Geometrical and mechanical modeling of polymeric multi-ply yarns

This work aims to describe and predict the complex mechanical behavior of polymeric cords used as reinforcements in tires. Starting from the observed microstructure of the cords and from macroscopic experimental tests performed on single-ply yarns, a comprehensive geometric and mechanical model is developed. The real geometry of the cord is replaced by an equivalent three-dimensional continuum of a cylindrical shape, with a properly defined non-isotropic inelastic constitutive behavior. The three-dimensional viscoelastic and viscoplastic material model developed by the authors for rayon fibers is employed for this purpose. The actual directions of filaments inside the cord are computed by an analytical model, accounting for the twist in the yarns and in the filaments inside each yarn. Such directions, relevant to points of the cord cross-section, are then averaged along the pitch of the cord to obtain mean directions which represent the virtual reinforcement directions to be used in the equivalent cylindrical-shaped model. This analysis strategy is implemented in a finite element procedure. For rayon cords, the developed simulation tool (fed with appropriate parameters) gives numerical results that compare well with the corresponding experimental results. This approach could be effectively utilized in the analysis of cord-reinforced rubber composites.