混杂纤维网络失效机制

杨伟超; 马勇; 张峰; 益小苏; 赵丽滨; 陈玉丽

doi:10.13801/j.cnki.fhclxb.20220719.002

混杂纤维网络失效机制

doi: 10.13801/j.cnki.fhclxb.20220719.002

杨伟超^1,,
马勇^1, ,,
张峰¹,
益小苏²,
赵丽滨^{3, 4},
陈玉丽^1, ,

1.
北京航空航天大学　航空科学与工程学院，北京 100191
2.
宁波诺丁汉大学　科学与工程学院，宁波 315100
3.
河北工业大学机械工程学院　河北省跨尺度智能装备技术重点实验室，天津 300401
4.
北京航空航天大学　宇航学院，北京 100191

基金项目: 国家自然科学基金(12172026)

详细信息

通讯作者:
马勇，博士，研究方向为复合材料力学　E-mail：mayong20076@buaa.edu.cn

陈玉丽，博士，教授，博士生导师，研究方向为复合材料/结构力学　E-mail：yulichen@buaa.edu.cn

中图分类号: TB332
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出版历程
- 收稿日期: 2022-06-10
- 修回日期: 2022-07-03
- 录用日期: 2022-07-08
- 网络出版日期: 2022-07-21
- 刊出日期: 2022-08-22

Failure mechanism of hybrid fiber networks

YANG Weichao^1
,,
MA Yong^{1
, ,},
ZHANG Feng¹,
YI Xiaosu²,
ZHAO Libin^{3, 4},
CHEN Yuli^{1
, ,}

1.
School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China
2.
Faculty of Science and Engineering, University of Nottingham Ningbo China, Ningbo 315100, China
3.
Hebei Key Laboratory of Trans-Scale Intelligent Equipment Technology, School of Mechanical Engineering, Hebei University of Technology, Tianjin 300401, China
4.
School of Astronautics, Beihang University, Beijing 100191, China

摘要

摘要: 纤维网络材料是一类广泛存在且具有重要应用前景的多功能轻质材料。目前研究主要集中于单一纤维网络材料，但实际应用中大部分纤维网络都是由不同性质纤维构成的混杂纤维网络，其性能和功能的设计空间更大，但失效机制也更复杂。为了进一步提升纤维网络材料的力学性能，深入研究混杂纤维网络的失效过程及失效机制非常重要。为此，本文建立了综合考虑纤维和纤维间连接力学性能的混杂纤维网络模型，系统地研究了混杂纤维网络的失效过程，并讨论分析了纤维混杂比例、纤维间连接强度及纤维总体积分数等因素的影响。结果表明，对于典型混杂纤维网络而言，随着纤维组分的变化，网络的失效存在连接损伤主导、连接与纤维损伤共同主导及纤维损伤主导三类不同的失效模式。其中，由连接和纤维损伤共同主导的失效，损伤分散于整个网络，连接和纤维会表现出协同作用，因此网络具有更好的韧性和强度。由此可见，混杂纤维网络力学性能的设计空间远大于单一纤维网络，具有更广阔的应用前景。
- 混杂纤维网络 /
- 复合材料 /
- 强度 /
- 韧性 /
- 失效机制
Abstract: Fiber network material is a kind of multifunctional lightweight material which exists widely and has important application prospect. At present, researches mainly focus on networks consisting of one type of fibers. However, in practice, most fiber networks are hybrid fiber networks composed of fibers with different properties, which have larger performance and function design space but more complex failure mechanism. In order to further improve the mechanical properties of fiber networks, it is very important to study the failure process and failure mechanism of hybrid fiber networks. Therefore, the hybrid fiber network model was established in this paper to take account of both the mechanical properties of fibers and the inter-fiber connections. Based on the model, the failure process of hybrid fiber networks was systematically studied, and the effects of the fiber mixture ratio, the strength of inter-fiber connections and the total fiber volume fraction were analyzed. The results show that for typical hybrid fiber networks, there are three failure modes: inter-fiber connection dominated failure, inter-fiber connection and fiber co-dominated failure, and fiber dominated failure, with the variation of fiber mixture ratio. When the failure is co-dominated by the connection and fiber damages, the damages disperse throughout the network, and the network presents better toughness and strength. Therefore, the design space of mechanical properties of hybrid fiber network is much larger than that of networks consisting of only one type of fibers, and the hybrid network exhibits a wider application prospect.
- hybrid fiber networks /
- composite materials /
- strength /
- toughness /
- failure mechanis

