Page 340 - Shigley's Mechanical Engineering Design

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Fatigue Failure Resulting from Variable Loading 315
• First-quadrant fatigue failure locus is concave-upward (Smith-Dolan), for example,
and as flat as Goodman. Brittle materials are more sensitive to midrange stress, being
lowered, but compressive midrange stresses are beneficial.
• Not enough work has been done on brittle fatigue to discover insightful generalities,
so we stay in the first and a bit of the second quadrant.
The most likely domain of designer use is in the range from −S ut ≤ σ m ≤ S ut . The
locus in the first quadrant is Goodman, Smith-Dolan, or something in between. The por-
tion of the second quadrant that is used is represented by a straight line between the
points −S ut , S ut and 0, S e , which has the equation

S e
S a = S e + − 1 S m −S ut ≤ S m ≤ 0 (for cast iron) (6–53)
S ut
Table A–24 gives properties of gray cast iron. The endurance limit stated is really
k a k b S and only corrections k c , k d , k e , and k f need be made. The average k c for axial

e
and torsional loading is 0.9.

3
EXAMPLE 6–13 A grade 30 gray cast iron is subjected to a load F applied to a 1 by -in cross-section
8
1
link with a -in-diameter hole drilled in the center as depicted in Fig. 6–31a. The sur-
4
faces are machined. In the neighborhood of the hole, what is the factor of safety guard-
ing against failure under the following conditions:
(a) The load F = 1000 lbf tensile, steady.
(b) The load is 1000 lbf repeatedly applied.
(c) The load fluctuates between −1000 lbf and 300 lbf without column action.
Use the Smith-Dolan fatigue locus.

Alternating stress, a
F
S ut

1 in 1 in D. drill r = –1.86
4
S = 18.5 kpsi
a

S e
r = 1
3 in
8
= 7.63
S a
S
F m
–S ut –9.95 0 7.63 10 20 30 S ut
Midrange stress , kpsi
m
(a) (b)
Figure 6–31
The grade 30 cast-iron part in axial fatigue with (a) its geometry displayed and (b) its designer’s fatigue diagram for the
circumstances of Ex. 6–13.