Fatigue crack-growth rate in ferrite martensite dual-phase steel

<p style="border: 0px; font-size: 13px; margin: 0px 0px 9px; padding: 0px; vertical-align: baseline; word-spacing: -0.15ex; text-align: justify; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; line-height: 20px">An empirical study is made on the fatigue crack growth rate in ferrite-martensite dual-phase (FMDP) steel. Particular attention is given to the effect of ferrite content in the range of 24.2% to 41.5% where good fatigue resistance was found at 33.8%. Variations in ferrite content did not affect the crack growth rate <span style="border: 0px; margin: 0px; padding: 0px; vertical-align: baseline; position: relative" class="mathmlsrc"><a style="color: #0156aa; border: 0px; margin: 0px; padding: 0px; vertical-align: baseline" title="View the MathML source" class="mathImg"><img style="border: 0px; margin: 0px; padding: 0px; vertical-align: bottom; display: inline; max-width: 600px" class="imgLazyJSB" src="http://ars.els-cdn.com/content/image/1-s2.0-016784429190028I-si1.gif" border="0" alt="View the MathML source" title="View the MathML source" width="53" height="18" /></a></span>when plotted against the effective stress intensity factor range <span style="border: 0px; margin: 0px; padding: 0px; vertical-align: baseline; position: relative" class="mathmlsrc"><a style="color: #0156aa; border: 0px; margin: 0px; padding: 0px; vertical-align: baseline" title="View the MathML source" class="mathImg"><img style="border: 0px; margin: 0px; padding: 0px; vertical-align: bottom; display: inline; max-width: 600px" class="imgLazyJSB" src="http://ars.els-cdn.com/content/image/1-s2.0-016784429190028I-si2.gif" border="0" alt="View the MathML source" title="View the MathML source" width="39" height="14" /></a></span> which was assumed to follow a linear relation with the crack tip stress intensity factor range <span style="border: 0px; margin: 0px; padding: 0px; vertical-align: baseline; position: relative" class="mathmlsrc"><span style="border: 0px; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline; font-family: STIXGeneral, STIXGeneral-Bold, STIXGeneral-BoldItalic, STIXGeneral-Italic, STIXIntegralsDisplay, STIXIntegralsDisplay-Bold, STIXIntegralsSmall, STIXIntegralsSmall-Bold, STIXIntegralsUp, STIXIntegralsUp-Bold, STIXIntegralsUpDisplay, STIXIntegralsUpDisplay-Bold, STIXIntegralsUpSmall, STIXIntegralsUpSmall-Bold, STIXNonUnicode, STIXNonUnicode-Bold, STIXNonUnicode-BoldItalic, STIXNonUnicode-Italic, STIXSize1Symbols, STIXSize1Symbols-Bold, STIXSize2Symbols, STIXSize2Symbols-Bold, STIXSize3Symbols, STIXSize3Symbols-Bold, STIXSize4Symbols, STIXSize4Symbols-Bold, STIXSize5Symbols, STIXVariants, STIXVariants-Bold; cursor: pointer; letter-spacing: 0.15em" class="formulatext stixSupport mathImg">ΔK</span></span>. A high <span style="border: 0px; margin: 0px; padding: 0px; vertical-align: baseline; position: relative" class="mathmlsrc"><a style="color: #0156aa; border: 0px; margin: 0px; padding: 0px; vertical-align: baseline" title="View the MathML source" class="mathImg"><img style="border: 0px; margin: 0px; padding: 0px; vertical-align: bottom; display: inline; max-width: 600px" class="imgLazyJSB" src="http://ars.els-cdn.com/content/image/1-s2.0-016784429190028I-si4.gif" border="0" alt="View the MathML source" title="View the MathML