Depth of cut per abrasive in fixed diamond wire sawing

Int J Adv Manuf Technol(2015)80:1337–1346DOI10.1007/s00170-015-7089-zORIGINAL ARTICLEDepth of cut per abrasive in fixed diamond wire sawing Chunhui Chung1·Van-Nhat Le2Received:22August2014/Accepted:25March2015/Published online:19April2015©Springer-Verlag London2015Abstract Because of the high requirement for quality, the surfaces of prime wafers have to be flat and without damages.During the first machining process in wafer manu-facturing,the defects introduced by wire sawing must be removed by the subsequent lapping,grinding,and polis-hing processes.Therefore,the quality of sliced wafer is very important.Fixed diamond wire saw,on which the diamond grains are coated as abrasives,has become the major tool to slice ingot into wafers.Ductile-regime machining is an attractive process to achieve crack free surface on brittle materials in abrasive machining process.The depth of cut of the abrasive is a hint for the transition between ductile-and brittle-regime machining.In order to understand the cutting behavior in fixed diamond wire sawing,this paper presents an investigation of depth of cut per abrasive based on the wire profile model developed by the authors.The simulation results show that the larger depths of cut are unavoidable in fixed diamond wire sawing because of the random position and size distribution of diamond grains on the wire.Although the number of active abrasives and the depths of cut at the bottom of slicing groove are larger than those at the side of the groove,few larger diamond Van-Nhat Lelenhat@.vnChunhui Chungchunhui.chung@.tw1Department of Mechanical Engineering,National Taiwan University of Science and Technology,Taipei,Taiwan2Faculty of International Training,Thai Nguyen University of Technology,Thai Nguyen,Vietnam grains may introduce larger depths of cut and cracks on the side,which is the sliced wafer surface.Effects of pro-cess parameters to the depth of cut distributions are also analyzed.The variation in number of active abrasives in cutting zone as well as their depth of cut shows the pos-sibility to increase process productivity without increasing the depths of cut of the diamond grains.Consequently, the surface quality could be remained without further deterioration.Keywords Wire sawing·Diamond wire·Abrasive machining1IntroductionWire saw has been the prevailing tool to slice hard and brittle ingots into thin-disk wafers in semiconductor and photovoltaic pared to inner-diameter saw (ID saw),the main advantages of the wire sawing process are lower kerf loss and less wafer surface damage.When the wafer size is increased according to high demand of wafer production as well as the trend of cost reduction,the wire saw is expected to be the major tool to slice450mm sil-icon wafer[1].Furthermore,the diamond-coated wire has been utilized to replace slurry wire sawing process due to its high efficiency and less waste[2,3].Figure1is an SEM image of a diamond-coated wire and its model[4]. Figure2gives a schematic view of typical wire sawing process.Researchers have focused on different aspects of the wire sawing process which can be classified into mate-rial removal mechanism[5–7],process modeling[8–11], and parametric study between process inputs and outputsFig.1SEM image of a diamond-coated wire(left)and its model (right)[4][12–16].In order to fulfill the strict requirements in wafer surface quality,some studies concentrate the ways to mini-mize surface defects by controlling wire and process param-eters[5,13,14].Some suggestions have been made for improving surface quality[6,12,13].Increasing the wire speed and decreasing the feed rate are often recommended to achieve better sliced surface.However,most of these con-clusions are made based on experimental results.The trade-off between wafer surface quality and process productivity is still difficult to be balanced.A study of Gao et al.shows the possibility of optimal wire sawing process in which the ductile cutting happens mostly at the sides of the cutting groove and produces less damage on wafer surface.The brittle fracture at the bottom of the wire results in appropriate productivity[17].How-ever,the assumption that the abrasive grains are distributed evenly on the wire surface is far different from those on actual wire.In addition,the assumption that all of abrasive grains are assumed to be involving in cutting is impracti-cal because even a small difference in size or position of one abrasive could affect whether the abrasive contributes in cutting or not.When machining brittle materials with other processes such as turning and grinding,it is often possible to achieve pure ductile cutting regime by well-controlled depth of cut under certain value[18,19].It is doubtful whether the pure ductile machining exists in wire sawing or not,since the specific investigation of the depth of cut per abrasive in wire sawing