层压复合材料分层扩展分析的虚拟裂纹闭合技术及其应用
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摘要
分层是是复合材料结构失效的主要原因之一。为了更合理有效的利用复合材料,有必要对复合材料分层机理进行研究分析。本文提出了一种基于虚拟裂纹闭合技术的界面元模型,用以模拟含初始损伤的复合材料结构的分层破坏问题。本文主要内容如下:
(1)介绍了虚拟裂纹闭合技术的原理、发展历史和应用。
(2)提出了一种基于虚拟裂纹闭合技术的界面元模型。该界面元被嵌入在模型分层的潜在路径上,用来计算结构的能量释放率,结合幂指数破坏准则,模拟复合材料的分层扩展。在实际模型中,由于裂尖前后单元长度的不同,会带来一定的分析误差。本文对其进行了适当的修正,以降低网格粗细变化所带来的不利影响。
(3)介绍了ABAQUS中UEL模块的界面、接口和开发用户自定义单元的流程,以及调用多个子程序的方法。
(4)引入双悬臂梁模型(DCB)、端边切口模型(ENF)和混合模式弯曲模型(MMB)来检验该界面元方法的可靠性。本文分别推导了DCB、ENF、MMB模型能量释放率和载荷位移关系的解析解。在有限元分析中,用界面元来模拟这三种模型的界面层。模拟结果与解析解吻合较好,证实了该方法模拟I型、II型和I、II混合型分层破坏的有效性和可靠性。
(5)在上述研究的基础上,本文最后将该方法引入工程实际问题,分别对三个含有不同初始损伤的复合材料T型接头的界面拉脱分层破坏进行数值模拟,取得了令人满意的结果。
One of the most common failure modes for composite structures is delamination. In order to utilizing the composite laminate more effectively, the delamination mechanics is necessary to be studied. In this thesis, an interface element model based on the virtual crack closure technique (VCCT) is introduced to study 2D delamination growth problem in composite. The main content of this thesis is summarized as follows:
(1) The approach, history and applications of the virtual crack closure technique is introduced.
(2) An interface element based on the virtual crack closure technique is defined in this thesis. The mechanics of the interface element is interpreted first. The interface element are embedded along the potential crack path in advance to calculate the strain energy release rate and simulate the delamination growth of composite laminates in conjunction with the power law fracture criteria. In practical models, the different length of the elements at the crack tip will induce inaccuracy in numerical modeling. Therefore, a necessary correction has been considered as a strategy to minimize the negative effect of change in mesh density on numerical results.
(3) The interface keywords, strategy and regulation of the user subroutine(UEL) in ABAQUS are presented. Besides, the method how to invoke user-defined elements is also mentioned in this thesis.
(4) The DCB, ENF and MMB models are taken in to validate this approach. The analytical solutions are deduced before the numerical simulation. Interface elements are employed to simulate the interface in these models. The results of the FE simulation agree well with analytical solutions. It confirms that the approach is reliable and feasible for modeling the delamination growth in composite laminates.
(5) Finally, the approach is applied in engineering problems. Three composite T-joints with different flaws are numerically simulated with the interface element. An excellent agreement is found between the numerical results and the experimental data.
(1)介绍了虚拟裂纹闭合技术的原理、发展历史和应用。
(2)提出了一种基于虚拟裂纹闭合技术的界面元模型。该界面元被嵌入在模型分层的潜在路径上,用来计算结构的能量释放率,结合幂指数破坏准则,模拟复合材料的分层扩展。在实际模型中,由于裂尖前后单元长度的不同,会带来一定的分析误差。本文对其进行了适当的修正,以降低网格粗细变化所带来的不利影响。
(3)介绍了ABAQUS中UEL模块的界面、接口和开发用户自定义单元的流程,以及调用多个子程序的方法。
(4)引入双悬臂梁模型(DCB)、端边切口模型(ENF)和混合模式弯曲模型(MMB)来检验该界面元方法的可靠性。本文分别推导了DCB、ENF、MMB模型能量释放率和载荷位移关系的解析解。在有限元分析中,用界面元来模拟这三种模型的界面层。模拟结果与解析解吻合较好,证实了该方法模拟I型、II型和I、II混合型分层破坏的有效性和可靠性。
(5)在上述研究的基础上,本文最后将该方法引入工程实际问题,分别对三个含有不同初始损伤的复合材料T型接头的界面拉脱分层破坏进行数值模拟,取得了令人满意的结果。
One of the most common failure modes for composite structures is delamination. In order to utilizing the composite laminate more effectively, the delamination mechanics is necessary to be studied. In this thesis, an interface element model based on the virtual crack closure technique (VCCT) is introduced to study 2D delamination growth problem in composite. The main content of this thesis is summarized as follows:
(1) The approach, history and applications of the virtual crack closure technique is introduced.
(2) An interface element based on the virtual crack closure technique is defined in this thesis. The mechanics of the interface element is interpreted first. The interface element are embedded along the potential crack path in advance to calculate the strain energy release rate and simulate the delamination growth of composite laminates in conjunction with the power law fracture criteria. In practical models, the different length of the elements at the crack tip will induce inaccuracy in numerical modeling. Therefore, a necessary correction has been considered as a strategy to minimize the negative effect of change in mesh density on numerical results.
(3) The interface keywords, strategy and regulation of the user subroutine(UEL) in ABAQUS are presented. Besides, the method how to invoke user-defined elements is also mentioned in this thesis.
(4) The DCB, ENF and MMB models are taken in to validate this approach. The analytical solutions are deduced before the numerical simulation. Interface elements are employed to simulate the interface in these models. The results of the FE simulation agree well with analytical solutions. It confirms that the approach is reliable and feasible for modeling the delamination growth in composite laminates.
