Transient Analysis of a Functionally Graded Ceramic/Metal Layer considering Lord-Shulman Theory

<table class="fixed-width table-group" id="tab4"><tr><td><table class="table"><colgroup><col style="width:9.23em"/><col style="width:3.40em"/><col style="width:5.52em"/><col style="width:4.27em"/><col style="width:4.42em"/><col style="width:3.74em"/><col style="width:2.84em"/></colgroup><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Wave speeds</td><td class="align_center" colspan="2">ZrO<sub>2</sub>/Ti-6Al-4V</td><td class="align_center" colspan="2">Si<sub>3</sub>NO<sub>4</sub>/SUS304</td><td class="align_center" colspan="2">Al<sub>2</sub>O<sub>3</sub>/Ni</td></tr><tr class="thead"><td class="align_center">ZrO<sub>2</sub></td><td class="align_center">Ti-6Al-4V</td><td class="align_center">Si<sub>3</sub>NO<sub>4</sub></td><td class="align_center">SUS304</td><td class="align_center">Al<sub>2</sub>O<sub>3</sub></td><td class="align_center">Ni</td></tr><tr><td class="thead-hr" colspan="7"><hr/></td></tr><tr><td class="align_left"><svg height="14.2627pt" id="M223" style="vertical-align:-8.30179pt" version="1.1" viewbox="-0.0498162 -5.96091 11.8692 14.2627" width="11.8692pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.142,0)"><path d="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z" id="g113-100"></path></g><g transform="matrix(.0091,0,0,-0.0091,0,6.333)"><path d="M569 322L535 336C513 285 468 245 413 245C385 245 355 267 330 286C290 315 247 343 198 343C123 343 73 274 42 202L76 188C98 239 143 279 198 279C226 279 256 257 281 238C321 209 364 181 413 181C488 181 538 250 569 322Z" id="g54-131"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.581,8.252)"><path d="M615 650H141L132 618C223 612 227 607 212 526L136 123C122 42 112 38 27 32L18 0H522C539 33 580 135 592 166L558 179C536 139 512 100 486 75C454 48 420 41 345 41C287 41 252 42 237 55C221 68 220 100 231 158L261 316H357C455 316 455 309 455 235H489L529 437H494C468 366 460 360 369 360H269L305 565C315 609 316 611 357 611H450C525 611 535 599 548 578C559 556 561 526 560 482L595 486L615 650Z" id="g50-70"></path></g></svg> (elastic)</td><td class="align_center">1.11</td><td class="align_center">1.00</td><td class="align_center">2.11</td><td class="align_center">1.00</td><td class="align_center">1.98</td><td class="align_center">1.00</td></tr><tr><td class="align_left"><svg height="21.4082pt" id="M224" style="vertical-align:-8.895499pt" version="1.1" viewbox="-0.0498162 -12.5127 51.3853 21.4082" width="51.3853pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,.142,0)"><path d="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 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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></g><g transform="matrix(.013,0,0,-0.013,33.426,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z" id="g113-42"></path></g><g transform="matrix(.0091,0,0,-0.0091,37.972,-5.996)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z" id="g50-50"></path></g><g transform="matrix(.0091,0,0,-0.0091,42.404,-5.996)"><path d="M381 704H317L48 -163H112L381 704Z" id="g50-48"></path></g><g transform="matrix(.0091,0,0,-0.0091,46.312,-5.996)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z" id="g50-51"></path></g></svg> (thermal)</td><td class="align_center">0.40</td><td class="align_center">1.25</td><td class="align_center">0.99</td><td class="align_center">1.25</td><td class="align_center">0.52</td><td class="align_center">1.25</td></tr><tr class="table-tr"><td colspan="7"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Normalized speeds of the elastic and the thermal wave in the different materials considered.</div>

Mathematical Problems in Engineering

tab4

Table 4

Table 4: Transient Analysis of a Functionally Graded Ceramic/Metal Layer considering Lord-Shulman Theory 