基于能量耗散理论的纯铜T2的低周疲劳寿命预测
|
摘要
目前的疲劳能量耗散理论还存在诸多问题,尤其缺乏对它进行全面研究。以往限于实验手段及理论知识,研究人员只能根据各自感兴趣的问题从不同的角度开展研究,但是随着科技的发展,各种高精度仪器的相继出现,实现这种全面研究已有可能。作者在前人的基础上,对疲劳耗散过程本身和疲劳耗散能量的计算给出了个人的观点。
作者分析了纯铜疲劳过程中的能量耗散过程,发现材料形变过程中消耗的机械功以多种能量形式耗散。其中绝大部分是以热耗散的形式散失于环境中和以显微结构畸变的形式贮存于材料中。通过分析热耗散及储能的变化规律,发现热耗散的不均匀分布使材料单元间产生热传导、材料与环境间产生热交换,并在材料中形成局域温度场；储能的变化引起材料微观结构的变化,甚至表面微观形貌的变化,这是与材料的损伤状态是直接相关的。大量研究表明,温度的变化与热耗散的变化具有自相似性,且能够反映材料疲劳变化的不同过程；表面微观形貌的变化与储能的变化是一致的,它反映了材料疲劳变化的不同状态。
本文介绍了疲劳过程中机械能耗的测试方法和结果。采用高精度的红外热像仪和远距高倍显微镜同步测量了光滑纯铜试样与缺口纯铜试样在疲劳过程中的温度变化与表面微观形貌变化。实验过程中发现温度与储能(表面微观形貌)在能量的基础上存在一定的联系。试样在变形的过程中,其表面温度变化与表面微观形貌变化存在明显的相关性。
作者根据试验分析,发现循环滞回能在循环初期变化很大,随后逐渐减小趋于稳定,在疲劳破坏发生前的最后阶段又迅速衰减。并且根据热传导的傅立叶定律、对流换热微分方程及能量耗散控制方程,推导出温度与疲劳寿命之间的关系。限于时间及试验手段,作者并没有得出温度与储能的关系。为此,作者希望通过下一步的深入研究,进一步解决目前存在的问题,完善疲劳能量耗散理论。
It is found that the existing energy dissipation-based fatigue theory has many deficiencies, especially an integrated study is lacked. The former researchers only studied the energy dissipation during fatigue from their most interested subjects due to lack of experimental condition and theory, however, with the appearance of advanced experiment apparatus, it is conceivable to achieve the integrated research. On the groundwork of former, the author hopes to give the fatigue's dissipation process itself a new explanation and a new governing equation of the energy dissipation group.
With the analysis of energy dissipation process during fatigue, the author finds that the mechanical energy is dissipated in various forms of energy. The energy mainly are the heat energy dissipated in the environment and the stored energy consumed by the deformation of the microstructures, which mainly is heat energy. Through analyzing thermal dissipation and stored energy during the fatigue damage, it is found that the thermal dissipation elevates the temperature of the specimen above that of the environment; thermal conduction takes place between the material volume units and thermal exchange between the specimen and the environment,which bring on local temperature field on the specimen. The energy stored in materials during fatigue changes the energy state of the materials, and the energy state reflects the change of the surface microstructures, which is directly related to the damage state. Many studies show that the change of temperature, which can reflect the dissimilar course of the fatigue behaviors of materials during low cycle fatigue, is self-similar with the change of thermal dissipation. The change of surface micrograph, which can reflect the dissimilar state of the fatigue behavior of materials, is coincident with the change of the stored energy.
In this paper, the test method and test result of the mechanical energy dissipation during fatigue are introduced. The temperature response and the micrograph change of copper under low cycle fatigue are studied by use of infrared photography instrument and remote high power objective microscopy. The temperature has one relation on the basis of energy with the surface The results showed that there exits obvious relationships between the measured temperature and the microscopic shape. The temperature and the microscopic occur to dissimilar change with the difference of loading mode and specimen shape.
Through analyzing the fatigue date, the author found that:The cyclic hysteretic energy is very high at its earlier cycle, and gradually it rises steadily at the steady cycle, but it decreases quickly before ruptures. According to the Fourier's Law of the thermal conduction, convectional equation, the governing equation of the energy dissipation, the author derived that the equation with temperature and fatigue life. The predicted lives were found to be in good agreement with the experimental results. The determinate relation between temperature and stored energy isn't obtained due to the lack of the experiment instruments and time. Therefore, the author hopes to solve this problem and perfect the energy dissipation-based fatigue theory through farther studies.
