3. Fatigue crack growth in polymeric materials:
In this connection, there is an interesting paper by Hertzberg et al. on
the fatigue failure of a polymer used in the lavatories [19].
Hertzberg was a student of Paul Paris and has done a significant amount
of work on the fatigue crack growth at Lehigh University. A more
exhaustive analysis of the behavior of polymers under fatigue is
presented in the book by Hertzberg and Manson [20].
Osorio [21] has done significant work on the R-ratio effects on FCG
in several polymeric materials. He has selected two modified
polyvinyl-chloride (PVC) polymers. One is called PVC-PIPE grade, and the
other is called DARVIC-110 grade materials. Both are amorphous
materials. The modification involves small additions that make them more
ductile and tough for applications. In addition, they have studied FCG
in Epoxy, which is a somewhat brittle material. The crazing may be
restricted to the crack tip plane at low R-ratios or mean stresses. At
high ratios or high Kmax values, the craze can spread
around the crack tip in the plastic zone, thereby increasing the crack
growth resistance of the material by energy dissipation. Craze formation
is governed more by tensile stress than cyclic stress. For viscoelastic
materials, deformation can also change with temperature and time. Hence
frequency effects become important. FCG behavior in the brittle Epoxy
will be different, where the fracture occurs by brittle crack extension,
which is also Kmax dependent.
Fig. 1 shows the crack growth behavior of PVC-PIPE grade polymer at 1Hz
at different R-ratios. Fig. 1a shows the data in terms of ΔK and Fig. 1b
in terms of Kmax parameters. The spread in the data in
terms of ΔK appears to be small except at low crack growth rates. In
terms of Kmax, the spread is more significant. Fig. 1c
shows ΔK-R curves at low crack growth rates, and Fig. 1d shows the
typical L-shaped ΔK-Kmax curves defining the limiting
values, ΔK* and Kmax* at each selected crack growth
rate. These L-shaped curves define the relative variation of the two
parameters to enforce the selected crack growth rates. The limiting
values indicate that both minima must be met for a crack to grow at the
selected growth rate while one or the other will be controlling. In
addition, each L-shaped curve defies a particular mechanism of crack
growth. If the mechanism changes the corresponding L-curve also changes
along with its new limiting values. Plotting of the limiting values ΔK*
vs. Kmax* defines the crack growth trajectory map for
the material. Each point in the trajectory defines a crack growth rate,
starting from the threshold. The 45o line with ΔK* =
Kmax* defines the pure fatigue line. The data
representing the material performance can deviate to the left of the
pure fatigue line depending on the extent of the superimposed
Kmax-dependent process present during crack growth. For
example, a viscoelastic deformation or deformation by crazing can shift
the curve to the left depending on their contribution. Fig. 1e shows the
crack growth trajectory map for the polymer. The trajectory initially
seems to move towards the pure-fatigue line as the crack growth rate
increases. With a further increase in crack growth rates, it diverges
from the pure fatigue line. Thus, the contribution from the
Kmax-dependent process appears to change with increasing
crack growth rate. The detailed fractographic analysis will be helpful
to identify the crack growth mechanisms involved.
Fig. 2 shows the behavior of the same material but at a higher
frequency, 10Hz. Interestingly, the author plotted the original data for
both frequencies in terms of Kmax and not ΔK, as
indicated in