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Mechanical Analysis of Thick-walled Filament Wound Composite Pipes under Pure Torsion Load: Safety Zones and Optimal Design

Applied Composite Materials volume 30, pages 485–505 (2023)Cite this article

Abstract

Thick-walled composite pipes made of fibre reinforced laminate are good candidates to replace traditional metal counterparts in fabricating such as drive shafts and drilling pipes. In this paper, the behaviour of thick-walled composite pipes subjected to torsion load is considered. The developed finite elements model and three-dimensional elasticity solution are presented to analyse the stress state of the pipe. The modified Tsai-Hill failure criterion is adapted for the stress analysis. The distribution of failure coefficients through the pipe thickness for different lay-ups is calculated. The parametric study is carried out to investigate the effects of fibre orientations, stacking sequences, layer thicknesses and the magnitudes of torsion on the pipe performance. The torsional response shows sensitivity to changes in winding angle. Although 45° reinforcement angle provides the highest torsional stiffness, the results indicate that it is not always the optimal solution due to the torsional strength. For multi-layered composite pipes, the optimum solution for the winding angle depends on the configurations and the stacking sequences. Finally, a new approach for pipe lay-up design to withstand the applied load is suggested, introducing ‘safety zones’, which represents reasonable fibre orientation to resist torsion load.

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Authors and Affiliations

  1. School of Engineering, University of Aberdeen, Aberdeen, AB24 3UE, UK

    Tianyu Wang, Marina Menshykova, Oleksandr Menshykov & Naomi K. Bokedal

  2. School of Engineering and Physical Sciences, Heriot Watt University, Edinburgh, EH14 4AS, UK

    Igor A. Guz

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  1. Tianyu Wang
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  2. Marina Menshykova
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  3. Oleksandr Menshykov
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  4. Igor A. Guz
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Correspondence to Marina Menshykova.

