Indentation Curves in Viscoplastic Alloys: Mathematical Model, Fitting Procedures, and Application to the Room-Temperature Creep of an Al-Sn Alloy

<div>Selected tensile curves at different strain rates showing the inverse strain rate sensitivity and PLC effect (serrated flow). The inset presents a ln-ln plot of <svg height="8.95973pt" id="M145" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -8.75334 5.44961 8.95973" width="5.44961pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,5.441,-.222)"><path d="M-161 571C-161 600 -183 623 -212 623C-238 623 -262 600 -262 571C-262 544 -238 520 -212 520C-183 520 -161 544 -161 571Z" id="g117-11"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="0" vert-adv-y="0"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M387 375C387 402 357 448 257 448C172 448 82 404 82 326C82 289 108 255 156 241V239C85 223 23 181 23 116C23 39 89 -12 182 -12C265 -12 336 31 378 91L361 114C320 73 269 47 216 47C157 47 115 82 115 137C115 191 160 219 218 219C243 219 262 218 272 217L304 259L302 266C295 265 281 264 255 264C195 264 163 294 163 335C163 377 200 416 249 416C293 416 321 389 329 342C331 332 335 329 341 329C355 329 387 352 387 375Z" id="g113-247"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="410" vert-adv-y="410"></glyph.data></g></svg> versus <svg height="12.5794pt" id="M146" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 11.5443 12.5794" width="11.5443pt" 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="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z" id="g113-108"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="503" vert-adv-y="503"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.474,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg> in formula (<a href="https://static-preview.hindawi.com/articles/amse/volume-2016/6909854/figures/#EEq1">1</a>); the slope of the plot corresponds to the exponent <svg height="6.34998pt" id="M147" style="vertical-align:-0.2063899pt" version="1.1" viewbox="-0.0498162 -6.14359 6.02377 6.34998" width="6.02377pt" 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="M213 67C239 136 257 225 255 300C253 353 242 447 164 447C112 447 54 389 41 319L67 309C90 362 117 377 134 377C184 377 189 277 190 239C193 153 164 43 146 -12H176C278 73 450 253 450 390C450 439 410 463 396 463C384 463 380 459 382 449C385 440 389 415 389 402C389 284 312 146 216 67H213Z" id="g185-47"></path><glyph.data ascent="989" descent="-303" horiz-adv-x="454" vert-adv-y="454"></glyph.data></g></svg> in formula (<a href="https://static-preview.hindawi.com/articles/amse/volume-2016/6909854/figures/#EEq18">18</a>); error bars represent the standard deviation on <svg height="12.5794pt" id="M148" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 24.1625 12.5794" width="24.1625pt" 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="M238 0V26C174 32 166 38 166 104V712C132 700 70 683 18 677V653C81 647 87 645 87 577V104C87 38 78 32 15 26V0H238Z" id="g121-106"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="253" vert-adv-y="253"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,3.289,0)"><path d="M524 0V26C466 32 460 36 460 104V297C460 393 411 449 331 449C302 449 276 437 248 419C223 402 201 387 181 372V451C137 432 90 420 42 411V388C96 378 102 374 102 310V104C102 38 97 33 29 26V0H246V26C187 32 181 36 181 104V339C211 365 250 390 290 390C357 390 381 345 381 276V109C381 40 374 32 315 26V0H524Z" id="g121-108"></path><glyph.data ascent="989" descent="-360" horiz-adv-x="547" vert-adv-y="547"></glyph.data></g><g transform="matrix(.013,0,0,-0.013,12.618,0)"><path d="M480 416C480 431 465 448 438 448C388 448 312 383 252 330C217 299 188 273 155 237H153L257 680C262 700 263 712 253 712C240 712 183 684 97 674L92 648L126 647C166 646 172 645 163 606L23 -6L29 -12C51 -5 77 2 107 8C115 62 130 128 142 180C153 193 179 220 204 241C231 170 259 106 288 54C317 0 336 -12 358 -12C381 -12 423 2 477 80L460 100C434 74 408 54 398 54C385 54 374 65 351 107C326 154 282 241 263 299C296 332 351 377 403 377C424 377 436 372 445 368C449 366 456 368 462 375C472 386 480 402 480 416Z" id="g113-108"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="503" vert-adv-y="503"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,19.092,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z" id="g50-49"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="487" vert-adv-y="487"></glyph.data></g></svg>.</div>

Advances in Materials Science and Engineering

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Figure 3

Figure 3: Indentation Curves in Viscoplastic Alloys: Mathematical Model, Fitting Procedures, and Application to the Room-Temperature Creep of an Al-Sn Alloy 

Figure 3 | Indentation Curves in Viscoplastic Alloys: Mathematical Model, Fitting Procedures, and Application to the Room-Temperature Creep of an Al-Sn Alloy 