多部位损伤结构的疲劳寿命预测
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摘要
多部位损伤是现役飞机的典型损伤形式,尤其在大型飞机结构中广泛存在,对飞机结构完整性构成严重威胁。现有限制单一主裂纹长度的损伤容限设计方法已不能保证结构的使用安全,亟待解决含多裂纹结构的耐久性/损伤容限设计与评定问题。针对这一课题,本文基于弹塑性断裂力学和疲劳断裂理论,在充分吸收借鉴国内外最新研究成果的基础上,开展多部位损伤板的应力强度因子研究与的疲劳扩展寿命预测,为老龄飞机结构完整性评估提供一套更加先进、完善、实用的损伤容限分析方法。
本文主要研究了多部位损伤结构的应力强度因子和疲劳扩展寿命预测。通过有限元方法,对实际结构可能出现的四种典型多部位损伤形式的应力强度因子进行了分析。并通过数值计算,详细讨论了结构尺寸和孔边裂纹间相对位置对应力强度因子的影响规律,得到了一系列对工程应用具有实用价值的结论。利用所得应力强度因子,裂纹扩展方向采用最大周向应力准则,结合工程中应用最为广泛的Paris公式对多裂纹板的疲劳寿命进行了预计,计算结果与现有试验结果比较吻合,且偏于保守,表明了该方法的可行性。
本文从试验及理论方向研究多裂纹板的拉伸破坏及疲劳断裂问题,各个环节都得到有关理论和试验的验证,表明了本文研究方法的正确性、计算结果的可靠性。由于力学响应的计算采用有限元方法,所以该方法适用于裂纹任意分布的多部位损伤板,可直接用于工程实际结构。
The structures of aging airplanes can be often characterized as Multiple site damage(MSD), which is more damage of aircraft structures, because the structures are designed according to the traditional damage tolerance which takes no account of MSD. MSD has been one of the most representative damages styles in the aircraft structures, which has badly threatened the structures integrality of aircraft. To provide a more advanced, ideal and practical damage tolerance analysis method, the stress intensity factor(SIF) of elements with MSD and fatigue life of the panel containing multiple cracks are obtained by finite element method in this thesis, based on the elastic-plastic and fatigue fracture mechanics.
This thesis consists of two sections. The first section focuses on the analysis of SIF of elements with MSD. Based on the elastic-plastic and fatigue fracture mechanics, with the help of FRANC2D/L, the SIF of different MSD model is computed and showing that the analysis results have good coherence with the literature data. Based on SIF, some factors that will affect SIF general, such as MSD crack length, the space between cracks, are discussed. Several conclusions valuable to practices are drawn. The second section focuses on fatigue life prediction of MSD panel. Fatigue life is calculated using Paris formulation. The direction is predicted by the maximum circumferential direction stress criterion. The predicated life is conservative to the experiments results.
Theories and numerical simulation are used to research the fracture of panels with multiple site damage, in which every main point are studied systematically and supported by theoretical results and/or experimental results. This approach has a good capacity of predication and can be applied in engineering.
本文主要研究了多部位损伤结构的应力强度因子和疲劳扩展寿命预测。通过有限元方法,对实际结构可能出现的四种典型多部位损伤形式的应力强度因子进行了分析。并通过数值计算,详细讨论了结构尺寸和孔边裂纹间相对位置对应力强度因子的影响规律,得到了一系列对工程应用具有实用价值的结论。利用所得应力强度因子,裂纹扩展方向采用最大周向应力准则,结合工程中应用最为广泛的Paris公式对多裂纹板的疲劳寿命进行了预计,计算结果与现有试验结果比较吻合,且偏于保守,表明了该方法的可行性。
本文从试验及理论方向研究多裂纹板的拉伸破坏及疲劳断裂问题,各个环节都得到有关理论和试验的验证,表明了本文研究方法的正确性、计算结果的可靠性。由于力学响应的计算采用有限元方法,所以该方法适用于裂纹任意分布的多部位损伤板,可直接用于工程实际结构。
The structures of aging airplanes can be often characterized as Multiple site damage(MSD), which is more damage of aircraft structures, because the structures are designed according to the traditional damage tolerance which takes no account of MSD. MSD has been one of the most representative damages styles in the aircraft structures, which has badly threatened the structures integrality of aircraft. To provide a more advanced, ideal and practical damage tolerance analysis method, the stress intensity factor(SIF) of elements with MSD and fatigue life of the panel containing multiple cracks are obtained by finite element method in this thesis, based on the elastic-plastic and fatigue fracture mechanics.
