氧化铝陶瓷激光热应力切割数值仿真与实验分析
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摘要
激光切割是一项重要的激光加工应用技术,其中非金属材料的激光加工也已成了研究热点。激光热应力切割技术通过激光束切割材料表面时引起的温度场梯度变化产生热应力,诱导并控制裂纹扩展,从而分割材料,是对玻璃、陶瓷等脆性材料切割的有效方法。相对于传统的金刚刀切割和激光汽化切割方式,具有切割面光滑,材料没有损失,微裂纹小等优点。
本文在自然科学基金项目的支持下,讨论了目前激光热应力切割陶瓷等脆性材料的研究现状及发展趋势,分析了激光热应力切割氧化铝陶瓷的机理,建立了激光切割的三维平面对称模型,研究了各切割参数对切割温度场和热应力场的影响分析,具体研究内容如下:
首先从脆性材料断裂理论出发,研究激光热应力切割中的裂纹扩展机理。通过Ansys建立三维对称切割有限元仿真模型。采用APDL编程语言,引进表面效应单元surf152,实现对激光移动热源及换热模型的仿真。
分析了激光热应力切割氧化铝陶瓷过程,研究了切割中的温度场和热应力场分布规律,揭示了温度场和应力场随激光功率、工件厚度和切割速度之间的关系。在激光切割路径上节点的正应力σy,在切割过程中经历“无应力‐拉应力‐压应力‐拉应力‐无应力”的变化过程,直至裂纹扩展。研究表明,激光功率和切割过程当中的最高温度成正比关系。功率增大,相同节点裂纹萌生越早,断裂时的拉应力σy更大。相同条件下切割速度增大,切割最高温度下降,越早发生断裂。
在理论研究的基础上,利用50W连续CO2激光器对不同规格的氧化铝陶瓷片进行热应力切割实验。实验验证了切割质量与激光功率、工件厚度和切割速度关系的理论分析结果,为切割参数优化提供了理论和生产指导。
最后,论文对所做的工作进行了总结,并对今后的进一步研究方向进行了展望。
Laser cutting is one of the most important application technologies in laser machining industry, and the laser processing of non-metallic materials has become the study object of many scholars. The laser-controlled thermal stress cutting induces and controls the crack propagation by using the thermal stress which is caused by the surface temperature field gradient in the laser cutting. And it is an effective manner to split the glass, ceramics and other brittle materials. Compared with the traditional diamond knife cutting and laser vaporization cutting, laser-controlled thermal stress cutting has many advantages such as smooth cutting surface, no loss of materials, small micro-cracks and so on.
Under the support of the project of natural science foundation, the paper discusses the present research status and development of laser-controlled thermal stress cutting, analyses the mechanism of laser cutting of alumina ceramic, establishes a three-dimensional symmetric model of laser cutting, and study the effect of various cutting parameters on temperature field and thermal stress field. The concrete research content is as follows:
Firstly, the paper analysis the crack propagation mechanism of laser-controlled thermal stress cutting based on brittle fracture theory, and establishes the three-dimensional symmetrical finite element model by using Ansys software. APDL programming language is adopted, and surface effect element surf152 is introduced to simulate the moving laser heat source and heat transfer model.
The laser-controlled thermal stress cutting process of alumina ceramics is studied, the law of the temperature field distribution and thermal stress distribution is analyzed, and the relationships between the temperature field and stress field with the laser power, workpiece thickness and cutting speed are revealed. The normal stressσy of nodes which are located in the laser cutting path is experienced in the cutting process of "no stress-tensile stress-compressive stress-tensile stress-no stress" until the crack propagation. The earlier the crack initiates with greater tensile stress when the laser power becomes greater. Under the same conditions, the sooner the fracture happens and the maximum temperature drops with cutting speed increased.
