运用连续损伤理论对结构损伤分析和寿命预测的研究
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摘要
金属结构的损伤分析和疲劳寿命预测是工程界研究的重要课题。金属结构的疲劳失效主要由两部分组成：疲劳裂纹形成期和裂纹扩展期。Paris方程能预测裂纹扩展期的疲劳寿命，但裂纹形成期的寿命无法用其进行计算。
本文旨在建立一个基于连续损伤力学理论的疲劳损伤分析模型，应用该模型分析金属结构的损伤，不仅能预测疲劳裂纹扩展期的寿命，还能预测裂纹形成期的寿命，解决工程中的实际问题。
理论知识和实践调研相结合，配合试验数据的研究方法。
通过实践调研，了解工程实际需要，获得基本数据；本文简要回顾了过去几十年该研究领域国内外的研究工作和成果，包括理论方面的研究和创新，以及各种试验方法和手段；扼要阐述了连续损伤力学理论的基本知识框架和理论体系。结合实验，对疲劳失效的原理进行剖析，详细论述疲劳失效的全过程，即微裂纹的萌生和增长，宏裂纹的形成和稳定扩展，最后失稳扩展导致疲劳断裂。对金属结构进行载荷分析和应力计算，分析疲劳裂纹的出现位置。
定义了一个新的损伤变量，并推导了损伤累积模型和寿命计算模型，模型表达式简洁，物理含义明确，能很好体现金属结构疲劳损伤的全过程。
简要介绍了经典的疲劳累积损伤理论和几个典型的损伤变量定义式。结合金属结构的特点，运用连续损伤力学理论，用结构的有效承载面积定义一个新的损伤变量，推导了疲劳累积损伤计算模型和疲劳寿命计算模型，在此基础上得出了疲劳累积损伤计算方程和相对应的疲劳寿命计算方程。在直角坐标系中绘制关系曲线，运用该模型分析了金属结构的损伤情况，预测疲劳寿命。
结合具体实验数据，用损伤计算方程和疲劳计算方程计算结构的损伤程度和剩余寿命，获得了满意的损伤值和疲劳寿命值。和实验数据进行比较，结果误差在允许范围内，说明文中提出的模型和计算方程是可行的，能够解决实际工程问题，实现了研究的最初设想和目的。并分析了研究成果的不足，展望了金属结构的累积损伤分析和疲劳寿命预测领域将来的发展前景。
The damage analysis and fatigue life prediction of metal structures is an important research domain in the engineering field. The fatigue failure process consists of two stages: fatigue crack initiation and crack propagation. The life of the second stage can be calculated by Paris formula, but Paris formula is no use to predict the life of the first stage.
The main purpose of this paper is to develop a fatigue and damage analysis model based on continuum damage mechanics. This model is applied to study damage evolution. Using the model the life of crack initiation can be predicted as well as the life of the crack propagation.
The following three factors are well combined with each other in this paper: theory knowledge, investigation and experiment.
Through investigation the real needs and the basic data have been mastered. In this paper, the research work and accomplishment in this domain in the past several decades has been reviewed in brief which includes research and innovation in theory and the main kinds of approaches in experiment. The basic knowledge frame and theory system of continuum damage mechanics has been introduced mainly. Combining with the experiment, the mechanism of fatigue failure has been analyzed in details and the whole process of fatigue failure has been illustrated. The loading analysis and stress calculation on the metal structures has been carried out, and the locations of fatigue cracks have been pointed out.
A new damage variable has been defined while a damage accumulation model and a fatigue life model have been developed. The whole process of fatigue damage accumulation in the metal structure has been well illuminated by the expressions of these two models.
The main classic fatigue cumulative damage theories and the representative definitions of damage variable have been introduced briefly. Considering the characteristic of the metal structure and using continuum damage mechanics, a new damage variable has been defined related to the effective loading area. Further more, a fatigue damage accumulation model and a fatigue life calculation model have been acquired and the relationship curves have been described in coordinates. The damage state and fatigue life can be confirmed instantaneously.
The experimental results have shown that a damage variable based on the effective loading area decrease can be used to measure cumulative damage and provide a good estimate of the fatigue damage process, as well as to predict the fatigue life. Thus, the original assumption and purpose are realized.
The disadvantage of this model has been illuminated and the development prospect of cumulative damage analysis and fatigue life prediction of metal structures has been suggested.
