Design of Hybrid Composites for Axial loads with Zero Coefficient of Thermal Expansion Zaffar M. Khan 1 and Asim Shahzad 2 Institute of Space Technology, Islamabad, Pakistan, 44000 Aerospace structures are influenced by changes in temperature. Coefficient of thermal expansion (CTE) is an important and significant material parameter of structural design of aerospace vehicles which require dimensional stability. Materials with zero CTE are required in structures subject to extreme temperature changes such as aerospace structures. In this paper analytical techniques are used to design a composite with zero CTE. A Matlab code is compiled for the calculation of CTE and longitudinal coefficient of thermal expansion (LCTE) for different fiber and matrix combinations is calculated. Effect of rigid body rotation (RBR) of laminate and ply stacking sequence on LCTE is also shown. MIC-MAC is finally used to design a hybrid laminate for carrying axial loads with zero LCTE. Nomenclature α = coefficient of thermal expansion φ = Ply orientation angle Ex = Modulus of elasticity of composite in the x direction Ey = Modulus of elasticity of composite in the y direction Ef = Modulus of elasticity of fiber Em = Modulus of elasticity of matrix Gf = Shear modulus of fiber Gm = Shear modulus of matrix Es = Shear modulus of composite T = T300/5200 K = Kevlar/Epoxy Vf = Volume fraction of fiber Vm = Volume fraction of matrix Introduction Since the invention of aircraft by Wright brothers, engineers have sought to improve the performance of aircraft, primarily a reduction in fuel consumption. An increase in the strength-to-weight ratio of airframes is one key parameter that has resulted in lower fuel bills for airlines and other aircraft operators, be it civil or military. Composite materials have widespread application in aerospace industry because of their superior physical and mechanical properties and high strength to weight ratio compared to the conventional materials. Deformation of materials and structures when subjected to changes in temperature 1 Insert Job Title, Department Name, Address/Mail Stop, and AIAA Member Grade for first author. 2 Research Assistant, Dept. of Aeronautics and Astronautics, Institute of Space Technology, Islamabad, Pakistan /tariqasim@yahoo.com, student member.
is a subject that has been studied for many years. Engineers account for temperature effects in their designs, because neglecting the temperature effects could result in failure [1]. Coefficient of thermal expansion (CTE) is an important and significant material parameter of structural design of aerospace vehicles which require dimensional stability. There is a requirement of composite materials with zero CTE for structures of aerospace vehicles which are exposed to different temperatures. Composites can be designed and tailored for zero CTE (CTE<0.0±0.4e-6/K), and to meet the strength to wait ratio and other mechanical properties requirements. Carbon, Kevlar, Graphite and Glass fibres are used to reinforce different kind of matrix. Composite laminates with different resins and fibre combinations are considered and their CTE values are measured analytically. The variation of CTE values of composite laminates with parameters, such as fibre type and ply angles is analysed. It is concluded that after meeting the mechanical requirement a composite can be tailored for zero CTE. Analytical The properties of fibre and matrices considered for laminates are listed in Table 1. Rule of mixture is used to calculate the longitudinal, transverse, shear modulus and poison ratios of laminates using the formulas listed below Ex EfVf EmVm 1 Vf Vm Ey Ef Em GfGm Es VmGf VfGm (1.1) The modulus components of composites are calculated using the following formulas m (1 ) x Qxx mex Qyy mey Qss Es y 1 (1.2) Table 1 Properties of fibre Fibre type CTE (25~150 C) α L ( 10 / K ) Carbon (T-300) -0.37~-0.28 Glass (HS-2) 2.34~3.50 Aramid (Kevlar-49) -3.6~-4.68