This thesis consists of two sections. The first section focuses on the analysis of SIF of elements with MSD. Based on the elastic-plastic and fatigue fracture mechanics, with the help of FRANC2D/L, the SIF of different MSD model is computed and showing that the analysis results have good coherence with the literature data. Based on SIF, some factors that will affect SIF general, such as MSD crack length, the space between cracks, are discussed. Several conclusions valuable to practices are drawn. The second section focuses on fatigue life prediction of MSD panel. Fatigue life is calculated using Paris formulation. The direction is predicted by the maximum circumferential direction stress criterion. The predicated life is conservative to the experiments results.
Theories and numerical simulation are used to research the fracture of panels with multiple site damage, in which every main point are studied systematically and supported by theoretical results and/or experimental results. This approach has a good capacity of predication and can be applied in engineering.
引文
[1] National Transportation Safety Board , Aircraft Accident Report , Report NTSB/AAR-89/03.
[2]郭树祥,多孔多裂纹加筋板的应力强度因子与剩余强度研究,南京,南京航空航天大学博士论文,2006.
[3] Swift T.Damage tolerance capability.International Journal of Fatigue,1994,16(1):75-94.
[4] Kuang J H,Chen C K,The failure of ligaments due to multiple-site damage using interactions of dugdale-type cracks.Fatigue & Fracture of Engineering Materials & Structures,1998,21:1147-1156.
[5] Jeong D Y,Brewer J C,On the linkup of multiple cracks,Engineering Fracture Mechanics.1995,51(2):233-238.
[6] Moukawsher E J,Heinimann M B,Grandt Jr A F.Residual strength of panels with multiple site damage.Journal of Aircraft,1996,33(5):1014-1021.
[7] Galatolo R,Nilsson K-F,An experimental and numerical analysis of residual strength of butt-joints panels with multiple site damage.Engineering Fracture Mechanics,2001,68:1437-1461.
[8] Seshadri B R,Newman Jr J C,Dawicke D S,Residual strength analysis of sitiffened and unstiffened panels-Part II: wide panels.Engineering Fracture Mechanics,2003,70:509-524.
[9] Hsu C-L,Lo J,Yu J et al.Residual strength analysis using CTOA criteria for fuselage structures containing multiple site damage.Engineering Fracture Mechanics,2003,70:525-545.
[10] Chen Y H.M-integral analysis for two-dimensional solids with strongly interacting microcracks.Part I:in an infinite brittle solid.International Journal of solids & Structures,2001,38:3193-3212.
[11] Wang L,Brust F W,Atluri S N.The elastic-plastic finite element alternating method EPFEAM and the prediction of fracture under WFD conditions in aircraft structures,part I: EPFEAM theory.Computational Mechanics,1997,19:356-369.
[12] Denda M.Mixed Mode I, II and III analysis of multiple cracks in plane anisotropicsolids by the BEM: a dislocation and point force approach.Engineering Analysis with Boundary Elements,2001,25:267-278.
[13]柯黎,王乘,詹福良,裂纹分析中的单节点二次边界元.固体力学学报,2002,23(1):54-64.
[14] Madenci E,Sergeev B,Shkarayev S.Boundary collocation method for multiple defect interactions in an anisotropic finite region.International Journal of Fracture,1998,94:339-355.
[15] Fett T.Weight functions for plates with periodical edge cracks.International Journal of Fracture,1996,78:R45-52.
[16]王庚荪,袁建新,含双周期裂纹群弹性板的弱化问题,力学学报,1995,27:37-50.
