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Future trends in predicting the complex fracture behaviour of rubber materials

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Abstract

Future trends in predicting the fracture behaviour of rubber materials (products) are discussed. A complex methodology for the determination of rubber fracture behaviour from the energy viewpoint based on simulating realistic loading conditions in services applied to a rubber matrix in a laboratory test set-up is introduced. Because this is a pure rubber matrix investigation, additional effects such as rubber product design or assembling the final performance can be fully avoided. This methodology requires instrumented and automated laboratory equipment—an intrinsic strength analyser and a tear and fatigue analyser which represent the first commercialization of a classic method for assessing long-term durability. These testing methods are applied to quantify the behaviour of rubber compounds over a broad range of tearing energies—from the fatigue threshold up to the critical tearing energy or the ultimate tear strength \(T_{\mathrm {C}}\) to determine the relationship between fatigue crack growth rates da/dn versus the tearing energy T. This complex methodology was evaluated for carbon-black-reinforced compounds based on pure natural rubber and butadiene rubber typical for tire applications. Finally, the determined data were correlated with previous work done by Lake and Lindley (J Appl Polym Sci 9:1233–1251, 1965) as well as with practical experiences of tire manufacturers.

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Abbreviations

a (mm):

Crack length

B (mm):

Thickness

b (–):

Proportionality constant

\(\beta \) (–):

Material constant

da/dn (mm/cycle):

Fatigue crack growth rate

f (N):

Cutting force

\(F_{\mathrm {C}}\) (J/m\(^{2}\)):

Cutting energy

l (mm):

Clamp distance

\(L_{0}\) (mm):

Length of sample

m (–):

Material constant

n (cycle):

Loading cycles

\(S_{\mathrm {0,C}}\) (J/m\(^{2}\)):

Intrinsic cutting energy

T (J/m\(^{2}\)):

Tearing energy

\(T_{0}\) (J/m\(^{2}\)):

Intrinsic strength

\(T_{\mathrm {C}}\) (J/m\(^{2}\)):

Ultimate tear strength

W (J):

Recoverable elastic strain energy

\(W_{\mathrm {dis}}\) (J):

Dissipated energy

\(W_{\mathrm {ext}}\) (J):

External work

\(W_\mathrm{P}\) (mm):

Width of sample

\(W_{\mathrm {sep }}\) (J):

Local work of separation

CB:

Carbon black

CCD:

Charge-coupled device

BR:

Butadiene rubber

E-SBR:

Emulsion styrene–butadiene rubber

FCG:

Fatigue crack growth

NR:

Natural rubber

ISA:

Intrinsic strength analyser

ISO:

International organization for standardization

LLC:

Limited liability company

phr:

Parts per hundred rubber

rpm:

Rotation per minute

SBR:

Styrene–butadiene rubber

TFA:

Tear and fatigue analyser

USA:

United States of America

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Acknowledgements

This article was written with the support of the project Centre of Polymer Systems—Strengthening Research Capacity (Reg. Number: CZ.1.05/2.1.00/19.0409) as well as NPU I (LO1504).

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Authors and Affiliations

  1. Centre of Polymer Systems, Tomas Bata University in Zlín, Tomas Bata Av. 5678, Zlín, Czech Republic

    Radek Stoček, Martin Stěnička & Petr Zádrapa

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  1. Radek Stoček
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Correspondence to Radek Stoček.

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Communicated by Victor Eremeyev and Holm Altenbach.

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Stoček, R., Stěnička, M. & Zádrapa, P. Future trends in predicting the complex fracture behaviour of rubber materials. Continuum Mech. Thermodyn. 33, 291–305 (2021). https://doi.org/10.1007/s00161-020-00887-z

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