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data-event-name="pinnable-header.vector-toc.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">hide</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">(Top)</div> </a> </li> <li id="toc-Stages_of_fatigue" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Stages_of_fatigue"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Stages of fatigue</span> </div> </a> <button aria-controls="toc-Stages_of_fatigue-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Stages of fatigue subsection</span> </button> <ul id="toc-Stages_of_fatigue-sublist" class="vector-toc-list"> <li id="toc-Crack_initiation" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Crack_initiation"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Crack initiation</span> </div> </a> <ul id="toc-Crack_initiation-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Crack_growth" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Crack_growth"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Crack growth</span> </div> </a> <ul id="toc-Crack_growth-sublist" class="vector-toc-list"> <li id="toc-Acceleration_and_retardation" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Acceleration_and_retardation"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.1</span> <span>Acceleration and retardation</span> </div> </a> <ul id="toc-Acceleration_and_retardation-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-Characteristics_of_fatigue" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Characteristics_of_fatigue"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Characteristics of fatigue</span> </div> </a> <ul id="toc-Characteristics_of_fatigue-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Timeline_of_research_history" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Timeline_of_research_history"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Timeline of research history</span> </div> </a> <ul id="toc-Timeline_of_research_history-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Predicting_fatigue_life" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Predicting_fatigue_life"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Predicting fatigue life</span> </div> </a> <button aria-controls="toc-Predicting_fatigue_life-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Predicting fatigue life subsection</span> </button> <ul id="toc-Predicting_fatigue_life-sublist" class="vector-toc-list"> <li id="toc-Stress-life_and_strain-life_methods" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Stress-life_and_strain-life_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Stress-life and strain-life methods</span> </div> </a> <ul id="toc-Stress-life_and_strain-life_methods-sublist" class="vector-toc-list"> <li id="toc-Miner's_rule" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Miner's_rule"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.1</span> <span>Miner's rule</span> </div> </a> <ul id="toc-Miner's_rule-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Stress-life_(S-N)_method" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Stress-life_(S-N)_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.2</span> <span>Stress-life (S-N) method</span> </div> </a> <ul id="toc-Stress-life_(S-N)_method-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Strain-life_(ε-N)_method" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Strain-life_(ε-N)_method"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1.3</span> <span>Strain-life (ε-N) method</span> </div> </a> <ul id="toc-Strain-life_(ε-N)_method-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Crack_growth_methods" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Crack_growth_methods"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Crack growth methods</span> </div> </a> <ul id="toc-Crack_growth_methods-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Dealing_with_fatigue" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Dealing_with_fatigue"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Dealing with fatigue</span> </div> </a> <button aria-controls="toc-Dealing_with_fatigue-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Dealing with fatigue subsection</span> </button> <ul id="toc-Dealing_with_fatigue-sublist" class="vector-toc-list"> <li id="toc-Design" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Design"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.1</span> <span>Design</span> </div> </a> <ul id="toc-Design-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Testing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Testing"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.2</span> <span>Testing</span> </div> </a> <ul id="toc-Testing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Repair" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Repair"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.3</span> <span>Repair</span> </div> </a> <ul id="toc-Repair-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Life_improvement" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Life_improvement"> <div class="vector-toc-text"> <span class="vector-toc-numb">5.4</span> <span>Life improvement</span> </div> </a> <ul id="toc-Life_improvement-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Fatigue_of_composites" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Fatigue_of_composites"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Fatigue of composites</span> </div> </a> <ul id="toc-Fatigue_of_composites-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Notable_fatigue_failures" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Notable_fatigue_failures"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Notable fatigue failures</span> </div> </a> <button aria-controls="toc-Notable_fatigue_failures-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Toggle Notable fatigue failures subsection</span> </button> <ul id="toc-Notable_fatigue_failures-sublist" class="vector-toc-list"> <li id="toc-Versailles_train_crash" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Versailles_train_crash"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.1</span> <span>Versailles train crash</span> </div> </a> <ul id="toc-Versailles_train_crash-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-de_Havilland_Comet" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#de_Havilland_Comet"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.2</span> <span>de Havilland Comet</span> </div> </a> <ul id="toc-de_Havilland_Comet-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Alexander_L._Kielland_oil_platform_capsizing" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Alexander_L._Kielland_oil_platform_capsizing"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.3</span> <span><i>Alexander L. Kielland</i> oil platform capsizing</span> </div> </a> <ul id="toc-Alexander_L._Kielland_oil_platform_capsizing-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Others" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Others"> <div class="vector-toc-text"> <span class="vector-toc-numb">7.4</span> <span>Others</span> </div> </a> <ul id="toc-Others-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span class="vector-toc-numb">9</span> <span>References</span> </div> </a> <ul id="toc-References-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Further_reading" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Further_reading"> <div class="vector-toc-text"> <span class="vector-toc-numb">10</span> <span>Further reading</span> </div> </a> <ul id="toc-Further_reading-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-External_links" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#External_links"> <div class="vector-toc-text"> <span class="vector-toc-numb">11</span> <span>External links</span> </div> </a> <ul id="toc-External_links-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Contents" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Toggle the table of contents" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Toggle the table of contents</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading">Fatigue (material): Difference between revisions</h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. Available in 44 languages" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-44" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">44 languages</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Metaalvermoeidheid" title="Metaalvermoeidheid – Afrikaans" lang="af" hreflang="af" data-title="Metaalvermoeidheid" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%83%D9%84%D8%A7%D9%84_(%D8%AE%D9%88%D8%A7%D8%B5_%D8%A7%D9%84%D9%85%D9%88%D8%A7%D8%AF)" title="كلال (خواص المواد) – Arabic" lang="ar" hreflang="ar" data-title="كلال (خواص المواد)" data-language-autonym="العربية" data-language-local-name="Arabic" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Fatiga_de_materiales" title="Fatiga de materiales – Asturian" lang="ast" hreflang="ast" data-title="Fatiga de materiales" data-language-autonym="Asturianu" data-language-local-name="Asturian" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A1%D1%82%D0%BE%D0%BC%D0%BB%D0%B5%D0%BD%D0%B0%D1%81%D1%86%D1%8C_%D0%BC%D0%B0%D1%82%D1%8D%D1%80%D1%8B%D1%8F%D0%BB%D0%B0%D1%9E" title="Стомленасць матэрыялаў – Belarusian" lang="be" hreflang="be" data-title="Стомленасць матэрыялаў" data-language-autonym="Беларуская" data-language-local-name="Belarusian" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A3%D0%BC%D0%BE%D1%80%D0%B0_%D0%BD%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D1%80%D0%B8%D0%B0%D0%BB%D0%B0" title="Умора на материала – Bulgarian" lang="bg" hreflang="bg" data-title="Умора на материала" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Fatiga_mec%C3%A0nica" title="Fatiga mecànica – Catalan" lang="ca" hreflang="ca" data-title="Fatiga mecànica" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/%C3%9Anava_materi%C3%A1lu" title="Únava materiálu – Czech" lang="cs" hreflang="cs" data-title="Únava materiálu" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Materialetr%C3%A6thed" title="Materialetræthed – Danish" lang="da" hreflang="da" data-title="Materialetræthed" data-language-autonym="Dansk" data-language-local-name="Danish" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Materialerm%C3%BCdung" title="Materialermüdung – German" lang="de" hreflang="de" data-title="Materialermüdung" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/V%C3%A4simus_(tugevus%C3%B5petus)" title="Väsimus (tugevusõpetus) – Estonian" lang="et" hreflang="et" data-title="Väsimus (tugevusõpetus)" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Fatiga_de_materiales" title="Fatiga de materiales – Spanish" lang="es" hreflang="es" data-title="Fatiga de materiales" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Laci%C4%9Do_(materialo)" title="Laciĝo (materialo) – Esperanto" lang="eo" hreflang="eo" data-title="Laciĝo (materialo)" data-language-autonym="Esperanto" data-language-local-name="Esperanto" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Nekea_materialetan" title="Nekea materialetan – Basque" lang="eu" hreflang="eu" data-title="Nekea materialetan" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AE%D8%B3%D8%AA%DA%AF%DB%8C_(%D9%85%D9%88%D8%A7%D8%AF)" title="خستگی (مواد) – Persian" lang="fa" hreflang="fa" data-title="خستگی (مواد)" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Fatigue_(mat%C3%A9riau)" title="Fatigue (matériau) – French" lang="fr" hreflang="fr" data-title="Fatigue (matériau)" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Strustuirse" title="Strustuirse – Irish" lang="ga" hreflang="ga" data-title="Strustuirse" data-language-autonym="Gaeilge" data-language-local-name="Irish" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%94%BC%EB%A1%9C_(%EC%9E%AC%EB%A3%8C)" title="피로 (재료) – Korean" lang="ko" hreflang="ko" data-title="피로 (재료)" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B6%E0%A5%8D%E0%A4%B0%E0%A4%BE%E0%A4%82%E0%A4%A4%E0%A4%BF_(%E0%A4%AA%E0%A4%A6%E0%A4%BE%E0%A4%B0%E0%A5%8D%E0%A4%A5)" title="श्रांति (पदार्थ) – Hindi" lang="hi" hreflang="hi" data-title="श्रांति (पदार्थ)" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Umor_materijala" title="Umor materijala – Croatian" lang="hr" hreflang="hr" data-title="Umor materijala" data-language-autonym="Hrvatski" data-language-local-name="Croatian" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kelelahan_(material)" title="Kelelahan (material) – Indonesian" lang="id" hreflang="id" data-title="Kelelahan (material)" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Fatica_(scienza_dei_materiali)" title="Fatica (scienza dei materiali) – Italian" lang="it" hreflang="it" data-title="Fatica (scienza dei materiali)" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%94%D7%AA%D7%A2%D7%99%D7%99%D7%A4%D7%95%D7%AA" title="התעייפות – Hebrew" lang="he" hreflang="he" data-title="התעייפות" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D2%9A%D0%B0%D0%B6%D1%83" title="Қажу – Kazakh" lang="kk" hreflang="kk" data-title="Қажу" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%9C%D0%B5%D1%82%D0%B0%D0%BB%D0%BB%D0%B4%D1%8B%D0%BD_%D1%87%D0%B0%D1%80%D1%87%D0%B0%D1%88%D1%8B" title="Металлдын чарчашы – Kyrgyz" lang="ky" hreflang="ky" data-title="Металлдын чарчашы" data-language-autonym="Кыргызча" data-language-local-name="Kyrgyz" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Materi%C4%81la_nogurums" title="Materiāla nogurums – Latvian" lang="lv" hreflang="lv" data-title="Materiāla nogurums" data-language-autonym="Latviešu" data-language-local-name="Latvian" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Kif%C3%A1rad%C3%A1s_(anyag%C3%A9)" title="Kifáradás (anyagé) – Hungarian" lang="hu" hreflang="hu" data-title="Kifáradás (anyagé)" 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It allows adding a reason in the summary.">undo</a></span></strong></div><div id="mw-diff-ntitle2"><a href="/wiki/User:ReyHahn" class="mw-userlink" title="User:ReyHahn" data-mw-revid="1258761345"><bdi>ReyHahn</bdi></a> <span class="mw-usertoollinks">(<a href="/wiki/User_talk:ReyHahn" class="mw-usertoollinks-talk" title="User talk:ReyHahn">talk</a> | <a href="/wiki/Special:Contributions/ReyHahn" class="mw-usertoollinks-contribs" title="Special:Contributions/ReyHahn">contribs</a>)</span><div class="mw-diff-usermetadata"><div class="mw-diff-userroles"><a href="/wiki/Wikipedia:Extended_confirmed_editors" class="mw-redirect" title="Wikipedia:Extended confirmed editors">Extended confirmed users</a></div><div class="mw-diff-usereditcount"><span>24,414</span> edits</div></div></div><div id="mw-diff-ntitle3"> <span class="comment comment--without-parentheses">closing merge</span></div><div id="mw-diff-ntitle5"><span class="mw-tag-markers"><a href="/wiki/Special:Tags" title="Special:Tags">Tag</a>: <span class="mw-tag-marker mw-tag-marker-mw-reverted">Reverted</span></span></div><div id="mw-diff-ntitle4"><a href="/w/index.php?title=Fatigue_(material)&diff=next&oldid=1258761345" title="Fatigue (material)" id="differences-nextlink">Next edit →</a></div></td> </tr><tr> <td colspan="2" class="diff-lineno">Line 2:</td> <td colspan="2" class="diff-lineno">Line 2:</td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><div>{{Redirect|Metal fatigue||Metal Fatigue (disambiguation)}}</div></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><div>{{Redirect|Metal fatigue||Metal Fatigue (disambiguation)}}</div></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><div>{{Redirect|Cyclic loading|the term for soil being liquefied as a result of stress|Soil liquefaction}}</div></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><div>{{Redirect|Cyclic loading|the term for soil being liquefied as a result of stress|Soil liquefaction}}</div></td> </tr> <tr> <td class="diff-marker" data-marker="−"></td> <td class="diff-deletedline diff-side-deleted"><div>{{merge from|Static fatigue|date=August 2024|discuss=Talk:Static fatigue#Merger discussion}}</div></td> <td colspan="2" class="diff-empty diff-side-added"></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><div>[[File:Pedalarm Bruch.jpg|thumb|Fracture surface of an aluminium crank arm from a bicycle. The dark area (due to oil, dirt and fretting) is a slow growth fatigue crack and may contain striations. The bright area is caused by sudden fracture.]]