本文旨在建立一个基于连续损伤力学理论的疲劳损伤分析模型，应用该模型分析金属结构的损伤，不仅能预测疲劳裂纹扩展期的寿命，还能预测裂纹形成期的寿命，解决工程中的实际问题。
理论知识和实践调研相结合，配合试验数据的研究方法。
通过实践调研，了解工程实际需要，获得基本数据；本文简要回顾了过去几十年该研究领域国内外的研究工作和成果，包括理论方面的研究和创新，以及各种试验方法和手段；扼要阐述了连续损伤力学理论的基本知识框架和理论体系。结合实验，对疲劳失效的原理进行剖析，详细论述疲劳失效的全过程，即微裂纹的萌生和增长，宏裂纹的形成和稳定扩展，最后失稳扩展导致疲劳断裂。对金属结构进行载荷分析和应力计算，分析疲劳裂纹的出现位置。
定义了一个新的损伤变量，并推导了损伤累积模型和寿命计算模型，模型表达式简洁，物理含义明确，能很好体现金属结构疲劳损伤的全过程。
简要介绍了经典的疲劳累积损伤理论和几个典型的损伤变量定义式。结合金属结构的特点，运用连续损伤力学理论，用结构的有效承载面积定义一个新的损伤变量，推导了疲劳累积损伤计算模型和疲劳寿命计算模型，在此基础上得出了疲劳累积损伤计算方程和相对应的疲劳寿命计算方程。在直角坐标系中绘制关系曲线，运用该模型分析了金属结构的损伤情况，预测疲劳寿命。
结合具体实验数据，用损伤计算方程和疲劳计算方程计算结构的损伤程度和剩余寿命，获得了满意的损伤值和疲劳寿命值。和实验数据进行比较，结果误差在允许范围内，说明文中提出的模型和计算方程是可行的，能够解决实际工程问题，实现了研究的最初设想和目的。并分析了研究成果的不足，展望了金属结构的累积损伤分析和疲劳寿命预测领域将来的发展前景。
The damage analysis and fatigue life prediction of metal structures is an important research domain in the engineering field. The fatigue failure process consists of two stages: fatigue crack initiation and crack propagation. The life of the second stage can be calculated by Paris formula, but Paris formula is no use to predict the life of the first stage.
The main purpose of this paper is to develop a fatigue and damage analysis model based on continuum damage mechanics. This model is applied to study damage evolution. Using the model the life of crack initiation can be predicted as well as the life of the crack propagation.
The following three factors are well combined with each other in this paper: theory knowledge, investigation and experiment.
Through investigation the real needs and the basic data have been mastered. In this paper, the research work and accomplishment in this domain in the past several decades has been reviewed in brief which includes research and innovation in theory and the main kinds of approaches in experiment. The basic knowledge frame and theory system of continuum damage mechanics has been introduced mainly. Combining with the experiment, the mechanism of fatigue failure has been analyzed in details and the whole process of fatigue failure has been illustrated. The loading analysis and stress calculation on the metal structures has been carried out, and the locations of fatigue cracks have been pointed out.
A new damage variable has been defined while a damage accumulation model and a fatigue life model have been developed. The whole process of fatigue damage accumulation in the metal structure has been well illuminated by the expressions of these two models.
The main classic fatigue cumulative damage theories and the representative definitions of damage variable have been introduced briefly. Considering the characteristic of the metal structure and using continuum damage mechanics, a new damage variable has been defined related to the effective loading area. Further more, a fatigue damage accumulation model and a fatigue life calculation model have been acquired and the relationship curves have been described in coordinates. The damage state and fatigue life can be confirmed instantaneously.
The experimental results have shown that a damage variable based on the effective loading area decrease can be used to measure cumulative damage and provide a good estimate of the fatigue damage process, as well as to predict the fatigue life. Thus, the original assumption and purpose are realized.
The disadvantage of this model has been illuminated and the development prospect of cumulative damage analysis and fatigue life prediction of metal structures has been suggested.
