A thermo-mechanical finite element material model for the rubber forming and vulcanization process: From unvulcanized to vulcanized rubber

Abstract

In this contribution, the transition in the thermo-mechanical properties of unvulcanized rubber during the vulcanization (curing) process is modeled by a material model for unvulcanized and vulcanized rubber (two-phase material) in the context of finite strain thermo-mechanics within the finite element method (FEM). For the vulcanization rate, a constitutive approach with few parameters is proposed representing the monotonic increase of the degree of vulcanization as a function of current temperature and the curing history. The material model taking into account the two phases of rubber uses different constitutive approaches for the isochoric part and the volumetric part for which a multiplicative split of the deformation gradient is considered. The isochoric part of the model consists of a hyperelastic spring and a dashpot device in series forming a Maxwell element with properties depending on the degree of vulcanization and temperature. Inelastic isochoric deformations during the forming and vulcanization process of rubber parts can be captured. The volumetric part consists of a hyperelastic spring and takes into account volume changes due to mechanical loads and temperature variations (thermal expansion). The proposed material model is formulated based on the displacement field, the temperature field, the degree of vulcanization and its kinetics. It is implemented into the thermo-mechanically coupled framework of the FEM in 3D for finite strains.