Predicting nonlinear stress–strain curves of unidirectional fibrous composites in consideration of stick–slip

A simple and efficient methodology is developed for computing nonlinear stress–strain curve of unidirectional fibrous nano-composites loaded in the direction of the perfectly aligned fibers. The method, based on shear lag analysis and derived from basic principles of continuum micromechanics, incorporates shear stick–slip constitutive law at the fiber–matrix interface. The matrix is modeled as elastic–plastic with linear isotropic strain hardening. The approach thus predicts the nonlinear behavior of the composite stress–strain curve due to both interfacial shear slippage of reinforcement fibers within the matrix and due to spread of plasticity within the matrix. The proposed method is compared to experimental results on aligned fibrous nano-composites and very good agreement is obtained when low values of interfacial shear strength are used. The study shows that when the interfacial bond between the matrix and the fiber is strong, higher stress concentration leads to spread of plasticity in the composite at lower bulk strains. However, when the bond is weak, interfacial slippage causes a relief in the accumulation of stress in the matrix. Both factors seem to provide reasonable explanation for the observed nonlinearity and improved stiffness of the composite. A set of parametric studies is also performed and the proposed method is compared to existing models.