A Fluid-Solid-Magnetic Coupling Algorithm of Internal Crack Growth in the Weld of Oil and Gas Pipelines

<table class="fixed-width table-group" id="tab3"><tr><td><table class="table"><colgroup><col style="width:7.96em"/><col style="width:6.85em"/><col style="width:7.96em"/><col style="width:6.85em"/><col style="width:7.96em"/><col style="width:10.19em"/></colgroup><tr><td class="thead-hr" colspan="6"><hr/></td></tr><tr class="thead"><td class="align_left">Elastic Modulus<br/><i>E</i>/GPa</td><td class="align_center">Poisson ratio<br/><svg height="9.39034pt" id="M110" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 7.34167 9.39034" width="7.34167pt" 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="M538 96L524 119C492 88 454 63 446 63C439 63 434 70 440 101C463 223 491 341 518 448H508L433 422L401 276C355 192 240 56 188 56C163 56 154 89 163 133C184 233 207 338 235 443L230 448L152 424L58 17C40 -60 23 -143 23 -185C23 -241 42 -261 63 -261C92 -261 117 -241 125 -227L124 -221C109 -209 89 -165 89 -103C89 -55 96 -13 105 26H107C121 -3 134 -12 151 -12C172 -12 194 -5 221 16C279 61 330 124 384 194H386C381 159 377 141 368 105C343 3 363 -12 383 -12C416 -12 486 35 538 96Z" id="g113-234"></path></g></svg></td><td class="align_center">Yield strength <br/><svg height="12.5794pt" id="M111" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 40.6535 12.5794" width="40.6535pt" 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="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z" id="g113-240"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.132)"><path d="M357 391C357 416 325 451 270 451C241 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28V0H311V28C221 34 212 39 212 124V281L286 262C297 261 316 261 331 263C429 275 526 338 526 468C526 533 501 579 462 609C422 638 364 650 293 650H46ZM212 559C212 588 215 600 223 606C230 613 251 618 279 618C361 618 430 572 430 464C430 337 350 302 285 302C252 302 225 309 212 314V559Z" id="g121-78"></path></g><g transform="matrix(.013,0,0,-0.013,34.714,0)"><path d="M433 39L423 65C413 59 399 54 387 54C370 54 352 69 352 114V299C352 352 342 392 307 422C285 440 255 449 225 449C168 437 102 399 75 379C56 365 44 353 44 339C44 315 69 296 87 296C101 296 111 303 116 319C124 349 133 371 145 385C156 397 171 404 190 404C241 404 275 364 275 291V274C253 256 180 229 120 209C65 190 39 159 39 110C39 47 88 -12 159 -12C189 -12 237 25 277 52C282 35 288 21 301 8C312 -3 333 -12 348 -12L433 39ZM275 84C256 65 221 48 195 48C164 48 124 73 124 124C124 161 146 180 185 198C206 208 254 229 275 240V84Z" id="g121-95"></path></g></svg></td><td class="align_center">Tangent modulus <i>E</i><sub><i>1</i></sub><svg 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475 389 446 366C425 418 382 449 334 449C303 449 279 437 253 421C222 403 201 385 180 371V452C135 432 85 419 41 411V388C99 379 102 374 102 310V103C102 38 93 32 27 26V0H238V26C189 32 180 38 180 103V338C210 363 250 390 289 390C351 390 377 348 377 275V103C377 37 368 32 306 26V0H520V26C465 32 456 38 456 101V296C456 314 455 326 453 338C491 369 529 390 565 390C628 390 653 345 653 274V107C653 36 642 32 583 26V0H797Z" id="g121-107"></path></g></svg></td><td class="align_center">Critical strain energy release rate of plane strain model <svg height="12.5794pt" id="M114" style="vertical-align:-3.29107pt" version="1.1" viewbox="-0.0498162 -9.28833 70.2924 12.5794" width="70.2924pt" 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="M673 297H417L411 270C517 261 522 258 506 183L487 92C476 38 428 19 360 19C207 19 123 132 123 287C123 472 243 631 441 631C557 631 617 583 617 469L647 472C650 545 655 604 658 632C625 643 554 666 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colspan="6"><hr/></td></tr><tr><td class="align_left">212</td><td class="align_center">0.288</td><td class="align_center">235</td><td class="align_center">6000</td><td class="align_center">120.7</td><td class="align_center">63. 02</td></tr><tr class="table-tr"><td colspan="6"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Mechanical properties of Q235 steel.</div>

Mathematical Problems in Engineering

tab3

Table 3

Table 3: A Fluid-Solid-Magnetic Coupling Algorithm of Internal Crack Growth in the Weld of Oil and Gas Pipelines 