</div></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><div>[[File:Pedalarm Bruch.jpg|thumb|Fracture surface of an aluminium crank arm from a bicycle. The dark area (due to oil, dirt and fretting) is a slow growth fatigue crack and may contain striations. The bright area is caused by sudden fracture.]]</div></td> </tr> <tr> <td class="diff-marker"></td> <td class="diff-context diff-side-deleted"><div>{{Mechanical failure modes}}</div></td> <td class="diff-marker"></td> <td class="diff-context diff-side-added"><div>{{Mechanical failure modes}}</div></td> </tr> </table><hr class='diff-hr' id='mw-oldid' /> <h2 class='diff-currentversion-title'>Revision as of 13:51, 21 November 2024</h2> <div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Initiation and propagation of cracks in a material due to cyclic loading</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Metal fatigue" redirects here. For other uses, see <a href="/wiki/Metal_Fatigue_(disambiguation)" class="mw-redirect mw-disambig" title="Metal Fatigue (disambiguation)">Metal Fatigue (disambiguation)</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">"Cyclic loading" redirects here. For the term for soil being liquefied as a result of stress, see <a href="/wiki/Soil_liquefaction" title="Soil liquefaction">Soil liquefaction</a>.</div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Pedalarm_Bruch.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Pedalarm_Bruch.jpg/220px-Pedalarm_Bruch.jpg" decoding="async" width="220" height="202" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Pedalarm_Bruch.jpg/330px-Pedalarm_Bruch.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Pedalarm_Bruch.jpg/440px-Pedalarm_Bruch.jpg 2x" data-file-width="2316" data-file-height="2129" /></a><figcaption>Fracture surface of an aluminium crank arm from a bicycle. The dark area (due to oil, dirt and fretting) is a slow growth fatigue crack and may contain striations. The bright area is caused by sudden fracture.</figcaption></figure> <style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist 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.sidebar-list-title,html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-night .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-list-title,html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle{background:transparent!important}html.skin-theme-clientpref-os .mw-parser-output .sidebar:not(.notheme) .sidebar-title-with-pretitle a{color:var(--color-progressive)!important}}@media print{body.ns-0 .mw-parser-output .sidebar{display:none!important}}</style><table class="sidebar nomobile nowraplinks"><tbody><tr><th class="sidebar-title">Mechanical failure modes</th></tr><tr><td class="sidebar-content hlist"> <ul><li><a href="/wiki/Buckling" title="Buckling">Buckling</a></li> <li><a href="/wiki/Corrosion" title="Corrosion">Corrosion</a></li> <li><a href="/wiki/Corrosion_fatigue" title="Corrosion fatigue">Corrosion fatigue</a></li> <li><a href="/wiki/Creep_(deformation)" title="Creep (deformation)">Creep</a></li> <li><a class="mw-selflink selflink">Fatigue</a></li> <li><a href="/wiki/Fouling" title="Fouling">Fouling</a></li> <li><a href="/wiki/Fracture" title="Fracture">Fracture</a></li> <li><a href="/wiki/Hydrogen_embrittlement" title="Hydrogen embrittlement">Hydrogen embrittlement</a></li> <li><a href="/wiki/Impact_(mechanics)" title="Impact (mechanics)">Impact</a></li> <li><a href="/wiki/Liquid_metal_embrittlement" title="Liquid metal embrittlement">Liquid metal embrittlement</a></li> <li><a href="/wiki/Mechanical_overload" title="Mechanical overload">Mechanical overload</a></li> <li><a href="/wiki/Metal-induced_embrittlement" title="Metal-induced embrittlement">Metal-induced embrittlement</a></li> <li><a href="/wiki/Stress_corrosion_cracking" title="Stress corrosion cracking">Stress corrosion cracking</a></li> <li><a href="/wiki/Sulfide_stress_cracking" title="Sulfide stress cracking">Sulfide stress cracking</a></li> <li><a href="/wiki/Thermal_shock" title="Thermal shock">Thermal shock</a></li> <li><a href="/wiki/Wear" title="Wear">Wear</a></li> <li><a href="/wiki/Yield_(engineering)" title="Yield (engineering)">Yielding</a></li></ul></td> </tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Mechanical_failure_modes" title="Template:Mechanical failure modes"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Mechanical_failure_modes" title="Template talk:Mechanical failure modes"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Mechanical_failure_modes" title="Special:EditPage/Template:Mechanical failure modes"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p>In <a href="/wiki/Materials_science" title="Materials science">materials science</a>, <b>fatigue</b> is the initiation and propagation of cracks in a material due to cyclic loading. Once a <b>fatigue crack</b> has initiated, it grows a small amount with each loading cycle, typically producing <a href="/wiki/Striation_(fatigue)" title="Striation (fatigue)">striations</a> on some parts of the fracture surface. The crack will continue to grow until it reaches a critical size, which occurs when the <a href="/wiki/Stress_intensity_factor" title="Stress intensity factor">stress intensity factor</a> of the crack exceeds the <a href="/wiki/Fracture_toughness" title="Fracture toughness">fracture toughness</a> of the material, producing rapid propagation and typically complete fracture of the structure. </p><p>Fatigue has traditionally been associated with the failure of metal components which led to the term <b>metal fatigue</b>. In the nineteenth century, the sudden failing of metal railway axles was thought to be caused by the metal <i>crystallising</i> because of the brittle appearance of the fracture surface, but this has since been disproved.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Most materials, such as composites, plastics and ceramics, seem to experience some sort of fatigue-related failure.<sup id="cite_ref-suresh04_2-0" class="reference"><a href="#cite_note-suresh04-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>To aid in predicting the fatigue life of a component, <a href="/wiki/Fatigue_testing" title="Fatigue testing">fatigue tests</a> are carried out using coupons to measure the rate of crack growth by applying constant amplitude cyclic loading and averaging the measured growth of a crack over thousands of cycles. However, there are also a number of special cases that need to be considered where the rate of crack growth is significantly different compared to that obtained from constant amplitude testing, such as the reduced rate of growth that occurs for small loads near the <i>threshold</i> or after the application of an <i>overload</i>, and the increased rate of crack growth associated with <i>short cracks</i> or after the application of an <i>underload</i>.<sup id="cite_ref-suresh04_2-1" class="reference"><a href="#cite_note-suresh04-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>If the loads are above a certain threshold, microscopic cracks will begin to <i>initiate</i> at <a href="/wiki/Stress_concentrations" class="mw-redirect" title="Stress concentrations">stress concentrations</a> such as holes, <a href="/wiki/Persistent_slip_bands" class="mw-redirect" title="Persistent slip bands">persistent slip bands</a> (PSBs), <a href="/wiki/Composite_material" title="Composite material">composite</a> interfaces or <a href="/wiki/Grain_boundaries" class="mw-redirect" title="Grain boundaries">grain boundaries</a> in metals.<sup id="cite_ref-Laird_3-0" class="reference"><a href="#cite_note-Laird-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> The <a href="/wiki/Stress_(physics)" class="mw-redirect" title="Stress (physics)">stress</a> values that cause fatigue damage are typically much less than the <a href="/wiki/Yield_(engineering)" title="Yield (engineering)">yield strength</a> of the material. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Stages_of_fatigue">Stages of fatigue</h2></div> <p>Historically, fatigue has been separated into regions of <i>high cycle fatigue</i> that require more than 10<sup>4</sup> cycles to failure where stress is low and primarily <a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">elastic</a> and <a href="/wiki/Low_cycle_fatigue" class="mw-redirect" title="Low cycle fatigue">low cycle fatigue</a> where there is significant plasticity. Experiments have shown that low cycle fatigue is also crack growth.<sup id="cite_ref-murakami05_4-0" class="reference"><a href="#cite_note-murakami05-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Fatigue failures, both for high and low cycles, all follow the same basic steps: crack initiation, crack growth stages I and II, and finally ultimate failure. To begin the process, cracks must nucleate within a material. This process can occur either at <a href="/wiki/Stress_concentration" title="Stress concentration">stress risers</a> in metallic samples or at areas with a high void density in polymer samples. These cracks propagate slowly at first during <i>stage I</i> crack growth along crystallographic planes, where <a href="/wiki/Shear_stress" title="Shear stress">shear stresses</a> are highest. Once the cracks reach a critical size they propagate quickly during <i>stage II</i> crack growth in a direction perpendicular to the applied force. These cracks can eventually lead to the ultimate failure of the material, often in a brittle catastrophic fashion. </p> <div class="mw-heading mw-heading3"><h3 id="Crack_initiation">Crack initiation</h3></div> <p>The formation of initial cracks preceding fatigue failure is a separate process consisting of four discrete steps in metallic samples. The material will develop cell structures and harden in response to the applied load. This causes the amplitude of the applied stress to increase given the new restraints on strain. These newly formed cell structures will eventually break down with the formation of persistent slip bands (PSBs). Slip in the material is localized at these PSBs, and the exaggerated slip can now serve as a stress concentrator for a crack to form. Nucleation and growth of a crack to a detectable size accounts for most of the cracking process. It is for this reason that cyclic fatigue failures seem to occur so suddenly where the bulk of the changes in the material are not visible without destructive testing. Even in normally ductile materials, fatigue failures will resemble sudden brittle failures. </p><p>PSB-induced slip planes result in intrusions and extrusions along the surface of a material, often occurring in pairs.<sup id="cite_ref-forsythe_5-0" class="reference"><a href="#cite_note-forsythe-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> This slip is not a <a href="/wiki/Microstructure" title="Microstructure">microstructural</a> change within the material, but rather a propagation of <a href="/wiki/Dislocations" class="mw-redirect" title="Dislocations">dislocations</a> within the material. Instead of a smooth interface, the intrusions and extrusions will cause the surface of the material to resemble the edge of a deck of cards, where not all cards are perfectly aligned. Slip-induced intrusions and extrusions create extremely fine surface structures on the material. With surface structure size inversely related to stress concentration factors, PSB-induced surface slip can cause fractures to initiate. </p><p>These steps can also be bypassed entirely if the cracks form at a pre-existing stress concentrator such as from an inclusion in the material or from a geometric stress concentrator caused by a sharp internal corner or fillet. </p> <div class="mw-heading mw-heading3"><h3 id="Crack_growth">Crack growth</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">See also: <a href="/wiki/Fracture_mechanics" title="Fracture mechanics">Fracture mechanics</a></div> <p>Most of the fatigue life is generally consumed in the crack growth phase. The rate of growth is primarily driven by the range of cyclic loading although additional factors such as mean stress, environment, overloads and underloads can also affect the rate of growth. Crack growth may stop if the loads are small enough to fall below a critical threshold. </p><p>Fatigue cracks can grow from material or manufacturing defects from as small as 10 μm. </p><p>When the rate of growth becomes large enough, fatigue striations can be seen on the fracture surface. Striations mark the position of the crack tip and the width of each striation represents the growth from one loading cycle. Striations are a result of plasticity at the crack tip. </p><p>When the stress intensity exceeds a critical value known as the fracture toughness, unsustainable <i>fast fracture</i> will occur, usually by a process of <a href="/wiki/Microvoid_coalescence" title="Microvoid coalescence">microvoid coalescence</a>. Prior to final fracture, the fracture surface may contain a mixture of areas of fatigue and fast fracture. </p> <div class="mw-heading mw-heading4"><h4 id="Acceleration_and_retardation">Acceleration and retardation</h4></div> <p>The following effects change the rate of growth:<sup id="cite_ref-suresh04_2-2" class="reference"><a href="#cite_note-suresh04-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <ul><li>Mean stress effect: Higher mean stress increases the rate of crack growth.