source" width="39" height="14" /></a></span> corresponds to uniformly distributed small size ferrite and martensite. No other appreciable correlation could be ralated to the microstructure morphology of the FMDP steel. The closure stress intensity factor <span style="border: 0px; margin: 0px; padding: 0px; vertical-align: baseline; position: relative" class="mathmlsrc"><a style="color: #0156aa; border: 0px; margin: 0px; padding: 0px; vertical-align: baseline" title="View the MathML source" class="mathImg"><img style="border: 0px; margin: 0px; padding: 0px; vertical-align: bottom; display: inline; max-width: 600px" class="imgLazyJSB" src="http://ars.els-cdn.com/content/image/1-s2.0-016784429190028I-si5.gif" border="0" alt="View the MathML source" title="View the MathML source" width="21" height="13" /></a></span>, however, is affected by the ferrite content with <span style="border: 0px; margin: 0px; padding: 0px; vertical-align: baseline; position: relative" class="mathmlsrc"><a style="color: #0156aa; border: 0px; margin: 0px; padding: 0px; vertical-align: baseline" title="View the MathML source" class="mathImg"><img style="border: 0px; margin: 0px; padding: 0px; vertical-align: bottom; display: inline; max-width: 600px" class="imgLazyJSB" src="http://ars.els-cdn.com/content/image/1-s2.0-016784429190028I-si6.gif" border="0" alt="View the MathML source" title="View the MathML source" width="64" height="17" /></a></span> reaching a maximum value of 0.7. In general, crack growth followed the interphase between the martensite and ferrite.</p><p style="border: 0px; font-size: 13px; margin: 0px 0px 9px; padding: 0px; vertical-align: baseline; word-spacing: -0.15ex; text-align: justify; color: #2e2e2e; font-family: 'Arial Unicode MS', 'Arial Unicode', Arial, 'URW Gothic L', Helvetica, Tahoma, sans-serif; line-height: 20px">Dividing the fatigue crack growth process into Stage I and II where the former would be highly sensitive to changes in <span style="border: 0px; margin: 0px; padding: 0px; vertical-align: baseline; position: relative" class="mathmlsrc"><span style="border: 0px; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline; font-family: STIXGeneral, STIXGeneral-Bold, STIXGeneral-BoldItalic, STIXGeneral-Italic, STIXIntegralsDisplay, STIXIntegralsDisplay-Bold, STIXIntegralsSmall, STIXIntegralsSmall-Bold, STIXIntegralsUp, STIXIntegralsUp-Bold, STIXIntegralsUpDisplay, STIXIntegralsUpDisplay-Bold, STIXIntegralsUpSmall, STIXIntegralsUpSmall-Bold, STIXNonUnicode, STIXNonUnicode-Bold, STIXNonUnicode-BoldItalic, STIXNonUnicode-Italic, STIXSize1Symbols, STIXSize1Symbols-Bold, STIXSize2Symbols, STIXSize2Symbols-Bold, STIXSize3Symbols, STIXSize3Symbols-Bold, STIXSize4Symbols, STIXSize4Symbols-Bold, STIXSize5Symbols, STIXVariants, STIXVariants-Bold; cursor: pointer; letter-spacing: 0.15em" class="formulatext stixSupport mathImg">ΔK</span></span> and the latter would increase with <span style="border: 0px; margin: 0px; padding: 0px; vertical-align: baseline; position: relative" class="mathmlsrc"><span style="border: 0px; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline; font-family: