基于多尺度方法的复合材料加筋板极限强度分析

张晓端; 刘斌; 吴卫国; 雷加静; 魏青

doi:10.19693/j.issn.1673-3185.03006

基于多尺度方法的复合材料加筋板极限强度分析

doi: 10.19693/j.issn.1673-3185.03006

张晓端^{1, 2,},
刘斌^1, ,,
吴卫国^1,,
雷加静³,
魏青³

1.
武汉理工大学绿色智能江海直达船舶与邮轮游艇研究中心，湖北武汉 430063
2.
武汉理工大学船海与能源动力工程学院，湖北武汉 430063
3.
中国舰船研究设计中心，湖北武汉 430064

基金项目: 国家自然科学基金资助项目(52271326)；中央高校基本科研业务费专项资金资助项目(2021III011XZ)

详细信息

作者简介:
张晓端，女，2000年生，硕士生。研究方向：船舶与海洋工程结构安全与可靠性。E-mail：a3068926542@126.com

刘斌，男，1985年生，博士，教授。研究方向：船舶与海洋工程结构安全与可靠性。E-mail：liubin8502@whut.edu.cn

吴卫国，男，1960年生，硕士，教授。研究方向：船舶与海洋工程结构安全与可靠性。E-mail：mailjt@163.com

雷加静，男，1984年生，硕士，高级工程师

魏青，女，1987年生，硕士，工程师

通信作者:
刘斌

中图分类号: U661.43；U668.5
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出版历程
- 收稿日期: 2022-07-14
- 修回日期: 2022-09-12
- 网络出版日期: 2023-03-31
- 刊出日期: 2023-04-28

Ultimate strength analysis of composite stiffened panels based on multi-scale approach

ZHANG Xiaoduan^{1, 2
,},
LIU Bin^{1
, ,},
WU Weiguo^1
,,
LEI Jiajing³,
WEI Qing³

1.
Green & Smart River-Sea-Going Ship, Cruise and Yacht Research Center, Wuhan University of Technology, Wuhan 430063, China
2.
School of Naval Architecture, Ocean and Energy Power Engineering, Wuhan University of Technology, Wuhan 430063, China
3.
China Ship Development and Design Center, Wuhan 430064, China

基于多尺度方法的复合材料加筋板极限强度分析由张晓端，等创作，采用知识共享署名4.0国际许可协议进行许可。

摘要

摘要: 目的复合材料内部结构形式多样，深入分析组分材料的损伤机理可为复合材料加筋板的极限强度研究提供基础。方法首先，采用多尺度方法，对船用玻璃纤维增强塑料（GFRP）复合材料加筋板进行微观、细观和宏观的力学分析，建立短切毡（CSM）、机织粗纱（WR）材料的微观和细观代表性体积单元（RVE）模型；然后，通过微观和细观RVE模型均匀化，获得宏观等效刚度，并采用ABAQUS软件的子程序VUMAT编写复合材料渐进损伤演化模型，分别得到微观和细观模型的损伤演化机理及宏观单层板等效强度。结果结果显示，采用多尺度方法可以很好地评估得到复合材料的宏观力学性能；复合材料加筋板的宏观极限强度主要由纤维束的失效决定。结论经多尺度分析得到的宏观材料参数可以用于该材料铺层加筋板的极限强度计算，复合材料的细观力学参数化研究可为材料加工工艺影响研究提供分析手段。
- 玻璃纤维增强塑料 /
- 复合材料 /
- 多尺度方法 /
- VUMAT子程序 /
- 渐进损伤 /
- 极限强度
Abstract: Objectives As composite materials have varied internal structures, an in-depth analysis of the damage mechanisms of their component materials can provide a research foundation for the ultimate strength analysis of composite stiffened panels. Methods The microscopic, mesoscopic and macroscopic mechanical analyses of marine glass fiber reinforced plastic (GFRP) composite stiffened panels are carried out using a multi-scale approach. Microscopic and mesoscopic representative volume element (RVE) models of chopped strand mat (CSM) and woven roving (WR) materials are established, and the macroscopic equivalent stiffness is obtained by homogenizing the RVE models. The ABAQUS VUMAT subroutine is used to code the progressive damage evolution model of the composite materials to derive the damage evolution mechanism of the microscopic and mesoscopic models respectively. The equivalent strength of macroscopic laminates is also obtained. Results The multi-scale approach can be used to accurately evaluate the macroscopic mechanical properties of composite materials, and the ultimate strength of composite stiffened panels is mainly determined by fiber bundle failure. Conclusions The obtained macroscopic material parameters can be used to calculate the ultimate strength of composite stiffened panels, while the parametric study of the mesomechanics of composite materials can provide an analysis tool for investigating the influence of material processing technology.
- glass-fiber reinforced plastic (GFRP) /
- composites /
- multi-scale approach /
- VUMAT subroutine /
- progressive damage /
- ultimate strength

