Can We Hear the Echos of Cracks?

The detection of cracks in mechanical engineering is mainly based on ultrasonic testing and Foucault currents. But even if they are efficient tools, this technology requires an important handling and is limited to the detection of cracks which are close to the source. Recently, several searchers have discussed the possibility of using waves as Lamb waves, for thin plates and shells, but also Love waves for bimaterials. In both cases the structure works as a wave guide and enables a long range propagation which is a promising possibility for detecting a crack quite far from the source. In this paper, we discuss the observability property of a small crack inside an open set using Love waves (the goal is to detect the beginning of the growth). It is proved that an adapted selection of these waves is necessary in order to avoid a black out which can occur for particular frequencies. This phenomenon is due to the fact that the crack has two extremities which can cancel their influence in a detection criterion. The main contribution of this paper is to discuss this point from a mathematical point of view, using an energy criterion requiring measurements quite far from the defect which should be detected.