含裂纹体构件的疲劳断裂可靠性
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摘要
对于那些长期经受交变载荷作用的机械零件和工程构件，疲劳破坏是一种主要的破坏模式。疲劳学无论从工程上还是从理论意义上都是一门重要学科。而结构的疲劳又是一个受到大量不确定因素影响的极其复杂的现象。作为断裂力学的一个新的分支，概率断裂力学从概率和统计的角度对结构进行疲劳可靠性分析，充分考虑了疲劳破坏过程中出现的不确定因素，将影响疲劳裂纹扩展速率的各参数看作是服从某一种概率分布的随机变量。这是应用于结构疲劳安全性评估中的一种科学合理的新方法。
本文主要通过对亚临界裂纹扩展阶段各种随机因素的统计分析，找到了可以推广应用的，体现两材料系数之间具有强负相关性的统计相关式，并验证了在一定条件下，材料系数是影响裂纹扩展速率的主要因素。论文的架构主要依据了下列几个基础理论：数理统计、概率论、疲劳学以及断裂力学等。论文包括以下几个部分的内容：
论文首先阐述了疲劳断裂可靠性一般理论以及应用于疲劳可靠性分析中的概率统计基础理论。介绍了概率断裂力学的理论基础，及疲劳破坏过程中裂纹扩展的一般规律，以及影响疲劳裂纹扩展的因素。
其次，论述了疲劳裂纹扩展公式中各随机参数对疲劳扩展速率的影响。将以往文献中通常看作是确定性的材料系数随机化，通过对大量数据进行数理统计的分析，将疲劳裂纹扩展速率Paris公式中材料系数c和n视为随机变量，采用最小二乘法对c和n进行数值拟合，从而得到二者的统计相关性表达式。
然后，采用Pearson x~2分布拟合检验的方法，对n进行非参数假设检验分析，判定其概率分布形式，并根据c和n之间的统计相关式，推得c的概率分布形式。进一步分析了二者对疲劳亚临界裂纹扩展寿命的影响。
最后，应用概率断裂力学方法(PFMA)，对含初始裂纹体的直升机金属材料(铝合金)构件的疲劳裂纹扩展寿命进行可靠性分析。通过算例，将疲劳裂纹扩展速率公式中的各个参量全部随机化，并预测构件在给定可靠度下的疲劳裂纹扩展寿命。
Fatigue failure is the main failure mode for the machinery parts and engineering structures under alternate loading over a long period of time. Fatigue is an important subject whether in theory or in engineering. It is the main work to predict fatigue life in fatigue damage Analysis. Usually the fracture theory are used in the fatigue crack propagation life estimation. After the Industrial Revolution in the early 19th century, the phenomenon of fatigue was taken into account and studied. A lot of research has been developed during the whole world, however, there are still many problems to be solved for researchers. Usually the fatigue life can be estimated by the determination method. However, the fatigue of structure is such a complicated phenomenon affected by many uncertainties that it is necessary to analyze the structural fatigue from the point of probability and statistics. Probabilistic Fracture Mechanics is a branch of fracture mechanics, so the various parameters affecting the fatigue propagationg a
re considered as randomized. It is an effective and new method to evaluate the structural fatigue reliability by Probabilistic Fracture Mechanics Approach (PFMA).
In this paper, through the statistical analysis of the random factors in the stage of sub-critical propagation of cracks, the statistical correlation equations between the two material coefficients are obtained and can be generalized. Furthermore, it can be concluded that cracks propagation rate is influenced greatly by material coefficients in the condition considered in this study. The paper is based on the following foundational theories: statistics, probability analysis, fatigue and fracture mechanics. The work includes several parts as the following:
Firstly, fatigue and fracture reliability theory is introduced, along with the statistics theory and its application in fatigue reliability analysis. The theory of probabilistic fracture mechanics is presented. Then the general rule and influential factors of cracks propagation occurred in fatigue failure are discussed.