</li> <li>Environment: Increased moisture increases the rate of crack growth. In the case of aluminium, cracks generally grow from the surface, where water vapour from the atmosphere is able to reach the tip of the crack and dissociate into atomic hydrogen which causes <a href="/wiki/Hydrogen_embrittlement" title="Hydrogen embrittlement">hydrogen embrittlement</a>. Cracks growing internally are isolated from the atmosphere and grow in a <a href="/wiki/Vacuum" title="Vacuum">vacuum</a> where the rate of growth is typically an order of magnitude slower than a surface crack.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup></li> <li>Short crack effect: In 1975, Pearson observed that short cracks grow faster than expected.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> Possible reasons for the short crack effect include the presence of the T-stress, the tri-axial stress state at the crack tip, the lack of crack closure associated with short cracks and the large plastic zone in comparison to the crack length. In addition, long cracks typically experience a threshold which short cracks do not have.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> There are a number of criteria for short cracks:<sup id="cite_ref-e647_9-0" class="reference"><a href="#cite_note-e647-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> <ul><li>cracks are typically smaller than 1 mm,</li> <li>cracks are smaller than the material microstructure size such as the grain size, or</li> <li>crack length is small compared to the plastic zone.</li></ul></li> <li>Underloads: Small numbers of underloads increase the rate of growth and may counteract the effect of overloads.</li> <li>Overloads: Initially overloads (> 1.5 the maximum load in a sequence) lead to a small increase in the rate of growth followed by a long reduction in the rate of growth.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Characteristics_of_fatigue">Characteristics of fatigue</h2></div> <ul><li>In metal alloys, and for the simplifying case when there are no macroscopic or microscopic discontinuities, the process starts with dislocation movements at the microscopic level, which eventually form persistent slip bands that become the nucleus of short cracks.</li> <li>Macroscopic and microscopic discontinuities (at the crystalline grain scale) as well as component design features which cause stress concentrations (holes, <a href="/wiki/Key_(engineering)" title="Key (engineering)">keyways</a>, sharp changes of load direction etc.) are common locations at which the fatigue process begins.</li> <li>Fatigue is a process that has a degree of randomness (<a href="/wiki/Stochastic" title="Stochastic">stochastic</a>), often showing considerable scatter even in seemingly identical samples in well controlled environments.</li> <li>Fatigue is usually associated with tensile stresses but fatigue cracks have been reported due to compressive loads.<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup></li> <li>The greater the applied stress range, the shorter the life.</li> <li>Fatigue life scatter tends to increase for longer fatigue lives.</li> <li>Damage is irreversible. Materials do not recover when rested.</li> <li>Fatigue life is influenced by a variety of factors, such as <a href="/wiki/Temperature" title="Temperature">temperature</a>, <a href="/wiki/Surface_finish" title="Surface finish">surface finish</a>, metallurgical microstructure, presence of <a href="/wiki/Oxidizing" class="mw-redirect" title="Oxidizing">oxidizing</a> or <a href="/wiki/Chemically_inert" title="Chemically inert">inert</a> chemicals, <a href="/wiki/Residual_stress" title="Residual stress">residual stresses</a>, scuffing contact (<a href="/wiki/Fretting" title="Fretting">fretting</a>), etc.</li> <li>Some materials (e.g., some <a href="/wiki/Steel" title="Steel">steel</a> and <a href="/wiki/Titanium" title="Titanium">titanium</a> alloys) exhibit a theoretical <a href="/wiki/Fatigue_limit" title="Fatigue limit">fatigue limit</a> below which continued loading does not lead to fatigue failure.</li> <li>High cycle <a href="/wiki/Fatigue_strength" class="mw-redirect" title="Fatigue strength">fatigue strength</a> (about 10<sup>4</sup> to 10<sup>8</sup> cycles) can be described by stress-based parameters. A load-controlled servo-hydraulic test rig is commonly used in these tests, with frequencies of around 20–50 Hz. Other sorts of machines—like resonant magnetic machines—can also be used, to achieve frequencies up to 250 Hz.</li> <li><a href="/wiki/Low-cycle_fatigue" title="Low-cycle fatigue">Low-cycle fatigue</a> (loading that typically causes failure in less than 10<sup>4</sup> cycles) is associated with localized plastic behavior in metals; thus, a strain-based parameter should be used for fatigue life prediction in metals. Testing is conducted with constant strain amplitudes typically at 0.01–5 Hz.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Timeline_of_research_history">Timeline of research history</h2></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Ewing_and_Humfrey_fatigue_cracks.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Ewing_and_Humfrey_fatigue_cracks.JPG/220px-Ewing_and_Humfrey_fatigue_cracks.JPG" decoding="async" width="220" height="266" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/Ewing_and_Humfrey_fatigue_cracks.JPG/330px-Ewing_and_Humfrey_fatigue_cracks.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/9/9d/Ewing_and_Humfrey_fatigue_cracks.JPG 2x" data-file-width="342" data-file-height="413" /></a><figcaption>Micrographs showing how surface fatigue cracks grow as material is further cycled. From Ewing & Humfrey, 1903</figcaption></figure> <ul><li>1837: <a href="/wiki/Wilhelm_Albert_(engineer)" title="Wilhelm Albert (engineer)">Wilhelm Albert</a> publishes the first article on fatigue. He devised a test machine for <a href="/wiki/Conveyor" class="mw-redirect" title="Conveyor">conveyor</a> chains used in the <a href="/wiki/Clausthal-Zellerfeld" title="Clausthal-Zellerfeld">Clausthal</a> <a href="/wiki/Mining" title="Mining">mines</a>.<sup id="cite_ref-schutz_11-0" class="reference"><a href="#cite_note-schutz-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></li> <li>1839: <a href="/wiki/Jean-Victor_Poncelet" title="Jean-Victor Poncelet">Jean-Victor Poncelet</a> describes metals as being 'tired' in his lectures at the military school at <a href="/wiki/Metz" title="Metz">Metz</a>.</li> <li>1842: <a href="/wiki/William_John_Macquorn_Rankine" class="mw-redirect" title="William John Macquorn Rankine">William John Macquorn Rankine</a> recognises the importance of <a href="/wiki/Stress_concentration" title="Stress concentration">stress concentrations</a> in his investigation of <a href="/wiki/Railroad" class="mw-redirect" title="Railroad">railroad</a> <a href="/wiki/Axle" title="Axle">axle</a> failures. The <a href="/wiki/Versailles_rail_accident" title="Versailles rail accident">Versailles train wreck</a> was caused by fatigue failure of a locomotive axle.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></li> <li>1843: <a href="/wiki/Joseph_Glynn_(engineer)" title="Joseph Glynn (engineer)">Joseph Glynn</a> reports on the fatigue of an axle on a locomotive tender. He identifies the <a href="/wiki/Keyway_(engineering)" class="mw-redirect" title="Keyway (engineering)">keyway</a> as the crack origin.</li> <li>1848: The <a href="/wiki/Railway_Inspectorate" class="mw-redirect" title="Railway Inspectorate">Railway Inspectorate</a> reports one of the first tyre failures, probably from a rivet hole in tread of railway carriage wheel. It was likely a fatigue failure.</li> <li>1849: <a href="/wiki/Eaton_Hodgkinson" title="Eaton Hodgkinson">Eaton Hodgkinson</a> is granted a "small sum of money" to report to the <a href="/wiki/UK_Parliament" class="mw-redirect" title="UK Parliament">UK Parliament</a> on his work in "ascertaining by direct experiment, the effects of continued changes of load upon iron structures and to what extent they could be loaded without danger to their ultimate security".</li> <li>1854: F. Braithwaite reports on common service fatigue failures and coins the term <i>fatigue</i>.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup></li> <li>1860: Systematic fatigue testing undertaken by Sir <a href="/wiki/William_Fairbairn" title="William Fairbairn">William Fairbairn</a> and <a href="/wiki/August_W%C3%B6hler" title="August Wöhler">August Wöhler</a>.</li> <li>1870: <a href="/wiki/August_W%C3%B6hler" title="August Wöhler">A. Wöhler</a> summarises his work on railroad axles. He concludes that cyclic stress range is more important than peak stress and introduces the concept of <i>endurance limit</i>.<sup id="cite_ref-schutz_11-1" class="reference"><a href="#cite_note-schutz-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup></li> <li>1903: Sir <a href="/wiki/James_Alfred_Ewing" class="mw-redirect" title="James Alfred Ewing">James Alfred Ewing</a> demonstrates the origin of fatigue failure in microscopic cracks.</li> <li>1910: O. H. Basquin proposes a log-log relationship for S-N curves, using Wöhler's test data.<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup></li> <li>1940: <a href="/wiki/Sidney_M._Cadwell" title="Sidney M. Cadwell">Sidney M. Cadwell</a> publishes first rigorous study of fatigue in rubber.<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup></li> <li>1945: A. M. Miner popularises Palmgren's (1924) linear damage hypothesis as a practical design tool.<sup id="cite_ref-miner_16-0" class="reference"><a href="#cite_note-miner-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup></li> <li>1952: <a href="/wiki/Waloddi_Weibull" title="Waloddi Weibull">W. Weibull</a> An S-N curve model.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup></li> <li>1954: The world's first commercial jetliner, the <a href="/wiki/De_Havilland_Comet" title="De Havilland Comet">de Havilland Comet</a>, suffers disaster as three planes break up in mid-air, causing de Havilland and all other manufacturers to redesign high altitude aircraft and in particular replace square apertures like windows with oval ones.</li> <li>1954: L. F. Coffin and S. S. Manson explain fatigue crack-growth in terms of <a href="/wiki/Plasticity_(physics)" title="Plasticity (physics)">plastic</a> <a href="/wiki/Strain_(materials_science)" class="mw-redirect" title="Strain (materials science)">strain</a> in the tip of cracks.</li> <li>1961: <a href="/wiki/Paul_C._Paris" title="Paul C. Paris">P. C. Paris</a> proposes methods for predicting the rate of growth of individual fatigue cracks in the face of initial scepticism and popular defence of Miner's phenomenological approach.</li> <li>1968: <a href="/wiki/Tatsuo_Endo_(engineer)" title="Tatsuo Endo (engineer)">Tatsuo Endo</a> and M. Matsuishi devise the <a href="/wiki/Rainflow-counting_algorithm" title="Rainflow-counting algorithm">rainflow-counting algorithm</a> and enable the reliable application of Miner's rule to <a href="/wiki/Random" class="mw-redirect" title="Random">random</a> loadings.<sup id="cite_ref-Matsuishi_19-0" class="reference"><a href="#cite_note-Matsuishi-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup></li> <li>1970: Smith, Watson, and Topper developed a mean stress correction model, where the fatigue damage in a cycle is determined by the product of the maximum stress and strain amplitude.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup></li> <li>1970: W. Elber elucidates the mechanisms and importance of <a href="/wiki/Crack_closure" title="Crack closure">crack closure</a> in slowing the growth of a fatigue crack due to the wedging effect of <a href="/wiki/Plastic_deformation" class="mw-redirect" title="Plastic deformation">plastic deformation</a> left behind the tip of the crack.<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup></li> <li>1973: M. W. Brown and K. J. Miller observe that fatigue life under multiaxial conditions is governed by the experience of the plane receiving the most damage, and that both tension and shear loads on the <a href="/wiki/Critical_plane_analysis" title="Critical plane analysis">critical plane</a> must be considered.<sup id="cite_ref-23" class="reference"><a href="#cite_note-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading2"><h2 id="Predicting_fatigue_life">Predicting fatigue life</h2></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Rainflow_fig2.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Rainflow_fig2.PNG/220px-Rainflow_fig2.PNG" decoding="async" width="220" height="125" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/2/20/Rainflow_fig2.PNG 1.5x" data-file-width="309" data-file-height="176" /></a><figcaption>Spectrum loading</figcaption></figure> <p>The <a href="/wiki/ASTM_International" title="ASTM International">American Society for Testing and Materials</a> defines <i>fatigue life</i>, <i>N<sub>f</sub></i>, as the number of stress cycles of a specified character that a specimen sustains before <a href="/wiki/Structural_failure" class="mw-redirect" title="Structural failure">failure</a> of a specified nature occurs.<sup id="cite_ref-Stephens_24-0" class="reference"><a href="#cite_note-Stephens-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup> For some materials, notably <a href="/wiki/Steel" title="Steel">steel</a> and <a href="/wiki/Titanium" title="Titanium">titanium</a>, there is a theoretical value for stress amplitude below which the material will not fail for any number of cycles, called a <a href="/wiki/Fatigue_limit" title="Fatigue limit">fatigue limit or endurance limit</a>.<sup id="cite_ref-Bathias_25-0" class="reference"><a href="#cite_note-Bathias-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup> However, in practice, several bodies of work done at greater numbers of cycles suggest that fatigue limits do not exist for any metals.<sup id="cite_ref-26" class="reference"><a href="#cite_note-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-28" class="reference"><a href="#cite_note-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup> </p><p>Engineers have used a number of methods to determine the fatigue life of a material:<sup id="cite_ref-29" class="reference"><a href="#cite_note-29"><span class="cite-bracket">[</span>29<span class="cite-bracket">]</span></a></sup> </p> <ol><li>the stress-life method,</li> <li>the strain-life method,</li> <li>the crack growth method and</li> <li>probabilistic methods, which can be based on either life or crack growth methods.