冲击后复合材料层合板的拉伸破坏行为研究
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摘要
复合材料由于具有比强度、比刚度高,抗疲劳性能好,可设计性,抗腐蚀等优点,正日益广泛地用于航空结构上。复合材料在受到冲击后,内部会出现基体开裂、纤维断裂、分层等多种损伤。这些损伤会大大降低复合材料的剩余强度和疲劳性能。因此,对复合材料层合板冲击后的剩余强度进行研究具有重要的理论意义和工程价值。
本文应用损伤等效和三维有限元分析的方法对含冲击损伤的复合材料层合板的剩余拉伸强度进行分析研究,建立了含冲击损伤复合材料层合板的等效损伤三维分析模型,并根据分析方法和分析模型,以ABAQUS软件为平台开发了相应的用户材料子程序(UMAT),并将该方法的分析结果与试验值进行比较,取得了较好的效果。
本文的主要研究工作如下:
(1)针对含冲击损伤层合板在拉伸载荷作用下的剩余拉伸强度和破坏过程,本文提出了将冲击损伤等效为圆孔的模型,将含冲击损伤层合板的剩余拉伸强度问题转化为含孔板的剩余拉伸强度问题。
(2)分析过程中,采用三维Hashin破坏准则和Camanho的参数退化方式,建立了三维分析模型。
(3)本文在分析过程中考虑了铺层角对层合板中单层的横向拉伸强度和剪切强度的影响,采用了Chang提出的就位强度公式,对每个单层赋予不同的材料属性。以ABAQUS软件为平台,编写了用户材料子程序(UMAT)。
(4)应用本文提出的三维分析模型,对不同铺层的含孔层合板预测了剩余拉伸强度和进行了损伤演化过程的模拟;对不同能量冲击后层合板的剩余拉伸强度进行了预测,模拟了在拉伸载荷作用下的失效过程。
As a new kind of material, composite materials have many merits such as high specific strength, high specific stiffness, high fatigue performance, good designable characteristic and high corrosion resistance ability. Nowadays, composite materials have been applied widely in aircraft structures. The impact damages will result in matrix crack, fiber breakage, delamination and so on, which can largely decrease the residual strength and fatigue performance. Therefore, it’s very important to research the residual strength of composite materials after impact.
In order to analysis the residual tensile strength of composite laminates after impact, a three dimentional equivalent damage model is proposed, which is based on equivalent damage model and three dimentional finite element analysis. Based on ABAQUS, a user subroutine to define a material's mechanical behavior (UMAT) is developed. Compared with the experimental result, the analysis tensile strength is accurate.
The main research works done in the dissertation include
(1) An equivalent hole model is proposed to predict the residual tensile strength of composite materials after impact and simulate the damage process of composite under tensile loading. Therefore, the tensile strength of composite materials after impact turns to the tensile strength of composite materials with an equivalent hole.
(2) In this research, we use three dimension Hashin damage criteria and Camanho material deterioration, and build a three dimensional analysis model.
(3) The ply angle can affect the matrix tensile and shear strength, hence, an in situ ply matrix tensile and shear strength formula proposed by Chang K Y is applied in this paper. Every ply is given different properties. In addition, a user subroutine to define a material`s mechanical behavior (UMAT) is developed in ABAQUS.
(4) With the three dimensional model proposed in this paper, we predict the residual tensile strength of composite with a hole and simulate the damage process under tensile loading. The residual tensile strength of composite with impact damage and the damage process are also predicted and simulated.
