涡扇发动机风扇叶片疲劳寿命评估与可靠性分析
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摘要
Ti-6Al-4V钛合金以其优异的中高温力学性能成为涡扇发动机低压转子部件的主要制造材料，位于涡扇发动机低压转子最前端的风扇叶片也是如此。大涵道比涡扇发动机的推力主要由风扇提供，复杂交变载荷作用下的疲劳断裂是风扇叶片的主要失效原因之一。本文将连续损伤累积理论和裂纹扩展理论应用于风扇叶片的疲劳研究，结合数值模拟和疲劳试验，对Ti-6Al-4V风扇叶片的损伤演化和裂纹扩展问题进行深入系统的研究，以掌握其损伤演化规律和裂纹扩展规律，研究其疲劳寿命评估和可靠性分析方法。论文主要工作如下：
(1)进行Ti-6Al-4V疲劳试验，包括拉伸试验、拉压疲劳试验、平面应变断裂韧性测试和裂纹扩展速率试验，以掌握材料力学性能、疲劳性能和裂纹扩展性能，分析损伤随加载循环的变化规律，分析应力比、裂纹闭合效应、断裂韧度对裂纹扩展速率的影响规律，为损伤演化方程和裂纹扩展速率方程的建立打下基础。
(2)考虑转矩对叶片损伤累积的影响，修正Chaboche单轴非线性损伤模型并将其推广至多轴。利用有限元方法模拟试件的S-N曲线，计算结果与试验数据吻合很好，证明所建损伤模型的准确性。利用神经网络方法拟合非线性损伤累积函数，搭建基于L-M算法的BP神经网络，样本测试结果显示该方法对损伤模型的逼近具有很好的效果。
(3)建立考虑应力比、裂纹闭合、断裂韧度和应力强度因子峰值的多参数裂纹扩展速率方程，并给出参数取值。计算试件的裂纹扩展速率和扩展寿命并与试验对比，结果显示所建多参数方程计算结果与试验吻合良好，证明模型的可用性。
(4)分析风扇叶片1000飞行小时功率谱，制订寿命评估中采用的典型工况。绘制叶片三维模型并进行网格划分，利用有限元方法计算不同工况中叶片在离心载荷、气动载荷和振动载荷作用下的应力分布，结合本文提出的寿命预测模型进行叶片设计疲劳寿命和剩余疲劳寿命的评估。
(5)建立非线性强度退化方程，并将其引入叶片的应力—强度干涉模型，计算叶片寿命周期内的可靠性，根据共因失效准则修正单个叶片的计算结果得到成组叶片的可靠度。将生存分析方法引入风扇叶片的可靠性分析中，利用Cox比例风险模型分析协变量对失效的贡献度，计算寿命周期内叶片的存活率和失效风险。
Due to the excellent mechanical property at medium-high temperature,Ti-6Al-4V titanium alloy becomes the main manufacturing material of turbofanengine low pressure (LP) rotor blade including the fan blade (FB) installed in the veryfront of the LP rotor. For high-bypass ratio turbofan engines, the fan supplies most ofthe thrust and fatigue fracture under the complex alternating loads becomes one of themain failure causes of the FBs. In this paper, based on the continuous damage theoryand crack growth theory and combined with numerical simulation and fatigue tests, ansystematic study was made on the damage evolution, crack growth, life prediction,and reliability anlysis of FB made of Ti-6Al-4V. The work can be summarized asfollows:
(1) A series of fatigue tests were conducted with Ti-6Al-4V standard specimen,including tensile test, push-pull fatigue test, plane strain fracture toughness test andcrack growth rate test, in order to obtain static mechanical properties, stress fatigueperformance and crack growth properties. And the test data was used for thefoundation and verification of the damage model and crack growth rate function. Thefatigue limits and damage variables of Ti-6Al-4V under different stress ratios weredetermined, and the effects on crack growth rate of Ti-6Al-4V of stress ratio, crackclosure effect, and fracture toughness was analyzed.
(2) A corrected nonlinear continuum damage model (CDM) of fan blade wasproposed based on the Chaboche’s uniaxial model. This correction model takes theeffect of torque brought by twisting into consideration.The S-N curve of the specimenwas simulated to verify the damage model, and the calculation results were agreedwith the experimental data. The approach that use the neural network (NN) to fit thenonlinear damage accumulation function was attempted and the back propagation (BP)NN based on L-M arithmetic is established. By determining the hidden neuronnumbers through numerous computations, the prediction results by BPNN shows agood agreement with the test data.
(3) A multi-parameter crack growth rate function considering stress ratio, crackclosure, fracture toughness, and the peak value of stress intensity factors was given,and the values of parameters in the equation were also provided. The crack growth rate and crack growth life of specimen were simulated, and the results ofmulti-parameter equation have a great agreement with the experimental data.
(4) The power spectral distribution of the blades in1000flight hours wasanalyzed, and four typical operating conditions used in the life evaluation of thisarticle were formulated. The3D model of the blade was dawned and the FE modelwas meshed. The stress distributions of the blade under centrifugal loads,aerodynamic loads, and vibration loads in different working conditions werecalculated. The designed fatigue life and remaining fatigue life of the blade areevaluated by using the life estimation model proposed above.
(5) A nonlinear strength degradation equation for Ti-6Al-4V was established andintroduced to the Stress-Strength interference model of the fan blade reliability.Moreover, common cause failure (CCF) model was used to popularize the reliabilitycalculation from single blade into a group of blade. Statistical method of survivalanalysis is also applied to the reliability analysis of fan blades, and Cox proportionalhazards model was used to analyze the contribution of covariates to the blade failure.The survival rate and failure risk of the fan blades in the life cycle were calculated.
