三点弯曲试样断裂力学理论建模与有限元分析
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摘要
在现代的生活中,随着系统结构越来越复杂,由金属材料的断裂所造成的问题也越来越严重,其原因大概可以分为脆性断裂,韧性断裂,疲劳开裂和环境腐蚀等等。但是,断裂力学的理论体系还不够健全,不足以完全避免此类失效。从事断裂力学的研究,要求研究者们有着扎实的数学背景,以及丰富的力学知识和机械工程领域的相关知识。值得欣慰的是,如今越来越多的研究人员开始关注该领域,他们的研究为理解和解决现实生活中的实际问题提供了理论指导,使工程设计人员更好地了解材料的断裂力学特性和更好地认识系统结构及零部件的力学特征。同时,对断裂力学基本理论的研究和进行相关的仿真,在实际的应用领域有着重要的价值。
为了分析电磁激振器中缓冲弹簧的失效问题,本文是通过将对标准测试试件三点弯曲试样特性的研究来完成的。本文选用的载荷为周期作用力来模拟电磁激振器中作用锤对缓冲弹簧的作用。
本文将集中对如下几个方面进行研究：电磁激振器中缓冲弹簧三点弯曲试样断裂力学理论模型的建立与分析计算,恒定载荷下静态应力强度因子的计算,等效三点弯曲模型的系统方程和周期作用力下的动态应力强度因子的理论分析和计算,最后再进行基于ABAQUS的有限元仿真及分析。同时,对该三点弯曲试样的寿命也进行相应的理论分析和计算,同时也对材料的选择的一般原则进行了基本的分析。本文也讨论了关于三点弯曲试样的等效质量-阻尼-刚度系统的系统方程与理论模型,理论上获得了动态应力强度因子的解析解的一般形式。这也为将来的研究中进一步分析缓冲弹簧的断裂力学特性打下了理论基础。
总之,本文基于工程实际使用中的电磁激振器中的缓冲弹簧实例,使用标准三点弯曲试样,对弹簧材料的断裂力学结构特性进行相关的理论研究和仿真分析。从而为未来进一步的研究奠定坚实的基础。
Fracture mechanics, as we all know, are closely related to our daily life. There are a lot of the disasters due to fracture, fatigue, or fraction. Even in the modern society, failure due to fracture, fatigue and fracture is going on all the time, because the theory in this field is not well established. Doing research in this field requires solid background in Mathematics together with knowledge in Solid Mechanics and Mechanical Engineering. Nowadays, however, more and more researchers are working in this field. These researches will give the better understanding with the materials and also the structure. It will be definitely a promising field in the future.
In order to do research for the the cushion spring from the Electromagnetic Exciter, a 3 Point-Bend Specimen (3PBS) has been chosen. The analyses will be carried on this specimen with different loading conditions. Failure will occur due to fracture or fatigue in the spring. Cyclic load are chosen as candidates for analysis in this paper.
In this dissertation, the following parts will be carried on:theoretical modelling for the 3PBS, the principal of material selection, analytical analysis for Dynamic Stress Intensity Factor, FEM analysis in ABQUS and discussion with the results. The Stress Intensity Factor (SIF) for different loading cases will be compared. The life time of the specimen in our model has also been evaluated. Further, some mathematical method for finding Dynamic Stress Intensity Factor (DSIF) will be discussed in this dissertation. The research for DSIF will be continued in future.
This dissertation will provide the general idea how to do the fracture mechanics analysis in a standard way for the cushion spring from the Electromagnetic Exciter. It can form the solid basis for deeper research in future.
为了分析电磁激振器中缓冲弹簧的失效问题,本文是通过将对标准测试试件三点弯曲试样特性的研究来完成的。本文选用的载荷为周期作用力来模拟电磁激振器中作用锤对缓冲弹簧的作用。
本文将集中对如下几个方面进行研究：电磁激振器中缓冲弹簧三点弯曲试样断裂力学理论模型的建立与分析计算,恒定载荷下静态应力强度因子的计算,等效三点弯曲模型的系统方程和周期作用力下的动态应力强度因子的理论分析和计算,最后再进行基于ABAQUS的有限元仿真及分析。同时,对该三点弯曲试样的寿命也进行相应的理论分析和计算,同时也对材料的选择的一般原则进行了基本的分析。本文也讨论了关于三点弯曲试样的等效质量-阻尼-刚度系统的系统方程与理论模型,理论上获得了动态应力强度因子的解析解的一般形式。这也为将来的研究中进一步分析缓冲弹簧的断裂力学特性打下了理论基础。
总之,本文基于工程实际使用中的电磁激振器中的缓冲弹簧实例,使用标准三点弯曲试样,对弹簧材料的断裂力学结构特性进行相关的理论研究和仿真分析。从而为未来进一步的研究奠定坚实的基础。
Fracture mechanics, as we all know, are closely related to our daily life. There are a lot of the disasters due to fracture, fatigue, or fraction. Even in the modern society, failure due to fracture, fatigue and fracture is going on all the time, because the theory in this field is not well established. Doing research in this field requires solid background in Mathematics together with knowledge in Solid Mechanics and Mechanical Engineering. Nowadays, however, more and more researchers are working in this field. These researches will give the better understanding with the materials and also the structure. It will be definitely a promising field in the future.