本文应用损伤等效和三维有限元分析的方法对含冲击损伤的复合材料层合板的剩余拉伸强度进行分析研究,建立了含冲击损伤复合材料层合板的等效损伤三维分析模型,并根据分析方法和分析模型,以ABAQUS软件为平台开发了相应的用户材料子程序(UMAT),并将该方法的分析结果与试验值进行比较,取得了较好的效果。
本文的主要研究工作如下:
(1)针对含冲击损伤层合板在拉伸载荷作用下的剩余拉伸强度和破坏过程,本文提出了将冲击损伤等效为圆孔的模型,将含冲击损伤层合板的剩余拉伸强度问题转化为含孔板的剩余拉伸强度问题。
(2)分析过程中,采用三维Hashin破坏准则和Camanho的参数退化方式,建立了三维分析模型。
(3)本文在分析过程中考虑了铺层角对层合板中单层的横向拉伸强度和剪切强度的影响,采用了Chang提出的就位强度公式,对每个单层赋予不同的材料属性。以ABAQUS软件为平台,编写了用户材料子程序(UMAT)。
(4)应用本文提出的三维分析模型,对不同铺层的含孔层合板预测了剩余拉伸强度和进行了损伤演化过程的模拟;对不同能量冲击后层合板的剩余拉伸强度进行了预测,模拟了在拉伸载荷作用下的失效过程。
As a new kind of material, composite materials have many merits such as high specific strength, high specific stiffness, high fatigue performance, good designable characteristic and high corrosion resistance ability. Nowadays, composite materials have been applied widely in aircraft structures. The impact damages will result in matrix crack, fiber breakage, delamination and so on, which can largely decrease the residual strength and fatigue performance. Therefore, it’s very important to research the residual strength of composite materials after impact.
In order to analysis the residual tensile strength of composite laminates after impact, a three dimentional equivalent damage model is proposed, which is based on equivalent damage model and three dimentional finite element analysis. Based on ABAQUS, a user subroutine to define a material's mechanical behavior (UMAT) is developed. Compared with the experimental result, the analysis tensile strength is accurate.
The main research works done in the dissertation include
(1) An equivalent hole model is proposed to predict the residual tensile strength of composite materials after impact and simulate the damage process of composite under tensile loading. Therefore, the tensile strength of composite materials after impact turns to the tensile strength of composite materials with an equivalent hole.
(2) In this research, we use three dimension Hashin damage criteria and Camanho material deterioration, and build a three dimensional analysis model.
(3) The ply angle can affect the matrix tensile and shear strength, hence, an in situ ply matrix tensile and shear strength formula proposed by Chang K Y is applied in this paper. Every ply is given different properties. In addition, a user subroutine to define a material`s mechanical behavior (UMAT) is developed in ABAQUS.
(4) With the three dimensional model proposed in this paper, we predict the residual tensile strength of composite with a hole and simulate the damage process under tensile loading. The residual tensile strength of composite with impact damage and the damage process are also predicted and simulated.
引文
[1]陈绍杰.复合材料及其应用的新进展[A].见:周履,王震鸣,范赋群主编.《复合材料及其结构的力学进展》(第一册)[C].广州:华南理工大学出版社,1991:166~182.
[2]沈真等.含缺陷复合材料层压板的压缩破坏机理[J].航空学报,1991,12(3):106~113.
[3] Abrate S. Impact on laminated composite materials[J]. Appl. Mech. Rev., 1991, 44(4), 155-190.
[4] Husman G E eta1. Residual strength characterization of laminated composites subjected to impact loading[S].ASTM STP 568,American society for Testing and Materials,Philadelphia,1975,92～113.
[5] Caprino G. Residual strength prediction of impacted CFRP laminates[J].J Compos Mater, 1984,18: 508～518.
[6] Avva V S, etal. Effect of impact and fatigue loads on the strength of graphite/epoxy composites[A]. In: J.M. Whitney ed. Composite Materials: Test and design (Seventh Conference) ASTM STP 893[C]. Philadelphia: American Society for Testing and Materials, 1986: 196~206.
[7] Lal K M. Residual strength assessment of low velocity impact damage of graphite-epoxy laminates[J]. Journal of Reinforced Plastics and Composites, 1983, 2: 226~238.
[8] Awerbuch J, Hahn H T. Hard object impact damage of metal matrix composites[J]. Journal of Composite Materials, 1976, 10: 231~258.