Table 2 Properties of resin Resin type CTE (25~150 C) α L ( 10 / K ) Phenolic epoxy (4211) 33.57~62.29 Bi-phenolic A (LWR-1) 39.43~62.49 Bimaleimide (QY8911) 34.77~57.73 Symmetric laminates with different fibre and resin types and ply orientations are studied. A laminate with specific resin and fibre combination and with a particular stacking sequence is considered. Thin laminate theory is used to calculate the compliance and stiffness matrices in local coordinate system for individual laminas, then the transformation matrices are used for the calculation of compliance and stiffness matrices in global coordinate system. We calculated the [A], [A*], [a] and [a*] matrices for the laminate. Coefficient of thermal expansions in longitudinal, transverse and shear directions is calculated by integrating the non-mechanical stress using the last sub-section method. By definition, free thermal expansions per degrees are thermal expansion coefficients[2]. a Q dz o i i j ij k a *[p q V,p q V,q V ] o i n n p,q ij n n * n n * n * 1 1 3 ( Qxx Qxy ) x ( Qxy Qyy ) y 2 (1.3) Using the formulas mentioned above the CTE for different combinations of fibre and resins and ply orientations is calculated and compared. Hybrid composite is designed to carry mainly axial loads and have zero LCTE using MIC-MAC. Results and Discussions Longitudinal, transverse and shear CTE values of different laminates are listed in Table 3. CTE values of composites are mainly influenced by fibres, while resin has only some effect so the resin with lowest value of CTE is used [3]. Results indicate that the larger the fibre CTE values, the larger the composite CTE values. Composite CTE in a particular direction is decided by the fibres involved and their orientation. Ply order and orientation is changed to achieve the desired CTE. Table 3 Properties of Laminates Fibre Resin α x ( 10 / K ) α y ( 10 / K ) Glass Epoxy -0.3 28.1 Graphite Epoxy -0.3 28.1 Kevlar Epoxy -4 79
Relationship between ply orientation and longitudinal coefficient of thermal expansion (LCTE) is studied and the results for two laminates are shown in Table 4 and Figure 1. So we can design a composite of desired LCTE value just by changing the ply orientation and laminates with zero or even negative CTE can be fabricated. Carbon/epoxy laminate shows a negative LCTE for 0 < φ<5 and zero LCTE (LCTE<0.0±0.4e-6/K) for 5 < φ<9. Table 4 Longitudinal CTE at different ply orientation Ply Angle (φ) LCTE Kevlar/Epoxy LCTE Carbon/Epoxy 0-4.00-0.30 10.11-1.44 0.58 20.22 5.92 3.09 30.33 17.17 6.95 40.44 30.94 11.65 50.56 45.51 16.64 60.67 59.09 21.29 70.78 70.01 25.02 80.89 76.92 27.39 91.01 78.97 28.09 101.12 75.91 27.04 109.21 70.01 25.02 121.34 56.54 20.41 131.46 42.61 15.65 141.57 28.06 10.67 151.68 14.67 6.09 161.79 4.10 2.47 171.91-2.36 0.26 180-4.00-0.30
LCTE (e-6/k) LCTE(e-6/K) 90.00 80.00 70.00 60.00 50.00 40.00 30.00 Carbon/Epoxy Kevlar/Epoxy 20.00 10.00 0.00-10.00 0 50 100 150 200 Ply Angle Figure 1 CTE vs. Ply angle The effect of stacking sequence on LCTE is observed, and Figure 2 shows the LCTE versus Rigid body rotation of laminate with different stacking sequence for Carbon/Epoxy. A [0,90] ns laminate have a constant LCTE value of 2.53, while [0 n,45,90] ns laminates have both positive and negative values of LCTE with respect to RBR but [0 n,45,-45,90] ns laminates have only positive values of LCTE. 9.00 8.00 7.00 6.00 5.00 4.00 3.00 2.00 1.00 0.00-1.00 [0,90]s [0,45,90]s [02,45,90]s [03,45,90]s [03,45,-45,90]s 0 50 100 150 200 RBR Figure 2 LCTE vs. RBR of Carbon/Epoxy Laminate for different stacking sequence
LCTE (e-6/k) Hybrid composites are extensively used to design and develop the composites with zero CTE. MIC-MAC (Micro-Macro-mechanics analysis software) is used for study of zero CTE of hybrid composites. A hybrid laminate consisting of T300/N5208 and Kevlar/Epoxy plies is used to design a composite with zero LCTE for carrying axial loads. The effect of stacking sequence on LCTE is observed, and Figure 3 shows the LCTE versus Rigid body rotation of a hybrid laminate with different stacking sequence of plies. Composite design guidelines are used to design a laminate for carrying mainly axial load. A laminate consisting of 60% plies of φ=0, 30% plies of φ=45, and 10% plies of φ=90 is used, two different hybrids with stacking sequence of [0 2T,45 T,-45 T,0 2K,90 K ] ns and [0 3T,45 T,-45 T,0 3K,45 K,-45 K,90 K ] ns have negative LCTE for 0 <RBR<9 and have zero LCTE for 0 <RBR<17. So these two hybrids can be used in shafts and beams which require zero CTE. 8.00 7.00 6.00 5.00 4.00 [02T,90T,0K] [02T,45T,90T,0K] [03T,45T,-45T,03K,45K,- 45K,90K] [02T,45T,-45T,02K,90K] 3.00 2.00 1.00 0.00-1.00 0 20 40 60 80 100 120 140 160 180 RBR Figure 3 LCTE vs. RBR of a Hybrid Laminate for different stacking sequence References 1. Wolff, E.G., Introduction to the dimensional stability of composite materials. 2004: DEStech Publications, Inc. 2. Tsai, S.W., Theory of composites design. 1992: Think composites Dayton. 3. Camacho, C.W., et al., Stiffness and thermal expansion predictions for hybrid short fiber composites. Polymer Composites, 1990. 11(4): p. 229-239.