Based on the theoretical study, alumina ceramic substrates offered by Xi'an Electronic Technology Co., Ltd are adopted to do the laser-controlled thermal stress cutting experiment. Laser cutting machine is 50W continuous carbon dioxide laser which is offered by Shanghai Institute of Laser Technology. Meanwhile, verify the theoretical relationship between the cutting quality and laser power, workpiece thickness as well as cutting speed to provide practical optimization of cutting parameters based on the cutting experiment.
Finally, the paper summarizes all the done work and views the study direction in future.
本文在自然科学基金项目的支持下,讨论了目前激光热应力切割陶瓷等脆性材料的研究现状及发展趋势,分析了激光热应力切割氧化铝陶瓷的机理,建立了激光切割的三维平面对称模型,研究了各切割参数对切割温度场和热应力场的影响分析,具体研究内容如下:
首先从脆性材料断裂理论出发,研究激光热应力切割中的裂纹扩展机理。通过Ansys建立三维对称切割有限元仿真模型。采用APDL编程语言,引进表面效应单元surf152,实现对激光移动热源及换热模型的仿真。
分析了激光热应力切割氧化铝陶瓷过程,研究了切割中的温度场和热应力场分布规律,揭示了温度场和应力场随激光功率、工件厚度和切割速度之间的关系。在激光切割路径上节点的正应力σy,在切割过程中经历“无应力‐拉应力‐压应力‐拉应力‐无应力”的变化过程,直至裂纹扩展。研究表明,激光功率和切割过程当中的最高温度成正比关系。功率增大,相同节点裂纹萌生越早,断裂时的拉应力σy更大。相同条件下切割速度增大,切割最高温度下降,越早发生断裂。
在理论研究的基础上,利用50W连续CO2激光器对不同规格的氧化铝陶瓷片进行热应力切割实验。实验验证了切割质量与激光功率、工件厚度和切割速度关系的理论分析结果,为切割参数优化提供了理论和生产指导。
最后,论文对所做的工作进行了总结,并对今后的进一步研究方向进行了展望。
Laser cutting is one of the most important application technologies in laser machining industry, and the laser processing of non-metallic materials has become the study object of many scholars. The laser-controlled thermal stress cutting induces and controls the crack propagation by using the thermal stress which is caused by the surface temperature field gradient in the laser cutting. And it is an effective manner to split the glass, ceramics and other brittle materials. Compared with the traditional diamond knife cutting and laser vaporization cutting, laser-controlled thermal stress cutting has many advantages such as smooth cutting surface, no loss of materials, small micro-cracks and so on.
Under the support of the project of natural science foundation, the paper discusses the present research status and development of laser-controlled thermal stress cutting, analyses the mechanism of laser cutting of alumina ceramic, establishes a three-dimensional symmetric model of laser cutting, and study the effect of various cutting parameters on temperature field and thermal stress field. The concrete research content is as follows:
Firstly, the paper analysis the crack propagation mechanism of laser-controlled thermal stress cutting based on brittle fracture theory, and establishes the three-dimensional symmetrical finite element model by using Ansys software. APDL programming language is adopted, and surface effect element surf152 is introduced to simulate the moving laser heat source and heat transfer model.
The laser-controlled thermal stress cutting process of alumina ceramics is studied, the law of the temperature field distribution and thermal stress distribution is analyzed, and the relationships between the temperature field and stress field with the laser power, workpiece thickness and cutting speed are revealed. The normal stressσy of nodes which are located in the laser cutting path is experienced in the cutting process of "no stress-tensile stress-compressive stress-tensile stress-no stress" until the crack propagation. The earlier the crack initiates with greater tensile stress when the laser power becomes greater. Under the same conditions, the sooner the fracture happens and the maximum temperature drops with cutting speed increased.
Based on the theoretical study, alumina ceramic substrates offered by Xi'an Electronic Technology Co., Ltd are adopted to do the laser-controlled thermal stress cutting experiment. Laser cutting machine is 50W continuous carbon dioxide laser which is offered by Shanghai Institute of Laser Technology. Meanwhile, verify the theoretical relationship between the cutting quality and laser power, workpiece thickness as well as cutting speed to provide practical optimization of cutting parameters based on the cutting experiment.
