Laser cutting of thick ceramic substrates by controlled fracture technique

Journal of Materials Processing Technology 136 (2003) 166 173 Laser cutting of thick ceramic substrates by controlled fracture technique Chwan-Huei Tsai *, Hong-Wen Chen Institute of Mechatronic Engineering, Huafan University, 1 Huafan Road, Shih-ting Hsiang, Taipei Hsien 223, Taiwan, ROC Received 9 August 2001; received in revised form 21 May 2002; accepted 8 January 2003 Abstract The laser cutting technique by controlled fracture can be used for the cutting of thick ceramic substrates by synchronously applying a Nd:YAG laser and a CO 2 laser on the substrate. The focused Nd:YAG laser is used to scribe a groove-crack on the surface of substrate and the defocused CO 2 laser is used to induce thermal stress. The thermal stress concentration will occur on the tip of the groove-crack and make it extend through the substrate, followed by the substrate separating controllably along the moving path of the laser beams. Under the power output of 60 W for both CO 2 laser and Nd:YAG laser, the maximum cutting speed that can be reached is 1.5 mm/s for a thick alumina sample. The reasons why the laser can break the thick substrates and why the breaking is controllable are studied in this paper. The SEM photographs of the separating surface are used to analyze the micro-mechanism of the fracture process. The temperature and stress distributions are analyzed by using the finite element software ANSYS. The relationships between laser power, cutting speed, and specimen geometry are obtained from the experimental analysis, and the phenomena are also explained from the results of stress analysis. # 2003 Elsevier Science B.V. All rights reserved. Keywords: Laser cutting; Ceramic substrate; Controlled fracture 1. Introduction Lambert et al. [1] originally developed the laser cutting technique for severing the glass or vitrocrystalline bodies. There are two lasers used in this process, the first of which has a wavelength such that at least 50% of the laser energy is used in the melting of a 0.2 mm deep groove-crack. The second laser beam generates thermal stress at the crack tip to make the material separate controllably. This method is the extension of the laser cutting of controlled fracture and the laser scribing method, previously proposed by Garibotti [2] and Lumley [3]. The cutting thickness can be greater than 5 mm for vitreous or vitrocrystalline material. In Garibotti s method [2] of laser scribing a brittle material, a laser is used to scribe the wafer along the desired separation line, the scribed wafers are then immersed in an ultrasonic cell and broken along the scribed lines by ultrasonic energy. It is necessary to concentrate the laser energy on a narrow line with the workpiece placed on the focal plane. The scribed substrates are broken along the scribed line by applying a mechanical force induced from the cracking roller. Lumley s laser cutting method [3] of controlled fracture has great potential to be applied in machining brittle material. * Corresponding author. Only a single laser is used in his invention. The applied laser energy produces a mechanical stress that causes the material to separate along the path of the laser beam. The material separation is similar to a crack extension and the fracture growth is controllable. Lumley [3] successfully applied this technique in the dicing of brittle materials such as alumina ceramic substrate and glass, by using the CO 2 laser. The laser power required is less than that for conventional laser evaporative cutting and laser scribing, and the cutting speed is much higher. Grove et al. [4] proposed a related method of controlled fracture for cutting glass, in which the cutting speed is higher. In the recent years, Kondratenko [5] and Unger and Wittenbecher [6] used a lower power laser to separate glass by using water as an additional coolant to produce tensile stress along the cutting path. These improvements of the controlled fracture method have been recognized as providing good prospects for it in the future. Tsai and Liou [7] proposed an explanation for why the material separation is controllable for the controlled fracture technique by using a single laser. They mentioned that the cutting process could be divided into three stages. The first is the initiation stage, where the fracture is initiated due to the tensile stress at the edge of the specimen. The second is the stable growth stage, where the stress near the laser spot is 0924-0136/03/$ see front matter # 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/s0924-0136(03)00134-1

