《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_brittleness26

Materials Processing Technology Jourmal of Materials Processing Technology 168(2005)75-82 www.elsevier.com/locate/jmatp The critical conditions of brittle-ductile transition and the factors infuencing the surface quality of brittle materials ultra-precision grinding Mingjun Chen", Qingliang Zhao, Shen Dong, Dan Li Precision Engineering Research Institute, Harbin Institute of Technology, Harbin 150001, China Received 21 August 2002; received in revised form 29 December 2003; accepted 1 1 November 2004 Abstract Based on the indentation experiments under different loads, the critical conditions for the brittle-ductile transition of the brittle materials has been investigated from dynamic grinding, and the factors influencing the surface quality of the brittle materials have been analysed ultra-precision grinding theoretically. After having carried out the grinding experiments of the brittle materials, it was shown that influence of the average grain size of the diamond wheel on the surface quality is prominent. Compared to the wheel grain size, influence of wheel speed and feed rate on the surface quality is in secondary; these experimental results were consistent with the theoretical analysis. In the case of Us=1200 m/min, f=0-20 um/rev, ap =0.1-10 um, only when the average grain size of the diamond wheel is less than 10 um, can the super-smooth surface(Ra: 6.200 nm, rms: 8.201 nm) be obtained by grinding in the ductile mode o 2004 Elsevier B.V. All rights reserved Keywords: Ultra-precision grinding; Brittle-ductile transition, Average grain size; Grinding in the ductile mode 1. Introduction In the grinding process of the brittle material, the reme mode of the material affects the surface quality. The latest With the development of science and technology, high grinding research shows that although the brittle materials quality products of the brittle materials with high surface have great brittleness, they still could be machined in ductile juality, such as various optical glasses, single crystal sili- mode with the optimized parameters, by which the surface con,micro-crystalline glass and ceramic bearings which are quality of the workpiece can be greatly improved. Many spe- very widely applied in space-flight and military equipments, cialists like T.G. Bifano, Y Namba, etc. have made amount are playing more and more important roles in many key in- of theoretical analysis and experimental research [3-71, but struments. In order to obtain the super-smooth surface of the with an absence of a persuasive theory. Therefore, the critical brittle materials, the following methods are usually adopted: conditions of the brittle-ductile transition of the brittle low efficiency and low profile accuracy of machined surface to be researched more deep/encing the surface quality need are inevitable. In recent years, the ultra-grinding technology In this paper, firstly, the critical conditions for the which enhances the parts accuracy and machining efficiency, brittle-ductile transition and main factors influencing the sur- has rapidly developed [1, 2] face quality were investigated from dynamic grinding theo- nt of grinding experi carried out; finally, the machined surface was detected with Corresponding author the atomic force microscope(AFM). Experimental results E-mailaddress:chenmingiunok@yahoo.com(M.Chen) proved the theoretical analysis of this paper to be correct 0924-0136/S-see front matter 3 2004 Elsevier B V. All rights reserved

Journal of Materials Processing Technology 168 (2005) 75–82 The critical conditions of brittle–ductile transition and the factors influencing the surface quality of brittle materials in ultra-precision grinding Mingjun Chen∗, Qingliang Zhao, Shen Dong, Dan Li Precision Engineering Research Institute, Harbin Institute of Technology, Harbin 150001, China Received 21 August 2002; received in revised form 29 December 2003; accepted 11 November 2004 Abstract Based on the indentation experiments under different loads, the critical conditions for the brittle–ductile transition of the brittle materials has been investigated from dynamic grinding, and the factors influencing the surface quality of the brittle materials have been analysed in ultra-precision grinding theoretically. After having carried out the grinding experiments of the brittle materials, it was shown that influence of the average grain size of the diamond wheel on the surface quality is prominent. Compared to the wheel grain size, influence of wheel speed and feed rate on the surface quality is in secondary; these experimental results were consistent with the theoretical analysis. In the case of υs = 1200 m/min, f = 0–20
m/rev, ap = 0.1–10
m, only when the average grain size of the diamond wheel is less than 10
m, can the super-smooth surface (Ra: 6.200 nm, rms: 8.201 nm) be obtained by grinding in the ductile mode. © 2004 Elsevier B.V. All rights reserved. Keywords: Ultra-precision grinding; Brittle–ductile transition; Average grain size; Grinding in the ductile mode 1. Introduction With the development of science and technology, high quality products of the brittle materials with high surface quality, such as various optical glasses, single crystal sili￾con, micro-crystalline glass and ceramic bearings which are very widely applied in space-flight and military equipments, are playing more and more important roles in many key in￾struments. In order to obtain the super-smooth surface of the brittle materials, the following methods are usually adopted: honing, lapping and polishing. However, shortcoming like low efficiency and low profile accuracy of machined surface are inevitable. In recent years, the ultra-grinding technology, which enhances the part’s accuracy and machining efficiency, has rapidly developed [1,2]. ∗ Corresponding author. E-mail address: chenmingiunok@yahoo.com (M. Chen). In the grinding process of the brittle material, the removal mode of the material affects the surface quality. The latest grinding research shows that although the brittle materials have great brittleness, they still could be machined in ductile mode with the optimized parameters, by which the surface quality of the workpiece can be greatly improved. Many spe￾cialists like T.G. Bifano, Y. Namba, etc. have made amount of theoretical analysis and experimental research [3–7], but with an absence of a persuasive theory. Therefore, the critical conditions of the brittle–ductile transition of the brittle ma￾terials and main factors influencing the surface quality need to be researched more deeply. In this paper, firstly, the critical conditions for the brittle–ductile transition and main factors influencing the sur￾face quality were investigated from dynamic grinding theo￾retically; and secondly, amount of grinding experiments were carried out; finally, the machined surface was detected with the atomic force microscope (AFM). Experimental results proved the theoretical analysis of this paper to be correct. 0924-0136/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jmatprotec.2004.11.002

