Simulation of buckling and delamination propagation of composite laminates with fiber bridging
-
摘要: 纤维增强复合材料层合板由于层间力学性能弱，容易出现分层损伤。分层的扩展往往伴随着纤维桥联效应，纤维桥联能显著增大层合板尤其是多向层合板分层扩展的阻力。考虑纤维桥联效应的三线性内聚力模型能表征分层扩展实验中断裂韧性的“R曲线”特征，比传统的双线性模型能更为准确地描述复合材料的分层扩展行为。本论文基于三线性内聚力模型，对含圆形分层复合材料层合板的轴向压缩进行数值模拟，探讨纤维桥联效应对分层扩展及后屈曲行为的影响规律。研究结果发现，纤维桥联对层合板的屈曲载荷影响较小；混合屈曲模式下，三线性模型预测的上下子板相对法向位移明显低于双线性模型；相同分层深度下，三线性模型预测的层合板后屈曲更早转变为整体屈曲模式。随着分层深度的增加，层合板的屈曲模式由局部屈曲逐步过渡为混合屈曲和整体屈曲；当分层深度较浅时，I型分层扩展占主导；随着分层深度的增加，I型分层逐渐减弱，而II型和III型分层扩展则显著增强；当分层接近板中面时，I型分层停止扩展，以II型及III型分层为主。Abstract: Fiber reinforced composite laminates are susceptible to delamination damage due to relatively weak inter-laminar mechanical properties. The growth of delamination is always accompanied by fiber bridging, which can significantly increase the resistance of delamination propagation, especially in the case of multidirectional lami-nates. Compared with the traditional bilinear model, a trilinear cohesive zone model with fiber bridging effects can describe the “R curve” characteristic of the fracture toughness shown in the delamination test, and consequently better characterize the delamination propagation behavior of composite laminates. In order to evaluate the effects of fiber bridging on the behaviors of delamination growth and post-buckling in composite laminates, a trilinear cohesive zone model was built to investigate the compressive behavior of composite laminates with a circular delamination. The results demonstrate that, fiber bridging has little effect on the buckling load of the laminates. The relative deflection between the upper and lower sub-laminate predicted by the trilinear model is much smaller than that predicted by the bilinear model under mixed buckling mode. The buckling mode predicted by the trilinear model transits to global buckling earlier than that predicted by the bilinear model at identical delamination depth. The post-buckling modes change from local buckling mode to mix mode buckling and finally global buckling with the increase of delamination depth. For shallow delamination, mode I delamination is prominent. With the increase of delamination depth, the mode I delamination gradually disappears, while the mode II and III delamination propagation increases significantly. For delamination close to the mid-plane of the laminate, the delamination propagation is dominated by mode II and mode III, without mode I growth.
-
图 1 内聚力单元
Figure 1. Cohesive element
δn—Relative displacement in the normal direction; δs, δt—Relative displacement in the tangential direction
图 2 双线性内聚力模型
Figure 2. Bilinear cohesive zone model
σi, δi (i = n, s, t)—Traction and relative displacement in the normal and tangential directions of the cohesive element; K— Stiffness of the cohesive element; K0—Initial stiffness of the cohesive element; d—Damage coefficient; σ0, δ0—Traction and relative displacement at the initial moment of element injury; δf—Relative displacement at element failure
图 3 传统三线性内聚力模型
Figure 3. Traditional trilinear cohesive zone model
σb, δb—Traction force and relative displacement at matrix failure; G1—Fracture toughness of the matrix; G2—Fracture toughness of bridged fibers; GC—Overall fracture toughness; m—Ratio of matrix fracture toughness to overall fracture toughness; n—Ratio of bridged fibers fracture toughness to overall fracture toughness
