Page 364 - Failure Analysis Case Studies II

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The prediction is of limited validity for KI less than 18 MPa Jm, since no failures had occurred
to specimens loaded to this level after 4 years.
Lewandowski et al. [2] give experimental data for alloy 6351 at tested at three temperatures in
specially prepared ingots doped with controlled Pb additions. Some of the data from Lewandowski
et al. is shown in Fig. 4. The data has been replotted by the authors on linear axes. The original
papers give the data on log-log axes, a fact which may conceal what is an important piece of
information; namely, that there appears to be a threshold to the growth curve. If this is assumed to
be the case then the Lewandowski data is closely described by the linear Eqns (3) and (4).
Upper bound growth rate lOOppm at 30°C (mm/year):
v = da/dt = 13.4x(KI-11.5). (3)
Upper bound growth rate 3Oppm at 30°C (mm/year):
u = da/dt = 7.73 x (Kl- 12.7). (4)

3.2. Threshold K, below which no growth occurs
One feature of these equations when written in this form is that they clearly imply that there is
threshold value of K, below which no growth occurs. This is KI = 11.5 MPa Jm for Eqn (3) and
K, = 12.7 MPa Jm for Eqn (4). This is consistent with the fact that in experiments no growth on
any test specimen has ever been recorded at KI below 10 MPa Jm. This is a key issue in determining
a realistic model for the growth in cylinders. It is a fact that, in traffic, many cylinders show no
evidence of crack growth even after being in use for many years and containing folds at the neck.

3.3. Growth rates predicted from previous work
Equations (1) and (2) relate to room temperature whereas Eqns (3) and (4) relate to 30 "C. Price
et al. [9] have reinterpreted the Lewandowski et al. data on the basis of temperature sensitivity data
given in that paper to determine that the growth rates would be reduced by a factor of about 4 for
temperatures of 18-20 "C. This means that at room temperature the first factors in the equations
should be 1.73+4 = 1.93 and 13.4+4 = 3.4.
To determine the crack driving stress intensity, the stresses presented for an aluminium cylinder
in Price et al. [ll] were used. Kr was estimated made using British Standards PD 6493: 1990 Level
2 for a crack of 4 mm depth by 20 mm long in the position shown on Fig. 1. If there is no residual
stress, KI is 5.54 MPa Jm.

300.00 ~ ~~
250.00 --

200.00 --
L
1 150.00--
2
E

-50.00 -
KI MPdm
Fig. 4. Data from Lewandowski er d. [2] for crack growth at 30 "C (solid lines). The upper data is for lOOppm
Pb and the lower data is for 30ppm. The data appear to obey a linear relationship (dashed lines). A linear
relationship implies there is a threshold below which no growth oocurs.