M. Chen et al. /Journal of Materials Processing Technology 168(2005)75-8 2. The critical conditions for the brittle-ductile transition of the brittle materials Radial crack 2.1. Experiment of diamond grain indentation George[8]analyzed the crack mechanisms of brittle ma- terials by measuring the hardness of the brittle materials un- der various loads. In order to study the mechanism of the brittle--ductile transition in the brittle materials. the indenta- tion experiments on single crystal silicon were conducted in Center crack our laboratory. Lateral crack Fig. I(a)shows a SEM photo of indentation on single Fig. 2. Two indentation shapes on the brittle material surface made by the there is only a concave of plastic deformation, indicating that when the load is low enough, there could be only plastic deformation on the brittle material surface. The load is o 06N where h is the micro-hardness of the material: a. the in Fig. I(b)and we can see that small radial cracks appear at geometry factor of the indenter; a=1.8854 and P is the the corners of the indentation, which means that single crystal silion has already started to fracture. Fig. 1(a) and(b)show the ductility of the brittle materials is adequate and it makes know that with an increasing load, the ductile the grinding in the ductile mode possible mation area would largen. If the value P exceeds the Fig. I(c)is the SEM photo of the brittle material surface value Pc of the brittle material, cracks appear under the hen the loads are 0.6N and Fig. I(d)with a load of.9N. ter. The relationship of critical load Pe of generating cracks Of which there are obvious cracks come into being on the on the material surface and the material fracture toughness is indentation surface of the brittle materials. Fig. 2 shows the as follows two typical indentation forms on the brittle material surfaces by the vickers diamond indenter From the indentation experiment, the following results P=ZoKre/Kic could be concluded. (a)When the load is very low, there is a deformation area where no is the integrative factor, 10=(1.0-1.6)x 10+and as in Fig. 1(a), whose deformation is the pure ductile Klc is the fracture toughness of the material deformation without any cracks, It is known that, by analyzing the process of the in- (b)When the load increases to the critical value, there are als are in ductile distortion while PPc, cracks will come into being inside the (c)When the load keeps on increasing, cracks can clearly be material and upon the material surface. From Eq.(1),we seen as in Fig. 1(d). It shows that when the normal load can see that the brittle-ductile transition depends mainly on reaches a bigger value, the brittle fracture will appear in the positive pressure of the single grain. That is to say the gle crystal silicon surf brittle-ductile transition relates to the feature size(2a) of Presume P be the normal load affecting the indentation the indentation, so we can get depth of cutting of the sin- on silicon surface. The relationship between Pand feature gle grain from the feature size(2a). Therefore, we can con- size of indentation 2a can be expressed as clude whether the grinding of the brittle materials is in a duc- tile mode or not depends on the cutting depth of the single Ho (1) Fig. 1. SEM photos of single-crystal silicon surface indented with different loads: (a)P=0.03 N; (b)P=0.06N;(c)P=0.6N; (d)P=0.9N

76 M. Chen et al. / Journal of Materials Processing Technology 168 (2005) 75–82 2. The critical conditions for the brittle–ductile transition of the brittle materials 2.1. Experiment of diamond grain indentation George [8] analyzed the crack mechanisms of brittle ma￾terials by measuring the hardness of the brittle materials un￾der various loads. In order to study the mechanism of the brittle–ductile transition in the brittle materials, the indenta￾tion experiments on single crystal silicon were conducted in our laboratory. Fig. 1(a) shows a SEM photo of indentation on single crystal silicon surface under load P, 0.03 N. It shows that there is only a concave of plastic deformation, indicating that when the load is low enough, there could be only plastic deformation on the brittle material surface. The load is 0.06 N in Fig. 1(b) and we can see that small radial cracks appear at the corners of the indentation, which means that single crystal siliocn has already started to fracture. Fig. 1(a) and (b) show the ductility of the brittle materials is adequate and it makes the grinding in the ductile mode possible. Fig. 1(c) is the SEM photo of the brittle material surface when the loads are 0.6 N and Fig. 1(d) with a load of 0.9 N. Of which there are obvious cracks come into being on the indentation surface of the brittle materials. Fig. 2 shows the two typical indentation forms on the brittle material surfaces by the Vickers diamond indenter. From the indentation experiment, the following results could be concluded: (a) When the load is very low, there is a deformation area as in Fig. 1(a), whose deformation is the pure ductile deformation without any cracks; (b) When the load increases to the critical value, there are cracks below the indenter where the stress concentration pattern is shown in Fig. 1(b) and (c); (c) When the load keeps on increasing, cracks can clearly be seen as in Fig. 1(d). It shows that when the normal load reaches a bigger value, the brittle fracture will appear in the single crystal silicon surface. Presume P be the normal load affecting the indentation on silicon surface. The relationship betweenPand feature size of indentation 2a can be expressed as P = αHa2 (1) Fig. 2. Two indentation shapes on the brittle material surface made by the Vickers diamond indenter. where H is the micro-hardness of the material; α, the geometry factor of the indenter; α = 1.8854 and P is the load. We know that with an increasing load, the ductile defor￾mation area would largen. If the value P exceeds the critical value Pc of the brittle material, cracks appear under the inden￾ter. The relationship of critical load Pc of generating cracks on the material surface and the material fracture toughness is as follows: Pc = λ0Klc
Klc H 3 (2) where λ0 is the integrative factor, λ0 = (1.0–1.6) × 104 and Klc is the fracture toughness of the material. It is known that, by analyzing the process of the in￾dentation made by the Vickers diamond indenter, materi￾als are in ductile distortion while P ≤ Pc, and on the other hand, when P > Pc, cracks will come into being inside the material and upon the material surface. From Eq. (1), we can see that the brittle–ductile transition depends mainly on the positive pressure of the single grain. That is to say the brittle–ductile transition relates to the feature size (2a) of the indentation, so we can get depth of cutting of the sin￾gle grain from the feature size (2a). Therefore, we can con￾clude whether the grinding of the brittle materials is in a duc￾tile mode or not depends on the cutting depth of the single grain. Fig. 1. SEM photos of single-crystal silicon surface indented with different loads: (a) P = 0.03 N; (b) P = 0.06 N; (c) P = 0.6 N; (d) P = 0.9 N.