(1)进行Ti-6Al-4V疲劳试验，包括拉伸试验、拉压疲劳试验、平面应变断裂韧性测试和裂纹扩展速率试验，以掌握材料力学性能、疲劳性能和裂纹扩展性能，分析损伤随加载循环的变化规律，分析应力比、裂纹闭合效应、断裂韧度对裂纹扩展速率的影响规律，为损伤演化方程和裂纹扩展速率方程的建立打下基础。
(2)考虑转矩对叶片损伤累积的影响，修正Chaboche单轴非线性损伤模型并将其推广至多轴。利用有限元方法模拟试件的S-N曲线，计算结果与试验数据吻合很好，证明所建损伤模型的准确性。利用神经网络方法拟合非线性损伤累积函数，搭建基于L-M算法的BP神经网络，样本测试结果显示该方法对损伤模型的逼近具有很好的效果。
(3)建立考虑应力比、裂纹闭合、断裂韧度和应力强度因子峰值的多参数裂纹扩展速率方程，并给出参数取值。计算试件的裂纹扩展速率和扩展寿命并与试验对比，结果显示所建多参数方程计算结果与试验吻合良好，证明模型的可用性。
(4)分析风扇叶片1000飞行小时功率谱，制订寿命评估中采用的典型工况。绘制叶片三维模型并进行网格划分，利用有限元方法计算不同工况中叶片在离心载荷、气动载荷和振动载荷作用下的应力分布，结合本文提出的寿命预测模型进行叶片设计疲劳寿命和剩余疲劳寿命的评估。
(5)建立非线性强度退化方程，并将其引入叶片的应力—强度干涉模型，计算叶片寿命周期内的可靠性，根据共因失效准则修正单个叶片的计算结果得到成组叶片的可靠度。将生存分析方法引入风扇叶片的可靠性分析中，利用Cox比例风险模型分析协变量对失效的贡献度，计算寿命周期内叶片的存活率和失效风险。
Due to the excellent mechanical property at medium-high temperature,Ti-6Al-4V titanium alloy becomes the main manufacturing material of turbofanengine low pressure (LP) rotor blade including the fan blade (FB) installed in the veryfront of the LP rotor. For high-bypass ratio turbofan engines, the fan supplies most ofthe thrust and fatigue fracture under the complex alternating loads becomes one of themain failure causes of the FBs. In this paper, based on the continuous damage theoryand crack growth theory and combined with numerical simulation and fatigue tests, ansystematic study was made on the damage evolution, crack growth, life prediction,and reliability anlysis of FB made of Ti-6Al-4V. The work can be summarized asfollows:
(1) A series of fatigue tests were conducted with Ti-6Al-4V standard specimen,including tensile test, push-pull fatigue test, plane strain fracture toughness test andcrack growth rate test, in order to obtain static mechanical properties, stress fatigueperformance and crack growth properties. And the test data was used for thefoundation and verification of the damage model and crack growth rate function. Thefatigue limits and damage variables of Ti-6Al-4V under different stress ratios weredetermined, and the effects on crack growth rate of Ti-6Al-4V of stress ratio, crackclosure effect, and fracture toughness was analyzed.
(2) A corrected nonlinear continuum damage model (CDM) of fan blade wasproposed based on the Chaboche’s uniaxial model. This correction model takes theeffect of torque brought by twisting into consideration.The S-N curve of the specimenwas simulated to verify the damage model, and the calculation results were agreedwith the experimental data. The approach that use the neural network (NN) to fit thenonlinear damage accumulation function was attempted and the back propagation (BP)NN based on L-M arithmetic is established. By determining the hidden neuronnumbers through numerous computations, the prediction results by BPNN shows agood agreement with the test data.
(3) A multi-parameter crack growth rate function considering stress ratio, crackclosure, fracture toughness, and the peak value of stress intensity factors was given,and the values of parameters in the equation were also provided. The crack growth rate and crack growth life of specimen were simulated, and the results ofmulti-parameter equation have a great agreement with the experimental data.
(4) The power spectral distribution of the blades in1000flight hours wasanalyzed, and four typical operating conditions used in the life evaluation of thisarticle were formulated. The3D model of the blade was dawned and the FE modelwas meshed. The stress distributions of the blade under centrifugal loads,aerodynamic loads, and vibration loads in different working conditions werecalculated. The designed fatigue life and remaining fatigue life of the blade areevaluated by using the life estimation model proposed above.
(5) A nonlinear strength degradation equation for Ti-6Al-4V was established andintroduced to the Stress-Strength interference model of the fan blade reliability.Moreover, common cause failure (CCF) model was used to popularize the reliabilitycalculation from single blade into a group of blade. Statistical method of survivalanalysis is also applied to the reliability analysis of fan blades, and Cox proportionalhazards model was used to analyze the contribution of covariates to the blade failure.The survival rate and failure risk of the fan blades in the life cycle were calculated.
引文
[1] L Kachanov, Time of the rupture process under creep conditions. Isv. Akad.Nauk. SSR. Otd Tekh. Nauk,1958,8:26-31.
[2] Y N Rabotnov, Paper68: On the Equation of State of Creep, in Proceedings ofthe Institution of Mechanical Engineers, Conference Proceedings,1963: SAGEPublications.
[3] J Janson, J Hult, Fracture mechanics and damage mechanics-A combinedapproach, in (International Congress of Theoretical and Applied Mechanics,14th, Delft, Netherlands, Aug.30-Sept.4,1976.) Journal de Mecanique Appliquee,1977.
[4]余寿文,冯西桥,损伤力学,北京:清华大学出版社1997.
[5]何晋瑞,金属高温疲劳,北京:科学出版社1988.