Finally, the paper summarizes all the done work and views the study direction in future.
引文
[1]陈树明.激光切割技术现状与发展[J].锻压机械,2002,28(2):3~5.
[2]黄开金,谢长生.激光切割的研究现状及展望[J].激光与光电子学进展,1998,(4):1~2.
[3]郝喜海,吴若梅,张继红.激光切割技术在机械制造中的应用及发展[J].机械制造,1999,37(8):9~11.
[4]肖克.CO2激光切割机在工业企业的应用前景[J].光机电信息,2004,(1):13~15.
[5]史晓强.低碳钢板的激光切割[J].激光技术,1998,22(6):343~345.
[6] Rajaram N., Sheikh J., Cheraghi S.H. CO2 laser cut quality of 4130 steel[J]. International Journal of Machine Tools & Manufacture, 2003, 43(4): 351~358.
[7] Wang J., Wong W.C.K. CO2 Laser Cutting of metallic coated sheet steels[J]. Journal of Materials Processing Technology, 1999, 95(1): 164~168.
[8] Leidinger D., Penz A., Schuoker D. Improved manufacturing processes with high power lasers[J]. Infrared Physics & Technology, 1995, 36(1): 251~266.
[9] Caiazzo F., Curcio F., Daurelio G. Laser cutting of different polymeric plastics(PE, PP and PC) by a CO2 1aser beam[J]. Journal of Materials Processing Technology, 2005, 159(3): 279~285.
[10] Ding Zhihong, Liu YongZhen, Weng ShiPing. Laser forming cutting once quenched high-sp eed tool steel (HSTS) disk-shaped milling cutter[J]. Proc. SPIE, 1998, 3550(323): 323~329.
[11]李亚江.切割技术及应用[M].北京:化学工业出版社,2004.
[12]邓英剑.激光切割及其在切割陶瓷材料中的应用[J].机械,2004, 31(3):55~60.
[13]周岩,刘晓胜,张显奎等.激光切割石英的切向裂纹研究[J].激光杂志,2003,24(4):73~75.
[14]许国良,李迎霞,黄素逸.激光切割玻璃的参数模型[J].华中科技大学学报,2007,35(7):48~50.
[15] Black I., Chua K.L. CO2 laser cutting of thick ceramic title[J]. Optical Laser Technology, 1997, 29 (4): 193~205.
[16] Tsai C.H., Shiu J.S. Laser cutting ceramics using an unstable fracture technique[J]. Journal of Laser Applications, 2009, 21(1): 57~62.
[17] Kalyanasundaram D., Shehata G., Neumann C. et al. Design and validation of a hybrid laser/water-jet machining system for brittle materials[J]. Journal of Laser Applications, 2008, 20(2): 127~134.
[18] Wee L.M., Crouse P.L., Li L. A statistical analysis of striation formation during laser cutting of ceramics[J]. International Journal of Advanced Manufacturing Technology, 2008, 36(7): 699~706.
[19] Brugan P., Cai G., Akarapu R. et al. Controlled-fracture of prescored alumina ceramics using simultaneous CO2 lasers[J]. Journal of Laser Applications, 2006, 18(3): 236~241.
[20] Segall A.E., Cai G., Akarapu R.A., et al. Fracture control of unsupported ceramics during laser machining using a simultaneous prescore[J]. Journal of Laser Applications, 2005, 17(1):57~62.
[21] Quintero F., Pou J., Lusqui?os F.A., et al. Comprehensive assessment of the CO2 laser cut quality of ceramics with different assist gas injection systems[J]. Journal of Laser Applications, 2004, 16(4): 212~220.
[22] Akarapu R., Li B.Q, Segall A.E. Finite element modeling of ablation phenomena and thermal stress evolution during a unique application of dual laser cutting of ceramics[J]. TMS Annual Meeting, 2003, 87~98.
