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