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A numerical study of ultraprecision machining of monocrystalline silicon with laser nano-structured diamond tools by atomistic simulation
Accepted Manuscript Title: A numerical study of ultraprecision machining of monocrystalline silicon with laser nano-structured diamond tools by atomistic simulation Author: Houfu Dai Genyu Chen Cong Zhou Qihong Fang Xinjiang Fei PII: DOI: Reference:
S0169-4332(16)32109-2 http://dx.doi.org/doi:10.1016/j.apsusc.2016.10.014 APSUSC 34108
To appear in:
APSUSC
Received date: Revised date: Accepted date:
7-6-2016 14-9-2016 3-10-2016
Please cite this article as: Houfu Dai, Genyu Chen, Cong Zhou, Qihong Fang, Xinjiang Fei, A numerical study of ultraprecision machining of monocrystalline silicon with laser nano-structured diamond tools by atomistic simulation, Applied Surface Science http://dx.doi.org/10.1016/j.apsusc.2016.10.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A numerical study of ultraprecision machining of monocrystalline silicon with laser nano-structured diamond tools by atomistic simulation
Houfu Daia,b, Genyu Chena,b, Cong Zhoua,b, Qihong Fanga, Xinjiang Feia,b
a
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China
b
Institute of Laser Technology, Hunan University, Changsha 410082, PR China
* Corresponding author at: State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China. Tel.: +86 731 88821772; fax: +86 731 88821772. E-mail address: [email protected] (G.Y. Chen).
Graphical abstract
1
Highlights
A laser nano-structured diamond tool in machining brittle material silicon causes a smaller hydrostatic stress, a less compressive normal stress, a lower temperature and a smaller cutting force.
The laser nano-structured diamond tool machining generates smaller chip volume and more beta-silicon phase.
The tool with V-shape groove can reduce the resistance to cutting during nanoscale machining process.
The potential energy of subsurface atoms for pyramid-structured tool is much lower than that of using non-structured tool and other structured tools.
The number of other atoms for pyramid-structured tool is much smaller than that of using non-structured tool and other structured tools.
ABSTRACT. Three-dimension molecular dynamics (MD) simulations is employed to investigate the ultraprecision machining of single crystal silicon with structured nanoscale diamond tool fabricated by laser. The advantages and disadvantages of diamond machining using structured tools are discussed in comparison with those of using non-structured tools. The von Mises stress distribution, hydrostatic stress distribution, atomic displacement, stress, the radial distribution function, cutting forces, frictional coefficient, subsurface temperature and potential energy during the nanometric machining process are studied. A theoretical analysis model is also established to investigate the subsurface damage mechanism by analyzing the distribution of residual stress during the nanoscale machining process. The results show that a structured nanoscale tool in machining brittle material silicon causes a smaller 2
hydrostatic stress, a less compressive normal stress
xx
and
yy , a lower temperature and a smaller
cutting force. However, the structured nanoscale tool machining results in smaller chip volume and more beta-silicon phase. Besides, the friction coefficient for tool with V-shape groove is smaller than those for non-structured tools and other structured nanoscale tools. This means that the tool with V-shape groove can reduce the resistance to cutting during the nanoscale machining process. In addition, the results also point out that the potential energy of subsurface atoms and the number of other atoms for pyramid-structured tool are much smaller than those of using non-structured tools and other structured nanoscale tools.
Keywords: Molecular Dynamics; Phase transformation; Laser nano-structured diamond tool; Subsurface damage; ultraprecision machining
1. Introduction A micro-structured surface can produce many predominant functions and features compared to smooth surface in the current industry. For example, the micro porosity and morphology patterned on single crystal silicon solar cells can improve the cells’ efficiency [1]. A surface encoder with micro angle grid surface is applied to multi-axis position measurement [2]. During the precision grinding of optical glass, the micro-structured coarse-grained diamond wheel reduces the subsurface damage depth compared with conventional coarse-grained diamond wheel [3]. Thus, in nanometric machining, a novel nano-structured diamond tool was used for ultraprecision machining of hard and brittle materials such as silicon, glass and ceramics so as to improve the machining performance, especially subsurface damage. Ultraprecision machining is a modern ultraprecision mechanical removal technique at nanoscale, 3
which has been applied to generate sub-nanometer level form accuracy and nanometric surface quality of components. For improving chipping efficiency and coolant flow at machining zone, many works have investigated the precision machining with laser structured grinding wheels or cutting tools. For example, Xie et al. [4] proposed using crossed grooving with a 60 0 V-tip of diamond grinding wheel to fabricate micro pyramid-structured silicon surface, and revealed that it could obtain good surface quality, high form-accuracy and efficient productivity compared with laser machining and etching, and also ensured a high aspect ratio compared with other mechanical processes. Sugihara et al. [5] proposed a cutting tool with a nano/micro-textured surface utilizing femto-second laser technology, and revealed that the surface significantly improved the anti-adhesiveness and lubricity. Kawasegi et al. [6] investigated the effect of the texture shape on the machinability of an aluminum alloy with a turning experiment, and indicated that the structured tools effectively improved the machinability of the alloy. Walter et al. [7] reported that the structured tools enabled between 25 to 50 % lower forces and significantly improved the force stability in long-term grinding operation. Okuyama et al. [8] and Zheng et al. [9] indicated that grinding temperatures can be reduced when using wheels with axial grooves. Hsieh et al. [10] found that the bond number of the microstructures was the primary factor responsible for the heat transfer enhancement of evaporative spray cooling on micro-structured silicon surface. However, works [3,7] pointed out that the best surface finish was still achieved with the non-structured tools. It is also found that the structured tool may lead to accelerated tool wear [7,11,12]. This is because the sharp tool tip much easily wears and becomes blunt during machining. Tool wear is a significant factor affecting the machined surface quality. Stavropoulos et al. [13] presented the design philosophy, restrictions and a consideration, of a combinational method for developing a process monitoring system 4
that is capable of monitoring simultaneously the spindle’s and tool’s condition during micro-milling operations. And they accomplished tool wear prediction by utilizing the experimental results that derived from third degree regression models and pattern recognition systems [14]. On the nanoscale, using both MD simulation and experimental methods, Cheng et al. [15] reported that the thermo-chemical wear is the basic wear mechanism of the diamond cutting tool. Goel et al. [16] confirmed the graphitization of diamond tool in the single point diamond turning process by adopting a MD simulation. The grinding aids (organic amines, alcohols, etc.) [17,18] acted as important auxiliary tool in grinding process, which can reduce tool wear and prevent adhesion during machining process. Heinz et al. [19-21] examined the adsorption mechanism of several organic amines and alcohols at different temperatures to understand their role as grinding aids. And they carried out MD analysis which showed that the computed agglomeration energies in adsorbed organic compounds correlate with the reduction in surface forces in the form of measured grinding efficiencies. Because the residual stress distribution could significantly affect the quality of machined components produced by traditional and nanoscale process. In particular, the residual stress is vital for the component’s characteristics, including fatigue life, corrosion resistance, and part distortion [22]. Besides, compressive residual stress on machined components could enhance the components durability and structural integrity. On the contrary, tensile residual stress would increase the possibility of material failure caused by corrosion, crack and fatigue [23,24]. As a result, a theoretical model is developed to better investigate the nanoscale machining with structured and non-structured tools by analyzing the distribution of residual stress during machining process. Some works have investigated the precision machining with laser nano-structured cutting tools by experiments [5,6]. Nevertheless, on one hand, the nanometric machining process involves only several 5
atomic layers on the workpiece surface, and the previous continuum mechanics method is not appropriate to analyze the nanometric machining process. On the other hand, we cannot get quick answers by experiment because of the limitations of the present real-time detect equipment, so it is difficult to observe the machining process and phenomena through experiment work. MD simulation has been confirmed to best suit for studying nanometric machining process [25,26]. Hence, the main purpose of the present study is to carry out MD simulations to investigate the ultraprecision machining and reveal the mechanism of machining nanostructures using structured nanoscale diamond tools. In order to benchmark the advantages and disadvantages of diamond turning using structured nanoscale tools, a comparison between using non-structured tools and structured nanoscale tools in nanometrc machining has been made in terms of von Mises stress distribution, hydrostatic stress distribution, atomic displacement, stress, the radial distribution function, cutting forces, frictional coefficient, subsurface temperature and potential energy.
