Mean-field simulation of kink band formation in unidirectional composites
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摘要: 纤维扭结是单向碳纤维复合材料(UD-CFRP)在受轴向载荷压缩下，由于纤维初始扭转而引起的一种破坏机制。对于此问题，以往的文献中提出了宏观模拟、微观模拟及解析法，但都存在一定的局限性。宏观模拟精度低，微观模拟计算量大，解析法无法进行有效几何分析。在以前的文献中作者开发了一种非线性平均场脱粘模型来研究单向复合材料的非线性力学行为，该模型不仅考虑了平均非对称基体塑性，还考虑了纤维-基体界面的脱粘失效等非线性特性。本文将首次在多尺度层面上进行单向复合材料的纤维扭结仿真。利用扭结模型来定义纤维初始扭转角并结合非线性平均场脱粘模型来研究纤维具有初始扭转角的扭结过程及纤维不同初始扭转角对应力应变响应的影响。结果表明，与其他数值模型及解析模型相比，非线性平均场脱粘模型能够从多尺度的层面达到同等精度但能更高效地预测扭结带的形成过程。
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关键词:
- 纤维扭结 /
- 纤维初始扭转 /
- 非线性平均场脱粘模型 /
- 平均非对称基体塑性 /
- 纤维-基体界面脱粘
Abstract: Fibre kinking is a failure mechanism of unidirectional carbon fibre-reinforced polymer (UD-CFRP) composites under longitudinal compression due to initial fibre misalignment. In view of this problem, macroscopic, microscopic and analytical methods have been proposed in the literature, but they all have certain limitations. Macroscopic models have poor prediction accuracy, microscopic models have high computational costs, analytical models can not be used on real geometries. In our previous work, a non-linear mean-field debonding model (NMFDM) was proposed to study non-linear effects of UD composites. The model considers not only the average asymmetric matrix plasticity (AAMP) but also the debonding failure of fibre-matrix interface. In this work, multi-scale simulations of kink band formation in UD composites were firstly investigated. Whereby a fibre kinking model was combined with the NMFDM for studying kink band formation of UD composites. The kink process of fibres under initial misalignment and the effect of different initial misalignment on stress and strain response were studied. The results show that the NMFDM can predict kind band formation on the multi-scale level in comparison with other numerical models and analytical models with the same accuracy but more efficiently. -
图 1 单向碳纤维复合材料(UD-CFRP)力学响应
Figure 1. Mechanical response of unidirectional carbon fibre-reinforced polymer (UD-CFRP)
γ—Fiber torsion angle; β—Kink angle; w—Kink bandwidth
图 2 具有纤维初始扭转角的UD复合材料及受载后扭结带形成
Figure 2. UD composite with initial fibre misalignment and kink-band formation
l—Length of UD-CFRP before loading; γ0—Initial fiber torsion angle
图 3 单根纤维上的应力状态
Figure 3. Traction on single fibre
${\sigma }_{\text{I}}$—Normal stress; $ {\tau }_{\text{1}} $ and $ {\tau }_{\text{2}} $—Shear stresses; t—Stress interface vector; n—First shear direction; $ {\text{s}}_{\text{1}} $ and $ {\text{s}}_{\text{2}} $—Normal directions
图 4 AS4/8552碳纤维/环氧基UD复合材料试验剪切应力应变和基体的应力-应变曲线
Figure 4. Experimental shear stress-strain curve of AS4/8552 UD composite and stress-strain curve of the matrix
图 5 基体的平均剪切应力-应变和应力-应变曲线及AS4/8552复合材料面内剪切响应曲线
Figure 5. Average shear stress-strain, stress-strain curves of the matrix and in-plane shear response of the AS4/8552 composite
图 6 UD-CFRP在轴向载荷压缩下的有限元模拟
Figure 6. Simulation of a UD-CFRP composite under longitudinal compression
RP—Feference point; U—Displacement; Ur—Rotation degrees of freedom; V1—Longitudinal compressive velocity