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图 1 混杂纤维网络模型：(a) 网络代表性面积单元(RAE)示意图；(b) 周期性代表单元建模过程示意图

Figure 1. Hybrid fiber networks: (a) Representative area element (RAE) of fiber networks; (b) Schematic diagram of the modeling process of a periodic RAE

L_x×L_y—Size of the representative area element; θ—Angle between the fiber and x-axis; A', B'—Corresponding point of A, B for the period boundray; A2, B2 and C2—Corresponding point of A1, B1 and C1

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图 2 纤维总体积分数V_f=40vol%时不同低刚度L纤维体积占比V_fL对应的应力-应变曲线 (a) 和网络韧性随低刚度L纤维体积占比V_fL的变化规律 (b)

Figure 2. Stress-strain curves of networks with different volume fractions of the L fiber V_fL(a) and toughness with variable volume fractions of the L fiber V_fL for the networks (b) with the total fiber volume fraction V_f=40vol%

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图 3 低刚度L纤维体积占比V_fL=0vol%时纤维网络应力-应变曲线和损伤-应变曲线 (a)、网络应力${\sigma _{{\text{net}}}} = \sigma _{{\text{net}}}^{\max }$(A点)时的损伤分布 (b) 和网络应力${\sigma _{{\text{net}}}}{\text{ = }}0.7\sigma _{{\text{net}}}^{{\text{max}}}$(B点)时的损伤分布 (c)

Figure 3. Stress-strain curve and damage fraction-strain curves (a), damage distributions when the stress of the network ${\sigma _{{\text{net}}}} = \sigma _{{\text{net}}}^{\max }$ (point A) (b) and damage distributions when ${\sigma _{{\text{net}}}}{\text{ = }}0.7\sigma _{{\text{net}}}^{{\text{max}}}$ (point B) (c) for the networks with the volume fraction of the L fiber V_fL=0vol%

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图 4 低刚度L纤维体积占比V_fL=40vol%时纤维网络应力-应变曲线和损伤-应变曲线 (a)、网络应力${\sigma _{{\text{net}}}} = \sigma _{{\text{net}}}^{\max }$(A点)时损伤分布 (b) 及网络应力${\sigma _{{\text{net}}}}{\text{ = }}0.7\sigma _{{\text{net}}}^{{\text{max}}}$(B点)时损伤分布 (c)

Figure 4. Stress-strain curve and damage fraction-strain curves (a), damage distributions when the stress of the network ${\sigma _{{\text{net}}}} = \sigma _{{\text{net}}}^{\max }$(point A) (b) and damage distributions when ${\sigma _{{\text{net}}}}{\text{ = }}0.7\sigma _{{\text{net}}}^{{\text{max}}}$ (point B) (c) for the networks with the volume fraction of the L fiber V_fL=40vol%

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图 5 低刚度L纤维体积占比V_fL=80vol%时纤维网络应力-应变曲线和损伤-应变曲线 (a)、网络应力${\sigma _{{\text{net}}}} = \sigma _{{\text{net}}}^{\max }$(A点)时损伤分布 (b) 和网络应力${\sigma _{{\text{net}}}}{\text{ = }}0.7\sigma _{{\text{net}}}^{{\text{max}}}$(B点)时损伤分布 (c)

Figure 5. Stress-strain curve and damage fraction-strain curves (a), damage distributions when the stress of the network ${\sigma _{{\text{net}}}} = \sigma _{{\text{net}}}^{\max }$ (point A) (b) and damage distributions when ${\sigma _{{\text{net}}}}{\text{ = }}0.7\sigma _{{\text{net}}}^{{\text{max}}}$(point B) (c) for the networks with the volume fraction of the L fiber V_fL=80vol%