作者分析了纯铜疲劳过程中的能量耗散过程,发现材料形变过程中消耗的机械功以多种能量形式耗散。其中绝大部分是以热耗散的形式散失于环境中和以显微结构畸变的形式贮存于材料中。通过分析热耗散及储能的变化规律,发现热耗散的不均匀分布使材料单元间产生热传导、材料与环境间产生热交换,并在材料中形成局域温度场；储能的变化引起材料微观结构的变化,甚至表面微观形貌的变化,这是与材料的损伤状态是直接相关的。大量研究表明,温度的变化与热耗散的变化具有自相似性,且能够反映材料疲劳变化的不同过程；表面微观形貌的变化与储能的变化是一致的,它反映了材料疲劳变化的不同状态。
本文介绍了疲劳过程中机械能耗的测试方法和结果。采用高精度的红外热像仪和远距高倍显微镜同步测量了光滑纯铜试样与缺口纯铜试样在疲劳过程中的温度变化与表面微观形貌变化。实验过程中发现温度与储能(表面微观形貌)在能量的基础上存在一定的联系。试样在变形的过程中,其表面温度变化与表面微观形貌变化存在明显的相关性。
作者根据试验分析,发现循环滞回能在循环初期变化很大,随后逐渐减小趋于稳定,在疲劳破坏发生前的最后阶段又迅速衰减。并且根据热传导的傅立叶定律、对流换热微分方程及能量耗散控制方程,推导出温度与疲劳寿命之间的关系。限于时间及试验手段,作者并没有得出温度与储能的关系。为此,作者希望通过下一步的深入研究,进一步解决目前存在的问题,完善疲劳能量耗散理论。
It is found that the existing energy dissipation-based fatigue theory has many deficiencies, especially an integrated study is lacked. The former researchers only studied the energy dissipation during fatigue from their most interested subjects due to lack of experimental condition and theory, however, with the appearance of advanced experiment apparatus, it is conceivable to achieve the integrated research. On the groundwork of former, the author hopes to give the fatigue's dissipation process itself a new explanation and a new governing equation of the energy dissipation group.
With the analysis of energy dissipation process during fatigue, the author finds that the mechanical energy is dissipated in various forms of energy. The energy mainly are the heat energy dissipated in the environment and the stored energy consumed by the deformation of the microstructures, which mainly is heat energy. Through analyzing thermal dissipation and stored energy during the fatigue damage, it is found that the thermal dissipation elevates the temperature of the specimen above that of the environment; thermal conduction takes place between the material volume units and thermal exchange between the specimen and the environment,which bring on local temperature field on the specimen. The energy stored in materials during fatigue changes the energy state of the materials, and the energy state reflects the change of the surface microstructures, which is directly related to the damage state. Many studies show that the change of temperature, which can reflect the dissimilar course of the fatigue behaviors of materials during low cycle fatigue, is self-similar with the change of thermal dissipation. The change of surface micrograph, which can reflect the dissimilar state of the fatigue behavior of materials, is coincident with the change of the stored energy.
In this paper, the test method and test result of the mechanical energy dissipation during fatigue are introduced. The temperature response and the micrograph change of copper under low cycle fatigue are studied by use of infrared photography instrument and remote high power objective microscopy. The temperature has one relation on the basis of energy with the surface The results showed that there exits obvious relationships between the measured temperature and the microscopic shape. The temperature and the microscopic occur to dissimilar change with the difference of loading mode and specimen shape.
Through analyzing the fatigue date, the author found that:The cyclic hysteretic energy is very high at its earlier cycle, and gradually it rises steadily at the steady cycle, but it decreases quickly before ruptures. According to the Fourier's Law of the thermal conduction, convectional equation, the governing equation of the energy dissipation, the author derived that the equation with temperature and fatigue life. The predicted lives were found to be in good agreement with the experimental results. The determinate relation between temperature and stored energy isn't obtained due to the lack of the experiment instruments and time. Therefore, the author hopes to solve this problem and perfect the energy dissipation-based fatigue theory through farther studies.
引文
1.傅祥炯等.结构疲劳与断裂[M].西安：西北工业大学出版社,1995.