STIXGeneral, STIXGeneral-Bold, STIXGeneral-BoldItalic, STIXGeneral-Italic, STIXIntegralsDisplay, STIXIntegralsDisplay-Bold, STIXIntegralsSmall, STIXIntegralsSmall-Bold, STIXIntegralsUp, STIXIntegralsUp-Bold, STIXIntegralsUpDisplay, STIXIntegralsUpDisplay-Bold, STIXIntegralsUpSmall, STIXIntegralsUpSmall-Bold, STIXNonUnicode, STIXNonUnicode-Bold, STIXNonUnicode-BoldItalic, STIXNonUnicode-Italic, STIXSize1Symbols, STIXSize1Symbols-Bold, STIXSize2Symbols, STIXSize2Symbols-Bold, STIXSize3Symbols, STIXSize3Symbols-Bold, STIXSize4Symbols, STIXSize4Symbols-Bold, STIXSize5Symbols, STIXVariants, STIXVariants-Bold; cursor: pointer; letter-spacing: 0.15em" class="formulatext stixSupport mathImg">ΔK</span></span> depending on the <span style="border: 0px; margin: 0px; padding: 0px; vertical-align: baseline; position: relative" class="mathmlsrc"><a style="color: #0156aa; border: 0px; margin: 0px; padding: 0px; vertical-align: baseline" title="View the MathML source" class="mathImg"><img style="border: 0px; margin: 0px; padding: 0px; vertical-align: bottom; display: inline; max-width: 600px" class="imgLazyJSB" src="http://ars.els-cdn.com/content/image/1-s2.0-016784429190028I-si9.gif" border="0" alt="View the MathML source" title="View the MathML source" width="115" height="18" /></a></span> ratio. The same data when correlated with the strain energy density factor range <span style="border: 0px; margin: 0px; padding: 0px; vertical-align: baseline; position: relative" class="mathmlsrc"><span style="border: 0px; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline; font-family: STIXGeneral, STIXGeneral-Bold, STIXGeneral-BoldItalic, STIXGeneral-Italic, STIXIntegralsDisplay, STIXIntegralsDisplay-Bold, STIXIntegralsSmall, STIXIntegralsSmall-Bold, STIXIntegralsUp, STIXIntegralsUp-Bold, STIXIntegralsUpDisplay, STIXIntegralsUpDisplay-Bold, STIXIntegralsUpSmall, STIXIntegralsUpSmall-Bold, STIXNonUnicode, STIXNonUnicode-Bold, STIXNonUnicode-BoldItalic, STIXNonUnicode-Italic, STIXSize1Symbols, STIXSize1Symbols-Bold, STIXSize2Symbols, STIXSize2Symbols-Bold, STIXSize3Symbols, STIXSize3Symbols-Bold, STIXSize4Symbols, STIXSize4Symbols-Bold, STIXSize5Symbols, STIXVariants, STIXVariants-Bold; cursor: pointer; letter-spacing: 0.15em" class="formulatext stixSupport mathImg">ΔS</span></span> showed negligible dependence on mean stress or <span style="border: 0px; margin: 0px; padding: 0px; vertical-align: baseline; position: relative" class="mathmlsrc"><span style="border: 0px; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline; font-family: STIXGeneral, STIXGeneral-Bold, STIXGeneral-BoldItalic, STIXGeneral-Italic, STIXIntegralsDisplay, STIXIntegralsDisplay-Bold, STIXIntegralsSmall, STIXIntegralsSmall-Bold, STIXIntegralsUp, STIXIntegralsUp-Bold, STIXIntegralsUpDisplay, STIXIntegralsUpDisplay-Bold, STIXIntegralsUpSmall, STIXIntegralsUpSmall-Bold, STIXNonUnicode, STIXNonUnicode-Bold, STIXNonUnicode-BoldItalic, STIXNonUnicode-Italic, STIXSize1Symbols, STIXSize1Symbols-Bold, STIXSize2Symbols, STIXSize2Symbols-Bold, STIXSize3Symbols, STIXSize3Symbols-Bold, STIXSize4Symbols, STIXSize4Symbols-Bold, STIXSize5Symbols, STIXVariants, STIXVariants-Bold; cursor: pointer; letter-spacing: 0.15em" class="formulatext stixSupport mathImg">R</span></span> ratio for Stage I crack growth. A parameter α involving the ratio of ultimate stress to yield stress, percent reduction of area and <span style="border: 0px; margin: 0px; padding: 0px; vertical-align: baseline; position: relative" class="mathmlsrc"><span style="border: 