[6] S Marco, W Starkey, A concept of fatigue damage. Trans. ASME,1954,76(4):627-632.
[7] J-L Chaboche, Continuous damage mechanics—a tool to describe phenomenabefore crack initiation. Nuclear Engineering and Design,1981,64(2):233-247.
[8] J Lemaitre, J Chaboche, A non-linear model of creep-fatigue damagecumulation and interaction. ONERA, TP no.1394,1974.8p,1974.
[9] J Lemaitre, J-L Chaboche, Mechanics of solid materials: Cambridge universitypress1994.
[10] J Chaboche, P Lesne, A NON‐LINEAR CONTINUOUS FATIGUEDAMAGE MODEL. Fatigue&fracture of engineering materials&structures,1988,11(1):1-17.
[11] D-G Shang, W-X Yao, A nonlinear damage cumulative model for uniaxialfatigue. International journal of fatigue,1999,21(2):187-194.
[12] J Lin, J Zhang, G Zhang, Aero-engine blade fatigue analysis based on nonlinearcontinuum damage model using neural networks. Chinese Journal ofMechanical Engineering,2012,25(2):338-345.
[13] G Cheng, A Plumtree, A fatigue damage accumulation model based oncontinuum damage mechanics and ductility exhaustion. International journal offatigue,1998,20(7):495-501.
[14] V Dattoma, S Giancane, R Nobile, Fatigue life prediction under variableloading based on a new non-linear continuum damage mechanics model.International journal of fatigue,2006,28(2):89-95.
[15] A Carpinteri, A Spagnoli, Multiaxial high-cycle fatigue criterion for hard metals.International journal of fatigue,2001,23(2):135-145.
[16] J Park, D Nelson, Evaluation of an energy-based approach and a critical planeapproach for predicting constant amplitude multiaxial fatigue life. Internationaljournal of fatigue,2000,22(1):23-39.
[17] P Lazzarin, L Susmel, A stress‐based method to predict lifetime undermultiaxial fatigue loadings. Fatigue&fracture of engineering materials&structures,2003,26(12):1171-1187.
[18] A Fatemi, D F Socie, A Critical Plane Approach to Multiaxial Fatigue DamageIncluding Out‐Of‐Phase Loading. Fatigue&fracture of engineeringmaterials&structures,1988,11(3):149-165.
[19] J Lemaitre, Coupled elasto-plasticity and damage constitutive equations.Computer Methods in Applied Mechanics and Engineering,1985,51(1):31-49.
[20] S De-Guang, W De-Jun, A new multiaxial fatigue damage model based on thecritical plane approach. International journal of fatigue,1998,20(3):241-245.
[21] M Brown, K Miller, A theory for fatigue failure under multiaxial stress-strainconditions. Proceedings of the Institution of Mechanical engineers,1973,187(1):745-755.
[22] A Kermanpur, H Sepehri Amin, S Ziaei-Rad, Failure analysis of Ti6Al4V gasturbine compressor blades. Engineering Failure Analysis,2008,15(8):1052-1064.
[23] S Oakley, D Nowell, Prediction of the combined high-and low-cycle fatigueperformance of gas turbine blades after foreign object damage. Internationaljournal of fatigue,2007,29(1):69-80.
[24]申秀丽,齐晓东,王荣桥,航空发动机涡轮榫接结构齿形基本参数研究.航空动力学报,2011,26(4):735-744.
[25]关玉璞,陈伟,高德平,航空发动机叶片外物损伤研究现状.航空学报,2007,28(4):851-857.
[26]岳珠峰,李立州,虞跨海,航空发动机涡轮叶片多学科设计优化,北京:科学出版社2007.
[27]林杰威,张俊红,张桂昌,基于连续非线性损伤的航空发动机叶片疲劳研究.机械工程学报,2010,46(18):66-70.
[28]陈立杰,谢里阳,某低压涡轮工作叶片高温低循环疲劳寿命预测.东北大学学报,2005,46(24):673-676.
[29] R Pelloux, Case studies of fatigue failures in aeronautical structures, inProceedings of Conference Fatigue,1993.
[30] C Inglis, Stresses in a plate due to the presence of cracks and sharp corners.Trans. Inst. Nav. Arch,1913,55(1):219-239.
[31] A A Griffith, The phenomena of rupture and flow in solids. Philosophicaltransactions of the royal society of london. Series A, containing papers of amathematical or physical character,1921,221:163-198.
[32] E Orowan, The fatigue of glass under stress. Nature,1944,154(3906):341-343.
[33] G R Irwin, Analysis of stresses and strains near the end of a crack traversing aplate. J. Appl. Mech.,1957.
[34] P C Paris, M P Gomez, W E Anderson, A rational analytic theory of fatigue.The trend in engineering,1961,13(1):9-14.
[35] K Walker, The effect of stress ratio during crack propagation and fatigue for2024-T3and7075-T6aluminum. Effects of environment and complex loadhistory on fatigue life, ASTM STP,1970,462:1-14.
[36] R G Forman, V Kearney, R Engle, Numerical analysis of crack propagation incyclic-loaded structures. Journal of basic Engineering,1967,89:459.
[37] A Hartman, J Schijve, The effects of environment and load frequency on thecrack propagation law for macro fatigue crack growth in aluminium alloys.Engineering Fracture Mechanics,1970,1(4):615-631.
[38] J Schijve, Observations on the prediction of fatigue crack growth propagationunder variable-amplitude loading. Fatigue Crack Growth Under SpectrumLoads, ASTM STP,1976,595:3-23.
[39] B Boyce, R Ritchie, Effect of load ratio and maximum stress intensity on thefatigue threshold in Ti–6Al–4V. Engineering Fracture Mechanics,2001,68(2):129-147.