2. M.A.Miner. Cumulative damage in fatigue[J]. Applied Mechanics,ASME,1945,67(12):159-164
3. S.S.Manson. Fatigue:a complex subject-some simple approximations [J]. Experimental Mechanics,1965,5(7):193-226.
4. Esin A. The microplastic strain energy criterion applied to fatigue. J Basic Engineering,1968, 90(1):28-31.
5. Esin A, Jones W J D. A theory of fatigue based on the microstructural accumulation of strain energy. Nuclear Engineering and Design,1966,6(4):292-299.
6. Zhao Tingshi. Low cycle fatigue life and plastic strain energy of medium carbon steel. Acta Metallurgica Sinica A:Physical Metallurgy &Materials Science,1993,64(4):268-271.
7. Tchankov D S, Vesselinov K V. Fatigue life prediction under random loading using total hysteresis energy. Int J Pressure Vessel Piping,1998,75(13):955-962.
8. Chang C S, Pimbley W T, Conway H D. An analysis of metal fatigue based on hysteresis energy. Experimental Mechanics,1968,8(3):133-140.
9. Martin D E. An energy criterion for low2cycle fatigue. J Basic Engineering,1961, 81(12):565-576.
10. Golos K, Ellyin F. A total strain energy density theory for cumulative fatigue damage. J Pressure Vessel Technology, ASME,1988,110(1):36-42.
11. Golos K, Ellyin F. Total strain energy density theory as a fatigue damage parameter. Advances in Fatigue Science and Technology, Proc. NATO Advanced Study Institute, Alvor, Portugal,1989.849-853.
12. TONG XiaoYan, YANGQingXiong,SUN Qin,et al. Influence of tensile mean strain on cyclic inelastic responses. Journal of Northwestern Polytechinical University,1992,10(4):441-447(In Chinese)(童小燕,杨庆雄,孙 秦,等.拉平均应变对循环非弹性响应的影响.西北工业大学学报,1992,10(4)：441-447)
13. Jhansale H R, Topper T H. Engineering analysis of the inelastic stress response of a structural metal under variable cyclic strains. Philadelphia PA:American Society for Testing and Materials(ASTM) STP 519,1971.246-272.
14. Halford G R. The energy required for fatigue. J Materials,1966,1(1):3-16
15. TUNG Xiaoyan, WAND Dejun, XU Hao. Investigation of cyclic energy in fatigue failure process. Int J Fatigue,1989,11(5):353-358.
16. TUNG Xiaoyan, WAND Dejun, Xu Hao. Cyclic hysteresis energy of carbon and alloy steels. Acta Metallurgica A,1990,3(1).123-126
17. YAO LeiJiang, TONG XiaoYan, LU ShengLi. Inelastic and thermal response during low cycle fatigue process. Journal of Northwestern Polytechinical University,2004,21(1):83-86(In Chinese)(姚磊江,童小燕,吕胜利.低周疲劳过程中的非弹性响应和热响应.西北工业大学学报,2004,21(1)：83-86)
18. Lefebvre D, Ellyin F. Cyclic response and inelastic strain energy in low cycle fatigue. Int J Fatigue,1984,6(1):9-16
19. Galietti U Morabito, Annaeva E. Energy2analysis of fatigue damage by thermographic technique. Proceedings of SPIE2The International Society for Optical Engineering, Orlando, 2002,4710:456-463.
20. YAO Leijiang, TONG Xiaoyan, YE Duyi. Energy dissipation structure during fatigue process. In:Proc 7th International Fatgiue Congress,2.Beijing,1999.741-744.
21. Zehnder A T, Babinsky E, Palmer T. Hybrid method for determining the fraction of plastic work converted to heat. Experimental Mechanics,1998,38(4):295-307
22. Hopkinson B, Williams G T. The elastic hysteresis of steel. Proc. Royal Soc Lond.1912, 87:10-17
23. Clarebrough L M, Hargreaves M E. Energy stored during fatigue of copper. J Metals, AIME, 1955,199(1):99-105
24. arry R, Joubet F, Gomaa A. Measuring the actual endurance limit of one specimen using a nondestructive method. J Engineering Material Technology, ASME,1981,103(1):71-76
25. Lanteigne J, Nguyen2Duy P. Energy balance approach to low-cycle fatigue. Int J Fracture, 1983,23(4):R147-R151
26. Blotny R, Kaleta J. A method for determining the heat energy of the fatigue process in metals under uniaxial stress:part 1. determination of the amount of heat liberated from a fatigue2tested specimen. Int J Fatigue,1986,8(1):29-34.