[23] Tsai C.H., Chen C.J. Formation of the breaking surface of alumina in laser cutting with a controlled fracture technique[J]. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2003, 217(4): 489~497.
[24] Tsai C.H., Chen H.W. Laser cutting of thick ceramic substrates by controlled fracture technique[J]. Journal of Materials Processing Technology, 2003, 136(1): 166~173.
[25] Tsai C.H., Liou C.S. Applying an on-line crack detection technique for laser cutting by controlled fracture[J]. International Journal of Advanced Manufacturing Technology, 2001, 18(10): 724~730.
[26] Quintero F., Pou J., Lusqui?os F., et al. Cutting of ceramic plates by optical fiber guided Nd:YAG laser[J]. Journal of Laser Applications, 2001, 13(2): 84~88.
[27] Pereles-Santiago V., Washington M., Brugan P., et al. Faster and damage-reduced laser cutting of thick ceramics using a simultaneous prescore approach[J]. Journal of Laser Applications, 2005, 17(4): 219~224.
[28] Li K., Sheng P. Plane stress model for fracture of ceramics during laser cutting[J]. International Journal of Machine Tools and Manufacture, 1995, 35(11): 1493~1506.
[29] Segall A.E., Cai G., Akarapu R. Studies on the use of offset and angled prescores for fracture control during laser machining of alumina ceramics[J]. Journal of Laser Applications, 2006, 18(4): 325~329.
[30] Maruo, Hiroshi, Miyamoto, et al. Mechanism of material removal in laser processing of ceramics - research of material processing with high power density laser[J]. Quarterly Journal of the Japan Welding Society, 1992, 10(3): 123~128.
[31] Seoung, Hwan LEE, Sun-Eung AHN. A Probabilistic Model for Crack Formation in Laser Cutting of Ceramics[J]. JSME International Journal Series C, 2003, 46(4): 1591~1597.
[32] Akarapu R., Asme M., Segall A.E., et al. Numerical Simulations of an Active-Stressing Technique for Delaying Fracture During Cutting of Alumina[J]. Journal of Manufacturing Science and Engineering, 2006, 128(4): 921~927.
[33] Tsai C.H., Liou C.S. Fracture Mechanism of Laser Cutting With Controlled Fracture[J]. Journal of Manufacturing Science and Engineering, 2003, 125(3): 519~528.
[34]张铭峰,张胜雄,郑劭家等.CO2激光控制断裂切割氧化铝陶瓷基片最佳条件的探讨[J].中国激光,2000,27(11):1045~1049.
[35]闫胤洲,季凌飞,鲍勇等.激光加工陶瓷裂纹行为的理论分析及实验验证[J].中国激光,2008,35(9):1401~1408.
[36]侯廉平,陈培峰,陈清明.射频激光对氧化铝陶瓷基片划片的研究[J].中国激光,2003,27(4):352~356.
[37] Ho C.Y., Wen M.Y., Ho J.E., et al. Temperature history for cutting of ceramics preheated by a CO2 laser[J]. Journal of Materials Processing Technology. 2007, 192(1): 525~531.
[38] Lumley R.M. Controlled separation of brittle materials using a laser[J]. American Ceramic Society Bulletin, 1969, 48: 850~854.
[39]Grove F. J., Wright D.C. Hamer F.M. Cutting of glass with a laser beam[F]. United States: 3543979, 1970.
[40] Kondratedo V.S. Method of splitting non-metallic materials[P]. United States: 5609284, 1997.
[41] Shahani A.R., Seyyedian M. Simulation of glass cutting with an impinging hot air jet[J]. International Journal of Solids and Structures, 2003, 41(5-6): 1313~1329.
[42] Molian R., Shrotriya P., Molian P. Fracture mode of CO2 laser cutting of aluminum nitride[J]. International Journal of Advanced Manufacturing Technology, 2008, 39(7): 725~733.
[43]叶圣麟,黄鑫,马军山等.液晶显示玻璃基板激光切割技术的实验研究[J].应用激光,2006,26(6):401~404.
