Multi scale modeling and simulation of the ultrasonic waves interfacing with welding flaws in steel material

Before a product can be developed, materials are the first step in the differentiation and engineering of matter. Therefore material constitutes the clay with which any human made product is built. Since the drawn of time, man has been using materials, but knowledge in this area is mainly based in experience. Today we have reached a revolutionary stage in the knowledge and the control of matter thanks to the progress made in modelling and simulation, which allow us to work within virtual reality and skip many costly prototype development stages. Generally the calculation models are based on empirical methods resulting from the compilation of numerous experiments and presented in the form of numerical laws with adjustable parameters. The multi-scale modelling due to the scale change ability, allows the understanding of the material phenomenon. So from the atom we can move on to the micrometric scale and from there on to the mille metric scale (size of test specimens used in laboratories). The wavelet theory seems to be the approach that can satisfy the multi-scale modelling. In our work, computer simulation of ultrasonic waves traveling inside the test specimen is considered to be a helpful tool to get information and physical understanding of wave phenomena inside the material, which can help us to a suitable prediction of the service life of the controlled component. The ultrasonic testing of steel welds is a commonly used method in non destructive testing. However the interpretation of the received information in a satisfactory way is not sure. In this paper we try to simulate the propagation of the ultrasonic wave in a homogeneous material with the modeling of the system response by the use of the wavelet theory as a multi-scale modeling technique.