Secondly, the influences of the random parameters on fatigue propagation are discussed in the fatigue propagation Paris formula. In the existing literature, the
material coefficients are simply considered as constants. Yet the material coefficients C and n in Paris formula are randomized in this study. Using the least square method, the statistical correlation between C and n is obtained through the numerical value collocation.
Then, using Pearson x2 testing method, one of the coefficients n following the rule of distribution in statistics is tested. Furthermore, according to the the statistical correlation between C and n , the influence of both C and n on propagation life of fatigue cracks is discussed.
Finally, applying Probabilistic Fracture Mechanics Approach (PFMA), the reliability analysis is carried out for helicopter metal material (aluminum alloy) structure having initial cracks. By an example, each parameters are randomized in the Paris formula, and the propagation life of fatigue of the structure is prognosticated on the presented reliability.
本文主要通过对亚临界裂纹扩展阶段各种随机因素的统计分析，找到了可以推广应用的，体现两材料系数之间具有强负相关性的统计相关式，并验证了在一定条件下，材料系数是影响裂纹扩展速率的主要因素。论文的架构主要依据了下列几个基础理论：数理统计、概率论、疲劳学以及断裂力学等。论文包括以下几个部分的内容：
论文首先阐述了疲劳断裂可靠性一般理论以及应用于疲劳可靠性分析中的概率统计基础理论。介绍了概率断裂力学的理论基础，及疲劳破坏过程中裂纹扩展的一般规律，以及影响疲劳裂纹扩展的因素。
其次，论述了疲劳裂纹扩展公式中各随机参数对疲劳扩展速率的影响。将以往文献中通常看作是确定性的材料系数随机化，通过对大量数据进行数理统计的分析，将疲劳裂纹扩展速率Paris公式中材料系数c和n视为随机变量，采用最小二乘法对c和n进行数值拟合，从而得到二者的统计相关性表达式。
然后，采用Pearson x~2分布拟合检验的方法，对n进行非参数假设检验分析，判定其概率分布形式，并根据c和n之间的统计相关式，推得c的概率分布形式。进一步分析了二者对疲劳亚临界裂纹扩展寿命的影响。
最后，应用概率断裂力学方法(PFMA)，对含初始裂纹体的直升机金属材料(铝合金)构件的疲劳裂纹扩展寿命进行可靠性分析。通过算例，将疲劳裂纹扩展速率公式中的各个参量全部随机化，并预测构件在给定可靠度下的疲劳裂纹扩展寿命。
Fatigue failure is the main failure mode for the machinery parts and engineering structures under alternate loading over a long period of time. Fatigue is an important subject whether in theory or in engineering. It is the main work to predict fatigue life in fatigue damage Analysis. Usually the fracture theory are used in the fatigue crack propagation life estimation. After the Industrial Revolution in the early 19th century, the phenomenon of fatigue was taken into account and studied. A lot of research has been developed during the whole world, however, there are still many problems to be solved for researchers. Usually the fatigue life can be estimated by the determination method. However, the fatigue of structure is such a complicated phenomenon affected by many uncertainties that it is necessary to analyze the structural fatigue from the point of probability and statistics. Probabilistic Fracture Mechanics is a branch of fracture mechanics, so the various parameters affecting the fatigue propagationg a
re considered as randomized. It is an effective and new method to evaluate the structural fatigue reliability by Probabilistic Fracture Mechanics Approach (PFMA).
In this paper, through the statistical analysis of the random factors in the stage of sub-critical propagation of cracks, the statistical correlation equations between the two material coefficients are obtained and can be generalized. Furthermore, it can be concluded that cracks propagation rate is influenced greatly by material coefficients in the condition considered in this study. The paper is based on the following foundational theories: statistics, probability analysis, fatigue and fracture mechanics. The work includes several parts as the following:
Firstly, fatigue and fracture reliability theory is introduced, along with the statistics theory and its application in fatigue reliability analysis. The theory of probabilistic fracture mechanics is presented. Then the general rule and influential factors of cracks propagation occurred in fatigue failure are discussed.