图 5 含圆形分层的层合板示意图：(a) 几何模型构成；(b)边界条件
Figure 5. Diagram of laminates with a circular delamination: (a) Composition of the geometric model; (b) Boundary conditions
D—Delamination depth; L, W—Length and width of finite element model; H—Thickness of finite element model; r—Radius of the initial delamination; RP-1, RP-2—Reference points for applying the load; U1, U2, U3—Displacement in three directions
图 6 不同分层深度下两种模型预测的T700/TDE85层合板载荷-位移曲线
Figure 6. Force-displacement curves predicted by two models with different delamination depths for T700/TDE85 laminates
图 7 分层深度 D/H = 0.1的T700/TDE85层合板分层扩展及屈曲：(a) 面外位移-载荷曲线；((b), (c)) 不同载荷下两种模型的屈曲模式；((d), (e)) 不同模型的分层扩展预测
Figure 7. Delamination growth and buckling for normalized delamination depth D/H = 0.1 of T700/TDE85 laminates: (a) Out-of-plane deflection vs. loading displacement; ((b), (c)) Buckling modes of two models under different loads; ((d), (e)) Delamination propagation predicted by different model
图 11 分层深度D/H = 0.5的T700/TDE85层合板分层扩展及屈曲：(a) 面外位移-载荷曲线；(b) 两种模型的屈曲模式；((c), (d)) 不同模型的分层扩展预测
Figure 11. Delamination growth and buckling for normalized delamination depth D/H = 0.5 of T700/TDE85 laminates: (a) Out-of-plane deflection vs. loading displacement; (b) Buckling mode of two models; ((c), (d)) Delamination propagation predicted by different model
图 8 分层深度D/H=0.25的T700/TDE85层合板分层扩展及屈曲：(a) 面外位移-载荷曲线；((b), (c)) 不同载荷下两种模型的屈曲模式；((d), (e)) 不同模型的分层扩展预测
Figure 8. Delamination growth and buckling for normalized delamination depth D/H=0.25 of T700/TDE85 laminates: (a) Out-of-plane deflection vs. loading displacement; ((b), (c)) Buckling modes of two models under different loads; ((d), (e)) Delamination propagation predicted by different model
图 9 分层深度D/H=0.3的T700/TDE85层合板分层扩展及屈曲：(a) 面外位移-载荷曲线；((b), (c), (d), (e)) 不同载荷下两种模型的屈曲模式；((f), (g)) 不同模型的分层扩展预测
Figure 9. Delamination growth and buckling for normalized delamination depth D/H=0.3 of T700/TDE85 laminates: (a) Out-of-plane deflection vs. loading displacement; ((b), (c), (d), (e)) Buckling modes of two models under different loads; ((f), (g)) Delamination propagation predicted by different model
图 10 分层深度D/H = 0.35的T700/TDE85层合板分层屈曲：(a) 面外位移-载荷曲线；(b) 两种模型的屈曲模式；((c), (d)) 不同模型的分层扩展预测
Figure 10. Delamination growth and buckling for normalized delamination depth D/H = 0.35 of T700/TDE85 laminates: (a) Out-of-plane deflection vs. loading displacement; (b) Buckling mode of two models; ((c), (d)) Delamination propagation predicted by different model
表 1 T700/TDE85单向板力学性能参数[35]
Table 1. Mechanical parameters of T700/TDE85 unidirectional laminates[35]
E11/MPa E22/MPa E33/MPa G12/MPa G13/MPa G23/MPa ν12 ν13 ν23 138000 10160 10160 5860 5860 4790 0.28 0.3 0.3 Notes: Eij—Young’s modulus; Gij—Shear modulus; vij—Poisson’s ratio, where subscripts i, j denote the principal material axes. 
下载: 导出CSV
K11/(N·mm−3) K22/(N·mm−3) K33/(N·mm−3) Nmax/MPa Smax/MPa Tmax/MPa GIC/(N·mm−1) GIIC/(N·mm−1) GIIIC/(N·mm−1) α 106 106 106 5 20 20 0.276 0.8 0.8 2 Notes: Kij—Interface stiffness; Nmax, Smax, Tmax—Interfacial strength in longitudinal and transverse directions, respectively; GiC—Fracture toughness; α—Power exponent factor.