2. Simulation Method
Fig. 1 shows the MD simulation models. These models consist of a single crystal silicon workpiece and a diamond tool. The diamond tool is assumed as an ideal rigid without any deformation since the diamond is much harder than the silicon. The dimension of silicon workpiece is
23 8.2 17.4 nm3 along the x-, y-, and z-direction. All of the machining tools are applied along the [1 0 0] direction on the (0 1 0) surface of workpiece. The workpiece includes three kinds of atoms: thermostat atoms, boundary atoms and Newtonian atoms. The boundary atoms are kept fixed in space to prevent the workpiece from translating during the machining process. The thermostat atoms are kept at a constant temperature of 300 K by velocity rescaling method. The motion of Newtonian atoms 6
obeys the classical Newton’s second law. Periodic boundary conditions are applied in the z direction. In this study, we study three different nano-structured diamond tools and non-structured diamond tools, namely, Pyramid tip tool (Pattern A), arc-shape groove tool (Pattern B), V-shape groove tool (Pattern C) and non-structured tools. More parameters of tool used in the present simulation are listed in TABLE II. Where groove factor is defined as the ratio between nominal surface area of the structured tool and nominal surface area of the non-structured tool [7]. There are three different atomic interactions in the current simulation of machining process. A Tersoff-type three-body potential is employed to express the interaction between silicon atoms [24-27]. The interaction between silicon atoms and diamond atoms is modeled by a Morse type two-body potential [27-30]. The interaction between diamond atoms is ignored because the tool is treated as a rigid body [27,30]. In this study, the machining velocity is 200m/s so as to save computational cost. It is noted that it is much higher than the real velocity during the machining process. However, according to many previous studies [27,31-33], MD simulation machined with relatively higher velocity could reveal the main characteristics of the subsurface deformation mechanism. A bigger depth of cut could increase the subsurface damage, reduce the machining efficient, and increase the cutting force [34]. Hence, a depth of cut of 1 nm is used in these simulations [33-36]. More parameters used in the present simulation are listed in TABLE I.
3. Results and Discussion
The cross-sectional views of the workpiece with different coordination numbers (CN) for different structured tools at grinding distance of 18nm is shown in Fig. 2(a-d). Clearly, a large number 7
of atoms appear around the diamond tool with five and six coordination atoms. And the atoms on free surface are changed into three-coordinated crystal structure. This is because under contact loading, silicon undergoes a series of phase transformations [37]. When the hydrostatic pressure reaches 10–13 GPa, alpha-silicon (Si-I, brittle) transforms to beta-silicon (Si-II, metallic and ductile) [28,38,39]. To further investigate the subsurface deformation mechanism in workpiece during the ultraprecision machining process for structured diamond tools, a statistic analysis of coordination number of the silicon atoms is given [40]. From Fig. 2(e)-(f), the number of atoms with five and six coordinated atoms versus machining distance for the four simulations is displayed, respectively. It is seen that although the number of five-coordinated and six-coordinated atoms increases as the machining distance increases, the five-coordinated atom increases more rapidly than the six-coordinated atom. The phenomena can be attributed to the instability of the beta-silicon below ∼4 GPa on unloading [38]. Thus, when the tool passes, metallic beta-silicon (more dense and low volume) loses its crystalline order and transforms into a-Si (more structural volume) and other phases, such as BC8 (bcc) and R8 (Rhombohedral) [41], which causes expansion and the consequent elastic recovery of the machined surface after the passing of the tool. Moreover, it can be observed from Fig. 2 (f) that when the diamond tool is non-structured, the number of six-coordinated atoms is the least. This indicates that for non-structured tool machining, less metallic and ductile beta-silicon forms from its original diamond cubic structure.
The stress components within the workpiece in a machining operation are defined in Fig. 3(a). For the investigation of von Mises stress and hydrostatic stress during the nanoscale machining process, each of the stress components
xx , yy , zz , xy , xz 8
and
yz
of atom i are calculated.
According to previous reports [27,28], where
(1/ )i (mi vi vi (1/ 2)i j rij fij ) , N
is the virial stress components of atom i,
, =x, y, z is the Cartesian components.
stands for the volume of the domain within the cut-off distance of atom i. mass, the
-component
and
-component
of the velocity of atom i, respectively. represents
the tensor product of vectors. N is the total number of atoms in the domain. of the vector
mi , vi and vi are the
rij is the -component
rij , rij is the distance between atom i and atom j. Fij is the -component of the
interaction force on atom i action by atom j. Von Mises stress and hydrostatic stress can be expressed as:
von 3( xy2 yz2 xz2 ) (1/ 2) ( xx yy ) 2 ( xx zz ) 2 ( zz yy ) 2
,
hydro (1/ 3)( xx yy zz ) . The von Mises stress distributions of workpiece for pattern B is illustrated in Fig. 3(b). High pressure phase transformation can be observed in machining ductile material silicon. Therefore, plastic deformation depends upon high pressure phase transformation (HPPT) and dislocation nucleation during the nanoscale machining process. Noted that a lot of dislocations nucleate are alongside HPPT, which indicates that HPPT first occurs, followed by stacking faults/twin structure, finally dislocations slipping along Si {111} planes [42]. Local hydrostatic stress distribution of workpiece for pattern B is calculated and shown in Fig. 3(c). Interestingly, high hydrostatic stress occurs in front of and beneath the tool edge. It is noted that the phase transformation silicon atoms (five coordinated and six coordinated) are also mostly located in this region (as shown in Fig. 2), which reveals that the evolution of crystalline phases is consistent with the distribution of hydrostatic stress [43]. Fig. 3(d) illustrates the displacement of atoms in the workpiece for pattern B during the machining process. The atoms are colored according to their displacements. It is found that the atoms in the chips and groove of tool have the maximum displacement, and the atoms in front of tool edge also significantly move under high hydrostatic stress (as shown in Fig. 3(c)). It reveals that 9
the silicon atoms on both sides of the tool flow along the groove of tool under high forces, which is beneficial to the heat dissipation of the subsurface atoms. Hydrostatic stress is a quantity associated with volume change leading to classic thermodynamic phase transitions in continuous matter, whereas von Mises stress measures shear deformation that governs shape change usually by the activation of defect transport mechanisms [44]. Therefore, hydrostatic stress and von Mises stress have made a contribution to the dislocation nucleation and motion, as well as the atoms phase transitions. Fig. 3(e) shows the average von Mises stress of subsurface atoms for different structured tools. It is clear that apart from pattern A (2.41 Gpa), the average von Mises stress of subsurface atoms for non-structured tool being 2.54 GPa is smaller than that of using the structured tools (2.57 Gpa for the pattern B, 2.62 Gpa for the pattern C). The variations of average hydrostatic stress of subsurface atoms with the machining distance for different structured tools are demonstrated in Fig. 3(f). It can be observed that the average hydrostatic stress of subsurface atoms rises rapidly at the initial machining stage, and then reaches a relatively stable stage as the machining distance increases. By comparing four different structured tools, obviously, the average hydrostatic stress of subsurface atoms for non-structured tools is larger than those for structured tools, which leads to bigger cutting forces.
The stress components in the subsurface of workpiece are demonstrated in Fig. 4. are the normal stresses in the x and y directions, and normal stress of subsurface atoms advance of the tool,
xx
xx
xy
xx
and
yy
stands for the shear stress. The average
is calculated and shown in Fig. 4(a). It is evident that with the
rapidly decreases at initial machining stage, and then slightly increases at
steady machining stage. The stress of subsurface atoms exhibits the similar trend for different 10
structured tools. The average normal stress Evidently,
yy
yy
of subsurface atoms is also shown in Fig. 4(b).
decreases as the machining distance increases for the four different structured tools. It
is evident from Fig. 4(a) and (b) that the normal stress
xx
and
yy
are the compressive stress. This
is due to the compression effect from the tool [27]. In addition, it is clear from Fig. 4(a) and (b) that the normal stress
xx
and
yy
for non-structured tools are overall more compressive than that of using
structured tools. The reason is that the workpiece undergoes higher drastic hydrostatic pressure when a non-structured tool is applied (as shown in Fig. 3(f)). The high hydrostatic pressure enables plastic deformation that concentrates in front of the tool edge, and in turn makes the single crystal silicon transformed into a more ductile state. The deformed silicon atoms are not able to return to its original diamond cubic structure. As such, the non-structured tools tend to machine silicon in a more ductile mode than corresponding structured tools under the same configuration of other machining parameters. Fig. 4(c) shows the average shear stress shear stress
xy
xy
of subsurface atoms for different structured tools. All
are averaged over the machining distance from 6 to 18 nm where machining is in a
steady stage. According to the work [45], dislocation emission will take place only when shear stress is larger than material flow stress. It can be seen from Fig. 4(c) that the shear stresses
xy
for pattern C
is much larger than that for non-structured tools. This result reveals that the partial dislocation emission is more likely to occur on a tool with V-shape grooves during the nanoscale machining process.
