Page 384 - Mechanical Behavior of Materials

Section 8.7 Plastic Zone Size, and Plasticity Limitations on LEFM 385

σ
y
σ
σ = 0 x
z
(a)
A
y
or

x
z
2r oσ t
A
Section A-A

(b)
B

y

x
t
z
2r oε

B σ
y Section B-B
σ x
σ z
(ε = 0)
z
Figure 8.44 Plastic zone, stress state, and fracture mode for (a) plane stress and
(b) plane strain.

As might be expected, the plastic zone size increases if the stress (hence K) is increased, and it
is smaller for the same K for materials with higher σ o . The plane stress plastic zone and the stress
state within it near the crack tip are illustrated in Fig. 8.44(a).
8.7.2 Plastic Zone Size for Plane Strain

Consider a cracked member where the thickness is large compared with the plastic zone size, as
in Fig. 8.44(b). The material outside the plastic zone is subjected to relatively low stresses σ x and