Page 140 - Plastics Engineering

Mechanical Behaviour of Plastics 123

F
t t t
1-7 Fo7

Fig. 2.63 Force displacement behaviour of an elastic cracked plate

The work done, aW, as a result of the change in crack length &a is shown
shaded in Fig. 2.63(b). This will be given by
aw = Fas + ;aFas (2.88)

Now using equations (2.87) and (2.88) in equation (2.84)

(2.89)

This equation may be simplified very conveniently if we consider the Compli-
ance, C, of the material. This is the reciprocal of stiffness and is given by
s
c=-
F
From this equation we may write

ad = FaC + CaF
and using this in equation (2.89) we get

(2.91)

where F, is the applied force at fracture.
This is a very important relationship in that it permits the fundamental mate-
rial property G, to be calculated Erom the fracture force, F,, and the variation
of compliance with crack length.