[40] S Dubey, A Soboyejo, W Soboyejo, An investigation of the effects of stressratio and crack closure on the micromechanisms of fatigue crack growth inTi-6Al-4V. Acta Materialia,1997,45(7):2777-2787.
[41] C-S Oh, J-H Song, Crack growth and closure behaviour of surface cracks underpure bending loading. International journal of fatigue,2001,23(3):251-258.
[42] V Sinha, C Mercer, W Soboyejo, An investigation of short and long fatiguecrack growth behavior of Ti–6Al–4V. Materials Science and Engineering: A,2000,287(1):30-42.
[43] S Shademan, A Soboyejo, J Knott, A physically-based model for the predictionof long fatigue crack growth in Ti–6Al–4V. Materials Science and Engineering:A,2001,315(1):1-10.
[44] K Sadananda, A Vasudevan, Crack tip driving forces and crack growthrepresentation under fatigue. International journal of fatigue,2004,26(1):39-47.
[45] M Croft, Z Zhong, N Jisrawi, Strain profiling of fatigue crack overload effectsusing energy dispersive X-ray diffraction. International journal of fatigue,2005,27(10):1408-1419.
[46] A Vasudevan, K Sadananda, G Glinka, Critical parameters for fatigue damage.International journal of fatigue,2001,23:39-53.
[47] J Ding, R Hall, J Byrne, Effects of stress ratio and temperature on fatigue crackgrowth in a Ti–6Al–4V alloy. International journal of fatigue,2005,27(10):1551-1558.
[48] Y Yamashita, Y Ueda, H Kuroki, Fatigue life prediction of small notched Ti–6Al–4V specimens using critical distance. Engineering Fracture Mechanics,2010,77(9):1439-1453.
[49] B Joadder, J Shit, S Acharyya, Fatigue Failure of Notched Specimen—AStrain-Life Approach. Materials Sciences and Applications,2011,2.
[50] W Shen, A Soboyejo, W Soboyejo, Probabilistic modeling of fatigue crackgrowth in Ti–6Al–4V. International journal of fatigue,2001,23(10):917-925.
[51] M Hohenbichler, R Rackwitz, First-order concepts in system reliability.Structural safety,1983,1(3):177-188.
[52] Y Xiang, Y Liu, Application of inverse first-order reliability method forprobabilistic fatigue life prediction. Probabilistic Engineering Mechanics,2011,26(2):148-156.
[53] A Der Kiureghian, H-Z Lin, S-J Hwang, Second-order reliabilityapproximations. Journal of Engineering Mechanics,1987,113(8):1208-1225.
[54] H P Gavin, S C Yau, High-order limit state functions in the response surfacemethod for structural reliability analysis. Structural safety,2008,30(2):162-179.
[55] A I Khuri, S Mukhopadhyay, Response surface methodology. WileyInterdisciplinary Reviews: Computational Statistics,2010,2(2):128-149.
[56] C Bucher, U Bourgund, A fast and efficient response surface approach forstructural reliability problems. Structural safety,1990,7(1):57-66.
[57] R H Myers, A I Khuri, W H Carter, Response Surface Methodology:1966–l988.Technometrics,1989,31(2):137-157.
[58] G Stefanou, The stochastic finite element method: past, present and future.Computer Methods in Applied Mechanics and Engineering,2009,198(9):1031-1051.
[59] E Rosseel, S Vandewalle, Iterative solvers for the stochastic finite elementmethod. SIAM Journal on Scientific Computing,2010,32(1):372-397.
[60] A Barth, C Schwab, N Zollinger, Multi-level Monte Carlo finite elementmethod for elliptic PDEs with stochastic coefficients. Numerische Mathematik,2011,119(1):123-161.
[61] R Y Rubinstein, D P Kroese, Simulation and the Monte Carlo method, Vol.707:Wiley-interscience2011.
[62] I B Gertsbakh, Y Shpungin, Models of network reliability: analysis,combinatorics, and Monte Carlo: CRC Press2011.
[63] A M Hasofer, N C Lind, Exact and invariant second-moment code format.Journal of the Engineering Mechanics Division,1974,100(1):111-121.
[64] A Der Kiureghian, P-L Liu, Structural reliability under incomplete probabilityinformation. Journal of Engineering Mechanics,1986,112(1):85-104.
[65] R G Ghanem, P D Spanos, Stochastic finite elements: a spectral approach:Courier Dover Publications2003.
[66] G I Schu ller, C G Bucher, U Bourgund, On efficient computational schemes tocalculate structural failure probabilities. Probabilistic Engineering Mechanics,1989,4(1):10-18.
[67] D W Hosmer Jr, S Lemeshow, S May, Applied survival analysis: regressionmodeling of time to event data, Vol.618: Wiley-Interscience2011.
[68] K Helsen, D C Schmittlein, Analyzing duration times in marketing: Evidencefor the effectiveness of hazard rate models. Marketing Science,1993,12(4):395-414.
[69] R G Miller Jr, Survival analysis: Wiley-Interscience2011.
[70] J Zhang, J Lin, G Zhang, High cycle fatigue life prediction and reliabilityanalysis of aeroengine blades. Transactions of Tianjin University,2012,18(6):456.
[71] N Sadou, H Demmou, Reliability analysis of discrete event dynamic systemswith Petri nets. Reliability Engineering&System Safety,2009,94(11):1848-1861.
[72] Y A Katsigiannis, P S Georgilakis, G J Tsinarakis, A novel colored fluidstochastic Petri net simulation model for reliability evaluation of wind/PV/dieselsmall isolated power systems. Systems, Man and Cybernetics, Part A: Systemsand Humans, IEEE Transactions on,2010,40(6):1296-1309.