Secondly, the influences of the random parameters on fatigue propagation are discussed in the fatigue propagation Paris formula. In the existing literature, the
material coefficients are simply considered as constants. Yet the material coefficients C and n in Paris formula are randomized in this study. Using the least square method, the statistical correlation between C and n is obtained through the numerical value collocation.
Then, using Pearson x2 testing method, one of the coefficients n following the rule of distribution in statistics is tested. Furthermore, according to the the statistical correlation between C and n , the influence of both C and n on propagation life of fatigue cracks is discussed.
Finally, applying Probabilistic Fracture Mechanics Approach (PFMA), the reliability analysis is carried out for helicopter metal material (aluminum alloy) structure having initial cracks. By an example, each parameters are randomized in the Paris formula, and the propagation life of fatigue of the structure is prognosticated on the presented reliability.
引文
[1] 储佳章，王建一．学科交叉融合，寿命定量设计．中国机械工程，1998，9(11)：1～2
[2] 高镇同，蒋新桐，熊峻江等．疲劳性能试验设计和数据处理．北京：北京航空航天大学出版社，1999，187
[3] J．W．Provan著．林富甲等译．概率断裂力学与可靠性．北京：航空工业出版社，1989，337
[4] 高镇同，熊峻江．疲劳可靠性．北京：北京航空航天大学出版社，2000
[5] 高镇同．疲劳应用统计学．北京：国防工业出版社，1986
[6] Campbell, G.S., Int. J. Fatigue, Oct. 1981, 181-185
[7] 刘文埏，郑铭仲，费斌军等．概率断裂力学与概率损伤容限耐久性．北京：北京航空航天出版社，1998，237
[8] 李庆芬．断裂力学及其工程应用．哈尔滨：哈尔滨工程大学出版社，1998，226～236
[9] 林富甲．结构可靠性．西安：西北工业大学出版社，1991，133～148
[10] 复旦大学数学系．概率论与数理统计．上海：上海科学技术出版社，1961，300
[11] [英] J．F．Knott P．A．Withey．断裂力学应用实例．北京：科学出版社，1995，84～97
[12] 钟群鹏等编著．断裂失效的概率分析和评估基础．北京：北京航空航天大学出版社，2000
[13] 郑修麟．金属疲劳的定量理论．西安：西北工业大学出版社，1994，248
[14] 方国尧，张鸿涛．固体火箭发动机系统可靠性分析与设计．北京：宇航出版社，1994，266
[15] 凌树森．可靠性在机械强度设计和寿命估计中的应用．北京：宇航出版社，1988，503
[16] 孔瑞莲等．航空发动机可靠性工程．北京：航空工业出版社，1996，577
[17] [美国] N·R·曼R·E·沙费尔等．可靠性与寿命数据的统计分析方法．北京：中国电子学会电子产品可靠性与质量管理专业学会，1980，196～267
[18] 胡昌寿．航天可靠性设计手册．北京：机械工业出版社，1999，244～262
[19] 张峻华．导弹和动载火箭结构强度可靠性设计指南(金属结构部分)．北京：宇航出版社，1994，273
[20] 罗辉．揭开材料破坏之谜——断裂力学入门．北京：机械工业出版社，1989，148
[21] 吴翊，李永乐，胡庆军．应用数理统计．长沙：国防科技大学出版社，1999，442
[22] 吴学仁主编．飞机结构金属材料力学性能手册．北京：航空工业出版社，1997
[23] 高镇同．疲劳性能测试．北京：国防工业出版社，1980