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Appendix

Appendix

$$\Psi \left(\mathrm{1,1}\right)=\left({\overline{C}}_{23}^{\left(1\right)}+\beta \left(1\right)\times {\overline{C}}_{33}^{\left(1\right)}\right)\times {r}_{1}^{\beta \left(1\right)-1}$$
$$\Psi \left(1,N+1\right)=\left({\overline{C}}_{23}^{\left(1\right)}-\beta \left(1\right)\times {\overline{C}}_{33}^{\left(1\right)}\right)\times {r}_{1}^{-\beta \left(1\right)-1}$$
$$\Psi \left(\mathrm{1,2}\times N+1\right)={\overline{C}}_{13}^{\left(1\right)}+{\alpha }_{1}^{\left(1\right)}\times \left({\overline{C}}_{23}^{\left(1\right)}+{\overline{C}}_{33}^{\left(1\right)}\right)$$
$$\Psi \left(\mathrm{1,2}\times N+2\right)=\left({\overline{C}}_{36}^{\left(1\right)}+{\alpha }_{2}^{\left(1\right)}\times \left({\overline{C}}_{23}^{\left(1\right)}+2\times {\overline{C}}_{33}^{\left(1\right)}\right)\right)*{r}_{1}$$
$$\Psi \left(N+\mathrm{1,1}\right)=\left({\overline{C}}_{23}^{\left(1\right)}+\beta \left(1\right)\times {\overline{C}}_{33}^{\left(1\right)}\right)\times {r}_{2}^{\beta \left(1\right)-1}$$
$$\Psi \left(N+\mathrm{1,2}\right)=-\left({\overline{C}}_{23}^{\left(2\right)}+\beta \left(2\right)\times {\overline{C}}_{33}^{\left(2\right)}\right)\times {r}_{2}^{\beta \left(2\right)-1}$$
$$\Psi \left(N+1,N+1\right)=\left({\overline{C}}_{23}^{\left(1\right)}-\beta \left(1\right)\times {\overline{C}}_{33}^{\left(1\right)}\right)\times {r}_{2}^{-\beta \left(1\right)-1}$$
$$\Psi \left(N+1,N+2\right)=-\left({\overline{C}}_{23}^{\left(2\right)}+\beta \left(2\right)\times {\overline{C}}_{33}^{\left(2\right)}\right)\times {r}_{2}^{-\beta \left(2\right)-1}$$
$$\Psi \left(N+\mathrm{1,2}\times N+1\right)={\overline{C}}_{13}^{\left(1\right)}-{\overline{C}}_{13}^{\left(2\right)}+{\alpha }_{1}^{\left(1\right)}\times \left({\overline{C}}_{23}^{\left(1\right)}+{\overline{C}}_{33}^{\left(1\right)}\right)-{\alpha }_{1}^{\left(2\right)}\times \left({\overline{C}}_{23}^{\left(2\right)}+{\overline{C}}_{33}^{\left(2\right)}\right)$$
$$\Psi \left(N+\mathrm{1,2}\times N+2\right)=\left({\overline{C}}_{36}^{\left(1\right)}-{\overline{C}}_{36}^{\left(2\right)}+{\alpha }_{2}^{\left(1\right)}\times \left({\overline{C}}_{23}^{\left(1\right)}+2\times {\overline{C}}_{33}^{\left(1\right)}\right)-{\alpha }_{2}^{\left(2\right)}\times \left({\overline{C}}_{23}^{\left(2\right)}+2\times {\overline{C}}_{33}^{\left(2\right)}\right)\right){\times r}_{2}$$
$$\Psi \left(2\times N,N\right)=\left({\overline{C}}_{23}^{\left(N\right)}+\beta \left(N\right)\times {\overline{C}}_{33}^{\left(N\right)}\right)\times {r}_{N+1}^{\beta \left(N\right)-1}$$
$$\Psi \left(2\times N,2\times N\right)=\left({\overline{C}}_{23}^{\left(N\right)}-\beta \left(N\right)\times {\overline{C}}_{33}^{\left(N\right)}\right)\times {r}_{N+1}^{-\beta \left(N\right)-1}$$
$$\Psi \left(2\times N,2\times N+1\right)={\overline{C}}_{13}^{\left(N\right)}+{\alpha }_{1}^{\left(N\right)}\times \left({\overline{C}}_{23}^{\left(N\right)}+{\overline{C}}_{33}^{\left(N\right)}\right)$$
$$\Psi \left(2\times N,2\times N+2\right)=\left({\overline{C}}_{36}^{\left(N\right)}+{\alpha }_{2}^{\left(N\right)}\times \left({\overline{C}}_{23}^{\left(N\right)}+2\times {\overline{C}}_{33}^{\left(N\right)}\right)\right)*{r}_{N+1}$$
$$\Psi \left(k,k-1\right)={r}_{k}^{\beta \left(k-1\right)}$$
$$\Psi \left(k,k\right)={-r}_{k}^{\beta \left(k\right)}$$
$$\Psi \left(k,k+N-1\right)={r}_{k}^{-\beta \left(k-1\right)}$$
$$\Psi \left(k,k+N\right)={-r}_{k}^{-\beta \left(k\right)}$$
$$\Psi \left(k,2\times N+1\right)=\left({\alpha }_{1}^{\left(k-1\right)}-{\alpha }_{1}^{\left(k\right)}\right)\times {r}_{k}$$
$$\Psi \left(k,2\times N+2\right)=\left({\alpha }_{2}^{\left(k-1\right)}-{\alpha }_{2}^{\left(k\right)}\right)\times {r}_{k}^{2}$$
$$\Psi \left(N+k-1,k-1\right)=\left({\overline{C}}_{23}^{\left(k-1\right)}+\beta \left(k-1\right)\times {\overline{C}}_{33}^{\left(k-1\right)}\right)\times {r}_{k}^{\beta \left(k-1\right)-1}$$