is still absent,and most of sliced wafers still show a few cracks on the surfaces.The model of diamond-coated wire was proposed by the authors[4].This model successfully represents the surface of diamond-coated wire with the wire parameters including random characteristics in positions and sizes of the abra-sives.The slicing process has been simulated in other work of the authors[20]in which the sliced wafer surface is generated using the proposed wire model.In this study,the investigation of depth of cut per abra-sive during fixed diamond wire sawing is presented.The existence of abrasive in cutting zone as well as its ran-dom characteristics is considered in the model.The number of active abrasives,the depth of cut per abrasive,and the amount of material removed by each abrasive are defined by simulating one cross section of the ingot during slicing.The cutting groove is updated by the cutting behavior of each abrasive which is identified by both ploughing model and indentation fracture model proposed in the previous works. The results show that the brittle machining regime mainly contributes in material removal.The variation in number of active abrasives in cutting zone as well as their depth of cut show the possibility to increase process productiv-ity without decreasing the wafer surface quality.The effects of process parameters to the distributions of depth of cut are also discussed.The approach makes it possible to pre-dict the surface and subsurface damages in fixed diamond wire sawing with different slicing parameters.In addition, the depth of cut of all abrasives must be controlled to reduce the subsurface damage.2Model of material removal in abrasive machining of hard and brittle materialIn machining hard and brittle materials,ductile cutting regime exists at low depth of cut[19].Some research on ductile mode cutting of crystalline silicon have been reported[5,21,22].The critical depth of cut,at which the cutting mechanism transforms from purely ductile to brittle mode,depends on material property,tool shape,and cut-ting conditions.Higher depth of cut not only introduces the fractures and cracks beneath bulk material and result in higher material removal,but also increases wafer surface and subsurface damages.On the contrary,ductile-regime machining,which yields crack-free surface,is likely to hap-pen at the depth of cut lower than critical value.Priorwork Fig.2Schematic of multi-wire sawinghas been done to predict the critical depth for transition from ductile to brittle mode of cutting [19].d c =0.15EHK c H 2(1)where K c is the fracture toughness,H is the hardness,andE is the Young’s modulus of workpiece material.This expression,while useful,does not explicitly account for the effects of grain tip geometry and the friction to the critical depth of cut.Experimental works show that the critical depth of cut for hard material such as sin-gle crystal silicon,STV glass,and sapphire substrate are found to be between 0.1and 0.5μm [22].Diamond scrib-ing tests have been carried out,and the transitions between ductile and brittle cutting regimes on mono-crystalline sil-icon are under various depths of penetration for different conditions [5].The depth of cut of each abrasive directly identifies the cutting regime of that abrasive.The material removed from bulk material of each abrasive is varied and depends on whether the cutting mechanism in brittle mode or duc-tile mode.In ductile mode,the material removed area is estimated by projected area of the penetrated abrasive tip following the slicing direction as seen in Fig.3.In brittle mode,in which the depth of cut is higher than critical value,the cracks propagated during loading helps to remove more material.It is assumed that the amount of material above the lateral cracks,which is calculated by the depth of the lat-eral crack,h ,and the length of the lateral crack,c ,will be removed after unloading (also see Fig.3).The depth and the length of the lateral crack can be obtained by the following equations [23,24].h ≈b ≈⎡⎣ E H12H 12⎤⎦(cot ψ)13P 12(2)andc =⎛⎝ζ12L M14⎞⎠(cot ψ)512E 12K 12c H12P 58(3)Fig.3Indentation model of single pyramidal indenter [23]where ζL =25×10−3,M =34,E is the Young’s modu-lus,H is the hardness,and K c is the fracture toughness of workpiece material.The normal load on the abrasive required to penetrate the workpiece is P =12πa 2H =12π(g tan ψ)2H (4)in which a is the radius of contact area and g is the depth of penetration of the abrasive.The length of lateral crack,according to theoretical ana-lysis as shown in Eq.3,could be an impractical value since the coefficients remain unchanged regardless of material properties and scribing conditions.For example,the criti-cal depth of cut of 0.5μm will introduce the lateral length of 22.7μm based on Eq.3,which is quite different from the results in the experimental work conducted by Wu et al.