[9] Poe C C Jr. Impact damage and residual tension strength of a thick graphiteepoxy rocket motor case[J]. Journal of Spacecraft and Rockets, 1992, 29(3): 394~404.
[10] Tian Z, Swanson S R. Resudual tensile strength prediction on a ply-by-ply baisis for laminates containing impact damage[J]. Journal of Composite Materials, 1992, 26: 1193~1206.
[11] Cairns D S. Impact and post-impact response of graphite/epoxy and kevlar/epoxy structures, Ph.D. dissertation, Massachusetts Institute of Technology.
[12] Wu E M. Application of fracture mechanics to anisotropic plates[J]. Journal of Applied Mechanics, 1967, 34: 967~974.
[13] Poe C C Jr. A unifying strain criterion for fracture of fibrous composite laminates[J]. Engineering Fracture Mechanics, 1983, 17: 153~171.
[14] Waddoups M E, Eisenmann J R. Macroscopic fracture mechanics of advanced composite materials[J]. Journal of Composite Materials, 1971, 5: 446~454.
[15] Caprino G. Lopresto V.The significance of indentation in the inspection of carbon fibre-reinforced plastic panels damaged by low-velocity impact[J]. Compos Sci Technol, 2000, 60: 1003～12.
[16] Whitney J M, Nuismer R J. Stress fracture criteria for laminated composites containing stress concentrations[J]. Journal of Composite Materials, 1974: 253~265.
[17] Cairns D S, Lagace P A. Residual tensile strength of graphite/epoxy and Kevlar/epoxy laminates with impact damage[A]. In: Garbo, S.P. ed. Composite Materials: Testing and Design (Ninth Volume), ASTM STP 1059[C]. Philadelphia: American Society for Testing and Materials,1990: 48~63.
[18] El-Zein M S, Reifsnider K L. On the prediction of tensile strength after impact of composite laminates[J]. Journal of Composites Technology & Research, 1990, 12(3): 147~154.
[19]程小全,邹健,俞彬彬,等.平面编织复合材料层合板低速冲击后的拉伸性能[J].复合材料学报, 2008, 25(5): 163~168.
[20] Lekhnitskii S G. Anisotropic plances[M]. New York: Gordon and Breach, 1968.
[21] Hashin Z. Failure criteria for unidirectional fiber composites [J] . Journal of Applied Mechanics, 1980, 47: 329~334.
[22] Chang F K, Chang K Y. A progressive failure damage model for laminated composites containing stress concent ration[J]. Journal of Composites Material, 1987, 21: 809~833.
[23]崔海坡,温卫东,崔海涛.复合材料层合板冲击损伤及剩余强度分析方法[J].固体力学学报, 2006, 27(3): 237~242.
[24] Hou J P, Petrinic N, Ruiz C, etal. Prediction of impact damage in composite plates[J]. Compos Sci Technol, 2000, 60: 273～281.
[25] Tserpes K I, Labeas G, etal. Strength prediction of bolted joints in graphite/epoxy composite laminates[J]. Composites, Part B, 2002, 33: 521～529.
[26] Chang F K, Zafer K. Modeling compression failure of laminated composites containing multiple through-the-width delaminations[J]. Journal of Composites Material, 1992, 26: 350~387.
[27] Tan S C, Perez J. Progressive failure of laminated composites with a hole under compressive loading[J]. J Reinf Plas Compos, 1993, 12: 1043～1057.
[28] Camanho P P, Matthews F L. A progressive damage model for mechanically fastened joints in composite laminates[J]. J Compos Mater , 1999, 33: 2248～2280.
[29]崔海坡,温卫东,崔海涛.复合材料层合板的低能冲击损伤及剩余拉伸强度研究[J].宇航学报, 2005, 26(6): 784~788.
[30] Wang Shi-Xun, Wu Lin-Zhi, MA Li. Low-velocity impact and residual tensile strength analysis to carbon fiber composite laminates[J]. Materials and Design, 2010, 31: 118~125.
