描述复合型疲劳裂纹扩展路径的等效模型
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摘要
复合型裂纹的扩展路径不同于Ⅰ型裂纹,会沿着与初始裂纹面不同的方向扩展,扩展路径的准确预测对扩展速率的评估具有重要的作用.采用最大周向应力准则和最小应变能密度准则进行扩展路径的预测时,开裂角的误差会使裂纹不断偏离实际路径,造成最终结果的较大偏差.论文将复合裂纹在扩展过程中的弯折裂纹简化为直线裂纹,对简化过程中所产生的误差进行定量分析,并在此基础上提出了一种描述复合型裂纹扩展路径的等效修正模型.将此模型写入ABAQUS扩展有限元模块,实现了基于等效修正模型的疲劳裂纹扩展程序.通过对含中心斜裂纹板的疲劳裂纹扩展试验,验证了该模型的有效性,预测的开裂角与试验结果基本一致,所得到的载荷循环次数低于试验值,对含裂纹结构的寿命评估偏于保守.
Fatigue fracture is a common failure type of engineering structures under load cycles.The crack existed in the structure is often a mixed-mode crack because the direction of the resultant load is not perpendicular to the crack surface.The mixed-mode crack does not grow along the direction of the initial crack surface,and it is different from that of mode I crack.Accurately predicting the behavior of crack propagation is of significance for crack growth rate evaluation.A common method is to simplify the broken crack as a straight line crack,which,however,will bring an accumulated error into the prediction of crack propagation while using the existing crack propagation criterion.The path calculated using that method deflects downwards,deviating from the real situation.In the present study,the cleavage angle is revised on the basis of analyzing the error caused by the common method,and the actual crack is simplified as an equivalent linear crack.Then,an equivalent modified model is proposed for describing the fatigue growth path of mixed-mode crack.The crack propagation of the mixed-mode crack can be predicted by incorporating this model into ABAQUS XFEM module.The proposed model is validated by the fatigue crack propagation experiments of 2024 aluminum alloy plate with inclined crack.It is found that the results predicted by the model are in agreement with the experimental results.First,the number of fatigue loading cycles computed using the proposed model is lower than that tested by experiments if the specimens are of the same initial crack length.The prediction using the present method is conservative.Second,the accuracy of the prediction is good if the cracked structure is mainly subjected to mode I load,while the maximum computed error is less than 10% if modeⅡload is more significant.
Fatigue fracture is a common failure type of engineering structures under load cycles.The crack existed in the structure is often a mixed-mode crack because the direction of the resultant load is not perpendicular to the crack surface.The mixed-mode crack does not grow along the direction of the initial crack surface,and it is different from that of mode I crack.Accurately predicting the behavior of crack propagation is of significance for crack growth rate evaluation.A common method is to simplify the broken crack as a straight line crack,which,however,will bring an accumulated error into the prediction of crack propagation while using the existing crack propagation criterion.The path calculated using that method deflects downwards,deviating from the real situation.In the present study,the cleavage angle is revised on the basis of analyzing the error caused by the common method,and the actual crack is simplified as an equivalent linear crack.Then,an equivalent modified model is proposed for describing the fatigue growth path of mixed-mode crack.The crack propagation of the mixed-mode crack can be predicted by incorporating this model into ABAQUS XFEM module.The proposed model is validated by the fatigue crack propagation experiments of 2024 aluminum alloy plate with inclined crack.It is found that the results predicted by the model are in agreement with the experimental results.First,the number of fatigue loading cycles computed using the proposed model is lower than that tested by experiments if the specimens are of the same initial crack length.The prediction using the present method is conservative.Second,the accuracy of the prediction is good if the cracked structure is mainly subjected to mode I load,while the maximum computed error is less than 10% if modeⅡload is more significant.
引文
[1]Ding F,Zhao T W,Jiang Y.A study of fatigue crack growth with changing loading direction[J].Engineering Fracture Mechanics,2006,74(13):2014-2029.
[2]Qian J,Fatemi A.Mixed mode fatigue crack growth:A Literature survey[J].Engineering Fracture Mechanics 1996,55(6):969-990.