[17]胡元太,赵兴华,沿抛物线分布的各向异性曲线裂纹问题.应用数学和力学,1995,16(2):107-115.
[18] Han Xueli,Wang Tzuchiang.Elastic fields of arbitrarily and periodically distributed cracks.In: Wang Tzuchiang,Chou Tsuwei,eds.Progress in Advanced Materials and Mechanics.Beijing:Chinese Journal of Mechanics Press,1996,688-693.
[19] Kuang J H,Chen C K.Equivalence for Two Interacting Parallel Cracks.ASME Journal of Pressure Vessel Technology,1998,120:424-430.
[20] Kuang J H,Chen C K,Alternating iteration method for interacting multiple crack problems,Fatigue Fract.Engng Mater.Struct.,1999,22:743-752.
[21]黎在良,蒋和洋,用裂纹张开位移全场拟合法求应力强度因子-边裂纹问题.固体力学学报,2000,21(4):355-360.
[22]陆建飞,王建华,沈为平.反平面圆形夹杂和多圆孔多裂纹相互作用问题.计算力学学报,2000,17(2):229-234.
[23] Xu X W,Sun L X,Fan X Q.Stress Concentration of Finite Composite Laminates Weakened by Multiple Elliptical Holes.International Journal of Solids & Structures,1995,32(20):3001-3014.
[24] Xu X W,Yue T M,Man H C.Stress analysis of finite composite laminate with multiple loaded holes.International Journal of Solids & Structures,1999,36:919-931.
[25] Xu X W,Man H C,Yue T M.Strength prediction of composite laminates with multiple elliptical holes.International Journal of Solids & Structures,2000,37:2887-2900.
[26]徐晓飞,多裂纹损伤容限分析方法及其应用研究,上海,同济大学博士论文,1999.
[27]朱青云等,某机中央翼下壁板疲劳裂纹扩展寿命估算.机械强度. 2004,26(S):234~236.
[28]黄小平,韩芸,崔维成,一种随机载荷作用下裂纹扩展寿命计算模型.中国力学学会大全2005.
[29]邹小理,樊蔚勋,疲劳裂纹扩展寿命的随机模型.固体力学学报. June 1997. Vol.18 No.2:167~171.
[30] Mark A. James,A plane stress finite element model for elastic-plastic mode I/II crack growth,[Doctor of Philosophy],Kansas State Unibversity,Manhattan,Kansas,1998.
[31] Lim,I.L.,Johnston,I.W.,Choi,etc,Improved numerical Inverse Isoparametric mapping technique for 2D mesh rezoning.Engineering Fracture Mechanics,1992,41(3):417-435.
[32] Kato,K.,Lee,N.S.,and Bathe,etc,Adaptive finite element analysis of large strain elastic response,Computers & structures, 1993,47(4/5):829-855.
[33] Dawicke DS,Sutton MA.CTOA and crack tunneling measurements in thin sheet 2024-T3 aluminum alloy.Experiment Mechanics,1994,34(4):357.
[34] Mahmoud S,Lease KB,Effect of specimen thickness on the characterization of CTOA in 2024-T351 aluminium alloy,Engineering Fracture Mechanics,2003,70(3~4):443~450.
[35] Shih CF,de Lorenzi HG,Andrews WR,Studies on crack initiation and stable crack growth,ASTM STP 1979,668:65~120.
[36] Kanninen MF,Rybicki EF,Stonesifer RB,etc,Elastic-plastic fracture mechanics for two-dimensional stable crack growth and instability problem.ASTM STP 1979,668:121~150.
[37] Brocks W,Yuan H,Numerical studies on stable crack growth.Defect Assessment in Components Fundamentals and Applications.ESIS Publication,1991,9:19~33.
[38] Newman Jr JC,Shivakumar KN,McCabe DE.Finite element fracture simulation of A533B steel sheet specimens.Defect Assessment in Components Fundamentals and Applications.ESIS Publication,1991,9:117~126.
[39] Ching-long Hsu,James Lo.Jin Yu,Xiao-gong Lee,etc,Residual strength analysis using CTOA criteria for fuselage structures containing multiple site damage,Engineering Fracture Mechanics,2002,70:525~545.
