Simulation of the ultrasonic wave propagation in solids

Historically, nondestructive testing (NDT) has been used for detecting macroscopic and microscopic discontinuities in structures after they have been in service for some time or in new ones. The prominent role in nondestructive testing ultrasonic has won because of the application versatility, sensitivity and convenience. It has become evident that it is practical and cost effective to expand the role of the testing to include all aspects of materials and structures production and application. The main research efforts are being directed at developing nondestructive techniques capable of monitoring production process, material integrity, the amount and rate of degradation during service. However, comprehensive understanding of the processes taking place in the testing specimen is available only by fully investigating testing instrumentation and method. It includes analysis of the characteristics of the equipment being used and analysis of the wave propagation in the structure under investigation. The task is rather complicated, because the series of the signal transformations from electrical to mechanical and vice versa are encountered, the behavior of the structure is predetermined in general by the non linear material properties and/or anisotropy. This problem could be treated as complex one, dealing with the problems of electrical and mechanical origin. This paper is devoted to the mechanical ones, trying to find ways for effective simulation of the signal propagation in the structure subjected to nondestructive testing. In many cases simplified methods (e.g., ray tracing) can be used, however they are not based upon the differential equations and, consequently, present only rough evaluation of the wave front propagation. On the other hand, finite element or finite difference methods enable to get adequate representation of the process, however, computer resource requirements are usually too great for problems of a practical value. The situation can be improved by developing efficient algorithms of numerical modeling based on deeper analysis of the wave propagation phenomenon. Namely, large areas of the structure could be treated as homogenous rectangle zones with respect to the ultrasonic’s signal wavelength and they could be meshed by uniform quadrilateral finite element mesh allowing to obtain the solution on a finite element level. Only boundary edges having complicated geometrical shape have to be approximated by comparatively small freely meshed zones