[5].In this study,the length of lateral crack induced by each abrasive is assumed to be about the size of plastic zone,b ,based on diamond scribing test on silicon and subsurface stress analysis [5].3Modeling of the depth of cut per abrasive in fixed diamond wire sawing3.1Coordinate setting and definitions of wire and cutting groove profileOne cross section of the silicon ingot is considered during slicing as depicted in Fig.4.In the figure,v x is wire speed and v z is feed rate.The polar coordinate system is set with the origin O fixed at the wire center and the polar axis is aligned in lateral direction of the wire as seen in Fig.5.TheFig.4Simulating section of the ingot during slicingFig.5Coordinate setting for the simulationCartesian coordinate system is also employed with the sameorigin with the polar coordinate.Coordinate y is set hori-zontally to the right,and positive z is vertically down as the wire slicing direction.It is assumed that the slicing process is at a steady state,in which the rate of wire slicing into the workpiece is the same as the feed rate without further bending the wire.Let Δt be the time interval which is defined small enough to achieve appropriate accuracy in the simulation.In one time interval,the length of the wire crossing the simulating area can be estimated as:ΔL =v x Δt(5)where v x is the wire speed.At each step,a new wire profile will be generated by the method in Section 3.2.In this model,the peripheral profile of bottom of the cut-ting groove and the wire are divided by N point which are equivalent to (N −1)segments.The polar element angle of each segment is:Δθ=180◦N −1(6)Let W i θi ,r w i and T i θi ,r t ibe the two arrays present-ing the cutting groove and the wire profiles in which r w i and r t i are the radial distances from the i th point of the cutting groove and the wire profile to the coordinate ori-gin,respectively.The two profiles can be also converted to W i y w i ,z w i and T i y t i ,z t i ,respectively,in the Cartesian coordinate system (also see Fig.5).The polar angle spec-ifying the i th position on the cutting groove and the wire profile is calculated as:θi =(i −1)Δθ,i =i...N(7)The wire center is fixed at the coordinate origin during simulation.The relative motion between cutting groove and the wire profile is required to simulate process feed rate.Therefore,workpiece is moving in negative z direction withthe increase of time in this model.In each step,the transver-sal distance is calculated by the process feed rate and the time interval:Δz =v z Δt(8)where v z is the process feed rate.The cutting groove after transformation is identified based on Cartesian coordinate system,as shown in Fig.6:W i y w i ,z w i,t +Δt =W i y w i ,z wi −Δz,t (9)After the coordinate transformation,the polar angle specifying the position of cutting groove profile is changed from θi to θ i ,as depicted in Fig.6,which can be calculated as:θ i =arctan z w i −Δzy w i (t) ≈jΔθ(10)Because the transversal distance depends on the time interval setting value as well as the feed rate,the angle θ i will not be aligned with any of the polar angles which are defined according to the polar element angle Δθ.Therefore,the i th position of the array representing the cutting groove will be moved to the j th position which is closest to the updated data point and best presents the cutting groove point after coordinate transformation.3.2Generation of wire profileThe model of diamond-coated wire has been developed by the authors [4,20].This model was employed in this study to generate the surface profile of diamond-coated wire.The wire profile is formed depending on wire parameters including random characteristics of abrasives.The steel core diameter,wire outer diameter,the size,shape,and density of abrasive abrasives are the main parameters of diamond-coated wire.The shape of diamond abrasive variesandFig.6Coordinate trasformation of W i for each stepdirectly affects the cutting efficiency of the process.To sim-plify the model,all of the diamond abrasives are considered to be conical shape with the tip angle of 2ψ,and all abra-sives contact to wire core surface.In addition,the sizes of abrasive grains are assumed to follow the Gaussian distri-bution according to the previous works [26].At each time interval,the wire profile with the length ΔL was generated and projected to the simulating cross section to study the depth of cut per abrasive.The number of abrasives on the bottom half of the wire crossing the ingot during time interval can be estimated as:ΔK =ηπdΔL 2=ηπdv x Δt 2(11)where d is the diameter of wire core and ηis the diamond abrasive density.The random position of abrasives is defined by the possibility of existence of an abrasive,which is:s =ΔK N =ηπdv x Δt 2N(12)where N is the number of nodes on the peripheral surface of bottom half of the wire.If the existence of an abrasive at the i th point is con-firmed,then the abrasive size,r g ,will be identified