</li></ol> <p>Whether using stress/strain-life approach or using crack growth approach, complex or variable amplitude loading is reduced to a series of fatigue equivalent simple cyclic loadings using a technique such as the <a href="/wiki/Rainflow-counting_algorithm" title="Rainflow-counting algorithm">rainflow-counting algorithm</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Stress-life_and_strain-life_methods">Stress-life and strain-life methods</h3></div> <p>A mechanical part is often exposed to a complex, often <a href="/wiki/Random" class="mw-redirect" title="Random">random</a>, sequence of loads, large and small. In order to assess the safe life of such a part using the fatigue damage or stress/strain-life methods the following series of steps is usually performed: </p> <ol><li>Complex loading is reduced to a series of simple cyclic loadings using a technique such as <a href="/wiki/Rainflow-counting_algorithm" title="Rainflow-counting algorithm">rainflow analysis</a>;</li> <li>A <a href="/wiki/Histogram" title="Histogram">histogram</a> of cyclic stress is created from the rainflow analysis to form a <a href="/w/index.php?title=Fatigue_damage_spectrum&action=edit&redlink=1" class="new" title="Fatigue damage spectrum (page does not exist)">fatigue damage spectrum</a>;</li> <li>For each stress level, the degree of cumulative damage is calculated from the S-N curve; and</li> <li>The effect of the individual contributions are combined using an algorithm such as <i>Miner's rule</i>.</li></ol> <p>Since S-N curves are typically generated for <i>uniaxial</i> loading, some equivalence rule is needed whenever the loading is multiaxial. For simple, proportional loading histories (lateral load in a constant ratio with the axial), <a href="/w/index.php?title=Sines_rule&action=edit&redlink=1" class="new" title="Sines rule (page does not exist)">Sines rule</a> may be applied. For more complex situations, such as non-proportional loading, <a href="/wiki/Critical_plane_analysis" title="Critical plane analysis">critical plane analysis</a> must be applied. </p> <div class="mw-heading mw-heading4"><h4 id="Miner's_rule"><span id="Miner.27s_rule"></span>Miner's rule</h4></div> <p>In 1945, Milton A. Miner popularised a rule that had first been proposed by <a href="https://sv.wikipedia.org/wiki/Arvid_Palmgren" class="extiw" title="sv:Arvid Palmgren">Arvid Palmgren</a> in 1924.<sup id="cite_ref-miner_16-1" class="reference"><a href="#cite_note-miner-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup> The rule, variously called <i>Miner's rule</i> or the <i>Palmgren–Miner linear damage hypothesis</i>, states that where there are <i>k</i> different stress magnitudes in a spectrum, <i>S<sub>i</sub></i> (1 ≤ <i>i</i> ≤ <i>k</i>), each contributing <i>n<sub>i</sub></i>(<i>S<sub>i</sub></i>) cycles, then if <i>N<sub>i</sub></i>(<i>S<sub>i</sub></i>) is the number of cycles to failure of a constant stress reversal <i>S<sub>i</sub></i> (determined by uni-axial fatigue tests), failure occurs when: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sum _{i=1}^{k}{\frac {n_{i}}{N_{i}}}=C}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mi>C</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum _{i=1}^{k}{\frac {n_{i}}{N_{i}}}=C}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a0f401186892d7f0e1888492f0c0f30d8590fed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:12.109ex; height:7.343ex;" alt="{\displaystyle \sum _{i=1}^{k}{\frac {n_{i}}{N_{i}}}=C}"></span></dd></dl> <p>Usually, for design purposes, C is assumed to be 1. This can be thought of as assessing what proportion of life is consumed by a linear combination of stress reversals at varying magnitudes. </p><p>Although Miner's rule may be a useful approximation in many circumstances, it has several major limitations: </p> <ol><li>It fails to recognize the probabilistic nature of fatigue and there is no simple way to relate life predicted by the rule with the characteristics of a probability distribution. Industry analysts often use design curves, adjusted to account for scatter, to calculate <i>N<sub>i</sub></i>(<i>S<sub>i</sub></i>).</li> <li>The sequence in which high vs. low stress cycles are applied to a sample in fact affect the fatigue life, for which Miner's Rule does not account. In some circumstances, cycles of low stress followed by high stress cause more damage than would be predicted by the rule.<sup id="cite_ref-30" class="reference"><a href="#cite_note-30"><span class="cite-bracket">[</span>30<span class="cite-bracket">]</span></a></sup> It does not consider the effect of an overload or high stress which may result in a compressive residual stress that may retard crack growth. High stress followed by low stress may have less damage due to the presence of compressive residual stress (or localized plastic damages around crack tip).</li></ol> <div class="mw-heading mw-heading4"><h4 id="Stress-life_(S-N)_method"><span id="Stress-life_.28S-N.29_method"></span>Stress-life (S-N) method</h4></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:BrittleAluminium320MPa_S-N_Curve.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/BrittleAluminium320MPa_S-N_Curve.svg/220px-BrittleAluminium320MPa_S-N_Curve.svg.png" decoding="async" width="220" height="132" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/BrittleAluminium320MPa_S-N_Curve.svg/330px-BrittleAluminium320MPa_S-N_Curve.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/BrittleAluminium320MPa_S-N_Curve.svg/440px-BrittleAluminium320MPa_S-N_Curve.svg.png 2x" data-file-width="900" data-file-height="540" /></a><figcaption>S-N curve for a brittle aluminium with an ultimate tensile strength of 320 MPa</figcaption></figure> <p>Materials fatigue performance is commonly characterized by an <i>S-N curve</i>, also known as a <i><a href="/wiki/August_W%C3%B6hler" title="August Wöhler">Wöhler</a> curve</i>. This is often plotted with the cyclic stress (<i>S</i>) against the cycles to failure (<i>N</i>) on a <a href="/wiki/Logarithmic_scale" title="Logarithmic scale">logarithmic scale</a>.<sup id="cite_ref-Burhan_and_Kim_31-0" class="reference"><a href="#cite_note-Burhan_and_Kim-31"><span class="cite-bracket">[</span>31<span class="cite-bracket">]</span></a></sup> S-N curves are derived from tests on samples of the material to be characterized (often called coupons or specimens) where a regular <a href="/wiki/Sine_wave" title="Sine wave">sinusoidal</a> stress is applied by a testing machine which also counts the number of cycles to failure. This process is sometimes known as <i>coupon testing</i>. For greater accuracy but lower generality component testing is used.<sup id="cite_ref-32" class="reference"><a href="#cite_note-32"><span class="cite-bracket">[</span>32<span class="cite-bracket">]</span></a></sup> Each coupon or component test generates a point on the plot though in some cases there is a <i>runout</i> where the time to failure exceeds that available for the test (see <a href="/wiki/Censoring_(statistics)" title="Censoring (statistics)">censoring</a>). Analysis of fatigue data requires techniques from <a href="/wiki/Statistics" title="Statistics">statistics</a>, especially survival analysis and <a href="/wiki/Linear_regression" title="Linear regression">linear regression</a>. </p><p>The progression of the <i>S-N curve</i> can be influenced by many factors such as stress ratio (mean stress),<sup id="cite_ref-33" class="reference"><a href="#cite_note-33"><span class="cite-bracket">[</span>33<span class="cite-bracket">]</span></a></sup> loading frequency, <a href="/wiki/Temperature" title="Temperature">temperature</a>, <a href="/wiki/Corrosion" title="Corrosion">corrosion</a>, residual stresses, and the presence of notches. A constant fatigue life (CFL) diagram<sup id="cite_ref-34" class="reference"><a href="#cite_note-34"><span class="cite-bracket">[</span>34<span class="cite-bracket">]</span></a></sup> is useful for the study of stress ratio effect. The <a href="/wiki/Goodman_relation" title="Goodman relation">Goodman line</a> is a method used to estimate the influence of the mean stress on the <a href="/wiki/Fatigue_strength" class="mw-redirect" title="Fatigue strength">fatigue strength</a>. </p><p>A Constant Fatigue Life (CFL) diagram is useful for stress ratio effect on S-N curve.<sup id="cite_ref-35" class="reference"><a href="#cite_note-35"><span class="cite-bracket">[</span>35<span class="cite-bracket">]</span></a></sup> Also, in the presence of a steady stress superimposed on the cyclic loading, the Goodman relation can be used to estimate a failure condition. It plots stress amplitude against mean stress with the fatigue limit and the <a href="/wiki/Ultimate_tensile_strength" title="Ultimate tensile strength">ultimate tensile strength</a> of the material as the two extremes. Alternative failure criteria include Soderberg and Gerber.<sup id="cite_ref-36" class="reference"><a href="#cite_note-36"><span class="cite-bracket">[</span>36<span class="cite-bracket">]</span></a></sup> </p><p>As coupons sampled from a homogeneous frame will display a variation in their number of cycles to failure, the S-N curve should more properly be a Stress-Cycle-Probability (S-N-P) curve to capture the probability of failure after a given number of cycles of a certain stress. </p><p>With body-centered cubic materials (bcc), the Wöhler curve often becomes a horizontal line with decreasing stress amplitude, i.e. there is a <i>fatigue strength</i> that can be assigned to these materials. With face-centered cubic metals (fcc), the Wöhler curve generally drops continuously, so that only a <i>fatigue limit</i> can be assigned to these materials.<sup id="cite_ref-37" class="reference"><a href="#cite_note-37"><span class="cite-bracket">[</span>37<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading4"><h4 id="Strain-life_(ε-N)_method"><span id="Strain-life_.28.CE.B5-N.29_method"></span>Strain-life (ε-N) method</h4></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Strain-N.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Strain-N.png/220px-Strain-N.png" decoding="async" width="220" height="205" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Strain-N.png/330px-Strain-N.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Strain-N.png/440px-Strain-N.png 2x" data-file-width="1096" data-file-height="1023" /></a><figcaption>Graph showing fatigue failure as a function of strain amplitude.</figcaption></figure> <p>When strains are no longer elastic, such as in the presence of stress concentrations, the total strain can be used instead of stress as a similitude parameter. This is known as the strain-life method. The total strain amplitude <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta \varepsilon /2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \varepsilon /2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff9a62cd226bb173b2dea8eea319f0951e0c6554" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.344ex; height:2.843ex;" alt="{\displaystyle \Delta \varepsilon /2}"></span> is the sum of the elastic strain amplitude <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta \varepsilon _{\text{e}}/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \varepsilon _{\text{e}}/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e410ad5f3e3a30258c0e8cca5b33da659282dbea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.307ex; height:2.843ex;" alt="{\displaystyle \Delta \varepsilon _{\text{e}}/2}"></span> and the plastic strain amplitude <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta \varepsilon _{\text{p}}/2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta \varepsilon _{\text{p}}/2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3d864a6bffc15db9c8fc9ff54b343e82d50d258e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:6.49ex; height:3.009ex;" alt="{\displaystyle \Delta \varepsilon _{\text{p}}/2}"></span> and is given by<sup id="cite_ref-suresh04_2-3" class="reference"><a href="#cite_note-suresh04-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-38" class="reference"><a href="#cite_note-38"><span class="cite-bracket">[</span>38<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\Delta \varepsilon \over 2}={\Delta \varepsilon _{\text{e}} \over 2}+{\Delta \varepsilon _{\text{p}} \over 2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>ε</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\Delta \varepsilon \over 2}={\Delta \varepsilon _{\text{e}} \over 2}+{\Delta \varepsilon _{\text{p}} \over 2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5e4d900e12b07c9d14c7594d98c35e2dad6bd3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:19.614ex; height:5.676ex;" alt="{\displaystyle {\Delta \varepsilon \over 2}={\Delta \varepsilon _{\text{e}} \over 2}+{\Delta \varepsilon _{\text{p}} \over 2}}"></span>.</dd></dl></dd></dl> <p>Basquin's equation for the elastic strain amplitude is </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\Delta \varepsilon _{\text{e}} \over 2}={\frac {\Delta \sigma }{2E}}={\frac {\sigma _{\text{a}}}{E}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>σ</mi> </mrow> <mrow> <mn>2</mn> <mi>E</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>a</mtext> </mrow> </msub> <mi>E</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\Delta \varepsilon _{\text{e}} \over 2}={\frac {\Delta \sigma }{2E}}={\frac {\sigma _{\text{a}}}{E}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69a7053c9bf3860e02b28407e9a1821ad8f31196" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:18.334ex; height:5.343ex;" alt="{\displaystyle {\Delta \varepsilon _{\text{e}} \over 2}={\frac {\Delta \sigma }{2E}}={\frac {\sigma _{\text{a}}}{E}}}"></span></dd></dl></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> is <a href="/wiki/Young%27s_modulus" title="Young's modulus">Young's modulus</a>. </p><p>The relation for high cycle fatigue can be expressed using the elastic strain amplitude </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\Delta \varepsilon _{\text{e}} \over 2}={\frac {\sigma _{\text{f}}^{\prime }}{E}}(2N_{\text{f}})^{b}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>e</mtext> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>f</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mi>E</mi> </mfrac> </mrow> <mo stretchy="false">(</mo> <mn>2</mn> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>f</mtext> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\Delta \varepsilon _{\text{e}} \over 2}={\frac {\sigma _{\text{f}}^{\prime }}{E}}(2N_{\text{f}})^{b}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ef6425f687a0641204516e1ee198556e23604eb4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.543ex; height:5.676ex;" alt="{\displaystyle {\Delta \varepsilon _{\text{e}} \over 2}={\frac {\sigma _{\text{f}}^{\prime }}{E}}(2N_{\text{f}})^{b}}"></span></dd></dl></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{\text{f}}^{\prime }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>f</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{\text{f}}^{\prime }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15b2738cc494b32528c458d2ee7705b8d5ab3e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.171ex; height:2.843ex;" alt="{\displaystyle \sigma _{\text{f}}^{\prime }}"></span> is a parameter that scales with tensile strength obtained by fitting experimental data, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{\text{f}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>f</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{\text{f}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/16e974241b1860d246b9b89e5b0aa7cc8005c93e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.71ex; height:2.509ex;" alt="{\displaystyle N_{\text{f}}}"></span> is the number of cycles to failure and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> is the slope of the log-log curve again determined by curve fitting. </p><p>In 1954, Coffin and Manson proposed that the fatigue life of a component was related to the plastic strain amplitude using </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\Delta \varepsilon _{\text{p}} \over 2}=\varepsilon _{\text{f}}^{\prime }(2N_{\text{f}})^{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>p</mtext> </mrow> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <msubsup> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>f</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <mn>2</mn> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>f</mtext> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\Delta \varepsilon _{\text{p}} \over 2}=\varepsilon _{\text{f}}^{\prime }(2N_{\text{f}})^{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d20d1d8e4bfbc3661f8a14a86bbe5a3a0363bae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:16.654ex; height:5.676ex;" alt="{\displaystyle {\Delta \varepsilon _{\text{p}} \over 2}=\varepsilon _{\text{f}}^{\prime }(2N_{\text{f}})^{c}}"></span>.