{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,2]],"date-time":"2025-08-02T05:22:47Z","timestamp":1754112167174,"version":"3.37.3"},"reference-count":24,"publisher":"IOP Publishing","issue":"5","license":[{"start":{"date-parts":[[2024,5,14]],"date-time":"2024-05-14T00:00:00Z","timestamp":1715644800000},"content-version":"vor","delay-in-days":13,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2024,5,14]],"date-time":"2024-05-14T00:00:00Z","timestamp":1715644800000},"content-version":"tdm","delay-in-days":13,"URL":"https:\/\/iopscience.iop.org\/info\/page\/text-and-data-mining"}],"content-domain":{"domain":["iopscience.iop.org"],"crossmark-restriction":false},"short-container-title":["Mater. Res. Express"],"published-print":{"date-parts":[[2024,5,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper suggests a simple methodology to optimize the uniaxial fatigue predictions for filled natural rubbers. In this study, the stress ratio <jats:inline-formula>\n                     <jats:tex-math>\n\n<\/jats:tex-math>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi>R<\/mml:mi>\n                     <\/mml:math>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"mrxad45baieqn1.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula> effect on rubber fatigue life is investigated numerically. For this purpose, a Finite Element model is developed to determine both amplitude and mean stress values in the critical zone of the considered specimen. The suggested model incorporates the <jats:inline-formula>\n                     <jats:tex-math>\n\n<\/jats:tex-math>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi>R<\/mml:mi>\n                     <\/mml:math>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"mrxad45baieqn2.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula> ratio effect using an equivalent stress amplitude. It is proven that the new model can efficiently describe the fatigue life for a large <jats:inline-formula>\n                     <jats:tex-math>\n\n<\/jats:tex-math>\n                     <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" overflow=\"scroll\">\n                        <mml:mi>R<\/mml:mi>\n                     <\/mml:math>\n                     <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"mrxad45baieqn3.gif\" xlink:type=\"simple\"\/>\n                  <\/jats:inline-formula>-value interval with higher accuracy.<\/jats:p>","DOI":"10.1088\/2053-1591\/ad45ba","type":"journal-article","created":{"date-parts":[[2024,4,30]],"date-time":"2024-04-30T22:44:48Z","timestamp":1714517088000},"page":"055307","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":3,"title":["A simple fatigue methodology for filled natural rubbers under positive and negative R ratios"],"prefix":"10.1088","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9629-145X","authenticated-orcid":true,"given":"Salma","family":"Belkhiria","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anis","family":"Abroug","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raouf","family":"Fathallah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"266","published-online":{"date-parts":[[2024,5,14]]},"reference":[{"key":"mrxad45babib1","first-page":"1","article-title":"FE and probabilistic analysis for rubber life estimation considering cracking energy density as a fatigue predictor","volume":"31","author":"Belkhiria","year":"2023","journal-title":"Polym. 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