As previously noted, the glue spall stress may cause spalling due to the propagation of preexisting surface cracks. On the other hand, utilizing linear elastic fracture mechanics we can examine the likelihood that cracks in the ice layer penetrate the underlying cementitious substrate, and account for the crack trajectory through the cement layer. Figure 1 shows the results of a finite element analysis which predicts the depth of crack penetration into the substrate. The plot shows the curves for several values of the Dunder's parameter, βD, which characterizes the elastic mismatch in the system. For the ice/cement system βD=-0.2. The grey bar along the abscissa indicates the relative substrate fracture energy, ΓC/Γf, that corresponds to the lower 25% of the measured values for the fracture toughness, KIC, of cement paste. The corresponding depth of penetration, d, into the cement surface is indicated by the grey bar on the y-axis; d is normalized by the thickness of the film (ice layer) on the surface. Therefore, this anaylsis indicates that the crack will penetrate up to a depth of 0.75 times the thickness of the ice layer or ~ 4mm. This thickness is similar to that observed during salt scaling studies. It must be noted that cementitious media is quasi-brittle, so the results of the fracture mechanics analysis are not exact.
Figure 1 - The depth of crack penetration vs the relative substrate fracture energy for
several values of the Dunder's parameter, βD. The gray bar along the abscissa represents the lower 25%
of the range of fracture toughness for cement paste. The corresponding grey bar on the y-axis indicates the expected depth of crack penetration d for
the range of cement paste KIc indicated. Note, the penetration depth is normalized by the thickness of the the ice layer, tf.
There are 3 situations that can occur when an edge crack forms in a film on a substrate, the crack will: 1) arrest in the film. 2) bifurcate along the substrate/film interface. 3) penetrate the underlying substrate. As noted above if the ice does not debond from the cementitious substrate cracks in the ice layer are expected to penetrate the cement binder. Empirical evidence indicates that, owing to mechanical interlocking, the bond between ice and hydrophobic surfaces is greater than the tensile strength of ice. The latter is especially true for cementitious surfaces where the roughness is much greater than the metal surfaces on which this trend was elucidated. Therefore, we can state with confidence that cracks in the ice layer will penetrate the cement surface.
In addition to these persuasive conclusions, fracture mechanics can account for the salt scaling damage morphology. When a crack in the ice layer enters the underlying cement, the driving force for crack penetration decreases as the crack tip moves away from the interface. This is physically sound, because the driving force is the mismatch strain. On the other hand, the edge cracks in the cement surface essentially form small ice/cement bi-material strips. Accordingly, the moment due to the mismatch strain tends to guide the penetrating crack into a trajectory that is parallel to the interface. This argument is clarified by plotting the mode I stress intensity for penetration, and propagation parallel to the interface as a function of crack depth (Figure 2). At a critical depth, the intensity for propagation parallel to the interface is greater than that for penetration. So the crack propagates into a trajectory that is parallel to the interface. As the crack turns into this trajectory it will deflect into a depth where the mode II stress intensity is zero, KII=0. Again, this is physically sound because the mode II stress intensity will tend to turn the crack toward, or away from the interface. For the ice/cement system, KII=0 at a depth of ~ 4 mm. At this depth the stress intensity for propagation parallel to the interface is, KI=0.1 MPa · m0.5, which is on the low end of the range of fracture toughness for cement paste. However, it is reasonable to suggest that this stress intensity is sufficient for delamination, because the cracks prefer to propagate through the interfacial transition zone (ITZ) between the aggregate and hydrated cement. The fracture toughness of the ITZ is, KIC=0.1 MPa · m0.5, so it is likely that the stress intensity at a depth of a few mm is high enough to result in crack propagation. This assertion is supported by many laboratory and field investigations that report scaling damage often circumscribes aggregate particles.