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Influence of the Ply Angle Deviation on the Out-of-Plane Deformation of the Composite Space Mirror

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Abstract

In order to discuss the influence of the ply angle deviation, six symmetric quasi-isotropic layup sequences imposed the fixed or random angle deviation were studied based on the numerical analysis, such as Monte Carlo stochastic finite element method and statistic analysis. The out-of-plane deformation was observed in spite of the symmetric quasi-isotropic sequences subjected to a temperature change due to the ply angle deviation in the space mirror. The surface peak-to-valley (PV), which is one kind of out-of-plane deformation, is proportional to the magnitude of the fixed angle deviation, and the mean of PVs is also proportional to the standard deviation of the random angle deviation. The out-of-plane deformation resulting from two-ply angle deviation indirectly satisfies the parallelogram law, and if each ply angle deviation is random independently, the probability density of that satisfies the Rayleigh distribution. In this paper, it is found that the most effective method to improve the surface accuracy of the space mirror is decreasing the standard deviation of the angle deviation, next to decreasing ply thickness and optimizing layup sequence, which is useful for application in the space mirror.

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References

  1. Hinckley, C.M.: Statistical evaluation of the variation in laminated composite properties resulting from ply angle misalignment. Proc. SPIE. 27, 497–511 (1990). https://doi.org/10.1117/12.21532

    Article  Google Scholar 

  2. Kasl, E.P., Mehie, G.V., Dyer, J.E., Clark, H.R., Connell, S.J., Sheikh, D.A.: Recent developments in composite-based optics. Proc. SPIE. 3356, 1–12 (1998). https://doi.org/10.1117/12.324492

    Google Scholar 

  3. Yang, Z.Y., Zhang, J.B., Xie, Y.J., Zhang, B.M., Sun, B.G., Guo, H.J.: Influence of layup and curing on the surface accuracy in the manufacturing of carbon Fiber reinforced polymer (CFRP) composite space mirrors. Appl. Compos. Mater. 24, 1447–1458 (2017). https://doi.org/10.1007/s10443-017-9595-7

    Article  Google Scholar 

  4. Parker, J.E., Lyons, J.J.: Development of optically flat mirrors using graphite/epoxy laminates. Proc. SPIE. 2540, 118–124 (1995). https://doi.org/10.1117/12.219510

    Article  Google Scholar 

  5. Chen, P.C., Bowers, C.W., Content, D.A., Marzouk, M., Romeo, R.C.: Advances in very lightweight composite mirror technology. Opt. Eng. 39, 2320–2329 (2000). https://doi.org/10.1117/1.1288125

    Article  Google Scholar 

  6. Romeo, R.C., Martin, R.N.: Progress in 1m-class, lightweight, CFRP composite mirrors for the ULTRA telescope. Proc. SPIE 6273, 62730S (2006). https://doi.org/10.1117/12.672221

  7. Arao, Y., Koyanagi, J., Utsunomiya, S., Kawada, H.: Effect of ply angle misalignment on out-of-plane deformation of symmetrical cross-ply CFRP laminates: accuracy of the ply angle alignment. Compos. Struct. 93, 1225–1230 (2011). https://doi.org/10.1016/j.compstruct.2010.10.019

    Article  Google Scholar 

  8. Tsai, S.W., Hahn, H.T.: Introduction to Composite Materials. Technomic, Westport (1980)

    Google Scholar 

  9. Arao, Y., Koyanagi, J., Takeda, S., Utsunomiya, S.: Geometrical stability of CFRP laminate considering ply angle misalignment. The 18th international conference on composite materials. In: Jeju (2011)

    Google Scholar 

  10. Yurgarits, S.W.: Measurement of small angle fiber misalignments in continuous fiber composites. Compos. Sci. Technol. 30, 279–293 (1987). https://doi.org/10.1016/0266-3538(87)90016-9

    Article  Google Scholar 

  11. Thompson, S.J., Bichon, S., Grant, R.J.: Influence of ply misalignment on form error in the manufacturing of CFRP mirrors. Opt. Mater. Express. 4, 79–91 (2014)

    Article  Google Scholar 

  12. Yang, Z.Y., Liu, Q.N., Zhang, B.M., Xu, L., Tang, Z.W., Xie, Y.J.: Influence of layup sequence on the surface accuracy of carbon Fiber composite space mirrors. Appl. Compos. Mater. (Online). https://doi.org/10.1007/s10443-018-9690-4

  13. Wu, Q.X.: Structural Reliability Analysis and Stochastic Finite Element Method. China Machine Press, Beijing (2005)

    Google Scholar 

  14. Ghanem, R.G., Spanos, P.D.: Stochastic Finite Elements a Spectral Approach. Springer, New York (1991)

    Book  Google Scholar 

  15. Montgomery, D.C., Runger, G.C.: Applied Statistics and Probability for Engineers. Wiley, New York (2003)

    Google Scholar 

  16. Zwillinger, D., Kokoska, S.: Standard Probability and Statistics Tables and Formulae. Chapman & Hall, Boca Raton (2000)

    Google Scholar 

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Acknowledgements

The authors will thank Dr. Hu Liqin for her great help in the statistical analysis. This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Authors and Affiliations

  1. Aerospace Research Institute of Materials & Processing Technology, Beijing, 100076, China

    Qingnian Liu, Yong Cai, Zhiyong Yang, Shuai Jiang & Shuang Leng

  2. Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, 100049, China

    Xiaojing Liu

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  1. Qingnian Liu
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  2. Yong Cai
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  3. Xiaojing Liu
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Correspondence to Qingnian Liu.

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Liu, Q., Cai, Y., Liu, X. et al. Influence of the Ply Angle Deviation on the Out-of-Plane Deformation of the Composite Space Mirror. Appl Compos Mater 26, 897–911 (2019). https://doi.org/10.1007/s10443-018-9756-3

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  • DOI: https://doi.org/10.1007/s10443-018-9756-3

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