C.-H. Tsai, H.-W. Chen / Journal of Materials Processing Technology 136 (2003) 166 173 167 highly compressive of creep deformation. After the passage of the laser beam, the compressive stress will be relaxed, which then induces a residual tensile stress, making the fracture grow from upper surface to lower surface of the substrate. The final stage is unstable fracture, the stress near the crack tip is a completely tensile stress through the thickness direction, and the crack extends unstably. Tsai and Liou [7,8] have published a series of papers describing the phenomenon and principle of controlled fracture by using a single laser. But the method is very limited for cutting thick substrates. For example, the maximum thickness of alumina substrate that can be cut is about 1 mm. The laser cutting of thick ceramic substrate by conventional evaporative method is less efficient and more expensive. According to Black and Chua [9], the cutting speed is not more than 1 mm/s for alumina ceramic tile of thickness 9.2 mm with the laser output power of 500 W. However, the high power laser will induce many cracks and burnout the cutting surface, reducing the surface quality. However, the present method requires much less laser power, causing few defects. The technique of Lambert et al. [1] can be used to cut a thick ceramic substrate by applying two lasers synchronously. But the principle and phenomenon of cutting thick substrates are much different from that of cutting thin substrates. The fracture mechanism has not been analyzed in detail and the phenomena for different cutting conditions have not yet been studied well. In addition, the mechanism by which the fracture is controllable has not yet been understood. In this paper, we focus on the investigation of the fracture mechanism for the cutting of thick ceramic substrate by controlled fracture technique. We also discuss the machining parameters, such as cutting speed and specimen size. The temperature and stress distribution are analyzed by using the finite element software ANSYS5.4. 2. Experiments of laser cutting with controlled fracture Fig. 1. Configuration of laser cutting system with controlled fracture technique. conductivity of 33.5 W/m 8C, and thermal diffusivity of 1:06 10 5 m 2 /s. The original dimensions of the substrates are 108 mm 108 mm 10 mm, 101:6mm 101:6mm 2 mm, and 101:6mm 101:6mm 1 mm. The focal plane of the Nd:YAG laser is placed on the surface of substrate and the laser beam is perpendicular to the surface of substrate. The focal plane of the CO 2 laser is placed on the upper surface from a distance of 8 mm, in which the diameter of the laser spot is about 373 mm. The CO 2 laser beam is inclined to the Nd:YAG laser beam at 158. The two laser beams are synchronously applied on the substrate and the power outputs are all of CW mode. 2.2. Fracture extension model of symmetrical cutting Cutting a straight line along a median plane is attributed to the symmetrical cutting condition. The photograph of four pieces of alumina substrate cut from the substrate of the size of 108 mm 108 mm 10 mm is shown in Fig. 2. In order to understand the mechanism of the symmetrical cutting 2.1. Laser cutting system and specimen The laser cutting system as shown in Fig. 1 is comprised of a CO 2 laser, a Nd:YAG laser, an XYZ positioning table, and a personal computer. The laser beams move across the upper surface of the workpiece mounted on a platform that can move in the x-, y-, and z-directions. The wavelengths of the CO 2 laser and Nd:YAG laser are 10.6 and 1.06 mm, respectively. The laser power outputs can be synchronized with the XYZ positioning table. The minimum diameters of the focused spot of the CO 2 laser and Nd:YAG laser are 73 and 32 mm, respectively. The experimental specimens used in this paper are alumina (Al 2 O 3 ) ceramic substrates produced by Kyocera Company (Japan). The purity of the alumina ceramic substrate is 99.6%, with a density of 3960 kg/m 3, Young s modulus of 400 GPa, coefficient of thermal expansion of 8:2 10 6 C 1, thermal Fig. 2. Photograph of cutting along a symmetrical straight line.

