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measured by applying
Eq. (4-82)
to data obtained with thick specimens. To illus-
trate the differences between plane stress and plane strain fracture modes, thin
polycarbonate specimens with thicknesses
3 mm are reported to have
G
c
values
of 10 kJ/m
2
, while the
G
Ic
of thick specimens is 1.5 kJ/m
2
. It will be useful to
consider a practical application of LEFM here.
#
EXAMPLE 4-5
Consider a study of the effect of preexisting flaws on the ability of PVC pipe to hold pressure
[19]
. The critical stress intensity factor, K
Ic
, is reported to be 1.08 MPa m
1/2
for PVC under
static load at 20
C. The stress (σ) in a pipe5 the internal pressure, P, 1 the hoop stress at
the inner surface:
σ5P 1
P½D 2 t
2t
(4-84)
where D is the outside diameter and t is the pipe wall thickness. In this case, D5250 mm
and t 517 mm. For pipe of this type Γ (in
Eq. 4-82
) is about 1.12
[20]
. Assuming that the
presence of 1 mm flaws will give a conservative estimate of pipe service life, we take
a51mmin
Eq. (4-82)
. The critical stress for failure is
1
:
08 MPa m
1=2
1
K
Ic
Γ½πa
σ
f
5
1=2
5
1=2
5
17
:
2 MPa
10
23
:
12
½
π
m
σ
f
5P 1
P½D 2 t
2t
57:85 P
c
where P
c
is the critical pressure for brittle fracture of the pipe. Hence,
17
:
2 MPa
7:85
52:19 MPa5318 psi
An otherwise well-made pipe will sustain steady pressures up to 2.19 MPa (318 psi)
without failing by brittle fracture if it contains initial flaws as large as 1 mm. Similar calcula-
tions show that initial flaws or inclusions smaller than 4.5 mm permit steady operation at
150 psi (1.03 MPa).
P
c
5
LEFM discussed to this point refers to the resistance of bodies to crack growth
under static loads. Crack growth under cyclic loading is faster than under static
loads at the same stress amplitudes, because the rate of loading and the damage
both increase with higher frequencies.
Polymers which yield extensively under stress exhibit nonlinear stress
strain
behavior. This invalidates the application of linear elastic fracture mechanics. It is
usually assumed that the LEFM approach can be used if the size of the plastic
zone is small compared to the dimensions of the object. Alternative concepts
have been proposed for rating the fracture resistance of tougher polymers, like
polyolefins, but empirical pendulum impact or dart drop tests are deeply
entrenched for judging such behavior.