Fig. 5(a) illustrates the relationship of other atoms with machining distance for different structured tools. It is obvious that other atoms increase with the increase of machining distance for different structured tools. The number of other atoms for non-structured tools, pattern B and pattern C are nearly the same. But the number of other atoms for pattern A is much lower than that of using other structured 11
tools. The radial distribution function, also called pair distribution functions or pair correlation functions, is the primary linkage between macroscopic thermodynamic properties and intermolecular interactions. As shown in Fig. 5(b), it is obvious that bond length is 2.35 Å of the largest number of atoms for the four simulations, which are consistent with the bond length of alpha-silicon (Si-I) in theory. It is well known that beta-silicon (Si-II) contains four nearest neighbours at a distance of 2.42
Å and two other neighbours at 2.58 Å [28]. it is obvious from Fig. 5(b) that the bond number with a length of 2.58
Å for non-structured tool is less than that of using structured tools, which
reconfirmed that for non-structured tool machining, there are less silicon atoms undergo phase transformation change from alpha-silicon to beta-silicon during the nanoscale ultraprecision machining process. Fig. 5(c-f) shows the atoms of different lattice structures for different structured tools at the machining distance of 18 nm, based on the common neighbor analysis (CNA) [46]. In this work, atoms are colored according to the calculated CNA values: Blue presents diamond cubic crystal structure atoms, and gray for other atoms including beta-silicon and dislocation atoms, as well as surface atoms. It is found from Fig. 5(c-f) that structured tools largely influence the dislocation from the penetrated surface. Furthermore, it can be seen that dislocation nucleation and growth on the (1 0 0) plane, and dislocation propagate along the [1 0 -1] (1 1 1) slip systems.
Fig. 6(a)-(d) demonstrates the surface morphologies and the residual cross-section profiles of the machining grooves for different structured tools at the machining distance of 18 nm. It is found that the cross-section profiles are strongly influenced by the structured tools, but the volume of material pileups on the sides of groove slightly affected. Fig. 6 (e) shows the number of atoms in chip versus the 12
machining distance for different structured tools. As known, with the advance of the tool, more workpiece atoms accumulate and pile up in front of and on both sides of the tool. A comparison of different structured tools indicates that the chipping volume for non-structured tool is the largest, and the pyramid-structured tool (pattern A) is the smallest. This means that structured tool reduce the material removal rate during the nanoscale machining process.
Force measurement is an important indicator of tool wear, normal force mainly influences surface error, as it tends to separate the tool away from the workpiece, and the tangential force causes displacements in the direction of cut chip thickness [47,48]. To further study the effects of structured tools, the forces during the machining process are obtained by summing the atomic forces of workpiece atoms on tool. The average tangential forces (in the x direction) and normal forces (in the y direction) for machining distances of 6-18 nm where machining is in a steady state are calculated, as shown in Fig. 7(a). The lateral force (in the z direction) is not calculated since its average value is zero during the machining process because of the balanced forces contributing from the two sides of the groove. From Fig. 7(a), both the tangential force and normal force for non-structured tools machining are bigger than that of using structured tools. The reason is that non-structured tool machining produces more chips
requiring larger forces to complete this machining process. This result also reveals that a structured tool can reduce the force of workpiece on tools during the nanoscale machining process. Friction coefficient is an important factor in nanoscale machining, which is defined as the ratio of the average tangential force to the average normal force, and it measures the material removal ability. Fig. 7(b) shows the average frictional coefficient for different structured tools. It can be observed that non-structured tool machining (0.936) experiences a slightly higher resistance rate than that of using 13
pattern C (0.929) but much lower than those of using other structured tools (1.265 for the pattern A, 1.263 for the pattern B). This result means that the tool with V-shape groove (pattern C) can reduce the resistance to cutting during the nanoscale machining process.
The temperature-displacement curves for subsurface atoms under different structured tools are shown in Fig. 8(a). In conventional machining operations, the energy from plastic deformation in the primary shear zone and sliding friction along the tool-chip interface generate heat. It can be seen from Fig. 8(a) that as the machining distance increases, the average temperature of subsurface atoms rapidly rises at initial machining stage, then reach a steady state. What’s more, it is clearly found that the temperature of subsurface for non-structured tools is the highest in that for structured tool machining, the silicon atoms on both sides of the tool are allowed to flow along the groove of tool under high forces, which accelerates the heat dissipation of the subsurface atoms. This result also reveals that structured tools are more conductive to reduce the temperature of workpiece subsurface comparing with non-structured tools. Potential energy is the energy of a system as a result of the atomic position or the particle arrangement of the system, which marks the stability of the system in energy [31]. The potential energy of subsurface atoms versus the machining distance for different structured tools is also plotted as shown in Fig. 8(b). Obviously, the potential energy of the subsurface atoms increases with the increase of machining distance. However, it is noted here that the potential energy of subsurface atoms increases more slowly at the plastic deformation stage than that at the initial elastic deformation stage. Additionally, a comparison of different structured tools indicates that the slops of potential energy to machining distance curves for the pattern C and pattern B are higher than that of using a non-structured 14
tool. However, the potential energy of subsurface atoms for pattern A is lower than that for non-structured tools. This means that the workpiece undergone different degrees of deformation during the nanoscale machining process using different structured tools. Based on the above analysis, conclusions can be drawn that during the nanometric machining process, the structured tools perform better in most of the investigated aspects. Moreover, the results suggest that pyramid-structured diamond tool is the most suitable structured tool for nanometric machining because the pyramid-structured tool machining results in the lowest von Mises stress and shear stress, the least number of other atoms, the smallest cutting force, the lowest subsurface temperature and potential energy.
4. Theoretical model
For a deeper understanding of friction and wear on the nanometric ultraprecision machining, a theoretical analysis model is established to study plastic deformation patterns and subsurface damage. Fig. 9 shows the Schematic of the machining process and the relevant residual stress field. With the advance of tool on the workpiece surface, it produces a scratch groove surrounded by a phase transformation region, which is encompassed in an elastic zone, as shown in Fig. 9. The residual stress field arises due to the plastic deformation and its components on the x-y plane at a depth z=c below the machining surface is given by [49-51].
x
x 2 B 2v( y02 z02 ) 2 2 02 2 5 (2vx04 y02 2 x02 y04 6vx02 y04 2 2 2 c ( y0 z0 ) ( y0 z0 ) 0 -2y06 4vy06 2vx04 z02 4 x02 y02 z02 2vx02 y02 z02 3 y04 z02 +6vy04 z02 2vx02 z04 4vx02 z04 z06 2vz06 )
15
(1)
y
x 2 B 2 y02 ( y02 3z02 ) 2 02 3 5 (2 x04 y04 6 x02 y06 2vx02 y06 2 2 2 3 c ( y0 z0 ) ( y0 z0 ) 0 +4y08 2vy08 6 x04 y02 z02 7 x02 y04 z02 6vx02 y04 z02 2vy06 z02 8vy06 z02 12 x02 y02 z04 6 v x02 y02 z04 15 y04 z04 12 v y04 z04 +x02 z06 2vx02 z06 8 y02 z06 8vy02 z06 z08 2vz08 )
z
x0 z02 2 B 2 z02 ( z02 3 y02 ) (6 x04 y02 15 x02 y04 9 y06 2 2 2 3 2 2 3 5 c ( y0 z0 ) ( y0 z0 ) 0 -2x04 z02 10 x02 y02 z02 12 y04 z02 5 x02 z04 3 y02 z04 6 z06 )
xy
2(1 v) x02 2(1 v) y02 z02 2vz02 2B y 0 c2 05
yz
(y02 z02 ) x yz 2B 4 y z 2 0 02 03 5 (4 x04 y02 10 x02 y04 0 0 2 2 2 3 c ( y0 z0 ) ( y0 z0 ) 0 6 y06 -4x04 z02 3 y04 z02 10 x02 z04 12 y02 z04 9 z06 )
zx Where
(2 x02 2 y02 z02 ) 2B z 0 c2 05
(2)
(3)
(4)
(5)
(6)
x0 x / c , y0 y / c , z0 z / c 1 , 0 x 2 y 2 z 2 / c , v is the Poisson’s
ratio of the materials, d is the phase transformation zone size. According to work [49,50], B represents the strength of the sliding blister field, it can be determined by
B Where f ,
3 fahE 4 (1 2 )(1 )
a, E
and
(7)
h are the compaction factor, the contact zone size, Yong’s modulus and the
depth of scratching, respectively. fE / H 1.09 as a critical value for sharp machining tool. H is the hardness. The stress components within the workpiece in a machining operation are defined in Fig. 3(a). For the investigation of residual stress, we focus on
x , y , and xy . The silicon materials in this
study, the following parameters are adapted in calculation: the Yong’s modulus E =160 Gpa, H =12.5 Gpa, Poisson’s ration
=0.22, h =1 nm, a =11.4 nm. 16
Fig. 10 shows the 3D distribution of the residual stress for
=0.22 and z0=1 on the x-y plane in
the vicinity of diamond tool during the scratching process. As shown in Fig. 10(b), as the tool moves along the x direction from x0=-6 to x0=0, the normal residual stress
x
during the scratching process. However, the normal residual stress advance of the tool. It is observed that normal residual stresses beneath the tool. But the shear residual stress
xy
firstly declines, and then rises
y
x
slightly declines with the and
y
are highly tensile
is slight compressive in the wake of the scratching
tool, while shear residual stress is tensile at both sides of the groove. It is clear from Fig. 10(b) that the tensile residual stress
x
the normal residual stress
reaches its maximum value just beneath the tool along the x-axis. However,
y
is reduced to its minimum value beneath the tool during the scratching
process. The normal residual stress
y
reaches its maximum value away from the x-axis on both
sides of the tool, and its value is much larger than shear residual stress
y .
