铺层角度对CFRP多向层板Ⅱ型分层扩展行为的影响

张寒松; 龚愉; 林文娟; 张建宇; 赵丽滨

doi:10.13801/j.cnki.fhclxb.20220329.001

铺层角度对CFRP多向层板Ⅱ型分层扩展行为的影响

doi: 10.13801/j.cnki.fhclxb.20220329.001

1.
重庆大学　航空航天学院，重庆 400044
2.
河北工业大学　机械工程学院，天津 300401

基金项目: 国家自然科学基金(12172067；11902054；12072052；12072005；11872131；U1864208)；中央高校基本科研业务费(2020CDJGFHK009)；重庆英才青年拔尖人才计划(CQYC2021059215)

详细信息

通讯作者:
龚愉，博士，副教授，硕士生导师，研究方向为复合材料力学　 E-mail: gongyu@cqu.edu.cn

中图分类号: TB332
计量
- 文章访问数: 966
- HTML全文浏览量: 456
- PDF下载量: 126
- 被引次数: 0
出版历程
- 收稿日期: 2022-01-25
- 修回日期: 2022-03-09
- 录用日期: 2022-03-18
- 网络出版日期: 2022-03-31
- 刊出日期: 2022-08-22

Effect of ply angle on mode II delamination propagation behavior of CFRP multidirectional laminates

1.
College of Aerospace Engineering, Chongqing University, Chongqing 400044, China
2.
School of Mechanical Engineering, Hebei University of Technology, Tianjin 300401, China

摘要

摘要: 碳纤维增强树脂复合材料(CFRP)因其良好的力学性能被逐渐应用于飞机主承力结构中。分层是复合材料层板最常见的损伤形式之一，也是飞机复合材料结构损伤容限设计与分析所关注的焦点问题。对于II型分层，现有研究主要针对单向层板展开，而工程实际中应用较多的是多向层板，对II型分层的铺层角度影响缺乏深入认识。为此，采用试验和数值方法开展了相关研究。首先设计了3种工程实际中常用界面(0°/5°、45°/−45°和90°/90°)的T700/QY9511碳纤维/双马来酰亚胺树脂基复合材料层板，所设计铺层可降低耦合作用并确保II型主导的分层扩展。采用端部开口弯曲装置开展了II型分层试验并测得了断裂韧性。结果表明：铺层角度对断裂韧性和分层失效行为影响显著。采用控制变量法建立了内聚力关键参数模型，在此基础上实现了多向层板II型分层扩展行为的模拟，预测的载荷-位移曲线响应与试验结果吻合很好，说明了有限元模型的有效性。有限元结果表明，基体损伤做功表现出随铺层角度增加而增加的趋势。为揭示基体损伤做功与分层前缘损伤区大小之间的关系，利用用户自定义子程序，模拟了不同界面试样的分层前缘损伤区域。
- 复合材料层板 /
- 分层 /
- 铺层角度 /
- 端部开口弯曲 /
- 断裂韧性
Abstract: Carbon fiber reinforced polymer (CFRP) is gradually used in aircraft main load-bearing structure due to its good mechanical properties. Delamination is one of the most common damage forms of composite laminates, and it is also the focus of damage tolerance design and analysis of aircraft composite structures. For mode II delamination, the existing research mainly focuses on unidirectional laminates, while multidirectional laminates are widely used in engineering practice, and there is a lack of in-depth understanding of the influence of ply angle on mode II delamination. Therefore, experimental and numerical investigations were conducted in this paper. Firstly, three different interfaces (0°/5°, 45°/−45° and 90°/90°) were designed for composite laminates made of T700/QY9511 carbon fiber/bismaleimide prepregs, in order to reduce the coupling effect and ensure the mode II dominant delamination propagation. The mode II delamination test was carried out using end-notched flexure device and the fracture toughness was measured. The results show that the ply angle has a significant effect on the fracture toughness and delamination failure behavior. The control variable method is used for establishing the key parameter model of cohesive zone model. On this basis, the simulation of mode II delamination propagation behavior of multidirectional laminates is realized. The predicted load-displacement curve response is in good agreement with the experimental results, which shows the effectiveness of the finite element model. The finite element results show that the energy dissipated by the matrix damage increases with the increase of interfacial angle. In order to reveal the relationship between the energy dissipated by matrix damage and the size of damage area around the crack tip, the damage area around the crack tip of specimens with different interfaces was simulated by using user-defined subroutine.
- composite laminate /
- delamination /
- ply angle /
- end-notched flexure /
- fracture toughness

HTML全文

图 1 ENF试样形式与几何尺寸

Figure 1. ENF specimen and geometrical dimensions

B—Specimen width; a₀—Length of the initial pre-crack; L—Half of the span; h—Half of the specimen thickness

