then, the high tensile stress induces a microcrack at a grain boundary when the chip adhering to the rake face is pulled upward. Tensile stress near the crack tip reaches 40 GPa, which is lower than the theoretical value of a WC nanoparticle (48 GPa) [25]. This decrease in material strength is caused by the grain boundaries in our model. The evolution of shear stress field is ordinary. It increases during the cut-in process and decreases as the tool withdraws. When the cutting edge becomes blunter (i.e., the 30 nm edge radius), the intergranular fracture is more serious as shown in Fig. 8c. However, no crack occurs during the conventional cutting simulation when using the blunter tool. Therefore, it is easy to destroy the surface quality when the tool edge becomes worn during vibration cutting, as indicated by the experiment.
Fig. 8

Stress field and microcrack formation of normal WC: a conventional cutting, b vibration cutting and c influence of edge radius

During ion implantation, a large number of material defects are introduced into the workpiece surface (Fig. 9a). To some extent, it can be considered as a refining effect because the grain is dispersed into small pieces by the defects near ion trajectories. As a result, the chip of implanted WC consists of a larger amorphous phase and smaller grains in conventional cutting (Fig. 9b). These implantation defects also absorb energy from the high-frequency vibration and improve the in-grain deformation. With decrease in the grain's stiffness, the intergranular fracture is significantly reduced, as shown in Fig. 9c. Stress fields that occur at the same instants in conventional and vibration cutting are shown in Fig. 10. The change in shear stress is more obvious than in hydrostatic stress after ion implantation. It implies that the deviatoric deformation is more sensitive to material defects than volume change in polycrystalline WC. Decrease in shear stress is a consequence of surface softening, as indicated by the nanoindentation results. Figure 11 shows a comparison of the cutting and thrust forces in different simulation conditions. The peak forces in vibration cutting on both normal and implanted WC are higher than those in conventional cutting. For the superhard material, the tool edge might be easily broken by these force peaks. On the other hand, cutting forces decrease after ion implantation, so tool wear is reduced, as shown in Fig. 5.
Fig. 9

Influence of ion implantation on the a surface lattice, b chip formation and c microfracture

Fig. 10

Influence of ion implantation on stress field in a conventional and b vibration cutting

Fig. 11

Cutting forces in different simulation conditions

5 Conclusions and Outlook

A fundamental study on the effects of ion implantation and elliptical ultrasonic vibration on the nanometric cutting of binderless tungsten carbide has been conducted in this paper. The analysis of tool wear and surface quality has shown that elliptical vibration has a negative effect on the machining of superhard material. Two major mechanisms, intergranular fracture and violent cutting force peaks, are revealed by molecular dynamics simulation. After ion implantation, amorphization in the surface layer reduces the strength and brittleness of tungsten carbide and significantly improves the machinability of both conventional and ultrasonic cutting. The chip can be formed through shear deformation rather than brittle fracture. Therefore, surface softening is critical in the cutting of superhard material.

On the other hand, it can be expected that vibration-assisted cutting would show its merits once the workpiece strength is fully reduced. For example, tool-workpiece separation improves the cooling, which prevents the graphitization of diamond tool at high temperatures. It also promotes chip removal and reduces the formation of build-up edge. In future work, the relationships between material strength and ultrasonic vibration loading as well as the optimization of the implantation process will be investigated with the aim of achieving better coupling of ion implantation and vibration-assisted cutting for the nanometric machining of tungsten carbides.

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 51320105009 & 61635008) and the ‘111’ project by the State Administration of Foreign Experts Affairs and the Ministry of Education of China (Grant No. B07014). The authors would like to thank Daniel de Simone from Innolite for the support in developing ultrasonic device and Liang Chen for his efforts in preparing the experiment.