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图 1 T型加筋板结构示意图

Figure 1. Layout of the T-stiffened panel

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图 2 多尺度分析流程图

Figure 2. Flow chart of multi-scale analysis

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图 3 CSM和WR的微观与细观RVE模型以及均匀化图解

Figure 3. Microscopic and mesoscopic RVE model of CSM and WR and their homogenization illustration

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图 4 等效弹性常数计算边界条件

Figure 4. Boundary conditions of the calculations of equivalent elastic constants

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图 5 材料属性退化模型

Figure 5. Model of material property degradation

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图 6 CSM和WR细观尺度轴向拉伸边界条件

Figure 6. Boundary conditions for axial tension of CSM and WR in the meso-scale

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图 7 等效应力−应变曲线及极限点的Mises应力云图

Figure 7. Equivalent stress-strain curves and Mises stress contours of limit point

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图 8 宏观加筋板边界条件

Figure 8. Boundary conditions of macro-scale stiffened panel

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图 9 GFRP复合材料加筋板应力−应变曲线及极限点的Mises应力云图

Figure 9. Stress-strain curve and Mises stress contours of limit point for GFRP composite stiffened panels

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图 10 宏观极限强度受细观参数变化的影响程度

Figure 10. Effect of meso-scale parameters on the marco-scale ultimate strength

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表 1 T型加筋板铺层情况

Table 1. The laying condition of T-stiffened panel

	铺层情况	铺层角度/(°)	铺层厚度/mm
底板	CSM/WR/CSM/WR/CSM/WR/CSM/WR/CSM	0	1.250 (CSM)，0.979 (WR)
T型材	CSM/WR/WR/WR/WR/CSM/WR/WR/WR/WR/WR/CSM	0	1.250 (CSM)，0.979 (WR)

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表 2 CSM和WR的微观RVE模型建模参数

Table 2. Modeling parameters for microscopic RVE models of CSM and WR

模型参数	CSM纤维束	WR纱线
组成	C-玻璃纤维丝、聚酯树脂	E-玻璃纤维丝、聚酯树脂
纤维排列方式	定向分布	定向分布
纤维丝直径/μm	0.014 5	0.014 5
纤维含量	0.71	0.80

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表 3 CSM和WR的细观RVE模型建模参数

Table 3. Modeling parameters for mesoscopic RVE models of CSM and WR

模型参数	CSM单层板	WR单层板
纤维排列方式	随机分布	编织型
纤维束参数	直径0.188 mm	纱线宽度1.80 mm，厚度0.15 mm，纱线间距2.00 mm
纤维含量	0.33	0.50

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表 4 纤维丝和基体材料参数

Table 4. Parameters of fiber and matrix material

材料参数	C-玻璃纤维丝	E-玻璃纤维丝	聚酯树脂基体
密度/(kg·m⁻³)	2 520	2 580	1 300
弹性模量/MPa	69 000	72 000	2 000
泊松比	0.20	0.22	0.35
强度/MPa	3 300	3 400	40

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表 5 CSM和WR的微观和细观等效刚度

Table 5. Microscopic and mesoscopic equivalent stiffness of CSM and WR

参数	微观		细观
参数	CSM纤维束	WR纱线	CSM单层板	WR单层板
E₁₁/MPa	34 343.0	37 257.0	6 529.5	14 228.5
E₂₂/MPa	7 434.0	7 794.0	6 529.5	14 228.5
E₃₃/MPa	6 705.0	7 445.0	6 529.5	5 083.0
G₁₂/MPa	3 376.0	3 376.0	2 473.3	2 055.0
G₁₃/MPa	2 915.0	3 022.0	2 473.3	1 511.0
G₂₃/MPa	2 585.0	2 554.0	2 473.3	1 511.0
V₁₂	0.25	0.26	0.32	0.12
V₁₃	0.26	0.26	0.32	0.38
V₂₃	0.42	0.37	0.32	0.38

