RESIDUAL STRESS FIELD ESTIMATION BY ULTRASONIC WAVES

In certain cases, the presence of residual stress reduces the strength of parts, hence, its detection and estimation is of great importance. Ultrasonic waves have the potential to be employed in nondestructive tests to do this task. The analysis is based on the acoustoelasticity properties of the material that studies changes in wave velocity when passing through a stressed medium. To derive the equations of motion for a particle in a stressed elastic solid, it is supposed that the displacement vector consists of two parts: a static part, which may be developed by a residual or applied stress field, and a dynamic part, which is produced due to wave propagation and is considered a small amplitude harmonic motion. The finite displacement theory is employed to derive the general form of the non linear equations of motion in three dimensions for an incident wave at various angles, which are made linear by the Taylor expansion method. Various components of the wave velocity are computed from linear equations as an eigenvalue problem. Relative velocity changes versus one dimensional stress and strain in an aluminum block, and the effect of wave incidence angle on the propagation velocity are established and plotted. It is shown that the speed of wave in a stressed elastic solid depends not only on the material properties of the solid, but, also, on the wave incidence angle and the propagation and particle displacement direction relative to the stress direction. From the presented diagrams, it is revealed that if the direction of incidence and propagation of the wave coincides with the direction of normal stress, then, the velocity of the longitudinal mode will decrease in tension and increase in compression. On the other hand, the velocity of shear wave will increase in tension and decrease in compression. These conclusions agree with the results in other references. Comparing the slope of relative velocity diagrams in a stressed body, we conclude that the velocity of longitudinal waves that are incident along the normal stress component, is greater than other wave modes, although the magnitude of this change is very small for either modes; say, about 0.6 percent for longitudinal waves at 70 MPa tension in aluminum. Therefore, precise measurement of the flight time of the wave is necessary.