The Equilibrium State of the Softened Elastomeric Nanocomposite under Uniaxial Loading and its Independence From the Method of Material Softening
DOI:
https://doi.org/10.17072/1993-0550-2024-4-95-103Keywords:
stress, strain, cyclic strain, stress relaxation, aging, tensile strain rate, Mullins softening effectAbstract
For a mathematical model of an elastomeric material, the researcher must describe its equilibrium curve. This curve can be obtained by very slow stretching or by stress relaxation points at a given deformation. Experimental studies of filled elastomers and the effect of stress relaxation at 100% deformation from the stretching rate were conducted. The aim of the study was to determine how the stretching rate of the material affects the equilibrium state of the nanocomposite. Tests were performed for the specimens of butadienenitrile rubber containing 40 parts by weight of black carbon and butadiene-styrene rubber containing 50 parts by weight of black carbon. The specimens were stretched to the strain of 100 % at the rates of 10, 100, 1200 %/min and then aged for 2 hours. The specimens were subjected to tensile-compressive loads up to the strain of 100 % during 200-cycle test, and then were aged at maximum strain for 2 hours. It was found that the tensile rate affects the stress relaxation only at the early stage of aging – up to 15 minutes – after which the stress relaxation curves coincide. In cyclic testing, a decrease in the stress magnitude at the point of maximum strain is very slow and does not coincide with the relaxation curves, but with increasing time of holding one can observe a complete coincidence of the stress and relaxation curves. Such behavior of elastomers is due to their viscoelasticity and the accumulation of damage during stress relaxation at maximum deformation and cyclic testing.References
Chaimoon K., Chindaprasirt P. An anisotropic hyperelastic model with an application to soft tisues // European Journal of Mechanics / A Solids. 2019. Vol. 78. Р. 103845. URL: doi:10.1016/j.euromechsol.2019.103845 (дата обращения: 10.10.2024).
Külcü I.D. A hyperelastic constitutive model for rubber-like materials // Archive of Applied Mechanics. 2020. Vol. 90. P. 615–622. URL: doi:10.1007/s00419-019-01629-7 (дата обращения: 10.10.2024).
Zhan L., Wang S., Qu S., Steinmann P., Xiao R. A general continuum damage model for soft composites // Journal of the Mechanics and Physics of Solids. 2023. Vol. 175, Is. 3. P. 105290. URL: https://doi.org/10.1016/j.jmps.2023.105290 (дата обращения: 10.10.2024).
Xiang Y., Zhong D., Rudykh S., Zhou H., Qu, S., & Yang, W. A Review of Physically Based and Thermodynamically Based Constitutive Models for Soft Materials // Journal of Applied Mechanics.2020. Vol. 87, no. 11. Р. 110801. URL: https://doi.org/10.1115/1.4047776 (дата обращения: 10.10.2024).
Akbari R., Morovati V., Dargazany R. Reverse physically motivated frameworks for investigation of strain energy function in rubber-like elasticity // International Journal of Mechanical Sciences. 2022. Vol. 221. P. 107110. URL: doi:10.1016/j.ijmecsci.2022.107110 (дата обращения: 10.10.2024).
Zhu P., Zhong Z. Constitutive modelling for the mullins effect with permanent set and induced anisotropy in particle-filled rubbers // Applied Mathematical Modelling. 2021. Vol. 97. P. 19–35. URL: doi: 10.1016/j.apm.2021.03.031 (дата обращения: 10.10.2024).
Zhong D., Xiang Y., Yin T., Yu H., Qu S., Yang W. A physically-based damage model for soft elastomeric materials with anisotropic Mullins effect // International Journal of Solids and Structure. 2019. Vol. 176–177. P. 121–134. URL: doi: 10.1016/j.ijsolstr.2019.05.018 (дата обращения: 10.10.2024).
Fazekas B., Goda T.J. Constitutive modelling of rubbers: Mullins effect, residual strain, time-temperature dependence // International Journal of Mechanical Sciences. 2021. Vol. 210. Р. 106735. URL: https://doi.org/10.1016/j.ijmecsci.2021.106735 (дата обращения: 10.10.2024).
Shadrin V.V., Svistkov A.L., Mokhireva K.A., Garishin O.K. Peculiarities of using dumbbell specimens made of elastomeric materials subject to finite deformation in complex loading tests // J. Letters on Materials. 2023 Vol. 13, no. 1. P. 56–61. URL: https://lettersonmaterials.com/Upload/Journals/42127/56-61_u.pdf (дата обращения: 10.10.2024).
