Computational homogenization of the debonding of rigid-particle reinforced elastomers: considering interphases

When a particle inclusion is embedded in a polymer matrix, the polymer tends to adsorb on the surface of the in-clusion. The effect of this may result in an interphasial zone between the particle and the polymer often referred toas “bound” rubber. The extent and composition of this zone depends on a number of factors, including the surfacearea and surface treatment of the particle, as well as the level of mixing and age of the composite [1]. Studies onthe failure of particle reinforced polymers have indicated that, at large strains, cracks/debonding (occurring at themicroscale) can have a signifi cant infl uence on the macroscopic response of these composites [1–3]. There hasbeen much work done on the debonding process of particle reinforced composite materials under small deforma-tions, but in recent years the interest in fi nite deformation debonding has increased. In this study we present a fullythree-dimensional model, using cohesive zone elements to account for the nonlinear debonding process betweenthe particles and the interphase, to simulate the behavior of these composites under fi nite deformations. The non-linear relation used for the cohesive model is the consistent, potential-based PPR model [4]. Our numerical modeluses the concept of reduced volume elements with periodic boundary conditions to represent isotropic materials. REFERENCES[1] Leblanc, J. L. Rubber-fi lled interactions and rheological properties in fi lled compounds. Progress in Polymer Science.2002, 27:627–687.[2] Ramier, J. Comportement mécanique d’élastomères chargés, Infl uence de l’adhésion charge – polymère, Infl uence de lamorphologie. PhD thesis, L’Institut National des Sciences Appliquées de Lyon, 2004.[3] Ramier, J., Chazeau, L., Gauthier, C. Infl uence of silica and its different surface treatments on the vulcanization processof silica fi lled SBR. Rubber Chemistry and Technology. 2007, 80, 183–193.[4] Park, K., Paulino, G.H., Roesler, J.R. A unifi ed potential-base cohesive model for mixed-mode fracture. Journal of theMechanics and Physics of Solids. 2009, 57, 891–908.