[31] Yeh H Y, Kim C H. The Yeh-Stratton criterion for composite materials[J]. J Compos Mater , 1994, 28: 926~939.
[32]程小全,张子龙,吴学仁.小尺寸试件层合板低速冲击后的剩余压缩强度[J].复合材料学报, 2002, 19(6): 8~12.
[33] Xiong Y, Poon C. A prediction method for the compressive strength of impact damaged composite laminates[J]. Composite Structures, 1995, 30: 357~367.
[34] Dost E F, Ilcewicz L B, Gosse J H. Sublaminate stability based modeling of impact damaged composite laminates[A]. In: Proceedings of the American Society for Compo sites, the 3rd Technical Conference of American Society for Composites [C]. Washington: Seattle, 1988: 354- 363.
[35] Gottesman T, Girshovich S, Drukker E, etal. Residual strength of impacted composites: Analysis and Tests[J]. J of Composites Technology & Research, 1994, 16(3): 244~255.
[36] Huang J Y. Prediction of the residual strength of laminated composites subjected to impact loading[J]. Journal of Materials Processing Technology, 1995, 54: 205~210.
[37] Whitcomb J D, Finite element analysis of instability-related delamination growth[J]. Journal of Composite Materials, 1981, 15: 403~426.
[38]陈普会.复合材料层压板及加筋板的损伤容限分析[博士学位论文].南京:南京航空航天大学, 1999.
[39] Soutis C, Curtis P T. Prediction of the post impact compressive strength of CFRP laminated composite[J]. Composites Science and Technology, 1996, 56: 677~684.
[40]程小全,郦正能.复合材料层合板低速冲击后压缩的损伤累积模型[J].应用数学和力学, 2005, 26(5): 569~576.
[41] Chang F K, Springer G S. The strength of fiber reinforced composite bends[J]. Journal of Composite Materials, 1986, 20: 30~45.
[42]崔海坡,温卫东,崔海涛.层合复合材料板的低速冲击损伤及剩余压缩强度研究[J].机械科学与技术, 2006, 25(9): 1013~1017.
[43] Chamis C C, Ginty C A, Fiber composite structural durability and damage tolerance: simplified predictive methods[J]. NASA Technical Memorandum 100179, 1~25.
[44]沈观林,胡更开.复合材料力学[M].北京:清华大学出版社, 2006, 39~42.
[45]蔡四维.复合材料结构力学[M].北京:人民交通出版社, 1987, 20~24.
[46]朱伯芳.有限单元法原理与应用[M].北京:中国水利出版社, 2009, 55~60.
[47]崔海坡.复合材料层合板冲击损伤及剩余强度研究[博士学位论文].南京:南京航空航天大学, 2006.
[48] Chang K Y, Liu Sheng, Chang F K. Damage tolerance of laminated composites containing an open hole and subjected to tensile loadings[J]. Journal of Composite Materials, 1991, 25: 274~301.
[49] Chang F K, Lessard L. Damage tolerance of laminated composites containing an open hole and subjected to compressive loading, Part I-Analysis [J]. Journal of Composite Materials, 1991, 25(1): 2~43.
[50] Lessard L. Compression failure in laminated composites containing an open hole[Ph.D. Dissertation]. Stanford University, 1989.
[51]郝勇,含孔复合材料层合板损伤破坏研究[D].南京:南京航空航天大学, 1999.
[2]沈真等.含缺陷复合材料层压板的压缩破坏机理[J].航空学报,1991,12(3):106~113.
[3] Abrate S. Impact on laminated composite materials[J]. Appl. Mech. Rev., 1991, 44(4), 155-190.
[4] Husman G E eta1. Residual strength characterization of laminated composites subjected to impact loading[S].ASTM STP 568,American society for Testing and Materials,Philadelphia,1975,92～113.
[5] Caprino G. Residual strength prediction of impacted CFRP laminates[J].J Compos Mater, 1984,18: 508～518.
