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During the 135 years since Hood rightly associated fatigue failure with the internal structure of a metal by wrongly concluding that the metal had “crystallized,” there have been many hundreds of metallographic studies of fatigue that have deluged us with observations from which we have not yet been able to extract a really satisfying understanding of the basic principles involved in fatigue. It seems that the time is ripe for the application of the recently developed methods of quantitative microscopy. In so doing, it is important to appreciate, however, that there exists a mathematically rigorous geometry of microstructure which directs and limits the kinds of observations that can yield exact relationships between microstructure and physical properties. Additive geometric properties, such as total volume or total area of surface, are shape-insensitive and, hence, are readily measured and related to additive physical properties like density or hardness. Conversely, the average geometric properties, such as grain size, or average curvature of surface, are shape-sensitive and are limited in their application to a situation in which a regularity of shape prevails. Of particular interest in the field of fatigue are the geometrical extrema that are associated with localized mechanical effects, such as fracture. These are observable after the fact, chiefly in the two-dimensional parameters of the fracture surface. The scope of the application of quantitative microscopy to the study of fatigue is broad and the prospect of obtaining useful results is excellent.
area fraction, average geometric properties, connectedness, curvature, dislocations, fatigue, fatigue mechanism, global parameters, grain size, microstructure, quantitative microscopy, structure-property relationship
Distinguished service professor, University of Florida, Gainesville, Fla.