Page 386 - Mechanical Behavior of Materials

Section 8.7 Plastic Zone Size, and Plasticity Limitations on LEFM 387

K-field

far-field
plastic
zone

Figure 8.45 A crack and its plastic zone, and the larger K-field that must exist for LEFM
to be applicable.

2r o h h

a (b – a)
b a (b – a)

(a) (b) (c) (d)

Figure 8.46 Small plastic zone compared with planar dimensions (a), and situations where
LEFM is invalid due to the plastic zones being too large compared with (b) crack length,
(c) uncracked ligament, and (d) member height.

Fig. 8.46(b), (c), or (d). As discussed in Section 8.9, a value of K calculated beyond the applicability
of LEFM underestimates the severity of the crack.

8.7.4 Plane Stress Versus Plane Strain

If the thickness is not large compared with the plastic zone, Poisson contraction in the thickness
direction occurs freely around the crack tip, resulting in yielding on shear planes inclined through
the thickness, as shown in Fig. 8.44(a). Fracture under plane stress also occurs along such inclined
planes.