A one-dimensional model for variations of longitudinal wave velocity under different thermal conditions

Ultrasonic testing is a versatile and important nondestructive testing method. In many industrial applications, ultrasonic testing is carried out at relatively high temperatures. Since the ultrasonic wave velocity is a function of the workpiece temperature, it is necessary to have a good understanding of how the wave velocity and test piece temperature are related. In this paper, variations of longitudinal wave velocity in the presence of a uniform temperature distribution or a thermal gradient is studied using one-dimensional theoretical and numerical models. The numerical model is based on finite element analysis. A linear temperature gradient is assumed and the length of the workpiece and the temperature of the hot side are considered as varying parameters. The workpiece is made of st37 steel, its length is varied in the range of 0.04-0.08 m and the temperature of the hot side is changed from 400 K to 1000 K. The results of the theoretical model are compared with those obtained from the finite element model (FEM) and very good agreement is observed.