[3]李军.弹塑性状态下复合型疲劳裂纹扩展研究[D].北京:北京理工大学,2014.(Li J.A Study on Elasticplastic Mixed-mode Fatigue Crack Propagation.[D].Beijing:Beijing Institute of Technology,2014.(in Chinese))
[4]嵇醒.断裂力学判据的评述[J].力学学报,2016,48(4):741-753.(Ji X.A critical review on criteria of fracture mechanics[J].Chinese Journal of Theoretical and Applied Mechanics,2016,48(4):741-753.(in Chinese))
[5]张敦福,李术才.修正的拉应力裂纹扩展准则及裂隙水压对裂纹扩展的影响[J].计算力学学报,2009,26(1):114-119.(Zhang D F,Li S C.The modified tensile stress crack propagation criterion and influence of cranny hydraulic pressure on crack propagation[J].Chinese Journal of Computational Mechanics,2009,26(1):114-119.(in Chinese))
[6]代鹏,冯森林.CT试样三维疲劳裂纹扩展数值模拟[J].计算力学学报,2011,28:33-36.(Dai P,Feng S L.Numerical simulation of 3Dfatigue crack growth of CT specimens[J].Chinese Journal of Computational Mechanics,2011,28:33-36.(in Chinese))
[7]彭国良,闫辉,杜太焦,张相华.I型裂纹虚拟裂纹闭合法的误差分析及修正[J].固体力学学报,2016,37(3):280-283.(Peng G L,Yan H,Du T J,Zhang X H.An error-correction analysis of the virtual crack closure technique for modeⅠcrack[J].Chinese Journal of Solid Mechanics,2016,37(3):280-283.(in Chinese))
[8]吴志学.表面裂纹疲劳扩展形状演化预测[J].应用力学学报,2010,27(4):783-786.(Wu Z X.Prediction of aspect ratio variation of surface cracks under fatigue loading[J].Chinese Journal of Applied Mechanics,2010,27(4):783-786.(in Chinese))
[9]方修君,金峰,王进廷.基于扩展有限元法的粘聚裂纹模型[J].清华大学学报,2007,47(3):344-347.(Fang X J,Jin F,Wang J T.Cohesive crack model based on extended finite element method[J].Journal of Tinghua University,2007,47(3):344-347.(in Chinese))
[10]刘丰,郑宏,李春光.基于NMM的EFG方法及其裂纹扩展模拟[J].力学学报,2016,46(4):582-590.(Liu F,Zheng H,Li C G.The NMM-based EFG method and simulation of crack propagation[J].Chinese Journal of Theoretical and Applied Mechanics,2016,46(4):582-590.(in Chinese))
[11]丁振宇,王效贵,高增梁.加载历史和裂纹闭合对疲劳裂纹扩展行为影响的数值模拟[J].工程力学,2013,30(8):244-250.(Ding Z Y,Wang X G,Gao Z L.Numerical simulation of the effect of loading history and crack closure on crack propagation behaviour[J].Engineering Mechanics,2013,30(8):244-250.(in Chinese))
[12]姜潮,龙湘云,韩旭,刘杰.一种随机裂纹结构的裂纹扩展路径分析方法[J].固体力学学报,2014,35(1):30-38.(Jiang C,Long X Y,Han X,Liu J.A crack propagation path analysis method of random cracked structure[J].Chinese Journal of Solid Mechanics,2014,35(1):30-38.(in Chinese))
[13]马世镶,胡视.CTS试件中复合型疲劳裂纹扩展[J].力学学报,2006,38(5):698-704.(Ma S X,Hu S.The mixed-mode propagation of fatigue crack in CTS specimen[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(5):698-704.(in Chinese))
[14]Motamedi D,Mohammadi S.Dynamic crack propagation analysis of Orthotropic media by the extended finite element method[J].International Journal of fracture,2010,161(1):21-39.
[15]任利,朱哲明,谢凌志,张茹,艾婷.复合型裂纹断裂的新准则[J].固体力学学报,2013,34(1):31-37.(Ren L,Zhu Z M,Xie L Z,Zhang R,Ai T.New Fracture criterion for mixed mode cracks[J].Chinese Journal of Solid Mechanics,2013,34(1):31-37.(in Chinese))
[16]郭万林,于培师.构件三维断裂与疲劳力学及其在航空工程中的应用[J].固体力学学报,2010,31(5):553-571.(Guo W L,Yu P S.Three dimensional fracture and fatigue mechanics of structures and ITS application in aeronautical engineering[J].Chinese Journal of Solid Mechanics,2010,31(5):553-571.(in Chinese))
[17]Sih G C.Strain-energy density factor applied to mixed-mode crack problems[J].International Journal of Fracture,1974,10:305-321.
[18]Anderson T L.Fracture Mechanics Fundamentals and Applications[M].(Second Edition).Boca Raton:CRC,1995.
[19]Borrego L P,Antunes F V,Costa J M,et al.Mixedmode fatigue crack growth behaviour in aluminium alloy[J].International Journal of Fatigue,2006,28(5-6):618-626.
[20]孙春方,丁垚赪,唐希文.AL6082铝合金疲劳性能[J].汽车技术,2009,6:55-58.(Sun C F,Ding Y Z,Tang X W.Fatigue property of aluminum 6082[J].Automobile Technology,2009,6:55-58.(in Chinese))
[21]Richard H A,Linnig W,Henn K.Fatigue crack propagation under combined loading[J].Forensic Eng,1991,3:99-109.
[2]Qian J,Fatemi A.Mixed mode fatigue crack growth:A Literature survey[J].Engineering Fracture Mechanics 1996,55(6):969-990.
