Bulk strain energy density in randomly reinforced polymer composites with antifriction dispersed additives

Bulk strain energy density was numerically simulated for epoxy-phenol-based composites randomly reinforced with short polyimide fibers, with antifriction dispersed polytetrafluoroethylene (PTFE) additives. A mathematical model was constructed using the notion of a stress concentration operator (fourth-rank tensor) that relates volume averaged, or external, stresses within a heterogeneous material with their local values within an individual heterogeneity. The simulation was based on a generalized singular approximation of random field theory used to solve a stochastic differential equation of equilibrium of an elastic medium. This approximation yields an explicit expression for stress concentration in a composite material. The explicit expression allows one to analyze the distribution of bulk strain energy density depending on the composition, structure, volume and mass fraction of heterogeneities, and on the type and value of applied load. We studied how the considered energy characteristic depends on the type of external mechanical loading and concentration of isotropic components in the model composites. It is shown that with the increasing concentration of polyimide fibers at a fixed concentration of PTFE inclusions, the bulk strain energy density values of all components decrease and approach each other independently of the type of external loading. The form of these dependences is nonlinear. A change in the mass fraction of dispersed PTFE inclusions in the model composites exerts little effect on local energy values of all components under any of the considered applied external loads.