Zhou J, Jiang L, Khayat R.E. A micro-macro constitutive model for finite-deformation viscoelasticity of elastomers with nonlinear viscosity // Journal of the Mechanics and Physics of Solids. 2018. Vol. 110. P. 137–154. URL: https://doi.org/10.1016/j.jmps.2017.09.016 (дата обращения: 10.10.2024).
Wei W., Yuan Y., Igarashi A., Zhu H., Luo K. Generalized hyper-viscoelastic modeling and experimental characterization of unfilled and carbon black filled natural rubber for civil structural applications // Construction and Building Materials. 2020. Vol. 253. Р. 119211. URL: doi: 11.1016/j.conbuildmat.2020.119211.
Ricker A., Gierig M., Wriggers P. Multiplicative, Non-Newtonian Viscoelasticity Models for Rubber Materials and Brain Tissues: Numerical Treatment and Comparative Studies // Archives of Computational Methods in Engineering. 2023. Vol. 30. P. 2889–2927. URL: https://doi.org/10.1007/s11831-023-09889-x (дата обращения: 10.10.2024).
Annarasa V., Popov A.A., De Focatiis D.S.A. A phenomenological constitutive model for the viscoelastic deformation of elastomers // Mechanics of Time-Dependent Materials. 2020. Vol. 24. P. 463–479. URL: https://doi.org/10.1007/s11043-020-09452-2 (дата обращения: 10.10.2024).
Anssari-Benam A., Hossain M. A pseudo-hyperelastic model incorporating the rate effects for isotropic rubber-like materials // Journal of the Mechanics and Physics of Solids. 2023. p. 105347. URL: doi: https://doi.org/10.1016/j.jmps.2023.105347 (дата обращения: 10.10.2024).
Mullins L., Tobin N.R. Stress softening in rubber vulcanizates. Part I. Use of a strain amplification factor to describe the elastic behavior of filler reinforced vulcanized rubber // J. Appl. Polym. Sci. 1965. Vol. 9, no. 9. P. 2993–3009. URL: https://doi.org/10.1002/app. 1965.070090906 (дата обращения: 10.10.2024).
Harwood J.A.C., Mullins L., Payne A.R. Stress softening in natural rubber vulcanizates. Part II. Stress softening effects in pure gum and filler loaded rubbers // J. Appl. Polym. Sci. 1965. Vol. 9, no. 9. P. 3011–3021. URL: https://doi.org/10.1002/app.1965.070090907 (дата обращения: 10.10.2024).
Rickaby S.R., Scott N.H. A cyclic stress softening model for the Mullins effect // International Journal of Solids and Structures. Elsevier. 2013. Vol. 50. P. 111–120. URL: www.elsever.com/locate/ijsolstr (дата обращения: 10.10.2024).
Diani J., Brieu M., Gilormini P. Observation and modeling of the anisotropic viscohyperelastick behavior of a rubberlike material // International Journal of Solids and Structures. Elsevier. 2006. V. 43. P. 3044–3056. URL: www.elsever.com/locate/ijsolstr (дата обращения: 10.10.2024).
Netzker C. Husnu D., Kaliske M. An andochronic plasticity formulation for filled rubber // International Journal of Solids and Structures. Elsevier. 2010. Vol. 47. P. 2371–2379. URL: www.elsevier.com/locate/ijsolstr (дата обращения: 10.10.2024).
Kislitsyn V.D., Svistkov A.L., Mokhireva K.A., Shadrin V.V. Determination of the inelastic behavior of viscoelastic materials using the new thermodynamic model // AIP Conference Pro-ceedings 2627, Is. 1, 030002 (2023) URL: https://doi.org/10.1063/5.0119254 (дата обращения: 10.10.2024).
Shadrin V.V. Recovery of the mechanical properties of rubber under thermal treatment // Polymer Science. 2005. Ser. B. Vol. 47, no. 7–8. P. 220–222. URL: https://www.researchgate.net/publication/280315559_Recovery_of_the_mechanical_properties_of_rubber_under_thermal_treatment_Polymer_Science_Ser_B_2005_-_V_47_No_7-8_-_P_220-222 (дата обращения: 10.10.2024).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Владимир Васильевич Шадрин
This work is licensed under a Creative Commons Attribution 4.0 International License.
Articles are published under license Creative Commons Attribution 4.0 International (CC BY 4.0).