[3]李军.弹塑性状态下复合型疲劳裂纹扩展研究[D].北京:北京理工大学,2014.(Li J.A Study on Elasticplastic Mixed-mode Fatigue Crack Propagation.[D].Beijing:Beijing Institute of Technology,2014.(in Chinese))
[4]嵇醒.断裂力学判据的评述[J].力学学报,2016,48(4):741-753.(Ji X.A critical review on criteria of fracture mechanics[J].Chinese Journal of Theoretical and Applied Mechanics,2016,48(4):741-753.(in Chinese))
[5]张敦福,李术才.修正的拉应力裂纹扩展准则及裂隙水压对裂纹扩展的影响[J].计算力学学报,2009,26(1):114-119.(Zhang D F,Li S C.The modified tensile stress crack propagation criterion and influence of cranny hydraulic pressure on crack propagation[J].Chinese Journal of Computational Mechanics,2009,26(1):114-119.(in Chinese))
[6]代鹏,冯森林.CT试样三维疲劳裂纹扩展数值模拟[J].计算力学学报,2011,28:33-36.(Dai P,Feng S L.Numerical simulation of 3Dfatigue crack growth of CT specimens[J].Chinese Journal of Computational Mechanics,2011,28:33-36.(in Chinese))
[7]彭国良,闫辉,杜太焦,张相华.I型裂纹虚拟裂纹闭合法的误差分析及修正[J].固体力学学报,2016,37(3):280-283.(Peng G L,Yan H,Du T J,Zhang X H.An error-correction analysis of the virtual crack closure technique for modeⅠcrack[J].Chinese Journal of Solid Mechanics,2016,37(3):280-283.(in Chinese))
[8]吴志学.表面裂纹疲劳扩展形状演化预测[J].应用力学学报,2010,27(4):783-786.(Wu Z X.Prediction of aspect ratio variation of surface cracks under fatigue loading[J].Chinese Journal of Applied Mechanics,2010,27(4):783-786.(in Chinese))
[9]方修君,金峰,王进廷.基于扩展有限元法的粘聚裂纹模型[J].清华大学学报,2007,47(3):344-347.(Fang X J,Jin F,Wang J T.Cohesive crack model based on extended finite element method[J].Journal of Tinghua University,2007,47(3):344-347.(in Chinese))
[10]刘丰,郑宏,李春光.基于NMM的EFG方法及其裂纹扩展模拟[J].力学学报,2016,46(4):582-590.(Liu F,Zheng H,Li C G.The NMM-based EFG method and simulation of crack propagation[J].Chinese Journal of Theoretical and Applied Mechanics,2016,46(4):582-590.(in Chinese))
[11]丁振宇,王效贵,高增梁.加载历史和裂纹闭合对疲劳裂纹扩展行为影响的数值模拟[J].工程力学,2013,30(8):244-250.(Ding Z Y,Wang X G,Gao Z L.Numerical simulation of the effect of loading history and crack closure on crack propagation behaviour[J].Engineering Mechanics,2013,30(8):244-250.(in Chinese))
[12]姜潮,龙湘云,韩旭,刘杰.一种随机裂纹结构的裂纹扩展路径分析方法[J].固体力学学报,2014,35(1):30-38.(Jiang C,Long X Y,Han X,Liu J.A crack propagation path analysis method of random cracked structure[J].Chinese Journal of Solid Mechanics,2014,35(1):30-38.(in Chinese))
[13]马世镶,胡视.CTS试件中复合型疲劳裂纹扩展[J].力学学报,2006,38(5):698-704.(Ma S X,Hu S.The mixed-mode propagation of fatigue crack in CTS specimen[J].Chinese Journal of Theoretical and Applied Mechanics,2006,38(5):698-704.(in Chinese))
[14]Motamedi D,Mohammadi S.Dynamic crack propagation analysis of Orthotropic media by the extended finite element method[J].International Journal of fracture,2010,161(1):21-39.
[15]任利,朱哲明,谢凌志,张茹,艾婷.复合型裂纹断裂的新准则[J].固体力学学报,2013,34(1):31-37.(Ren L,Zhu Z M,Xie L Z,Zhang R,Ai T.New Fracture criterion for mixed mode cracks[J].Chinese Journal of Solid Mechanics,2013,34(1):31-37.(in Chinese))
[16]郭万林,于培师.构件三维断裂与疲劳力学及其在航空工程中的应用[J].固体力学学报,2010,31(5):553-571.(Guo W L,Yu P S.Three dimensional fracture and fatigue mechanics of structures and ITS application in aeronautical engineering[J].Chinese Journal of Solid Mechanics,2010,31(5):553-571.(in Chinese))
[17]Sih G C.Strain-energy density factor applied to mixed-mode crack problems[J].International Journal of Fracture,1974,10:305-321.
[18]Anderson T L.Fracture Mechanics Fundamentals and Applications[M].(Second Edition).Boca Raton:CRC,1995.
[19]Borrego L P,Antunes F V,Costa J M,et al.Mixedmode fatigue crack growth behaviour in aluminium alloy[J].International Journal of Fatigue,2006,28(5-6):618-626.
[20]孙春方,丁垚赪,唐希文.AL6082铝合金疲劳性能[J].汽车技术,2009,6:55-58.(Sun C F,Ding Y Z,Tang X W.Fatigue property of aluminum 6082[J].Automobile Technology,2009,6:55-58.(in Chinese))
[21]Richard H A,Linnig W,Henn K.Fatigue crack propagation under combined loading[J].Forensic Eng,1991,3:99-109.