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

Abstract

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 elastovisco-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.

Finite Element Simulation of Radial Tire Building and Shaping Processes Using an Elasto-Viscoplastic Model

“…Compared to the tire building process, the tire shaping process, which is widely considered to be the most important process in tire production, has received much more attention over the years. Most of these studies focus on the state-of-cure (SOC) of the rubber material during the curing process and try to find the optimum curing time and pressure to achieve the optimal performance of the finished tire [28][29][30][31][32]. However, the deformation of rubber materials and cord reinforcements during the shaping process has not been extensively investigated.…”

Investigation of rubber flow during tire shaping process by experiment and numerical simulations

“…However, this study ignored the presence of cords inside the tire. Thomas Berger et al 21 investigated the phase change of unvulcanized to vulcanized rubber described by a thermo‐mechanical material model within the finite element method (FEM) during the tire manufacturing process. Imadeddin Zreid 22 proposed a tire cord material model considering thermal shrinkage to reconstruct dimension differences observed between PCI and no‐PCI tires, confirming that the variations in dimensions between the PCI and no‐PCI tires are related to the thermomechanical properties of the polymeric cords.…”

ALE formulation for thermomechanical inelastic material models applied to tire forming and curing simulations

“…Molding typically leads to large geometrical changes of the tire profile to achieve the desired final shape. The description of rubber in its green and cured phases as well as the transition between the two phases as a single material model has been recently proposed in [1,10]. In these works, material models are formulated using finite strain theory and utilizing the multiplicative split of the deformation gradient, which allows the use of advanced inelastic rubber models.…”