In order to do research for the the cushion spring from the Electromagnetic Exciter, a 3 Point-Bend Specimen (3PBS) has been chosen. The analyses will be carried on this specimen with different loading conditions. Failure will occur due to fracture or fatigue in the spring. Cyclic load are chosen as candidates for analysis in this paper.
In this dissertation, the following parts will be carried on:theoretical modelling for the 3PBS, the principal of material selection, analytical analysis for Dynamic Stress Intensity Factor, FEM analysis in ABQUS and discussion with the results. The Stress Intensity Factor (SIF) for different loading cases will be compared. The life time of the specimen in our model has also been evaluated. Further, some mathematical method for finding Dynamic Stress Intensity Factor (DSIF) will be discussed in this dissertation. The research for DSIF will be continued in future.
This dissertation will provide the general idea how to do the fracture mechanics analysis in a standard way for the cushion spring from the Electromagnetic Exciter. It can form the solid basis for deeper research in future.
引文
[1]D. Brook,王克仁等译.工程断裂力学基础[M].北京：科学出版社,1980
[2]沈明荣.岩体力学[M].上海：同济大学出版社,1999
[3]王启智,汪坤.脆性材料三点弯曲试样的最大荷载及其挠度和刚度[J].四川大学学报(工程科学版).2005(37)：1-5
[4]冯秀艳,郭香华,方岱宁等.微薄梁三点弯曲的尺度效应研究[J].力学学报,2007(39)：479-485
[5]Bertram broberg. Formelsamlingi Hallfasthtslara(Swedish)[M]. Sweden:Kungliga Tekniska Hogskokan,1990
[6]刘德顺,李夕兵,朱萍玉.冲击机械动力学与反演设计[M].北京：科学出版社,2008
[7]T.L.Anderson. Fracture Mechanics, Fundamentals and Applications [M]. New York:CRC Press,1995
[8]Liu J. Researches of mechanics on electromagnetic vibration machine [J]. Proceedings of Sino-American Int Tech Trans Symposium, Shenyang,1993
[9]李建生.振式电磁振动机振动系统的计算与分析[J].贵州农学院学报,1997(02)：70-75
[10]陈海明等.共振式电磁激振器振动系统的仿真分析[J].机床与液压,2004(07)：20-22
[11]潘宁,扬书同,崔少波.电磁激振器的设计应用形式[J].山东电子,1998(01)：28-29
[12]http://en.wikipedia.org/wiki/Spring_(device)[Z],2009-03
[13]汪曾祥,魏先英,刘祥至.弹簧设计手册[M].上海：上海科学技术文献出版社,1986
[14]张英会.弹簧[M],北京：机械工业出版社,1982
[15]汪曾祥,魏先英,刘祥至.弹簧设计手册[M],上海：上海科学技术文献出版社,1986
[16]卞宗林.中国弹簧行业发展概况[J].金属制品,1995(01)：1-5
[17]钟卫洲,罗景润.冲击载荷下三点弯曲试样的有限元分析[J].环境技术,2004(01)：7-9,14
[18]王元清,武延民,石永久等.含裂纹三点弯曲试样裂纹尖端应力状态分析[J].低温建筑技术,2006(01)：37-38,59
[19]门长峰,刘爽,张道刘.基于有限元的三点弯曲试样固有频率研究[J].天津工程师范学院学报,2009(01)：44-46
[20]钟卫洲,罗景润,徐伟芳等.三点弯曲试样动态应力强度因子计算研究[J].实验力学,2005(4)：601-604
[21]姜风春,刘瑞堂,张晓欣.三点弯曲试样动应力强度因子求解的振动分析方法[J].工程力学,2002(04)：81-84
[22]李晓蔚,刘毅,郁世刚.三点弯曲试样裂纹撕裂扩展的研究[J].东北工学院学报,1989(04)：445-451
[23]P. R. Marur. An engineering approach to impact analysis of notched beam by conventional beam elements [J]. Computers & Structures,1996,59(6):1115-1120
[24]Fengchun Jiang, Aashish Rohtagi, Kenneth S, etal. Analysis of dynamic responses for a pre-cracked three point bend specimen [J]. International Journal of Fracture 127, 2004:147-165
[25]P. R. Marur. On the effect of higher vibration modes in analysis of three-point bend testing [J]. International Journal of Fracture 77,1996:367-379
[26]B. A. Crouch. Finite element modeling of three point bend impact test [J]. Computers & Structures,1993(1):167-173