</dd></dl></dd></dl> <p>Combining the elastic and plastic portions gives the total strain amplitude accounting for both low and high cycle fatigue </p> <dl><dd><dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\Delta \varepsilon \over 2}={\frac {\sigma _{\text{f}}^{\prime }}{E}}(2N_{\text{f}})^{b}+\varepsilon _{\text{f}}^{\prime }(2N_{\text{f}})^{c}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>ε</mi> </mrow> <mn>2</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>f</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mi>E</mi> </mfrac> </mrow> <mo stretchy="false">(</mo> <mn>2</mn> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>f</mtext> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>b</mi> </mrow> </msup> <mo>+</mo> <msubsup> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>f</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msubsup> <mo stretchy="false">(</mo> <mn>2</mn> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>f</mtext> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>c</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\Delta \varepsilon \over 2}={\frac {\sigma _{\text{f}}^{\prime }}{E}}(2N_{\text{f}})^{b}+\varepsilon _{\text{f}}^{\prime }(2N_{\text{f}})^{c}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14a734519740a03b8eba1fc9c596ae5962c414dd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:27.975ex; height:5.676ex;" alt="{\displaystyle {\Delta \varepsilon \over 2}={\frac {\sigma _{\text{f}}^{\prime }}{E}}(2N_{\text{f}})^{b}+\varepsilon _{\text{f}}^{\prime }(2N_{\text{f}})^{c}}"></span>.</dd></dl></dd></dl> <p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma _{f}'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>σ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> <mo>′</mo> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma _{f}'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c5af682dd84544c28d8359da37021f678b0e5ed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.464ex; height:3.176ex;" alt="{\displaystyle \sigma _{f}'}"></span> is the fatigue strength coefficient, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> is the fatigue strength exponent, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \varepsilon _{f}'}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>ε</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> <mo>′</mo> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \varepsilon _{f}'}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25439be540e0fccc5a1e8629a3a4f53b1066bad8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:2.22ex; height:3.176ex;" alt="{\displaystyle \varepsilon _{f}'}"></span> is the fatigue ductility coefficient, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span> is the fatigue ductility exponent, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{f}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N_{f}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9421adeea835bee666f5990a88a150fa0da49174" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.003ex; height:2.843ex;" alt="{\displaystyle N_{f}}"></span> is the number of cycles to failure (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2N_{f}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>f</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2N_{f}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eb0caf94b8d8e749ac561befb71fc6d942355127" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:4.165ex; height:2.843ex;" alt="{\displaystyle 2N_{f}}"></span> being the number of reversals to failure). </p> <div class="mw-heading mw-heading3"><h3 id="Crack_growth_methods">Crack growth methods</h3></div> <p>An estimate of the fatigue life of a component can be made using a <a href="/wiki/Crack_growth_equation" title="Crack growth equation">crack growth equation</a> by summing up the width of each increment of crack growth for each loading cycle. Safety or scatter factors are applied to the calculated life to account for any uncertainty and variability associated with fatigue. The rate of growth used in crack growth predictions is typically measured by applying thousands of constant amplitude cycles to a coupon and measuring the rate of growth from the change in compliance of the coupon or by measuring the growth of the crack on the surface of the coupon. Standard methods for measuring the rate of growth have been developed by ASTM International.<sup id="cite_ref-e647_9-1" class="reference"><a href="#cite_note-e647-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> </p><p>Crack growth equations such as the <a href="/wiki/Paris%27_law" title="Paris' law">Paris–Erdoğan equation</a> are used to predict the life of a component. They can be used to predict the growth of a crack from 10 um to failure. For normal manufacturing finishes this may cover most of the fatigue life of a component where growth can start from the first cycle.<sup id="cite_ref-murakami05_4-1" class="reference"><a href="#cite_note-murakami05-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> The conditions at the crack tip of a component are usually related to the conditions of test coupon using a characterising parameter such as the stress intensity, <a href="/wiki/J-integral" title="J-integral">J-integral</a> or <a href="/wiki/Crack_tip_opening_displacement" title="Crack tip opening displacement">crack tip opening displacement</a>. All these techniques aim to match the crack tip conditions on the component to that of test coupons which give the rate of crack growth. </p><p>Additional models may be necessary to include retardation and acceleration effects associated with overloads or underloads in the loading sequence. In addition, small crack growth data may be needed to match the increased rate of growth seen with small cracks.<sup id="cite_ref-39" class="reference"><a href="#cite_note-39"><span class="cite-bracket">[</span>39<span class="cite-bracket">]</span></a></sup> </p><p>Typically, a cycle counting technique such as rainflow-cycle counting is used to extract the cycles from a complex sequence. This technique, along with others, has been shown to work with crack growth methods.<sup id="cite_ref-40" class="reference"><a href="#cite_note-40"><span class="cite-bracket">[</span>40<span class="cite-bracket">]</span></a></sup> </p><p>Crack growth methods have the advantage that they can predict the intermediate size of cracks. This information can be used to schedule inspections on a structure to ensure safety whereas strain/life methods only give a life until failure. </p> <div class="mw-heading mw-heading2"><h2 id="Dealing_with_fatigue">Dealing with fatigue</h2></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:New_Guide_Available_for_Fractography_of_Ceramics_and_Glasses_(5941062316).jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/New_Guide_Available_for_Fractography_of_Ceramics_and_Glasses_%285941062316%29.jpg/220px-New_Guide_Available_for_Fractography_of_Ceramics_and_Glasses_%285941062316%29.jpg" decoding="async" width="220" height="152" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a6/New_Guide_Available_for_Fractography_of_Ceramics_and_Glasses_%285941062316%29.jpg/330px-New_Guide_Available_for_Fractography_of_Ceramics_and_Glasses_%285941062316%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/a/a6/New_Guide_Available_for_Fractography_of_Ceramics_and_Glasses_%285941062316%29.jpg 2x" data-file-width="355" data-file-height="246" /></a><figcaption>Fracture surface in a glass rod showing beach marks surrounding the initiation site.</figcaption></figure> <div class="mw-heading mw-heading3"><h3 id="Design">Design</h3></div> <p>Dependable design against fatigue-failure requires thorough education and supervised experience in <a href="/wiki/Structural_engineering" title="Structural engineering">structural engineering</a>, <a href="/wiki/Mechanical_engineering" title="Mechanical engineering">mechanical engineering</a>, or <a href="/wiki/Materials_science" title="Materials science">materials science</a>. There are at least five principal approaches to life assurance for mechanical parts that display increasing degrees of sophistication:<sup id="cite_ref-41" class="reference"><a href="#cite_note-41"><span class="cite-bracket">[</span>41<span class="cite-bracket">]</span></a></sup> </p> <ol><li>Design to keep stress below threshold of <a href="/wiki/Fatigue_limit" title="Fatigue limit">fatigue limit</a> (infinite lifetime concept);</li> <li><a href="/wiki/Fail-safe" title="Fail-safe">Fail-safe</a>, <a href="/wiki/Graceful_degradation" class="mw-redirect" title="Graceful degradation">graceful degradation</a>, and <a href="/wiki/Fault-tolerant_design" class="mw-redirect" title="Fault-tolerant design">fault-tolerant design</a>: Instruct the user to replace parts when they fail. Design in such a way that there is no <a href="/wiki/Single_point_of_failure" title="Single point of failure">single point of failure</a>, and so that when any one part completely fails, it does not lead to <a href="/wiki/Catastrophic_failure" title="Catastrophic failure">catastrophic failure</a> of the entire system.</li> <li><a href="/wiki/Safe-life_design" title="Safe-life design">Safe-life design</a>: Design (conservatively) for a fixed life after which the user is instructed to replace the part with a new one (a so-called <i>lifed</i> part, finite lifetime concept, or "safe-life" design practice); <a href="/wiki/Planned_obsolescence" title="Planned obsolescence">planned obsolescence</a> and <a href="/wiki/Disposable_product" title="Disposable product">disposable product</a> are variants that design for a fixed life after which the user is instructed to replace the entire device;</li> <li><a href="/wiki/Damage_tolerance" title="Damage tolerance">Damage tolerance</a>: Is an approach that ensures aircraft safety by assuming the presence of cracks or defects even in new aircraft. Crack growth calculations, periodic inspections and component repair or replacement can be used to ensure critical components that may contain cracks, remain safe. Inspections usually use <a href="/wiki/Nondestructive_testing" title="Nondestructive testing">nondestructive testing</a> to limit or monitor the size of possible cracks and require an <a href="/wiki/Accuracy" class="mw-redirect" title="Accuracy">accurate</a> prediction of the rate of crack-growth between inspections. The designer sets some <a href="/wiki/Aircraft_maintenance_checks" title="Aircraft maintenance checks">aircraft maintenance checks</a> schedule frequent enough that parts are replaced while the crack is still in the "slow growth" phase. This is often referred to as damage tolerant design or "retirement-for-cause".</li> <li><a href="/wiki/Reliability_Engineering" class="mw-redirect" title="Reliability Engineering">Risk Management</a>: Ensures the probability of failure remains below an acceptable level. This approach is typically used for aircraft where acceptable levels may be based on probability of failure during a single flight or taken over the lifetime of an aircraft. A component is assumed to have a crack with a probability distribution of crack sizes. This approach can consider variability in values such as crack growth rates, usage and critical crack size.<sup id="cite_ref-42" class="reference"><a href="#cite_note-42"><span class="cite-bracket">[</span>42<span class="cite-bracket">]</span></a></sup> It is also useful for considering damage at multiple locations that may interact to produce <i>multi-site</i> or <a href="/wiki/Widespread_fatigue_damage" title="Widespread fatigue damage">widespread fatigue damage</a>. Probability distributions that are common in data analysis and in design against fatigue include the <a href="/wiki/Log-normal_distribution" title="Log-normal distribution">log-normal distribution</a>, <a href="/wiki/Extreme_value_theory" title="Extreme value theory">extreme value distribution</a>, <a href="/wiki/Birnbaum%E2%80%93Saunders_distribution" title="Birnbaum–Saunders distribution">Birnbaum–Saunders distribution</a>, and <a href="/wiki/Weibull_distribution" title="Weibull distribution">Weibull distribution</a>.</li></ol> <div class="mw-heading mw-heading3"><h3 id="Testing">Testing</h3></div> <p><a href="/wiki/Fatigue_testing" title="Fatigue testing">Fatigue testing</a> can be used for components such as a coupon or a <i>full-scale test article</i> to determine: </p> <ol><li>the rate of crack growth and fatigue life of components such as a coupon or a full-scale test article.</li> <li>location of critical regions</li> <li>degree of <a href="/wiki/Fail-safe" title="Fail-safe">fail-safety</a> when part of the structure fails</li> <li>the origin and cause of the crack initiating defect from <a href="/wiki/Fractography" title="Fractography">fractographic</a> examination of the crack.</li></ol> <p>These tests may form part of the certification process such as for <a href="/wiki/Airworthiness_certificate" title="Airworthiness certificate">airworthiness certification</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Repair">Repair</h3></div> <ol><li><b>Stop drill</b> Fatigue cracks that have begun to propagate can sometimes be stopped by <a href="/wiki/Drilling" title="Drilling">drilling</a> holes, called <i>drill stops</i>, at the tip of the crack.<sup id="cite_ref-Material_Technologies_43-0" class="reference"><a href="#cite_note-Material_Technologies-43"><span class="cite-bracket">[</span>43<span class="cite-bracket">]</span></a></sup> The possibility remains of a new crack starting in the side of the hole.