27. Blotny R, Kaleta J. A method for determining the heat energy of the fatigue process in metals under uniaxial stress:Part 2. Measurement of the temperature of a fatigue specimen by means of thermovision camera2computer system. Int J Fatigue,1986,8(1):35-39
28. Birol Y. What happens to the energy input during fatigue crack propagation. Material Science and Engineering,1988, A104:117-125.
29. Wong A K,Kirby C. A Hybrid numericalΠexperimental technique for determine the heat dissipated during low cycle fatigue. Engineering Fracture Mechanics,1990,37(3):493-453.
30. Kaleta J, Blotny R, Harig H. Energy stored in a specimen under fatigue limit loading conditions. J Testing & Evaluation,1990,19(4):326-333
31. TONG XiaoYan. Energetical theories on fatigue life prediction. Chinese Journal of Metal Science & Technology,1992,8(4):266-272 (InChinese)(童小燕.疲劳寿命预测的能量理论.金属科学与技术,1992,8(4)：266-272)
32. TONG Xiaoyan, YANG Qingxiong. Thermodynamic analysis of fatigue damage process, In: Proc 3rd International Conference Low Cycle Fatigue and Elatio2Plastic Behavior of Materials, Berlin,1992.321-325
33.徐京娟,邓志煜,张同俊.金属物理性能分析.上海科学技术出版社.伤害.1988
34.П.И.波卢欣著,黄克琴等译.塑性变形的物理基础.冶金工业出版社.北京.1989
35. C.S. Barrett and T.B. Massalski. Structure of Metals,3rd ed., McGraw-Hill, New York,1966
36. P.R. Gillis. Dislocation mechanisms as possible sources of acoustic emission. Materials Research and Standards,1971,11 (3):11
37. D. Fang and A. Berkovits. Acoustic emission during fatigue of a nickel base superalloy. J. Acoustic Emission,1993,11(5):85
38. D.H. Kohn and P. Ducheyne. Source of acoustic emission during fatigue of Ti-6Al-4V:effect of microstructure. J. Material Science,1992,27:1633
39. D. Fang and A. Berkovits. Evaluation of fatigued damage accumulation by acoustic emission, Fatigue Fract Engng Mater Struct,1994,17(9):1057
40. L.I. Maslov and O.M. Gradov. Fracture energy analysis via acoustic emission. Int J Fatigue, 1986,8(2):67
41. G Weatherly, J.M. Tichmarsh and C.B. Scruby. Acoustic emission monitoring of fatigue in 7010 aluminum alloys. Material Science Technology,1986,2(2):374
42. D.E.Martin.An energy criterion for low-cycle fatigue[J].Trans ASME J Basic Engng,1961,83 (12):52-60
43.周家章,张文孝.2A80铝合金材料热疲劳寿命研究[J].大连水产学院学报,2002,17(2)：141-145
44.王正,马玉华,何鑫等.16MnR轴对称三维应力状态下高温低周疲劳寿命评价[J].石油化工高等学校学报,2000,13(3)：60-64
45. Xiao L, Gu H C. Plastic energy dissipation model for lifetime prediction of zirconium and zircaloy-4 fatigued at RT and 400℃[J]. J Engng Mater Tech, ASME,1998,120(2):114-121
46. Koh S K. Fatigue damage evaluation of a high pressure tube steel using cyclic strain energy density[J]. International Journal of Pressure Vessels and Piping,2002,79(12):791-798
47. Zuo J Z, Al Th Kermanidis, Sp G Pantelakis. Strain energy density prediction of fatigue crack growth from hole of aging aircraft structures[J]. Theoretical and Applied Fracture Mechanics, 2002,38(1):37-51
48. Lee B L, Kim K S, Nam K M. Fatigue analysis under variable amplitude loading using an energy parameter [J]. International Journal of Fatigue,2003,25(7):621-631
