The geometry of surface cracks

Abstract

The question of the cracking of thin surface layers or coatings arises in a number of different applications. For example, it occurs in enamel and other protective coatings due to stresses set up by cooling and is also observed in the stress crazing of plastics. Cracking o f surface coatings is also important in connection with thermal shock. An analogous form of surface cracks appears in prolonged dry weather in the dried-out mud at the bot tom of lakes and reservoirs. The cracking generally occurs in the form of irregular honeycombs or polygon patterns. The general form of such patterns may be explained by application of the principle of least work, and an analysis of the geometry of such cracks is given below. It is assumed that the material is homogeneous and is in the form of a plane surface; during cooling, the tension is assumed uniform and increases progressively until it exceeds the fracture strength. The rectilinear surface cracks which develop form polygons which cover the surface or part of the surface affected. If the internal tension T per unit length at any instant is assumed to be constant in every direction at each point, then, assuming the rupture to take place for a unit depth, we consider a resulting rectilinear crack, such as AB, shown in fig. 1. Suppose that under tension it has opened uniformly by an amount RQ, so that on either side of the crack there is a corresponding displacement of the material perpendicular to the axis of the crack. The width varies from one crack to another, but is assumed to be uniform for each individual crack.