Development of styrene butadiene rubber-butadiene rubber with a hyperelastic model for vehicle tire design

Angki Apriliandi Rachmat; Muhammad Hisyam Ramadhan; Yati Mardiyati; I Wayan Suweca; Tatacipta Dirgantara; Angki Apriliandi Rachmat; Muhammad Hisyam Ramadhan; Yati Mardiyati; I Wayan Suweca; Tatacipta Dirgantara

doi:10.55981/j.mev.2025.1201

Development of styrene butadiene rubber-butadiene rubber with a hyperelastic model for vehicle tire design

Angki Apriliandi Rachmat, Muhammad Hisyam Ramadhan, Yati Mardiyati, I Wayan Suweca, Tatacipta Dirgantara

Abstract

This paper proposes a mathematical correlation between styrene butadiene rubber (SBR)-butadiene rubber (BR) composition and hyperelastic model parameters for numerical studies in vehicle tire design. Experimental, numerical, and curve-fitting methods were employed in this research. Experimental tests were conducted using tensile tests for SBR-BR. The numerical study of the SBR-BR tensile test was carried out using several classic hyperelastic models. The best hyperelastic model was selected based on the smallest deviation between numerical and experimental results. Curve-fitting was done between the best hyperelastic model parameters and the compound to obtain a new correlation, and it was validated. This research shows that the neo-Hookean model with 6 % deviation is the most suitable for the SBR-BR, and the mathematical correlation for SBR-BR composition and C₁₀ is linearly correlated. SBR60 %-BR40 % shows the optimum composition for non-pneumatic tires with the characteristic of maximum tensile strength 16.71 MPa, elongation 251 %, and 200 % modulus 13.04 MPa.

10.55981/j.mev.2025.1201

Keywords

mathematical correlation; styrene butadiene rubber; butadiene rubber; hyperelastic model; vehicle tire.

Full Text:

PDF

References

B. Erman, J. E. Mark, and C. M. Roland, “The Science and Technology of Rubber”, 4. ed. Amsterdam Heidelberg: Elsevier Academic Press, 2013.

V.M. Il’in and A.K. Rezova, “Styrene Butadiene Rubber: Production Worldwide,” Int. Polym. Sci. Technol., vol. 42, no. 10, pp. 35–44, Oct. 2015

Y. Dong, Y. Zhao, U. Hossain, Y. He, and P. Liu, “Life cycle assessment of vehicle tires : A systematic review,” Clean. Environ. Syst., vol. 2, no. March, p. 100033, 2021,

Y. Deng, Z. Wang, H. Shen, J. Gong, and Z. Xiao, “A comprehensive review on non-pneumatic tyre research,” Mater. Des., vol. 227, p. 111742, 2023,

“Verified market reports,” August 2024. Accessed: Aug. 13, 2024. [Online].

Z. Hryciów, J. Jackowski, and M. Żmuda, “The Influence of Non-Pneumatic Tyre Structure on its Operational Properties,” Int. J. Automot. Mech. Eng., vol. 17, no. 3, pp. 8168–8178, 2020,

D. P. Flanagan, P. Touchet, and H. O. Feuer, “Elastomers for Tracked Vehicles: 1980-1997 Program to Improve Durability of Rubber Tank Pads for Army Tracked Vehicles,” 2015. [Online].

Y. Yunazwin azaruddin, E. Leksono, and Z. Abidin, “Pengembangan Sistem Kontrol Traksi Mobil Elektrik Berbasis Rekonstruksi Keadaan Kecepatan Model Roda,” J. Mechatronics, Electr. Power, Veh. Technol., vol. 01, no. 2, pp. 2087–3379, 2010, [Online].

Bergstorm Edward W., “Wear Resistant Rubber Tank Track Pads,” 1975. [Online].

Y. Xu, Y. Liu, Y. Gao, L. Liu, and L. Zhang, “Designing high-performance green tire treads by reinforcing the styrene-butadiene rubber/silica interface with chain difunctionalization,” Compos. Part B Eng., vol. 290, p. 111887, 2025,

W. Liu, K. Cheng, and J. Wang, “Failure analysis of the rubber track of a tracked transporter,” Adv. Mech. Eng., vol. 10, no. 7, pp. 1–8, Jul. 2018,

Z. Zhang, F. Guo, Y. Ke, C. Xiang, and X. Jia, “Effect of vulcanization on deformation behavior of rubber seals: Thermal–mechanical–chemical coupling model, numerical studies, and experimental validation,” Mater. Des., vol. 224, Dec. 2022,

P. Meethum and C. Suvanjumrat, “Numerical Study of Dynamic Hydroplaning Effects on Motorcycle Tires,” Int. J. Automot. Mech. Eng., vol. 20, no. 1, pp. 10192–10210, 2023,

C. C. Ihueze and C. O. Mgbemena, “Modeling Hyperelastic Behavior of Natural Rubber/Organomodified Kaolin Composites Oleochemically Derived from Tea Seed Oils (Camellia sinensis) for Automobile Tire Side Walls Application,” J. Sci. Res. Reports, pp. 2528–2542, 2014,

M. Miñano and F. J. Montáns, “A formulation for hyperelastic damaged materials,” Civil-Comp Proc., vol. 108, pp. 1–12, 2015,

A. Rajesh, B. Satya Narayana, and K.Sreeramulu, “Characterization of Hyperelastic Material Using Experimental Data and Finite Element Simulation,” Mater. Today Proc., vol. 24, pp. 1660–1669, 2020,

U. Gudsoorkar and R. Bindu, “Computer simulation of hyper elastic re-treaded tire rubber with ABAQUS,” in Materials Today: Proceedings, Elsevier Ltd, 2020, pp. 1992–2001.

