Rubber Characterization for Tire Modeling

With advances in computing technologies more emphasis is being placed on virtual tire testing over experimental testing to reduce development cycle times. Since tire rubber exhibits a complex history and temperature dependent mechanical response, a thorough virtual analysis of tires necessitates the use of non-linear viscoelastic material models in conjunction with numerical techniques like FEA. An important undertaking in running these analyses is the development of an experimental program to generate reliable data for calibrating material models. This paper presents important aspects of rubber behavior that should be considered while developing such a program. These include: appropriate selection of test conditions, pre-conditioning of specimens and specimen heating effects. In addition, two aspects are investigated in detail: (1) a mean/static strain effect on dynamic properties and (2) Payne effect and its recovery with time during thermo-mechanical testing.

The mean strain effect is found to exist in the uni-axial deformation mode where the dynamic storage and loss moduli vary with the magnitude of static/mean strain level applied during testing. This can be attributed to the non-linearity in the static stress-strain response. Interestingly, the loss tangent is found to be only mildly sensitive to the static strain level. This effect has important implications while choosing the right test conditions for material characterization.

The Payne effect in filled elastomers is well known in the rubber community and has important ramifications in a thermo-mechanical DMA test where it is desired to test at multiple strain and temperature conditions using a single sample in order to avoid both, expensive sample preparation and sample-to-sample variation in material properties which can be of the order of 15-20%. In this regard, the Payne effect and its rate of recovery must be considered during testing if accurate dynamic material data is desired. Here, the effect of time and temperature on low strain amplitude modulus recovery following higher strain amplitude loading is studied. The extent of recovery is found to vary with the compound and is accelerated at higher temperatures. Based on these results, a simple correction is proposed to account for the error introduced in dynamic mechanical properties measured in a thermo-mechanical DMA due to incomplete Payne effect recovery.

In conclusion, we can say that a good experimental program for tire rubber characterization should include strain, strain rate and temperature conditions similar to those seen in service in order to get the best representative description of rubber in modeling. In addition, applying the corrections outlined in this paper leads to reliable experimental data sets for material model calibration.