Extraction of Material Parameters for Static and Dynamic Modeling of Carbon Black Filled Natural Rubbers

Abstract: Volvo Car Corporation (Volvo Cars) develops powertrain mounting systems that uses components made up largely of filled rubber materials. The development of such components is today relying on external suppliers to design components based on requirements set by Volvo. To reduce costs and lead-time in the development process the possibility of in-house design of such components at Volvo Cars is being investigated. For this to be possible, knowledge must be built concerning modelling the mechanical properties of rubber materials. As part of this a parameter extraction method for modelling of filled rubber materials intended for finite element use has been developed in this project. Both a simple static model fitting procedure and a more complex dynamic model fitting procedure are detailed. Mechanical testing of four filled natural rubber materials with varying hardnesswas carried out at the facilities of Volvo Cars and recommendations have been made regarding the limits of the equipment and the specific test body geometry used. It was found that the lower limit for dynamic testing in regards to displacement amplitude is 0.02 mm. The highest frequency recommended is dependent on the material hardness but a higher limit of 200 Hz is recommended for the softest material investigated. The upper limit was found to be necessary due to inertia effects in the material. The models used to describe the static behaviour were hyperelastic phenomenological models independent on the second invariant such as the Yeoh and the linear neo-Hookean models. The dynamic model used the overlay method to capture therate and amplitude dependent properties of filled rubber. A generalized viscoelastic-elastoplastic rheological model using Maxwell and friction elements in parallel with alinear elastic element was presented and used. These were limited to having maximumfive of each element and no attempts at minimizing this number was made in this work.The dynamic model was fitted to experimental data using a minimization procedure focusing on dynamic modulus and damping at a range of frequencies and strain amplitudes.The proposed fitting procedure is a three segment loop in which FE simulationsof the experimental data is used as both a correction and a validation tool.Model validation showed good correlation of the fitted model to measured databefore correction was attempted. The correction step did not improve the model qualityand the reason for this was identified as poor post-processing. The proposed method together with lessons learned during the course of the project will be of importance for the future in-house development of rubber components at Volvo Cars.