Page 141 - Plastics Engineering

1 24 Mechanical Behaviour of Plastics

Example 2.19 During tensile tests on 4 mm thick acrylic sheets of the
type shown in Fig. 2.63(a), the force-displacement characteristics shown in
Fig. 2.64(a) were recorded when the crack lengths were as indicated. If the
sheet containing a 12 mm long crack fractured at a force of 330 N, determine
the fracture toughness of the acrylic and calculate the applied force necessary
to fracture the sheets containing the other crack sizes.
Solution The compliance (S/F) of each sheet may be determined from the
slope of the graph in Fig. 2.64(a). A plot of compliance, C, against crack
dimension, a, is shown in Fig. 2.64(b) and from this the parameter dC/da
may be obtained. This is also shown plotted on Fig. 2.64(b). Using this, for
a = 6 mm, it may be seen that dC/da = 115 x N-I.
Thus, from equation (2.91)

As this is a material constant, it may be used to calculate F, for the other
crack sizes. For example, for a = 2 mm, dC/da = 7 x N-' so

Fc = \/2(0.004)1.56 10-6 x lo3 = 1.34 kN
7
x
Similarly for a = 3,4,5 and 5.5 mm the fracture loads would be 1.15 kN,
0.98 kN, 0.71 kN and 0.5 kN respectively.

1.6
1
1.4

1.2
A 1.0
B

8 o*8
0.6
0.4

0.2

0 10 20 30 40 50 60
Displacement (pm)

Fig. 2.64(a) Force-displacement characteristics for cracked plate