Elastic interfaces in random media and their application to fatigue fracture

This dissertation looks at elastic interfaces in disordered media and their application to fracture mechanics, in particular fatigue fractures. The work goes through three publications, of which one is experimental, one numerical, and one analytical. The fracturing of materials under repetitive stress is called fatigue. We are interested in the propagation of a single crack and the Paris-Erdogan law, which states that the crack's velocity grows as a power of a function known as the stress intensity factor. Often it is enough to look at just the largest crack in a solid, as it is the one that advances the fastest and eventually splits the object under long enough loading. Elastic interfaces describe self-interacting boundaries between two systems. In this case, the boundary is the front of a crack, the deepest part of the crack inside a material. Elastic forces inside the material try to keep the crack front straight even if the material is rough in composition. As one part of the crack front advances, it pulls its neighbors forward. The numerical publication looks at chain reactions of movement called avalanches in the elastic interface model. Avalanches are often defined as signals that are greater than some threshold, for example to separate relevant data from noise. Avalanches are however scale-free in size, so the choice of the threshold alters the results. Our results show how different distributions of avalanches change with the threshold and how a threshold determines whether the avalanches are correlated or not. We also show that previously found seismological behavior in interface movement results from how it has been defined. The experimental publication looks at microscopic jumps in crack movement and how they result in the Paris-Erdogan law. The jumps are found to follow the same distribution for different loading schemes, even though they result in different average speeds and different slopes for the Paris-Erdogan law. The distributions, however, differ in their cutoffs, so faster average movement results from the jump distribution lasting longer. The analytical publication compares slow thermally induced interface movement to the Paris-Erdogan law and to periodic movement in other systems such as magnetic domain walls. We find that the results for magnetic domain walls describe fatigue fractures better than the results intended for fractures. This implies that previously found material parameters for planar cracks might not be correct for fatigue experiments.