What’s more, the shear residual stress
xy
xy
and normal residual stress
also reaches its maximum value away from the
x-axis on both sides of the tool. From the distribution of residual stress, it should be noted that residual stress plays an important role in the scratching process and is known to contribute to the component’s surface properties and performances. For example, the compressive residual stresses are regard as beneficial in that they help decrease the crack rates, and then enhance the structural integrity [23,24].
5. Conclusions In this work, large-scale MD simulations are carried out to study the nanoscale machining process when using structured tools and non-structured tools. According to the simulation results, Main conclusions are drawn as following:
17
1) The structured tools have a significant effect on nanometric machining process. Results show that for non-structured tool machining, less metallic and ductile beta-silicon forms from its original diamond cubic structure. The silicon atoms on both sides of the tool flow along the groove of tools under high forces, which is beneficial to the heat dissipation of the subsurface atoms. 2) The average hydrostatic stress of subsurface atoms for non-structured tools is larger than that for structured tools, which makes the normal stress
xx
and
yy for non-structured tool overall
more compressive than that of using structured tools. 3) The non-structured nanoscale tool machining results in more chip volume. However, the temperature of subsurface for non-structured tool machining is higher than that of using structured tools. This means that the structured tool is more conductive to reduce the temperature of workpiece subsurface comparing with a non-structured tool. Additionally, the potential energy of subsurface atoms and the number of other atoms for pyramid-structured tool are much lower than that of using other structured tools. 4) Both the tangential force and normal force for non-structured tool machining are bigger than that of using structured tools. The reason is that non-structured tool machining produces more chips
requiring larger forces to complete this machining process. However, the friction coefficient for tools with V-shape groove is smaller than those for non-structured tools and other structured nanoscale tools. This means that the tools with V-shape groove can reduce the resistance to cutting during the nanoscale machining process. 5) The results of theoretical model indicate that residual stress plays an important role in the scratching process and is known to contribute to the component’s surface properties and performances. 6) In future work, the influence of structured nanoscale diamond tool on subsurface damage and 18
material removal during the nanometric machining process will be further studied, such as groove factor, groove shape, groove direction, groove depth, groove width. Furthermore, the MD simulation results will be compared with the experiment results.
Acknowledgements The authors would like to appreciate the support from the National Science and Technology Major Project of the Ministry of Science and Technology of China (No.2012ZX04003101)
19
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[36] Tong Z, Liang Y, Yang X, et al. Investigation on the thermal effects during nanometric cutting process while using nanoscale diamond tools. The International Journal of Advanced Manufacturing Technology, 2014, 74(9-12): 1709-1718. [37] Handbook of Surfaces and Interfaces of Materials: Surface and interface phenomena. Academic Press, 2001. [38] V. Domnich, Y. Gogotsi, S. Dub. Effect of phase transformations on the shape of the unloading curve in the nanoindentation of silicon. Applied Physics Letters. 76(2000) 2214-2216. [39] Y. H. Lin, T. C. Chen. A molecular dynamics study of phase transformations in mono-crystalline Si under nanoindentation. Applied Physics A. 92(2008) 571-578. [40] H. Dai, G. Chen, Q. Fang, et al. The effect of tool geometry on subsurface damage and material removal in nanometric cutting single-crystal silicon by a molecular dynamics simulation. Applied Physics A. 122(2016) 804. [41] Y. Gogotsi, G. Zhou, S. S Ku, et al. Raman microspectroscopy analysis of pressure-induced metallization in scratching of silicon. Semiconductor science and technology. 16(2001) 345. [42] Y. Q Wu, H. Huang, J. Zou, et al. Nanoscratch-induced deformation of single crystal silicon. Journal of Vacuum Science & Technology B. 27(2009) 1374-1377. [43] K. Mylvaganam, L.C. Zhang, P. Eyben, et al. Evolution of metastable phases in silicon during nanoindentation: mechanism analysis and experimental verification. Nanotechnology. 20 (2009) 305705. [44] G.L.W. Cross. Silicon nanoparticles: Isolation leads to change. Nature nanotechnology. 6(2011) 467-468. [45] M.B. Cai, X.P. Li, M. Rahman. Study of the temperature and stress in nanoscale ductile mode cutting of silicon using molecular dynamics simulation. Journal of Materials Processing Technology. 192 (2007) 607-612. [46] D. Faken, H. Jónsson. Systematic analysis of local atomic structure combined with 3D computer graphics. Computational Materials Science. 2(1994) 279-286. [47] C. Wang, K. Cheng, N. Nelson, et al. Cutting force–based analysis and correlative observations on the tool wear in diamond turning of single-crystal silicon. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture. 2014 0954405414543316.
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[48] S. Goel, X. Luo, A. Agrawal, et al. Diamond machining of silicon: a review of advances in molecular dynamics simulation[J]. International Journal of Machine Tools and Manufacture. 88 (2015) 131-164. [49] Y. Ahn, T. N. Farris, and S. Chandrasekar. Sliding microindentation fracture of brittle materials: Role of elastic stress fields. Mechanics of materials. 29(1998) 143-152. [50] X. Jing, S. Maiti, G. Subhash. A New Analytical Model for Estimation of Scratch‐Induced Damage in Brittle Solids. Journal of the American Ceramic Society. 90(2007) 885-892. [51] D. Ghosh, G. Subhash, R. Radhakrishnan, et al. Scratch-induced microplasticity and microcracking in zirconium diboride–silicon carbide composite. Acta Materialia. 56(2008) 3011-3022.
24
Fig. 1
MD simulation model of nanometric precision machining of silicon with nano-structured
diamond tool: (a) the 3D model of non-structured diamond tool machining; (b) surface morphologies of pyramid-structured diamond tool (pattern A); (c) surface morphologies of diamond tool with arc-shape groove and V-shape groove; (d) diamond tool with arc-shape groove (pattern B); (e) diamond tool with V-shape groove (pattern C).
25
Fig. 2 The cross-section view of the atomic positions for different structured tools at machining distance of 18 nm. (a) Non-structured tool, (b) Pattern A, (c) Pattern B and (d) Pattern C. Atoms are colored according to coordination number (CN). (Four-coordinated diamond cubic silicon atoms are invisible). (e) and (f) are the number of atoms with five-coordinate and six-coordinate nearest neighbors against machining distance, respectively.
26
Fig. 3
Stress components in the machining (a), von Mises stress distribution (b), hydrostatic stress
distribution (c), atomic displacement (The atoms are colored according to their displacements) (d), average von Mises stress of subsurface under different structured tools (e), and average hydrostatic stress of subsurface versus the machining distance for different structured tools (f).
27
Fig. 4
Stress evolution of the subsurface of workpiece for different structured tools: (a)
and (c)
xy .
28
xx , yy ,
Fig. 5
Evolution of other atoms for different structured tools (a). The radial distribution function of
workpiece atoms in MD model for different structured tools (b). The partial cross-sectional views of studying the influence of nano-structured tools is (c) non-structured tool, (d) pattern A, (e) pattern B and (f) pattern C at the machining distance of 18 nm. Atoms are colored according to the calculated CNA values in (c)-(f) (Diamond cubic crystal structure in blue, other atoms in gray)
29
Fig. 6
Surface morphologies of studying the influence of different structured tools is (a)
non-structured tool, (b) pattern A, (c) pattern B and (d) pattern C workpiece after machining at machining distance of 18 nm. The height of atoms differs with colors. (e) The number of atoms in chips against the machining distance.
30
Fig. 7
Variation of the average force (a) and frictional coefficient (b) under different structured tools
at machining distance of 18 nm.