M Chen et al. /Journal of Materials Processing Technology 168(2005)75-82 wheel ing parameters. Therefore, the critical condition that changes from brittle to ductile mode can be calculated from theory S workpiece 2. 3. The critical condition of the brittle-ductile transition in the grinding process From the above analysis, we know that the material re- moval of the workpiece surface is cut and scored by a large number of grains in grinding process, so the critical condition of the brittle-ductile transition depends on cutting thickness of a single grain. When maximum cutting thickness of a sin- Fig 3. Diagram of a grinding process of the cutting edge of a grain or gle grain is acquired, the grains are assumed as an equivalent octahedron. Therefore, in ultra-precision grinding, sectional 2.2. Analysis of the contact state of grinding wheel and plan of the diamond grain on the workpiece is very similar to workpiece the pattern of indentation experiments. Only four planes of the Vickers diamond indenter are in contact with the work- In ultra-precision grinding, both the feed rate f and depth piece in the indentation experiments. It means that the shape of cutting ap are small. Therefore, only each grain removes a of the Vickers diamond indenter is equal to that of the oc- small amount of the material of the workpiece. Fig 3 shows tahedron grain But in ultra-precision grinding process, only the diagram of the grinding process of cutting edge of a di- one or two planes of the octahedron grain are in contact the amond grain on the wheel. In this figure, cutting thickness workpiece all along [10] of a single grain can be obtained form the kinetic relation In ultra-precision grinding, the grinding depth ap is very between the wheel and the workpiece. When the grain is at small and always to be several microns. So, under other con- the top surface of the workpiece, as shown in Fig. 4, cutting ditions remain unchanged, the normal grinding force depends thickness of one grain is maximum. on the grain cutting thickness ag, as shown in Fig. 5. The fea- To calculate maximum cutting thickness of the grain, it is ture size of indentation is that 2a= 2agtg(ao/2), where ao is assumed that [91 top angle. Due to only one or two planes of the octahedron (1) Depth of cutting is very small so that cutting arc of the grain are in contact the workpiece surface, so the half of the grain supports load in grinding process. According to mea grain can be approximately considered as a straight line. suring method of the micro-hardness, the superficial area of (2)The grains are distributed equidistantly along the circle grain contacting with the workpiece can be acquired by of the wheel ()The grains can be approximated as an equivalent octahe- Agc= 1/2ag tan-(oo/2) (4) dron. And its top angle participates in work From Eq (1), Pgc can be achieved by According to these assumptions, maximum cutting thick- ness of one grain can be obtained by Pge=1/2aa2 tan2(ao/2)H amax=/ 42 However, in grinding process, every grain of the wheel ap/de ( works discontinuously. And, at the moment the grains come in contact with the workpiece, a very strong impulse will be where Uw is the feed rate: Us, the tangential speed of the induced. According to Kalthoff's study on the dynamic frac- wheel;, Nd, the number of the dynamic effective cutting edge, ture toughness under the impulse load, using static fracture C, the constant of cut; ap, the depth of cut; de, the equivalent toughness Kic to study the regularity of dynamic crack is ab- diameter of the wheel solutely wrong. That is to say, obviously using static fracture The maximum cutting thickness of a single grain can be toughness Kic to study the regularity of dynamic crack cannot calculated approximately through properly changing grind- accurately reflect dynamic fracture character of the materials graIn D/2-ap Fig. 5. Actual graphics of cut of perfect grain: (a)fracture mode(amax>ag); Fig. 4. Diagram of grain in small thickness of cut (b) fracture and ductile mode(amax =ag); and(c)ductile mode(agmax <ag)