[40] Dawicke DS,Newman Jr JC,Bigelow CA.Three-dimension CTOA and constraint effects during stable tearing in a thin-sheet material.ASTM STP 1995,1256:223-242.
[41] Erdogan F.and Sih G.C.,On the crack extension in plates under plane loading andtransverse shear.Journal of Basic Engineering,1963,December:519~527.
[42] Amstutz B.A.,Sutton M .A .,Dawicker,etc,Effects of mixed mode I/II loading and grain orientation on crack initiation and stable tearing in 2024-T3 aluminum.Fatigue and Fracture Mechanics,ASTM STP,1996b,27:1296.
[43] Dalle Donne C.and Doker H.,Plane stress crack resistance curves of and inclined crack under Bi-Axial Loading,Multi-Axial Fatigue and Deformation Testing Technique,ASTM STP,1997,1280:243~263.
[44] Ghosal A.K.and Narasmhan R.,A finite element analysis of mixed-mode fracture initiation by ductile failure mechanisms.Journal of Mechanics and Physics of Solids,1994,42(6):953~978.
[45] Sutton,M.A.,Zhao,W.,Bone,etc,Prediction of crack growth direction for mode I/II loading using small-scale yielding and void initiation/growth concepts.International Journal of Fracture,1997,83,275~290.
[46] Chao,Y.J.and Liu,On the failure of cracks under mixed-mode loads,International Journal of Fracture,1998,87(3):201~223.
[47]中国航空研究院编著,应力强度因子手册.科学出版社,1993年.
[48]航空工业部科学技术委员会,应力集中系数手册,高等教育出版社. 176~177. 1990.
[49] D.S.Dawicke,J.C.Newman,Jr,Analysis and prediction of multiple-site damage (MSD) fatigue crack growth,NASA,August,1992.
[50] Paris, P., Twenty years of Reflection on Questions Involving Fatigue Crack Growth, Fatigue Thresholds. J. Backlund, A.F. Blom, and C.J. Beever (eds.), Chamelem, London, pp.3~10, 1982.
[51] Forman, R.G., Kearney, V.E., and Engle, R.M., Numberical Analysis of Crack Propagation in Cyclic-loaded Structure. Joural of Basic Engineering, 89, pp.459~464, 1967.
[52] Walker, K., The Effect of Stress Ratio During Crack Propagation and Fatigue for 2024-T3 and 7075-T5 Aluminum, Effects of Environment and Complex Load History on Fatigue Life. ASTMSP 462, American Society for Testing and Material, Philadelphia, Pa., pp.1~14, 1970.
[53]张松林,多裂纹板破坏过程模拟及寿命预测,南京,南京航空航天大学硕士论文,2007.
[2]郭树祥,多孔多裂纹加筋板的应力强度因子与剩余强度研究,南京,南京航空航天大学博士论文,2006.
[3] Swift T.Damage tolerance capability.International Journal of Fatigue,1994,16(1):75-94.
[4] Kuang J H,Chen C K,The failure of ligaments due to multiple-site damage using interactions of dugdale-type cracks.Fatigue & Fracture of Engineering Materials & Structures,1998,21:1147-1156.
[5] Jeong D Y,Brewer J C,On the linkup of multiple cracks,Engineering Fracture Mechanics.1995,51(2):233-238.
[6] Moukawsher E J,Heinimann M B,Grandt Jr A F.Residual strength of panels with multiple site damage.Journal of Aircraft,1996,33(5):1014-1021.
[7] Galatolo R,Nilsson K-F,An experimental and numerical analysis of residual strength of butt-joints panels with multiple site damage.Engineering Fracture Mechanics,2001,68:1437-1461.
[8] Seshadri B R,Newman Jr J C,Dawicke D S,Residual strength analysis of sitiffened and unstiffened panels-Part II: wide panels.Engineering Fracture Mechanics,2003,70:509-524.
[9] Hsu C-L,Lo J,Yu J et al.Residual strength analysis using CTOA criteria for fuselage structures containing multiple site damage.Engineering Fracture Mechanics,2003,70:525-545.
