Final answer:
The fiber fraction required for a composite to have the fibers handle 85% of the load can be calculated using the rule of mixtures. The density can also be estimated with the rule of mixtures, while the transverse modulus estimation is more complex and dependent on various factors.
Step-by-step explanation:
To determine the fiber fraction that would be required for a composite with titanium fibers in a polycarbonate matrix to have the fibers handle 85% of a longitudinal tensile load, the rule of mixtures for a composite can be used. This rule states that the modulus of the composite (Ec) is given by the equation: Ec = VfEf + (1-Vf)Em, where Vf is the volume fraction of the fibers, Ef is the modulus of the fiber, and Em is the modulus of the matrix. Knowing that we want the fibers to handle 85% of the load, we can rearrange the rule of mixtures to solve for Vf as Vf = (Ec - Em) / (Ef - Em).
For the estimation of density, another rule of mixtures can be applied: \(
ho_c = V_f\rho_f + (1 - V_f)\rho_m\), where \(
ho_c\) is the density of the composite, \(
ho_f\) is the density of the fibers, and \(
ho_m\) is the density of the matrix.
The transverse modulus of the composite can be more complex to estimate due to the different load distribution in transverse loading as compared to longitudinal loading. It requires additional information such as the shape, orientation, and distribution of the fibers, as well as the properties of both the fibers and the matrix.