49. Ellyin. Effect of tensile-mean-strain on plastic strain energy and cyclic response.[J], Engng Mater Tech, Trans ASME,1985,107(2):119-126
50. Ellyin F,Golos K,Xia Z. J Eng Mater Technol,1991,113(1):1-12
51.潘广和,官飞.估算低周疲劳寿命能量法的探讨[J].农业机械学报,1994,25(4)：106-111
52.陈凌,蒋家羚,范志超,低周疲劳寿命预测的能量模型探讨[J],金属学报,2006,42(2)：195-200
53. Huang Y, Lin X, Xu J. Thermography study on fatigue fracture of metals[J]. Acta Metall, 1988,24(3):207-213
54.童小燕,王德俊,徐灏.疲劳损伤过程的热耗散分析[J].金属学报,1992,28(4)：163-169
55. Yao L J, Tong X Y, Ye D Y. Numerical simulation of temperature field during fatigue process[A].21st Congress of the International Council of the Aeronautical Sciences(ICAS'98). Melbourne, Australia.1998
56. M.P.Luong, Infrared thermographic scanning of fatigue in metals[J], Neclear Engng and Design 1995(158)363-376
57. F.Cura,A new iteration method for the thermographic determination of fatigue limit in steels[J], Inter J Fatigue,2005(27):453-459
58.JA Charles,FJ Appl,JE Francis.Thermographic determination of fatigue damage[J].Transactions, Journal of Engineering Materials and Technology,1978,100(4):200-203
59. O.A. Plekhov.Theoretical analysis, infrared and structural investigations of energy dissipation in metals under cyclic loading[J], Materials Science and Engineering,2006
60. G.Meneghetti.Analysis of the fatigue strength of a stainless steel based on the energy dissipation[J]. Int J Fatigue,2007(29):81-94
61. G. R. Halford. The energy required for fatigue[J]. J Materials,1966,1(1):3-18
62.童小燕,孙秦,杨庆雄等.疲劳寿命预测能量方法的试验验证及其参数系统分析[J].西北工业大学学报,1993,11(2)：133-138
63.Lefebvre D,Neale K W, Ellyin F. J Eng Mater Techno 1.1988,103(1):1-10
64. Tchankov D S.Vesselinov K V. Int J Pressure Vessel Piping,1998,75:95-99
65. Xiao Z,Kujawski D,Ellyln F. Int J Fatigue,1996,18,33-38
66. Ellyin F,Golos K,Xia Z.J Eng Mater Technol,1991,113(1):1-12
67. Ellyin F,Xia Z. J Eng Mater Technol,1993,115(4):4-14
68. Ellyin F. Mech Res Commun,1974,1(4):21-29
69.童小燕,疲劳过程的能耗分析及其寿命估算的能量方法[D]：[博士学位论文],沈阳：东北工学院,1989
70. C.E Feltner,JD. Morrow. Microplastic strain hysteresis energy as a criterion for fatigue fracture [J].Trans ASME J Basic Engng,1961,83(12):15-22
71. Lemaitre J,Chobche J L.Mechanics of Solids Materials[D]. [PhD thesis]. Cambridge: Cambridge University,1990
72. Biot MA.Thermoelasticity and irreversible thermodynamics. [J].Appl Phys1956;27(3):240-253.
73. Rocca R, Bever MB. The thermoelastic effect in iron and nickel as a function of temperature.[J] Trans Am Inst Mech Eng 1950,188:327-353.
74. Yang B, Liaw PK, Wang H, eta. Thermographic investigation of the fatigue behavior of reactor pressure vessel steels[J]. Mater Sci Eng 2001,314:131-139.
75. Dillon OW. Coupled thermoplasticity. [J]. Mech Phys Solids 1963,11:21-23.
76. Bodner SR, Partom I, Partom Y. Uniaxial cyclic loading of elasticviscoplastic materials. J Appl Mech 1979;46:805-10.
77. Morrow J. Cyclic plastic strain energy and fatigue of metals[J].Internal friction, damping, and cyclic plasticity, ASTM,STP378,1965,45-84.
78. GR Halford, The fatigue toughness of metals:a data compilation[R], T.and A.M. Report No. 265, University of Illinois,1964.
