Materials for engineering, 3rd Edition - (Malestrom)

Determination of mechanical properties 51
thick in order that most of the deformation occurs under conditions of plane
strain. Figure 2.11 illustrates the effect of specimen thickness on the measured
value of the fracture toughness, K c : the fracture toughness can be halved as
the stress conditions change from plane stress to plane strain with increasing
specimen thickness. Once under plane strain, however, the value of the
toughness becomes independent of the thickness and this value is referred to
as K Ic , and is regarded as a material parameter. The corresponding value of
G Ic may be calculated from equation [2.15].
The two requirements of a relatively small plastic zone and plane strain
conditions impose conditions upon the test-piece dimensions which have to
be fulfilled in valid fracture toughness tests. These dimensions are always
stated in the appropriate testing standards, e.g. BS 7448 (1991).
In circumstances of extensive plasticity, an alternative toughness parameter
has been proposed, namely the crack tip opening displacement (CTOD),
usually given the symbol δ. The CTOD is obtained from the reading of a
clip-gauge placed across the crack mouth and, under conditions of fracture,
a critical value of δ c is determined. If the yield stress of the material is σ y , the
toughness may then be obtained from the relation:
G c = σ y δ c [2.18]
2.6.1 The J integral
There are types of material, e.g. elastomers, which behave in a non-linear
elastic manner, i.e. their reversible stress–strain graph is curved. The energy
Fracture toughness K c
K lc
Specimen thickness
2.11 Change in fracture toughness with specimen thickness.