</li> <li><b>Blend</b>. Small cracks can be blended away and the surface cold worked or shot peened.</li> <li><b>Oversize holes</b>. Holes with cracks growing from them can be drilled out to a larger hole to remove cracking and bushed to restore the original hole. Bushes can be cold shrink <a href="/wiki/Interference_fit" title="Interference fit">Interference fit</a> bushes to induce beneficial compressive residual stresses. The oversized hole can also be cold worked by drawing an oversized mandrel through the hole.<sup id="cite_ref-44" class="reference"><a href="#cite_note-44"><span class="cite-bracket">[</span>44<span class="cite-bracket">]</span></a></sup></li> <li><b>Patch</b>. Cracks may be repaired by installing a patch or repair fitting. Composite patches have been used to restore the strength of aircraft wings after cracks have been detected or to lower the stress prior to cracking in order to improve the fatigue life.<sup id="cite_ref-45" class="reference"><a href="#cite_note-45"><span class="cite-bracket">[</span>45<span class="cite-bracket">]</span></a></sup> Patches may restrict the ability to monitor fatigue cracks and may need to be removed and replaced for inspections.</li></ol> <div class="mw-heading mw-heading3"><h3 id="Life_improvement">Life improvement</h3></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Example_HiFIT-treated_assembly.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Example_HiFIT-treated_assembly.jpg/220px-Example_HiFIT-treated_assembly.jpg" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Example_HiFIT-treated_assembly.jpg/330px-Example_HiFIT-treated_assembly.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/ae/Example_HiFIT-treated_assembly.jpg/440px-Example_HiFIT-treated_assembly.jpg 2x" data-file-width="3264" data-file-height="2448" /></a><figcaption>Example of a HFMI treated steel highway bridge to avoid fatigue along the weld transition.</figcaption></figure> <ol><li><b>Change material</b>. Changes in the materials used in parts can also improve fatigue life. For example, parts can be made from better fatigue rated metals. Complete replacement and redesign of parts can also reduce if not eliminate fatigue problems. Thus <a href="/wiki/Helicopter_rotor" title="Helicopter rotor">helicopter rotor</a> blades and <a href="/wiki/Propeller_(aircraft)" class="mw-redirect" title="Propeller (aircraft)">propellers</a> in metal are being replaced by <a href="/wiki/Composite_material" title="Composite material">composite</a> equivalents. They are not only lighter, but also much more resistant to fatigue. They are more expensive, but the extra cost is amply repaid by their greater integrity, since loss of a rotor blade usually leads to total loss of the aircraft. A similar argument has been made for replacement of metal fuselages, wings and tails of aircraft.<sup id="cite_ref-46" class="reference"><a href="#cite_note-46"><span class="cite-bracket">[</span>46<span class="cite-bracket">]</span></a></sup></li> <li><b>Induce residual stresses</b> <a href="/wiki/Peening" title="Peening">Peening</a> a surface can reduce such tensile stresses and create compressive <a href="/wiki/Residual_stress" title="Residual stress">residual stress</a>, which prevents crack initiation. Forms of peening include: <a href="/wiki/Shot_peening" title="Shot peening">shot peening</a>, using high-speed projectiles, <a href="/wiki/High-frequency_impact_treatment" title="High-frequency impact treatment">high-frequency impact treatment</a> (also called high-frequency mechanical impact) using a mechanical hammer,<sup id="cite_ref-47" class="reference"><a href="#cite_note-47"><span class="cite-bracket">[</span>47<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-48" class="reference"><a href="#cite_note-48"><span class="cite-bracket">[</span>48<span class="cite-bracket">]</span></a></sup> and <a href="/wiki/Laser_peening" title="Laser peening">laser peening</a> which uses high-energy laser pulses. <a href="/wiki/Low_plasticity_burnishing" title="Low plasticity burnishing">Low plasticity burnishing</a> can also be used to induce compresses stress in fillets and cold work mandrels can be used for holes.<sup id="cite_ref-49" class="reference"><a href="#cite_note-49"><span class="cite-bracket">[</span>49<span class="cite-bracket">]</span></a></sup> Increases in fatigue life and strength are proportionally related to the depth of the compressive residual stresses imparted. Shot peening imparts compressive residual stresses approximately 0.005 inches (0.1 mm) deep, while laser peening can go 0.040 to 0.100 inches (1 to 2.5 mm) deep, or deeper.<sup id="cite_ref-50" class="reference"><a href="#cite_note-50"><span class="cite-bracket">[</span>50<span class="cite-bracket">]</span></a></sup><sup class="noprint Inline-Template" style="white-space:nowrap;">[<i><a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability"><span title="The material near this tag failed verification of its source citation(s). (January 2019)">failed verification</span></a></i>]</sup></li> <li><b>Deep cryogenic treatment</b>. The use of Deep Cryogenic treatment has been shown to increase resistance to fatigue failure. Springs used in industry, auto racing and firearms have been shown to last up to six times longer when treated. Heat checking, which is a form of thermal cyclic fatigue has been greatly delayed.<sup id="cite_ref-51" class="reference"><a href="#cite_note-51"><span class="cite-bracket">[</span>51<span class="cite-bracket">]</span></a></sup></li> <li><b>Re-profiling</b>. Changing the shape of a stress concentration such as a hole or cutout may be used to extend the life of a component. <a href="/wiki/Shape_optimization" title="Shape optimization">Shape optimisation</a> using numerical optimisation algorithms have been used to lower the stress concentration in wings and increase their life.<sup id="cite_ref-52" class="reference"><a href="#cite_note-52"><span class="cite-bracket">[</span>52<span class="cite-bracket">]</span></a></sup></li></ol> <div class="mw-heading mw-heading2"><h2 id="Fatigue_of_composites">Fatigue of composites</h2></div> <p><a href="/wiki/Composite_material" title="Composite material">Composite materials</a> can offer excellent resistance to fatigue loading. In general, composites exhibit good <a href="/wiki/Fracture_toughness" title="Fracture toughness">fracture toughness</a> and, unlike metals, increase fracture toughness with increasing strength. The critical damage size in composites is also greater than that for metals.<sup id="cite_ref-53" class="reference"><a href="#cite_note-53"><span class="cite-bracket">[</span>53<span class="cite-bracket">]</span></a></sup> </p><p>The primary mode of damage in a metal structure is cracking. For metal, cracks propagate in a relatively well-defined manner with respect to the applied stress, and the critical crack size and rate of crack propagation can be related to specimen data through analytical fracture mechanics. However, with composite structures, there is no single damage mode which dominates. Matrix cracking, delamination, debonding, voids, fiber fracture, and composite cracking can all occur separately and in combination, and the predominance of one or more is highly dependent on the <a href="/wiki/Lamination" title="Lamination">laminate</a> orientations and loading conditions.<sup id="cite_ref-:0_54-0" class="reference"><a href="#cite_note-:0-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> In addition, the unique joints and attachments used for composite structures often introduce modes of <a href="/wiki/Failure_(material)" class="mw-redirect" title="Failure (material)">failure</a> different from those typified by the laminate itself.<sup id="cite_ref-55" class="reference"><a href="#cite_note-55"><span class="cite-bracket">[</span>55<span class="cite-bracket">]</span></a></sup> </p><p>The composite damage propagates in a less regular manner and damage modes can change. Experience with composites indicates that the rate of damage propagation in does not exhibit the two distinct regions of initiation and propagation like metals. The crack initiation range in metals is propagation, and there is a significant quantitative difference in rate while the difference appears to be less apparent with composites.<sup id="cite_ref-:0_54-1" class="reference"><a href="#cite_note-:0-54"><span class="cite-bracket">[</span>54<span class="cite-bracket">]</span></a></sup> Fatigue cracks of composites may form in the <a href="/wiki/Matrix_(composite)" title="Matrix (composite)">matrix</a> and propagate slowly since the matrix carries such a small fraction of the applied <a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">stress</a>. And the <a href="/wiki/Fiber" title="Fiber">fibers</a> in the wake of the crack experience fatigue damage. In many cases, the damage rate is accelerated by deleterious interactions with the environment like <a href="/wiki/Redox" title="Redox">oxidation</a> or corrosion of fibers.<sup id="cite_ref-56" class="reference"><a href="#cite_note-56"><span class="cite-bracket">[</span>56<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Notable_fatigue_failures">Notable fatigue failures</h2></div> <div class="mw-heading mw-heading3"><h3 id="Versailles_train_crash">Versailles train crash</h3></div> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Meudon_1842.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Meudon_1842.jpg/220px-Meudon_1842.jpg" decoding="async" width="220" height="139" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Meudon_1842.jpg/330px-Meudon_1842.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Meudon_1842.jpg/440px-Meudon_1842.jpg 2x" data-file-width="2517" data-file-height="1585" /></a><figcaption>Versailles train disaster</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Tender_fatigued_axle.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Tender_fatigued_axle.JPG/220px-Tender_fatigued_axle.JPG" decoding="async" width="220" height="89" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Tender_fatigued_axle.JPG/330px-Tender_fatigued_axle.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/Tender_fatigued_axle.JPG/440px-Tender_fatigued_axle.JPG 2x" data-file-width="1511" data-file-height="609" /></a><figcaption>Drawing of a fatigue failure in an axle by Joseph Glynn, 1843</figcaption></figure> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Versailles_rail_accident" title="Versailles rail accident">Versailles rail accident</a></div> <p>Following the <a href="/wiki/Louis-Philippe_I,_King_of_the_French" class="mw-redirect" title="Louis-Philippe I, King of the French">King Louis-Philippe I</a>'s celebrations at the <a href="/wiki/Palace_of_Versailles" title="Palace of Versailles">Palace of Versailles</a>, a train returning to Paris crashed in May 1842 at <a href="/wiki/Meudon" title="Meudon">Meudon</a> after the leading locomotive broke an axle. The carriages behind piled into the wrecked engines and caught fire. At least 55 passengers were killed trapped in the locked carriages, including the explorer <a href="/wiki/Jules_Dumont_d%27Urville" title="Jules Dumont d'Urville">Jules Dumont d'Urville</a>. This accident is known in France as the <span title="French-language text"><i lang="fr">"Catastrophe ferroviaire de Meudon"</i></span>. The accident was witnessed by the British locomotive engineer <a href="/wiki/Joseph_Locke" title="Joseph Locke">Joseph Locke</a> and widely reported in Britain. It was discussed extensively by engineers, who sought an explanation. </p><p>The derailment had been the result of a broken <a href="/wiki/Locomotive" title="Locomotive">locomotive</a> axle. <a href="/wiki/William_John_Macquorn_Rankine" class="mw-redirect" title="William John Macquorn Rankine">Rankine's</a> investigation of broken axles in Britain highlighted the importance of stress concentration, and the mechanism of crack growth with repeated loading. His and other papers suggesting a crack growth mechanism through repeated stressing, however, were ignored, and fatigue failures occurred at an ever-increasing rate on the expanding railway system. Other spurious theories seemed to be more acceptable, such as the idea that the metal had somehow "crystallized". The notion was based on the crystalline appearance of the fast fracture region of the crack surface, but ignored the fact that the metal was already highly crystalline. </p> <div class="mw-heading mw-heading3"><h3 id="de_Havilland_Comet">de Havilland Comet</h3></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main articles: <a href="/wiki/BOAC_Flight_781" title="BOAC Flight 781">BOAC Flight 781</a> and <a href="/wiki/South_African_Airways_Flight_201" title="South African Airways Flight 201">South African Airways Flight 201</a></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Comet_1_G-ALYP_-_wreckage_recovered_png.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Comet_1_G-ALYP_-_wreckage_recovered_png.png/220px-Comet_1_G-ALYP_-_wreckage_recovered_png.png" decoding="async" width="220" height="154" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/70/Comet_1_G-ALYP_-_wreckage_recovered_png.png/330px-Comet_1_G-ALYP_-_wreckage_recovered_png.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/70/Comet_1_G-ALYP_-_wreckage_recovered_png.png/440px-Comet_1_G-ALYP_-_wreckage_recovered_png.png 2x" data-file-width="1100" data-file-height="770" /></a><figcaption>The recovered (shaded) parts of the wreckage of <i>G-ALYP</i> and the site (arrowed) of the failure</figcaption></figure> <p>Two <a href="/wiki/De_Havilland_Comet" title="De Havilland Comet">de Havilland Comet</a> passenger jets broke up in mid-air and crashed within a few months of each other in 1954. As a result, systematic tests were conducted on a <a href="/wiki/Fuselage" title="Fuselage">fuselage</a> immersed and pressurised in a water tank. After the equivalent of 3,000 flights, investigators at the <a href="/wiki/Royal_Aircraft_Establishment" title="Royal Aircraft Establishment">Royal Aircraft Establishment</a> (RAE) were able to conclude that the crash had been due to failure of the pressure cabin at the forward <a href="/wiki/Radio_direction_finder" class="mw-redirect" title="Radio direction finder">Automatic Direction Finder</a> window in the roof. This 'window' was in fact one of two apertures for the <a href="/wiki/Antenna_(radio)" title="Antenna (radio)">aerials</a> of an electronic navigation system in which opaque <a href="/wiki/Fibreglass" class="mw-redirect" title="Fibreglass">fibreglass</a> panels took the place of the window 'glass'. The failure was a result of metal fatigue caused by the repeated pressurisation and de-pressurisation of the aircraft cabin. Also, the supports around the windows were riveted, not bonded, as the original specifications for the aircraft had called for. The problem was exacerbated by the <a href="/wiki/Rivet" title="Rivet">punch rivet</a> construction technique employed. Unlike drill riveting, the imperfect nature of the hole created by punch riveting caused manufacturing defect cracks which may have caused the start of fatigue cracks around the rivet. </p> <figure class="mw-default-size mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/File:Fuselage_of_de_Havilland_Comet_Airliner_G-ALYP.JPG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Fuselage_of_de_Havilland_Comet_Airliner_G-ALYP.JPG/220px-Fuselage_of_de_Havilland_Comet_Airliner_G-ALYP.JPG" decoding="async" width="220" height="98" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Fuselage_of_de_Havilland_Comet_Airliner_G-ALYP.JPG/330px-Fuselage_of_de_Havilland_Comet_Airliner_G-ALYP.