79.贾沛泰,海一峰,国内外常用金属材料书册[M],江苏科学技术出版社,1999
80.郑兆平,曾汉生,丁翠娇,刘占增,蒋扬虎,朱小平红外热成像测温技术及其应用第25卷第1期红外技术2003年1月
81.Gla Rosa, A.Risitano, Thermographic methodology for rapid detenmnation of the fatigue limit of materials and mechanical components International journal of fatigue 22 (2000) 65-73
2. M.A.Miner. Cumulative damage in fatigue[J]. Applied Mechanics,ASME,1945,67(12):159-164
3. S.S.Manson. Fatigue:a complex subject-some simple approximations [J]. Experimental Mechanics,1965,5(7):193-226.
4. Esin A. The microplastic strain energy criterion applied to fatigue. J Basic Engineering,1968, 90(1):28-31.
5. Esin A, Jones W J D. A theory of fatigue based on the microstructural accumulation of strain energy. Nuclear Engineering and Design,1966,6(4):292-299.
6. Zhao Tingshi. Low cycle fatigue life and plastic strain energy of medium carbon steel. Acta Metallurgica Sinica A:Physical Metallurgy &Materials Science,1993,64(4):268-271.
7. Tchankov D S, Vesselinov K V. Fatigue life prediction under random loading using total hysteresis energy. Int J Pressure Vessel Piping,1998,75(13):955-962.
8. Chang C S, Pimbley W T, Conway H D. An analysis of metal fatigue based on hysteresis energy. Experimental Mechanics,1968,8(3):133-140.
9. Martin D E. An energy criterion for low2cycle fatigue. J Basic Engineering,1961, 81(12):565-576.
10. Golos K, Ellyin F. A total strain energy density theory for cumulative fatigue damage. J Pressure Vessel Technology, ASME,1988,110(1):36-42.
11. Golos K, Ellyin F. Total strain energy density theory as a fatigue damage parameter. Advances in Fatigue Science and Technology, Proc. NATO Advanced Study Institute, Alvor, Portugal,1989.849-853.
12. TONG XiaoYan, YANGQingXiong,SUN Qin,et al. Influence of tensile mean strain on cyclic inelastic responses. Journal of Northwestern Polytechinical University,1992,10(4):441-447(In Chinese)(童小燕,杨庆雄,孙 秦,等.拉平均应变对循环非弹性响应的影响.西北工业大学学报,1992,10(4)：441-447)
13. Jhansale H R, Topper T H. Engineering analysis of the inelastic stress response of a structural metal under variable cyclic strains. Philadelphia PA:American Society for Testing and Materials(ASTM) STP 519,1971.246-272.
14. Halford G R. The energy required for fatigue. J Materials,1966,1(1):3-16
15. TUNG Xiaoyan, WAND Dejun, XU Hao. Investigation of cyclic energy in fatigue failure process. Int J Fatigue,1989,11(5):353-358.
16. TUNG Xiaoyan, WAND Dejun, Xu Hao. Cyclic hysteresis energy of carbon and alloy steels. Acta Metallurgica A,1990,3(1).123-126
17. YAO LeiJiang, TONG XiaoYan, LU ShengLi. Inelastic and thermal response during low cycle fatigue process. Journal of Northwestern Polytechinical University,2004,21(1):83-86(In Chinese)(姚磊江,童小燕,吕胜利.低周疲劳过程中的非弹性响应和热响应.西北工业大学学报,2004,21(1)：83-86)
18. Lefebvre D, Ellyin F. Cyclic response and inelastic strain energy in low cycle fatigue. Int J Fatigue,1984,6(1):9-16
19. Galietti U Morabito, Annaeva E. Energy2analysis of fatigue damage by thermographic technique. Proceedings of SPIE2The International Society for Optical Engineering, Orlando, 2002,4710:456-463.
20. YAO Leijiang, TONG Xiaoyan, YE Duyi. Energy dissipation structure during fatigue process. In:Proc 7th International Fatgiue Congress,2.Beijing,1999.741-744.
21. Zehnder A T, Babinsky E, Palmer T. Hybrid method for determining the fraction of plastic work converted to heat. Experimental Mechanics,1998,38(4):295-307
22. Hopkinson B, Williams G T. The elastic hysteresis of steel. Proc. Royal Soc Lond.1912, 87:10-17
23. Clarebrough L M, Hargreaves M E. Energy stored during fatigue of copper. J Metals, AIME, 1955,199(1):99-105
24. arry R, Joubet F, Gomaa A. Measuring the actual endurance limit of one specimen using a nondestructive method. J Engineering Material Technology, ASME,1981,103(1):71-76
25. Lanteigne J, Nguyen2Duy P. Energy balance approach to low-cycle fatigue. Int J Fracture, 1983,23(4):R147-R151
26. Blotny R, Kaleta J. A method for determining the heat energy of the fatigue process in metals under uniaxial stress:part 1. determination of the amount of heat liberated from a fatigue2tested specimen. Int J Fatigue,1986,8(1):29-34.