[44]陶伟明,毕国丽,章惠全等.钙基玻璃板激光热应力切割过程的有限元仿真[J].浙江大学学报,2005,39(9):1423~1426.
[45] Paris P., Gomez M.P., Anderson W.E. A Rational Analytical Theory of Fatigue[J]. The Trend in Engineering, 1961, 13(1): 9~14.
[46] Paris P.C., Erdogan F.A. Critical Analysis of Crack Propagation Laws[M]. J. Basic Engineering, 1963, 85: 528~534.
[47] Sehitoglu H., Gall K., Garci A.M. Recent Advances in Fatigue Crack Growth Modeling[J]. Int. J. Fract, 1996, 80(2): 165~192.
[48] Oliva V., Cseplo L., Materna A., et al. FEM Simulation of Fatigue Crack Growth[J]. Material Science and Engineering, 1997, A234-236: 517~520.
[49] Dougherty J.D., Padovan J., Srivatsan T.S. Fatigue Crack Propagation and Closure Behavior of Modified 1070 Steel: Finite Element study[J]. Engineering Fracture Mechanics, 1997, 56(2): 189~212.
[50] Zhang J., Zhang J, Du Sh. Elastic-Plastic Finite Element Analysis and Experimental Study of Short and Long Fatigue Crack Growth[J]. Engineering Fracture Mechanics, 2001, 68(14): 1591~1605.
[51] Miller K.J. Metal Fatigue Past Current and Future[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 1991, 205(5): 291~304.
[52]严宗达,王洪礼.热应力[M],北京:高等教育出版社,1993.
[53]沃国纬,王元淳.弹性力学[M],上海:上海交通大学出版社,1998.
[54]切列帕诺夫.脆性断裂力学(黄克智等译)[M],北京:科学出版社,1990.
[55]丁遂栋.断裂力学[M],北京:机械出版社,1997.
[56]王勋成,邵敏.有限元基本原理和数值方法[M],北京:清华大学出版社,2003.
[57]徐兴,郭乙木,沈永兴.非线性有限元及程序设计[M],杭州:浙江大学出版社,1993.
[2]黄开金,谢长生.激光切割的研究现状及展望[J].激光与光电子学进展,1998,(4):1~2.
[3]郝喜海,吴若梅,张继红.激光切割技术在机械制造中的应用及发展[J].机械制造,1999,37(8):9~11.
[4]肖克.CO2激光切割机在工业企业的应用前景[J].光机电信息,2004,(1):13~15.
[5]史晓强.低碳钢板的激光切割[J].激光技术,1998,22(6):343~345.
[6] Rajaram N., Sheikh J., Cheraghi S.H. CO2 laser cut quality of 4130 steel[J]. International Journal of Machine Tools & Manufacture, 2003, 43(4): 351~358.
[7] Wang J., Wong W.C.K. CO2 Laser Cutting of metallic coated sheet steels[J]. Journal of Materials Processing Technology, 1999, 95(1): 164~168.
[8] Leidinger D., Penz A., Schuoker D. Improved manufacturing processes with high power lasers[J]. Infrared Physics & Technology, 1995, 36(1): 251~266.
[9] Caiazzo F., Curcio F., Daurelio G. Laser cutting of different polymeric plastics(PE, PP and PC) by a CO2 1aser beam[J]. Journal of Materials Processing Technology, 2005, 159(3): 279~285.
[10] Ding Zhihong, Liu YongZhen, Weng ShiPing. Laser forming cutting once quenched high-sp eed tool steel (HSTS) disk-shaped milling cutter[J]. Proc. SPIE, 1998, 3550(323): 323~329.
[11]李亚江.切割技术及应用[M].北京:化学工业出版社,2004.
[12]邓英剑.激光切割及其在切割陶瓷材料中的应用[J].机械,2004, 31(3):55~60.
[13]周岩,刘晓胜,张显奎等.激光切割石英的切向裂纹研究[J].激光杂志,2003,24(4):73~75.
