Flexural Stiffnesses of and Dimensional Stability in Circular Quasi-isotropic Laminate Mirrors

Abstract

Composite fiber reinforced plastics are being given favorable consideration for emerging applications in large aperture telescopes, such as the Hubble telescope or communication dishes. Many lightweight mirror fabrication concepts are currently being pursued. Presently, the technology is limited because it has an incomplete understanding of the mechanics associated with quasi-isotropic laminates for diffraction-limited displacement constraints, and lack of understanding for effects of resin buffer layers on composite mirrors for high surface smoothness. In this dissertation document, radial stiffness associated with stacking sequence effects in quasi-isotropic laminates (pi/n, where n=3, 4, and 6) and dimensional stability in the composite laminates are investigated numerically. The numerical results show that directional dependency of flexural stiffness in the laminates, which is strongly associated with stacking sequences, is a significant factor causing unfavorable sinusoidal surface waviness. The maximum radial flexural stiffness variation is found as ±12.85% in pi/3 laminate while a minimum of ±5.63% is found in pi/4 laminate. Mechanics of maximum asymmetry by ±2º misorientation based on ideal pi/n laminate lay-ups are evaluated and the results are compared with ideal lay-up sequence cases. The calculated extensional and flexural stiffness values from the maximum asymmetric cases are within less than 0.05%. As such, the radial flexural stiffness variations in quasi-isotropic laminates are shown to be more problematic than asymmetry caused by common manufacturing variance. The types of surface deformations in quasi-isotropic laminates associated with directional dependency of flexural stiffness are evaluated using finite element analyses. Also, fiber print-through in replicated composite mirrors and the effects of the resin buffer layer present in the mirrors for mitigation of the fiber print-through are investigated and discussed. Numerical results reveal that there will be an unfavorable sinusoidal surface deformation in each ideal pi/n laminate and the shapes are strongly associated with principal fiber directions due to stacking sequence effects. The surface deformations in quasi-isotropic laminates are shown to be typical and such surface deformations are inevitable when composite mirrors are fabricated from discrete layers of anisotropic carbon fiber reinforced plastics. Moreover, the use of additional resin layers appears to more adversely influence the composite mirror substrates. The validation of predicted surface deformations and dimensional distortions are achieved by comparing experimental results on a 8-inch-diameter composite mirror sample fabricated at the University of Kansas Dept. of Aerospace Engineering (KUAE) and Bennett Optical Research (BOR). A study of quasi-homogeneous materials such as short fiber products as alternative composite materials is investigated. Furthermore, the relation between resin property effects and corresponding resin thickness effects is evaluated and discussed. The analyses provide information on alternative types of materials that primarily affect optical performance and thus are most important for precision optics. Based on the results, locally varying radial surface deformations in quasi-isotropic laminates fabricated from continuous fiber reinforced plastics distort optical performance. These surface deformations might be eliminated by utilizing short fiber materials and a soft resin system with a very low coefficient of thermal expansion compared to conventional resins.