下载: 全尺寸图片幻灯片

图 2 ENF试验的三点弯加载方案示意图

Figure 2. Sketch of the three-point bending in ENF test

下载: 全尺寸图片幻灯片

图 3 T700/QY9511碳纤维/双马来酰亚胺树脂基复合材料多向层板ENF试样载荷-位移曲线

Figure 3. Load-displacement curves of T700/QY9511 carbon fiber reinforced bismaleimide composite multidirectional laminate ENF specimens

下载: 全尺寸图片幻灯片

图 4 T700/QY9511多向层板ENF试样分层路径图片

Figure 4. Pictures of crack path of T700/QY9511 multidirectional laminate ENF specimens

下载: 全尺寸图片幻灯片

图 5 II型分层双线性本构关系

Figure 5. Bilinear constitutive law of mode II delamination

P—Load; σ—Stress; δ—Displacement; K₀—Interfacial stiffness; d—Damage variable; σ⁰_II—Interfacial strength; δ⁰_II—Displacement when damage initiation occurs; δ^f_II—Displacement when the interface just loses its bearing capacity

下载: 全尺寸图片幻灯片

图 6 T700/QY9511多向层板ENF试样的有限元模型 (a)、预制裂尖 (b) 和变形模拟结果 (c)

Figure 6. Numerical model (a), pre-crack tip (b) and simulated results (c) of T700/QY9511 multidirectional laminate ENF specimen

下载: 全尺寸图片幻灯片

图 7 0°/5°铺层角度T700/QY9511多向层板试样内聚力单元参数的确定

Figure 7. Determination of cohesive element parameters of T700/QY9511 multidirectional laminates with 0°/5° interface

下载: 全尺寸图片幻灯片

图 8 不同界面强度下T700/QY9511多向层板的模拟结果

Figure 8. Simulated results of T700/QY9511 multidirectional laminates under different interfacial strengths

下载: 全尺寸图片幻灯片

图 9 T700/QY9511多向层板内聚力单元的Mises应力云图

Figure 9. Mises stress in cohesive elements of T700/QY9511 multidirectional laminates

下载: 全尺寸图片幻灯片

图 10 T700/QY9511多向层板II型分层过程能量消耗情况示意图

Figure 10. Schematic diagram of energy consumption in mode II delamination process of T700/QY9511 multidirectional laminates

下载: 全尺寸图片幻灯片

图 11 基于奇异元的T700/QY9511多向层板数值模型：(a) ENF有限元模型；(b) 裂尖网格；(c) 三维奇异元示意图

Figure 11. Numerical model of T700/QY9511 multidirectional laminates based on singular element: (a) ENF FE model; (b) Mesh around crack tip; (c) Sketch of 3D singular element

下载: 全尺寸图片幻灯片

图 12 T700/QY9511多向层板裂纹尖端应力状态

Figure 12. Stress status of crack tip in T700/QY9511 multidirectional laminates

σ_x—Stress along the x direction; τ_xz—Shear stress in the x-o-z plane; θ—Ply angle adjacent to the interface

下载: 全尺寸图片幻灯片

图 13 不同界面T700/QY9511多向层板试样的分层前缘损伤区

Figure 13. Damage area around crack tip of T700/QY9511 multidirectional laminates with different interfaces

下载: 全尺寸图片幻灯片

表 1 复合材料多向层板端部开口弯曲(ENF)试样铺层信息

Table 1. Stacking sequences of the composite multidirectional laminate end-notched flexure (ENF) specimens

No.	Ply-up	Delamination interface	D_c	B_t	Flexural modulus E_fx
ENF-1	0°₁₆//(5°/−5°/0°₆)_S	0°/5°	0.0096	0.0063	129.2947
ENF-2	(45°/−45°/0°₆)_S//(−45°/45°/0°₆)_S	45°/−45°	0.1527	0.0308	67.9749
ENF-3	(90°/0°/90°/0°₅)_S//(90°/0°/90°/0°₅)_S	90°/90°	0.0020	≈0	69.6301
Notes: D_c and B_t—Dimensionless parameters; //—Location of the prefabricated crack introduced during manufacturing.