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表 6 CSM和WR细观和宏观的强度值

Table 6. Meso-and macro-scale strength values of CSM and WR

等效材料参数		轴向拉伸应力/MPa	轴向压缩应力/MPa	横向拉伸应力/MPa	横向压缩应力/MPa	面内剪切应力/MPa	面外剪切应力/MPa
细观	CSM纤维束	1 523.0	1 547.2	116.5	221.0	30	60.5
细观	WR纱线	1 650.0	1 685.5	211.2	236.9	31.2	107.3
宏观	CSM单层板	79.0	117.5	79.0	117.5	33.0	33.0
宏观	WR单层板	118.0	91.5	118.0	91.5	43.0	57.0

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表 7 CSM和WR单层板的力学性能

Table 7. Mechanical properties of CSM and WR laminates

力学参数	CSM单层板		WR单层板
力学参数	计算值	规范值	计算值	规范值
极限拉伸强度/MPa	79	< 91	118	< 190
拉伸模量/MPa	6 529.5	< 6 950.0	14 228.5	< 14 500.0
极限压缩强度/MPa	117.5	< 121.5	91.5	< 147.0
极限剪切强度/MPa	33.0	< 64.4	57.0	< 78.0
剪切模量/MPa	2 473.3	< 2 801.0	2 055.0	< 3 090.0

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表 8 参数化建模参数

Table 8. Parametric modeling parameters

参数	数值
CSM纤维束含量	0.27，0.30，0.33，0.36，0.39
CSM纤维束直径/mm	0.15，0.17，0.19，0.21，0.23
WR编织角度/(º)	35，40，45，50，55
WR纱线横截面积/mm²	0.19，0.20，0.21，0.22，0.23

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参考文献(23)

