Page 263 - Shigley's Mechanical Engineering Design

bud29281_ch05_212-264.qxd 11/27/2009 6:46 pm Page 238 pinnacle s-171:Desktop Folder:Temp Work:Don't Delete (Jobs):MHDQ196/Budynas:

238 Mechanical Engineering Design
Figure 5–20 Modified Mohr B

–S
A plot of experimental data ut
points obtained from tests on 30 S ut
cast iron. Shown also are the
graphs of three failure theories
of possible usefulness for A
–120 – S uc –90 –60 –30 30 S
brittle materials. Note points A, ut
B, C, and D. To avoid
congestion in the first quadrant, ASTM No. 30 C.I.
= 31 kpsi, S = 109 kpsi –30 –S
points have been plotted for S ut uc ut B
σ A >σ B as well as for the A = –1
Coulomb-Mohr B
opposite sense. (Source of
–60 A
data: Charles F. Walton (ed.),
Iron Castings Handbook,
Iron Founders’Society, 1971, Maximum-normal-stress
pp. 215, 216, Cleveland, Ohio.) –90

B –S
uc
–120
A
C
D –150

5–10 Failure of Brittle Materials Summary
We have identified failure or strength of brittle materials that conform to the usual
meaning of the word brittle, relating to those materials whose true strain at fracture
is 0.05 or less. We also have to be aware of normally ductile materials that for some
reason may develop a brittle fracture or crack if used below the transition tempera-
ture. Figure 5–20 shows data for a nominal grade 30 cast iron taken under biaxial
stress conditions, with several brittle failure hypotheses shown, superposed. We note
the following:
• In the first quadrant the data appear on both sides and along the failure curves of
maximum-normal-stress, Coulomb-Mohr, and modified Mohr. All failure curves are
the same, and data fit well.
• In the fourth quadrant the modified Mohr theory represents the data best, whereas the
maximum-normal-stress theory does not.
• In the third quadrant the points A, B, C, and D are too few to make any suggestion
concerning a fracture locus.

5–11 Selection of Failure Criteria

For ductile behavior the preferred criterion is the distortion-energy theory, although
some designers also apply the maximum-shear-stress theory because of its simplicity
and conservative nature. In the rare case when S yt = S yc , the ductile Coulomb-Mohr
method is employed.
For brittle behavior, the original Mohr hypothesis, constructed with tensile, compres-
sion, and torsion tests, with a curved failure locus is the best hypothesis we have. However,
the difficulty of applying it without a computer leads engineers to choose modifications,