下载: 导出CSV
表 3 三线性内聚力模型界面参数
Table 3. Interface parameters of the trilinear cohesive zone model
K11/(N·mm−3) K22/(N·mm−3) K33/(N·mm−3) Nmax/MPa Smax/MPa Tmax/MPa GIC/(N·mm−1) GIIC/(N·mm−1) GIIIC/(N·mm−1) α σb δb 106 106 106 5.25 21 21 0.359 1.04 1.04 2 0.2 0.11 Notes: σb—Maximum bridging stress; δb—Initial displacement of bridge fiber damage.
下载: 导出CSV
-
[1] 赵丽滨, 龚愉, 张建宇. 纤维增强复合材料层合板分层扩展行为研究进展[J]. 航空学报, 2019, 40(1):171-199.ZHAO Libing, GONG Yu, ZHANG Jianyu. A survey on delamination growth behavior in fiber reinforced compo-site laminates[J]. Acta Aeronautica et Astronautica Sinica,2019,40(1):171-199(in Chinese). [2] 王雪明, 谢富原, 李敏, 等. 热压罐成型复合材料构件分层缺陷影响因素分析[C]// 杜善义. 第十五届全国复合材料学术会议论文集(上册). 国防工业出版社, 2008: 537-541.WANG Xueming, XIE Fuyuan, LI Ming, et al. Factor analy-sis of delamination in composite components porduced by autoclave process[C]// DU Shanyi. Proceedings of the 15th national conference on composite materials (Volume I). National Defense Industry Press, 2008: 537-541(in Chinese). [3] FOOTE R M L, MAI Y W, COTTERELL B. Crack growth resistance curves in strain-softening materials[J]. Journal of the Mechanics & Physics of Solids,1986,34(6):593-607. [4] SMITH E. Displacement control crack-growth instability in an elastic-softening material[J]. Journal of Materials Science,1994,29(1):276-280. doi: 10.1007/BF00356604 [5] CARPINTERI A, CADAMURO E, VENTURA G. Fiber-reinforced concrete in flexure: A cohesive/overlapping crack model application[J]. Materials and Structures,2015,48(1/2):235-247. doi: 10.1617/s11527-013-0179-1 [6] STEPHEN S J, GETTU R, FERREIRA L E T, et al. Assessment of the toughness of fibre-reinforced concrete using the R-curve approach[J]. Sādhanā,2018,43(3):1-6. [7] LEI W, HUA Z, LINGYU B, et al. Effect of fiber hybridization, strain rate and W/C ratio on the impact behavior of hybrid FRC[J]. Materials,2019,12(17):2780. doi: 10.3390/ma12172780 [8] GONG Y, ZHANG B R, HALLETT S. Delamination migration in multidirectional composite laminates under mode I quasi-static and fatigue loading[J]. Composite Structures,2018,189:160-176. doi: 10.1016/j.compstruct.2018.01.074 [9] GONG Y, ZHANG B, MUKHOPADHYAY S, et al. Experimental study on delamination migration in multidirec-tional laminates under mode II static and fatigue loading, with comparison to mode I[J]. Composite Structures,2018,201:683-698. doi: 10.1016/j.compstruct.2018.06.081 [10] BRUNNER A J, BLACKMAN B R K, DAVIES P. A status report on delamination resistance testing of polymer-matrix composites[J]. Engineering Fracture Mechanics,2007,75(9):2779-2794. [11] BRUNNER A J, BLACKMAN B R K. Delamination fracture in cross-ply laminates: What can be learned from experiment?[J]. European Structural Integrity Society,2003,32:433-444. [12] DE MORAIS A B, DE MOURA M F, MARQUES A T, et al. Mode-I interlaminar fracture of carbon/epoxy cross-ply composites[J]. Composites Science and Technology,2002,62(5):679-686. doi: 10.1016/S0266-3538(01)00223-8 [13] GONG Y, CHEN X J, LI W C, et al. Delamination in carbon fiber epoxy DCB laminates with different stacking sequences: R-curve behavior and bridging traction-separation relation[J]. Composite Structures,2021,262:113605. doi: 10.1016/j.compstruct.2021.113605 [14] DE