M. Chen et al. / Journal of Materials Processing Technology 168 (2005) 75–82 77 Fig. 3. Diagram of a grinding process of the cutting edge of a grain on the wheel. 2.2. Analysis of the contact state of grinding wheel and workpiece In ultra-precision grinding, both the feed rate f and depth of cutting ap are small. Therefore, only each grain removes a small amount of the material of the workpiece. Fig. 3 shows the diagram of the grinding process of cutting edge of a di￾amond grain on the wheel. In this figure, cutting thickness of a single grain can be obtained form the kinetic relation between the wheel and the workpiece. When the grain is at the top surface of the workpiece, as shown in Fig. 4, cutting thickness of one grain is maximum. To calculate maximum cutting thickness of the grain, it is assumed that [9]: (1) Depth of cutting is very small so that cutting arc of the grain can be approximately considered as a straight line. (2) The grains are distributed equidistantly along the circle of the wheel. (3) The grains can be approximated as an equivalent octahe￾dron. And its top angle participates in work. According to these assumptions, maximum cutting thick￾ness of one grain can be obtained by agmax = 4υw υsNdC ap/de 1/2 (3) where υw is the feed rate; υs, the tangential speed of the wheel; Nd, the number of the dynamic effective cutting edge; C, the constant of cut; ap, the depth of cut; de, the equivalent diameter of the wheel. The maximum cutting thickness of a single grain can be calculated approximately through properly changing grind￾Fig. 4. Diagram of grain in small thickness of cut. ing parameters. Therefore, the critical condition that changes from brittle to ductile mode can be calculated from theory. 2.3. The critical condition of the brittle–ductile transition in the grinding process From the above analysis, we know that the material re￾moval of the workpiece surface is cut and scored by a large number of grains in grinding process, so the critical condition of the brittle–ductile transition depends on cutting thickness of a single grain. When maximum cutting thickness of a sin￾gle grain is acquired, the grains are assumed as an equivalent octahedron. Therefore, in ultra-precision grinding, sectional plan of the diamond grain on the workpiece is very similar to the pattern of indentation experiments. Only four planes of the Vickers diamond indenter are in contact with the work￾piece in the indentation experiments. It means that the shape of the Vickers diamond indenter is equal to that of the oc￾tahedron grain. But in ultra-precision grinding process, only one or two planes of the octahedron grain are in contact the workpiece all along [10]. In ultra-precision grinding, the grinding depth ap is very small and always to be several microns. So, under other con￾ditions remain unchanged, the normal grinding force depends on the grain cutting thickness ag, as shown in Fig. 5. The fea￾ture size of indentation is that 2a = 2agtg(α0/2), where α0 is top angle. Due to only one or two planes of the octahedron grain are in contact the workpiece surface, so the half of the grain supports load in grinding process. According to mea￾suring method of the micro-hardness, the superficial area of grain contacting with the workpiece can be acquired by Agc = 1/2a2 g tan2(α0/2) (4) From Eq. (1), Pgc can be achieved by Pgc = 1/2αa2 g tan2(α0/2)H (5) However, in grinding process, every grain of the wheel works discontinuously. And, at the moment the grains come in contact with the workpiece, a very strong impulse will be induced. According to Kalthoff’s study on the dynamic frac￾ture toughness under the impulse load, using static fracture toughness Kic to study the regularity of dynamic crack is ab￾solutely wrong. That is to say, obviously using static fracture toughness Kic to study the regularity of dynamic crack cannot accurately reflect dynamic fracture character of the materials Fig. 5. Actual graphics of cut of perfect grain: (a) fracture mode (agmax > ag); (b) fracture and ductile mode (agmax = ag); and (c) ductile mode (agmax < ag).

M Chen et al. /ournal of Materials Processing Technology 168(2005)75-8 under the impulse load. Experimental results on the plane im- the grinding in the ductile mode are that maximum cutting pulse specimen performed by Clifton et al. and results show depth of single grain should be less than the critical cutting that Kid is about 60% of the Kic when applying the equiv- depth alent forces to metal surfaces. For the brittle materials. K The maximum cutting depth formula of the single grain is about or less than 30% of Kic. Moreover, the grains will can be obtained through analysis of contact state of the wheel affect the driving force of the machines spindle after impact- and the workpiece the workpiece's surface. At a very short impact moment, For the number of the dynamic effective cutting edge(Nd) a strong impulse will be produced. As a result, comparable the measured effective cutting edge on the unit area along the to indentation tests where the loads were added slowly, the contracting arc of the wheel and the workpiece, is given by domino effect of grinding marks on the specimen surface is [11] greatly different in shape and dimension. Therefore, in for mula(2),substituting Kid for Kic, and dynamic impulse load Na=Ag[c1//271p()(]1/6 Ped for static load Pc is more suitable for the actual grinding process. So where Ag is the proportional coefficient of the static cutting PC=hk/K, (6) of the cutting edge; ks, the form coefficient of the wheel; t the feed rate; Us, the tangential speed of the wheel; ap, the combining formula(5)with formula(6), the critical cut ing depth of the brittle-ductile transition during grinding depth of cut; de, the equivalent diameter of the wheel Through the above analysis, we can find that only when process can be obtained by ultra-precision grinding 2入0/Kd the ductile mode From Eqs. ( 3)and(9), it is shown that fo (7) maximum cutting depth(agmax), the effect of the change of the average grain size is large, the influence of the wheel For grinding process of the brittle material, we have con- speed and the workpiece speed is secondary, and the effect idered the effect of the impact loads on critical conditions of the grinding depth is at least. On the other side, we can of the brittle-ductile transition. But lots of active organic find from Eq. 8), that the coolant has a biggish effect on the molecules exist in the coolant during the grinding. When cutting depth(agc). The changes of the parameter Ko will these molecules adsorb on the workpieces surface, chemi- ect agc and it will affect the surface quality of machined cal, physical and other's activation will come into being be- workpiece. Therefore, for machined surface quality of the tween the coolant and the workpiece's surface, which will brittle materials in ultra-precision grinding, we get some main change the materials hardness and fracture toughness. Fur- factors and their affecting degree thermore, different coolants have different chemical compo- nents and their effects differ from each other So. we must consider coolant's influence on the brittle-ductile transition 4. Experimental conditions in grinding process. We assume the affecting coefficient to brittle-ductile of the coolant is Ko, and Ko of different coolant 4.1. The ultra-precision grinding machine cannot be the same. We can get a0)./2入0/Kud The spindle of the grinder on the ultra-precision machine age=Ko cot ah (8) uses an air bearing with a maximum rotational speed of 80000 rpm, and a turning accuracy of 0. 1 um. The work Eq (8)is the formula used to calculate depth of cutting piece spindle uses an air bearing with a turning accuracy of in the critical condition of the brittle-ductile transition The 0.05 um thanks to its very high rigidity and high vibration equation considers the impulse loads in grinding process and absorptivity. The grinding depth of the machine can be co coolant's influence on the hardness and fracture toughness. trolled in the range of 0. l um in grinding process. Several So, it will accord with actual grinding process better and gives hyperbaric coolant were used more theoretical guidance for ultra-precision grinding of the brittle materials in the ductile mode 4.2. The grinding wheels, grinding parameters and 3. Theoretical analysis of the factors influencing the a cast-iron bonded diamond wheel with a diameter of surface quality in ultra-precision grinding process 8 mm was applied in experiments. The average grain size of the wheel has seven types correspond to 40, 28, 20, 14, 10 For the brittle materials, only when the grinding of the 7 and 2.5 um. The discharge dressing principle was adopted brittle materials is worked in ductile mode, the surface quality for wheel dressing, The wheel was dressed in the following of machined workpiece can be improved. The conditions of parameter: the wheel speed us was 10000 rpm, the speed of