[73] F Chen, X Yu, Method for Constructing Operation Reliability Model ofHigh-Speed Railway System Based on Petri Net, in Third InternationalConference on Transportation Engineering (ICTE),2011.
[74] V Kumar, N Gupta, A Petri Net Model For Deciding Availability of MostReliable Cost Effective Fragment Access Path in Distributed Database Systems.International Journal of Information and Telecommunication Technology (ISSN:0976-5972),2010,2(1).
[75] H M Gomes, A M Awruch, Comparison of response surface and neural networkwith other methods for structural reliability analysis. Structural safety,2004,26(1):49-67.
[76] J Deng, D Gu, X Li, Structural reliability analysis for implicit performancefunctions using artificial neural network. Structural safety,2005,27(1):25-48.
[77] S Chatterjee, J Singh, S Nigam, A Study of a Single Multiplicative Neuron(SMN) Model for Software Reliability Prediction, in Innovations in IntelligentMachines-3.2013, Springer.89-102.
[78] H Martz, R Wailer, Bayesian reliability analysis of complex series/parallelsystems of binomial subsystems and components. Technometrics,1990,32(4):407-416.
[79] P Weber, L Jouffe, Complex system reliability modelling with dynamic objectoriented bayesian networks (DOOBN). Reliability Engineering&SystemSafety,2006,91(2):149-162.
[80] D Straub, A Der Kiureghian, Bayesian network enhanced with structuralreliability methods: methodology. Journal of Engineering Mechanics,2010,136(10):1248-1258.
[81] S Kotz, M Pensky, The stress-strength model and its generalizations: theory andapplications: Imperial College Press2003.
[82] S Ery lmaz, A new perspective to stress–strength models. Annals of the Instituteof Statistical Mathematics,2011,63(1):101-115.
[83] W K Chung, Some stress-strength reliability models. MicroelectronicsReliability,1982,22(2):277-280.
[84] A Freudenthal, E Gumbel, Physical and statistical aspects of fatigue. Advancesin applied mechanics,1956,4(1):116-156.
[85] K C Kapur, L R Lamberson, Reliability in engineering design. New York, JohnWiley and Sons, Inc.,1977.605p.,1977,1.
[86] W Bao, H Han, Z Huang, Numerical simulations of fracture problems bycoupling the FEM and the direct method of lines. Computer Methods in AppliedMechanics and Engineering,2001,190(37):4831-4846.
[87] H Han, The artificial boundary method-numerical solutions of partialdifferential equations on unbounded domains. Frontiers and Prospects ofContemporary Applied Mathematics,2005,6:33-58.
[88] H-Z Huang, Z-W An, A discrete stress-strength interference model with stressdependent strength. Reliability, IEEE Transactions on,2009,58(1):118-122.
[89] J Lemaitre, Evaluation of dissipation and damage in metals submitted todynamic loading. Mechanical behavior of materials,1972:540-549.
[90]中国质量技术监督局, GB/T228-2002,金属材料室温拉伸试验方法,北京:中国标准出版社,2002.
[91]中国质量技术监督局, GB/T2975-1998,钢及钢产品力学性能试验取样位置及试样制备[S],北京:中国标准出版社,1998.
[92]中国质量技术监督局, GB/T3075-2008,金属材料疲劳试验轴向力控制方法,北京:中国标准出版社,2008.
[93]尚德广,姚卫星,单轴非线性连续疲劳损伤累积模型的研究.航空学报,1998,19(6):647-656.
[94]中国质量技术监督局, GB/T4161-2007,金属材料平面应变断裂韧度KIC试验方法[S],北京:中国标准出版社,2007.
[95]中国质量技术监督局, GB/T6398-2000,金属材料疲劳裂纹扩展速率试验方法,北京:中国标准出版社,2000.
[96]顾永维,安伟光,安海,静载和疲劳载荷共同作用下的结构可靠性分析.兵工学报,2007(12):1473-1477.
[97] J L McClelland, D E Rumelhart, P R Group, Parallel distributed processing.Explorations in the microstructure of cognition,1986,2.
[98] J J Moré, The Levenberg-Marquardt algorithm: implementation and theory, inNumerical analysis.1978, Springer.105-116.
[99] K Sadananda, A Vasudevan, I Kang, Effect of superimposed monotonic fracturemodes on the ΔK and Kmaxparameters of fatigue crack propagation. ActaMaterialia,2003,51(12):3399-3414.
[100]曾庆会,模态试验中跑点测量时传感器附加质量影响的消除.南京航空航天大学学报,1994,26(5):692-695.
[101]岳珠峰,镍基单晶涡轮叶片结构强度设计,北京:科学出版社2008.
[102] K S Chana, U K Singh, T Povey, Turbine Heat Transfer and AerodynamicMeasurements and Predictions for a1.5Stage Configuration,2004: ASME.
[103]高鹏,谢里阳,考虑强度退化的零件及系统可靠性分析.机械工程学报,2010,46(24):162-167.
[104] B I Sandor, Fundamentals of cyclic stress and strain: Univ of Wisconsin Pr1972.
[105] Z WANG, L-y XIE, J-y ZHANG, Reliability Model of System with CommonCause Failure Under Repeated Random Load. Acta Aeronautica et AstronauticaSinica,2007: S1.
[2] Y N Rabotnov, Paper68: On the Equation of State of Creep, in Proceedings ofthe Institution of Mechanical Engineers, Conference Proceedings,1963: SAGEPublications.