B. Yenigun, E. Gkouti, G. Barbaraci, and A. Czekanski, “Identification of Hyperelastic Material Parameters of Elastomers by Reverse Engineering Approach,” Materials (Basel)., vol. 15, no. 24, Dec. 2022,

X. Li and Y. Wei, “Classic strain energy functions and constitutive tests of rubber-like materials,” Rubber Chem. Technol., vol. 88, no. 4, pp. 604–627, Dec. 2015,

B. Fazekas and T. J. Goda, “Constitutive modelling of rubbers: Mullins effect, residual strain, time-temperature dependence,” Int. J. Mech. Sci., vol. 210, Nov. 2021,

M. G. Zhang et al., “Investigation on Mullins effect of rubber materials by spherical indentation method,” Forces Mech., vol. 4, Oct. 2021,

S. Samaei, M. H. R. Ghoreishy, and G. Naderi, “Effects of SBR molecular structure and filler type on the hyper-viscoelastic behavior of SBR/BR radial tyre tread compounds using a combined numerical/experimental approach,” Iran. J. Polym. Sci. Technol., vol. 32, no. 1, pp. 65–78, May 2019,

P. Thavamani, A. K. Bhowmick, and D. Khastgir, “Effect of ageing on strength and wear of tank track pad compounds,” Wear, vol. 170, no. 1, pp. 25–32, Nov. 1993,

H. He, Q. Zhang, Y. Zhang, J. Chen, L. Zhang, and F. Li, “A comparative study of 85 hyperelastic constitutive models for both unfilled rubber and highly filled rubber nanocomposite material,” Nano Mater. Sci., vol. 4, no. 2, pp. 64–82, Jun. 2022,

A. R. Zubir, K. Hudha, and N. H. Amer, “Enhanced Modeling of Crumple zone in Vehicle Crash Simulation Using Modified Kamal model Optimized with Gravitational Search Algorithm,” Automot. Exp., vol. 6, no. 2, pp. 372–383, 2023,

Y. Fan, G. D. Fowler, and M. Zhao, “The past, present and future of carbon black as a rubber reinforcing filler – A review,” J. Clean. Prod., vol. 247, p. 119115, Feb. 2020,

H. Boukfessa and B. Bezzazi, “The effect of carbon black on the curing and mechanical properties of natural rubber/ acrylonitrile- butadiene rubber composites,” J. Appl. Res. Technol., vol. 19, no. 3 SE-Articles, pp. 194–201, Jun. 2021,

L. M. N. Amin, I. Hanafi, and O. Nadras, “Comparative study of Bentonite filled acrylonitrile butadiene rubber and carbon black filled NBR composites properties,” Int. J. Automot. Mech. Eng., vol. 15, no. 3, pp. 5468–5475, 2018,

R. Umunakwe et al., “Effect of Varied Cure Temperature on the Cure Behavior, Mechanical Properties and Heat Build-Up of Solid Tire Tread Compound Containing Different Particles Sizes of Ground Tire Rubber,” J. Appl. Sci. Process Eng., vol. 11, no. 1, pp. 60–77, 2024,

A. N. Standard, “Standard Test Methods for Vulcanized Rubber and Thermoplastic Elastomers-Tension, ASTM D412,’’ American Society for Testing and Materials, Washington, D.C., USA, September 13, 1968. 1969. [Online].

B. Grynkiewicz-Bylina, B. Rakwic, M. Gawlik-Jędrysiak, M. Szymiczek, and B. Chmielnicki, “Methodology for Testing the Uniformity of the Composition of a Batch of Polymer Materials on the Example of Sbr Rubber Granulates in the Aspect of Potential Applications,” Adv. Sci. Technol. Res. J., vol. 18, no. 7, pp. 354–363, 2024,

V. Mykhailiuk et al., “Derivation of Material Constants for Experimental SKR-788 Silicone Samples via Simulation Modeling and Laboratory Testing,” Adv. Sci. Technol. Res. J., vol. 18, no. 5, pp. 268–276, 2024,

M. Fujikawa, N. Maeda, J. Yamabe, and M. Koishi, “Performance evaluation of hyperelastic models for carbon-black-filled SBR vulcanizates,” Rubber Chem. Technol., vol. 93, no. 1, pp. 142–156, 2020,

A. A. Rachmat, T. Dirgantara, I. W. Suweca, and Y. Mardiyati, “Kaji Numerik Ground Pad Shoe Kendaraan Tempur Dengan Model Material Hyperelastic,” Mesin, vol. 30, no. 1, pp. 64–74, 2024,

Touchet, Paul et al., “United states patent; ‘rubber compound for track vehicle tracks pad,’” 1993 [Online].

P. Sae-oui, K. Suchiva, C. Sirisinha, W. Intiya, P. Yodjun, and U. Thepsuwan, “Effects of Blend Ratio and SBR Type on Properties of Carbon Black-Filled and Silica-Filled SBR/BR Tire Tread Compounds,” Adv. Mater. Sci. Eng., vol. 2017, no. 1, p. 2476101, Jan. 2017.