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Finite Element Analysis of Thermo-Mechanical Properties of 3D Braided Composites

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Abstract

This paper presents a modified finite element model (FEM) to investigate the thermo-mechanical properties of three-dimensional (3D) braided composite. The effective coefficients of thermal expansion (CTE) and the meso-scale mechanical response of 3D braided composites are predicted. The effects of the braiding angle and fiber volume fraction on the effective CTE are evaluated. The results are compared to the experimental data available in the literature to demonstrate the accuracy and reliability of the present method. The tensile stress distributions of the representative volume element (RVE) are also outlined. It is found that the stress of the braiding yarn has a significant increase with temperature rise; on the other hand, the temperature change has an insignificant effect on the stress of the matrix. In addition, a rapid decrease in the tensile strength of 3D braided composites is observed with the increase in temperature. It is revealed that the thermal conditions have a significant effect on the strength of 3D braided composites. The present method provides an effective tool to predict the stresses of 3D braided composites under thermo-mechanical loading.

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Acknowledgments

The authors would like to thank the Foundation of Heilongjiang Department of Education (12521102), the National Natural Science Foundation of China (11272110, 9101602, 10972070) and the Science and Technology Innovation Team in University of Heilongjiang Province.

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Authors and Affiliations

  1. Department of Engineering Mechanics, Harbin University of Science and Technology, Harbin, 150080, People’s Republic of China

    Li-li Jiang, Guo-dong Xu, Su Cheng, Xia-mei Lu & Tao Zeng

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  1. Li-li Jiang
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  2. Guo-dong Xu
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  3. Su Cheng
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  4. Xia-mei Lu
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  5. Tao Zeng
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Correspondence to Tao Zeng.

Appendix A

Appendix A

The stiffness matrix of the braiding yarns is

$$ \left[{D}_Y\right]={\left[T\right]}^T\left[{D}_Y^{\prime}\right]\left[T\right] $$
(A-1)

where [D ′ Y ] is the stiffness matrix referred to the material coordinate system

$$ \left[{D}_Y^{\prime}\right]=={\left[\begin{array}{cccccc}\hfill \frac{1}{E_{11}}\hfill & \hfill -\frac{\gamma_{12}}{E_{11}}\hfill & \hfill -\frac{\gamma_{31}}{E_{33}}\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill -\frac{\gamma_{12}}{E_{11}}\hfill & \hfill \frac{1}{E_{11}}\hfill & \hfill -\frac{\gamma_{31}}{E_{33}}\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill -\frac{\gamma_{31}}{E_{33}}\hfill & \hfill -\frac{\gamma_{31}}{E_{33}}\hfill & \hfill \frac{1}{E_{33}}\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill \frac{1}{G_{31}}\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill \frac{1}{G_{31}}\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill \frac{1}{G_{12}}\hfill \end{array}\right]}^{-1} $$
(A-2)

[T] is the transformation matrix

$$ \left[T\right]=\left[\begin{array}{cccccc}\hfill {l}_1^2\hfill & \hfill {m}_1^2\hfill & \hfill {n}_1^2\hfill & \hfill 2{m}_1{n}_1\hfill & \hfill 2{n}_1{l}_1\hfill & \hfill 2{l}_1{m}_1\hfill \\ {}\hfill {l}_2^2\hfill & \hfill {m}_2^2\hfill & \hfill {n}_2^2\hfill & \hfill 2{m}_2{n}_2\hfill & \hfill 2{n}_2{l}_2\hfill & \hfill 2{l}_2{m}_2\hfill \\ {}\hfill {l}_3^2\hfill & \hfill {m}_3^2\hfill & \hfill {n}_3^2\hfill & \hfill 2{m}_3{n}_3\hfill & \hfill 2{n}_3{l}_3\hfill & \hfill 2{l}_3{m}_3\hfill \\ {}\hfill {l}_2{l}_3\hfill & \hfill {m}_2{m}_3\hfill & \hfill {n}_2{n}_3\hfill & \hfill {m}_2{m}_3+{m}_3{n}_2\hfill & \hfill {n}_2{l}_3+{n}_3{l}_2\hfill & \hfill {l}_2{m}_3+{l}_3{m}_2\hfill \\ {}\hfill {l}_3{l}_1\hfill & \hfill {m}_3{m}_1\hfill & \hfill {n}_3{n}_1\hfill & \hfill {m}_3{n}_1+{m}_1{n}_3\hfill & \hfill {n}_3{l}_1+{n}_1{l}_3\hfill & \hfill {l}_3{m}_1+{l}_1{m}_3\hfill \\ {}\hfill {l}_1{l}_2\hfill & \hfill {m}_1{m}_2\hfill & \hfill {n}_1{n}_2\hfill & \hfill {m}_1{n}_2+{m}_2{n}_1\hfill & \hfill {n}_1{l}_2+{n}_2{l}_1\hfill & \hfill {l}_1{m}_2+{l}_2{m}_1\hfill \end{array}\right] $$
(A-3)

where (l i , m i , n i ) (i = 1, 2, 3) are the direction cosines between the axial direction of the braiding yarns and axis of the global coordinate system (X-Y-Z).

The stiffness matrix of the resin is

$$ \left[{D}_M\right]==\left[\begin{array}{cccccc}\hfill \frac{1}{E_m}\hfill & \hfill -\frac{\gamma_m}{E_m}\hfill & \hfill -\frac{\gamma_m}{E_m}\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill -\frac{\gamma_m}{E_m}\hfill & \hfill \frac{1}{E_m}\hfill & \hfill -\frac{\gamma_m}{E_m}\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill -\frac{\gamma_m}{E_m}\hfill & \hfill -\frac{\gamma_m}{E_m}\hfill & \hfill \frac{1}{E_m}\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill \frac{2\left(1+{\gamma}_m\right)}{E_m}\hfill & \hfill 0\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill \frac{2\left(1+{\gamma}_m\right)}{E_m}\hfill & \hfill 0\hfill \\ {}\hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill 0\hfill & \hfill \frac{2\left(1+{\gamma}_m\right)}{E_m}\hfill \end{array}\right] $$
(A-4)

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Jiang, Ll., Xu, Gd., Cheng, S. et al. Finite Element Analysis of Thermo-Mechanical Properties of 3D Braided Composites. Appl Compos Mater 21, 325–340 (2014). https://doi.org/10.1007/s10443-013-9339-2

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