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 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.

Highlights

  • Rubber is used in a large variety of applications in industry

  • The fully thermomechanical simulation of a tire production process from the uncured green tire that is pressed into a mould, exposed to heat to enforce vulcanization and phase change of the tire to obtain the final cured tire, has not been addressed so far

  • The different rate of curing at the beginning of the vulcanization process is modelled via a linear temperature dependency of the power term m = m1 θ + m2

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Summary

Introduction

Rubber is used in a large variety of applications in industry. With certain fillers like carbon black or sulfur, its properties can be tuned for every specific application. The model in [9] is developed further for non-isothermal cases and with a temperature dependent power term, see [11,12] These models are applied to a tire cross-section in the mould, where only the heat transfer problem and the vulcanization process are addressed. The fully thermomechanical simulation of a tire production process from the uncured green tire that is pressed into a mould, exposed to heat to enforce vulcanization and phase change of the tire to obtain the final cured tire, has not been addressed so far. In this contribution, a thermo-mechanical consistent framework is presented for the phase change of rubber from the uncured to the cured phase. The production process of a tire from green tire to cured tire is shown and carried out by a finite element simulation

State of curing
Thermo-mechanically consistent vulcanization framework
Fundamental equations of motion
Free energy function and Kirchhoff stress
Evolution law of the curing strain
Thermo-mechanical consistency
Vulcanization model based on the micro-sphere model
Kinematic description
Rheological model and free energy function
Uncured rubber model
Algorithmic stresses and tangents
Uncured rubber phase
Cured rubber phase
Rubber block simulation
Tire production simulation
Vulcanization simulation
Post curing inflation
Findings
Conclusion

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