accord-ing to probability density function as follows:p(r g )=1√2πσe−(μ+log (r g ))22σ2(13)where μand σare abrasive mean size and standard devia-tion of abrasive size range,respectively.The radial distance of abrasive tip to the center of the wire T i θi ,r t iis definedFig.7Defining wire profileFig.8Conflicts in identifying the wire profileas:r t i =d2+r g (14)The profile of diamond-coated wire at the neighboring points,j th ,is also updated according to the geometry of diamond abrasive as (Fig.7):r tj≈r t i −r t i θij cot ψ(15)There will be conflicts in updating radial profile if two abrasives are overlapped,as seen in Fig.8.In this case,the radial profile at the overlapped point,i th ,will be updated as:r t i =max r t iA ,r tiB (16)where r t iA and r t iBare two radial distances updated by the two overlapped abrasives A and B,respectively.3.3Updating cutting groove profile based by cutting regime of each abrasiveThe initial cutting groove profile W i θi ,r w iis defined by outer diameter of the wire,d o :r w i =d 02,i =1...N(17)If there exists an abrasive at the considering point,the depth of cut of the abrasive is defined by the disparity between the cutting groove and wire profile.It is assumed that the elastic deformation of the workpiece and the wire has no effect to the depth of cut of the active abrasives.Therefore,the depth of cut of an active abrasive is:g i =r t i −r wi (18)Fig.9Different cutting behaviors in cutting zone of wire sawing processThe cutting groove profile is updated based on the amount of material removed by individual active abrasive,as illustrated in Fig.9,which is identified according to cutting behaviors as follows:–No interaction between abrasive and workpiece (Abra-sive A):g i ≤0r w i =max r w i ,r t i=r w i (19)–Cutting regime is in ductile mode (Abrasive C):0≤g i ≤g c ,where g c is the critical value depth of cut,at which the cutting transits from ductile to brittle mode.r w i =max r w i ,r t i=r ti (20)–Cutting regime is in brittle mode (Abrasive B):g i >g c r w i =r w i +h(21)where h is the depth of lateral crack introduced by thecurrent abrasive,which can be obtained by Eq.2.For ductile machining,the profile of cutting groove is updated by the shapes of diamond grains.For brittle machining,the profile of cutting groove is updated accord-ing to the indentation cracking model as illustrated in Fig.3.4Simulation procedureFigure 10presents the simulation procedure of the proposed model.The simulation starts with the input of the wire and process parameters.The time interval and polar angle ele-ment are also defined in the simulation input stage.At each loop,the number of abrasives and the position and size of each abrasive grain are identified to generate new wire profile based on the given parameters.The cutting groove profile is then updated by the cutting behavior of individual abrasive and then transformed to the new coordinate by sim-ulating process feed rate.The positions of active abrasives and their depth of cut are recorded at eachstep.Fig.10Simulation procedure5Simulation resultsThe program of numerical simulation was compiled in MATLAB program.Three simulations have been conducted with different process parameters.The time interval,ele-ment polar angle,and total feed were set at 10−3s,0.1◦,and 500μm,respectively.The abrasive tip angle is assumed to be 90◦.The properties of single crystalline silicon are listed in Table 1.Table 2shows the parameters of the wire which were retrieved from SEM images.The critical depth of cut of single crystalline silicon is assumed to be 0.5μm accord-ing to the previous works [5,22].Different feed rate and wire speed were set as listed in Table 3in order to investigate the effects of these parameters to abrasive cutting behav-ior in wire sawing.Figure 11is an example of illustration during simulation.Table 1Material properties of single crystalline silicon [27]Young’s modulus Hardness Fracture toughness 127GPA10GPa0.7MPaTable2Wire saw parametersParameters Unit ValueWire outer diameterμm250 Core diameterμm190 Abrasive mean sizeμm50 Abrasive size rangeμm40–60 Abrasive density Abrasive/mm250The abrasives which contact the workpiece and con-tribute to material removal are considered as active abra-sives.We define active abrasive ratio as the ratio of the number of active abrasives to the number of all abrasives passing the cross section in the simulation.The simulation results of active abrasive rates are listed in Table4.These results indicate that the assumption of all abrasives involved in cutting in wire sawing process is impractical.Figures12,13,and14are the graphs of the depth of cut per abrasive during slicing with different feed rates and wire speeds.Although the cutting frequency with lower depth of cut is higher than that of with higher depth of cut,a lot of abrasives are still cutting with the depths of cut larger than critical value.Under different process