<!DOCTYPE html>
<html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-0 vector-toc-not-available vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-0 skin-theme-clientpref-day vector-sticky-header-enabled" lang="de" dir="ltr"><head>
<meta charset="UTF-8">
<title>Coffin-Manson-Modell</title>
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="icon" type="image/png" href="./_res_/favicon.png">
<link rel="canonical" href="https://de.wikipedia.org/wiki/Coffin-Manson-Modell"> <link href="./_mw_/ext.math.styles.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.wikimediamessages.styles.css" rel="stylesheet" type="text/css">
<link href="./_mw_/skins.vector.icons.css" rel="stylesheet" type="text/css">
<link href="./_mw_/skins.vector.search.codex.styles.css" rel="stylesheet" type="text/css">
<link href="./_mw_/skins.vector.styles.css" rel="stylesheet" type="text/css">
<meta name="ResourceLoaderDynamicStyles" content="">
<link href="./_mw_/ext.gadget.citeRef.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.gadget.defaultPlainlinks.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.gadget.dewikiCommonHide.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.gadget.dewikiCommonLayout.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.gadget.dewikiCommonStyle.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.gadget.dewikiDarkmode.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.gadget.dewikiResponsive.css" rel="stylesheet" type="text/css">
<link href="./_mw_/ext.gadget.specialSearch.css" rel="stylesheet" type="text/css">
<link rel="stylesheet" type="text/css" href="./_mw_/site.styles.css">
<link rel="stylesheet" type="text/css" href="./_mw_/noscript.css">
<link rel="stylesheet" type="text/css" href="./_res_/footer.css">
<link rel="stylesheet" type="text/css" href="./_res_/vector-2022.css">
</head>
<body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject page-Coffin-Manson-Modell rootpage-Coffin-Manson-Modell skin-vector-2022 action-view">
<div class="mw-page-container">
<div class="mw-page-container-inner">
<div class="mw-content-container">
<main id="content" class="mw-body">
<header class="mw-body-header vector-page-titlebar">
<h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Coffin-Manson-Modell</span></h1>
</header>
<a id="top"></a>
<div id="bodyContent" class="vector-body ve-init-mw-desktopArticleTarget-targetContainer" aria-labelledby="firstHeading" data-mw-ve-target-container="">
<div id="contentSub">
<div id="mw-content-subtitle"></div>
</div>
<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="de" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="de" dir="ltr">
<p>Die <b>Coffin-Manson-Beziehung</b> beschreibt in der <a href="Werkstofftechnik" class="mw-redirect" title="Werkstofftechnik">Werkstofftechnik</a> den Verlauf der <a href="Dehnung" title="Dehnung">Dehnungs</a><a href="W%C3%B6hlerlinie" class="mw-redirect" title="Wöhlerlinie">wöhlerlinie</a> im Low-Cycle-Fatigue-Bereich (LCF), also etwa im Bereich von 1 bis 10<sup>5</sup> <a href="Schwingspiel" class="mw-redirect" title="Schwingspiel">Schwingspielen</a> (<a href="Kurzzeitfestigkeit" class="mw-redirect" title="Kurzzeitfestigkeit">Kurzzeitfestigkeit</a>).
In diesem Bereich werden Bauteile so stark beansprucht, dass im Zyklus <a href="Plastische_Verformung" class="mw-redirect" title="Plastische Verformung">plastische Verformungen</a> auftreten. Laut Coffin und Manson bestimmt hier im Wesentlichen die plastische Dehnungs<a href="Amplitude" title="Amplitude">amplitude</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\Delta \epsilon _{\mathrm {pl} }}{2}}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<msub>
<mi>ϵ<!-- ϵ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">p</mi>
<mi mathvariant="normal">l</mi>
</mrow>
</mrow>
</msub>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle {\frac {\Delta \epsilon _{\mathrm {pl} }}{2}}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/127af233d8ae3f3028a66f2dd4e454839bd7b3a1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:5.32ex; height:5.676ex;" alt="{\displaystyle {\frac {\Delta \epsilon _{\mathrm {pl} }}{2}}}" loading="lazy"></span> die <a href="Lebensdauer_(Technik)" class="mw-redirect" title="Lebensdauer (Technik)">Lebensdauer</a>:
</p>
<dl><dd><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\Delta \epsilon _{\mathrm {pl} }}{2}}=\epsilon _{\mathrm {f} }'\cdot (N_{\mathrm {B} })^{c}}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<msub>
<mi>ϵ<!-- ϵ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">p</mi>
<mi mathvariant="normal">l</mi>
</mrow>
</mrow>
</msub>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<mo>=</mo>
<msubsup>
<mi>ϵ<!-- ϵ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">f</mi>
</mrow>
</mrow>
<mo>′</mo>
</msubsup>
<mo>⋅<!-- ⋅ --></mo>
<mo stretchy="false">(</mo>
<msub>
<mi>N</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">B</mi>
</mrow>
</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 {\frac {\Delta \epsilon _{\mathrm {pl} }}{2}}=\epsilon _{\mathrm {f} }'\cdot (N_{\mathrm {B} })^{c}}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/4870a2073768b66cb9e6327925809d45c764a39c.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:17.901ex; height:5.676ex;" alt="{\displaystyle {\frac {\Delta \epsilon _{\mathrm {pl} }}{2}}=\epsilon _{\mathrm {f} }'\cdot (N_{\mathrm {B} })^{c}}" loading="lazy"></span></dd></dl>
