An improved pull-out model for the composites with curved reinforcement

Due to the low bending stiffness and large aspect ratio, nanofillers with curved morphology are ubiquitous in composites, providing a potential avenue to achieve superior mechanical properties and functionalities. However, the theoretical understanding of the morphology-properties relationship in such composites remains constrained due to the difficulties in precisely defining the boundary conditions required for establishing a fully analytical model. In this study, we propose an improved shear-lag model that overcomes these challenges to investigate the influence of reinforcement's curved morphology on the pull-out mechanical behaviors of composites, which enables accurate prediction of stress distributions and interfacial debonding. Our investigation reveals that among the two morphology-related parameters, namely waviness and curvature, the pull-out behaviors and properties of the composites are more sensitive to the former parameter. A higher degree of waviness actually contributes to enhanced load transfer efficiency and larger pull-out loads. Meanwhile, we demonstrate that the load transfer from the curved reinforcement to the matrix, as well as the maximum pull-out load, can be improved by increasing the length and volume fraction of graphene, as well as the frictional stress. Additionally, we identify a critical Young's modulus ratio of approximately 16 between the reinforcement and matrix, serving as a predictive criterion for determining debonding locations. Overall, this study provides deep insights into the pull-out behavior of composites with curved reinforcement and presents theoretical inspirations for designing and optimizing advanced composites to achieve high strength and toughness simultaneously.