Page 147 - Plastics Engineering

130 Mechanical Behaviour of Plastics
(d) Penny shaped internal crack

(2.104)

assuming a << D
(e) Semi-elliptical surface flaw
(..) 1.12
K = ~(na)'/~ (2.105)

(0 Three point bending

3FL {
K = 2~~312 1.93 (G) 'I2 - 3.07 ( $)312 + 14.53 ( $)*I2
~

-25.11 (G)'l2+25.8 ($)9/2} (2.106)

or
(2.107)

Thus the basis of the LEFM design approach is that
(a) all materials contain cracks or flaws
(b) The stress intensity value, K, may be calculated for the particular loading
and crack configuration
(c) failure is predicted if K exceeds the critical value for the material.
The critical stress intensity factor is sometimes referred to as the fracture
toughness and will be designated K,. By comparing equations (2.96) and (2.99)
it may be seen that K, is related to G, by the following equation

(EG,)'/~ = K, (2.108)

This is for plane stress and so for the plane strain situation

(2.109)

Table 2.2 gives typical values of K1, for a range of plastics
Example 2.20 A cylindrical vessel with an outside radius of 20 mm and an
inside radius of 12 mm has a radial crack 3.5 mm deep on the outside surface.
If the vessel is made from polystyrene which has a critical stress intensity factor
of 1.0 MN m-3/2 calculate the maximum permissible pressure in this vessel.