引文
[1]李之中，卢薇．起重机钢结构疲劳试验及疲劳设计研究．山西科技，2001，4：42～43
[2]肖汉斌，陶德馨．起重机金属结构剩余寿命估算方法的研究．水利电力机械，1998，3：30～32
[3]Z.X.Li, T.H.T.Chan, J.M.Ko. Fatigue analysis and life prediction of bridges with structural health monitoring data --Part.Ⅰ: methodology and strategy. International Journal of Fatigue, 2001, (23):45～53
[4]T.H.T.Chan, Z.X.Li, J.M.Ko. Fatigue analysis and life prediction of bridges with structural health monitoring data —Part Ⅱ: application. International Journal of Fatigue, 2001, (23) :55～64
[5]高崇仁，翟甲昌，陶元芳．起重机主要构件剩余疲劳寿命的研究方法．起重运输机械，1999，5：8～9
[6]顾华，顾益民，李力．关于起重机金属结构剩余疲劳寿命的讨论．水利电力劳动保护，2000，2：37～38
[7]孙广先，冯元生．一种基于剩余强度衰减的疲劳寿命可靠性分析模型．机械强度，2000，22(2)：129～133
[8]聂宏，常龙．基于局部应力应变估算高周疲劳寿命．南京航空航天大学学报，2000，32(1)：75～79
[9]郭建生，孙国正．用断裂力学法估算焊接钢结构的疲劳寿命．起重运输机械，1999，10：9～12
[10]郭祖华，平安，王德俊．结构疲劳寿命估算的计算机仿真．东北大学学报，1998，19(3)：302～305
[11]N.BONORA, G.M.NEWAZ. Low cycle fatigue life estimation for ductile metals using a nonlinear continuum damage mechanics model. International Journal of Solids Structures, 1998, 35(16):1881～1894
[12]A.Fatemi, L.Yang. Cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials. International Journal of Fatigue, 1998, 20(1):9～34
[13]Guangxu Cheng, Alan Plumtree. A fatigue damage accumulation model based on continuum damage mechanics and ductility exhaustion. International Journal of Fatigue, 1998, 20(7):495～501
[14]Y.C.Xiao, S.Li,Z.Gao. A continuum damage mechanics model for high cycle fatigue. International Journal of Fatigue, 1998, 20(7): 503～508
[15]Baidurya Bhattacharya, Bruce Ellingwood. Continuum damage mechanics analysis of fatigue crack initiation. International Journal of Fatigue, 1998, 20(9): 631～639
[16]V.A.Kopnov. Fatigue life prediction of the metalwork of a travelling gantry crane. Engineering Failure Analysis, 1999, 6:131～141
[17]L.Franke, G.Dierkes. A non-linear fatigue damage rule with an exponent based on a crack growth boundary condition. International Journal of Fatigu, 1999, 21 : 761～767
[18]Asok Ray, Ravindra Patankar. Fatigue crack growth under variable-amplitude loading: Part Ⅰ Model formulation in state-space setting. Applied Mathematical Modelling, 2001, 25:979～994
[19]Asok Ray, Ravindra Patankar. Fatigue crack growth under variable-amplitude loading : Part Ⅱ Code development and model validation. Applied Mathematical Modelling, 2001,25:995～1013
[20]楼志文．损伤力学．西安交通大学出版社，1991，9：91～104
[21]李兆霞．损伤力学及其应用．科学出版社，2002，7：1～15，131～151，153
[22]鹿晓阳．连续损伤力学的基本理论方法及工程应用．山东建筑工程学院学报，1994，9(2)，：1～7
[23]刘达列．疲劳破坏的连续性损伤力学模型的研究．浙江大学硕士学位论文．2002．
[24]易成，沈世钊．疲劳裂纹扩展理论及其在混凝土疲劳性能研究中的应用．哈尔滨建筑大学学报，2000，33(5)：20～24
[25]王生，翟甲昌．桥式类型起重机箱形梁变幅疲劳试验研究．太原重型机械学院学报，1996，17(2)：139～144
[26]郑惠强．金属结构．同济大学出版社，1996．3：1～97
[27]王金诺，于兰峰．起重运输机金属结构．2002．5：1～60，179～233
[28]翟甲昌，王生，申增元，李忆祥．桥式起重机焊接箱形梁的疲劳试验．起重运输机械，1994，2：3～8
[29]李忆祥．起重机焊接箱形梁的疲劳试验．山西机械，2000，2：55～58
[30]程文明，王金诺．桥门式起重机疲劳裂纹扩展寿命的模拟估算．起重运输机械，2001，2：1～4
[31]沈为，彭立华．疲劳损伤演变方程与寿命估算—连续损伤力学的应用．机械强度，1994，16(2)：52～57
[32]程光旭．压力容器低周疲劳寿命的损伤力学理论研究．西安交通大学学报，1994，28(8)：59～64
