A Dislocation-Based Theory for the Deformation Hardening Behavior of DP Steels: Impact of Martensite Content and Ferrite Grain Size

<table>Friction stress, <svg height="10.875" id="M228" style="vertical-align:-3.25793pt" version="1.1" viewbox="0 0 18.799999 10.875" width="18.799999" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.875)">
<g transform="translate(72,-63.3)">
<text transform="matrix(1,0,0,-1,-71.95,66.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜎</tspan>
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<text transform="matrix(1,0,0,-1,-64.61,63.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑖</tspan>
<tspan style="font-size: 8.75px; " x="2.7218721" y="0">0</tspan>
</text>
</g>
</g>
</svg>, the work hardening component, <svg height="10.825" id="M229" style="vertical-align:-3.22282pt" version="1.1" viewbox="0 0 26.8125 10.825" width="26.8125" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.825)">
<g transform="translate(72,-63.34)">
<text transform="matrix(1,0,0,-1,-71.95,66.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜎</tspan>
</text>
<text transform="matrix(1,0,0,-1,-64.61,63.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">d</tspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">e</tspan>
<tspan style="font-size: 8.75px; " x="8.2618876" y="0">f</tspan>
</text>
</g>
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</svg> (8%) and flow stress at 8% plastic strain, <svg height="6.9875002" id="M230" style="vertical-align:-0.13794pt" version="1.1" viewbox="0 0 9.3000002 6.9875002" width="9.3000002" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,6.9875)">
<g transform="translate(72,-66.41)">
<text transform="matrix(1,0,0,-1,-71.95,66.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜎</tspan>
</text>
</g>
</g>
</svg>(8%) versus martensite volume fraction, <svg height="14.5625" id="M231" style="vertical-align:-3.20526pt" version="1.1" viewbox="0 0 17.1875 14.5625" width="17.1875" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.5625)">
<g transform="translate(72,-60.35)">
<text transform="matrix(1,0,0,-1,-71.95,63.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑓</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.01,60.47)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝑚</tspan>
</text>
</g>
</g>
</svg>.</table>

Journal of Metallurgy

fig15

Figure 15

Figure 15: A Dislocation-Based Theory for the Deformation Hardening Behavior of DP Steels: Impact of Martensite Content and Ferrite Grain Size 