Analysis of Interaction of Multiple Cracks Based on Tip Stress Field Using Extended Finite Element Method

<div>Shaded plots of the von Mises stress <svg height="9.41642pt" id="M259" style="vertical-align:-3.27283pt" version="1.1" viewbox="-0.0498162 -6.14359 19.1204 9.41642" width="19.1204pt" 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"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.76,3.132)"><path d="M478 437H300V411C357 404 363 393 347 345C325 280 293 190 258 107C229 178 188 284 163 354C147 397 149 405 203 411V437H-2V411C52 403 59 396 82 339C130 222 176 109 220 -11H248C304 138 356 261 390 336C417 395 425 404 478 411V437Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.001,3.132)"><path d="M797 0V26C739 32 732 36 732 103V296C732 394 682 449 605 449C576 449 550 437 529 423C504 407 475 389 446 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"></path></g></svg> for the multiple-crack example: (a) 5 parallel edge cracks (case 1); (b) 5 randomly located cracks (case 2) (lengths in m).</div>

Journal of Applied Mathematics

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Figure 12

Figure 12: Analysis of Interaction of Multiple Cracks Based on Tip Stress Field Using Extended Finite Element Method 