0px; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline; font-family: STIXGeneral, STIXGeneral-Bold, STIXGeneral-BoldItalic, STIXGeneral-Italic, STIXIntegralsDisplay, STIXIntegralsDisplay-Bold, STIXIntegralsSmall, STIXIntegralsSmall-Bold, STIXIntegralsUp, STIXIntegralsUp-Bold, STIXIntegralsUpDisplay, STIXIntegralsUpDisplay-Bold, STIXIntegralsUpSmall, STIXIntegralsUpSmall-Bold, STIXNonUnicode, STIXNonUnicode-Bold, STIXNonUnicode-BoldItalic, STIXNonUnicode-Italic, STIXSize1Symbols, STIXSize1Symbols-Bold, STIXSize2Symbols, STIXSize2Symbols-Bold, STIXSize3Symbols, STIXSize3Symbols-Bold, STIXSize4Symbols, STIXSize4Symbols-Bold, STIXSize5Symbols, STIXVariants, STIXVariants-Bold; cursor: pointer; letter-spacing: 0.15em" class="formulatext stixSupport mathImg">R</span></span> is introduced for Stage II crack growth so that the <span style="border: 0px; margin: 0px; padding: 0px; vertical-align: baseline; position: relative" class="mathmlsrc"><a style="color: #0156aa; border: 0px; margin: 0px; padding: 0px; vertical-align: baseline" title="View the MathML source" class="mathImg"><img style="border: 0px; margin: 0px; padding: 0px; vertical-align: bottom; display: inline; max-width: 600px" class="imgLazyJSB" src="http://ars.els-cdn.com/content/image/1-s2.0-016784429190028I-si13.gif" border="0" alt="View the MathML source" title="View the MathML source" width="53" height="18" /></a></span> data for different <span style="border: 0px; margin: 0px; padding: 0px; vertical-align: baseline; position: relative" class="mathmlsrc"><span style="border: 0px; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline; font-family: STIXGeneral, STIXGeneral-Bold, STIXGeneral-BoldItalic, STIXGeneral-Italic, STIXIntegralsDisplay, STIXIntegralsDisplay-Bold, STIXIntegralsSmall, STIXIntegralsSmall-Bold, STIXIntegralsUp, STIXIntegralsUp-Bold, STIXIntegralsUpDisplay, STIXIntegralsUpDisplay-Bold, STIXIntegralsUpSmall, STIXIntegralsUpSmall-Bold, STIXNonUnicode, STIXNonUnicode-Bold, STIXNonUnicode-BoldItalic, STIXNonUnicode-Italic, STIXSize1Symbols, STIXSize1Symbols-Bold, STIXSize2Symbols, STIXSize2Symbols-Bold, STIXSize3Symbols, STIXSize3Symbols-Bold, STIXSize4Symbols, STIXSize4Symbols-Bold, STIXSize5Symbols, STIXVariants, STIXVariants-Bold; cursor: pointer; letter-spacing: 0.15em" class="formulatext stixSupport mathImg">R</span></span> would collapse onto a single curve with a narrow scatter band when plotted against <span style="border: 0px; margin: 0px; padding: 0px; vertical-align: baseline; position: relative" class="mathmlsrc"><span style="border: 0px; font-size: 14px; margin: 0px; padding: 0px; vertical-align: baseline; font-family: STIXGeneral, STIXGeneral-Bold, STIXGeneral-BoldItalic, STIXGeneral-Italic, STIXIntegralsDisplay, STIXIntegralsDisplay-Bold, STIXIntegralsSmall, STIXIntegralsSmall-Bold, STIXIntegralsUp, STIXIntegralsUp-Bold, STIXIntegralsUpDisplay, STIXIntegralsUpDisplay-Bold, STIXIntegralsUpSmall, STIXIntegralsUpSmall-Bold, STIXNonUnicode, STIXNonUnicode-Bold, STIXNonUnicode-BoldItalic, STIXNonUnicode-Italic, STIXSize1Symbols, STIXSize1Symbols-Bold, STIXSize2Symbols, STIXSize2Symbols-Bold, STIXSize3Symbols, STIXSize3Symbols-Bold, STIXSize4Symbols, STIXSize4Symbols-Bold, STIXSize5Symbols, STIXVariants, STIXVariants-Bold; cursor: pointer; letter-spacing: 0.15em" class="formulatext stixSupport mathImg">αΔS</span></span>.</p>