Thermomechanical-Phase Transformation Simulation of High-Strength Steel in Hot Stamping

<table class="figure-group"><tr class="fig-image" id="a"><td><object data="https://static.hindawi.com/articles/mpe/volume-2015/982785/figures/982785.fig.002a.svgz" name="982785.fig.002a" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(a) </b>Martensite transformation temperature</td></tr><tr class="fig-image" id="b"><td><object data="https://static.hindawi.com/articles/mpe/volume-2015/982785/figures/982785.fig.002b.svgz" name="982785.fig.002b" type="image/svg+xml"></object></td></tr><tr class="fig-caption"><td><b>(b) </b>Material parameter <svg height="9.49473pt" id="M29" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.70228 9.49473" width="6.70228pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M482 498C482 606 448 710 328 710C138 710 24 416 24 218C24 99 58 -12 184 -12C373 -12 482 294 482 498ZM395 521C395 483 391 449 383 395H128C158 537 226 671 312 671C388 671 395 566 395 521ZM375 342C348 190 284 25 192 25C128 25 109 116 109 199C109 243 112 292 121 342H375Z" id="g50-230"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="506" vert-adv-y="506"></glyph.data></g></svg></td></tr></table>

<div>Relationships of the martensite start temperature <svg height="11.7574pt" id="M26" style="vertical-align:-3.16066pt" version="1.1" viewbox="-0.0498162 -8.59674 16.4742 11.7574" width="16.4742pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M1006 650H829L492 147L357 650H174L166 618C270 609 275 601 247 502L194 315C158 189 136 127 122 96C104 56 80 37 18 32L12 0H256L263 32C181 40 176 51 183 98C188 132 197 179 226 281L299 541H301L433 6H458L809 551H811L753 141C739 41 734 39 650 32L642 0H917L923 32C836 39 827 41 839 142L887 535C896 610 901 612 997 618L1006 650Z" id="g50-78"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="1030" vert-adv-y="1030"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,12.35,3.001)"><path d="M357 391C357 416 325 451 270 451C241 451 179 431 146 400C109 365 97 334 97 307C97 248 143 213 196 180C250 146 261 123 261 101C261 75 237 40 190 40C153 40 110 72 86 109C81 116 68 119 55 112C37 102 24 87 24 66C24 30 85 -12 137 -12C229 -12 331 62 331 140C331 189 304 218 236 260C197 284 164 309 164 346C164 381 194 400 220 400C259 400 282 380 304 350C310 342 321 339 330 344C347 353 357 372 357 391Z" id="g50-116"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="381" vert-adv-y="381"></glyph.data></g></svg> and material parameter <svg height="9.49473pt" id="M27" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.28833 6.70228 9.49473" width="6.70228pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M482 498C482 606 448 710 328 710C138 710 24 416 24 218C24 99 58 -12 184 -12C373 -12 482 294 482 498ZM395 521C395 483 391 449 383 395H128C158 537 226 671 312 671C388 671 395 566 395 521ZM375 342C348 190 284 25 192 25C128 25 109 116 109 199C109 243 112 292 121 342H375Z" id="g50-230"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="506" vert-adv-y="506"></glyph.data></g></svg> with the variation to equivalent stress <svg height="9.87318pt" id="M28" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -9.66678 7.61571 9.87318" width="7.61571pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><rect height="0.69159" width="7.51608" x="0" y="-8.92538"></rect><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M558 454L532 470C512 451 497 442 465 442C421 442 376 450 318 450C146 450 24 313 24 164C24 46 91 -12 183 -12C317 -12 439 105 439 247C439 306 428 346 382 385L383 389C414 384 450 379 485 379C517 379 539 412 558 454ZM357 273C357 191 313 28 205 28C149 28 111 79 111 160C111 266 175 396 280 396C298 396 328 386 341 357C353 331 357 315 357 273Z" id="g50-240"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="576" vert-adv-y="576"></glyph.data></g></svg>.</div>

Mathematical Problems in Engineering

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Figure 2

Figure 2: Thermomechanical-Phase Transformation Simulation of High-Strength Steel in Hot Stamping 