[6] Avva V S, etal. Effect of impact and fatigue loads on the strength of graphite/epoxy composites[A]. In: J.M. Whitney ed. Composite Materials: Test and design (Seventh Conference) ASTM STP 893[C]. Philadelphia: American Society for Testing and Materials, 1986: 196~206.
[7] Lal K M. Residual strength assessment of low velocity impact damage of graphite-epoxy laminates[J]. Journal of Reinforced Plastics and Composites, 1983, 2: 226~238.
[8] Awerbuch J, Hahn H T. Hard object impact damage of metal matrix composites[J]. Journal of Composite Materials, 1976, 10: 231~258.
[9] Poe C C Jr. Impact damage and residual tension strength of a thick graphiteepoxy rocket motor case[J]. Journal of Spacecraft and Rockets, 1992, 29(3): 394~404.
[10] Tian Z, Swanson S R. Resudual tensile strength prediction on a ply-by-ply baisis for laminates containing impact damage[J]. Journal of Composite Materials, 1992, 26: 1193~1206.
[11] Cairns D S. Impact and post-impact response of graphite/epoxy and kevlar/epoxy structures, Ph.D. dissertation, Massachusetts Institute of Technology.
[12] Wu E M. Application of fracture mechanics to anisotropic plates[J]. Journal of Applied Mechanics, 1967, 34: 967~974.
[13] Poe C C Jr. A unifying strain criterion for fracture of fibrous composite laminates[J]. Engineering Fracture Mechanics, 1983, 17: 153~171.
[14] Waddoups M E, Eisenmann J R. Macroscopic fracture mechanics of advanced composite materials[J]. Journal of Composite Materials, 1971, 5: 446~454.
[15] Caprino G. Lopresto V.The significance of indentation in the inspection of carbon fibre-reinforced plastic panels damaged by low-velocity impact[J]. Compos Sci Technol, 2000, 60: 1003～12.
[16] Whitney J M, Nuismer R J. Stress fracture criteria for laminated composites containing stress concentrations[J]. Journal of Composite Materials, 1974: 253~265.
[17] Cairns D S, Lagace P A. Residual tensile strength of graphite/epoxy and Kevlar/epoxy laminates with impact damage[A]. In: Garbo, S.P. ed. Composite Materials: Testing and Design (Ninth Volume), ASTM STP 1059[C]. Philadelphia: American Society for Testing and Materials,1990: 48~63.
[18] El-Zein M S, Reifsnider K L. On the prediction of tensile strength after impact of composite laminates[J]. Journal of Composites Technology & Research, 1990, 12(3): 147~154.
[19]程小全,邹健,俞彬彬,等.平面编织复合材料层合板低速冲击后的拉伸性能[J].复合材料学报, 2008, 25(5): 163~168.
[20] Lekhnitskii S G. Anisotropic plances[M]. New York: Gordon and Breach, 1968.
[21] Hashin Z. Failure criteria for unidirectional fiber composites [J] . Journal of Applied Mechanics, 1980, 47: 329~334.
[22] Chang F K, Chang K Y. A progressive failure damage model for laminated composites containing stress concent ration[J]. Journal of Composites Material, 1987, 21: 809~833.
[23]崔海坡,温卫东,崔海涛.复合材料层合板冲击损伤及剩余强度分析方法[J].固体力学学报, 2006, 27(3): 237~242.
[24] Hou J P, Petrinic N, Ruiz C, etal. Prediction of impact damage in composite plates[J]. Compos Sci Technol, 2000, 60: 273～281.
[25] Tserpes K I, Labeas G, etal. Strength prediction of bolted joints in graphite/epoxy composite laminates[J]. Composites, Part B, 2002, 33: 521～529.
[26] Chang F K, Zafer K. Modeling compression failure of laminated composites containing multiple through-the-width delaminations[J]. Journal of Composites Material, 1992, 26: 350~387.
[27] Tan S C, Perez J. Progressive failure of laminated composites with a hole under compressive loading[J]. J Reinf Plas Compos, 1993, 12: 1043～1057.