168 C.-H. Tsai, H.-W. Chen / Journal of Materials Processing Technology 136 (2003) 166 173 with controlled fracture technique, the separation surface along the cutting path is investigated. While using the lasers to cut an alumina substrate with a thickness of 10 mm, the laser beams traverse a distance but do not go through the substrate completely, then the cutting is stopped and the specimen is picked up. The separation of the specimen is similar to the crack propagation along the cutting path, although the crack is invisible to the naked eye. In order to distinguish the different fracture regions on the separation surface, dark ink is painted along the cutting path to the final position of laser spot, and the ink penetrates to the separated surfaces. Then the specimen is stripped to be broken as two pieces along the cutting path, and the dark ink only is on the surface that has been separated. The pictures of the separation surfaces are shown in Fig. 3, showing cutting speeds of 1 and 2 mm/s, and the laser powers of 50 W for both CO 2 laser and Nd:YAG laser. The picture in Fig. 3 can be divided into three regions: (1) the groove-crack region due to the focused Nd:YAG laser (black strip), (2) the controlled fracture region due to the defocused CO 2 laser (gray surface), and (3) the unfractured region (white surface). It is found that the depths of groovecrack region are about 0.63 and 0.43 mm for the cutting speeds of 1 and 2 mm/s, respectively. Some of the laser heat is absorbed to melt the material, thus decrease the bonding strength, and then the material will solidify and induce a primary short groove-crack that closely follows the laser spot path. The controlled fracture region is due to the short groove-crack extending from top to bottom after the laser spot has passed over. It is obvious that the propagation crack tip of the cutting edge is always lager than the movement of the laser spot. Fig. 3. Separation surface along the cutting path for cutting speed (a) 1 mm/s and (b) 2 mm/s. The distance between the crack tip and the laser spot is 3.8 and 2.3 mm for the cutting speeds of 1 and 2 mm/s, respectively. However, the lager distance does not have any notable relation with the cutting speed. This phenomenon is different from the controlled fracture technique for thin substrate, in which the lager distance is longer for the higher cutting speed. The most important phenomenon is that the fracture region will not be uniform throughout the thickness for the high cutting speed before the cutting is completed. The substrate is partially separated and a blind crack is formed. At the final stage, the unstable fracture is induced and the unfractured region will separate immediately. The unstable fracture is accomplished with a loud sound that can be heard at the end of the cutting experiment. 2.3. Fracture extension model of asymmetrical cutting Cutting a straight line but not along the median plane as well as cutting a curve include asymmetrical cutting. The stress state at the crack tip is not pure mode I for the asymmetrical cutting. The picture of straight line cutting is shown in Fig. 4a for a specimen size of 108 mm 108 mm 10 mm, with the cutting path is along the quarter part of the specimen. According to the study of cutting of a thin substrate by Tsai and Liou [7], if the stress is not symmetrical with the crack, the actual fracture trajectory will deviate away from the desired cutting path. But in the present experiment of cutting a thick substrate, the actual fracture trajectory is consistent with the desired cutting path on the top surface, whereas the deviation is severe on the bottom surface. Thus, the separation surface along the thickness direction becomes a warped surface. The reason for this is that the stress concentration exists at the initial groove-crack produced by focused Nd:YAG laser, so that the crack extension will follow the initial crack. Since the stress at the groove-crack tip is not pure mode I along the thickness direction, the groove-crack extension along the thickness will deviate away from the vertical line. The process of cutting a curve is geometrically asymmetric. In this situation, the crack tip of the groove-crack will behave as the mixed mode stress condition and the crack growth will not exactly follow the path of laser spot. The fracture frontier along the cutting direction will also behave as the mixed mode stress condition, so that the actual fracture trajectory will deviate from the moving path of the laser beam. The picture of the sine curve cutting is shown in Fig. 4b, showing that the fracture trajectory slightly deviates from the desired sine curve. When using the laser cutting technique by controlled fracture to cut a right angle, the actual fracture trajectory will deviate from the desired right angle and become a rounded angle. This deviation is due to the lag of the separated crack tip to the laser spot. When the laser spot arrives at the turning point, the crack tip has not reached the turning point. At this instant, the laser beam as well as the crack tip turn in the perpendicular direction. Because the crack tip has not reached