27. Blotny R, Kaleta J. A method for determining the heat energy of the fatigue process in metals under uniaxial stress:Part 2. Measurement of the temperature of a fatigue specimen by means of thermovision camera2computer system. Int J Fatigue,1986,8(1):35-39
28. Birol Y. What happens to the energy input during fatigue crack propagation. Material Science and Engineering,1988, A104:117-125.
29. Wong A K,Kirby C. A Hybrid numericalΠexperimental technique for determine the heat dissipated during low cycle fatigue. Engineering Fracture Mechanics,1990,37(3):493-453.
30. Kaleta J, Blotny R, Harig H. Energy stored in a specimen under fatigue limit loading conditions. J Testing & Evaluation,1990,19(4):326-333
31. TONG XiaoYan. Energetical theories on fatigue life prediction. Chinese Journal of Metal Science & Technology,1992,8(4):266-272 (InChinese)(童小燕.疲劳寿命预测的能量理论.金属科学与技术,1992,8(4)：266-272)
32. TONG Xiaoyan, YANG Qingxiong. Thermodynamic analysis of fatigue damage process, In: Proc 3rd International Conference Low Cycle Fatigue and Elatio2Plastic Behavior of Materials, Berlin,1992.321-325
33.徐京娟,邓志煜,张同俊.金属物理性能分析.上海科学技术出版社.伤害.1988
34.П.И.波卢欣著,黄克琴等译.塑性变形的物理基础.冶金工业出版社.北京.1989
35. C.S. Barrett and T.B. Massalski. Structure of Metals,3rd ed., McGraw-Hill, New York,1966
36. P.R. Gillis. Dislocation mechanisms as possible sources of acoustic emission. Materials Research and Standards,1971,11 (3):11
37. D. Fang and A. Berkovits. Acoustic emission during fatigue of a nickel base superalloy. J. Acoustic Emission,1993,11(5):85
38. D.H. Kohn and P. Ducheyne. Source of acoustic emission during fatigue of Ti-6Al-4V:effect of microstructure. J. Material Science,1992,27:1633
39. D. Fang and A. Berkovits. Evaluation of fatigued damage accumulation by acoustic emission, Fatigue Fract Engng Mater Struct,1994,17(9):1057
40. L.I. Maslov and O.M. Gradov. Fracture energy analysis via acoustic emission. Int J Fatigue, 1986,8(2):67
41. G Weatherly, J.M. Tichmarsh and C.B. Scruby. Acoustic emission monitoring of fatigue in 7010 aluminum alloys. Material Science Technology,1986,2(2):374
42. D.E.Martin.An energy criterion for low-cycle fatigue[J].Trans ASME J Basic Engng,1961,83 (12):52-60
43.周家章,张文孝.2A80铝合金材料热疲劳寿命研究[J].大连水产学院学报,2002,17(2)：141-145
44.王正,马玉华,何鑫等.16MnR轴对称三维应力状态下高温低周疲劳寿命评价[J].石油化工高等学校学报,2000,13(3)：60-64
45. Xiao L, Gu H C. Plastic energy dissipation model for lifetime prediction of zirconium and zircaloy-4 fatigued at RT and 400℃[J]. J Engng Mater Tech, ASME,1998,120(2):114-121
46. Koh S K. Fatigue damage evaluation of a high pressure tube steel using cyclic strain energy density[J]. International Journal of Pressure Vessels and Piping,2002,79(12):791-798
47. Zuo J Z, Al Th Kermanidis, Sp G Pantelakis. Strain energy density prediction of fatigue crack growth from hole of aging aircraft structures[J]. Theoretical and Applied Fracture Mechanics, 2002,38(1):37-51
48. Lee B L, Kim K S, Nam K M. Fatigue analysis under variable amplitude loading using an energy parameter [J]. International Journal of Fatigue,2003,25(7):621-631
49. Ellyin. Effect of tensile-mean-strain on plastic strain energy and cyclic response.[J], Engng Mater Tech, Trans ASME,1985,107(2):119-126