78 M. Chen et al. / Journal of Materials Processing Technology 168 (2005) 75–82 under the impulse load. Experimental results on the plane im￾pulse specimen performed by Clifton et al. and results show that Kid is about 60% of the Kic when applying the equiv￾alent forces to metal surfaces. For the brittle materials, Kid is about or less than 30% of Kic. Moreover, the grains will affect the driving force of the machine’s spindle after impact￾ing the workpiece’s surface. At a very short impact moment, a strong impulse will be produced. As a result, comparable to indentation tests where the loads were added slowly, the domino effect of grinding marks on the specimen surface is greatly different in shape and dimension. Therefore, in for￾mula (2), substituting Kid for Kic, and dynamic impulse load Pcd for static load Pc is more suitable for the actual grinding process. So, Pc = λ0Kld
Kld H 3 (6) combining formula (5) with formula (6), the critical cut￾ting depth of the brittle–ductile transition during grinding process can be obtained by agc = cot α0 2  2λ0 a
Kld H 2 (7) For grinding process of the brittle material, we have con￾sidered the effect of the impact loads on critical conditions of the brittle–ductile transition. But lots of active organic molecules exist in the coolant during the grinding. When these molecules adsorb on the workpiece’s surface, chemi￾cal, physical and other’s activation will come into being be￾tween the coolant and the workpiece’s surface, which will change the material’s hardness and fracture toughness. Fur￾thermore, different coolants have different chemical compo￾nents and their effects differ from each other. So, we must consider coolant’s influence on the brittle–ductile transition in grinding process. We assume the affecting coefficient to brittle–ductile of the coolant isK0, andK0 of different coolant cannot be the same. We can get agc = K0 cot α0 2  2λ0 a
Kld H 2 (8) Eq. (8) is the formula used to calculate depth of cutting in the critical condition of the brittle–ductile transition. The equation considers the impulse loads in grinding process and coolant’s influence on the hardness and fracture toughness. So, it will accord with actual grinding process better and gives more theoretical guidance for ultra-precision grinding of the brittle materials in the ductile mode. 3. Theoretical analysis of the factors influencing the surface quality in ultra-precision grinding process For the brittle materials, only when the grinding of the brittle materials is worked in ductile mode, the surface quality of machined workpiece can be improved. The conditions of the grinding in the ductile mode are that maximum cutting depth of single grain should be less than the critical cutting depth. The maximum cutting depth formula of the single grain can be obtained through analysis of contact state of the wheel and the workpiece. For the number of the dynamic effective cutting edge (Nd), the measured effective cutting edge on the unit area along the contracting arc of the wheel and the workpiece, is given by [11] Nd = Ag[c1] 2/3 2 ks 1/3 υw υs 1/3 ap de 1/6 (9) where Ag is the proportional coefficient of the static cutting edges (Ag ≈ 1.2); c1, the coefficient correlating the density of the cutting edge; ks, the form coefficient of the wheel; υw, the feed rate; υs, the tangential speed of the wheel; ap, the depth of cut; de, the equivalent diameter of the wheel. Through the above analysis, we can find that only when agmax < ac, the brittle material is ultra-precision grinding in the ductile mode. From Eqs. (3) and (9), it is shown that for maximum cutting depth (agmax), the effect of the change of the average grain size is large, the influence of the wheel speed and the workpiece speed is secondary, and the effect of the grinding depth is at least. On the other side, we can find from Eq. (8), that the coolant has a biggish effect on the cutting depth (agc). The changes of the parameter K0 will affect agc and it will affect the surface quality of machined workpiece. Therefore, for machined surface quality of the brittle materials in ultra-precision grinding, we get some main factors and their affecting degree. 4. Experimental conditions 4.1. The ultra-precision grinding machine The spindle of the grinder on the ultra-precision machine uses an air bearing with a maximum rotational speed of 80 000 rpm, and a turning accuracy of 0.1
m. The work￾piece spindle uses an air bearing with a turning accuracy of 0.05
m thanks to its very high rigidity and high vibration absorptivity. The grinding depth of the machine can be con￾trolled in the range of 0.1
m in grinding process. Several hyperbaric coolant were used. 4.2. The grinding wheels, grinding parameters and inspect instruments A cast-iron bonded diamond wheel with a diameter of 8 mm was applied in experiments. The average grain size of the wheel has seven types correspond to 40, 28, 20, 14, 10, 7 and 2.5
m. The discharge dressing principle was adopted for wheel dressing, The wheel was dressed in the following parameter: the wheel speed υs was 10 000 rpm, the speed of