图 7 纤维初始扭转角γ0为2°的AS4/8552复合材料压应力-应变曲线、纤维角度及基体的剪切应力-应变曲线
Figure 7. Compression stress-strain curve of AS4/8552 composite with initial fiber torsion angle
$ {\text{γ}}_{\text{0}}\text{}\text{=}\text{}\text{2°} $ , fibre angle and shear stress-strain curve of the matrix
图 8 AS4/8552复合材料四个阶段的纤维角度γ((a)~(b))、轴向应力
$ {\text{σ}}_{\text{11}} $ ((c)~(d))、面内剪切应力$ {\text{τ}}_{\text{12}} $ ((e)~(f))、基体的剪切应力$ {\text{τ}}_{\text{M12}} $ ((g)~(h))、基体的横向应力$ {\text{σ}}_{\text{M22}} $ ((i)~(j))和基体的等效塑性应变$ {{e}}_{\text{v}} $ 图((k)~(l))Figure 8. Contours of AS4/8552 composite with fibre angle γ ((a)-(b)), longitudinal stress
$ {\text{σ}}_{\text{11}} $ ((c)-(d)), in-plane shear stress$ {\text{τ}}_{\text{12}} $ ((e)-(f)), shear stress of the matrix$ {\text{τ}}_{\text{M12}} $ ((g)-(h)), transverse stress of matrix$ {\text{σ}}_{\text{M22}} $ ((i)-(j)) and equivalent plastic strain$ {{e}}_{\text{v}} $ ((k)-(l)) of the matrix at the four phases
图 9 非线性平均场脱粘模型(NMFDM)的模拟结果与其他模型关于AS4/8552复合材料的应力-应变曲线
Figure 9. Stress-strain curves of the simulated results of the non-linear mean-field debonding model (NMFDM) with other models regarding compressive of AS4/8552 composite
图 10 非线性平均场脱粘模型(NMFDM)的模拟结果与其他模型关于AS4/8552复合材料纤维角度-应变曲线
Figure 10. Angle-strain curves of the simulated results of the non-linear mean-field debonding model (NMFDM) with other models regarding fibre of AS4/8552 composite
图 11 AS4/8552复合材料在不同纤维初始扭转角下的压应力-应变曲线
Figure 11. Stress-strain curves of AS4/8552 composite under longitudinal with different initial misalignment
表 1 8552树脂基体材料参数
Table 1. Material parameters of the 8552 matrix
Parameter of the matrix $ {\kappa }_{\text{M}}^{\text{el}} $ $ {\kappa }_{\text{M}\text{i}}^{\text{pl}} $ $ {{E}}_{\text{M}} $/MPa $ {{v}}_{\text{M}} $ $ {{Y}}_{\text{0}{i}} $/MPa $ {{H}}_{\text{1}{i}} $/MPa $ {{b}}_{{i}} $ $ {{H}}_{\text{2}{i}} $/MPa For shear (i=1) 3.97×103 0.32 67 3525 58 1.78×10−4 For non-shear (i=2) 67 6025 54 1.75×10−5 Notes: $ {\kappa }_{\text{M}}^{\text{el}} $ and $ {\kappa }_{\text{M}}^{\text{pl}} $—Elastic set and plastic set of the matrix; $ {{E}}_{\text{M}} $—Modulus of elasticity of the matrix; $ {{v}}_{\text{M}} $—Poisson's ratio of the matrix; $ {{Y}}_{\text{0}} $—Initial yield stress;$ {{H}}_{\text{1}} $ and $ {{H}}_{\text{2}} $—Hardening parameters; b—Material parameter. 
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表 2 AS4纤维和纤维-基体界面材料参数
Table 2. Material parameters of the AS4 fibre and the fibre-matrix interface
Material parameter $ {{E}}_{\text{F0}} $/MPa $ {{c}}^{\text{F}} $ $ {{v}}_{\text{F}} $ $ \mu $ k $ {\sigma }_{\text{I}}^{\text{cr}} $/MPa α $ {\kappa }_{\text{F}} $ 2.4×105 18.7 0.23 — — — — $ {\kappa }_{\text{I}} $ — — — 0.41 0.21 22.5 1.22 Notes: $ {\kappa }_{\text{F}} $ and $ {\kappa }_{\text{I}} $—Parameters sets of the fibre and the interface; $ {{E}}_{\text{F0}} $—Initial fibre stiffness; $ {{c}}^{\text{F}} $—Constant; $ {{v}}_{\text{F}} $—Poisson's ratio of the fibre; $ \mu $, k—Material parameters; $ {\sigma }_{\text{I}}^{\text{cr}} $—Equivalent interface strength; α—Constant.
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