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Modeling and Experimental Verification of Torsional Deformation Constitutive Model of Tread Rubber Based on Digital Image Correlation

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Abstract

Due to the complex constitutive relationship of tread rubber and the strong non-linearity of the dynamic contact relationship between tread rubber and road surface, the torsional deformation characteristics and distribution mechanism are difficult to be modeled theoretically in the tire contact patch. In order to accurately express the nonlinear flexible large deformation of tire tread block under torsional condition, the constitutive theory modeling of tread rubber based on continuum mechanics and the constitutive model verification based on improved digital image correlation are studied. A novel constitutive model considering the hyperelastic, viscoelastic and frictional property of tread rubber is established. A full-field measuring equipment for torsional deformation of tread block is established based on machine vision technology. The digital image sequence of instantaneous torsion deformation is analyzed by the improved digital image correlation to obtain the strain rate distribution characteristics and distribution law of the marker points and the whole area of the tread block. The analysis results demonstrate that the proposed constitutive model is feasible to predict the full-field distribution characteristics and distribution trend of tread rubber blocks in the contact patch.

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References

  1. Pacejka H (2006) Tyre and vehicle dynamics. Butterworth-Heinemann 1:1–60. https://doi.org/10.1016/B978-0-7506-6918-4.X5000-X

  2. Rajamani R (2012) Vehicle dynamics and control. Springer New York 4:51–93. https://doi.org/10.1007/0-387-28823-6

  3. Brusarosco M, Cigada A, Manzoni S (2011) Measurement and analysis of tyre and tread block dynamics due to contact phenomena. Veh Syst Dyn 49:855–869

    Article  Google Scholar 

  4. Potter T (2014) Dynamics and Stability of Rolling Viscoelastic Tires. United States. https://doi.org/10.2172/1171547

  5. Jung SP, Park TW, Chung WS (2011) Dynamic analysis of rubber-like material using absolute nodal coordinate formulation based on the non-linear constitutive law. Nonlinear Dyn 63:149–157

    Article  Google Scholar 

  6. Beda T (2014) An approach for hyperelastic model-building and parameters estimation a review of constitutive models. Eur Polym J 50:97–108

    Article  CAS  Google Scholar 

  7. Bechir H, Chevalier L, Chaouche M, Boufala K (2006) Hyperelastic constitutive model for rubber-like materials based on the first seth strain measures invariant. Eur J Mech 25:110–124

    Article  Google Scholar 

  8. Mooney M (1940) A theory of large elastic deformation. J Appl Phys 11:582–592

    Article  Google Scholar 

  9. Yeoh HO (2012) Characterization of elastic properties of carbon-black-filled rubber vulcanizates. Rubber Chem Technol 63:792–805

    Article  Google Scholar 

  10. Ogden W (1986) R, Recent advances in the phenomenological theory of rubber elasticity. Rubber Chem Technol 59:361–383

    Article  CAS  Google Scholar 

  11. Muhr AH (2005) Modeling the stress-strain behavior of rubber. Rubber Chem Technol 78:391–425

    Article  CAS  Google Scholar 

  12. Treloar L (1943) Rg, The elasticity of a network of long-chain molecules. Rubber Chem Technol 16:746–751

    Article  Google Scholar 

  13. Hubert M, James E (1943) Theory of the elastic properties of rubber. J Chem Phys 11. https://doi.org/10.1063/1.1723785

  14. Flory PJ, Rehner J (1943) Statistical mechanics of cross-linked polymer networks. J Chem Phys 11:512–520

    Article  CAS  Google Scholar 

  15. Arruda EM, Boyce MC (1993) A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J Mech Phys Solids 41:389–412

    Article  CAS  Google Scholar 

  16. Miaojuan P (2006) Research on nonlinear constitutive relationship of permanent deformation in asphalt pavements. Series GPhysics Mech Astron 33–44

  17. Drozdov AD (1998) Mechanics of viscoelastic solids. John Wiley Sons. https://www.directtextbook.com/isbn/0471975125

  18. Bernstein B, Kearsley EA, Zapas LJ (1963) A study of stress relaxation with finite strain. J Rheol 7:391–410

    Google Scholar 

  19. Coleman BD, Noll W (1961) Foundations of linear viscoelasticity. Rev Mod Phys 33:239–249

    Article  Google Scholar 

  20. Gemant A (2009) On fractional differentials. Philos Mag 25:540–549

    Article  Google Scholar 

  21. Bagley RL, Torvik PJ (1979) Experimental verification of a generalized derivative uniaxial shear constitutive relation for the elastomer 3M–467. J Acoust Soc Am 65:58–71

    Article  Google Scholar 

  22. Bagley L (1998) R, On the Fractional calculus model of viscoelastic behavior. J Rheol 30:133–155

    Article  Google Scholar 

  23. Alison HL, Evangelos T (1989) Optical measurement method. EP88307458.5. https://www.surechembl.org/document/EP-0304230-A2

  24. Takaya Y, Hayashi T, Michihata M (2014) Displacement measuring device and displacement measuring method. US13959076. https://www.mianfeiwendang.com/doc/09918d2d8e9577c057051e49692a223a04334858

  25. Verbruggen TW (2012) Device and method for measuring strain. EP09775358B1. https://www.mysciencework.com/patent/show/device-method-measuring-strain-EP2417417B1