M Chen et al. /Journal of Materials Processing Technology 168(2005)75-82 H(GPa) E(GPa H(GPa) (optical glass FCDI 3.38 79.58 GCI 9.5 4.75 63.7 Lac 12 5.78 93.88 3.58 52.23 GC4 138 NbFI 108.68 the dressing instrument Uw was 500 rpm and depth of cutting After grinding, the k9 ground surface was observed with the ap was 0. I um. After the wheel had been dressed, its profile Nanoscope Illa. Through observation, we found that in the ccuracy was 0. I um grinding process, there existed three kinds of grinding mode In the experiment, we chose optical glass(K9)and micro- fracture mode, fracture and ductile mode and ductile mode, crystalline glass(GCI)as the grinding materials with the as shown in Fig. 6. When agmax >ac, it was in the fracture grinding parameters of Us=1200 m/min, f=0-20 um/rev, grinding mode, when agmax ac, it was in the fracture and and ap=0.1-10 um ductile grinding mode, and when agmax a) (b) fracture and ductile mode(ama=a) (e)ductile mode(amx <a,) ig. 6. Three grinding mode of optical glass(K9)

M. Chen et al. / Journal of Materials Processing Technology 168 (2005) 75–82 79 Table 1 Mechanical properties of partial optic glasses and micro-crystalline Material (optical glass) H (GPa) E (GPa) Material (micro-crystalline) H (GPa) E (GPa) FCD1 3.38 79.58 GC1 9.50 130 K9 4.75 63.70 GC2 9.40 130 LaC12 5.78 93.88 GC3 9.30 123 FD6 3.58 52.23 GC4 10.00 138 NbF1 6.62 108.68 GC5 8.20 113 the dressing instrument υw was 500 rpm and depth of cutting ap was 0.1
m. After the wheel had been dressed, its profile accuracy was 0.1
m. In the experiment, we chose optical glass (K9) and micro￾crystalline glass (GC1) as the grinding materials with the grinding parameters of υs = 1200 m/min, f = 0–20
m/rev, and ap = 0.1–10
m. After grinding trials, the grinding surfaces were inspected by the Nanoscope IIIa (Dimension 3100, Digital Instru￾ments). 5. Experimental results and discussion In order to validate the correctness of the theory, firstly, we calculated the critical value of the brittle–ductile transi￾tion of brittle material. Table 1 shows the mechanical char￾acters of partial optical glasses and microcrystalline glasses and Table 2 shows the maximum cutting depth of the wheels with different grain sizes and the critical cutting depths of the materials. Firstly, we adopted the seven types of diamond wheel, respectively, under the condition of υs = 1200 m/min, f = 3
m/rev and ap = 1
m, experimental material was K9. After grinding, the K9 ground surface was observed with the Nanoscope IIIa. Through observation, we found that in the grinding process, there existed three kinds of grinding mode: fracture mode, fracture and ductile mode and ductile mode, as shown in Fig. 6. When agmax > ac, it was in the fracture grinding mode, when agmax ≈ ac, it was in the fracture and ductile grinding mode, and when agmax < ac, it was in the ductile grinding mode. After grinding, the relationship be￾tween average grain size and surface roughness is shown in Fig. 7. Form Fig. 7, the influence of the average grain size of the wheel on the machined result was pretty large. The experiment also shows that only with average grain size be￾low 10
m can ultra-precision grinding in the ductile mode be obtained. Thereafter, the diamond wheel the average grain size of 2.5
m was adopted under unchanged grinding parameters of f = 1
m/rev and ap = 1
m, except that only the wheel speed was changed for grinding optical glass K9. After grinding, the relationship between the wheel speed and surface rough￾ness was shown in Fig. 8, which indicates that the degree of influence of the wheel speed on surface roughness is less than that of the influence of the average grain size of the wheel. Table 2 Maximum cutting depth of the wheel with different grain and critical cutting depth of the materials Average grain size (
m) Maximum cutting depth, agmax (
m) Critical cutting depth (
m) a b agc(K9) agc(GC1) 40 0.5748 0.5873 0.2443 0.2058 20 0.2873 0.3718 0.2443 0.2058 14 0.1831 0.2602 0.2443 0.2058 10 0.1308 0.1859 0.2443 0.2058 2.5 0.0915 0.0651 0.2443 0.2058 a The grinding parameters were: υs = 1200 m/min, υw = 2 mm/s, de = 8 mm, ap = 1
m. b The grinding parameters were: υs = 900 m/min, υw = 10 mm/s, de = 200 mm, ap = 1
m. Fig. 6. Three grinding mode of optical glass (K9)

