A thermo-mechanical material model for rubber curing and tire manufacturing simulation

In this contribution, the phase change of unvulcanized to vulcanized rubber is described by a thermo-mechanical material model within the finite element method (FEM) framework. Before the vulcanization process (curing), rubber exhibits an elasto-visco-plastic behaviour with significant irreversible deformations without a distinct yield surface. After exposing rubber to high temperature, the molecular chains build-up crosslinks among each other and its mechanical behaviour changes to stiffer viscoelastic material. The proposed model assumes, that both phases are present during the vulcanization process. The ratio changes from the uncured phase at the beginning to the cured phase according to the current state of cure. A constitutive curing formulation is introduced into the model, to capture the shape change during the vulcanization and to ensure, that the second law of thermodynamics is fulfilled. A multiplicative split of the deformation gradient is assumed to describe incompressible material. Thermal expansion due to the change of temperature is taken into account in the volumetric part, as well as shrinkage during the vulcanization process. In the isochoric part, the phase change from elasto-visco-plastic to viscoelastic material is described by micro-macro transition based on the micro-sphere model. The consistent formulation of the material model and its tangent are important for a successful implementation into a three-dimensional finite strain FEM framework. The capabilities of the model are shown by the simulation of an axisymmetric tire production process starting at the green tire inserted into the heating press up to a post-cure inflation step.