Identification of the optimal carbon fiber shape for cost-specific compressive performance

Carbon fiber composites offer superior mechanical performance compared to nearly all other useful materials for the design of structures. However, for cost-driven industries, such as with the wind energy and vehicle industries, the cost of commercial carbon fiber materials is often prohibitive for their usage compared to alternatives. This paper develops an approach to optimize fiber geometries for use in carbon fiber reinforced polymers to increase the compressive strength per unit cost. Compressive strength is a composite property that depends on the fiber, matrix, and interface, and an exact analytic expression does not exist that can accurately represent these complicated relationships. The approach taken instead is to use a weighted summation between the fiber cross-sectional area moment of inertia and perimeter as a proxy for compressive strength, with different weightings explored within the paper. Analyses are performed to identify optimal fiber geometries that increase the cost-specific compressive strength based on various assumptions and desired fiber volume fraction. Robust optimal shapes are identified which outperform circular fibers due to increases in area moment of inertia and perimeter, as well as decreases in carbon fiber processing costs.