parameters in the simulations,the number of brittle regime cutting abrasives always occupy a small portion of the total number of active abrasives.Thus,it seems impossible to obtain the pure duc-tile machining regime in wire sawing process.The surface and subsurface damages introduced by brittle cutting always take place in sliced wafer surface.Figure12shows the distribution of depth of cut under different feed rates.When doubling the feed rate,there is a significant decrease in number of abrasive cutting in duc-tile mode.The number of cutting abrasives with the depth of cut above1.4μm is larger with higher feed rate.How-ever,it is insignificant compared to the number of active abrasives in ductile mode.It is expected that these active abrasives in brittle mode contribute much more material removal than those in ductile mode.Figure13is the com-parison of the depth of cut distributions under different wire speeds.The plot shows the increasing number of ductile cut-ting abrasive when the wire speed is doubled.It is noted that increasing wire speed or decreasing feed rate increases sig-nificantly the number of ductile cutting abrasives while the Table3Process parameters in the simulationSimulation Wire speed Feed rate(m/s)(μm/s)A5 6.25B10 6.25C1012.5Fig.11Display of a simulation.The profile of diamond-coated wire was projected to the simulation sectionnumber of brittle cutting abrasives decreases,although the change is insignificant for brittle mode.However,the mate-rial removal still relies on brittle cutting regime even though the number of ductile cutting abrasives is large.When both feed rate and wire speed are doubled,the dis-tributions of the depth of cut seem unchanged as shown in Fig.14.According to Table4(simulation A and C), the average depth of cut and the active abrasive rate have not changed much when both increased feed rate and wire speed.This comparison shows that the process productivity can be increased without increasing damage on sliced wafer surface by increasing feed rate proportionally with respect to wire speed.This result is similar to other works based on the experimental results[12,14].The distribution of active abrasive in cutting zone is shown in Fig.15.The position angle is measured from the horizontal axis.There are more active abrasives at the bot-tom of the wire than those at other positions in cutting groove during slicing.The comparison between the number of active abrasive and the depth of cut in different area in cutting zone is shown in Fig.16.The ranges of side and bot-tom area of the cutting groove are defined from0◦to10◦for the side cutting and80◦to90◦for the bottom cutting.They have different numbers of active abrasives as well as the depth of cut per abrasive.More active abrasives with higher depth of cut take place at the bottom of cutting groove rather than the side.In addition,the depth of cut over2μm is almost not available in side cutting range.This result indi-cates that ductile-regime machining dominates the side-wall Table4Active abrasive ratio and average depth of cutSimulation Active abrasive ratio Average depth of cut(μm)A0.23%0.68B0.15%0.58C0.22%0.70Fig.12Comparison of depth of cut distribution under different feed rate (v x =10m/s and total feed of 500μm)cutting.However,large depth of cut still exists.This is the reason why the cracks on the sliced wafer surface always exist.6DiscussionFrom the simulation results,it is clear that the number of active abrasives and the depth of cut per abrasive depend on the interaction of wire speed and feed rate.In abrasive machining process,the number of active abrasives is not measurable,as well as the active abrasive ratio.This is the reason why we study this topic by simulations.The three simulation results are illustrated and compared in Figs.12,13,and 14.Either the double of wire speed or the half of feed rate increases the usage of wire length.However,the number of active abrasives is not proportional to theincreaseFig.13Comparison of depth of cut distribution under different wire speed (v z =6.25μm/s and total feed of 500μm)Fig.14Comparison of depth of cut distribution under different wire speed and feed rate (total feed of 500μm)of wire speed or inverse proportional to the decrease of feed rate.The reason is because of the transition between ductile-and brittle-regime machining.Higher feed rate will reduce the time of machining and the usage of wire.However,each abrasive must remove more material and penetrate deeper into the workpiece.It can be observed from Fig.12that the number of active abrasives with depth of cut over 1.4μm in higher feed rate is larger than that of in lower feed rate.These abrasives with larger depth of cut can remove much more material due to the brittle fracture.The decrease of wire speed also reduces the usage of wire length and num-ber of active abrasives,as shown in Fig.13.However,more active abrasives remove material with