Fig. 8
Effect of structured tool. (a) Variation of average temperature of subsurface, and (b) variation
of potential energy of subsurface.
31
Fig. 9
(a) Schematic of the machining process. (b) A diagram of the cross-sectional view of the model.
Note that the cross-sectional view is perpendicular to the machining direction.
Fig. 10
Distribution of residual stress (a). Normal residual stress
residual stress
xy
x
(b),
y
(c) and shear
(d) on the x-y plane. The blue triangle indicates the position of the scratching tool,
and the pink arrow indicates the scratching direction.
32
TABLE I.
Simulation parameters
Workpiece Materials Tool Materials Dimension of workpiece Numbers of silicon atoms in the workpiece Depth of cut Workpiece machining surface Initial temperature Machining distance Time step Machining speed
TABLE II.
Silicon diamond
23 nm 8.2 nm 17.4 nm
168864 1 nm [1 0 0] on (0 1 0) surface 300 K 0-18 nm 1fs
200 m/s
Processing conditions for the four simulation cases of nano-scale machining
MD model
Groove orientation,
non-structured
o
Groove
Groove
depth, nm
width, nm
0
0
Groove shape
Groove factor,% 100
Pattern A
30 and -30
1
2
Pyramid tip
Pattern B
30
0.4
0.8
arc-shape
27.27
Pattern C
30
0.4
0.8
V-shape
27.27
33
S0169-4332(16)32109-2 http://dx.doi.org/doi:10.1016/j.apsusc.2016.10.014 APSUSC 34108
To appear in:
APSUSC
Received date: Revised date: Accepted date:
7-6-2016 14-9-2016 3-10-2016
Please cite this article as: Houfu Dai, Genyu Chen, Cong Zhou, Qihong Fang, Xinjiang Fei, A numerical study of ultraprecision machining of monocrystalline silicon with laser nano-structured diamond tools by atomistic simulation, Applied Surface Science http://dx.doi.org/10.1016/j.apsusc.2016.10.014 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
A numerical study of ultraprecision machining of monocrystalline silicon with laser nano-structured diamond tools by atomistic simulation
Houfu Daia,b, Genyu Chena,b, Cong Zhoua,b, Qihong Fanga, Xinjiang Feia,b
a
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China
b
Institute of Laser Technology, Hunan University, Changsha 410082, PR China
* Corresponding author at: State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, PR China. Tel.: +86 731 88821772; fax: +86 731 88821772. E-mail address: [email protected] (G.Y. Chen).
Graphical abstract
1
Highlights
A laser nano-structured diamond tool in machining brittle material silicon causes a smaller hydrostatic stress, a less compressive normal stress, a lower temperature and a smaller cutting force.
The laser nano-structured diamond tool machining generates smaller chip volume and more beta-silicon phase.
The tool with V-shape groove can reduce the resistance to cutting during nanoscale machining process.
The potential energy of subsurface atoms for pyramid-structured tool is much lower than that of using non-structured tool and other structured tools.
The number of other atoms for pyramid-structured tool is much smaller than that of using non-structured tool and other structured tools.
ABSTRACT. Three-dimension molecular dynamics (MD) simulations is employed to investigate the ultraprecision machining of single crystal silicon with structured nanoscale diamond tool fabricated by laser. The advantages and disadvantages of diamond machining using structured tools are discussed in comparison with those of using non-structured tools. The von Mises stress distribution, hydrostatic stress distribution, atomic displacement, stress, the radial distribution function, cutting forces, frictional coefficient, subsurface temperature and potential energy during the nanometric machining process are studied. A theoretical analysis model is also established to investigate the subsurface damage mechanism by analyzing the distribution of residual stress during the nanoscale machining process. The results show that a structured nanoscale tool in machining brittle material silicon causes a smaller 2
hydrostatic stress, a less compressive normal stress
xx
and
yy , a lower temperature and a smaller
cutting force. However, the structured nanoscale tool machining results in smaller chip volume and more beta-silicon phase. Besides, the friction coefficient for tool with V-shape groove is smaller than those for non-structured tools and other structured nanoscale tools. This means that the tool with V-shape groove can reduce the resistance to cutting during the nanoscale machining process. In addition, the results also point out that the potential energy of subsurface atoms and the number of other atoms for pyramid-structured tool are much smaller than those of using non-structured tools and other structured nanoscale tools.
Keywords: Molecular Dynamics; Phase transformation; Laser nano-structured diamond tool; Subsurface damage; ultraprecision machining
1. Introduction A micro-structured surface can produce many predominant functions and features compared to smooth surface in the current industry. For example, the micro porosity and morphology patterned on single crystal silicon solar cells can improve the cells’ efficiency [1]. A surface encoder with micro angle grid surface is applied to multi-axis position measurement [2]. During the precision grinding of optical glass, the micro-structured coarse-grained diamond wheel reduces the subsurface damage depth compared with conventional coarse-grained diamond wheel [3]. Thus, in nanometric machining, a novel nano-structured diamond tool was used for ultraprecision machining of hard and brittle materials such as silicon, glass and ceramics so as to improve the machining performance, especially subsurface damage. Ultraprecision machining is a modern ultraprecision mechanical removal technique at nanoscale, 3
which has been applied to generate sub-nanometer level form accuracy and nanometric surface quality of components. For improving chipping efficiency and coolant flow at machining zone, many works have investigated the precision machining with laser structured grinding wheels or cutting tools. For example, Xie et al. [4] proposed using crossed grooving with a 60 0 V-tip of diamond grinding wheel to fabricate micro pyramid-structured silicon surface, and revealed that it could obtain good surface quality, high form-accuracy and efficient productivity compared with laser machining and etching, and also ensured a high aspect ratio compared with other mechanical processes. Sugihara et al. [5] proposed a cutting tool with a nano/micro-textured surface utilizing femto-second laser technology, and revealed that the surface significantly improved the anti-adhesiveness and lubricity. Kawasegi et al. [6] investigated the effect of the texture shape on the machinability of an aluminum alloy with a turning experiment, and indicated that the structured tools effectively improved the machinability of the alloy. Walter et al. [7] reported that the structured tools enabled between 25 to 50 % lower forces and significantly improved the force stability in long-term grinding operation. Okuyama et al. [8] and Zheng et al. [9] indicated that grinding temperatures can be reduced when using wheels with axial grooves. Hsieh et al. [10] found that the bond number of the microstructures was the primary factor responsible for the heat transfer enhancement of evaporative spray cooling on micro-structured silicon surface. However, works [3,7] pointed out that the best surface finish was still achieved with the non-structured tools. It is also found that the structured tool may lead to accelerated tool wear [7,11,12]. This is because the sharp tool tip much easily wears and becomes blunt during machining. Tool wear is a significant factor affecting the machined surface quality. Stavropoulos et al. [13] presented the design philosophy, restrictions and a consideration, of a combinational method for developing a process monitoring system 4
that is capable of monitoring simultaneously the spindle’s and tool’s condition during micro-milling operations. And they accomplished tool wear prediction by utilizing the experimental results that derived from third degree regression models and pattern recognition systems [14]. On the nanoscale, using both MD simulation and experimental methods, Cheng et al. [15] reported that the thermo-chemical wear is the basic wear mechanism of the diamond cutting tool. Goel et al. [16] confirmed the graphitization of diamond tool in the single point diamond turning process by adopting a MD simulation. The grinding aids (organic amines, alcohols, etc.) [17,18] acted as important auxiliary tool in grinding process, which can reduce tool wear and prevent adhesion during machining process. Heinz et al. [19-21] examined the adsorption mechanism of several organic amines and alcohols at different temperatures to understand their role as grinding aids. And they carried out MD analysis which showed that the computed agglomeration energies in adsorbed organic compounds correlate with the reduction in surface forces in the form of measured grinding efficiencies. Because the residual stress distribution could significantly affect the quality of machined components produced by traditional and nanoscale process. In particular, the residual stress is vital for the component’s characteristics, including fatigue life, corrosion resistance, and part distortion [22]. Besides, compressive residual stress on machined components could enhance the components durability and structural integrity. On the contrary, tensile residual stress would increase the possibility of material failure caused by corrosion, crack and fatigue [23,24]. As a result, a theoretical model is developed to better investigate the nanoscale machining with structured and non-structured tools by analyzing the distribution of residual stress during machining process. Some works have investigated the precision machining with laser nano-structured cutting tools by experiments [5,6]. Nevertheless, on one hand, the nanometric machining process involves only several 5
atomic layers on the workpiece surface, and the previous continuum mechanics method is not appropriate to analyze the nanometric machining process. On the other hand, we cannot get quick answers by experiment because of the limitations of the present real-time detect equipment, so it is difficult to observe the machining process and phenomena through experiment work. MD simulation has been confirmed to best suit for studying nanometric machining process [25,26]. Hence, the main purpose of the present study is to carry out MD simulations to investigate the ultraprecision machining and reveal the mechanism of machining nanostructures using structured nanoscale diamond tools. In order to benchmark the advantages and disadvantages of diamond turning using structured nanoscale tools, a comparison between using non-structured tools and structured nanoscale tools in nanometrc machining has been made in terms of von Mises stress distribution, hydrostatic stress distribution, atomic displacement, stress, the radial distribution function, cutting forces, frictional coefficient, subsurface temperature and potential energy.