$$\Psi \left(N+k-1,k\right)=-\left({\overline{C}}_{23}^{\left(k\right)}+\beta \left(k\right)\times {\overline{C}}_{33}^{\left(k\right)}\right)\times {r}_{k}^{\beta \left(N\right)-1}$$
$$\Psi \left(N+k-1,N+k-1\right)=\left({\overline{C}}_{23}^{\left(k-1\right)}-\beta \left(k-1\right)\times {\overline{C}}_{33}^{\left(k-1\right)}\right)\times {r}_{k}^{-\beta \left(k-1\right)-1}$$
$$\Psi \left(N+k-1,N+k\right)=-\left({\overline{C}}_{23}^{\left(k\right)}-\beta \left(k\right)\times {\overline{C}}_{33}^{\left(k\right)}\right)\times {r}_{k}^{-\beta \left(N\right)-1}$$
$$\Psi \left(N+k-\mathrm{1,2}\times N+1\right)={\overline{C}}_{13}^{\left(k-1\right)}-{\overline{C}}_{13}^{\left(k\right)}+{\alpha }_{1}^{\left(k-1\right)}\times \left({\overline{C}}_{23}^{\left(k-1\right)}+{\overline{C}}_{33}^{\left(k-1\right)}\right)-{\alpha }_{1}^{\left(k\right)}\times \left({\overline{C}}_{23}^{\left(k\right)}+{\overline{C}}_{33}^{\left(k\right)}\right)$$
$$\Psi \left(N+k-\mathrm{1,2}\times N+2\right)=\left({\alpha }_{2}^{\left(k-1\right)}\times \left({\overline{C}}_{23}^{\left(k-1\right)}+2\times {\overline{C}}_{33}^{\left(k-1\right)}\right)-{\alpha }_{2}^{\left(k\right)}\times \left({\overline{C}}_{23}^{\left(k\right)}+2\times {\overline{C}}_{33}^{\left(k\right)}\right)+{\overline{C}}_{36}^{\left(k-1\right)}-{\overline{C}}_{36}^{\left(k\right)}\right)*{r}_{k}$$
$$\left(k=2\dots N\right)$$
$$\Psi \left(2\times N+1,k\right)=\frac{{\overline{C}}_{12}^{\left(k\right)}+\beta \left(k\right)\times {\overline{C}}_{13}^{\left(k\right)}}{1+\beta \left(k\right)}\times \left({r}_{k+1}^{\beta \left(k\right)+1}-{r}_{k}^{\beta \left(k\right)+1}\right)$$
$$\Psi \left(2\times N+1,N+k\right)=\frac{{\overline{C}}_{12}^{\left(k\right)}-\beta \left(k\right)\times {\overline{C}}_{13}^{\left(k\right)}}{1-\beta \left(k\right)}\times \left({r}_{k+1}^{-\beta \left(k\right)+1}-{r}_{k}^{-\beta \left(k\right)+1}\right)$$
$$\Psi \left(2\times N+2,k\right)=\frac{{\overline{C}}_{26}^{\left(k\right)}+\beta \left(k\right)\times {\overline{C}}_{36}^{\left(k\right)}}{2+\beta \left(k\right)}\times \left({r}_{k+1}^{\beta \left(k\right)+2}-{r}_{k}^{\beta \left(k\right)+2}\right)$$
$$\Psi \left(2\times N+2,N+k\right)=\frac{{\overline{C}}_{26}^{\left(k\right)}-\beta \left(k\right)\times {\overline{C}}_{36}^{\left(k\right)}}{2-\beta \left(k\right)}\times \left({r}_{k+1}^{-\beta \left(k\right)+2}-{r}_{k}^{-\beta \left(k\right)+2}\right)$$
$$\left(k=1\dots N\right)$$
$$\Psi \left(2\times N+\mathrm{1,2}\times N+1\right)=\sum_{1}^{N}\left({\overline{C}}_{11}^{\left(k\right)}+{\alpha }_{1}^{\left(k\right)}\times \left({\overline{C}}_{12}^{\left(k\right)}+{\overline{C}}_{13}^{\left(k\right)}\right)\right)\times \frac{{r}_{k+1}^{2}-{r}_{k}^{2}}{2}$$
$$\Psi \left(2\times N+\mathrm{1,2}\times N+2\right)=\sum_{1}^{N}\left({\overline{C}}_{16}^{\left(k\right)}+{\alpha }_{2}^{\left(k\right)}\times \left({\overline{C}}_{12}^{\left(k\right)}+2\times {\overline{C}}_{13}^{\left(k\right)}\right)\right)\times \frac{{r}_{k+1}^{3}-{r}_{k}^{3}}{3}$$
$$\Psi \left(2\times N+\mathrm{2,2}\times N+1\right)=\sum_{1}^{N}\left({\overline{C}}_{16}^{\left(k\right)}+{\alpha }_{1}^{\left(k\right)}\times \left({\overline{C}}_{26}^{\left(k\right)}+{\overline{C}}_{36}^{\left(k\right)}\right)\right)\times \frac{{r}_{k+1}^{3}-{r}_{k}^{3}}{3}$$
$$\Psi \left(2\times N+\mathrm{2,2}\times N+2\right)=\sum_{1}^{N}\left({\overline{C}}_{66}^{\left(k\right)}+{\alpha }_{2}^{\left(k\right)}\times \left({\overline{C}}_{26}^{\left(k\right)}+2\times {\overline{C}}_{36}^{\left(k\right)}\right)\right)\times \frac{{r}_{k+1}^{4}-{r}_{k}^{4}}{4}$$
$$\left(k=1\dots N\right)$$

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Wang, T., Menshykova, M., Menshykov, O. et al. Mechanical Analysis of Thick-walled Filament Wound Composite Pipes under Pure Torsion Load: Safety Zones and Optimal Design. Appl Compos Mater 30, 485–505 (2023). https://doi.org/10.1007/s10443-022-10088-3

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