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A modified rule of mixtures is required to account for the experimentally observed nonlinear variation of tensile strength. A modified Halpin–Tsai model was presented to predict the Young’s modulus of multiscale reinforced composites with both micron-sized and nano-sized reinforcements. In the composites, both micron-sized fillers—carbon fibers—and nano-sized fillers—rubber nanoparticles and carbon nanotubes—are added into the epoxy resin matrix. Carbon fibers can help epoxy resins increase both the tensile strength and Young’s modulus, while rubber nanoparticles and carbon nanotubes can improve the toughness without sacrificing other properties. Mechanical experiments and scanning electron microscopy observations were used to study the effects of the micron-sized and nano-sized reinforcements and their combination on tensile and toughness properties of the composites. The results showed that the combined use of multiscale reinforcements had synergetic effects on both the strength and the toughness of the composites.

advances in mechanical engineering/advances in mechanical engineering

Modified rule of mixtures and Halpin–Tsai model for prediction of tensile strength of micron-sized reinforced composites and Young’s modulus of multiscale reinforced composites for direct extrusion fabrication