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Prediction of Process-Induced Distortions in L-Shaped Composite Profiles Using Path-Dependent Constitutive Law

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Abstract

In this paper, the corner spring-in angles of AS4/8552 L-shaped composite profiles with different thicknesses are predicted using path-dependent constitutive law with the consideration of material properties variation due to phase change during curing. The prediction accuracy mainly depends on the properties in the rubbery and glassy states obtained by homogenization method rather than experimental measurements. Both analytical and finite element (FE) homogenization methods are applied to predict the overall properties of AS4/8552 composite. The effect of fiber volume fraction on the properties is investigated for both rubbery and glassy states using both methods. And the predicted results are compared with experimental measurements for the glassy state. Good agreement is achieved between the predicted results and available experimental data, showing the reliability of the homogenization method. Furthermore, the corner spring-in angles of L-shaped composite profiles are measured experimentally and the reliability of path-dependent constitutive law is validated as well as the properties prediction by FE homogenization method.

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Acknowledgments

This work reported here was part of the Fundamental Research Funds for the Central Universities supported by Wuhan University of Technology.

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Authors and Affiliations

  1. State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, 122 Luoshi Road, Wuhan, 430070, Hubei, China

    Anxin Ding, Shuxin Li, Jihui Wang, Aiqing Ni, Liangliang Sun & Lei Chang

  2. Department of Mechanical Engineering, University of Bristol, Bristol, BS8 1TR, UK

    Shuxin Li

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  1. Anxin Ding
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Correspondence to Shuxin Li or Aiqing Ni.

Appendix

Appendix

The AS4 fiber mechanical properties are assumed to be transversely in the SCM. Thus five independent elastic constants for fiber are present, including Young’s modulus and the Poisson’s ratio in the transverse direction (E 22f and ν 23f ), Young’s modulus and the Poisson’s ratio in the longitudinal direction (E 11f and ν 12f ) and the shear modulus in the longitudinal direction (G 12f ). The SCM proposed by Bogetti and Gillesoie [10] are given as follows:

$$ \begin{array}{l}{E}_{11}={E}_{11f}{V}_f+{E}_r\left(1-{V}_f\right)+\left[\frac{4\left({\nu}_r-{\nu^2}_{12f}\right){k}_f{k}_r{G}_r\left(1-{V}_f\right){V}_f}{\left({k}_f+{G}_r\right){k}_r+\left({k}_f-{k}_r\right){G}_r{V}_f}\right]\\ {}{E}_{22}={E}_{33}=\frac{1}{{\left(4{k}_T\right)}^{-1}+{\left(4{G}_{23}\right)}^{-1}+\left({\nu}_{12}^2/{E}_{11}\right)}\\ {}{G}_{12}={G}_{13}={G}_r\left[\frac{\left({G}_{12f}+{G}_r\right)+\left({G}_{12f}-{G}_r\right){V}_f}{\left({G}_{12f}+{G}_r\right)-\left({G}_{12f}-{G}_r\right){V}_f}\right]\\ {}{G}_{23}=\frac{G_r\left[{k}_r\left({G}_r+{G}_{23f}\right)+2{G}_{23f}{G}_r+{k}_r\left({G}_{23f}-{G}_r\right){V}_f\right]}{k_r\left({G}_r+{G}_{23f}\right)++2{G}_{23f}{G}_r-\left({k}_r+2{G}_r\right)\left({G}_{23f}-{G}_r\right){V}_f}\\ {}{\nu}_{12}={\nu}_{13}={\nu}_{12f}{V}_f+{\nu}_r\left(1-{V}_f\right)+\left[\frac{\left({\nu}_r-{\nu}_{12f}\right)\left({k}_r-{k}_f\right){G}_r\left(1-{V}_f\right){V}_f}{\left({k}_f+{G}_r\right){k}_r+\left({k}_f-{k}_r\right){G}_r{V}_f}\right]\\ {}{\nu}_{23}=\frac{2{E}_{11}{k}_T-{E}_{11}{E}_{22}-4{\nu}_{12}^2{k}_T{E}_{22}}{2{E}_{11}{k}_T}\end{array} $$
(A.1)

where k f k r and k T are the isotropic plane strain bulk modulus for fiber, resin and composite materials, respectively. They can be defined by:

$$ \begin{array}{l}{k}_f=\frac{E_{11f}}{2\left(1-{\nu}_{12f}-2{\nu^2}_{12f}\right)}\kern1.50em \\ {}\kern0.5em {k}_{\mathrm{r}}=\frac{E_{\mathrm{r}}}{2\left(1-{\nu}_{\mathrm{r}}-2{\nu}_{\mathrm{r}}^2\right)}\kern1em \\ {}{k}_T=\frac{\left({k}_f+{G}_r\right){k}_{\mathrm{r}}+\left({k}_f-{k}_{\mathrm{r}}\right){G}_r{V}_f}{\left({k}_f+{G}_r\right)-\left({k}_f-{k}_{\mathrm{r}}\right){V}_f}\end{array} $$
(A.2)

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Ding, A., Li, S., Wang, J. et al. Prediction of Process-Induced Distortions in L-Shaped Composite Profiles Using Path-Dependent Constitutive Law. Appl Compos Mater 23, 1027–1045 (2016). https://doi.org/10.1007/s10443-016-9501-8

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