C.-H. Tsai, H.-W. Chen / Journal of Materials Processing Technology 136 (2003) 166 173 169 Fig. 4. Photographs of asymmetrical cutting for (a) straight line, (b) curved line, and (c) right angle. the turning point of right angle, the actual fracture trajectory severely deviates from the desired right angle. The picture of right angle cutting of alumina substrate is shown in Fig. 4c. The CO 2 laser power is 53 W, the Nd:YAG laser power is 63 W, and the cutting speed is 1 mm/s. The lagging distance at the turning point is 5 mm. It is also found that the higher cutting speed will induce a greater lagging distance. In addition, ceramic fragments will sometimes be induced between the actual fracture trajectory and the applied laser path. For most conditions, the fracture along the path of laser spot is weaker than that of the actual fracture trajectory for the curve cutting. 2.4. Cutting speed, laser power, and specimen width In order to investigate the relation between cutting speed, laser power and width of specimen, the three sizes of the alumina ceramic substrate are selected as specimens. Their dimensions are: wider specimen 108 mm 108 mm10 mm, middle specimen 54 mm 108 mm 10 mm, and narrow specimen 27 mm 108 mm 10 mm. The experimental results of the maximum cutting speed, which can be reached fordifferentpoweroutputsofco 2 laser,areshowninthefig.5. The Nd:YAG laser power is constant at 60 and 80 W, which can induce a constant depth of groove-crack. It can be seen that if the specimen width is narrower, the maximum cutting speed that can be reached is higher. The phenomena can be explained from the stress that is analyzed in Section 4. The groovecrack is produced by Nd:YAG laser, so that the Nd:YAG laser power is related to the depth of groove-crack, and the larger depth of groove-crack can provide a higher cutting speed. The relation between the CO 2 laser power and the maximum cutting speed which can be reached for the substrate thickness of 1 and 2 mm is shown in Fig. 6. The solid lines indicate the case for 1 mm thickness and 35 W constant Nd:YAG laser power, and the dashed lines indicate the case for 2 mm thickness and 45 W constant Nd:YAG laser power. The relation between the Nd:YAG laser power and the maximum cutting speed which can be reached for different substrate sizes is shown in Fig. 7. The solid lines indicate the case for 1 mm thickness and 15 W constant CO 2 laser power. The dashed lines indicate the case for 2 mm thickness and 37 W constant CO 2 laser power. The principle of controlled fracture for the cutting of thick substrate is based on the stress concentration on the groovecrack tip. The relation between the maximum separating

170 C.-H. Tsai, H.-W. Chen / Journal of Materials Processing Technology 136 (2003) 166 173 Fig. 5. CO 2 laser power vs. maximum cutting speeds for different specimen width under constant Nd:YAG laser power of 60 W (solid lines) and 80 W (dashed lines). Substrate thickness is 10 mm. Fig. 7. Nd:YAG laser power vs. maximum cutting speeds for different specimen widths. Solid lines indicate the case for 1 mm thickness and 15 W constant CO 2 laser power. Dashed lines indicate the case for 2 mm thickness and 37 W constant CO 2 laser power. speed and the groove-crack depth under the constant power output of CO 2 laser is shown in Fig. 8. For the deeper groove-crack, the maximum cutting speed that can be reached is higher. The groove-crack is produced by the focused Nd:YAG laser, so that the groove-crack depth is related to the power output of the Nd:YAG laser. 2.5. Cutting quality The surfaces produced by laser cutting with controlled fracture are very smooth and with very few defects. The arithmetic average surface roughness R a is 2 mm. For the laser cutting conditions including power output of 60 W for Fig. 8. Required groove-crack depth vs. cutting speed for substrate 2 mm thick and 108 mm wide. CO 2 laser power is 37 W. both CO 2 laser and Nd:YAG laser, and the laser moving speed is 1 mm/s. The surfaces are much better than the conventional laser cutting of evaporating the material. The roughness profile of the breaking surface is shown in Fig. 9. Fig. 6. CO 2 laser power vs. maximum cutting speeds for different specimen widths. Solid lines indicate the case for 1 mm thickness and 35 W constant Nd:YAG laser power. Dashed lines indicate the case for 2 mm thickness and 45 W constant Nd:YAG laser power. Fig. 9. Roughness profile of the breaking surface.

C.-H. Tsai, H.-W. Chen / Journal of Materials Processing Technology 136 (2003) 166 173 171 3. Fractography of breaking surface For the fractography observation, the alumina ceramic substrate is cut with the laser power 60 W for both CO 2 laser and Nd:YAG laser. The spot diameter of the defocused CO 2 laser is 373 mm and that of the focused Nd:YAG laser is 32 mm, and the cutting speed for both is 1 mm/s. The photograph of the scanning electron microscopy of the fracture surface along the cutting path is shown in Fig. 10. It is clear that the breaking surface can be divided into four regions, the laser evaporation region, the columnar grain region, the intergranular fracture region and the transgranular fracture region. The depths of the four regions are about 80, 220, 280, and 9420 mm, respectively. The magnified images of the columnar grain region and the intergranular fracture regions are shown in Fig. 11. Fig. 10. SEM photographs of fracture surface of alumina substrate. Mark 1 is the laser evaporation region, 2 the columnar grain region, 3 the intergranular fracture region, and 4 is the transgranular fracture region. Voids exist at the intersection between the two regions. The high laser power output generates a high temperature that makes the material evaporate. The formation of the voids is due to the evaporation bubbles which are formed too late to escape to the atmosphere. This phenomenon is different from the cutting of thin substrates with low laser power. Upon applying a laser to the substrate surface, the laser heat will evaporate the material and generate a shallow groove, which is the laser