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Fuselage_of_de_Havilland_Comet_Airliner_G-ALYP.JPG/440px-Fuselage_of_de_Havilland_Comet_Airliner_G-ALYP.JPG 2x" data-file-width="3204" data-file-height="1422" /></a><figcaption>The fuselage roof fragment of <i>G-ALYP</i> on display in the Science Museum in London, showing the two ADF windows at which the initial failure occurred.<sup id="cite_ref-57" class="reference"><a href="#cite_note-57"><span class="cite-bracket">[</span>57<span class="cite-bracket">]</span></a></sup></figcaption></figure> <p>The Comet's pressure cabin had been designed to a <a href="/wiki/Safety_factor" class="mw-redirect" title="Safety factor">safety factor</a> comfortably in excess of that required by British Civil Airworthiness Requirements (2.5 times the cabin <a href="/wiki/Proof_test" title="Proof test">proof test</a> pressure as opposed to the requirement of 1.33 times and an ultimate load of 2.0 times the cabin pressure) and the accident caused a revision in the estimates of the safe loading strength requirements of airliner pressure cabins. </p><p>In addition, it was discovered that the <a href="/wiki/Stress_(physics)" class="mw-redirect" title="Stress (physics)">stresses</a> around pressure cabin apertures were considerably higher than had been anticipated, especially around sharp-cornered cut-outs, such as windows. As a result, all future <a href="/wiki/Jet_airliner" title="Jet airliner">jet airliners</a> would feature windows with rounded corners, greatly reducing the stress concentration. This was a noticeable distinguishing feature of all later models of the Comet. Investigators from the RAE told a public inquiry that the sharp corners near the Comets' window openings acted as initiation sites for cracks. The skin of the aircraft was also too thin, and cracks from manufacturing stresses were present at the corners. </p> <div class="mw-heading mw-heading3"><h3 id="Alexander_L._Kielland_oil_platform_capsizing"><i>Alexander L. Kielland</i> oil platform capsizing</h3></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:ALK_columns_fractures_english.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/ALK_columns_fractures_english.png/220px-ALK_columns_fractures_english.png" decoding="async" width="220" height="209" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/ALK_columns_fractures_english.png/330px-ALK_columns_fractures_english.png 1.5x, //upload.wikimedia.org/wikipedia/commons/d/d7/ALK_columns_fractures_english.png 2x" data-file-width="400" data-file-height="380" /></a><figcaption>Fractures on the right side of the Alexander L. Kielland rig</figcaption></figure> <p><a href="/wiki/Alexander_L._Kielland_(platform)" title="Alexander L. Kielland (platform)"><i>Alexander L. Kielland</i></a> was a Norwegian <a href="/wiki/Semi-submersible" title="Semi-submersible">semi-submersible</a> <a href="/wiki/Drilling_rig" title="Drilling rig">drilling rig</a> that <a href="/wiki/Capsize" class="mw-redirect" title="Capsize">capsized</a> whilst working in the <a href="/wiki/Ekofisk_oil_field" title="Ekofisk oil field">Ekofisk oil field</a> in March 1980, killing 123 people. The capsizing was the worst disaster in Norwegian waters since World War II. The rig, located approximately 320 km east of <a href="/wiki/Dundee" title="Dundee">Dundee</a>, Scotland, was owned by the Stavanger Drilling Company of Norway and was on hire to the United States company <a href="/wiki/Phillips_Petroleum" class="mw-redirect" title="Phillips Petroleum">Phillips Petroleum</a> at the time of the disaster. In driving rain and mist, early in the evening of 27 March 1980 more than 200 men were off duty in the accommodation on <i>Alexander L. Kielland</i>. The wind was gusting to 40 knots with waves up to 12 m high. The rig had just been winched away from the <i>Edda</i> production platform. Minutes before 18:30 those on board felt a 'sharp crack' followed by 'some kind of trembling'. Suddenly the rig heeled over 30° and then stabilised. Five of the six anchor cables had broken, with one remaining cable preventing the rig from capsizing. The <a href="/wiki/Angle_of_list" title="Angle of list">list</a> continued to increase and at 18:53 the remaining anchor cable snapped and the rig turned upside down. </p><p>A year later in March 1981, the investigative report<sup id="cite_ref-58" class="reference"><a href="#cite_note-58"><span class="cite-bracket">[</span>58<span class="cite-bracket">]</span></a></sup> concluded that the rig collapsed owing to a fatigue crack in one of its six bracings (bracing D-6), which connected the collapsed D-leg to the rest of the rig. This was traced to a small 6 mm fillet weld which joined a non-load-bearing flange plate to this D-6 bracing. This flange plate held a sonar device used during drilling operations. The poor profile of the fillet weld contributed to a reduction in its fatigue strength. Further, the investigation found considerable amounts of <a href="/wiki/Lamellar_tearing" class="mw-redirect" title="Lamellar tearing">lamellar tearing</a> in the flange plate and cold cracks in the butt weld. Cold cracks in the welds, increased stress concentrations due to the weakened flange plate, the poor weld profile, and cyclical stresses (which would be common in the <a href="/wiki/North_Sea" title="North Sea">North Sea</a>), seemed to collectively play a role in the rig's collapse. </p> <div class="mw-heading mw-heading3"><h3 id="Others">Others</h3></div> <ul><li>The 1862 <a href="/wiki/Hartley_Colliery_Disaster" class="mw-redirect" title="Hartley Colliery Disaster">Hartley Colliery Disaster</a> was caused by the fracture of a steam engine beam and killed 204 people.</li> <li>The 1919 Boston <a href="/wiki/Great_Molasses_Flood" title="Great Molasses Flood">Great Molasses Flood</a> has been attributed to a fatigue failure.</li> <li>The 1948 <a href="/wiki/Northwest_Airlines_Flight_421" title="Northwest Airlines Flight 421">Northwest Airlines Flight 421</a> crash due to fatigue failure in a wing spar root</li> <li>The <a href="/wiki/1957_Cebu_Douglas_C-47_crash" title="1957 Cebu Douglas C-47 crash">1957 "Mt. Pinatubo"</a>, presidential plane of <a href="/wiki/President_of_the_Philippines" title="President of the Philippines">Philippine President</a> <a href="/wiki/Ramon_Magsaysay" title="Ramon Magsaysay">Ramon Magsaysay</a>, crashed due to engine failure caused by metal fatigue.</li> <li>The 1965 capsize of the UK's first offshore oil platform, the <a href="/wiki/Sea_Gem" title="Sea Gem">Sea Gem</a>, was due to fatigue in part of the suspension system linking the hull to the legs.</li> <li>The 1968 <a href="/wiki/Los_Angeles_Airways_Flight_417" title="Los Angeles Airways Flight 417">Los Angeles Airways Flight 417</a> lost one of its main rotor blades due to fatigue failure.</li> <li>The 1968 <a href="/wiki/MacRobertson_Miller_Airlines_Flight_1750" title="MacRobertson Miller Airlines Flight 1750">MacRobertson Miller Airlines Flight 1750</a> lost a wing due to improper maintenance leading to fatigue failure.</li> <li>The 1969 <a href="/wiki/General_Dynamics_F-111_Aardvark" title="General Dynamics F-111 Aardvark">F-111A</a> crash due to a fatigue failure of the wing pivot fitting from a material defect resulted in the development of the <a href="/wiki/Damage_tolerance" title="Damage tolerance">damage-tolerant</a> approach for fatigue design.<sup id="cite_ref-59" class="reference"><a href="#cite_note-59"><span class="cite-bracket">[</span>59<span class="cite-bracket">]</span></a></sup></li> <li>The <a href="/wiki/1977_Dan-Air_Boeing_707_crash" title="1977 Dan-Air Boeing 707 crash">1977 Dan-Air Boeing 707 crash</a> caused by fatigue failure resulting in the loss of the right horizontal stabilizer.</li> <li>The 1979 <a href="/wiki/American_Airlines_Flight_191" title="American Airlines Flight 191">American Airlines Flight 191</a> crashed after engine separation attributed to fatigue damage in the pylon structure holding the engine to the wing, caused by improper maintenance procedures.</li> <li>The 1980 <a href="/wiki/LOT_Flight_7" class="mw-redirect" title="LOT Flight 7">LOT Flight 7</a> crashed due to fatigue in an engine turbine shaft resulting in engine disintegration leading to loss of control.</li> <li>The 1985 <a href="/wiki/Japan_Airlines_Flight_123" class="mw-redirect" title="Japan Airlines Flight 123">Japan Airlines Flight 123</a> crashed after the aircraft lost its vertical stabilizer due to faulty repairs on the rear bulkhead.</li> <li>The 1988 <a href="/wiki/Aloha_Airlines_Flight_243" title="Aloha Airlines Flight 243">Aloha Airlines Flight 243</a> suffered an explosive decompression at 24,000 feet (7,300 m) after a fatigue failure.</li> <li>The 1989 <a href="/wiki/United_Airlines_Flight_232" title="United Airlines Flight 232">United Airlines Flight 232</a> lost its tail engine due to fatigue failure in a fan disk hub.</li> <li>The 1992 <a href="/wiki/El_Al_Flight_1862" title="El Al Flight 1862">El Al Flight 1862</a> lost both engines on its right-wing due to fatigue failure in the pylon mounting of the #3 Engine.</li> <li>The 1998 <a href="/wiki/Eschede_train_disaster" title="Eschede train disaster">Eschede train disaster</a> was caused by fatigue failure of a single composite wheel.</li> <li>The 2000 <a href="/wiki/Hatfield_rail_crash" title="Hatfield rail crash">Hatfield rail crash</a> was likely caused by <a href="/wiki/Rolling_contact_fatigue" title="Rolling contact fatigue">rolling contact fatigue</a>.</li> <li>The 2000 <a href="/wiki/Firestone_and_Ford_tire_controversy" title="Firestone and Ford tire controversy">recall of 6.5 million Firestone tires</a> on Ford Explorers originated from fatigue crack growth leading to separation of the tread from the tire.<sup id="cite_ref-60" class="reference"><a href="#cite_note-60"><span class="cite-bracket">[</span>60<span class="cite-bracket">]</span></a></sup></li> <li>The 2002 <a href="/wiki/China_Airlines_Flight_611" title="China Airlines Flight 611">China Airlines Flight 611</a> disintegrated in-flight due to fatigue failure.</li> <li>The 2005 <a href="/wiki/Chalk%27s_Ocean_Airways_Flight_101" title="Chalk's Ocean Airways Flight 101">Chalk's Ocean Airways Flight 101</a> lost its right wing due to fatigue failure brought about by inadequate maintenance practices.</li> <li>The 2009 <a href="/wiki/Viareggio_train_derailment" title="Viareggio train derailment">Viareggio train derailment</a> due to fatigue failure.</li> <li>The <a href="/wiki/2009_Sayano%E2%80%93Shushenskaya_power_station_accident" class="mw-redirect" title="2009 Sayano–Shushenskaya power station accident">2009 Sayano–Shushenskaya power station accident</a> due to metal fatigue of turbine mountings.</li> <li>The 2017 <a href="/wiki/Air_France_Flight_66" class="mw-redirect" title="Air France Flight 66">Air France Flight 66</a> had in-flight engine failure due to cold dwell fatigue fracture in the fan hub.</li> <li>The 2023 <a href="/wiki/Titan_submersible_implosion" title="Titan submersible implosion">Titan submersible implosion</a> is thought to have occurred due to fatigue <a href="/wiki/Delamination" title="Delamination">delamination</a> of the carbon-fiber material used for the hull.</li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2></div> <ul><li><a href="/wiki/Aviation_safety" title="Aviation safety">Aviation safety</a> – State in which risks associated with aviation are at an acceptable level</li> <li><a href="/wiki/Basquin%27s_Law_of_Fatigue" class="mw-redirect" title="Basquin's Law of Fatigue">Basquin's Law of Fatigue</a></li> <li><a href="/wiki/Critical_plane_analysis" title="Critical plane analysis">Critical plane analysis</a> – Analysis of multiaxial stresses and strains</li> <li><a href="/wiki/Embedment" title="Embedment">Embedment</a></li> <li><a href="/wiki/Forensic_materials_engineering" title="Forensic materials engineering">Forensic materials engineering</a> – branch of forensic engineering<span style="display:none" class="category-wikidata-fallback-annotation">Pages displaying wikidata descriptions as a fallback</span></li> <li><a href="/wiki/Fractography" title="Fractography">Fractography</a> – Study of the fracture surfaces of materials</li> <li><a href="/w/index.php?title=Smith_fatigue_strength_diagram&action=edit&redlink=1" class="new" title="Smith fatigue strength diagram (page does not exist)">Smith fatigue strength diagram</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://de.wikipedia.org/wiki/Dauerfestigkeitsschaubild_nach_Smith" class="extiw" title="de:Dauerfestigkeitsschaubild nach Smith">de</a>]</span>, a diagram by British mechanical engineer <a href="/w/index.php?title=James_Henry_Smith&action=edit&redlink=1" class="new" title="James Henry Smith (page does not exist)">James Henry Smith</a><span class="noprint" style="font-size:85%; font-style: normal;"> [<a href="https://de.wikipedia.org/wiki/James_Henry_Smith" class="extiw" title="de:James Henry Smith">de</a>]</span></li> <li><a href="/wiki/Solder_fatigue" title="Solder fatigue">Solder fatigue</a> – Degradation of solder due to deformation under cyclic loading</li> <li><a href="/wiki/Thermo-mechanical_fatigue" title="Thermo-mechanical fatigue">Thermo-mechanical fatigue</a></li> <li><a href="/wiki/Vibration_fatigue" title="Vibration fatigue">Vibration fatigue</a></li> <li><i><a href="/wiki/International_Journal_of_Fatigue" title="International Journal of Fatigue">International Journal of Fatigue</a></i></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free 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Waveland Press. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4786-0838-7" title="Special:BookSources/978-1-4786-0838-7"><bdi>978-1-4786-0838-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mechanical+Behavior+of+Materials%3A+Second+Edition&rft.pub=Waveland+Press&rft.date=2005-12-16&rft.isbn=978-1-4786-0838-7&rft.aulast=Courtney&rft.aufirst=Thomas+H.