Scaling phenomena in fatigue and fracture

The general classification of scaling laws will be presented and the basic concepts of modern similarity analysis - intermediate asymptotics, complete and incomplete similarity - will be introduced and discussed. The examples of scaling laws corresponding to complete similarity will be given. The Paris scaling law in fatigue will be discussed as an instructive example of incomplete similarity. It will be emphasized that in the Paris law the powers are not the material constants. Therefore, the evaluation of the life-time of structures using the data obtained from standard fatigue tests requires some precautions.