[1]	BROCKENBROUGH J R, SURESH S, WIENECKE H A. Deformation of metal-matrix composites with continu-ous fibers: geometrical effects of fiber distribution and shape[J]. Acta Metallurgica et Materialia, 1991, 39(5): 735–752. doi: 10.1016/0956-7151(91)90274-5
[2]	BROWN H C, LEE H J, CHAMIS C C. Fiber shape effects on metal matrix composite behavior[C]//Internation-al SAMPE Symposium and Exhibition. Anaheim, CA: [s.n.], 1992.
[3]	吕毅, 吕国志, 吕胜利. 细观力学方法预测单向复合材料的宏观弹性模量[J]. 西北工业大学学报, 2006, 24(6): 787–790. doi: 10.3969/j.issn.1000-2758.2006.06.025 LÜ Y, LÜ G Z, LÜ S L. Semi-theoretical and engineering prediction of macroscopic elastic moduli of unidirectional composites[J]. Journal of Northwestern Polytechnical University, 2006, 24(6): 787–790 (in Chinese). doi: 10.3969/j.issn.1000-2758.2006.06.025
[4]	ZHANG B M, YANG Z, SUN X Y, et al. A virtual experimental approach to estimate composite mechanical properties: modeling with an explicit finite element method[J]. Computational Materials Science, 2010, 49(3): 645–651. doi: 10.1016/j.commatsci.2010.06.007
[5]	SHEN X L, GONG L D. Numerical modeling of braid-ed composites using energy method[C]//Proceedings of the ASME 2014 International Mechanical Engineering Congress and Exposition. Montreal, Canada: American Society of Mechanical Engineers, 2014: 1-6.
[6]	LIU Z, ZHU C, ZHU P. Generation of random fiber distributions for unidirectional fiber-reinforced composites based on particle swarm optimizer[J]. Polymer Composites, 2019, 40(4): 1643–1653. doi: 10.1002/pc.24912
[7]	YU X G, CUI J Z. The prediction on mechanical properties of 4-step braided composites via two-scale method[J]. Composites Science and Technology, 2007, 67(3/4): 471–480.
[8]	LI X, GUAN Z D, LI Z S, et al. A new stress-based multi-scale failure criterion of composites and its validation in open hole tension tests[J]. Chinese Journal of Aero-nautics, 2014, 27(6): 1430–1441. doi: 10.1016/j.cja.2014.10.009
[9]	LIANG B, ZHANG W Z, FENNER J S, et al. Multi-scale modeling of mechanical behavior of cured woven textile composites accounting for the influence of yarn angle variation[J]. Composites Part A: Applied Science and Manufacturing, 2019, 124: 105460. doi: 10.1016/j.compositesa.2019.05.028
[10]	ZHANG Y F, GUO Q W, CHEN X M, et al. Effect of apertures on tensile property of warp-reinforced 2.5D woven composites notched plates[J]. Composite Structures, 2020, 252: 112693. doi: 10.1016/j.compstruct.2020.112693
[11]	张宪丰. 平纹编织陶瓷基复合材料孔边应力多尺度分析[D]. 南昌: 南昌大学, 2021. ZHANG X F. Multi-scale analysis of hole edge stress in plain weave ceramic matrix composites[D]. Nanchang: Nanchang University, 2021 (in Chinese).
[12]	陈占光. 基于多尺度方法的含孔机织复合材料强度分析研究[D]. 哈尔滨: 哈尔滨工业大学, 2021. CHEN Z G. Strength analysis of woven composites with holes based on multi-scale method[D]. Harbin: Harbin Institute of Technology, 2021 (in Chinese).
[13]	梅志远. 舰船复合材料结构物应用工程技术特点及内涵分析[J]. 中国舰船研究, 2021, 16(2): 1–8. doi: 10.19693/j.issn.1673-3185.02098 MEI Z Y. Characteristic analysis and prospect of applied engineering technology for composite structures of naval ships[J]. Chinese Journal of Ship Research, 2021, 16(2): 1–8 (in Chinese). doi: 10.19693/j.issn.1673-3185.02098
[14]	施兴华, 任恒嘉, 许文强, 等. CFRP修复含裂纹加筋板极限强度仿真研究[J]. 中国舰船研究, 2019, 14(4): 47–54. doi: 10.19693/j.issn.1673-3185.01436 SHI X H, REN H J, XU W Q, et al. Simulation study on ultimate strength of CFRP-reinforced cracked stiffened panels[J]. Chinese Journal of Ship Research, 2019, 14(4): 47–54 (in Chinese). doi: 10.19693/j.issn.1673-3185.01436
[15]	LIOYD'S REGISTER. Rules and regulations for the classification of special service craft[M]. London, U. K: Marine & Shipping, 2020.
[16]	周琪琛. 二维编织陶瓷基复合材料的多尺度力学性能研究[D]. 哈尔滨: 哈尔滨工业大学, 2020. ZHOU Q C. Research on mechanical properties of 2D woven ceramic matrix composites based on multi-scale method[D]. Harbin: Harbin Institute of Technology, 2020 (in Chinese).
[17]	PAN Y, IORGA L, PELEGRI A A. Numerical generation of a random chopped fiber composite RVE and its elastic properties[J]. Composites Science and Technology, 2008, 68(13): 2792–2798. doi: 10.1016/j.compscitech.2008.06.007
[18]	OMAIREY S L, DUNNING P D, SRIRAMULA S. Development of an ABAQUS plugin tool for periodic RVE homogenisation[J]. Engineering with Computers, 2019, 35(2): 567–577. doi: 10.1007/s00366-018-0616-4
[19]	XIA Z H, ZHANG Y F, ELLYIN F. A unified periodical boundary conditions for representative volume elements of composites and applications[J]. International Journal of Solids and Structures, 2003, 40(8): 1907–1921. doi: 10.1016/S0020-7683(03)00024-6
[20]	ZHOU Y, LU Z X, YANG Z Y. Progressive damage analysis and strength prediction of 2D plain weave composites[J]. Composites Part B:Engineering, 2013, 47: 220–229. doi: 10.1016/j.compositesb.2012.10.026
[21]	HASHIN Z. Failure criteria for unidirectional fiber composites[J]. Journal of Applied Mechanics, 1980, 47(2): 329–334. doi: 10.1115/1.3153664
[22]	邵校. 短纤维增强复合材料细观建模与多尺度性能分析[D]. 大连: 大连理工大学, 2020. SHAO X. The micro-modeling and multi-scale performance analysis on the short fiber reinforced composites[D]. Dalian: Dalian University of Technology, 2020 (in Chinese).
[23]	伊鹏跃, 于哲峰, 汪海. 复合材料层压板低速冲击刚度退化仿真方案研究[J]. 力学季刊, 2012, 33(3): 469–475. doi: 10.3969/j.issn.0254-0053.2012.03.018 YI P Y, YU Z F, WANG H. Stiffness degradation methodology for low-velocity impact simulation in composite laminate[J]. Chinese Quarterly of Mechanics, 2012, 33(3): 469–475 (in Chinese). doi: 10.3969/j.issn.0254-0053.2012.03.018