[24] 丁遂栋．断裂力学．北京：机械工业出版社，1997，220(192～203)
[25] 张峻华．结构可靠性设计与分析．北京：宇航出版社，1989，314～333
[26] 方开泰，许建伦．统计分布．北京：科学出版社，1987，366
[27] Statistical Analysis of Fatigue Data, ASTM STP744,1981
[28] 周川霖．概率断裂力学在寿命估计中的应用．福州大学学报(自然科学版)，1994，22(4)：80～84
[29] 周则恭．概率断裂力学在压力容器中的应用．北京：中国石化出版社，1996
[30] [英]S．Suresh著，王中光译．材料的疲劳(第二版)．北京：国防工业出版社，1999
[31] 郑修麟．金属疲劳的定量理论．西安：西北工业大学出版社，1994
[32] 王泓．材料疲劳裂纹扩展和断裂定量规律的研究：[硕士学位论文]．西安：西北工业大学材料科学与工程学院，2002
[33] Kopnov V A , Residual Life, Linear Fatigue Damage Accumulation and Optimal Stopping, Reliability Engineering and System Safety, 1993, 40, 319～325
[34] Thoft-Christensen P, Murotsu Y, Application of Structral Systems Reliability Theory, Spinger-Verlag, Berlin, Heidelberg, NewYork, Tokyo, 1986
[35] Moses F, Ststem Reliability Development in Structral Engineering, Struct.Safety, 1982
[36] Kirkemo, F, Application of Probabilistic Fracture Mechanics to offshore structures, Appl.Mech..rev.,41(2)(1988),61～84
[37] Schijve J.Fatigue of Engineering Materials andStructure.V5, 1982
[38] Hald A. Stiatistical Theroy with Engineering Application, 1982
[39] [美]R．T．安德森编，曾纪科，杨启善等译．可靠性设计手册．北京：国防工业出版社，1981
[40] Glinka, G., Engng.Fract.Mech.,1985,22(5),839～854
[41] 中国科学院数学研究所概率统计室编．常用数理统计表．北京：科学出版社，1979
[42] 李庆芬．断裂力学及其工程应用．哈尔滨：哈尔滨工程大学出版社，1998
[43] 聂国华，翁智远，刘人怀．用概率断裂力学方法预测管状接头的疲劳寿命．应刚数学和力学，1994，(11)：963～969
[44] 高镇同，熊峻江．疲劳／断裂可靠性研究现状与展望．机械强度，1995，17(3)：61～82
[45] 熊峻江，彭俊华，高镇同．断裂韧性和断裂门槛值可靠性测定方法．北京航空航天大学学报，2002，26(6)：694～696
[46] A Guide for Fatigue Testing and. The Statistical Analysis of Fatigue Data.ASTM,STP91 A, 1964
[47] 范天佑．断裂力学基础．南京：江苏科学出版社，1985
[48] 罗毅，高镇同．疲劳寿命可靠性分析模型．机械强度，1994，16(3)：64～66
[49] 邓增杰，周敬恩．工程材料的断裂与疲劳．北京：机械工业出版社，1995
[50] J. C. Newman, Jr. A dvances in Fatigue and Fracture Mechanics Analyses for Metallic Aircraft Structures. Langley Research Center, Hanwton, Virginia, 2000
[51] 幸坤涛．在役钢结构吊车梁疲劳可靠性与安全控制研究：[博士学位论文]．大连：大连理工大学，2002
[2] 高镇同，蒋新桐，熊峻江等．疲劳性能试验设计和数据处理．北京：北京航空航天大学出版社，1999，187
[3] J．W．Provan著．林富甲等译．概率断裂力学与可靠性．北京：航空工业出版社，1989，337
[4] 高镇同，熊峻江．疲劳可靠性．北京：北京航空航天大学出版社，2000
[5] 高镇同．疲劳应用统计学．北京：国防工业出版社，1986
[6] Campbell, G.S., Int. J. Fatigue, Oct. 1981, 181-185
[7] 刘文埏，郑铭仲，费斌军等．概率断裂力学与概率损伤容限耐久性．北京：北京航空航天出版社，1998，237