[14]许国良,李迎霞,黄素逸.激光切割玻璃的参数模型[J].华中科技大学学报,2007,35(7):48~50.
[15] Black I., Chua K.L. CO2 laser cutting of thick ceramic title[J]. Optical Laser Technology, 1997, 29 (4): 193~205.
[16] Tsai C.H., Shiu J.S. Laser cutting ceramics using an unstable fracture technique[J]. Journal of Laser Applications, 2009, 21(1): 57~62.
[17] Kalyanasundaram D., Shehata G., Neumann C. et al. Design and validation of a hybrid laser/water-jet machining system for brittle materials[J]. Journal of Laser Applications, 2008, 20(2): 127~134.
[18] Wee L.M., Crouse P.L., Li L. A statistical analysis of striation formation during laser cutting of ceramics[J]. International Journal of Advanced Manufacturing Technology, 2008, 36(7): 699~706.
[19] Brugan P., Cai G., Akarapu R. et al. Controlled-fracture of prescored alumina ceramics using simultaneous CO2 lasers[J]. Journal of Laser Applications, 2006, 18(3): 236~241.
[20] Segall A.E., Cai G., Akarapu R.A., et al. Fracture control of unsupported ceramics during laser machining using a simultaneous prescore[J]. Journal of Laser Applications, 2005, 17(1):57~62.
[21] Quintero F., Pou J., Lusqui?os F.A., et al. Comprehensive assessment of the CO2 laser cut quality of ceramics with different assist gas injection systems[J]. Journal of Laser Applications, 2004, 16(4): 212~220.
[22] Akarapu R., Li B.Q, Segall A.E. Finite element modeling of ablation phenomena and thermal stress evolution during a unique application of dual laser cutting of ceramics[J]. TMS Annual Meeting, 2003, 87~98.
[23] Tsai C.H., Chen C.J. Formation of the breaking surface of alumina in laser cutting with a controlled fracture technique[J]. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, 2003, 217(4): 489~497.
[24] Tsai C.H., Chen H.W. Laser cutting of thick ceramic substrates by controlled fracture technique[J]. Journal of Materials Processing Technology, 2003, 136(1): 166~173.
[25] Tsai C.H., Liou C.S. Applying an on-line crack detection technique for laser cutting by controlled fracture[J]. International Journal of Advanced Manufacturing Technology, 2001, 18(10): 724~730.
[26] Quintero F., Pou J., Lusqui?os F., et al. Cutting of ceramic plates by optical fiber guided Nd:YAG laser[J]. Journal of Laser Applications, 2001, 13(2): 84~88.
[27] Pereles-Santiago V., Washington M., Brugan P., et al. Faster and damage-reduced laser cutting of thick ceramics using a simultaneous prescore approach[J]. Journal of Laser Applications, 2005, 17(4): 219~224.
[28] Li K., Sheng P. Plane stress model for fracture of ceramics during laser cutting[J]. International Journal of Machine Tools and Manufacture, 1995, 35(11): 1493~1506.
[29] Segall A.E., Cai G., Akarapu R. Studies on the use of offset and angled prescores for fracture control during laser machining of alumina ceramics[J]. Journal of Laser Applications, 2006, 18(4): 325~329.
[30] Maruo, Hiroshi, Miyamoto, et al. Mechanism of material removal in laser processing of ceramics - research of material processing with high power density laser[J]. Quarterly Journal of the Japan Welding Society, 1992, 10(3): 123~128.
[31] Seoung, Hwan LEE, Sun-Eung AHN. A Probabilistic Model for Crack Formation in Laser Cutting of Ceramics[J]. JSME International Journal Series C, 2003, 46(4): 1591~1597.
[32] Akarapu R., Asme M., Segall A.E., et al. Numerical Simulations of an Active-Stressing Technique for Delaying Fracture During Cutting of Alumina[J]. Journal of Manufacturing Science and Engineering, 2006, 128(4): 921~927.
