Carbon-fiber reinforced epoxy is being used as the outer surface material in high-performance aircraft where the surface temperatures are elevated because of the friction with air. The maximum-use temperature for epoxy resin is approximately 260°C. A composite sheet is produced from 75 vol % carbon fiber and 25 vol % epoxy resin. Assume that the epoxy and carbon are stress free at room temperature, and the composite is heated from room temperature (22°C) to 260°C during service. The elastic modulus of the carbon fiber is 380 GPa, the ultimate tensile strength is 2.4 GPa, and the axial thermal expansion coefficient is –0.7×10-6 K-1 . The elastic modulus of the epoxy resin is 4 GPa, the ultimate tensile strength is 0.07 GPa, and the thermal expansion coefficient is 60×10-6 K-1 .
(a) Calculate the thermal stresses, both the magnitude and sign, in the epoxy matrix and in the carbon fibers at 260°C. Assume that each material is elastic at all temperatures, and that there is good interface bonding.
(b) Calculate the composite strain in heating from 22°C to 260°C.
(c) Is there any component of this design that might cause a problem? Comment on the results in comparison to the data provided. If data is not available on these components, justify your evaluation of this design based upon your knowledge of these materials.
(a) There are two unknowns; the strain in the fibers and the strain in the matrix. If we know the strain we can calculate the stress since the material is assumed to be elastic. Once we know the strain in the fiber and in the matrix the composite strain can be calculated. Since there are two unknowns we are going to need two equations to solve for the two unknowns. One equation comes from the observation that there is no applied stress to the composite in the axial direction. The composite stress must be zero.
(b) The composite strain is solved from
(c) The fiber tensile stress is low in comparison to the fiber tensile strength, the fibers are ok. The matrix stress is in compression and the tensile strength of epoxy is 0.07 GPa. Epoxy is a brittle material, and brittle materials have higher compressive strength than
tensile strength, the matrix compressive strength should be greater than the applied compressive stress.
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