M Chen et al. /ournal of Materials Processing Technology 168(2005)75-8 rms a 2年 rms Diamond wheel average grain size Feed rate Fig. 7. Relative curve of the mean grain size vs. the surface roughness Fig 9. Relative curve of the feed rate of workpiece vs the surface roughness. Fig. 9 shows the relationship between surface roughness and feed rate. In the experiment, the diamond wheel of In order to machine the microcrystalline(gci), the whee 2.5 um was used with the parameters of us=1200 m/min and with a average grain size(.5 um) was used under the pa ap=l um. Through changing the feed rate f, the machined rameters of Us=1200 m/min, f=3 um/rev and ap=1 um,the sample surfaces were inspected by the Nanoscope Illa with grinding in the ductile mode was obtained. Figs. II and 12 the results shown in Fig 9, which indicates that the degree of show the microscope graph of the machined optical glass in- influence of the feed rate on the surface roughness is as much spected by the Nanoscope Illa. The surface roughness: Ra is as that of the wheel speed and they are clearly less than that 6.200 nm. rms is 8.201 nm of the influence of the average grain size At last, we did some grinding experiments on the micro- Fig 10 shows the relationship between the surface rough- crystalline glass. The wheel with a average grain size ness and the grinding dept pth. In the experiment, the dia-(2.5 um)was used under the parameters of us=1200 m/min mond wheel of 10 um was used with the parameters of f=3 um/rev and ap =l um without coolant. The machined Us=1200 m/min, and f=l um/rev. Through changing the surface result is shown in Fig. 13, which indicates that grinding depth ap, the machined optical glass(K9)was fi- there are some deep striations on the surface, further more nally inspected by the Nanoscope Illa with the results show some striations are removed in the fracture mode. The sur in Fig. 10, which indicates that the degree of the infuence of face roughness Ra is 39.043 nm and rms is 46. nm the grinding depth on the surface roughness was small, and compared to using coolant(Fig. 12), the results are it is less than that of influence of wheel speed and feed rate worse rms ∽E=2 rms 02505075112515175222525 Grinding depth Fig 8. Relative curve of the wheel speed vs. the surface roughness Fig. 10. Relative curve of grinding depth vs. the surface roughness

80 M. Chen et al. / Journal of Materials Processing Technology 168 (2005) 75–82 Fig. 7. Relative curve of the mean grain size vs. the surface roughness. Fig. 9 shows the relationship between surface roughness and feed rate. In the experiment, the diamond wheel of 2.5
m was used with the parameters of υs = 1200 m/min and ap = 1
m. Through changing the feed rate f, the machined sample surfaces were inspected by the Nanoscope IIIa with the results shown in Fig. 9, which indicates that the degree of influence of the feed rate on the surface roughness is as much as that of the wheel speed and they are clearly less than that of the influence of the average grain size. Fig. 10 shows the relationship between the surface rough￾ness and the grinding depth. In the experiment, the dia￾mond wheel of 10
m was used with the parameters of υs = 1200 m/min, and f = 1
m/rev. Through changing the grinding depth ap, the machined optical glass (K9) was fi- nally inspected by the Nanoscope IIIa with the results show in Fig. 10, which indicates that the degree of the influence of the grinding depth on the surface roughness was small, and it is less than that of influence of wheel speed and feed rate. Fig. 8. Relative curve of the wheel speed vs. the surface roughness. Fig. 9. Relative curve of the feed rate of workpiece vs. the surface roughness. In order to machine the microcrystalline (GC1), the wheel with a average grain size (2.5
m) was used under the pa￾rameters of υs = 1200 m/min, f = 3
m/rev and ap = 1
m, the grinding in the ductile mode was obtained. Figs. 11 and 12 show the microscope graph of the machined optical glass in￾spected by the Nanoscope IIIa. The surface roughness: Ra is 6.200 nm, rms is 8.201 nm. At last, we did some grinding experiments on the micro￾crystalline glass. The wheel with a average grain size (2.5
m) was used under the parameters of υs = 1200 m/min, f = 3
m/rev and ap = 1
m without coolant. The machined surface result is shown in Fig. 13, which indicates that there are some deep striations on the surface, further more some striations are removed in the fracture mode. The sur￾face roughness Ra is 39.043 nm and rms is 46.623 nm, compared to using coolant (Fig. 12), the results are worse. Fig. 10. Relative curve of grinding depth vs. the surface roughness

