Surface modifications are known as efficient technologies for advanced carbon fibers to achieve significant improvement of interface adhesion in composites, one of which is to increase the surface roughness in the fiber's longitudinal direction in practice. As a result, many microridges and grooves are produced on carbon fiber's surfaces. How does the surface roughness influence the carbon fiber's pull-out behavior? Are there any restrictions on the relation between the aspect ratio and surface roughness of fibers in order to obtain an optimal interface? Considering the real morphology on carbon fiber's surface, i.e., longitudinal roughness, an improved shear-lag theoretical model is developed in this paper in order to investigate the interface characteristics and fiber pull-out for carbon fiber-reinforced thermosetting epoxy resin (brittle) composites. Closed-form solutions to the carbon fiber stress are obtained as well as the analytical load-displacement relation during pullout, and the apparent interfacial shear strength (IFSS). It is found that the interfacial adhesion and the apparent IFSS are effectively strengthened and improved due to the surface roughness of carbon fibers. Under a given tensile load, an increasing roughness will result in a decreasing fiber stress in the debonded zone and a decreasing debonded length. Furthermore, it is interesting to find that, for a determined surface roughness, an optimal aspect ratio, about 30∼45, of carbon fibers exists, at which the apparent IFSS could achieve the maximum. Comparison to the existing experiments shows that the theoretical model is feasible and reasonable to predict the experimental results, and the theoretical results should have an instructive significance for practical designs of carbon/epoxy composites.

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