2. Simulation Method
Fig. 1 shows the MD simulation models. These models consist of a single crystal silicon workpiece and a diamond tool. The diamond tool is assumed as an ideal rigid without any deformation since the diamond is much harder than the silicon. The dimension of silicon workpiece is
23 8.2 17.4 nm3 along the x-, y-, and z-direction. All of the machining tools are applied along the [1 0 0] direction on the (0 1 0) surface of workpiece. The workpiece includes three kinds of atoms: thermostat atoms, boundary atoms and Newtonian atoms. The boundary atoms are kept fixed in space to prevent the workpiece from translating during the machining process. The thermostat atoms are kept at a constant temperature of 300 K by velocity rescaling method. The motion of Newtonian atoms 6
obeys the classical Newton’s second law. Periodic boundary conditions are applied in the z direction. In this study, we study three different nano-structured diamond tools and non-structured diamond tools, namely, Pyramid tip tool (Pattern A), arc-shape groove tool (Pattern B), V-shape groove tool (Pattern C) and non-structured tools. More parameters of tool used in the present simulation are listed in TABLE II. Where groove factor is defined as the ratio between nominal surface area of the structured tool and nominal surface area of the non-structured tool [7]. There are three different atomic interactions in the current simulation of machining process. A Tersoff-type three-body potential is employed to express the interaction between silicon atoms [24-27]. The interaction between silicon atoms and diamond atoms is modeled by a Morse type two-body potential [27-30]. The interaction between diamond atoms is ignored because the tool is treated as a rigid body [27,30]. In this study, the machining velocity is 200m/s so as to save computational cost. It is noted that it is much higher than the real velocity during the machining process. However, according to many previous studies [27,31-33], MD simulation machined with relatively higher velocity could reveal the main characteristics of the subsurface deformation mechanism. A bigger depth of cut could increase the subsurface damage, reduce the machining efficient, and increase the cutting force [34]. Hence, a depth of cut of 1 nm is used in these simulations [33-36]. More parameters used in the present simulation are listed in TABLE I.
3. Results and Discussion
The cross-sectional views of the workpiece with different coordination numbers (CN) for different structured tools at grinding distance of 18nm is shown in Fig. 2(a-d). Clearly, a large number 7
of atoms appear around the diamond tool with five and six coordination atoms. And the atoms on free surface are changed into three-coordinated crystal structure. This is because under contact loading, silicon undergoes a series of phase transformations [37]. When the hydrostatic pressure reaches 10–13 GPa, alpha-silicon (Si-I, brittle) transforms to beta-silicon (Si-II, metallic and ductile) [28,38,39]. To further investigate the subsurface deformation mechanism in workpiece during the ultraprecision machining process for structured diamond tools, a statistic analysis of coordination number of the silicon atoms is given [40]. From Fig. 2(e)-(f), the number of atoms with five and six coordinated atoms versus machining distance for the four simulations is displayed, respectively. It is seen that although the number of five-coordinated and six-coordinated atoms increases as the machining distance increases, the five-coordinated atom increases more rapidly than the six-coordinated atom. The phenomena can be attributed to the instability of the beta-silicon below ∼4 GPa on unloading [38]. Thus, when the tool passes, metallic beta-silicon (more dense and low volume) loses its crystalline order and transforms into a-Si (more structural volume) and other phases, such as BC8 (bcc) and R8 (Rhombohedral) [41], which causes expansion and the consequent elastic recovery of the machined surface after the passing of the tool. Moreover, it can be observed from Fig. 2 (f) that when the diamond tool is non-structured, the number of six-coordinated atoms is the least. This indicates that for non-structured tool machining, less metallic and ductile beta-silicon forms from its original diamond cubic structure.
The stress components within the workpiece in a machining operation are defined in Fig. 3(a). For the investigation of von Mises stress and hydrostatic stress during the nanoscale machining process, each of the stress components
xx , yy , zz , xy , xz 8
and
yz
of atom i are calculated.
According to previous reports [27,28], where
(1/ )i (mi vi vi (1/ 2)i j rij fij ) , N
is the virial stress components of atom i,
, =x, y, z is the Cartesian components.
stands for the volume of the domain within the cut-off distance of atom i. mass, the
-component
and
-component
of the velocity of atom i, respectively. represents
the tensor product of vectors. N is the total number of atoms in the domain. of the vector
mi , vi and vi are the
rij is the -component
rij , rij is the distance between atom i and atom j. Fij is the -component of the
interaction force on atom i action by atom j. Von Mises stress and hydrostatic stress can be expressed as:
von 3( xy2 yz2 xz2 ) (1/ 2) ( xx yy ) 2 ( xx zz ) 2 ( zz yy ) 2
,
hydro (1/ 3)( xx yy zz ) . The von Mises stress distributions of workpiece for pattern B is illustrated in Fig. 3(b). High pressure phase transformation can be observed in machining ductile material silicon. Therefore, plastic deformation depends upon high pressure phase transformation (HPPT) and dislocation nucleation during the nanoscale machining process. Noted that a lot of dislocations nucleate are alongside HPPT, which indicates that HPPT first occurs, followed by stacking faults/twin structure, finally dislocations slipping along Si {111} planes [42]. Local hydrostatic stress distribution of workpiece for pattern B is calculated and shown in Fig. 3(c). Interestingly, high hydrostatic stress occurs in front of and beneath the tool edge. It is noted that the phase transformation silicon atoms (five coordinated and six coordinated) are also mostly located in this region (as shown in Fig. 2), which reveals that the evolution of crystalline phases is consistent with the distribution of hydrostatic stress [43]. Fig. 3(d) illustrates the displacement of atoms in the workpiece for pattern B during the machining process. The atoms are colored according to their displacements. It is found that the atoms in the chips and groove of tool have the maximum displacement, and the atoms in front of tool edge also significantly move under high hydrostatic stress (as shown in Fig. 3(c)). It reveals that 9
the silicon atoms on both sides of the tool flow along the groove of tool under high forces, which is beneficial to the heat dissipation of the subsurface atoms. Hydrostatic stress is a quantity associated with volume change leading to classic thermodynamic phase transitions in continuous matter, whereas von Mises stress measures shear deformation that governs shape change usually by the activation of defect transport mechanisms [44]. Therefore, hydrostatic stress and von Mises stress have made a contribution to the dislocation nucleation and motion, as well as the atoms phase transitions. Fig. 3(e) shows the average von Mises stress of subsurface atoms for different structured tools. It is clear that apart from pattern A (2.41 Gpa), the average von Mises stress of subsurface atoms for non-structured tool being 2.54 GPa is smaller than that of using the structured tools (2.57 Gpa for the pattern B, 2.62 Gpa for the pattern C). The variations of average hydrostatic stress of subsurface atoms with the machining distance for different structured tools are demonstrated in Fig. 3(f). It can be observed that the average hydrostatic stress of subsurface atoms rises rapidly at the initial machining stage, and then reaches a relatively stable stage as the machining distance increases. By comparing four different structured tools, obviously, the average hydrostatic stress of subsurface atoms for non-structured tools is larger than those for structured tools, which leads to bigger cutting forces.
The stress components in the subsurface of workpiece are demonstrated in Fig. 4. are the normal stresses in the x and y directions, and normal stress of subsurface atoms advance of the tool,
xx
xx
xy
xx
and
yy
stands for the shear stress. The average
is calculated and shown in Fig. 4(a). It is evident that with the
rapidly decreases at initial machining stage, and then slightly increases at
steady machining stage. The stress of subsurface atoms exhibits the similar trend for different 10
structured tools. The average normal stress Evidently,
yy
yy
of subsurface atoms is also shown in Fig. 4(b).
decreases as the machining distance increases for the four different structured tools. It
is evident from Fig. 4(a) and (b) that the normal stress
xx
and
yy
are the compressive stress. This
is due to the compression effect from the tool [27]. In addition, it is clear from Fig. 4(a) and (b) that the normal stress
xx
and
yy
for non-structured tools are overall more compressive than that of using
structured tools. The reason is that the workpiece undergoes higher drastic hydrostatic pressure when a non-structured tool is applied (as shown in Fig. 3(f)). The high hydrostatic pressure enables plastic deformation that concentrates in front of the tool edge, and in turn makes the single crystal silicon transformed into a more ductile state. The deformed silicon atoms are not able to return to its original diamond cubic structure. As such, the non-structured tools tend to machine silicon in a more ductile mode than corresponding structured tools under the same configuration of other machining parameters. Fig. 4(c) shows the average shear stress shear stress
xy
xy
of subsurface atoms for different structured tools. All
are averaged over the machining distance from 6 to 18 nm where machining is in a
steady stage. According to the work [45], dislocation emission will take place only when shear stress is larger than material flow stress. It can be seen from Fig. 4(c) that the shear stresses
xy
for pattern C
is much larger than that for non-structured tools. This result reveals that the partial dislocation emission is more likely to occur on a tool with V-shape grooves during the nanoscale machining process.