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DQcYSAAAAQBAJ%26dq%3DMechanical%2BBehavior%2Bof%2BMaterials%26pg%3DPR3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFatigue+%28material%29" class="Z3988"></span></span> </li> <li id="cite_note-57"><span class="mw-cite-backlink"><b><a href="#cite_ref-57">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090107042926/http://objectwiki.sciencemuseum.org.uk/wiki/Fuselage_of_de_Havilland_Comet_Airliner_G-ALYP">"ObjectWiki: Fuselage of de Havilland Comet Airliner G-ALYP"</a>. Science Museum. 24 September 2009. Archived from <a rel="nofollow" class="external text" href="http://objectwiki.sciencemuseum.org.uk/wiki/Fuselage_of_de_Havilland_Comet_Airliner_G-ALYP">the original</a> on 7 January 2009<span class="reference-accessdate">. Retrieved <span class="nowrap">9 October</span> 2009</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=ObjectWiki%3A+Fuselage+of+de+Havilland+Comet+Airliner+G-ALYP&rft.pub=Science+Museum&rft.date=2009-09-24&rft_id=http%3A%2F%2Fobjectwiki.sciencemuseum.org.uk%2Fwiki%2FFuselage_of_de_Havilland_Comet_Airliner_G-ALYP&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFatigue+%28material%29" class="Z3988"></span></span> </li> <li id="cite_note-58"><span class="mw-cite-backlink"><b><a href="#cite_ref-58">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1"><i>The Alexander L. Kielland accident, Report of a Norwegian public commission appointed by royal decree of March 28, 1980, presented to the Ministry of Justice and Police March</i>. Norwegian Public Reports 1981:11. Norwegian Ministry of Justice and Public Security. 1981. <a href="/wiki/ASIN_(identifier)" class="mw-redirect" title="ASIN (identifier)">ASIN</a> <a rel="nofollow" class="external text" href="https://www.amazon.com/dp/B0000ED27N">B0000ED27N</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Alexander+L.+Kielland+accident%2C+Report+of+a+Norwegian+public+commission+appointed+by+royal+decree+of+March+28%2C+1980%2C+presented+to+the+Ministry+of+Justice+and+Police+March&rft.series=Norwegian+Public+Reports+1981%3A11&rft.pub=Norwegian+Ministry+of+Justice+and+Public+Security&rft.date=1981&rft_id=https%3A%2F%2Fwww.amazon.com%2Fdp%2FB0000ED27N%23id-name%3DASIN&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFatigue+%28material%29" class="Z3988"></span></span> </li> <li id="cite_note-59"><span class="mw-cite-backlink"><b><a href="#cite_ref-59">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFRedmond" class="citation web cs1">Redmond, Gerard. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20190427131335/https://www.ndt.net/apcndt2001/papers/912/912.htm">"From 'Safe Life' to Fracture Mechanics - F111 Aircraft Cold Temperature Proof Testing at RAAF Amberley"</a>. Archived from <a rel="nofollow" class="external text" href="https://www.ndt.net/apcndt2001/papers/912/912.htm">the original</a> on 27 April 2019<span class="reference-accessdate">. Retrieved <span class="nowrap">17 April</span> 2019</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=From+%27Safe+Life%27+to+Fracture+Mechanics+-+F111+Aircraft+Cold+Temperature+Proof+Testing+at+RAAF+Amberley&rft.aulast=Redmond&rft.aufirst=Gerard&rft_id=https%3A%2F%2Fwww.ndt.net%2Fapcndt2001%2Fpapers%2F912%2F912.htm&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFatigue+%28material%29" class="Z3988"></span></span> </li> <li id="cite_note-60"><span class="mw-cite-backlink"><b><a href="#cite_ref-60">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAnsberry2001" class="citation news cs1">Ansberry, C. (5 February 2001). <a rel="nofollow" class="external text" href="https://www.wsj.com/articles/SB981125867324708466">"In Firestone Tire Study, Expert Finds Vehicle Weight Was Key in Failure"</a>. <i>Wall Street Journal</i><span class="reference-accessdate">. Retrieved <span class="nowrap">6 September</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Wall+Street+Journal&rft.atitle=In+Firestone+Tire+Study%2C+Expert+Finds+Vehicle+Weight+Was+Key+in+Failure&rft.date=2001-02-05&rft.aulast=Ansberry&rft.aufirst=C.&rft_id=https%3A%2F%2Fwww.wsj.com%2Farticles%2FSB981125867324708466&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFatigue+%28material%29" class="Z3988"></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">PDL Staff (1995). <i>Fatigue and Tribological Properties of Plastics and Elastomers</i>. Plastics Design Library. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-884207-15-0" title="Special:BookSources/978-1-884207-15-0"><bdi>978-1-884207-15-0</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fatigue+and+Tribological+Properties+of+Plastics+and+Elastomers&rft.pub=Plastics+Design+Library&rft.date=1995&rft.isbn=978-1-884207-15-0&rft.au=PDL+Staff&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFatigue+%28material%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation journal cs1">Leary, M.; Burvill, C. (2009). "Applicability of published data for fatigue-limited design". <i>Quality and Reliability Engineering International</i>. <b>25</b> (8): 921–932. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1002%2Fqre.1010">10.1002/qre.1010</a>. <a href="/wiki/S2CID_(identifier)" class="mw-redirect" title="S2CID (identifier)">S2CID</a> <a rel="nofollow" class="external text" href="https://api.semanticscholar.org/CorpusID:206432498">206432498</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Quality+and+Reliability+Engineering+International&rft.atitle=Applicability+of+published+data+for+fatigue-limited+design&rft.volume=25&rft.issue=8&rft.pages=921-932&rft.date=2009&rft_id=info%3Adoi%2F10.1002%2Fqre.1010&rft_id=https%3A%2F%2Fapi.semanticscholar.org%2FCorpusID%3A206432498%23id-name%3DS2CID&rft.aulast=Leary&rft.aufirst=M.&rft.au=Burvill%2C+C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFatigue+%28material%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">Dieter, G. E. (2013). <i>Mechanical Metallurgy</i>. <a href="/wiki/McGraw-Hill" class="mw-redirect" title="McGraw-Hill">McGraw-Hill</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1259064791" title="Special:BookSources/978-1259064791"><bdi>978-1259064791</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mechanical+Metallurgy&rft.pub=McGraw-Hill&rft.date=2013&rft.isbn=978-1259064791&rft.aulast=Dieter&rft.aufirst=G.+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFatigue+%28material%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">Little, R.E.; Jebe, E.H. (1975). <i>Statistical Design of Fatigue Experiments</i>. <a href="/wiki/John_Wiley_%26_Sons" class="mw-redirect" title="John Wiley & Sons">John Wiley & Sons</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-470-54115-9" title="Special:BookSources/978-0-470-54115-9"><bdi>978-0-470-54115-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Statistical+Design+of+Fatigue+Experiments&rft.pub=John+Wiley+%26+Sons&rft.date=1975&rft.isbn=978-0-470-54115-9&rft.aulast=Little&rft.aufirst=R.E.&rft.au=Jebe%2C+E.H.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFatigue+%28material%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">Schijve, J. (2009). <i>Fatigue of Structures and Materials</i>. <a href="/wiki/Springer_Publishing" title="Springer Publishing">Springer</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4020-6807-2" title="Special:BookSources/978-1-4020-6807-2"><bdi>978-1-4020-6807-2</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fatigue+of+Structures+and+Materials&rft.pub=Springer&rft.date=2009&rft.isbn=978-1-4020-6807-2&rft.aulast=Schijve&rft.aufirst=J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFatigue+%28material%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">Lalanne, C. (2009). <i>Fatigue Damage</i>. <a href="/wiki/ISTE_Ltd" class="mw-redirect" title="ISTE Ltd">ISTE</a> - <a href="/wiki/Wiley_(publisher)" title="Wiley (publisher)">Wiley</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-84821-125-4" title="Special:BookSources/978-1-84821-125-4"><bdi>978-1-84821-125-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fatigue+Damage&rft.pub=ISTE+-+Wiley&rft.date=2009&rft.isbn=978-1-84821-125-4&rft.aulast=Lalanne&rft.aufirst=C.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFatigue+%28material%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">Pook, L. (2007). <i>Metal Fatigue, What it is, Why it matters</i>. Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-1-4020-5596-6" title="Special:BookSources/978-1-4020-5596-6"><bdi>978-1-4020-5596-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Metal+Fatigue%2C+What+it+is%2C+Why+it+matters&rft.pub=Springer&rft.date=2007&rft.isbn=978-1-4020-5596-6&rft.aulast=Pook&rft.aufirst=L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFatigue+%28material%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">Draper, J. (2008). <i>Modern Metal Fatigue Analysis</i>. EMAS. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-947817-79-4" title="Special:BookSources/978-0-947817-79-4"><bdi>978-0-947817-79-4</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Modern+Metal+Fatigue+Analysis&rft.pub=EMAS&rft.date=2008&rft.isbn=978-0-947817-79-4&rft.aulast=Draper&rft.aufirst=J.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFatigue+%28material%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">Suresh, S. (2004). <i>Fatigue of Materials</i>. <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-0-521-57046-6" title="Special:BookSources/978-0-521-57046-6"><bdi>978-0-521-57046-6</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fatigue+of+Materials&rft.pub=Cambridge+University+Press&rft.date=2004&rft.isbn=978-0-521-57046-6&rft.aulast=Suresh&rft.aufirst=S.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFatigue+%28material%29" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite class="citation book cs1">Kim, H. S. (2018). <a rel="nofollow" class="external text" href="https://bookboon.com/en/mechanics-of-solids-and-fracture-ebook"><i>Mechanics of Solids and Fracture, 3rd ed</i></a>. <a href="/w/index.php?title=Bookboon,_London&action=edit&redlink=1" class="new" title="Bookboon, London (page does not exist)">Bookboon, London</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-87-403-2393-1" title="Special:BookSources/978-87-403-2393-1"><bdi>978-87-403-2393-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mechanics+of+Solids+and+Fracture%2C+3rd+ed&rft.pub=Bookboon%2C+London&rft.date=2018&rft.isbn=978-87-403-2393-1&rft.aulast=Kim&rft.aufirst=H.+S.&rft_id=https%3A%2F%2Fbookboon.com%2Fen%2Fmechanics-of-solids-and-fracture-ebook&rfr_id=info%3Asid%2Fen.wikipedia.org%3AFatigue+%28material%29" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="External_links">External links</h2></div> <style data-mw-deduplicate="TemplateStyles:r1235681985">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:var(--background-color-interactive-subtle,#f8f9fa);display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1;min-width:0}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><style data-mw-deduplicate="TemplateStyles:r1237033735">@media print{body.ns-0 .mw-parser-output .sistersitebox{display:none!important}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .sistersitebox img[src*="Wiktionary-logo-en-v2.svg"]{background-color:white}}</style><div class="side-box side-box-right plainlinks sistersitebox"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png" decoding="async" width="30" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/45px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/4/4a/Commons-logo.svg/59px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span></div> <div class="side-box-text plainlist">Wikimedia Commons has media related to <span style="font-weight: bold; font-style: italic;"><a href="https://commons.wikimedia.org/wiki/Category:Material_fatigue" class="extiw" title="commons:Category:Material fatigue">Material fatigue</a></span>.</div></div> </div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20050830021748/http://www.sv.vt.edu/classes/MSE2094_NoteBook/97ClassProj/anal/kelly/fatigue.html">Fatigue</a> Shawn M. Kelly</li> <li><a rel="nofollow" class="external text" href="http://www.campoly.com/index.php/download_file/view/204/108/">Application note on fatigue crack propagation in UHMWPE</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131104004739/http://www.campoly.com/index.php/download_file/view/204/108/">Archived</a> 2013-11-04 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a></li> <li><a rel="nofollow" class="external text" href="https://www.youtube.com/watch?v=LhUclxBUV_E">fatigue test video</a> Karlsruhe University of Applied Sciences</li> <li><a rel="nofollow" class="external text" href="https://www.efatigue.com/training/Strain_Life_Method.pdf">Strain life method</a> G. Glinka</li> <li><a rel="nofollow" class="external text" href="https://www.efatigue.com/training/Chapter_9.pdf">Fatigue from variable amplitude loading</a> A. Fatemi</li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output 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hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Authority_control_databases_frameless&#124;text-top&#124;10px&#124;alt=Edit_this_at_Wikidata&#124;link=https&#58;//www.wikidata.org/wiki/Q507234#identifiers&#124;class=noprint&#124;Edit_this_at_Wikidata" style="font-size:114%;margin:0 4em"><a href="/wiki/Help:Authority_control" title="Help:Authority control">Authority control databases</a> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q507234#identifiers" title="Edit this at Wikidata"><img alt="Edit this at Wikidata" src="//upload.wikimedia.org/wikipedia/en/thumb/8/8a/OOjs_UI_icon_edit-ltr-progressive.svg/10px-OOjs_UI_icon_edit-ltr-progressive.svg.png" decoding="async" width="10" height="10" class="mw-file-element" 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class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="疲労 (工学)"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00573505">Japan</a></span></span></li><li><span class="uid"><span class="rt-commentedText tooltip tooltip-dotted" title="únava materiálu"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph128339&CON_LNG=ENG">Czech Republic</a></span></span></li><li><span class="uid"><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007555882705171">Israel</a></span></li></ul></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Other</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"><ul><li><span class="uid"><a rel="nofollow" class="external text" href="http://esu.com.ua/search_articles.php?id=30069">Encyclopedia of Modern Ukraine</a></span></li></ul></div></td></tr></tbody></table></div></div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Fatigue_(material)&oldid=1258761345">https://en.wikipedia.org/w/index.php?title=Fatigue_(material)&oldid=1258761345</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Fracture_mechanics" title="Category:Fracture mechanics">Fracture mechanics</a></li><li><a href="/wiki/Category:Materials_degradation" title="Category:Materials degradation">Materials degradation</a></li><li><a href="/wiki/Category:Mechanical_failure_modes" 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