MOURA M F S F, CAMPILHO R D S G, AMARO A M, et al. Interlaminar and intralaminar fracture characterization of composites under mode I loading[J]. Composite Structures,2010,92(1):144-149. doi: 10.1016/j.compstruct.2009.07.012 [15] PEREIRA A B, DE MORAIS A B. Mode I interlaminar fracture of carbon/epoxy multidirectional laminates[J]. Composites Science and Technology,2004,64(13):2261-2270. [16] GONG Y, HOU Y, ZHAO L, et al. A modified mode I cohe-sive zone model for the delamination growth in DCB lami-nates with the effect of fiber bridging[J]. International Journal of Mechanical Sciences,2020,176:105514. doi: 10.1016/j.ijmecsci.2020.105514 [17] HU P, PULUNGAN D, TAO R, et al. An experimental study on the influence of intralaminar damage on interlaminar delamination properties of laminated composites[J]. Composites Part A,2020,131:105783. doi: 10.1016/j.compositesa.2020.105783 [18] LACHAUD F, PAROISSIEN E, MICHEL L. Validation of a simplified analysis for the simulation of delamination of CFRP composite laminated materials under pure mode I[J]. Composite Structures,2020,237:111897. doi: 10.1016/j.compstruct.2020.111897 [19] CHOI N S. Delamination fracture of multidirectional carbon-fiber/epoxy composites under mode I, mode II and mixed-mode I/II loading[J]. Journal of Composite Materials,1999,33(1):73-100. doi: 10.1177/002199839903300105 [20] PEREIRA A B, DE MORAIS A B, MARQUES A T, et al. Mode II interlaminar fracture of carbon/epoxy multidirectional laminates[J]. Composites Science and Technology,2003,64(10):1653-1659. [21] GONG Y, ZHAO L B, ZHANG J Y, et al. Delamination propagation criterion including the effect of fiber bridging for mixed-mode I/II delamination in CFRP multi-directional laminates[J]. Composites Science and Technology,2017,151:302-309. doi: 10.1016/j.compscitech.2017.09.002 [22] GONG Y, ZHAO L B, ZHANG B, et al. R-curve behaviour of the mixed-mode I/II delamination in carbon/epoxy lami-nates with unidirectional and multidirectional interfaces[J]. Composite Structures,2019,223:110949. doi: 10.1016/j.compstruct.2019.110949 [23] BAE H, KANG M, WOO K, et al. Test and analysis of modes I, II and mixed-mode I/II delamination for carbon/epoxy composite laminates[J]. International Journal of Aeronau-tical and Space Sciences,2019,20(3):636-652. doi: 10.1007/s42405-019-00170-9 [24] XU X P, NEEDLEMAN A. Void nucleation by inclusion debonding in a crystal matrix[J]. Modelling & Simulation in Materials Science & Engineering,1999,1(2):111-132. [25] VIGGO T, JOHN W H. The relation between crack growth resistance and fracture process parameters in elastic-plastic solids[J]. Journal of the Mechanics and Physics of Solids,1992,40(6):1377-1397. doi: 10.1016/0022-5096(92)90020-3 [26] MANGALGIRI P D, JOHNSON W S. Investigation of fiber bridging in double cantilever beam specimens[J]. Journal of Composites, Technology and Research,1987,9(1):10. doi: 10.1520/CTR10421J [27] YAO L, CUI H, ALDERLIESTEN R C, et al. Thickness effects on fibre-bridged fatigue delamination growth in compo-sites[J]. Composites Part A,2018,110:21-28. doi: 10.1016/j.compositesa.2018.04.015 [28] LIU W L, CHEN P H. Theoretical analysis and experi-mental investigation of the occurrence of fiber bridging