Page 143 - Plastics Engineering

126 Mechanical Behaviour of Plastics

F

Fig. 2.65 Loading of cracked plate

So, combining equations (2.94) and (2.95)

and in practice it is found that k 2: R, so

nu;a
G, = - (2.96)
E
This is an alternative form of equation (2.91) and expresses the fundamental
material parameter G, in terms the applied stress and crack size. From a knowl-
edge of G, it is therefore possible to specify the maximum permissible applied
stress for a given crack size, or vice versa. It should be noted that, strictly
speaking, equation (2.96) only applies for the situation of plane stress. For
plane strain it may be shown that material toughness is related to the stress
system by the following equation.
nu:a
2
GI, = -(1 - v ) (2.97)
E
where v is the lateral contraction ratio (Poissons ratio).
Note that the symbol GI, is used for the plane strain condition and since this
represents the least value of toughness in the material, it is this value which is
usually quoted. Table 2.2 gives values for GI, for a range of plastics.