下载: 导出CSV

表 2 T700/QY9511多向层板ENF试样的挠度和临界载荷值

Table 2. Deflection and critical load values of T700/QY9511 multidirectional laminate ENF specimens

Delamination interface	No.	Width/ mm	Deflection/ mm	Critical load/N
0°/5°	ENF-1-1	25.01	1.90	1119
	ENF-1-2	25.01	2.27	1235
	ENF-1-3	25.01	2.16	1067
45°/−45°	ENF-2-1	24.94	2.59	1016
	ENF-2-2	24.98	2.88	915
	ENF-2-3	25.00	2.53	1038
90°/90°	ENF-3-1	24.99	2.23	811
	ENF-3-2	25.04	2.40	727
	ENF-3-3	25.07	2.17	774

下载: 导出CSV

表 3 不同分层界面T700/QY9511多向层板ENF试样的断裂韧性试验值

Table 3. Fracture toughness values of T700/QY9511 multidirectional laminate ENF specimens with different interfaces

Delamination interface	No.	G_ⅡC/(J·m⁻²)	Average value/( J·m⁻²)	Standard deviation/(J·m⁻²)	C_v/%
0°/5°	ENF-1-1	805.22	912.94	133.16	14.59
	ENF-1-2	1061.83
	ENF-1-3	871.77
45°/−45°	ENF-2-1	1000.79	997.57	3.31	0.33
	ENF-2-2	997.77
	ENF-2-3	994.17
90°/90°	ENF-3-1	686.81	660.12	26.51	4.02
	ENF-3-2	659.78
	ENF-3-3	633.77
Notes: G_ⅡC—Mode II strain energy release rate; C_v—Coefficient of variation.

下载: 导出CSV

表 4 不同界面强度下T700/QY9511多向层板临界载荷模拟值与试验均值对比

Table 4. Simulated and experimental values of critical load of T700/QY9511 multidirectional laminates under various interfacial strengths

Delamination interface	Interfacial strength/MPa	Simulated result of critical load/N	Average test value/N	Relative error/%
0°/5°	30	990.3	1140.3	−13.2
	40	1113.4		−2.4
	50	1154.4		1.2
45°/−45°	50	881.6	989.7	−10.9
	60	1012.5		2.3
	70	1165.9		17.8
90°/90°	35	701.7	770.7	−9.0
	45	781.3		1.4
	50	870.8		13.0

下载: 导出CSV

表 5 T700/QY9511多向层板分层起始时刻裂尖应变能释放率(SERR)分量

Table 5. Strain energy release rate (SERR) components of crack tip at the delamination initiation moment of T700/QY9511 multidirectional laminates

Delamination interface	G_I/(J·m⁻²)	G_II/( J·m⁻²)	G_III/( J·m⁻²)	G_II/ (G_I+G_II+G_III)
0°/5°	0.26	894.08	1.15	1.00
45°/-45°	0.68	950.52	28.32	0.97
90°/90°	0.06	608.03	1.09	1.00
Notes: G_I—Mode I strain energy release rate; G_II—Mode II strain energy release rate; G_III—Mode III strain energy release rate.

下载: 导出CSV

参考文献(25)