evaporation region, about 80 mm deep. The adjacent material of this groove bottom is melted but not evaporated. After the passage of the laser beam, the rapid solidification and subsequent solid-state cooling take place. The columnar grain grows from a separate nucleus in the interface of molten layer and solid region, staying parallel to the temperature gradient direction. At the instant of solidification, the main crack is formed at the columnar grain boundary along the direction of thickness. There are minor cracks generated at the cross section and on the top surface. The depth of the crack is equal to the columnar grain length. The nearest neighbor to the columnar grain region is the intergranular fracture region. This region is subjected to the high temperature but has not reached the melting point. The strength of grain bonding is reduced for the high temperature and anisotropic thermal deformation, so that the cracks will extend along the grain boundary. The final region is transgranular fracture region, which is the largest part of the breaking surface. Since the laser heat has less affection on the grain boundary of the transgranular fracture region, the grain bonding could not be destroyed and the crack extension would penetrate the grain. The unstable fracture of the transgranular fracture occurs after the intergranular fracture. There are minor cracks generated at the cutting edge, as shown in Fig. 11. The minor cracks are due to the resolidification and crystal anisotropy, and they will extend from the columnar grain region to the intergranular fracture region. Fig. 11. SEM photograph of columnar grain region and intergranular fracture region. Arrow indicates the voids and branch minor cracks. Fig. 12. SEM photograph of melting groove. Arrow indicates the branch minor cracks.

172 C.-H. Tsai, H.-W. Chen / Journal of Materials Processing Technology 136 (2003) 166 173 The top surface of the melting groove is shown in Fig. 12. The groove formation is due to the Nd:YAG laser and the width of the melting groove is about 330 mm. The minor cracks grow from the edge of the breaking surface. The cracking is induced by the solidification process and is affected by the heat input and cutting speed. 4. Finite element analysis 4.1. Basic assumption In order to analyze the actual fracture phenomena, the finite element software ANSYS5.4 is used to solve the temperature and stress distributions. For thick substrates, the temperature and stress field should be three-dimensional distributions. The laser beam traverses the surface like a point heat source moving in a three-dimensional body. Most of the focused Nd:YAG laser energy will be absorbed to form a groove-crack, and part of the laser energy will be reflected out. However, the defocused CO 2 laser energy is absorbed by the material and induces the thermal stress. The CO 2 laser energy will not melt the material and part of it will be reflected out. Because the reflected laser energy is difficult to estimate, the following results will contain an unknown factor a. The factor a represents the ratio of the laser energy used to generate the thermal stress to the total lasers energy. The formation of the groove-crack due to the focused Nd:YAG involves the phase change, which is not considered in this analysis. Thus, in the calculation of finite element analysis a groove-crack is considered to be pre-existing. Because less laser power is used, the stress analysis can be only confined to the elastic deformation. The material properties such as the heat transfer properties and mechanical properties are assumed to be temperature independent. Even though the following results cannot provide an actual stress solution, the results still provide a valuable reference. The configuration of the specimen and the coordinates system are shown in Fig. 13. The separation surface is located on the xz-plane and the laser moves along the positive x-direction. 4.2. Wider substrate The specimen size is 108 mm 108 mm 10 mm and the thickness is 10 mm. The power output of CO 2 laser is Fig. 14. Stress distribution of s yy at y ¼ 0. Substrate width is 108 mm. 80 W and Nd:YAG laser is 60 W. At time t ¼ 0, the two laser beams are applied at the specimen edge (i.e., x ¼ y ¼ 0, z ¼ 10 mm), and then move in the x-direction at a constant speed, v ¼ 1 mm/s. For this loading condition a small groove-crack of depth about 1 mm is induced by the Nd:YAG laser. The separation of the substrate is lager than the moving of the laser spot, in which the lagging distance is 4 mm. The ANSYS5.4 software is used to calculate the transient temperature and stress distributions during the cutting process for the time interval t ¼ 0 30 s. The input power of heat source is 140 W. The stress s yy distributions along the fracture plane at z ¼ 8:5, 8, 6, 4, 0 mm for t ¼ 30 s, are shown in Fig. 14. At this time, the laser beams arrive at x ¼ 30 mm and the separation frontier is at x ¼ 26 mm. The stresses s yy near the separation frontier (x ¼ 26 27 mm, z ¼ 4 9 mm) are strongly tensile and the stresses on the other region are compressive. The tensile stresses may induce the fracture along the z-direction of thickness, and the breaking is initiated at the edge of groove-crack. The compressive stresses can make the cutting free from unstable fracture. The applied laser heat will generate a tensile stress through the thickness of the thick substrate that is different from the cutting of thin substrate. The laser cutting for a thin substrate with controlled fracture technique will induce a Fig. 13. Configuration of the substrate and the coordinate system.