[3] J Janson, J Hult, Fracture mechanics and damage mechanics-A combinedapproach, in (International Congress of Theoretical and Applied Mechanics,14th, Delft, Netherlands, Aug.30-Sept.4,1976.) Journal de Mecanique Appliquee,1977.
[4]余寿文,冯西桥,损伤力学,北京:清华大学出版社1997.
[5]何晋瑞,金属高温疲劳,北京:科学出版社1988.
[6] S Marco, W Starkey, A concept of fatigue damage. Trans. ASME,1954,76(4):627-632.
[7] J-L Chaboche, Continuous damage mechanics—a tool to describe phenomenabefore crack initiation. Nuclear Engineering and Design,1981,64(2):233-247.
[8] J Lemaitre, J Chaboche, A non-linear model of creep-fatigue damagecumulation and interaction. ONERA, TP no.1394,1974.8p,1974.
[9] J Lemaitre, J-L Chaboche, Mechanics of solid materials: Cambridge universitypress1994.
[10] J Chaboche, P Lesne, A NON‐LINEAR CONTINUOUS FATIGUEDAMAGE MODEL. Fatigue&fracture of engineering materials&structures,1988,11(1):1-17.
[11] D-G Shang, W-X Yao, A nonlinear damage cumulative model for uniaxialfatigue. International journal of fatigue,1999,21(2):187-194.
[12] J Lin, J Zhang, G Zhang, Aero-engine blade fatigue analysis based on nonlinearcontinuum damage model using neural networks. Chinese Journal ofMechanical Engineering,2012,25(2):338-345.
[13] G Cheng, A Plumtree, A fatigue damage accumulation model based oncontinuum damage mechanics and ductility exhaustion. International journal offatigue,1998,20(7):495-501.
[14] V Dattoma, S Giancane, R Nobile, Fatigue life prediction under variableloading based on a new non-linear continuum damage mechanics model.International journal of fatigue,2006,28(2):89-95.
[15] A Carpinteri, A Spagnoli, Multiaxial high-cycle fatigue criterion for hard metals.International journal of fatigue,2001,23(2):135-145.
[16] J Park, D Nelson, Evaluation of an energy-based approach and a critical planeapproach for predicting constant amplitude multiaxial fatigue life. Internationaljournal of fatigue,2000,22(1):23-39.
[17] P Lazzarin, L Susmel, A stress‐based method to predict lifetime undermultiaxial fatigue loadings. Fatigue&fracture of engineering materials&structures,2003,26(12):1171-1187.
[18] A Fatemi, D F Socie, A Critical Plane Approach to Multiaxial Fatigue DamageIncluding Out‐Of‐Phase Loading. Fatigue&fracture of engineeringmaterials&structures,1988,11(3):149-165.
[19] J Lemaitre, Coupled elasto-plasticity and damage constitutive equations.Computer Methods in Applied Mechanics and Engineering,1985,51(1):31-49.
[20] S De-Guang, W De-Jun, A new multiaxial fatigue damage model based on thecritical plane approach. International journal of fatigue,1998,20(3):241-245.
[21] M Brown, K Miller, A theory for fatigue failure under multiaxial stress-strainconditions. Proceedings of the Institution of Mechanical engineers,1973,187(1):745-755.
[22] A Kermanpur, H Sepehri Amin, S Ziaei-Rad, Failure analysis of Ti6Al4V gasturbine compressor blades. Engineering Failure Analysis,2008,15(8):1052-1064.
[23] S Oakley, D Nowell, Prediction of the combined high-and low-cycle fatigueperformance of gas turbine blades after foreign object damage. Internationaljournal of fatigue,2007,29(1):69-80.
[24]申秀丽,齐晓东,王荣桥,航空发动机涡轮榫接结构齿形基本参数研究.航空动力学报,2011,26(4):735-744.
[25]关玉璞,陈伟,高德平,航空发动机叶片外物损伤研究现状.航空学报,2007,28(4):851-857.
[26]岳珠峰,李立州,虞跨海,航空发动机涡轮叶片多学科设计优化,北京:科学出版社2007.
[27]林杰威,张俊红,张桂昌,基于连续非线性损伤的航空发动机叶片疲劳研究.机械工程学报,2010,46(18):66-70.
[28]陈立杰,谢里阳,某低压涡轮工作叶片高温低循环疲劳寿命预测.东北大学学报,2005,46(24):673-676.
[29] R Pelloux, Case studies of fatigue failures in aeronautical structures, inProceedings of Conference Fatigue,1993.
[30] C Inglis, Stresses in a plate due to the presence of cracks and sharp corners.Trans. Inst. Nav. Arch,1913,55(1):219-239.
[31] A A Griffith, The phenomena of rupture and flow in solids. Philosophicaltransactions of the royal society of london. Series A, containing papers of amathematical or physical character,1921,221:163-198.
[32] E Orowan, The fatigue of glass under stress. Nature,1944,154(3906):341-343.
[33] G R Irwin, Analysis of stresses and strains near the end of a crack traversing aplate. J. Appl. Mech.,1957.
[34] P C Paris, M P Gomez, W E Anderson, A rational analytic theory of fatigue.The trend in engineering,1961,13(1):9-14.
[35] K Walker, The effect of stress ratio during crack propagation and fatigue for2024-T3and7075-T6aluminum. Effects of environment and complex loadhistory on fatigue life, ASTM STP,1970,462:1-14.
[36] R G Forman, V Kearney, R Engle, Numerical analysis of crack propagation incyclic-loaded structures. Journal of basic Engineering,1967,89:459.
[37] A Hartman, J Schijve, The effects of environment and load frequency on thecrack propagation law for macro fatigue crack growth in aluminium alloys.Engineering Fracture Mechanics,1970,1(4):615-631.