50. Ellyin F,Golos K,Xia Z. J Eng Mater Technol,1991,113(1):1-12
51.潘广和,官飞.估算低周疲劳寿命能量法的探讨[J].农业机械学报,1994,25(4)：106-111
52.陈凌,蒋家羚,范志超,低周疲劳寿命预测的能量模型探讨[J],金属学报,2006,42(2)：195-200
53. Huang Y, Lin X, Xu J. Thermography study on fatigue fracture of metals[J]. Acta Metall, 1988,24(3):207-213
54.童小燕,王德俊,徐灏.疲劳损伤过程的热耗散分析[J].金属学报,1992,28(4)：163-169
55. Yao L J, Tong X Y, Ye D Y. Numerical simulation of temperature field during fatigue process[A].21st Congress of the International Council of the Aeronautical Sciences(ICAS'98). Melbourne, Australia.1998
56. M.P.Luong, Infrared thermographic scanning of fatigue in metals[J], Neclear Engng and Design 1995(158)363-376
57. F.Cura,A new iteration method for the thermographic determination of fatigue limit in steels[J], Inter J Fatigue,2005(27):453-459
58.JA Charles,FJ Appl,JE Francis.Thermographic determination of fatigue damage[J].Transactions, Journal of Engineering Materials and Technology,1978,100(4):200-203
59. O.A. Plekhov.Theoretical analysis, infrared and structural investigations of energy dissipation in metals under cyclic loading[J], Materials Science and Engineering,2006
60. G.Meneghetti.Analysis of the fatigue strength of a stainless steel based on the energy dissipation[J]. Int J Fatigue,2007(29):81-94
61. G. R. Halford. The energy required for fatigue[J]. J Materials,1966,1(1):3-18
62.童小燕,孙秦,杨庆雄等.疲劳寿命预测能量方法的试验验证及其参数系统分析[J].西北工业大学学报,1993,11(2)：133-138
63.Lefebvre D,Neale K W, Ellyin F. J Eng Mater Techno 1.1988,103(1):1-10
64. Tchankov D S.Vesselinov K V. Int J Pressure Vessel Piping,1998,75:95-99
65. Xiao Z,Kujawski D,Ellyln F. Int J Fatigue,1996,18,33-38
66. Ellyin F,Golos K,Xia Z.J Eng Mater Technol,1991,113(1):1-12
67. Ellyin F,Xia Z. J Eng Mater Technol,1993,115(4):4-14
68. Ellyin F. Mech Res Commun,1974,1(4):21-29
69.童小燕,疲劳过程的能耗分析及其寿命估算的能量方法[D]：[博士学位论文],沈阳：东北工学院,1989
70. C.E Feltner,JD. Morrow. Microplastic strain hysteresis energy as a criterion for fatigue fracture [J].Trans ASME J Basic Engng,1961,83(12):15-22
71. Lemaitre J,Chobche J L.Mechanics of Solids Materials[D]. [PhD thesis]. Cambridge: Cambridge University,1990
72. Biot MA.Thermoelasticity and irreversible thermodynamics. [J].Appl Phys1956;27(3):240-253.
73. Rocca R, Bever MB. The thermoelastic effect in iron and nickel as a function of temperature.[J] Trans Am Inst Mech Eng 1950,188:327-353.
74. Yang B, Liaw PK, Wang H, eta. Thermographic investigation of the fatigue behavior of reactor pressure vessel steels[J]. Mater Sci Eng 2001,314:131-139.
75. Dillon OW. Coupled thermoplasticity. [J]. Mech Phys Solids 1963,11:21-23.
76. Bodner SR, Partom I, Partom Y. Uniaxial cyclic loading of elasticviscoplastic materials. J Appl Mech 1979;46:805-10.
77. Morrow J. Cyclic plastic strain energy and fatigue of metals[J].Internal friction, damping, and cyclic plasticity, ASTM,STP378,1965,45-84.
78. GR Halford, The fatigue toughness of metals:a data compilation[R], T.and A.M. Report No. 265, University of Illinois,1964.
79.贾沛泰,海一峰,国内外常用金属材料书册[M],江苏科学技术出版社,1999
80.郑兆平,曾汉生,丁翠娇,刘占增,蒋扬虎,朱小平红外热成像测温技术及其应用第25卷第1期红外技术2003年1月
81.Gla Rosa, A.Risitano, Thermographic methodology for rapid detenmnation of the fatigue limit of materials and mechanical components International journal of fatigue 22 (2000) 65-73