C.-H. Tsai, H.-W. Chen / Journal of Materials Processing Technology 136 (2003) 166 173 173 Fig. 15. Stress distribution of s yy at y ¼ 0. Substrate width is 54 mm. compressive stress, after the passage of laser beam, the compressive stress will be released and induce a residual tensile stress. 4.3. Middle substrate In this section, the relation between the maximum cutting speed and the specimen size is studied, using the medium sized sspecimen of 54 mm 108 mm 10 mm. The laser cutting conditions are the same as the above section. The stresses s yy distributed along the fracture plane at z ¼ 8:5, 8, 6, 4, 0 mm for t ¼ 30 s, are shown in Fig. 15. At this time, the laser beams arrive at x ¼ 30 mm and the separation frontier is at x ¼ 26 mm. The stresses s yy near the separation frontier (x ¼ 26 27:5 mm, z ¼ 0 9 mm) are strongly tensile and the stresses on the other region are compressive. The stresses near the frontier are positive and greater than the case of wider specimen. The area of the tensile stress region for the middle specimen is larger than that of the wider specimen. This result can explain why the cutting speed of the narrow specimen is faster than that of the wider one. 5. Conclusion The laser cutting technique by controlled fracture is successfully applied in cutting thick alumina substrate. Two laser beams of focused Nd:YAG laser and defocused CO 2 laser are synchronously applied on the substrate. The Nd:YAG laser is used to scribe a groove-crack at the surface of substrate and the CO 2 laser is used to generate the thermal stress. The thermal stress concentration at the tip of the groove-crack will make it extend through the substrate, and then the substrate will be separated controllably along the moving path of the laser beams. For the narrow specimen, 10 mm thick and 27 mm wide, the maximum cutting speed that can be reached is 3 mm/s under the 60 W Nd:YAG and 44 W CO 2 laser output. The cutting speed is influenced greatly by the width of the specimen. The maximum cutting speed that can be reached for the narrow specimen is higher than that for the wider specimen. The tensile stress will be induced at the groovecrack edge, so that the groove-crack will propagate along the thickness direction (z-direction) and the substrate will be separated. The fracture growth in the thickness direction is unstable, but the fracture extension in the transverse direction (x-direction) is stable. The most important phenomenon is that the fracture region will not be uniform of throughout the thickness for the high cutting speed before the cutting is completed. The substrate is partially separated and the blind crack is formed. At the final stage, the unstable fracture will be induced and the unfractured region will separate instantaneously. Acknowledgements The authors gratefully acknowledge the financial support of this research by the National Science Council (Republic of China) under Grant NSC 89-2212-E-211-004 to Huafan University. References [1] E. Lambert, J.-L. Lambert, B. De Longueville, Severing of glass or vitrocrystalline bodies, US Patent 3,935,419 (1976). [2] D.J. Garibotti, Dicing of micro-semiconductors, US Patent 3,112,850 (1963). [3] R.M. Lumley, Controlled separation of brittle materials using a laser, Am. Ceram. Soc. Bull. 48 (1969) 850 854. [4] F.J. Grove, D.C. Wright, F.M. Hamer, Cutting of glass with a laser beam, US Patent 3,543,979 (1970). [5] V.S. Kondratenko, Method of splitting non-metallic materials, US Patent 5,609,284 (1997). [6] U. Unger, W. Wittenbecher, The cutting edge of laser technology, Glass 75 (1998) 101 102. [7] C.H. Tsai, C.S. Liou, Fracture mechanism of laser cutting with controlled fracture, ASME J. Manuf. Sci. Eng., in press. [8] C.H. Tsai, C.S. Liou, Apply on-line crack detection technique to laser cutting with controlled fracture, Int. J. Adv. Manuf. Technol. 18 (2001) 724 730. [9] I. Black, K.L. Chua, Laser cutting of thick ceramic tile, Opt. Technol. 29 (1997) 193 205.