Fig. 5(a) illustrates the relationship of other atoms with machining distance for different structured tools. It is obvious that other atoms increase with the increase of machining distance for different structured tools. The number of other atoms for non-structured tools, pattern B and pattern C are nearly the same. But the number of other atoms for pattern A is much lower than that of using other structured 11
tools. The radial distribution function, also called pair distribution functions or pair correlation functions, is the primary linkage between macroscopic thermodynamic properties and intermolecular interactions. As shown in Fig. 5(b), it is obvious that bond length is 2.35 Å of the largest number of atoms for the four simulations, which are consistent with the bond length of alpha-silicon (Si-I) in theory. It is well known that beta-silicon (Si-II) contains four nearest neighbours at a distance of 2.42
Å and two other neighbours at 2.58 Å [28]. it is obvious from Fig. 5(b) that the bond number with a length of 2.58
Å for non-structured tool is less than that of using structured tools, which
reconfirmed that for non-structured tool machining, there are less silicon atoms undergo phase transformation change from alpha-silicon to beta-silicon during the nanoscale ultraprecision machining process. Fig. 5(c-f) shows the atoms of different lattice structures for different structured tools at the machining distance of 18 nm, based on the common neighbor analysis (CNA) [46]. In this work, atoms are colored according to the calculated CNA values: Blue presents diamond cubic crystal structure atoms, and gray for other atoms including beta-silicon and dislocation atoms, as well as surface atoms. It is found from Fig. 5(c-f) that structured tools largely influence the dislocation from the penetrated surface. Furthermore, it can be seen that dislocation nucleation and growth on the (1 0 0) plane, and dislocation propagate along the [1 0 -1] (1 1 1) slip systems.
Fig. 6(a)-(d) demonstrates the surface morphologies and the residual cross-section profiles of the machining grooves for different structured tools at the machining distance of 18 nm. It is found that the cross-section profiles are strongly influenced by the structured tools, but the volume of material pileups on the sides of groove slightly affected. Fig. 6 (e) shows the number of atoms in chip versus the 12
machining distance for different structured tools. As known, with the advance of the tool, more workpiece atoms accumulate and pile up in front of and on both sides of the tool. A comparison of different structured tools indicates that the chipping volume for non-structured tool is the largest, and the pyramid-structured tool (pattern A) is the smallest. This means that structured tool reduce the material removal rate during the nanoscale machining process.
Force measurement is an important indicator of tool wear, normal force mainly influences surface error, as it tends to separate the tool away from the workpiece, and the tangential force causes displacements in the direction of cut chip thickness [47,48]. To further study the effects of structured tools, the forces during the machining process are obtained by summing the atomic forces of workpiece atoms on tool. The average tangential forces (in the x direction) and normal forces (in the y direction) for machining distances of 6-18 nm where machining is in a steady state are calculated, as shown in Fig. 7(a). The lateral force (in the z direction) is not calculated since its average value is zero during the machining process because of the balanced forces contributing from the two sides of the groove. From Fig. 7(a), both the tangential force and normal force for non-structured tools machining are bigger than that of using structured tools. The reason is that non-structured tool machining produces more chips
requiring larger forces to complete this machining process. This result also reveals that a structured tool can reduce the force of workpiece on tools during the nanoscale machining process. Friction coefficient is an important factor in nanoscale machining, which is defined as the ratio of the average tangential force to the average normal force, and it measures the material removal ability. Fig. 7(b) shows the average frictional coefficient for different structured tools. It can be observed that non-structured tool machining (0.936) experiences a slightly higher resistance rate than that of using 13
pattern C (0.929) but much lower than those of using other structured tools (1.265 for the pattern A, 1.263 for the pattern B). This result means that the tool with V-shape groove (pattern C) can reduce the resistance to cutting during the nanoscale machining process.
The temperature-displacement curves for subsurface atoms under different structured tools are shown in Fig. 8(a). In conventional machining operations, the energy from plastic deformation in the primary shear zone and sliding friction along the tool-chip interface generate heat. It can be seen from Fig. 8(a) that as the machining distance increases, the average temperature of subsurface atoms rapidly rises at initial machining stage, then reach a steady state. What’s more, it is clearly found that the temperature of subsurface for non-structured tools is the highest in that for structured tool machining, the silicon atoms on both sides of the tool are allowed to flow along the groove of tool under high forces, which accelerates the heat dissipation of the subsurface atoms. This result also reveals that structured tools are more conductive to reduce the temperature of workpiece subsurface comparing with non-structured tools. Potential energy is the energy of a system as a result of the atomic position or the particle arrangement of the system, which marks the stability of the system in energy [31]. The potential energy of subsurface atoms versus the machining distance for different structured tools is also plotted as shown in Fig. 8(b). Obviously, the potential energy of the subsurface atoms increases with the increase of machining distance. However, it is noted here that the potential energy of subsurface atoms increases more slowly at the plastic deformation stage than that at the initial elastic deformation stage. Additionally, a comparison of different structured tools indicates that the slops of potential energy to machining distance curves for the pattern C and pattern B are higher than that of using a non-structured 14
tool. However, the potential energy of subsurface atoms for pattern A is lower than that for non-structured tools. This means that the workpiece undergone different degrees of deformation during the nanoscale machining process using different structured tools. Based on the above analysis, conclusions can be drawn that during the nanometric machining process, the structured tools perform better in most of the investigated aspects. Moreover, the results suggest that pyramid-structured diamond tool is the most suitable structured tool for nanometric machining because the pyramid-structured tool machining results in the lowest von Mises stress and shear stress, the least number of other atoms, the smallest cutting force, the lowest subsurface temperature and potential energy.
4. Theoretical model
For a deeper understanding of friction and wear on the nanometric ultraprecision machining, a theoretical analysis model is established to study plastic deformation patterns and subsurface damage. Fig. 9 shows the Schematic of the machining process and the relevant residual stress field. With the advance of tool on the workpiece surface, it produces a scratch groove surrounded by a phase transformation region, which is encompassed in an elastic zone, as shown in Fig. 9. The residual stress field arises due to the plastic deformation and its components on the x-y plane at a depth z=c below the machining surface is given by [49-51].