[28] Camanho P P, Matthews F L. A progressive damage model for mechanically fastened joints in composite laminates[J]. J Compos Mater , 1999, 33: 2248～2280.
[29]崔海坡,温卫东,崔海涛.复合材料层合板的低能冲击损伤及剩余拉伸强度研究[J].宇航学报, 2005, 26(6): 784~788.
[30] Wang Shi-Xun, Wu Lin-Zhi, MA Li. Low-velocity impact and residual tensile strength analysis to carbon fiber composite laminates[J]. Materials and Design, 2010, 31: 118~125.
[31] Yeh H Y, Kim C H. The Yeh-Stratton criterion for composite materials[J]. J Compos Mater , 1994, 28: 926~939.
[32]程小全,张子龙,吴学仁.小尺寸试件层合板低速冲击后的剩余压缩强度[J].复合材料学报, 2002, 19(6): 8~12.
[33] Xiong Y, Poon C. A prediction method for the compressive strength of impact damaged composite laminates[J]. Composite Structures, 1995, 30: 357~367.
[34] Dost E F, Ilcewicz L B, Gosse J H. Sublaminate stability based modeling of impact damaged composite laminates[A]. In: Proceedings of the American Society for Compo sites, the 3rd Technical Conference of American Society for Composites [C]. Washington: Seattle, 1988: 354- 363.
[35] Gottesman T, Girshovich S, Drukker E, etal. Residual strength of impacted composites: Analysis and Tests[J]. J of Composites Technology & Research, 1994, 16(3): 244~255.
[36] Huang J Y. Prediction of the residual strength of laminated composites subjected to impact loading[J]. Journal of Materials Processing Technology, 1995, 54: 205~210.
[37] Whitcomb J D, Finite element analysis of instability-related delamination growth[J]. Journal of Composite Materials, 1981, 15: 403~426.
[38]陈普会.复合材料层压板及加筋板的损伤容限分析[博士学位论文].南京:南京航空航天大学, 1999.
[39] Soutis C, Curtis P T. Prediction of the post impact compressive strength of CFRP laminated composite[J]. Composites Science and Technology, 1996, 56: 677~684.
[40]程小全,郦正能.复合材料层合板低速冲击后压缩的损伤累积模型[J].应用数学和力学, 2005, 26(5): 569~576.
[41] Chang F K, Springer G S. The strength of fiber reinforced composite bends[J]. Journal of Composite Materials, 1986, 20: 30~45.
[42]崔海坡,温卫东,崔海涛.层合复合材料板的低速冲击损伤及剩余压缩强度研究[J].机械科学与技术, 2006, 25(9): 1013~1017.
[43] Chamis C C, Ginty C A, Fiber composite structural durability and damage tolerance: simplified predictive methods[J]. NASA Technical Memorandum 100179, 1~25.
[44]沈观林,胡更开.复合材料力学[M].北京:清华大学出版社, 2006, 39~42.
[45]蔡四维.复合材料结构力学[M].北京:人民交通出版社, 1987, 20~24.
[46]朱伯芳.有限单元法原理与应用[M].北京:中国水利出版社, 2009, 55~60.
[47]崔海坡.复合材料层合板冲击损伤及剩余强度研究[博士学位论文].南京:南京航空航天大学, 2006.
[48] Chang K Y, Liu Sheng, Chang F K. Damage tolerance of laminated composites containing an open hole and subjected to tensile loadings[J]. Journal of Composite Materials, 1991, 25: 274~301.
[49] Chang F K, Lessard L. Damage tolerance of laminated composites containing an open hole and subjected to compressive loading, Part I-Analysis [J]. Journal of Composite Materials, 1991, 25(1): 2~43.
[50] Lessard L. Compression failure in laminated composites containing an open hole[Ph.D. Dissertation]. Stanford University, 1989.
[51]郝勇,含孔复合材料层合板损伤破坏研究[D].南京:南京航空航天大学, 1999.
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