[10] Chen Y H.M-integral analysis for two-dimensional solids with strongly interacting microcracks.Part I:in an infinite brittle solid.International Journal of solids & Structures,2001,38:3193-3212.
[11] Wang L,Brust F W,Atluri S N.The elastic-plastic finite element alternating method EPFEAM and the prediction of fracture under WFD conditions in aircraft structures,part I: EPFEAM theory.Computational Mechanics,1997,19:356-369.
[12] Denda M.Mixed Mode I, II and III analysis of multiple cracks in plane anisotropicsolids by the BEM: a dislocation and point force approach.Engineering Analysis with Boundary Elements,2001,25:267-278.
[13]柯黎,王乘,詹福良,裂纹分析中的单节点二次边界元.固体力学学报,2002,23(1):54-64.
[14] Madenci E,Sergeev B,Shkarayev S.Boundary collocation method for multiple defect interactions in an anisotropic finite region.International Journal of Fracture,1998,94:339-355.
[15] Fett T.Weight functions for plates with periodical edge cracks.International Journal of Fracture,1996,78:R45-52.
[16]王庚荪,袁建新,含双周期裂纹群弹性板的弱化问题,力学学报,1995,27:37-50.
[17]胡元太,赵兴华,沿抛物线分布的各向异性曲线裂纹问题.应用数学和力学,1995,16(2):107-115.
[18] Han Xueli,Wang Tzuchiang.Elastic fields of arbitrarily and periodically distributed cracks.In: Wang Tzuchiang,Chou Tsuwei,eds.Progress in Advanced Materials and Mechanics.Beijing:Chinese Journal of Mechanics Press,1996,688-693.
[19] Kuang J H,Chen C K.Equivalence for Two Interacting Parallel Cracks.ASME Journal of Pressure Vessel Technology,1998,120:424-430.
[20] Kuang J H,Chen C K,Alternating iteration method for interacting multiple crack problems,Fatigue Fract.Engng Mater.Struct.,1999,22:743-752.
[21]黎在良,蒋和洋,用裂纹张开位移全场拟合法求应力强度因子-边裂纹问题.固体力学学报,2000,21(4):355-360.
[22]陆建飞,王建华,沈为平.反平面圆形夹杂和多圆孔多裂纹相互作用问题.计算力学学报,2000,17(2):229-234.
[23] Xu X W,Sun L X,Fan X Q.Stress Concentration of Finite Composite Laminates Weakened by Multiple Elliptical Holes.International Journal of Solids & Structures,1995,32(20):3001-3014.
[24] Xu X W,Yue T M,Man H C.Stress analysis of finite composite laminate with multiple loaded holes.International Journal of Solids & Structures,1999,36:919-931.
[25] Xu X W,Man H C,Yue T M.Strength prediction of composite laminates with multiple elliptical holes.International Journal of Solids & Structures,2000,37:2887-2900.
[26]徐晓飞,多裂纹损伤容限分析方法及其应用研究,上海,同济大学博士论文,1999.
[27]朱青云等,某机中央翼下壁板疲劳裂纹扩展寿命估算.机械强度. 2004,26(S):234~236.
[28]黄小平,韩芸,崔维成,一种随机载荷作用下裂纹扩展寿命计算模型.中国力学学会大全2005.
[29]邹小理,樊蔚勋,疲劳裂纹扩展寿命的随机模型.固体力学学报. June 1997. Vol.18 No.2:167~171.
[30] Mark A. James,A plane stress finite element model for elastic-plastic mode I/II crack growth,[Doctor of Philosophy],Kansas State Unibversity,Manhattan,Kansas,1998.
[31] Lim,I.L.,Johnston,I.W.,Choi,etc,Improved numerical Inverse Isoparametric mapping technique for 2D mesh rezoning.Engineering Fracture Mechanics,1992,41(3):417-435.
[32] Kato,K.,Lee,N.S.,and Bathe,etc,Adaptive finite element analysis of large strain elastic response,Computers & structures, 1993,47(4/5):829-855.