larger depth of cut,and more fracture are expected.During wire sawing process,the abrasives at the bottom of diamond-coated wire penetrate directly into the work-piece with the increase of feed.It is expected thattheseFig.15Distribution of active abrasives in cutting zone (v x =10m/s;v z =12.5μm/s and total feed of 500μm)Fig.16Number of active abrasives and the depth of cut in side and bottom cutting zone(v x=10m/s;v z=12.5μm/s and total feed of500μm)abrasives contribute most of material removal.For the abra-sives at the side,the motion of the diamond grains is parallel to the wall of slicing groove,which results in shallow depth of cut.Figure16illustrates the distribution of number of active abrasives with respect to the depth of cut.The num-ber of active abrasives in side cutting is less than that in bottom cutting.In addition,the number of active abrasives in side cutting reduces quickly with the increase of depth of cut.However,it is unavoidable that the larger depth of cut still happens occasionally in side cutting,which results in the cracks on the sliced wafer surface.Although the larger depth of cut cannot be avoided at the side of slicing groove,it is observed that the increase of wire speed and the decrease of feed rate can reduce the number of active abrasives with larger depth of cut.The trade-off between the process productivity and the wafer surface qual-ity can be discussed by the simulation results presented in this paper.The material removal can be maintained effec-tively while ductile-regime cutting dominates the two sides of the wire with the increase of wire speed to the machine limitation.Reduction of feed rate is an alternate method which also reduces the productivity,however.7ConclusionIn this paper,the model to investigate the depth of cut per abrasive has been developed.Different cutting behaviors of abrasive and their characteristics including random features in size and position are considered in the puter simulation has been employed to study the depth of cut per abrasive as well as its distribution.The conclusions are as follows:–The number of abrasives that contributes in cutting is small compared to the number of abrasives on the wire.More active abrasives take place on bottom of the wire than other positions during slicing.–Material removal during slicing is mainly contributed by brittle cutting regime.Pure ductile-regime machin-ing seems to be unattainable since the large depths of cut are frequently involved in slicing.–It is possible to increase the process productivity without increasing wafer surface and subsurface dam-ages because the distribution of depth of cut remains unchanged when increasing feed rate is proportioned with the wire speed.The approach presented in this study could be used to opti-mize practical wire sawing to increase process yield while limiting the wafer surface damage.References1.Goldstein M,Watanabe M(2008)450mm silicon waferschallenges—Wafer thickness scaling.In:Honolulu,HI,United states,2008.ECS transactions.Electrochemical Society Inc., pp3–132.Tso P-L,Yan B-H(2005)A study of slicing process with thindiamond wire.In:3rd international conference on leading edge manufacturing in21st century,LEM,Nagoya,Japan,2005.Japan Society of Mechanical Engineers,pp619–6243.Sugawara J,Yamakawa M,Mizoguchi A(2001)Development offixed-abrasive grain wire saw.SEI Tech Rev52:87–904.Chung C,Nhat LV(2013)Surface generation of diamond coatedwire for wire sawing process.In:16th international conference on advances in materials and processing technologies.AMPT,Taipei, p20135.Wu H,Melkote SN(2008)Study of ductile-to-brittle transition insingle grit diamond scribing of silicon:Application to wire sawing of silicon wafers.J Eng Mater Technol134(4):1–86.Gao Y,Ge P,Li S(2009)Investigation of subsurface damagedepth of single crystal silicon in electroplated wire saw slicing.In:15th conference on abrasive technology in China:advances in grinding and abrasive technology,Laubisrutistr.24,Stafa-Zuerich, CH-8712,Switzerland,2009.Key engineering materials.Trans Tech Publications Ltd,pp306–3107.Chung C(2012)Abrasive distribution of the fixed diamond wirein wire sawing process.Adv Mater Res579:145–1528.Li J,Kao I,Prasad V(1998)Modeling stresses of contacts inwire saw slicing of polycrystalline and crystalline ingots:applica-tion to silicon wafer production.J Electron Packag120(2):123–1289.Liedke T,Kuna M(2011)A macroscopic mechanical model of thewire sawing process.Int J Mach Tools Manuf51(9):711–720 10.Liedke T,Kuna M(2013)Discrete element simulation ofmicromechanical removal processes during wire sawing.Wear 304(1–2):77–8211.Nassauer B,Hess A,Kuna M(2014)Numerical and experimentalinvestigations of micromechanical processes during wire sawing.Int J Solids Struct51(14):2656–266512.Teomete E(2011)Effect of process parameters on surface qualityfor wire saw cutting of alumina ceramic.Gazi University J Sci 24(2):291–297。