Comparison of experimental and theoretical transverse elastic modulus of carbon fibers

The transverse elastic modulus of PAN-based carbon fibers as measured by experimental methods, calculated from theoretical equations and analyzed by the finite element method (FEM) is discussed. Raman spectroscopy was the primary method utilized to measure the transverse elastic modulus of carbon fibers in carbon-fiber reinforced plastics (CFRP). A lead oxide (PbO) thin film was deposited on the surface of a CFRP specimen using physical vapor deposition as the pretreatment in order to measure the strains of the carbon fibers and epoxy matrix phases by Raman spectroscopy. Since the relation between the Raman peak wave number of PbO thin films and tensile strain has already been developed, the transverse strain of the carbon fibers could be measured. The transverse strain of the carbon fibers was analyzed using a 2-D FEM model. The transverse modulus of the carbon fibers was determined by fitting the experimental result from Raman spectroscopy to the FEM model. The determined transverse modulus (10.4 GPa) is compared with those experimentally measured by nanoindentation (13.4 GPa), numerically analyzed using 2-D and 3-D FEM models (5.25 GPa and 28.7 GPa, respectively), and theoretically calculated from the Mori–Tanaka, Halpin–Tsai, and Uemura equations (24.8 GPa, 17.4 GPa, and 28.4 GPa, respectively).