Citation: Sukcharoen, K.;
Noraphaiphipaksa, N.; Hasap, A.;
Kanchanomai, C. Experimental and
Numerical Evaluations of Localized
Stress Relaxation for Vulcanized
Rubber. Polymers 2022, 14, 873.
https://doi.org/10.3390/
polym14050873
Academic Editors: Yuan Yao, Yi Liu
and Stefano Sfarra
Received: 27 January 2022
Accepted: 21 February 2022
Published: 23 February 2022
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polymers
Article
Experimental and Numerical Evaluations of Localized Stress
Relaxation for Vulcanized Rubber
Kijvanish Sukcharoen
1
, Nitikorn Noraphaiphipaksa
1,2
, Anat Hasap
3
and Chaosuan Kanchanomai
1,
*
1
Department of Mechanical Engineering, Faculty of Engineering, Thammasat University,
Pathumthani 12120, Thailand; sukcharoen@engr.tu.ac.th (K.S.); noraphaiphipaksa@gmail.com (N.N.)
2
Nitikorn Research Partner Co., Ltd., Lumlukka, Pathumthani 12150, Thailand
3
Railway Transportation System Testing Center, Thailand Institute of Scientific and Technological Research,
Pathumthani 12120, Thailand; anat@tistr.or.th
* Correspondence: kchao@engr.tu.ac.th; Tel.: +66-02-564-3001; Fax: +66-02-564-3010
Abstract: Vulcanized rubbers are commonly used to provide the energy absorption under com-
pressive deformation from other engineering components. However, if a constant compressive
deformation is maintained on rubber, the load response is not constant but decreases with time;
i.e., the stress relaxation. A decrease in force response with time of rubber can be experimentally
evaluated by the stress relaxation test. In the present work, the localized stress of vulcanized rubber
during a compressive stress relaxation test (i.e., ASTM D6147) was evaluated. Hyperelastic behavior
was assumed during rapid application of strain, while the viscoelastic behavior was assumed during
stress relaxation. Hyperelastic and viscoelastic parameters were experimentally evaluated using a
standard specimen. Finite element analysis (FEA) models were applied for the predictions of stress
relaxations of rubbers with various geometries and applied strains. FEA results were in good agree-
ment with results of the stress relaxation tests. Localized stresses in rubber during rapid application
of compressive strain and stress relaxation were successfully evaluated. The findings can give the
localized phenomena of vulcanized rubber during a stress relaxation test, which can be used as a
guideline for the design, usage, and improvement of rubber and viscoelastic polymeric components.
Keywords: stress relaxation; localized stress; viscoelastic; rubber; finite element analysis
1. Introduction
Vulcanized rubbers are commonly used to provide the energy absorption under
compressive deformation from other engineering components. They can be operated
under large deformation from compressive load, and recovers to the original dimension
when the compressive load is removed. However, if a constant compressive deformation
is maintained on rubber, the load response is not constant but decreases with time; i.e.,
the stress relaxation [1]. During assembly of engineering components, the compressive
deformation of rubber can be induced from the weight of the components as well as the
assembled load. With the increase in operation period, the tightness of the assembly may
be compromised by the stress relaxation of rubber.
A decrease in force response with time of rubber can be experimentally evaluated by
the stress relaxation test. Under the jurisdiction of ASTM Committee on Rubber, as well
as ASTM Subcommittee on Time and Temperature-Dependent Physical Properties, the
ASTM D6147 [2] has been proposed for determining the force decay of vulcanized rubber
or thermoplastic elastomer under a constant compressive deformation. Based on ASTM
D6147 recommendations, the compression of a specimen to the specified value should be
completed within 30 s. Subsequently, the deformation is maintained constant, while the
reduction in force response with time was measured.
Under rapid application of compressive strain, the stress–strain relationship of rubber
is assumed to be non-linearly elastic, isotropic, and incompressible. As a constitutive
Polymers 2022, 14, 873. https://doi.org/10.3390/polym14050873 https://www.mdpi.com/journal/polymers