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ABSTRACT:The cross-linking mechanisms of sulfur vulcanization are not analytically known and, therefore, reticulation kinetics has to be deduced macroscopically from standardized tests. One of the most popular laboratory test to characterize curing and reversion is the oscillating disk rheometer ODR, which gives a quantitative assessment of scorch, cure rate, and state of cure. In this article, a numerical two-step approach, which is based on the utilization of experimental ODR data and aimed at predicting the degree of vulcanization of thick rubber items cured with accelerated sulfur, is presented. In step one, a composite numerical three-function curve is used to fit experimental rheometer data, able to describe the increases of the viscosity at successive curing times and at different controlled temperatures, requiring only few points of the experimental cure curve to predict the global behavior. Both the case of indefinite increase of the torque and reversion can be reproduced with the model. In step two, considering the same rubber compound of step one, numerical cure curves at different temperatures are collected in a database and successively implemented in a Finite Element software, which is specifically developed to perform thermal analyzes on complex 2D/3D geometries. As an example, an extruded thick EPDM section is considered and meshed through eight-noded isoparametric plane elements. Several FEM simulations are repeated by changing exposition time t c and external curing temperature T n , to evaluate for each (t c ,T n ) couple the corresponding mechanical properties of the item at the end of the thermal treatment. A recently presented bisectional approach, alternating tangent (AT), is used to drastically reduce the computational efforts required to converge to the optimal solution associated with the maximum value of an output property, tensile strength.

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A simple numerical model for the interpretation of the reaction kinetics in ethylene-propylene-diene monomer (EPDM) vulcanized with accelerated sulfur is presented. The model is based on the assumption that during vulcanization, a number of partial reactions occurs, both in series and in parallel, which determine the formation of intermediate compounds, including activated and matured polymers. Once written a standard first-order differential equation (DIFF-EQ) for each partial reaction, an ordinary DIFF-EQ system (ODEs), was obtained and solved through Runge-Kutta algorithms. Alternatively and more efficiently, a single second-order nonhomogenous DIFF-EQ with constant coefficients was deduced, for which a closed-form solution was derived, provided that the nonhomogenous term was approximated with an exponential function. Kinetic constants were evaluated through experimental data fitting on standard rheometer tests. To assess model predictions, an experimental campaign at different temperatures on two EPDM compounds was performed. They exhibited moderate reversion at intermediate and high curing temperatures. A nonlinear least-squares fitting was performed to evaluate unknown constants entering into the DIFF-EQ model proposed. Scaled rheometer curves fit rather well, also in the presence of reversion. In addition, partial reaction kinetic constants were provided: this gave an interesting insight into the different reticulation processes occurring during vulcanization.