Page 336 - Mechanical Behavior of Materials

Section 8.2 Preliminary Discussion 337

presence of a crack.) Repairs necessitated by cracks may involve replacing a part or modifying it,
as by machining away a small crack to leave a smooth surface, or by reinforcing the cracked region
in some manner.
In this chapter, we will introduce fracture mechanics and study its application to failure under
static loading. Later, in Chapter 11, we will consider growth of cracks due to cyclic loading.

8.2 PRELIMINARY DISCUSSION

Before introducing the details of fracture mechanics, it is useful to make some observations
concerning the general nature of cracks and their effects.

8.2.1 Cracks as Stress Raisers
Consider an elliptical hole in a plate of material, as illustrated in Fig. 8.3(a). For purposes of
discussion, the hole is assumed to be small compared with the width of the plate and to be aligned
with its major axis perpendicular to the direction of a uniform stress, S, applied remotely. The
uniform stress field is altered in the neighborhood of the hole, as illustrated for one particular case
in Fig. 8.3(b).
The most notable effect of the hole is its influence on the stress σ y parallel to S. Far from the
hole, this stress is equal to S. If examined along the x-axis of (b), the value of σ y rises sharply near
the hole and has a maximum value at the edge of the hole. This maximum value depends on the
proportions of the ellipse and its tip radius ρ:

c c
!
σ y = S 1 + 2 = S 1 + 2 (8.1)
d ρ

8
y
S k = 7
t
σ σ y
2 S 6 x
ρ = d σ x
c
h
4 σ y c/d = 3
t
d
c
b 2 σ
x
0
1 2 3 4 5
(a) (b) x/ρ

Figure 8.3 Elliptical hole in a wide plate under remote uniform tension, and the stress
distribution along the x-axis near the hole for one particular case.