[38] J Schijve, Observations on the prediction of fatigue crack growth propagationunder variable-amplitude loading. Fatigue Crack Growth Under SpectrumLoads, ASTM STP,1976,595:3-23.
[39] B Boyce, R Ritchie, Effect of load ratio and maximum stress intensity on thefatigue threshold in Ti–6Al–4V. Engineering Fracture Mechanics,2001,68(2):129-147.
[40] S Dubey, A Soboyejo, W Soboyejo, An investigation of the effects of stressratio and crack closure on the micromechanisms of fatigue crack growth inTi-6Al-4V. Acta Materialia,1997,45(7):2777-2787.
[41] C-S Oh, J-H Song, Crack growth and closure behaviour of surface cracks underpure bending loading. International journal of fatigue,2001,23(3):251-258.
[42] V Sinha, C Mercer, W Soboyejo, An investigation of short and long fatiguecrack growth behavior of Ti–6Al–4V. Materials Science and Engineering: A,2000,287(1):30-42.
[43] S Shademan, A Soboyejo, J Knott, A physically-based model for the predictionof long fatigue crack growth in Ti–6Al–4V. Materials Science and Engineering:A,2001,315(1):1-10.
[44] K Sadananda, A Vasudevan, Crack tip driving forces and crack growthrepresentation under fatigue. International journal of fatigue,2004,26(1):39-47.
[45] M Croft, Z Zhong, N Jisrawi, Strain profiling of fatigue crack overload effectsusing energy dispersive X-ray diffraction. International journal of fatigue,2005,27(10):1408-1419.
[46] A Vasudevan, K Sadananda, G Glinka, Critical parameters for fatigue damage.International journal of fatigue,2001,23:39-53.
[47] J Ding, R Hall, J Byrne, Effects of stress ratio and temperature on fatigue crackgrowth in a Ti–6Al–4V alloy. International journal of fatigue,2005,27(10):1551-1558.
[48] Y Yamashita, Y Ueda, H Kuroki, Fatigue life prediction of small notched Ti–6Al–4V specimens using critical distance. Engineering Fracture Mechanics,2010,77(9):1439-1453.
[49] B Joadder, J Shit, S Acharyya, Fatigue Failure of Notched Specimen—AStrain-Life Approach. Materials Sciences and Applications,2011,2.
[50] W Shen, A Soboyejo, W Soboyejo, Probabilistic modeling of fatigue crackgrowth in Ti–6Al–4V. International journal of fatigue,2001,23(10):917-925.
[51] M Hohenbichler, R Rackwitz, First-order concepts in system reliability.Structural safety,1983,1(3):177-188.
[52] Y Xiang, Y Liu, Application of inverse first-order reliability method forprobabilistic fatigue life prediction. Probabilistic Engineering Mechanics,2011,26(2):148-156.
[53] A Der Kiureghian, H-Z Lin, S-J Hwang, Second-order reliabilityapproximations. Journal of Engineering Mechanics,1987,113(8):1208-1225.
[54] H P Gavin, S C Yau, High-order limit state functions in the response surfacemethod for structural reliability analysis. Structural safety,2008,30(2):162-179.
[55] A I Khuri, S Mukhopadhyay, Response surface methodology. WileyInterdisciplinary Reviews: Computational Statistics,2010,2(2):128-149.
[56] C Bucher, U Bourgund, A fast and efficient response surface approach forstructural reliability problems. Structural safety,1990,7(1):57-66.
[57] R H Myers, A I Khuri, W H Carter, Response Surface Methodology:1966–l988.Technometrics,1989,31(2):137-157.
[58] G Stefanou, The stochastic finite element method: past, present and future.Computer Methods in Applied Mechanics and Engineering,2009,198(9):1031-1051.
[59] E Rosseel, S Vandewalle, Iterative solvers for the stochastic finite elementmethod. SIAM Journal on Scientific Computing,2010,32(1):372-397.
[60] A Barth, C Schwab, N Zollinger, Multi-level Monte Carlo finite elementmethod for elliptic PDEs with stochastic coefficients. Numerische Mathematik,2011,119(1):123-161.
[61] R Y Rubinstein, D P Kroese, Simulation and the Monte Carlo method, Vol.707:Wiley-interscience2011.
[62] I B Gertsbakh, Y Shpungin, Models of network reliability: analysis,combinatorics, and Monte Carlo: CRC Press2011.
[63] A M Hasofer, N C Lind, Exact and invariant second-moment code format.Journal of the Engineering Mechanics Division,1974,100(1):111-121.
[64] A Der Kiureghian, P-L Liu, Structural reliability under incomplete probabilityinformation. Journal of Engineering Mechanics,1986,112(1):85-104.
[65] R G Ghanem, P D Spanos, Stochastic finite elements: a spectral approach:Courier Dover Publications2003.
[66] G I Schu ller, C G Bucher, U Bourgund, On efficient computational schemes tocalculate structural failure probabilities. Probabilistic Engineering Mechanics,1989,4(1):10-18.
[67] D W Hosmer Jr, S Lemeshow, S May, Applied survival analysis: regressionmodeling of time to event data, Vol.618: Wiley-Interscience2011.
[68] K Helsen, D C Schmittlein, Analyzing duration times in marketing: Evidencefor the effectiveness of hazard rate models. Marketing Science,1993,12(4):395-414.
[69] R G Miller Jr, Survival analysis: Wiley-Interscience2011.
[70] J Zhang, J Lin, G Zhang, High cycle fatigue life prediction and reliabilityanalysis of aeroengine blades. Transactions of Tianjin University,2012,18(6):456.
[71] N Sadou, H Demmou, Reliability analysis of discrete event dynamic systemswith Petri nets. Reliability Engineering&System Safety,2009,94(11):1848-1861.
