A strain rate dependent constitutive model for uncured rubber

Abstract

The paper at hand introduces a constitutive model for the strain rate dependent viscoelastic-viscoplastic behavior of uncured rubber. For its characterization, monotonic tensile tests, multi-step relaxation tests, cyclic creep tests and loading/unloading tests with changing strain rate every cycle were conducted. In the monotonic tensile tests, the uncured rubber exhibits strongly nonlinear features at four different strain rates. The initial stiffness in the monotonic stress-strain curve increases with increasing strain rate. Furthermore, strain hardening becomes apparent with increasing strain rate and, conversely, strain softening or failure accompanied by necking becomes evident with a decreasing strain rate. In multi-step relaxation tests, nonlinear non-equilibrium properties were observed at three different strain rates. The results in cyclic-creep tests show that the plastic deformation rapidly decreases as the strain rate increases. Through the loading/unloading test with varying strain rates, the process dependent behavior of uncured rubber was observed. In order to represent the strain rate and process dependency, internal variables are introduced into the model, resulting in nonlinear viscosity. The proposed constitutive equation is developed based on the so-called micro-sphere model. The rheological model consists of three parts. The generalized Maxwell element represents the nonlinear initial behavior. The Kelvin element represents the phenomena on strain softening and viscoelastic properties. Finally, a Maxwell element connected to a Kelvin element in parallel represents the behavior of strain hardening or continuous strain softening. The proposed model is compared to each test result. The rate and process dependent behavior of the proposed approach is represented qualitatively well. The capability of the introduced formulation is evaluated by a finite element simulation of the building process of a tire.