[33] Dawicke DS,Sutton MA.CTOA and crack tunneling measurements in thin sheet 2024-T3 aluminum alloy.Experiment Mechanics,1994,34(4):357.
[34] Mahmoud S,Lease KB,Effect of specimen thickness on the characterization of CTOA in 2024-T351 aluminium alloy,Engineering Fracture Mechanics,2003,70(3~4):443~450.
[35] Shih CF,de Lorenzi HG,Andrews WR,Studies on crack initiation and stable crack growth,ASTM STP 1979,668:65~120.
[36] Kanninen MF,Rybicki EF,Stonesifer RB,etc,Elastic-plastic fracture mechanics for two-dimensional stable crack growth and instability problem.ASTM STP 1979,668:121~150.
[37] Brocks W,Yuan H,Numerical studies on stable crack growth.Defect Assessment in Components Fundamentals and Applications.ESIS Publication,1991,9:19~33.
[38] Newman Jr JC,Shivakumar KN,McCabe DE.Finite element fracture simulation of A533B steel sheet specimens.Defect Assessment in Components Fundamentals and Applications.ESIS Publication,1991,9:117~126.
[39] Ching-long Hsu,James Lo.Jin Yu,Xiao-gong Lee,etc,Residual strength analysis using CTOA criteria for fuselage structures containing multiple site damage,Engineering Fracture Mechanics,2002,70:525~545.
[40] Dawicke DS,Newman Jr JC,Bigelow CA.Three-dimension CTOA and constraint effects during stable tearing in a thin-sheet material.ASTM STP 1995,1256:223-242.
[41] Erdogan F.and Sih G.C.,On the crack extension in plates under plane loading andtransverse shear.Journal of Basic Engineering,1963,December:519~527.
[42] Amstutz B.A.,Sutton M .A .,Dawicker,etc,Effects of mixed mode I/II loading and grain orientation on crack initiation and stable tearing in 2024-T3 aluminum.Fatigue and Fracture Mechanics,ASTM STP,1996b,27:1296.
[43] Dalle Donne C.and Doker H.,Plane stress crack resistance curves of and inclined crack under Bi-Axial Loading,Multi-Axial Fatigue and Deformation Testing Technique,ASTM STP,1997,1280:243~263.
[44] Ghosal A.K.and Narasmhan R.,A finite element analysis of mixed-mode fracture initiation by ductile failure mechanisms.Journal of Mechanics and Physics of Solids,1994,42(6):953~978.
[45] Sutton,M.A.,Zhao,W.,Bone,etc,Prediction of crack growth direction for mode I/II loading using small-scale yielding and void initiation/growth concepts.International Journal of Fracture,1997,83,275~290.
[46] Chao,Y.J.and Liu,On the failure of cracks under mixed-mode loads,International Journal of Fracture,1998,87(3):201~223.
[47]中国航空研究院编著,应力强度因子手册.科学出版社,1993年.
[48]航空工业部科学技术委员会,应力集中系数手册,高等教育出版社. 176~177. 1990.
[49] D.S.Dawicke,J.C.Newman,Jr,Analysis and prediction of multiple-site damage (MSD) fatigue crack growth,NASA,August,1992.
[50] Paris, P., Twenty years of Reflection on Questions Involving Fatigue Crack Growth, Fatigue Thresholds. J. Backlund, A.F. Blom, and C.J. Beever (eds.), Chamelem, London, pp.3~10, 1982.
[51] Forman, R.G., Kearney, V.E., and Engle, R.M., Numberical Analysis of Crack Propagation in Cyclic-loaded Structure. Joural of Basic Engineering, 89, pp.459~464, 1967.
[52] Walker, K., The Effect of Stress Ratio During Crack Propagation and Fatigue for 2024-T3 and 7075-T5 Aluminum, Effects of Environment and Complex Load History on Fatigue Life. ASTMSP 462, American Society for Testing and Material, Philadelphia, Pa., pp.1~14, 1970.
[53]张松林,多裂纹板破坏过程模拟及寿命预测,南京,南京航空航天大学硕士论文,2007.