The fraction of the load carried by the Kevlar 49 fibers can be determined by considering the tensile strength and tensile modulus of elasticity of both the Kevlar fibers and the epoxy matrix.
To calculate this fraction, we need to compare the tensile strength of the Kevlar fibers to the combined tensile strength of the Kevlar fibers and the epoxy matrix. The tensile strength of the Kevlar 49 fibers is given as 0.550 x 10^6 psi, while the tensile strength of the epoxy resin is given as 11.0 x 10^3 psi.
The fraction of the load carried by the Kevlar 49 fibers can be calculated as follows:
Fraction of load carried by Kevlar 49 fibers = (Tensile strength of Kevlar 49 fibers) / (Tensile strength of Kevlar 49 fibers + Tensile strength of epoxy resin)
= 0.550 x 10^6 psi / (0.550 x 10^6 psi + 11.0 x 10^3 psi)
= 0.550 x 10^6 psi / (0.550 x 10^6 psi + 0.011 x 10^6 psi)
= 0.550 x 10^6 psi / 0.561 x 10^6 psi
= 0.980
Therefore, the fraction of the load carried by the Kevlar 49 fibers is approximately 98.0 percent.
In summary, the Kevlar 49 fibers carry around 98.0 percent of the load in the composite material with 53 percent Kevlar fibers in epoxy. This calculation is based on comparing the tensile strength of the Kevlar 49 fibers to the combined tensile strength of the Kevlar fibers and the epoxy matrix.