Page 187 - Mechanical Behavior of Materials

188 Chapter 4 Mechanical Testing: Tension Test and Other Basic Tests

200
Fracture
160
P , Force, N 120

80

40

0 0.02 0.04 0.06 0.08 0.10
v, Displacement, mm

Figure P4.37

4.38 Bend strengths from Eq. 4.34 are given below for 100 three-point bending tests on alumina
(Al 2 O 3 ) ceramic. The specimens were approximately 3.12 mm square, and the distance
between supports was 40.0 mm. These data are from tests conducted by students in a
laboratory course during a three-year period from 2006 to 2009.
(a) Using equations from Appendix B, calculate the sample mean, standard deviation, and
coefficient of variation. Also plot a histogram analogous to Fig. B.1 of numbers of
samples versus the bend strength.
(b) Write a paragraph concisely discussing the statistical variation in these data. Does the
variation seem relatively small or relatively large? What do you think are the major
causes of the variation?

Table P4.38

σ fb , Bend Strength, MPa
443 358 328 398 438 457 345 475 445 387
437 446 389 373 459 422 383 409 442 521
477 437 454 422 472 385 368 391 449 527
433 324 302 406 335 415 364 398 445 473
416 386 405 397 410 424 417 471 442 348
524 437 392 471 425 428 429 463 454 379
360 477 426 458 452 362 417 426 458 387
419 329 451 376 441 355 447 431 369 359
464 350 426 426 435 429 442 505 443 403
333 431 404 382 426 457 425 449 471 404

Section 4.10
4.39 What characteristics are needed for the steel cable that supports and moves a ski lift? What
materials tests would be important in judging the suitability of a given steel for this use?