In this Part I of a two-part paper, a constitutive model for polymeric cords is proposed in order to represent the thermo-mechanical behavior, such as thermal shrinkage and large deformations during the curing and post-curing process in tires. A series of experiments, including tensile test, free shrinkage test, and shrinkage force test, are performed and compared to the proposed model using the identified material parameters.
In this Part II of a two-part paper, a way of modeling axisymmetric rebars to represent the thermal shrinkage of polymeric cords within a thermo-mechanically coupled algorithm is presented without the assumption of a smeared layer. The mechanical characteristics of the proposed approach are compared to the classical approach using only one four-node axisymmetric element with unit dimensions. In addition, the shrinkage behavior of a simplified model made only of plies is discussed. The deformation behavior of polymeric cords during the tire manufacturing process, from the in-molding where a tire is formed by a mold under high pressure and temperature to curing and cooling, is addressed. Finally, the predicted profiles with and without post-cure inflation are compared to the test results.
The strain rate dependence of uncured rubber is investigated through a series of tensile tests (monotonic, multistep relaxation, cyclic creep tests) at different strain rates. In addition, loading/unloading tests in which the strain rate is varied every cycle are carried out to observe their dependence on the deformation history. A strain rate–dependent viscoelastic–viscoplastic constitutive model is proposed with the nonlinear viscosity and process-dependent recovery properties observed in the test results. Those properties are implemented by introducing evolution equations for additional internal variables. The identified material parameters capture the experiments qualitatively well. The proposed model is also evaluated by finite element simulations of the building process of a tire, followed by the in-molding.
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