in unidirectional laminates under mode I loading[J]. Composite Structures,2021,257:113383. doi: 10.1016/j.compstruct.2020.113383 [29] DÁVILA C G A, ROSE C P, CAMANHO P. A procedure for superposing linear cohesive laws to represent multiple damage mechanisms in the fracture of composites[J]. International Journal of Fracture,2009,158(2):211-223. doi: 10.1007/s10704-009-9366-z [30] AIROLDI A, DÁVILA C G. Identification of material parameters for modelling delamination in the presence of fibre bridging[J]. Composite Structures,2012,94(11):3240-3249. doi: 10.1016/j.compstruct.2012.05.014 [31] 侯怡鑫. 含纤维桥接的复合材料层合板分层扩展内聚力模型[D]. 重庆: 重庆大学, 2018.HOU Yixin. Cohesive model for delamination in composite multidirectional laminates with fiber bridging[D]. Chongqing: Chongqing University, 2018(in Chinese). [32] SHOKRIEH M M, RAJABPOUR-SHIRAZI H, HEIDARI-RARANI M, et al. Simulation of mode I delamination propagation in multidirectional composites with R-curve effects using VCCT method[J]. Computational Materials Science,2012,65:66-73. doi: 10.1016/j.commatsci.2012.06.025 [33] FARMAND-ASHTIANI E, ALANIS D, CUGNONI J, et al. Delamination in cross-ply laminates: Identification of traction separation relations and cohesive zone modeling[J]. Composites Science and Technology,2015,119:85-92. doi: 10.1016/j.compscitech.2015.09.025 [34] LI S, NIE J, QIAN J, et al. Initial post-buckling and growth of a circular delamination bridged by nonlinear fibers[J]. Journal of Applied Mechanics,2000,67(4):777-784. doi: 10.1115/1.1313534 [35] 张璐. 含分层缺陷复合材料层合板分层扩展行为与数值模拟研究[D]. 哈尔滨: 哈尔滨工业大学, 2012.ZHANG Lu. Numerical analysis and experimental study on propagation behavior of laminated composite plates with embedded delamination[D]. Harbin: Harbin Institute of Technology, 2012(in Chinese). [36] 张东哲, 林智育, 林仁邦, 等. 含分层复合材料结构压缩强度研究[J]. 复合材料科学与工程, 2020(12):64-73. doi: 10.3969/j.issn.1003-0999.2020.12.011ZHANG Dongzhe, LIN Zhiyu, LIN Renbang, et al. Study of compressive strength of composite structure with delami-nation[J]. Composites Science and Engineering,2020(12):64-73(in Chinese). doi: 10.3969/j.issn.1003-0999.2020.12.011 [37] 熊颖, 薛江红, 陈叔华, 等. 考虑界面接触效应的复合材料层合板分层屈曲的三维有限元分析[J]. 机械强度, 2019, 41(2):377-382.XIONG Ying, XUE Jianghong, CHEN Shuhua, et al. Three-dimensional finite element analysis of delamination buckling of composite laminates with contact effect at the interfaces of delamination[J]. Journal of Mechanical Strength,2019,41(2):377-382(in Chinese). [38] SENTHIL K, AROCKIARAJAN A, PALANINATHAN R, et al. Defects in composite structures: Its effects and prediction methods-A comprehensive review[J]. Composite Structures,2013,106:139-149. doi: 10.1016/j.compstruct.2013.06.008 [39] WANG K, ZHAO L, HONG H, et al. An analytical model for evaluating the buckling, delamination propagation, and failure behaviors of delaminated composites under uni-axial compression[J]. Composite Structures,2019,223:110937. doi: 10.1016/j.compstruct.2019.110937 [40] HWANG S F, LIU G H. Buckling behavior of composite laminates with multiple delaminations under uniaxial compression[J]. Composite Structures,2001,53(2):235-243. doi: 10.1016/S0263-8223(01)00007-1 -
下载:
点击查看大图
计量
- 文章访问数: 1119
- HTML全文浏览量: 406
- PDF下载量: 136
- 被引次数: 0