  26. Chu YC, Chen KH, Chen JH, Tseng HK, Chang YS (2014) A novel optical method for measuring the thin film stress. International Symposium on Photonics and Optoelectronics 381–384. https://doi.org/10.1117/12.2069833

  27. Wahl F, So S, Wong K (2010) A hybrid optical-digital image processing method for surface inspection. Ibm J Res Dev 27:376–385

    Article  Google Scholar 

  28. Tao L, Yang Z, Yi W, Duan C, Wang Z (2020) Research on digital image correlation method used for strain detection. J Phys Conf Ser 1453:12051

    Article  Google Scholar 

  29. Li J, Yang G, Siebert T, Shi MF, Yang L (2018) A method of the direct measurement of the true stress-strain curve over a large strain range using multi-camera digital image correlation. Opt Lasers Eng 107:194–201

    Article  Google Scholar 

  30. Hiraoka N, Matsuzaki R, Todoroki A (2009) Concurrent monitoring of in-plane strain and out-of-plane displacement of tire using digital image correlation method. J Solid Mech Mater Eng 3:1148–1159

    Article  Google Scholar 

  31. Gao X, Zhuang Y, Liu S, Fan W, Chen Q (2020) High-speed 3D digital image correlation for rolling deformation of tire sidewall and measuring dynamiccontact patch length. Appl Opt 59

  32. Gao X, Zhuang Y, Liu S (2020) High-speed 3D digital image correlation for measuring tire rolling resistance coefficient. Measurement 171:108830

    Article  Google Scholar 

  33. Gao X, Zhuang Y, Liu S, Zhu CW, Chen Q (2019) Digital image correlation to analyze slip state of tire tread block in the cornering condition. Optik 185:571–584

    Article  Google Scholar 

  34. Gil-Negrete N, Vinolas J, Kari L (2009) A nonlinear rubber material model combining fractional order viscoelasticity and amplitude dependent effects. J Appl Mech 76:11009

    Article  Google Scholar 

  35. Bagley RL, Torvik PJ (2000) A theoretical basis for the application of fractional calculus to viscoelasticity. J Rheol 27:201–210

    Article  Google Scholar 

  36. Papoulia KD, Panoskaltsis VP, Kurup NV, Korovajchuk I (2010) Rheological representation of fractional order viscoelastic material models. Rheol Acta 49:381–400

    Article  CAS  Google Scholar 

  37. Makris N, Constantinou MC (1991) fractional-derivative maxwell model for viscous dampers. J Struct Eng 117:2708–2724

    Article  Google Scholar 

  38. Pritz T (2015) Analysis of four-parameter fractional derivative model of real solid materials. J Sound Vib 195:103–115

    Article  Google Scholar 

  39. Atanackovic TM (2002) A modified zener model of a viscoelastic body. Contin Mech Thermodyn 14:137–148

    Article  Google Scholar 

  40. Aytac A (2014) A new fractional derivative model for linearly viscoelastic materials and parameter identification via genetic algorithms. Rheol Acta 53:219–233

    Article  Google Scholar 

  41. Dill EH (2006) Continuum mechanics: elasticity, plasticity, viscoelasticity. CRC Press 5:1–26. https://doi.org/10.1201/9781420009828

    Article  Google Scholar 

  42. Oden JT, Martins J (1985) Models and computational methods for dynamic friction phenomena. Comput Methods Appl Mech Eng 52:527–634

    Article  Google Scholar 

  43. Shabana AA (2012) Computational continuum mechanics. Cambridge University Press 6:231–284. https://onlinelibrary.wiley.com/doi/book/10.1002/9781119293248

  44. Shabana AA (1998) A computer implementation of the absolute nodal coordinate formulation for flexible multibody dynamics. Nonlinear Dyn 16:293–306

    Article  Google Scholar 

  45. Langerholc M, Slavi J, Bolte M (2013) Absolute nodal coordinates in digital image correlation. Exp Mech 53:807–818

    Article  Google Scholar 

  46. Orteu J (2009) Image Correlation for shape, motion and deformation measurements, image correlation for shape, motion and deformation measurements.

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Acknowledgements

This research was supported by the Science and Technology Research Project of Education Department of Jilin Province (JJKH20220677KJ), the National Natural Science Foundation of China (61790564) and the National Key Research and Development Program of China (2018YFB0104804).

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Authors and Affiliations

  1. School of Mechatronic Engineering, Changchun University of Technology, Changchun, 130012, Jilin, China

    X. Gao, Y. Wang, X. Yue, Y. Liu, Y. Yan & J. Wang

  2. Department of Chassis Parts, North China Vehicle Research Institute, Beijing, 100072, China

    W. Fan & Z. Long

  3. Durable Section of Chassis Test and Research Department, CATARC Automotive Test Center (Tianjin) Co., Ltd, Tianjin, 130012, China

    X. Li

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  1. X. Gao
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Correspondence to X. Gao.

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Gao, X., Wang, Y., Fan, W. et al. Modeling and Experimental Verification of Torsional Deformation Constitutive Model of Tread Rubber Based on Digital Image Correlation. Exp Tech 47, 749–765 (2023). https://doi.org/10.1007/s40799-022-00583-4

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