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A three-function numerical model for the prediction of vulcanization-reversion of rubber during sulfur curing



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 tc and external curing temperature Tn, to evaluate for each (tc,Tn) 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. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011