  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 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 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