[8] 李庆芬．断裂力学及其工程应用．哈尔滨：哈尔滨工程大学出版社，1998，226～236
[9] 林富甲．结构可靠性．西安：西北工业大学出版社，1991，133～148
[10] 复旦大学数学系．概率论与数理统计．上海：上海科学技术出版社，1961，300
[11] [英] J．F．Knott P．A．Withey．断裂力学应用实例．北京：科学出版社，1995，84～97
[12] 钟群鹏等编著．断裂失效的概率分析和评估基础．北京：北京航空航天大学出版社，2000
[13] 郑修麟．金属疲劳的定量理论．西安：西北工业大学出版社，1994，248
[14] 方国尧，张鸿涛．固体火箭发动机系统可靠性分析与设计．北京：宇航出版社，1994，266
[15] 凌树森．可靠性在机械强度设计和寿命估计中的应用．北京：宇航出版社，1988，503
[16] 孔瑞莲等．航空发动机可靠性工程．北京：航空工业出版社，1996，577
[17] [美国] N·R·曼R·E·沙费尔等．可靠性与寿命数据的统计分析方法．北京：中国电子学会电子产品可靠性与质量管理专业学会，1980，196～267
[18] 胡昌寿．航天可靠性设计手册．北京：机械工业出版社，1999，244～262
[19] 张峻华．导弹和动载火箭结构强度可靠性设计指南(金属结构部分)．北京：宇航出版社，1994，273
[20] 罗辉．揭开材料破坏之谜——断裂力学入门．北京：机械工业出版社，1989，148
[21] 吴翊，李永乐，胡庆军．应用数理统计．长沙：国防科技大学出版社，1999，442
[22] 吴学仁主编．飞机结构金属材料力学性能手册．北京：航空工业出版社，1997
[23] 高镇同．疲劳性能测试．北京：国防工业出版社，1980
[24] 丁遂栋．断裂力学．北京：机械工业出版社，1997，220(192～203)
[25] 张峻华．结构可靠性设计与分析．北京：宇航出版社，1989，314～333
[26] 方开泰，许建伦．统计分布．北京：科学出版社，1987，366
[27] Statistical Analysis of Fatigue Data, ASTM STP744,1981
[28] 周川霖．概率断裂力学在寿命估计中的应用．福州大学学报(自然科学版)，1994，22(4)：80～84
[29] 周则恭．概率断裂力学在压力容器中的应用．北京：中国石化出版社，1996
[30] [英]S．Suresh著，王中光译．材料的疲劳(第二版)．北京：国防工业出版社，1999
[31] 郑修麟．金属疲劳的定量理论．西安：西北工业大学出版社，1994
[32] 王泓．材料疲劳裂纹扩展和断裂定量规律的研究：[硕士学位论文]．西安：西北工业大学材料科学与工程学院，2002
[33] Kopnov V A , Residual Life, Linear Fatigue Damage Accumulation and Optimal Stopping, Reliability Engineering and System Safety, 1993, 40, 319～325
[34] Thoft-Christensen P, Murotsu Y, Application of Structral Systems Reliability Theory, Spinger-Verlag, Berlin, Heidelberg, NewYork, Tokyo, 1986
[35] Moses F, Ststem Reliability Development in Structral Engineering, Struct.Safety, 1982
[36] Kirkemo, F, Application of Probabilistic Fracture Mechanics to offshore structures, Appl.Mech..rev.,41(2)(1988),61～84
[37] Schijve J.Fatigue of Engineering Materials andStructure.V5, 1982
[38] Hald A. Stiatistical Theroy with Engineering Application, 1982
[39] [美]R．T．安德森编，曾纪科，杨启善等译．可靠性设计手册．北京：国防工业出版社，1981
[40] Glinka, G., Engng.Fract.Mech.,1985,22(5),839～854
[41] 中国科学院数学研究所概率统计室编．常用数理统计表．北京：科学出版社，1979
[42] 李庆芬．断裂力学及其工程应用．哈尔滨：哈尔滨工程大学出版社，1998
[43] 聂国华，翁智远，刘人怀．用概率断裂力学方法预测管状接头的疲劳寿命．应刚数学和力学，1994，(11)：963～969
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