x
x 2 B 2v( y02 z02 ) 2 2 02 2 5 (2vx04 y02 2 x02 y04 6vx02 y04 2 2 2 c ( y0 z0 ) ( y0 z0 ) 0 -2y06 4vy06 2vx04 z02 4 x02 y02 z02 2vx02 y02 z02 3 y04 z02 +6vy04 z02 2vx02 z04 4vx02 z04 z06 2vz06 )
15
(1)
y
x 2 B 2 y02 ( y02 3z02 ) 2 02 3 5 (2 x04 y04 6 x02 y06 2vx02 y06 2 2 2 3 c ( y0 z0 ) ( y0 z0 ) 0 +4y08 2vy08 6 x04 y02 z02 7 x02 y04 z02 6vx02 y04 z02 2vy06 z02 8vy06 z02 12 x02 y02 z04 6 v x02 y02 z04 15 y04 z04 12 v y04 z04 +x02 z06 2vx02 z06 8 y02 z06 8vy02 z06 z08 2vz08 )
z
x0 z02 2 B 2 z02 ( z02 3 y02 ) (6 x04 y02 15 x02 y04 9 y06 2 2 2 3 2 2 3 5 c ( y0 z0 ) ( y0 z0 ) 0 -2x04 z02 10 x02 y02 z02 12 y04 z02 5 x02 z04 3 y02 z04 6 z06 )
xy
2(1 v) x02 2(1 v) y02 z02 2vz02 2B y 0 c2 05
yz
(y02 z02 ) x yz 2B 4 y z 2 0 02 03 5 (4 x04 y02 10 x02 y04 0 0 2 2 2 3 c ( y0 z0 ) ( y0 z0 ) 0 6 y06 -4x04 z02 3 y04 z02 10 x02 z04 12 y02 z04 9 z06 )
zx Where
(2 x02 2 y02 z02 ) 2B z 0 c2 05
(2)
(3)
(4)
(5)
(6)
x0 x / c , y0 y / c , z0 z / c 1 , 0 x 2 y 2 z 2 / c , v is the Poisson’s
ratio of the materials, d is the phase transformation zone size. According to work [49,50], B represents the strength of the sliding blister field, it can be determined by
B Where f ,
3 fahE 4 (1 2 )(1 )
a, E
and
(7)
h are the compaction factor, the contact zone size, Yong’s modulus and the
depth of scratching, respectively. fE / H 1.09 as a critical value for sharp machining tool. H is the hardness. The stress components within the workpiece in a machining operation are defined in Fig. 3(a). For the investigation of residual stress, we focus on
x , y , and xy . The silicon materials in this
study, the following parameters are adapted in calculation: the Yong’s modulus E =160 Gpa, H =12.5 Gpa, Poisson’s ration
=0.22, h =1 nm, a =11.4 nm. 16
Fig. 10 shows the 3D distribution of the residual stress for
=0.22 and z0=1 on the x-y plane in
the vicinity of diamond tool during the scratching process. As shown in Fig. 10(b), as the tool moves along the x direction from x0=-6 to x0=0, the normal residual stress
x
during the scratching process. However, the normal residual stress advance of the tool. It is observed that normal residual stresses beneath the tool. But the shear residual stress
xy
firstly declines, and then rises
y
x
slightly declines with the and
y
are highly tensile
is slight compressive in the wake of the scratching
tool, while shear residual stress is tensile at both sides of the groove. It is clear from Fig. 10(b) that the tensile residual stress
x
the normal residual stress
reaches its maximum value just beneath the tool along the x-axis. However,
y
is reduced to its minimum value beneath the tool during the scratching
process. The normal residual stress
y
reaches its maximum value away from the x-axis on both
sides of the tool, and its value is much larger than shear residual stress
y .
What’s more, the shear residual stress
xy
xy
and normal residual stress
also reaches its maximum value away from the
x-axis on both sides of the tool. From the distribution of residual stress, it should be noted that residual stress plays an important role in the scratching process and is known to contribute to the component’s surface properties and performances. For example, the compressive residual stresses are regard as beneficial in that they help decrease the crack rates, and then enhance the structural integrity [23,24].
5. Conclusions In this work, large-scale MD simulations are carried out to study the nanoscale machining process when using structured tools and non-structured tools. According to the simulation results, Main conclusions are drawn as following:
17
1) The structured tools have a significant effect on nanometric machining process. Results show that for non-structured tool machining, less metallic and ductile beta-silicon forms from its original diamond cubic structure. The silicon atoms on both sides of the tool flow along the groove of tools under high forces, which is beneficial to the heat dissipation of the subsurface atoms. 2) The average hydrostatic stress of subsurface atoms for non-structured tools is larger than that for structured tools, which makes the normal stress
xx
and
yy for non-structured tool overall
more compressive than that of using structured tools. 3) The non-structured nanoscale tool machining results in more chip volume. However, the temperature of subsurface for non-structured tool machining is higher than that of using structured tools. This means that the structured tool is more conductive to reduce the temperature of workpiece subsurface comparing with a non-structured tool. Additionally, the potential energy of subsurface atoms and the number of other atoms for pyramid-structured tool are much lower than that of using other structured tools. 4) Both the tangential force and normal force for non-structured tool machining are bigger than that of using structured tools. The reason is that non-structured tool machining produces more chips
requiring larger forces to complete this machining process. However, the friction coefficient for tools with V-shape groove is smaller than those for non-structured tools and other structured nanoscale tools. This means that the tools with V-shape groove can reduce the resistance to cutting during the nanoscale machining process. 5) The results of theoretical model indicate that residual stress plays an important role in the scratching process and is known to contribute to the component’s surface properties and performances. 6) In future work, the influence of structured nanoscale diamond tool on subsurface damage and 18
material removal during the nanometric machining process will be further studied, such as groove factor, groove shape, groove direction, groove depth, groove width. Furthermore, the MD simulation results will be compared with the experiment results.
Acknowledgements The authors would like to appreciate the support from the National Science and Technology Major Project of the Ministry of Science and Technology of China (No.2012ZX04003101)
19
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[48] S. Goel, X. Luo, A. Agrawal, et al. Diamond machining of silicon: a review of advances in molecular dynamics simulation[J]. International Journal of Machine Tools and Manufacture. 88 (2015) 131-164. [49] Y. Ahn, T. N. Farris, and S. Chandrasekar. Sliding microindentation fracture of brittle materials: Role of elastic stress fields. Mechanics of materials. 29(1998) 143-152. [50] X. Jing, S. Maiti, G. Subhash. A New Analytical Model for Estimation of Scratch‐Induced Damage in Brittle Solids. Journal of the American Ceramic Society. 90(2007) 885-892. [51] D. Ghosh, G. Subhash, R. Radhakrishnan, et al. Scratch-induced microplasticity and microcracking in zirconium diboride–silicon carbide composite. Acta Materialia. 56(2008) 3011-3022.
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Fig. 1
MD simulation model of nanometric precision machining of silicon with nano-structured
diamond tool: (a) the 3D model of non-structured diamond tool machining; (b) surface morphologies of pyramid-structured diamond tool (pattern A); (c) surface morphologies of diamond tool with arc-shape groove and V-shape groove; (d) diamond tool with arc-shape groove (pattern B); (e) diamond tool with V-shape groove (pattern C).
25
Fig. 2 The cross-section view of the atomic positions for different structured tools at machining distance of 18 nm. (a) Non-structured tool, (b) Pattern A, (c) Pattern B and (d) Pattern C. Atoms are colored according to coordination number (CN). (Four-coordinated diamond cubic silicon atoms are invisible). (e) and (f) are the number of atoms with five-coordinate and six-coordinate nearest neighbors against machining distance, respectively.
26
Fig. 3
Stress components in the machining (a), von Mises stress distribution (b), hydrostatic stress
distribution (c), atomic displacement (The atoms are colored according to their displacements) (d), average von Mises stress of subsurface under different structured tools (e), and average hydrostatic stress of subsurface versus the machining distance for different structured tools (f).
27
Fig. 4
Stress evolution of the subsurface of workpiece for different structured tools: (a)
and (c)
xy .
28
xx , yy ,
Fig. 5
Evolution of other atoms for different structured tools (a). The radial distribution function of
workpiece atoms in MD model for different structured tools (b). The partial cross-sectional views of studying the influence of nano-structured tools is (c) non-structured tool, (d) pattern A, (e) pattern B and (f) pattern C at the machining distance of 18 nm. Atoms are colored according to the calculated CNA values in (c)-(f) (Diamond cubic crystal structure in blue, other atoms in gray)
29
Fig. 6
Surface morphologies of studying the influence of different structured tools is (a)
non-structured tool, (b) pattern A, (c) pattern B and (d) pattern C workpiece after machining at machining distance of 18 nm. The height of atoms differs with colors. (e) The number of atoms in chips against the machining distance.
30
Fig. 7
Variation of the average force (a) and frictional coefficient (b) under different structured tools
at machining distance of 18 nm.
Fig. 8
Effect of structured tool. (a) Variation of average temperature of subsurface, and (b) variation
of potential energy of subsurface.
31
Fig. 9
(a) Schematic of the machining process. (b) A diagram of the cross-sectional view of the model.
Note that the cross-sectional view is perpendicular to the machining direction.
Fig. 10
Distribution of residual stress (a). Normal residual stress
residual stress
xy
x
(b),
y
(c) and shear
(d) on the x-y plane. The blue triangle indicates the position of the scratching tool,
and the pink arrow indicates the scratching direction.
32
TABLE I.
Simulation parameters
Workpiece Materials Tool Materials Dimension of workpiece Numbers of silicon atoms in the workpiece Depth of cut Workpiece machining surface Initial temperature Machining distance Time step Machining speed
TABLE II.
Silicon diamond
23 nm 8.2 nm 17.4 nm
168864 1 nm [1 0 0] on (0 1 0) surface 300 K 0-18 nm 1fs
200 m/s
Processing conditions for the four simulation cases of nano-scale machining
MD model
Groove orientation,
non-structured
o
Groove
Groove
depth, nm
width, nm
0
0
Groove shape
Groove factor,% 100
Pattern A
30 and -30
1
2
Pyramid tip
Pattern B
30
0.4
0.8
arc-shape
27.27
Pattern C
30
0.4
0.8
V-shape
27.27
33