Propagation of Ultrasound in Claddings

Nondestructive testing with ultrasound is a standard procedure in the nuclear power industry. To develop and qualify testing procedures extensive experimental work on test blocks is usually required. This can take a lot of time and therefore be quite costly. A good mathematical model of the testing situation is therefore of great value as it can reduce the experimental work to a great extent. A good model can be very useful for parametric studies, as a pedagogical tool, and for the qualification of testing procedures. In anisotropic materials, e.g. austenitic welds, the propagation of ultrasound becomes much more complicated as compared to isotropic materials. Therefore, modelling is even more useful for anisotropic materials. The present project has been concerned with the propagation of ultrasound in claddings, i.e. a layer of material used for corrosion protection. This is often an austenitic steel that is welded onto the surface to be protected. For modelling purposes it may be a valid assumption to take the cladding as homogeneous but anisotropic. A complicating factor with a cladding is, however, that the interface between the cladding and the interface is often corrugated. This corrugation can have pronounced effects on the transmission of ultrasound through the interface and can thus change the detectability of defects in the cladding. To model the propagation of ultrasound in claddings the null field approach is adopted. This has the advantage that the problem is reduced to a type of integral equations on the interface, which is further reduced to one period of the interface if it is periodic. The interface has, in fact, been taken as sinusoidal, both because this is reasonably realistic and because it simplifies the computations. Alternative methods, primarily FEM and EFIT, use volume discretizations and in 3D this often leads to very large problems and excessive execution times. The modelling is performed both in 2D and 3D, and in addition one part of the project has been concerned with the derivation and evaluation of approximate boundary conditions to simulate the corrugated interface with periodic boundary conditions on a (fictitious) flat interface. This simplifies the computations and could be of particular value when modelling defects in the cladding by integral equation techniques. Some numerical results are given showing the capabilities of the programs. Only a combination with an isotropic ferritic base material and an anisotropic austenitic cladding is considered, but both the tilt and skew of the austenite and the height of the corrugations are varied. Only a 45 deg 1 MHz SV probe is used to excite waves in the structure. To get a good overview of the wave propagation field plots of the ultrasound are given. These are given at a fixed frequency and thus show the wavefronts, wavelengths, and direction of propagation. But the travel time information is of course missing. The results show that both the tilt and the skew of the anisotropy have very important effects on the transmission of the ultrasound into the cladding (and thus on the detectability of defects there). The height of the corrugation is also of importance, and the heights that are found in practice will in many cases have strong effects on the transmission of ultrasound into the cladding. The approximate boundary conditions are evaluated by comparisons with the exact calculations, and the conclusion is that they are useful for small corrugation heights. The heights that are found in practice will often violate the range of applicability of the approximate boundary conditions