<p>mit
</p>
<ul><li><span class="mwe-math-element mwe-math-element-inline"><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_{\mathrm {B} }}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msub>
<mi>N</mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">B</mi>
</mrow>
</mrow>
</msub>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle N_{\mathrm {B} }}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/281dcf348663bba3102f2a02c9fccf74cbf7ffc7.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.262ex; height:2.509ex;" alt="{\displaystyle N_{\mathrm {B} }}" loading="lazy"></span> = Zahl der Zyklen bis zum <a href="Bruchmechanik" title="Bruchmechanik">Bruch</a></li>
<li><span class="mwe-math-element mwe-math-element-inline"><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="./_assets_/eb734a37dd21ce173a46342d1cc64c92/86a67b81c2de995bd608d5b2df50cd8cd7d92455.svg" 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}" loading="lazy"></span> = <a href="Materialerm%C3%BCdung" title="Materialermüdung">Ermüdungs</a><a href="Duktilit%C3%A4t" title="Duktilität">duktilität</a>; für duktile Werkstoffe gilt: <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -0{,}7\leq c\leq -0{,}5}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mo>−<!-- − --></mo>
<mn>0</mn>
<mrow class="MJX-TeXAtom-ORD">
<mo>,</mo>
</mrow>
<mn>7</mn>
<mo>≤<!-- ≤ --></mo>
<mi>c</mi>
<mo>≤<!-- ≤ --></mo>
<mo>−<!-- − --></mo>
<mn>0</mn>
<mrow class="MJX-TeXAtom-ORD">
<mo>,</mo>
</mrow>
<mn>5</mn>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle -0{,}7\leq c\leq -0{,}5}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/e2523d7bdc498facf0a7494e0f818a4994606626.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:16.764ex; height:2.509ex;" alt="{\displaystyle -0{,}7\leq c\leq -0{,}5}" loading="lazy"></span></li>
<li><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \epsilon _{\mathrm {f} }'}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<msubsup>
<mi>ϵ<!-- ϵ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">f</mi>
</mrow>
</mrow>
<mo>′</mo>
</msubsup>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \epsilon _{\mathrm {f} }'}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/48aefc44d9dface227002129de9de9f38f0baaf5.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:1.788ex; height:2.843ex;" alt="{\displaystyle \epsilon _{\mathrm {f} }'}" loading="lazy"></span> = Ermüdungsduktilitätskoeffizient (f für engl. <i>fatigue</i>), entspricht in etwa der wahren Dehnung beim Bruch (im quasistatischen Zugversuch).</li></ul>
<p>In einer <a href="Logarithmenpapier#Doppeltlogarithmisches_Papier" title="Logarithmenpapier">doppeltlogarithmischen Auftragung</a> ergibt sich daraus eine fallende Gerade, wobei gegenüber dem <i>normalen</i> Wöhlerdiagramm auf der <a href="Ordinate" class="mw-redirect" title="Ordinate">Ordinate</a> jetzt <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \log \left({\frac {\Delta \epsilon _{\mathrm {pl} }}{2}}\right)}">
<semantics>
<mrow class="MJX-TeXAtom-ORD">
<mstyle displaystyle="true" scriptlevel="0">
<mi>log</mi>
<mo><!-- --></mo>
<mrow>
<mo>(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mfrac>
<mrow>
<mi mathvariant="normal">Δ<!-- Δ --></mi>
<msub>
<mi>ϵ<!-- ϵ --></mi>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">p</mi>
<mi mathvariant="normal">l</mi>
</mrow>
</mrow>
</msub>
</mrow>
<mn>2</mn>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</mstyle>
</mrow>
<annotation encoding="application/x-tex">{\displaystyle \log \left({\frac {\Delta \epsilon _{\mathrm {pl} }}{2}}\right)}</annotation>
</semantics>
</math></span><img src="./_assets_/eb734a37dd21ce173a46342d1cc64c92/745c6b7bc70b9d7dd1c3ead1711e92417a483c1f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:11.713ex; height:6.343ex;" alt="{\displaystyle \log \left({\frac {\Delta \epsilon _{\mathrm {pl} }}{2}}\right)}" loading="lazy"></span> aufgetragen wird.
</p>
<div class="mw-heading mw-heading2"><h2 id="Siehe_auch">Siehe auch</h2></div>
<ul><li><a href="Basquin-Gleichung" title="Basquin-Gleichung">Basquin-Gleichung</a></li></ul>
<div class="mw-heading mw-heading2"><h2 id="Literatur">Literatur</h2></div>
<ul><li>Ralf Bürgel, Hans Jürgen Maier, Thomas Niendorf: <i>Handbuch Hochtemperatur-Werkstofftechnik: Grundlagen, Werkstoffbeanspruchungen, Hochtemperaturlegierungen und -beschichtungen</i>, Springer Fachmedien Wiesbaden, Wiesbaden 2015, ISBN 978-3-658-10591-4, S. 196–200</li></ul></div><!--htdig_noindex--><div><div class="zim-footer">
Dieser Artikel wurde von <a class="external text" title="Zuletzt bearbeitet am 2022-06-04" href="https://de.wikipedia.org/wiki/?title=Coffin-Manson-Modell&oldid=223425123">Wikipedia</a> herausgegeben. Der Text ist unter <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.de">Creative Commons Attribution-Share Alike 4.0</a> verfügbar, sofern nicht anders angegeben. Für die Mediendateien können zusätzliche Bedingungen gelten.
</div>
</div><!--/htdig_noindex--></div>
</div>
</main>
</div>
</div>
</div>
<script src="./_webp_/webpHandler.js"></script>
</body></html>