本研究主要探討接觸式球鏡預力負載下，雷射切割鈉鈣玻璃的裂紋生長情形。藉由雷射熱源產生熱應力以熱裂法的方式使玻璃表面產生裂紋，同時利用接觸式球鏡對試件施以預力負載，控制裂紋的生長型態。數值分析分為兩部分，第一部分利用光學分析軟體ZEMAX確認雷射光路以及加工光斑尺寸，並與實驗結果比較。第二部分利用有限元素軟體ANSYS，以熱機非耦合的方式，計算雷射熱源以及預力負載時之試件溫度與應力變化。
實驗方面以連續式1064 nm Nd-YAG雷射加熱鈉鈣玻璃之塗碳表面，利用接觸式球鏡配合夾具產生一彎曲預力並進行切割加工。以雷射功率與預力為實驗參數，探討表面裂紋生長與裂紋深度。實驗結果顯示，因為試件邊界的影響，在切割起始端易產生交叉裂紋，且隨著功率提高，起始端的交叉裂紋分佈長度也會增長。若提高預力負載，能使切割前段的交叉裂紋分佈長度縮短，適當的預力可使的側向裂紋數減少，且裂紋深度隨著預力提高而增加，進而提高切割品質。

This study mainly focuses on the investigation of the crack growth of glass in laser cleavage with a pre-load from a contact ball-lens. In the numerical analysis of the optical characteristics for the ball-lens, the laser spot size and intensity profile were simulated by ZEMAX software and compared with the experimental measurement. Furthermore the temperature and stress distribution of the glass with various laser power and pre-loads were simulated by ANSYS software.
In the experimental approach, an Nd-YAG laser with a wavelength of 1064 nm was used to heat the carbon coating surface of the soda-lime glass through the contact ball-lens. The result shows that the increase of laser power will increase the distribution length of the side crack. Also the penetration depth of the crack will increase with the laser power and pre-load. However the distribution length of the side crack was reduced with the increase of the pre-load and it could extend the length of the straight cut and the penetration depth. It can be found the region of the side crack was dramatically reduced by an appropriate pre-load and the cutting quality was improved in the present study.

[1] Lumley R. M., Controlled separation of brittle materials using a laser, American Ceramic Society Bulletin, Vol. 48, No.9, pp.850-854.
[2] Kang H.S., Hong S.K., Oh S.C., Choi J. Y., Song M. G.,Cutting glass by laser,Proceedings of SPIE - The International Society for Optical Engineering, v 4426,p 367-370, 2002.
[3] Kim K.R.,Kim J.H., Farson D. F., Choi H.W., Kim K.H., Hybrid laser cutting for flat panel display glass, Japanese Journal of Applied Physics, v 47, n 8 PART 3, p 6978-6981, 2008.
[4] Tsai C. H., Liou C.S., Applying an On-line Crack Detection Technique For Laser Cutting by Controlled Fracture, International Journal of Advanced Manufacturing Technology, v 18, n 10, p 724-730, 2001.
[5] Nisar S., Li L., Sheikh M. A., Pinkerton A. J., The effect of continuous and pulsed beam modes on cut path deviation in diode laser cutting of glass, International Journal of Advanced Manufacturing Technology, v 49, n 1-4, p 167-175, 2010.
[6] Yang L. J., Wang Y., Tian Z.G., Cai N., YAG laser cutting soda-lime glass with controlled fracture and volumetric heat absorption, International Journal of Machine Tools and Manufacture, v 50, n 10, p 849-859, 2010.
[7] Jiao J.K., Wang X.B., A numerical simulation of machining glass by dual CO2-laser beams, Optics and Laser Technology, v 40, n 2, p 297-301, 2008.
[8] Nisar S., Li L., Sheikh M. A., Pinkerton A. J., Safdar S., The effect of laser beam geometry on cut path deviation in diode laser chip-free cutting of glass, Journal of Manufacturing Science and Engineering, Transactions of the ASME, v 132, n 1,p 0110021-0110029, 2010.
[9] Masayuki I., Takayuki S., Eiji M, Yoshimi T., Atsushi O., Fumio M., Study on laser braking of glass plate generation and growth of vertical cracks by scribing., Journal of the Japan Society for precision engineering, v.62,n3,pp413-417,1996.
[10] Pan C.T., Hsieh C.C., Su C.Y., Liu Z.S., Study of cutting quality for TFT-LCD glass substrate, International Journal of Advanced Manufacturing Technology, v 39, n 11-12, p 1071-1079, 2008.
[11] Tasi C. H., Lin B. C., Laser cutting with controlled fracture and pre-bending applied to LCD glass separation, Int J Adv Manuf rechnol, v.32, pp.1155-1162,2007.
[12] Masayoshi K., Naoki U., Etusji O., Ryuji S., Kazuhiro A., Kenshi F., Advanced Dicing Technology for Semiconductor Wafer—Stealth Dicing, IEEE Transactions on Semiconductor Manufacturing, v 20, n 3, p 259-265, 2007.
[13] Koji Y., Noboru H., Hideki M., Etsuji O., Three dimensional thermal stress analysis on laser scribing of glass, Precision Engineering, v 32, n 4, p 301-308, 2008.
[14] Koji Y., Noboru H., Hideki M., Etsuji O., Influence of thermal expansion coefficient in laser scribing of glass, Precision Engineering, v 34, n 1, p 70-75, 2010.
[15] Lin J.M. Wang Y.Z., Characterization of the laser cleaving on glass sheets with a line-shape laser beam, Optics and Laser Technology, v 39, n 5, p 892-899, July 2007.
[16] Wu W. H., Huang K.C., Tseng S.F., Multi-sphere mirror design of YAG laser applied for glass substrate cutting, Advanced Materials Research, v 264-265, p 1246-1251, 2011.
[17] 丁勝懋,雷射工程導論,中央圖書出版社,1998
[18] Karstensen H.,Laser Diode to Single-Mode Fiber Coupling with Ball Lenses., Journal of Optical Communications,pp42 49,1988
[19] Johnson K.L., Contact Mechanics,.Press Syndicate of the University of Cambridge., New York., 1985.
[20] Anderson Ted L., Fracture Mechanics Fundamentals and Applications. Third Edition.,Taylor & Francis Group, London, 2004.
[21] Karube K., KarubeN.Laser-induced cleavage of LCD glass as full-body cutting, Invited Paper, Proc. Of SPIE, Vol.6880, n.688007,2008.
[22] Paterson N., Tawn A., Williams K., Nurse A. D., On the numerical modeling of laser shearing of glass sheet used to optimize production methods ,Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, v.218, n1, pp1-12, 2004.
[23] Zhou Y.C., Zhu Z.M., Duan Z. P., Thermal fracture characteristics induced by laser beam, International Jounal of Solids and Structures, v.38, pp.5647-5660, 2001.
[24] 陳信吉,ANSYS入門,全華圖書股份有限公司,2009.
[25] Steem W. M.,Laser material processing, Springer London, p219, 1998.
[26] Bansal N. P.,Doremus R. H., Handbook of glass properties, Academic Press, Inc.,Orlando, 1986.
[27] 張恒瑞, 雷射熱裂法之玻璃裂紋應力分析及高速攝影,國立成功大學機械工 程研究所碩士論文,2012