Final answer:
To achieve the highest modulus composite with half as many carbon fibers as glass fibers, align the carbon fibers along the direction of highest stress and use the rule of mixtures for unidirectional composites to calculate E1. The specific modulus values and volume fractions are required for a precise calculation.
Step-by-step explanation:
To create a composite with the highest modulus (E1), the fibers must be arranged in a manner that leverages the strength and stiffness of both the carbon fibers and the glass fibers. Given that there are half as many carbon fibers as glass fibers, the optimal arrangement would typically align the carbon fibers along the direction of highest stress, as carbon fibers offer higher stiffness and strength compared to glass fibers. This arrangement takes advantage of the high modulus of carbon fibers while using the glass fibers to provide supplementary reinforcement and overall structural integrity.
When calculating the modulus of the composite (E1), we consider the rule of mixtures for a unidirectional composite which is given as:
E1 = Vc * Ec + Vg * Eg
Where:
Vc = volume fraction of carbon fibers
Ec = modulus of carbon fibers
Vg = volume fraction of glass fibers
Eg = modulus of glass fibers
Assuming the volume fractions are proportional to the number of fibers and knowing the modulus values for carbon and glass fibers, the E1 for the composite can be calculated. However, we need the specific modulus values and the volume fractions to calculate a numerical value for E1.