Multiresponse optimization of carbon fiber graphene rubber modified epoxy composites using response surface methodology

Carbon fiber reinforced epoxy composites offer high specific strength and stiffness but suffer from intrinsic brittleness and limited damage tolerance. Though elastomeric modifiers improve toughness and graphene provide nanoscale crack-bridging potential, their combined influence in multiscale hybrid systems often results in competing effects on strength and weight. In this study, carbon fiber-graphene-rubber modified epoxy composites were fabricated using vacuum bagging and systematically optimized through Box-Behnken response surface methodology to balance tensile strength, flexural strength, and weight. Tensile strengths up to 1267 MPa and flexural strengths up to 1602 MPa were achieved within the investigated parameter space. ANOVA revealed carbon fiber content as the dominant factor (F > 1500 for tensile; F > 1550 for flexural), while graphene exhibited significant interaction effects with carbon fiber (p < 0.001). Rubber addition enhanced ductility but introduced nonlinear trade-offs in strength and weight. The developed regression models demonstrated excellent predictive capability (R2 > 0.99), enabling identification of optimized compositions that balance mechanical performance and mass. Fractographic analysis revealed crack deflection, fiber pull-out, and matrix toughening mechanisms governing the observed property trends. The study provides a quantitative framework for multi-objective optimization of multiscale hybrid epoxy composites for structural lightweight applications.