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图 6 混杂纤维网络刚度 (a) 和强度 (b) 随低刚度L纤维体积占比V_fL的变化规律(纤维总体积分数V_f=40vol%)

Figure 6. Modulus (a) and strength (b) of networks with variable volume fractions of the L fiber V_fL for the networks with the total fiber volume fraction V_f=40vol%

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图 7 混杂纤维网络中LL连接强度变化时网络强度随低刚度L纤维体积占比V_fL的变化规律(纤维总体积分数V_f=40vol%)

Figure 7. Strength of networks with variable strength of the LL connection and variable volume fractions of the L fiber (Total fiber volume fraction V_f=40vol%)

${\hat F_{{\text{c-HL}}}} $—Dimensionless strength of HH connection; ${\hat F_{{\text{c-HH}}}} $—Dimensionless strength of LL connection

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图 8 纤维总体积分数V_f=40vol%时不同无量纲强度${\hat F_{{\rm{c - LL}}}}$及L纤维体积占比V_fL下纤维网络应力-应变曲线和损伤-应变曲线：(a) ${\hat F_{{\rm{c - LL}}}} = 0.17$，V_fL=20vol%；(b) ${\hat F_{{\rm{c - LL}}}} = 0.17$，V_fL =100vol%；(c) ${\hat F_{{\rm{c - LL}}}} = 0.3$，V_fL =20vol%；(d) ${\hat F_{{\rm{c - LL}}}} = 0.3$，V_fL =40vol%

Figure 8. Stress-strain curves and damage fraction-strain curves of fiber networks with variable dimensionless connection strength ${\hat F_{{\rm{c - LL}}}}$ and volume fractions of the L fiber V_fL for the total fiber volume fraction V_f=40vol%: (a) ${\hat F_{{\rm{c - LL}}}} = 0.17$, V_fL=20vol%; (b) ${\hat F_{{\rm{c - LL}}}} = 0.17$, V_fL=100vol%; (c) ${\hat F_{{\rm{c - LL}}}} = 0.3$, V_fL=20vol%; (d) ${\hat F_{{\rm{c - LL}}}} = 0.3$, V_fL=40vol%

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图 9 纤维总体积分数V_f不同时纤维网络的模量 (a) 和强度 (b) 随L纤维体积占比V_fL的变化

Figure 9. Modulus (a) and strength (b) of fiber networks with variable volume fractions of the L fiber V_fL for networks with different total fiber volume fractions V_f

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图 10 纤维总体积分数V_f从30vol%至50vol%变化时单一纤维网络和混杂纤维网络的模量-强度可设计空间 (a) 和强度-韧性可设计空间 (b) (区域边界由线性插值获得)

Figure 10. Modulus-strength phase diagram (a) and strength-toughness phase diagram of networks (b) for the fiber networks with the total fiber volume fraction V_f changing from 30vol% to 50vol% (Region boundary is obtained by linear interpolation)

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表 1 纤维的力学及几何参数

Table 1. Mechanical and geometric parameters for fibers

Fiber type	Modulus E_f/GPa	$\rm Strength\;\sigma _{\text{f} }^{\text{b} } /MPa$	Length l_f/mm	Diameter d_f/μm
H	134	3000	1.0	10.0
L	35	150	0.5	7.1

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表 2 纤维间连接的本构和参数

Table 2. Constitutive relations and the relative parameters for connections

	Type	Stiffness k_c/(N·mm⁻¹)	Failure load $ F_{\text{c}}^{\text{b}} $/mN
	HH	8.7	1.0
	HL	8.7	4.8
	LL	8.7	4.8
Notes: Δu_c—Relative displacement of two nodes of a connected element; $F^{\rm{b}}_{\text{ c-LL}} $, $F^{\rm{b}}_{\text{ c-HL}} $, $F^{\rm{b}}_{\text{c-HH}} $—Critical failure load of LL connection, HL connection and HH connection.

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