ABSTRACT
In recent years, many material models have been developed for crosslinked rubbery polymers. Due to advances in computer power and simulation techniques, the interests of engineers and rubber companies exanpded to simulating the total production process of their products. Therefore, an appropriate material formulation of the unvulcanised raw material and its transition to the vulcanised state is necessary. In the unvulcanised state, rubber has not yet built up polymer crosslinks and shows a visco-plastic behaviour without a pronounced ground state elasticity. In this contribution, a thermo-mechanical constitutive model for unvulcanised rubber material is presented. The rheological approach consists of two parts, which characterise rate-independent and rate-dependent features. In the first part, a non-linear elastic spring is connected to a Kelvin element with a dashpot. The used endochronic evolution law for the dashpot ensures rate-independent plasticity without a distinct yield surface. The rate-dependent part consists of a non-linear elastic spring connected in series to a parallel system of a Maxwell element and a viscous dashpot. The single dashpot models rate-dependency of the initial loading, while the Maxwell element is responsible for the kinematic hardening. To model temperature dependency of the unvulcanised rubber, the free energy functions of the nonlinear springs are multiplied by a temperature-dependent scaling function. Therefore, the internal and external work contributions are computed and lead to heating of the material when a cyclic load is applied. For a numerically efficient formulation, the rheological model is formulated within the micro-sphere approach. In this case, only a one-dimensional formulation of the material model is required.While the material is exposed to high temperature, the polymer chains will build up its crosslinks and change from visco-plastic to visco-elastic behaviour. With a kinetic model, the state of cure for every integration point inside a finite element model is predicted. During the evolution of the state of cure, the constitutive law of the material will be changed accordingly. The entanglements of the chains will reduce its volume and a permanent set of the material causes a new equilibrium state, which is different compared to the reference configuration.