[72] Y A Katsigiannis, P S Georgilakis, G J Tsinarakis, A novel colored fluidstochastic Petri net simulation model for reliability evaluation of wind/PV/dieselsmall isolated power systems. Systems, Man and Cybernetics, Part A: Systemsand Humans, IEEE Transactions on,2010,40(6):1296-1309.
[73] F Chen, X Yu, Method for Constructing Operation Reliability Model ofHigh-Speed Railway System Based on Petri Net, in Third InternationalConference on Transportation Engineering (ICTE),2011.
[74] V Kumar, N Gupta, A Petri Net Model For Deciding Availability of MostReliable Cost Effective Fragment Access Path in Distributed Database Systems.International Journal of Information and Telecommunication Technology (ISSN:0976-5972),2010,2(1).
[75] H M Gomes, A M Awruch, Comparison of response surface and neural networkwith other methods for structural reliability analysis. Structural safety,2004,26(1):49-67.
[76] J Deng, D Gu, X Li, Structural reliability analysis for implicit performancefunctions using artificial neural network. Structural safety,2005,27(1):25-48.
[77] S Chatterjee, J Singh, S Nigam, A Study of a Single Multiplicative Neuron(SMN) Model for Software Reliability Prediction, in Innovations in IntelligentMachines-3.2013, Springer.89-102.
[78] H Martz, R Wailer, Bayesian reliability analysis of complex series/parallelsystems of binomial subsystems and components. Technometrics,1990,32(4):407-416.
[79] P Weber, L Jouffe, Complex system reliability modelling with dynamic objectoriented bayesian networks (DOOBN). Reliability Engineering&SystemSafety,2006,91(2):149-162.
[80] D Straub, A Der Kiureghian, Bayesian network enhanced with structuralreliability methods: methodology. Journal of Engineering Mechanics,2010,136(10):1248-1258.
[81] S Kotz, M Pensky, The stress-strength model and its generalizations: theory andapplications: Imperial College Press2003.
[82] S Ery lmaz, A new perspective to stress–strength models. Annals of the Instituteof Statistical Mathematics,2011,63(1):101-115.
[83] W K Chung, Some stress-strength reliability models. MicroelectronicsReliability,1982,22(2):277-280.
[84] A Freudenthal, E Gumbel, Physical and statistical aspects of fatigue. Advancesin applied mechanics,1956,4(1):116-156.
[85] K C Kapur, L R Lamberson, Reliability in engineering design. New York, JohnWiley and Sons, Inc.,1977.605p.,1977,1.
[86] W Bao, H Han, Z Huang, Numerical simulations of fracture problems bycoupling the FEM and the direct method of lines. Computer Methods in AppliedMechanics and Engineering,2001,190(37):4831-4846.
[87] H Han, The artificial boundary method-numerical solutions of partialdifferential equations on unbounded domains. Frontiers and Prospects ofContemporary Applied Mathematics,2005,6:33-58.
[88] H-Z Huang, Z-W An, A discrete stress-strength interference model with stressdependent strength. Reliability, IEEE Transactions on,2009,58(1):118-122.
[89] J Lemaitre, Evaluation of dissipation and damage in metals submitted todynamic loading. Mechanical behavior of materials,1972:540-549.
[90]中国质量技术监督局, GB/T228-2002,金属材料室温拉伸试验方法,北京:中国标准出版社,2002.
[91]中国质量技术监督局, GB/T2975-1998,钢及钢产品力学性能试验取样位置及试样制备[S],北京:中国标准出版社,1998.
[92]中国质量技术监督局, GB/T3075-2008,金属材料疲劳试验轴向力控制方法,北京:中国标准出版社,2008.
[93]尚德广,姚卫星,单轴非线性连续疲劳损伤累积模型的研究.航空学报,1998,19(6):647-656.
[94]中国质量技术监督局, GB/T4161-2007,金属材料平面应变断裂韧度KIC试验方法[S],北京:中国标准出版社,2007.
[95]中国质量技术监督局, GB/T6398-2000,金属材料疲劳裂纹扩展速率试验方法,北京:中国标准出版社,2000.
[96]顾永维,安伟光,安海,静载和疲劳载荷共同作用下的结构可靠性分析.兵工学报,2007(12):1473-1477.
[97] J L McClelland, D E Rumelhart, P R Group, Parallel distributed processing.Explorations in the microstructure of cognition,1986,2.
[98] J J Moré, The Levenberg-Marquardt algorithm: implementation and theory, inNumerical analysis.1978, Springer.105-116.
[99] K Sadananda, A Vasudevan, I Kang, Effect of superimposed monotonic fracturemodes on the ΔK and Kmaxparameters of fatigue crack propagation. ActaMaterialia,2003,51(12):3399-3414.
[100]曾庆会,模态试验中跑点测量时传感器附加质量影响的消除.南京航空航天大学学报,1994,26(5):692-695.
[101]岳珠峰,镍基单晶涡轮叶片结构强度设计,北京:科学出版社2008.
[102] K S Chana, U K Singh, T Povey, Turbine Heat Transfer and AerodynamicMeasurements and Predictions for a1.5Stage Configuration,2004: ASME.
[103]高鹏,谢里阳,考虑强度退化的零件及系统可靠性分析.机械工程学报,2010,46(24):162-167.
[104] B I Sandor, Fundamentals of cyclic stress and strain: Univ of Wisconsin Pr1972.
[105] Z WANG, L-y XIE, J-y ZHANG, Reliability Model of System with CommonCause Failure Under Repeated Random Load. Acta Aeronautica et AstronauticaSinica,2007: S1.