[27]P.R.Marur,K.R.Y.Simha,P.S.Nair.Dynamic analysis of three-point bend specimen under impact [J]. International Journal of Fracture 68,1994:261-273
[28]R.K.Luo,W.J.Mortel, X.P.Wu. Failure fatigue investigation of anti-vibration springs [J]. Engineering Failure Analysis,2009(05):1366-1378
[29]R. K. Luo, W. X. Wu. Failure fatigue analysis of anti-vibration rubber spring [J]. Engineering Failure Analysis,2006(1):110-116
[30]http://www.mcanv.com/qaimpf.htm[Z],2009-03
[31]http://www.newmaker.com/art_5238.html[Z],2010-04
[32]http://me.seu.edu.cn/course/mechdesign/netcourse/20020101.htm[Z],2010-04
[33]Y. Yamada, Toshio Kuwabara. Materials for springs [M], Japan:Japan Society of Spring Engineers. Springer,2007
[34]http://www3.hi.is/-thorstur/teaching/cont/Continuum_CommonBeamFormulas.pdf [Z],2009-04
[35]http://courses.washington.edu/me354a/chap3.pdf[Z],2009-04,
[36]http://physics.uwstout.edu/Statstr/Strength/Beams/beam51.htm [Z],2009-04,
[37]Tore Dahlberg Anders Ekberg:Failure Fracture Fatigue, an introduction [M]. Lund: Studentlitterature,2002
[38]http://courses.washington.edu/me354a/chap3.pdf[Z],2009-04
[39]http://physics.uwstout.edu/Statstr/Strength/Beams/beam51.htm [Z],2009-04
[40]http://en.wikipedia.org/wiki/Stress_intensity_factor [Z],2009-05
[41]Bertram broberg. etc, Formelsamlingi Hallfasthtslara(Swedish) [M]. Stockholm:Kungliga Tekniska Hogskokan,1990
[42]http://www.gatewaycoalition.org/files/materials_engineering/rractdoc.html[Z],2009-05
[43]A K Bhargava. Engineering materials [M]. New Delhi:PHI Learning Pvt. Ltd,2004
[44]http://www.efunda.com/materials/alloys/alloy_steels/show_alloy.cfm?ID=AISI_4340&prop =all&Page_Title=AISI%204340 [Z],2009-05
[45]Williams,J.G. The analysis of dynamic fracture using lumped mass-spring modes [J]. International Journal of fracture 33,1987:47-59
[46]http://www.roymech.co.uk/Useful_Tables/ARM/Safety_Factors.html[Z],2009-05
[47]庄茁等,ABAQUS非线性有限元分析与实例[M].北京：科学出版社,2005
[48]何涛,杨竟,金鑫等,ANSYS 10.0/LS-DYNA非线性有限元分析实例指导教程[M].北京：机械工业出版社,2007
[49]Ibragimov, N.H. A practical course in Differential Equations and Mathematical Modelling (3rd edition) [M]. Sweden:ALGA Publications,2006
[2]沈明荣.岩体力学[M].上海：同济大学出版社,1999
[3]王启智,汪坤.脆性材料三点弯曲试样的最大荷载及其挠度和刚度[J].四川大学学报(工程科学版).2005(37)：1-5
[4]冯秀艳,郭香华,方岱宁等.微薄梁三点弯曲的尺度效应研究[J].力学学报,2007(39)：479-485
[5]Bertram broberg. Formelsamlingi Hallfasthtslara(Swedish)[M]. Sweden:Kungliga Tekniska Hogskokan,1990
[6]刘德顺,李夕兵,朱萍玉.冲击机械动力学与反演设计[M].北京：科学出版社,2008
[7]T.L.Anderson. Fracture Mechanics, Fundamentals and Applications [M]. New York:CRC Press,1995
[8]Liu J. Researches of mechanics on electromagnetic vibration machine [J]. Proceedings of Sino-American Int Tech Trans Symposium, Shenyang,1993
[9]李建生.振式电磁振动机振动系统的计算与分析[J].贵州农学院学报,1997(02)：70-75
[10]陈海明等.共振式电磁激振器振动系统的仿真分析[J].机床与液压,2004(07)：20-22
[11]潘宁,扬书同,崔少波.电磁激振器的设计应用形式[J].山东电子,1998(01)：28-29
[12]http://en.wikipedia.org/wiki/Spring_(device)[Z],2009-03
[13]汪曾祥,魏先英,刘祥至.弹簧设计手册[M].上海：上海科学技术文献出版社,1986
[14]张英会.弹簧[M],北京：机械工业出版社,1982
[15]汪曾祥,魏先英,刘祥至.弹簧设计手册[M],上海：上海科学技术文献出版社,1986
[16]卞宗林.中国弹簧行业发展概况[J].金属制品,1995(01)：1-5
[17]钟卫洲,罗景润.冲击载荷下三点弯曲试样的有限元分析[J].环境技术,2004(01)：7-9,14