[33] Tsai C.H., Liou C.S. Fracture Mechanism of Laser Cutting With Controlled Fracture[J]. Journal of Manufacturing Science and Engineering, 2003, 125(3): 519~528.
[34]张铭峰,张胜雄,郑劭家等.CO2激光控制断裂切割氧化铝陶瓷基片最佳条件的探讨[J].中国激光,2000,27(11):1045~1049.
[35]闫胤洲,季凌飞,鲍勇等.激光加工陶瓷裂纹行为的理论分析及实验验证[J].中国激光,2008,35(9):1401~1408.
[36]侯廉平,陈培峰,陈清明.射频激光对氧化铝陶瓷基片划片的研究[J].中国激光,2003,27(4):352~356.
[37] Ho C.Y., Wen M.Y., Ho J.E., et al. Temperature history for cutting of ceramics preheated by a CO2 laser[J]. Journal of Materials Processing Technology. 2007, 192(1): 525~531.
[38] Lumley R.M. Controlled separation of brittle materials using a laser[J]. American Ceramic Society Bulletin, 1969, 48: 850~854.
[39]Grove F. J., Wright D.C. Hamer F.M. Cutting of glass with a laser beam[F]. United States: 3543979, 1970.
[40] Kondratedo V.S. Method of splitting non-metallic materials[P]. United States: 5609284, 1997.
[41] Shahani A.R., Seyyedian M. Simulation of glass cutting with an impinging hot air jet[J]. International Journal of Solids and Structures, 2003, 41(5-6): 1313~1329.
[42] Molian R., Shrotriya P., Molian P. Fracture mode of CO2 laser cutting of aluminum nitride[J]. International Journal of Advanced Manufacturing Technology, 2008, 39(7): 725~733.
[43]叶圣麟,黄鑫,马军山等.液晶显示玻璃基板激光切割技术的实验研究[J].应用激光,2006,26(6):401~404.
[44]陶伟明,毕国丽,章惠全等.钙基玻璃板激光热应力切割过程的有限元仿真[J].浙江大学学报,2005,39(9):1423~1426.
[45] Paris P., Gomez M.P., Anderson W.E. A Rational Analytical Theory of Fatigue[J]. The Trend in Engineering, 1961, 13(1): 9~14.
[46] Paris P.C., Erdogan F.A. Critical Analysis of Crack Propagation Laws[M]. J. Basic Engineering, 1963, 85: 528~534.
[47] Sehitoglu H., Gall K., Garci A.M. Recent Advances in Fatigue Crack Growth Modeling[J]. Int. J. Fract, 1996, 80(2): 165~192.
[48] Oliva V., Cseplo L., Materna A., et al. FEM Simulation of Fatigue Crack Growth[J]. Material Science and Engineering, 1997, A234-236: 517~520.
[49] Dougherty J.D., Padovan J., Srivatsan T.S. Fatigue Crack Propagation and Closure Behavior of Modified 1070 Steel: Finite Element study[J]. Engineering Fracture Mechanics, 1997, 56(2): 189~212.
[50] Zhang J., Zhang J, Du Sh. Elastic-Plastic Finite Element Analysis and Experimental Study of Short and Long Fatigue Crack Growth[J]. Engineering Fracture Mechanics, 2001, 68(14): 1591~1605.
[51] Miller K.J. Metal Fatigue Past Current and Future[J]. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 1991, 205(5): 291~304.
[52]严宗达,王洪礼.热应力[M],北京:高等教育出版社,1993.
[53]沃国纬,王元淳.弹性力学[M],上海:上海交通大学出版社,1998.
[54]切列帕诺夫.脆性断裂力学(黄克智等译)[M],北京:科学出版社,1990.
[55]丁遂栋.断裂力学[M],北京:机械出版社,1997.
[56]王勋成,邵敏.有限元基本原理和数值方法[M],北京:清华大学出版社,2003.
[57]徐兴,郭乙木,沈永兴.非线性有限元及程序设计[M],杭州:浙江大学出版社,1993.