What is it about?

The J-integral approach manifests itself in an efficient way to determine the crack growth and failure mechanism of tread and sidewall compounds used in tyres. Therefore, for a pure shear (PS) specimen of carbon black filled natural rubber, the J-integral formula was vivisected, and the material parameters were defined using the concepts of solid mechanics considering the planar stress conditions. Theoretical calculations, experimental observations, and finite element analysis were executed to calculate the J value for different strain percentages. Different hyperelastic material models were used to understand the hyperelastic behavior of the test compound, but Yeoh model was found to be the best fit with the least error against the experimental test data. The frequency sweep dynamic mechanical analyzer test was done to observe the viscoelastic response of the material. It was observed that the J value decreased with decreasing contour radius and had exhibited stark difference with the global tearing energy values, indicating the effects of stress softening and the dependence of J value on the elastic characteristics of the material. Further, the J value attained from finite element methods for a random strain 22% was used to predict the crack growth rate of the pre-notched PS specimen.

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Why is it important?

In the present work, an effort was taken to derive the J-integral expression as mentioned in Equation (2) for a PS specimen of carbon black filled natural rubber (NRC) using planar tension test data and state that the tearing energy term in Equation (4) is similar to the theoretical energy release rate (J-value) for a notched specimen at a specified strain percentage, and that J-integral value is the energy release rate which stays constant for a specimen at a particular strain percentage. Further, the energy release rate (J-value) was calculated using theoretical calculations, finite element analysis, and experimental methods against strain percentages 15%, 20%, 25%, and 30% for comparison. Regarding finite element analysis, the hyperelastic test data for Abaqus software was obtained from uniaxial hyperelastic test. Different models like Neo-Hookean, Mooney-Rivlin, and Yeoh were equated to compare the results with hyperelastic test data. It was found that the Yeoh model was the best fit for the domain of strain percentage values. The frequency sweep dynamic mechanical analyzer test was done at 1% strain/room temperature to determine the viscoelastic behavior of the compound. The results achieved were added as a combined test data with the additional planar tension test data in Abaqus software to obtain the J value. At last, we have calculated the crack growth rate (dc/dn) for all the strain percentages (15, 20, 25, 30) with the ancillary plots of dc/dn versus energy release rate. As B and β are material constants, so they were noted from experimental observations and dc/dn for a random strain value of 22% was predicted.

Perspectives

By this work, we conclude that our approach toward predicting the crack growth rate would be crucial for understanding the life cycle of blend compounds used in tread and sidewall sections of tyre exposed to extreme road conditions where strain percentage, temperature, and frequency have a synergistic role to play for the cut and chip behavior. Further, by using the the crack growth rate prediction, one can attempt to understand different energy absorption and release mechanisms at the crack closure points due to defect sites in tyres in future.

Anandarup Bhattacharyya
Chonbuk National University

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This page is a summary of: Insights on the J‐integral expression of pure shear carbon black filled natural rubber specimen and predicting the crack growth rate using finite element method, SPE Polymers, December 2023, Wiley,
DOI: 10.1002/pls2.10111.
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