M. Chen et al. / Journal of Materials Processing Technology 168(2005)75-82 of the material, the coolant and so on. Eq.(8)con- siders the impulse load in grinding process, as well as the coolant's influence on the hardness and fracture 400 toughness, which will accord with actual machining pro- cess better and gives more theoretical guidance to ultra- precision grinding of the brittle materials in the ductile (3 vas obtained and the cracks do not appe我后 )The average grain size of the diamond wheel is a very mportant influence on the machined surface roughness If the wheels with an average grain s an 10 gr inding of optical glass in he value of machined surface roughness is also a func- tion of both wheel speed and feed rate. Two parameter's nfluencing degree on the ground surface roughness is less than that of the average grain size of the diamond Fig. 11. AFM microscope graph of the grinding surface of GCI wheel (4)The influence of grinding depth on the surface roughness is at least. When the grinding of the brittle materials is in ductile mode, the parameter almost does impact no fluence on the surface roughness (5) When the wheel with an average grain size(2.5 um)is adopted, a super-smooth surface(Ra is 6.200 nm, rms is 8.201 nm)can be obtained. Acknowledgements The author gratefully acknowledges the support for this Fig 12. AFM micro-topography of the grinding surface of GCI work received from the national natural science fund of China and Harbin City Science Foundation. The contact num- ber is 50175022 and 2002AFXXJ046 References optics manufacturing tech nologies, in: Proceedings IE on Advanced Optical Manufacturing and Testing 2000vol.4231,pp.8 pt mean(Rz [2] P.B. Leadbeater, M. Clarke, w.J. Wills-Moren, T.J. Wilson, A unique machine for grinding large, off-axis optical components: the OAGm 2500, Precision eng.1l(4)(1989)191-196 3]K.Subramanian, S. Ramanath, et al., Mechanisms of material re ci.Eng119(1997)509519 O uM [4]HY. Lin, J. L. Chu, The indentation method for the brittle-ductile ansition in silicon single crystals, in: Progress in Precision En- gineering and Nanotechnology, Braunschweig, Germany, 1997, pp Fig. 13. AFM microscope graph of the grinding surface of GCl(without coolant) []G. Thaoms Bifano, K. Douglas Depiero, Chemo mechanical effects in ductile-regime machining of glass, Precision Eng. 15(4)(1993) 6. Conclusion 238-247 [6]Y. Namba, M. Abe, Ultra-precision grinding of optical glasses to produce super-smooth surfaces, Ann. CIRP 42(1)(1993)417- From the above analysis, we can conclude 7M. Chen, D Shen, et al., Study on critic tion of brittle-ductile (1) The brittle-ductile transition of the brittle materials cor- transition of brittle materials of ultra-precision grinding, High Tech- relates to dynamic fracture toughness, micro-hardness nol. Lett. 10(2)(200064-67

M. Chen et al. / Journal of Materials Processing Technology 168 (2005) 75–82 81 Fig. 11. AFM microscope graph of the grinding surface of GC1. Fig. 12. AFM micro-topography of the grinding surface of GC1. Fig. 13. AFM microscope graph of the grinding surface of GCl. (without coolant). 6. Conclusion From the above analysis, we can conclude: (1) The brittle–ductile transition of the brittle materials cor￾relates to dynamic fracture toughness, micro-hardness of the material, the coolant and so on. Eq. (8) con￾siders the impulse load in grinding process, as well as the coolant’s influence on the hardness and fracture toughness, which will accord with actual machining pro￾cess better and gives more theoretical guidance to ultra￾precision grinding of the brittle materials in the ductile mode. (2) The average grain size of the diamond wheel is a very important influence on the machined surface roughness. If the wheels with an average grain size less than 10
m were used, the grinding of optical glass in ductile mode was obtained and the cracks do not appear. (3) The value of machined surface roughness is also a func￾tion of both wheel speed and feed rate. Two parameter’s influencing degree on the ground surface roughness is less than that of the average grain size of the diamond wheel. (4) The influence of grinding depth on the surface roughness is at least. When the grinding of the brittle materials is in ductile mode, the parameter almost does impact no influence on the surface roughness. (5) When the wheel with an average grain size (2.5
m) is adopted, a super-smooth surface (Ra is 6.200 nm, rms is 8.201 nm) can be obtained. Acknowledgements The author gratefully acknowledges the support for this work received from the National Natural Science Fund of China and Harbin City Science Foundation. The contact num￾ber is 50175022 and 2002AFXXJ046. References [1] M. Harvey Pollicove, Next generation optics manufacturing tech￾nologies, in: Proceedings of the SPIE on Advanced Optical Manufacturing and Testing Technology 2000, vol. 4231, pp. 8– 15. [2] P.B. Leadbeater, M. Clarke, W.J. Wills-Moren, T.J. Wilson, A unique machine for grinding large, off-axis optical components: the OAGM 2500, Precision Eng. 11 (4) (1989) 191–196. [3] K. Subramanian, S. Ramanath, et al., Mechanisms of material re￾moval in the precision production grinding of ceramics, J. Manuf. Sci. Eng. 119 (1997) 509–519. [4] H.Y. Lin, J.L. Chu, The indentation method for the brittle–ductile transition in silicon single crystals, in: Progress in Precision En￾gineering and Nanotechnology, Braunschweig, Germany, 1997, pp. 536–539. [5] G. Thaoms Bifano, K. Douglas Depiero, Chemo mechanical effects in ductile-regime machining of glass, Precision Eng. 15 (4) (1993) 238–247. [6] Y. Namba, M. Abe, Ultra-precision grinding of optical glasses to produce super-smooth surfaces, Ann. CIRP 42 (1) (1993) 417– 420. [7] M. Chen, D. Shen, et al., Study on critical condition of brittle–ductile transition of brittle materials of ultra-precision grinding, High Tech￾nol. Lett. 10 (2) (2000) 64–67

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82 M. Chen et al. / Journal of Materials Processing Technology 168 (2005) 75–82 [8] J. George, Micro-indentation analysis of di-ammonium hydro￾gen cirate single crystals, J. Mater. Sci. 20 (1985) 3150– 3156. [9] S.C. Salm, Modern Grinding Process Technology, MoGraw-Hill Inc., New York, 1992. [10] G.S. Reichenbach, T.E. Mayer, S. Kalpakcioglu, M.C. Shaw, The role of chip thickness in grinding, Trans. ASME 78 (1956) 847. [11] M. Chen, D. Shen, D. Li, F. Zhang, Study on the influence factors of the surfaces quality in ultra-precision grinding machining of brittle materials, Chin. J. Mech. Eng. 37 (3) (2001) 1–4