[33]N.BONORA, G.M.NEWAZ. Low cycle fatigue life estimation for ductile metals using a nonlinear continuum damage mechanics model. International Journal of Solids Structures, 1998, 35 (16): 1881～1894
[34]S.DHAR, RAJU.SETHURAMANT, P.M.DIXIT.A continuum damage mechanics model for void growth and micro crack initiation. Engineering Fracture Mechanics, 1996, 53(6):917～928
[35]张安哥，谢敏．疲劳失效的连续损伤力学估算方法．华东交通大学学报，1995，12(1)：11～18
[36]A.Cipollina, A.Lopez-Inojosa, J.Florez-Lopez. A sinplefied damage mechanics approach to nonlinear analysis of frames. Computers & Struetures, 1995, 54 (6) : 1113～1126
[37]Noriyoshi Maeda, Yakayuki Watanabe, Miehiaki Yoshino, Wen wei Gu. Fundamental study on applications of damage mechanics to evaluation of material degradation. Nuclear Engineering and Design, 1996, 167: 69～76
[38]Dusan Krajcinovic. Damage mechanics: accomplishment, trends and needs. International Journal of Solids and Structures, 2000, 37: 267～277
[39]VLADYSLAV, P.GOLUB. Non-linear one-dimensional continuum damage theory. International Journal of Mechanics Science, 1996, 38(10) :1139～1150
[40]N.BONORA. A nonlinear CDM model for ductile failure. Engineering Fracture Mechanics, 1997, 58(2) : 11～28
[41]Francisco Armero, Sergio Oller. A general framework for continuum damage models. International Journal of Solids and Structures, 2000, 37:7437～7464
[42]王俊龙，朱金龙，胡凤娟．铁路龙门起重机箱形主梁疲劳寿命计算．上海铁道学院学报，1995，16(2)：65～70
[2]肖汉斌，陶德馨．起重机金属结构剩余寿命估算方法的研究．水利电力机械，1998，3：30～32
[3]Z.X.Li, T.H.T.Chan, J.M.Ko. Fatigue analysis and life prediction of bridges with structural health monitoring data --Part.Ⅰ: methodology and strategy. International Journal of Fatigue, 2001, (23):45～53
[4]T.H.T.Chan, Z.X.Li, J.M.Ko. Fatigue analysis and life prediction of bridges with structural health monitoring data —Part Ⅱ: application. International Journal of Fatigue, 2001, (23) :55～64
[5]高崇仁，翟甲昌，陶元芳．起重机主要构件剩余疲劳寿命的研究方法．起重运输机械，1999，5：8～9
[6]顾华，顾益民，李力．关于起重机金属结构剩余疲劳寿命的讨论．水利电力劳动保护，2000，2：37～38
[7]孙广先，冯元生．一种基于剩余强度衰减的疲劳寿命可靠性分析模型．机械强度，2000，22(2)：129～133
[8]聂宏，常龙．基于局部应力应变估算高周疲劳寿命．南京航空航天大学学报，2000，32(1)：75～79
[9]郭建生，孙国正．用断裂力学法估算焊接钢结构的疲劳寿命．起重运输机械，1999，10：9～12
[10]郭祖华，平安，王德俊．结构疲劳寿命估算的计算机仿真．东北大学学报，1998，19(3)：302～305
[11]N.BONORA, G.M.NEWAZ. Low cycle fatigue life estimation for ductile metals using a nonlinear continuum damage mechanics model. International Journal of Solids Structures, 1998, 35(16):1881～1894
[12]A.Fatemi, L.Yang. Cumulative fatigue damage and life prediction theories: a survey of the state of the art for homogeneous materials. International Journal of Fatigue, 1998, 20(1):9～34
[13]Guangxu Cheng, Alan Plumtree. A fatigue damage accumulation model based on continuum damage mechanics and ductility exhaustion. International Journal of Fatigue, 1998, 20(7):495～501
[14]Y.C.Xiao, S.Li,Z.Gao. A continuum damage mechanics model for high cycle fatigue. International Journal of Fatigue, 1998, 20(7): 503～508
