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。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。利用扭结模型对以前作者本人开发的非线性平均场脱粘模型进行扩展来定义纤维初始扭转角从而研究纤维具有初始扭转角的扭结过程，以及纤维不同初始扭转角对应力应变响应的影响。研究结果表明(如 图1 所示)，非线性平均场脱粘模型与其他数值模型以及解析模型相比，能够从多尺度的层面有效地预测单向碳纤维复合材料在轴向载荷压缩下的纤维扭结的演化过程。此仿真方法相较于以往的文献中提出的宏观模拟、微观模拟以及解析法，达到同等精度但能更高效的优势，解决了在构件尺度上如何准确的预测纤维扭结失效的问题。非线性平均场脱粘模型对纤维扭结的预测结果(a)非线性平均场脱粘模型的模拟结果与其他模型关于应力-应变 $ {\text{σ}}_{\text{c}} $ -$ {{ \varepsilon }}_{\text{c}} $ 作对比(b)单向碳纤维复合材料在不同纤维初始扭转角下的压应力-应变$ {\text{σ}}_{\text{c}} $ -$ {{ \varepsilon }}_{\text{c}} $ 曲线-
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 2 具有纤维初始扭转角的单向复合材料以及受载后扭结带形成
Figure 2. UD composite with initial fibre misalignment and kink-band formation
图 3 单根纤维上的应力状态
Figure 3. Traction on single fibre
$ {\text{σ}}_{\text{I}} $ is normal stress; $ {\text{τ}}_{\text{1}} $ and $ {\text{τ}}_{\text{2}} $ are the shear stresses; t is the stress interface vector; n is the first shear direction; $ {\text{s}}_{\text{1}} $ and $ {\text{s}}_{\text{2}} $ are the 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-应变曲线以及AS4/8552复合材料面内剪切响应曲线
Figure 5. Average shear stress-strain, stress-strain curve 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
图 7 纤维初始扭转角为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 fibre misalignment
$ {\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，轴向应力
$ {\text{σ}}_{\text{11}} $ ，面内剪切应力$ {\text{τ}}_{\text{12}} $ ，基体的剪切应力$ {\text{τ}}_{\text{M12}} $ ，基体的横向应力$ {\text{σ}}_{\text{M22}} $ 和基体的等效塑性应变$ {\text{e}}_{\text{v}} $ 图Figure 8. Contours of AS4/8552 composite with fibre angle γ，longitudinal stress
$ {\text{σ}}_{\text{11}} $ ，in-plane shear stress$ {\text{τ}}_{\text{12}} $ ，shear stress of the matrix$ {\text{τ}}_{\text{M12}} $ , transverse stress of matrix$ {\text{σ}}_{\text{M22}} $ and equivalent plastic strain$ {\text{e}}_{\text{v}} $ of the matrix at the four phases
图 9 非线性平均场脱粘模型(NMFDM)的模拟结果与其它模型关于AS4/8552复合材料应力-应变
$ {\text{σ}}_{\text{c}} $ -$ {{ \varepsilon }}_{\text{c}} $ 作对比Figure 9. Comparison of the simulated results of the non-linear mean-field debonding model (NMFDM) with other models regarding compressive stress vs. compressive strain of AS4/8552 composite
图 10 非线性平均场脱粘模型(NMFDM)的模拟结果与其它模型关于AS4/8552复合材料纤维角度-应变γ-
$ {{ \varepsilon }}_{\text{c}} $ 对比Figure 10. Comparison of the simulated results of the non-linear mean-field debonding model (NMFDM) with other models regarding fibre angle vs. compressive strain 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
$ {\text{σ}}_{\text{c}} $ -$ {{ \varepsilon }}_{\text{c}} $ 曲线Figure 11. Compressive 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 $ {\text{к}}_{\text{M}}^{\text{el}} $ $ {\text{к}}_{\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: $ {\text{к}}_{\text{M}}^{\text{el}} $ and $ {\text{к}}_{\text{M}}^{\text{pl}} $ are the elastic set and plastic set of the matrix; $ {\text{E}}_{\text{M}} $ is the modulus of elasticity of the matrix; $ {\text{v}}_{\text{M}} $ is the Poisson's ratio of the matrix; $ {\text{Y}}_{\text{0}} $ is the initial yield stress;$ {\text{H}}_{\text{1}} $ and $ {\text{H}}_{\text{2}} $ are the hardening parameters; b is the 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}} $ $ \text{μ} $ k $ {\text{σ}}_{\text{I}}^{\text{cr}} $/MPa α $ {\text{к}}_{\text{F}} $ 2.4×105 18.7 0.23 $ {\text{к}}_{\text{I}} $ 0.41 0.21 22.5 1.22 Notes: $ {\text{к}}_{\text{F}} $ and $ {\text{к}}_{\text{I}} $ are the parameters sets of the fibre and the interface; $ {\text{E}}_{\text{F0}} $ is the initial fibre stiffness; $ {\text{c}}^{\text{F}} $ is a constant; $ {\text{v}}_{\text{F}} $ is the Poisson's ratio of the fibre; $ \text{μ} $ and k are material parameters; $ {\text{σ}}_{\text{I}}^{\text{cr}} $ denotes the equivalent interface strength; α is a constant.
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