References

  1. 1.
    Ren YH, Zhang B, Zhou ZX (2009) Specific energy in grinding of tungsten carbides of various grain sizes. CIRP Ann Manuf Technol 58(1):299–302CrossRefGoogle Scholar
  2. 2.
    Fang FZ, Zhang XD, Weckenmann A, Zhang GX, Evans C (2013) Manufacturing and measurement of freeform optics. CIRP Ann Manuf Technol 62(2):823–846CrossRefGoogle Scholar
  3. 3.
    Wang DY, Zhang XY, Zhang DY (2018) Fabrication of a Peristome surface structure of Nepenthes alata by elliptical vibration cutting. Nanomanuf Metrol 1(4):209–216CrossRefGoogle Scholar
  4. 4.
    Nath C, Rahman M, Neo KS (2009) Machinability study of tungsten carbide using PCD tools under ultrasonic elliptical vibration cutting. Int J Mach Tool Manuf 49(14):1089–1095CrossRefGoogle Scholar
  5. 5.
    Nath C, Rahman M, Neo KS (2009) A study on the effect of tool nose radius in ultrasonic elliptical vibration cutting of tungsten carbide. J Mater Process Technol 209(17):5830–5836CrossRefGoogle Scholar
  6. 6.
    Suzuki N, Haritani M, Yang JB, Hino R, Shamoto E (2007) Elliptical vibration cutting of tungsten alloy molds for optical glass parts. CIRP Ann Manuf Technol 56(1):127–130CrossRefGoogle Scholar
  7. 7.
    Zhang J, Suzuki N, Wang Y, Shamoto E (2014) Fundamental investigation of ultra-precision ductile machining of tungsten carbide by applying elliptical vibration cutting with single crystal diamond. J Mater Process Technol 214(11):2644–2659CrossRefGoogle Scholar
  8. 8.
    Amini S, Khosrojerdi MR, Nosouhi R, Behbahani S (2014) An experimental investigation on the machinability of Al2O3 in vibration-assisted turning using PCD tool. Mater Manuf Process 29(3):331–336CrossRefGoogle Scholar
  9. 9.
    Lakhdari F, Bouzid D, Belkhir N, Herold V (2017) Surface and subsurface damage in Zerodur® glass ceramic during ultrasonic assisted grinding. Int J Adv Manuf Tech 90(5–8):1993–2000CrossRefGoogle Scholar
  10. 10.
    Chen WQ, Zheng L, Teng XY, Yang K, Huo DH (2018) Cutting mechanism investigation in vibration-assisted machining. Nanomanuf Metrol 1(4):268–276CrossRefGoogle Scholar
  11. 11.
    Fang FZ, Xu FF (2018) Recent advances in micro/nano-cutting: effect of tool edge and material properties. Nanomanuf Metrol 1:4–31CrossRefGoogle Scholar
  12. 12.
    Zhu B, Zhao D, Zhao H, Guan J, Hou P, Wang S, Qian L (2017) A study on the surface quality and brittle–ductile transition during the elliptical vibration-assisted nanocutting process on monocrystalline silicon via molecular dynamic simulations. RSC Adv 7(7):4179–4189CrossRefGoogle Scholar
  13. 13.
    Dai H, Du H, Chen J, Chen G (2019) Influence of elliptical vibration on the behavior of silicon during nanocutting. Int J Adv Manuf Technol 102:3597–3612CrossRefGoogle Scholar
  14. 14.
    Fang FZ, Chen YH, Zhang XD, Hu XT, Zhang GX (2011) Nanometric cutting of single crystal silicon surfaces modified by ion implantation. CIRP Ann Manuf Technol 60(1):527–530CrossRefGoogle Scholar
  15. 15.
    Wang JS, Fang FZ, Zhang XD (2015) An experimental study of cutting performance on monocrystalline germanium after ion implantation. Precis Eng 39:220–223CrossRefGoogle Scholar
  16. 16.
    Tanaka H, Shimada S (2013) Damage-free machining of monocrystalline silicon carbide. CIRP Ann Manuf Technol 62(1):55–58CrossRefGoogle Scholar
  17. 17.
    Matossian JN, Vajo JJ, Wysocki JA, Bellon ME (1993) Plasma ion implantation (PII) to improve the wear life of tungsten carbide drill bits used in printed wiring board (PWB) fabrication. Surf Coat Tech 62(1–3):595–599CrossRefGoogle Scholar
  18. 18.
    Blackley WS, Scattergood RO (1991) Ductile-regime machining model for diamond turning of brittle materials. Precis Eng 13(2):95–103CrossRefGoogle Scholar
  19. 19.
    Hirel P (2015) Atomsk: a tool for manipulating and converting atomic data files. Comput Phys Commun 197:212–219CrossRefGoogle Scholar
  20. 20.
    Juslin N, Erhart P, Träskelin P, Nord J, Henriksson KO, Nordlund K, Salonen E, Albe K (2005) Analytical interatomic potential for modeling nonequilibrium processes in the W–C–H system. J Appl Phys 98(12):123520CrossRefGoogle Scholar
  21. 21.
    Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117(1):1–19CrossRefzbMATHGoogle Scholar
  22. 22.
    Stukowski A (2009) Visualization and analysis of atomistic simulation data with OVITO–the open visualization tool. Model Simul Mater Sci 18(1):015012MathSciNetCrossRefGoogle Scholar
  23. 23.
    Ye GG, Xue SF, Jiang MQ, Tong XH, Dai LH (2013) Modeling periodic adiabatic shear band evolution during high speed machining Ti-6Al-4 V alloy. Int J Plast 40:39–55CrossRefGoogle Scholar
  24. 24.
    Wang JS, Zhang XD, Fang FZ, Chen RT (2018) A numerical study on the material removal and phase transformation in the nanometric cutting of silicon. Appl Surf Sci 455:608–615CrossRefGoogle Scholar
  25. 25.
    Zavodinsky VG (2010) Small tungsten carbide nanoparticles: Simulation of structure, energetics, and tensile strength. Int J Refract Met Hard Mater 28(3):446–450CrossRefGoogle Scholar

Copyright information

© International Society for Nanomanufacturing and Tianjin University and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Jinshi Wang
    • 1
  • Fengzhou Fang
    • 1
    • 2
    Email author
  • Guangpeng Yan
    • 1
  • Yuebin Guo
    • 3
    • 4
  1. 1.State Key Laboratory of Precision Measuring Technology and Instruments, Centre of Micro/Nano Manufacturing Technology (MNMT)Tianjin UniversityTianjinChina
  2. 2.Centre of Micro/Nano Manufacturing Technology (MNMT-Dublin)University College DublinDublinIreland
  3. 3.Department of Mechanical and Aerospace EngineeringRutgers UniversityPiscatawayUSA
  4. 4.New Jersey Advanced Manufacturing Institute, Rutgers UniversityPiscatawayUSA

Personalised recommendations