An experimental method for estimating the tearing energy in rubber-like materials using the true stored energy

Abstract A method for determining the critical tearing energy in rubber-like materials is proposed. In this method, the energy required for crack propagation in a rubber-like material is determined by the change of recovered elastic energy which is obtained by deducting the dissipated energy due to...

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Autor principal:	Elsiddig Elmukashfi
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/6bb08bccdc5c45d2a2acc1aa5136882c
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spelling	oai:doaj.org-article:6bb08bccdc5c45d2a2acc1aa5136882c2021-12-02T15:07:47ZAn experimental method for estimating the tearing energy in rubber-like materials using the true stored energy10.1038/s41598-021-95151-y2045-2322https://doaj.org/article/6bb08bccdc5c45d2a2acc1aa5136882c2021-08-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-95151-yhttps://doaj.org/toc/2045-2322Abstract A method for determining the critical tearing energy in rubber-like materials is proposed. In this method, the energy required for crack propagation in a rubber-like material is determined by the change of recovered elastic energy which is obtained by deducting the dissipated energy due to different inelastic processes from the total strain energy applied to the system. Hence, the classical method proposed by Rivlin and Thomas using the pure shear tear test is modified using the actual stored elastic energy. The total dissipated energy is evaluated using cyclic pure shear and simple shear dynamic experiments at the critical stretch level. To accurately estimate the total dissipated energy, the unloading rate is determined from the time the crack takes to grow an increment. A carbon-black-filled natural rubber is examined in this study. In cyclic pure shear experiment, the specimens were cyclically loaded under quasi-static loading rate of $$0.01~{\rm {s}}^{-1}$$ 0.01 s - 1 and for different unloading rates, i.e. $$0.01$$ 0.01 , $$0.1$$ 0.1 and $$1.0~{\rm {s}}^{-1}$$ 1.0 s - 1 . The simple shear dynamic experiment is used to obtain the total dissipated energy at higher frequencies, i.e. $$0.5$$ 0.5 - $$18~{\rm {Hz}}$$ 18 Hz which corresponds to unloading rates $$0.46$$ 0.46 - $$16.41~{\rm {s}}^{-1}$$ 16.41 s - 1 , using the similarities between simple and pure shear deformation. The relationship between dissipated energy and unloading stretch rate is found to follow a power-law such that cyclic pure shear and simple shear dynamic experiments yield similar result. At lower unloading rates (i.e. $${\dot{\lambda }}_{\rm {U}} < 1.0~{\rm {s}}^{-1}$$ λ ˙ U < 1.0 s - 1 ), Mullins effect dominates and the viscous dissipation is minor, whereas at higher unloading rates, viscous dissipation becomes significant. At the crack propagation unloading rate $$125.2~{\rm {s}}^{-1}$$ 125.2 s - 1 , the viscous dissipation is significant such that the amount of dissipated energy increases approximately by $$125.4\%$$ 125.4 % from the lowest unloading rate. The critical tearing energy is obtained to be $$7.04~{\rm {kJ}}/{\rm {m}}^{2}$$ 7.04 kJ / m 2 using classical method and $$5.12~{\rm {kJ}}/{\rm {m}}^{2}$$ 5.12 kJ / m 2 using the proposed method. Hence, the classical method overestimates the critical tearing energy by approximately $$37.5\%$$ 37.5 % .Elsiddig ElmukashfiNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-11 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Elsiddig Elmukashfi An experimental method for estimating the tearing energy in rubber-like materials using the true stored energy
description	Abstract A method for determining the critical tearing energy in rubber-like materials is proposed. In this method, the energy required for crack propagation in a rubber-like material is determined by the change of recovered elastic energy which is obtained by deducting the dissipated energy due to different inelastic processes from the total strain energy applied to the system. Hence, the classical method proposed by Rivlin and Thomas using the pure shear tear test is modified using the actual stored elastic energy. The total dissipated energy is evaluated using cyclic pure shear and simple shear dynamic experiments at the critical stretch level. To accurately estimate the total dissipated energy, the unloading rate is determined from the time the crack takes to grow an increment. A carbon-black-filled natural rubber is examined in this study. In cyclic pure shear experiment, the specimens were cyclically loaded under quasi-static loading rate of $$0.01~{\rm {s}}^{-1}$$ 0.01 s - 1 and for different unloading rates, i.e. $$0.01$$ 0.01 , $$0.1$$ 0.1 and $$1.0~{\rm {s}}^{-1}$$ 1.0 s - 1 . The simple shear dynamic experiment is used to obtain the total dissipated energy at higher frequencies, i.e. $$0.5$$ 0.5 - $$18~{\rm {Hz}}$$ 18 Hz which corresponds to unloading rates $$0.46$$ 0.46 - $$16.41~{\rm {s}}^{-1}$$ 16.41 s - 1 , using the similarities between simple and pure shear deformation. The relationship between dissipated energy and unloading stretch rate is found to follow a power-law such that cyclic pure shear and simple shear dynamic experiments yield similar result. At lower unloading rates (i.e. $${\dot{\lambda }}_{\rm {U}} < 1.0~{\rm {s}}^{-1}$$ λ ˙ U < 1.0 s - 1 ), Mullins effect dominates and the viscous dissipation is minor, whereas at higher unloading rates, viscous dissipation becomes significant. At the crack propagation unloading rate $$125.2~{\rm {s}}^{-1}$$ 125.2 s - 1 , the viscous dissipation is significant such that the amount of dissipated energy increases approximately by $$125.4\%$$ 125.4 % from the lowest unloading rate. The critical tearing energy is obtained to be $$7.04~{\rm {kJ}}/{\rm {m}}^{2}$$ 7.04 kJ / m 2 using classical method and $$5.12~{\rm {kJ}}/{\rm {m}}^{2}$$ 5.12 kJ / m 2 using the proposed method. Hence, the classical method overestimates the critical tearing energy by approximately $$37.5\%$$ 37.5 % .
format	article
author	Elsiddig Elmukashfi
author_facet	Elsiddig Elmukashfi
author_sort	Elsiddig Elmukashfi
title	An experimental method for estimating the tearing energy in rubber-like materials using the true stored energy
title_short	An experimental method for estimating the tearing energy in rubber-like materials using the true stored energy
title_full	An experimental method for estimating the tearing energy in rubber-like materials using the true stored energy
title_fullStr	An experimental method for estimating the tearing energy in rubber-like materials using the true stored energy
title_full_unstemmed	An experimental method for estimating the tearing energy in rubber-like materials using the true stored energy
title_sort	experimental method for estimating the tearing energy in rubber-like materials using the true stored energy
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/6bb08bccdc5c45d2a2acc1aa5136882c
work_keys_str_mv	AT elsiddigelmukashfi anexperimentalmethodforestimatingthetearingenergyinrubberlikematerialsusingthetruestoredenergy AT elsiddigelmukashfi experimentalmethodforestimatingthetearingenergyinrubberlikematerialsusingthetruestoredenergy
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An experimental method for estimating the tearing energy in rubber-like materials using the true stored energy

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