[18]王元清,武延民,石永久等.含裂纹三点弯曲试样裂纹尖端应力状态分析[J].低温建筑技术,2006(01)：37-38,59
[19]门长峰,刘爽,张道刘.基于有限元的三点弯曲试样固有频率研究[J].天津工程师范学院学报,2009(01)：44-46
[20]钟卫洲,罗景润,徐伟芳等.三点弯曲试样动态应力强度因子计算研究[J].实验力学,2005(4)：601-604
[21]姜风春,刘瑞堂,张晓欣.三点弯曲试样动应力强度因子求解的振动分析方法[J].工程力学,2002(04)：81-84
[22]李晓蔚,刘毅,郁世刚.三点弯曲试样裂纹撕裂扩展的研究[J].东北工学院学报,1989(04)：445-451
[23]P. R. Marur. An engineering approach to impact analysis of notched beam by conventional beam elements [J]. Computers & Structures,1996,59(6):1115-1120
[24]Fengchun Jiang, Aashish Rohtagi, Kenneth S, etal. Analysis of dynamic responses for a pre-cracked three point bend specimen [J]. International Journal of Fracture 127, 2004:147-165
[25]P. R. Marur. On the effect of higher vibration modes in analysis of three-point bend testing [J]. International Journal of Fracture 77,1996:367-379
[26]B. A. Crouch. Finite element modeling of three point bend impact test [J]. Computers & Structures,1993(1):167-173
[27]P.R.Marur,K.R.Y.Simha,P.S.Nair.Dynamic analysis of three-point bend specimen under impact [J]. International Journal of Fracture 68,1994:261-273
[28]R.K.Luo,W.J.Mortel, X.P.Wu. Failure fatigue investigation of anti-vibration springs [J]. Engineering Failure Analysis,2009(05):1366-1378
[29]R. K. Luo, W. X. Wu. Failure fatigue analysis of anti-vibration rubber spring [J]. Engineering Failure Analysis,2006(1):110-116
[30]http://www.mcanv.com/qaimpf.htm[Z],2009-03
[31]http://www.newmaker.com/art_5238.html[Z],2010-04
[32]http://me.seu.edu.cn/course/mechdesign/netcourse/20020101.htm[Z],2010-04
[33]Y. Yamada, Toshio Kuwabara. Materials for springs [M], Japan:Japan Society of Spring Engineers. Springer,2007
[34]http://www3.hi.is/-thorstur/teaching/cont/Continuum_CommonBeamFormulas.pdf [Z],2009-04
[35]http://courses.washington.edu/me354a/chap3.pdf[Z],2009-04,
[36]http://physics.uwstout.edu/Statstr/Strength/Beams/beam51.htm [Z],2009-04,
[37]Tore Dahlberg Anders Ekberg:Failure Fracture Fatigue, an introduction [M]. Lund: Studentlitterature,2002
[38]http://courses.washington.edu/me354a/chap3.pdf[Z],2009-04
[39]http://physics.uwstout.edu/Statstr/Strength/Beams/beam51.htm [Z],2009-04
[40]http://en.wikipedia.org/wiki/Stress_intensity_factor [Z],2009-05
[41]Bertram broberg. etc, Formelsamlingi Hallfasthtslara(Swedish) [M]. Stockholm:Kungliga Tekniska Hogskokan,1990
[42]http://www.gatewaycoalition.org/files/materials_engineering/rractdoc.html[Z],2009-05
[43]A K Bhargava. Engineering materials [M]. New Delhi:PHI Learning Pvt. Ltd,2004
[44]http://www.efunda.com/materials/alloys/alloy_steels/show_alloy.cfm?ID=AISI_4340&prop =all&Page_Title=AISI%204340 [Z],2009-05
[45]Williams,J.G. The analysis of dynamic fracture using lumped mass-spring modes [J]. International Journal of fracture 33,1987:47-59
[46]http://www.roymech.co.uk/Useful_Tables/ARM/Safety_Factors.html[Z],2009-05
[47]庄茁等,ABAQUS非线性有限元分析与实例[M].北京：科学出版社,2005
[48]何涛,杨竟,金鑫等,ANSYS 10.0/LS-DYNA非线性有限元分析实例指导教程[M].北京：机械工业出版社,2007
[49]Ibragimov, N.H. A practical course in Differential Equations and Mathematical Modelling (3rd edition) [M]. Sweden:ALGA Publications,2006