Principles of Fracture Mechanics

Abstract

When a solid is subjected to a certain system of external loads under a given set of environmental conditions, in most cases the response is simply one of deformation in the sense that topologically the medium remains unchanged. In this case, at least conceptually, the solution of the problem presents no difficulty, that is, after the appropriate material characterization it can be formulated as an initial-boundary value problem and all the desired field quantities may be obtained upon solving the related field equations. On the other hand, in addition to deformations taking place in the body, if new surfaces are created within the medium as a result of excessive applied loads, the body is said to undergo fracture. From the viewpoint of physical applications and mathematical modeling, in this case one generally distinguishes two types of problems, namely fracture initiation and fracture propagation. For a given solid with a given defect geometry, in the former one needs to evaluate the critical level of the applied loads corresponding to the inception of the fracture process. Since no new surfaces have as yet been created, here the related mechanics problem is again a deformation type of problem complemented by an appropriate fracture criterion which relates the inherent fracture resistance of the solid to the applied loads and geometry of the medium.