[15]Baidurya Bhattacharya, Bruce Ellingwood. Continuum damage mechanics analysis of fatigue crack initiation. International Journal of Fatigue, 1998, 20(9): 631～639
[16]V.A.Kopnov. Fatigue life prediction of the metalwork of a travelling gantry crane. Engineering Failure Analysis, 1999, 6:131～141
[17]L.Franke, G.Dierkes. A non-linear fatigue damage rule with an exponent based on a crack growth boundary condition. International Journal of Fatigu, 1999, 21 : 761～767
[18]Asok Ray, Ravindra Patankar. Fatigue crack growth under variable-amplitude loading: Part Ⅰ Model formulation in state-space setting. Applied Mathematical Modelling, 2001, 25:979～994
[19]Asok Ray, Ravindra Patankar. Fatigue crack growth under variable-amplitude loading : Part Ⅱ Code development and model validation. Applied Mathematical Modelling, 2001,25:995～1013
[20]楼志文．损伤力学．西安交通大学出版社，1991，9：91～104
[21]李兆霞．损伤力学及其应用．科学出版社，2002，7：1～15，131～151，153
[22]鹿晓阳．连续损伤力学的基本理论方法及工程应用．山东建筑工程学院学报，1994，9(2)，：1～7
[23]刘达列．疲劳破坏的连续性损伤力学模型的研究．浙江大学硕士学位论文．2002．
[24]易成，沈世钊．疲劳裂纹扩展理论及其在混凝土疲劳性能研究中的应用．哈尔滨建筑大学学报，2000，33(5)：20～24
[25]王生，翟甲昌．桥式类型起重机箱形梁变幅疲劳试验研究．太原重型机械学院学报，1996，17(2)：139～144
[26]郑惠强．金属结构．同济大学出版社，1996．3：1～97
[27]王金诺，于兰峰．起重运输机金属结构．2002．5：1～60，179～233
[28]翟甲昌，王生，申增元，李忆祥．桥式起重机焊接箱形梁的疲劳试验．起重运输机械，1994，2：3～8
[29]李忆祥．起重机焊接箱形梁的疲劳试验．山西机械，2000，2：55～58
[30]程文明，王金诺．桥门式起重机疲劳裂纹扩展寿命的模拟估算．起重运输机械，2001，2：1～4
[31]沈为，彭立华．疲劳损伤演变方程与寿命估算—连续损伤力学的应用．机械强度，1994，16(2)：52～57
[32]程光旭．压力容器低周疲劳寿命的损伤力学理论研究．西安交通大学学报，1994，28(8)：59～64
[33]N.BONORA, G.M.NEWAZ. Low cycle fatigue life estimation for ductile metals using a nonlinear continuum damage mechanics model. International Journal of Solids Structures, 1998, 35 (16): 1881～1894
[34]S.DHAR, RAJU.SETHURAMANT, P.M.DIXIT.A continuum damage mechanics model for void growth and micro crack initiation. Engineering Fracture Mechanics, 1996, 53(6):917～928
[35]张安哥，谢敏．疲劳失效的连续损伤力学估算方法．华东交通大学学报，1995，12(1)：11～18
[36]A.Cipollina, A.Lopez-Inojosa, J.Florez-Lopez. A sinplefied damage mechanics approach to nonlinear analysis of frames. Computers & Struetures, 1995, 54 (6) : 1113～1126
[37]Noriyoshi Maeda, Yakayuki Watanabe, Miehiaki Yoshino, Wen wei Gu. Fundamental study on applications of damage mechanics to evaluation of material degradation. Nuclear Engineering and Design, 1996, 167: 69～76
[38]Dusan Krajcinovic. Damage mechanics: accomplishment, trends and needs. International Journal of Solids and Structures, 2000, 37: 267～277
[39]VLADYSLAV, P.GOLUB. Non-linear one-dimensional continuum damage theory. International Journal of Mechanics Science, 1996, 38(10) :1139～1150
[40]N.BONORA. A nonlinear CDM model for ductile failure. Engineering Fracture Mechanics, 1997, 58(2) : 11～28
[41]Francisco Armero, Sergio Oller. A general framework for continuum damage models. International Journal of Solids and Structures, 2000, 37:7437～7464
[42]王俊龙，朱金龙，胡凤娟．铁路龙门起重机箱形主梁疲劳寿命计算．上海铁道学院学报，1995，16(2)：65～70
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