(5) Finally, the approach is applied in engineering problems. Three composite T-joints with different flaws are numerically simulated with the interface element. An excellent agreement is found between the numerical results and the experimental data.
引文
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[2] Dugdale D.S. Yieding of steels containing slits [J]. Mech.Phys.Solids, 1960, 8: 100~104.
[3] Barenblatt.G. The mathematical theory of equilibrium cracks in brittles fracture [J]. Advances in Applied Mechanics. 1962, 7:55~129.
[4]孙启星,陈普会.整体复合材料结构失效分析的粘聚区模型[J].南京航空航天大学学报,2008,40(4):442~446.
[5]彭维周,蒲天游.碳化硅/铝复合材料界面结构透射电镜研究[J].复合材料学报,1989,6(1):75~92.
[6]周储伟,杨卫,方岱宁.内聚力界面单元与复合材料的界面损伤分析[J].力学学报,1999,(03):117~122.
[7] Han, T., Ural,A., Chen, C.-S.,Zehnder, A.T.,Ingraffea, A.R, and Billington,S.L. Delamination Buckling and Propagation Analysis of Honeycomb Panels Using a Cohesive Element Approach[J]. International Journal of Fracture, 115(2):101~123.
[8] R. Krueger. The virtual crack closure technique: History, approach and applications. ICASE Report No. 2002-10, Hampton, VA, USA, 2002.
[9] G.R. IRWIN. Fracture I[M]. in Handbuch der Physik VI, Flugge, Ed., 1958, 558~590.
[10] Shivakumar, K.N., Tan, P.W. and Newman, J.C., A virtual crack-closure technique for calculating stress intensity factors for cracked three dimensional bodies[J]. Int. J. Fract. 1979,36:43~50.
[11] Shivakumar, K.N. and Raju, I.S. An equivalent domain integral method for three-dimensional mixed-mode fracture problems [J]. Eng. Fract. Mech. 1978, 42(6): 935~959.
[12] Shivakumar, K.N., Tan, P.W. and Newman. A virtual crack-closure technique for calculating stress intensity factors for cracked three dimensional bodies[J]. Int. J. Fract. 1979,36:43~50.
[13] A. Leski, W. Beres, Application of the virtual crack closure technique to stress intensity factor calculations, NRC Canada, Structures and Materials Laboratory Report, No. LTR-SMPL-2003-0158, Ottawa, 2003.
[14] Lorenzi, H.G., On the energy release rate and the J-integral for 3-D crack configurations [J]. Int. J. Fract. 1977, 19:183~193.
[15] Gaudenzi P, Perugini P, Riccio A. Post-buckling behavior of composite panels in the presence of unstable delaminations[J]. Composite structures, 2001, 51:301~309.
[16]陈浩然,于瑾,白瑞祥.含分层损伤复合材料等三角形格栅加筋板的起裂和扩展过程研究[J].复合材料学报,2008,25:173~77.
[17]王蔓,李泽成,白瑞祥.复合材料格栅加筋板的分层扩展特性[J].吉林大学学报(工学版),2007, 37(1), 229~233.
[18]危银涛,杨挺青,万志敏.改进的虚裂纹闭合技术及其在复合材料脱层分析中的应用[J].计算力学学报,2000,17(3):308~312.
[19]谢伟,黄其青.改进的三维虚拟裂纹闭合方法[J].西北工业大学学报,2008,26(1).
[20]闫相桥.含裂缝的复合材料及非均匀材料的断裂力学研究,[博士学位论文].哈尔滨:哈尔滨工业大学,1989.
[21] Murthy P L N, Chamis C C. Composite Interlaminar Fracture Toughness: Three-Dimensional Finite Element Modeling for Mixed Mode I, II, and Fracture[C].ASTM STP972 , J.D.Whitcomb, Ed., 1988,:23~40.
[22]潘建伍,碳纤维抗弯加固钢筋混凝土梁的剥离破坏研究,[博士学位论文].南京:东南大学,2005.
[23] T. Nishioka and S.N. Atluri, Numerical modeling of dynamic crack propagation in finite bodies by moving singular elements. Part I[J], J Appl Mech 1980, 47 (3) :570~576.
[24] J.Rethore, A. Gravouil and A. Combescure, A stable numerical scheme for the finite element simulation of dynamic crack propagation with remeshing[J], Comput Meth Appl Mech Eng (2004), 193:4493~4510.
[25]陈欣.界面元法的开裂和损伤梯度模型及其工程应用,[博士学位论文].北京:清华大学,2004.
[26]赵宁,卓家寿.动力分析的刚体-界面元与有限元耦合法[J].河海大学学报,1994,(06).
[27]方义琳,卓家寿,章青.具有任意形状单元离散模型的界面元法[J].工程力学,1998,(02).
[28]叶碧泉,羿旭明,斬胜勇．用界面单元法分析复合材料界面力学性能[J].应用数学和力学,1996,17:343~348.
[29]温卫东,康继东,孙晓玲.三维带离心力问题的随机边界元法及在涡轮盘可靠性分析中的应用[J].南京航空航天大学学报(英文版),1995,(02).
[30] Xie D and Biggers, Jr. SB, Progressive crack growth analysis using interface element based on the virtual crack closure technique[J]. Finite Elements in Analysis and Design, 42(2006): 977~984.
[31] Xie D and Biggers, Jr. SB, Strain energy release rate calculation for a moving delamination front of arbitrary shape based on virtual crack closure technique, Part II: Sensitivity Study onModeling Details [J]. Engineering Fracture Mechanics, 73(2006): 786~801.
[32] Xie D and Biggers, Jr. SB, Strain energy release rate calculation for a moving delamination front of arbitrary shape based on virtual crack closure technique, Part I: Formulation and Validation[J], Engineering Fracture Mechanics, 73(2006): 771~785.
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