[1]	杜善义, 关志东. 我国大型客机先进复合材料技术应对策略思考[J]. 复合材料学报, 2008, 25(1):1-10. doi: 10.3321/j.issn:1000-3851.2008.01.001 DU Shanyi, GUAN Zhidong. Strategic considerations for development of advanced composite technology for large commercial aircraft in China[J]. Acta Materiae Compositae Sinica,2008,25(1):1-10(in Chinese). doi: 10.3321/j.issn:1000-3851.2008.01.001
[2]	杜善义. 先进复合材料与航空航天[J]. 复合材料学报, 2007, 24(1):1-12. doi: 10.3321/j.issn:1000-3851.2007.01.001 DU Shanyi. Advanced composite materials and aerospace engineering[J]. Acta Materiae Compositae Sinica,2007,24(1):1-12(in Chinese). doi: 10.3321/j.issn:1000-3851.2007.01.001
[3]	TEIMOURI F, HEIDARI-RARANI M, HAJI ABOUTALEBI F. Finite element modeling of mode I fatigue delamination growth in composites under large-scale fiber bridging[J]. Composite Structures,2021,263:113716.
[4]	BIN MOHAMED REHAN M S, ROUSSEAU J, FONTAINE S, et al. Experimental study of the influence of ply orientation on DCB mode-I delamination behavior by using multidirectional fully isotropic carbon/epoxy laminates[J]. Composite Structures, 2017, 161(Supplement C): 1-7.
[5]	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, 39(1):1-28. ZHAO L B, GONG Y, ZHANG J Y. A survey on delamination growth behavior in fiber reinforced composite laminates[J]. Acta Aeronautica et Astronautica Sinica,2019,39(1):1-28(in Chinese).
[6]	李玉龙, 刘会芳. 加载速率对层间断裂韧性的影响[J]. 航空学报, 2015, 36(8):2620-2650. LI Y L, LIU H F. Loading rate effect on interlaminar fracture toughness[J]. Acta Aeronautica et Astronautica Sinica,2015,36(8):2620-2650(in Chinese).
[7]	HYUNG Y C, CHANG F. A model for predicting damage in graphite/epoxy laminated composites resulting from low-velocity point impact[J]. Journal of Composite Materials,1992,26(14):2134-2169. doi: 10.1177/002199839202601408
[8]	郭壮壮, 徐武, 余音. 低温环境下测试复合材料I型层间断裂韧性的简易方法[J]. 复合材料学报, 2019, 36(5):1210-1215. GUO Z Z, XU W, YU Y. A simple method for determining the mode I interlaminar fracture toughness of composite at low temperature[J]. Acta Materiae Compositae Sinica,2019,36(5):1210-1215(in Chinese).
[9]	GARULLI T, CATAPANO A, FANTERIA D, et al. Experimental assessment of fully-uncoupled multi-directional specimens for mode I delamination tests[J]. Composites Science and Technology,2020,200:108421. doi: 10.1016/j.compscitech.2020.108421
[10]	LAKSIMI A, AHMED BENYAHIA A, BENZEGGAGH M L, et al. Initiation and bifurcation mechanisms of cracks in multi-directional laminates[J]. Composites Science and Technology,2000,60(4):597-604. doi: 10.1016/S0266-3538(99)00179-7
[11]	DAVIDSON B D, KRUGER R, KOING M. Effect of stacking sequence on energy release rate distributions in multidirectional DCB and ENF specimens[J]. Engineering Fracture Mechanics,1996,55(4):557-569. doi: 10.1016/S0013-7944(96)00037-9
[12]	OZDIL F, CARLSSON L A, DAVIES P. Beam analysis of angle-ply laminate end-notched flexure specimens[J]. Composites Science and Technology,1998,58(12):1929-1938. doi: 10.1016/S0266-3538(98)00018-9
[13]	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,2004,64(10):1653-1659.
[14]	PEREIRA A B, DE MORAIS A B. Mode II interlaminar fracture of glass/epoxy multidirectional laminates[J]. Composites Part A: Applied Science and Manufacturing,2004,35(2):265-272. doi: 10.1016/j.compositesa.2003.09.028
[15]	CHAI H. Interlaminar shear fracture of laminated composites[J]. International Journal of Fracture,1990,43(2):117-131. doi: 10.1007/BF00036181
[16]	HERRÁEZ M, PICHLER N, PAPPAS G A, et al. Experiments and numerical modelling on angle-ply laminates under remote mode II loading[J]. Composites Part A: Applied Science and Manufacturing,2020,134:105886. doi: 10.1016/j.compositesa.2020.105886
[17]	POLAHA J J, DAVIDSON B D, HUDSON R C, et al. Effects of mode ratio, ply orientation and precracking on the delamination toughness of a laminated composite[J]. Journal of Reinforced Plastics and Composites,1996,15(2):141-173. doi: 10.1177/073168449601500202
[18]	SALAMAT-TALAB M, SHOKRIEH M M, MOHAGHEGH M. On the R-curve and cohesive law of glass/epoxy end-notch flexure specimens with 0//θ interface fiber angles[J]. Polymer Testing,2020,93:106992.
[19]	CHOI N S, KINLOCH A J, WILLIAMS J G. 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]	TAO J, SUN C T. Influence of ply orientation on delamination in composite laminates[J]. Journal of Composite Materials,1998,32(21):1933-1947. doi: 10.1177/002199839803202103
[21]	HWANG J H, KWON O, LEE C S, et al. Interlaminar fracture and low-velocity impact of carbon/epoxy composite materials[J]. Mechanics of Composite Materials,2000,36(2):117-130. doi: 10.1007/BF02681828
[22]	中国航空工业总公司. 碳纤维复合材料层合板II型层间断裂韧性G_IIC试验方法: HB 7403—1996[S]. 北京: 中国标准出版社, 1996 China Aviation Industry Corporation. Test method for mode II interlaminar fracture toughness G_IIC of carbon fiber composite laminates: HB 7403—1996[S]. Beijing: China Standards Press, 1996(in Chinese).
[23]	李西宁, 王悦舜, 周新房. 复合材料层合板分层损伤数值模拟方法现状[J]. 复合材料学报, 2021, 38(4):1076-1086. LI Xining, WANG Yueshun, ZHOU Xinfang. Status of numerical simulation methods for delamination damage of composite laminates[J]. Acta Materiae Compositae Sinica,2021,38(4):1076-1086(in Chinese).
[24]	ZHAO L, GONG Y, ZHANG J, et al. Simulation of delamination growth in multidirectional laminates under mode I and mixed mode I/II loadings using cohesive elements[J]. Composite Structures,2014,116:509-522. doi: 10.1016/j.compstruct.2014.05.042
[25]	CAMANHO P P, DÁVILA C G, PINHO S T, et al. Prediction of in situ strengths and matrix cracking in composites under transverse tension and in-plane shear[J]. Composites Part A: Applied Science and Manufacturing,2006,37(2):165-176. doi: 10.1016/j.compositesa.2005.04.023