Propagation of Ultrasonic Plane Waves in a Plastically Deformed Medium

Abstract

The detection and sizing of cracks during inspection of structures is typically achieved by ultrasonic techniques; both time-of-flight and scattered amplitude techniques are employed. However, when a component containing a fatigue grown crack is unloaded, a zone of reverse (compressive) plastic deformation forms near the crack tip and a certain part of the crack is “closed” (in contact) over an undetermined length. Thus the ultrasonic waves pass through the closed crack faces and one obtains an underestimate of the crack size which leads to a nonconservative reliability analysis. If, however, the region of plastically deformed material can be identified, it would be possible to determine a better estimate of the size of the crack. Towards this end, we first explore the effect of plastic deformation on the propagation speed of the ultrasonic waves. A general theory for the propagation of plane waves in an elastic-plastic body undergoing finite plastic deformation was developed by Johnson [1]. However, very few experimental results are available in this area. Moreover, the available experimental results consider only some wave polarizations and some specific stress states (tension or compression). Furthermore, empirical correlations seem to be preferred over the theoretical models. Fisher [2] indicates that in 2024-T351 and 7075-T651 A1 alloys, the acoustoelastic law, △V = A V, is followed even beyond yield with the same constant of proportionality. Pao and Hirao [3] indicate that the change in the wave speeds AV can be decomposed into two parts: one due to the elastic stresses and the other due to plastic deformation; the former disappears on unloading while the latter remains. The dependence of the change in wave speeds △V on the plastic strain ep is shown to be linear for small strains (<0.6%) in carbon steel (C1018), but bilinear in 6061-T6 and pure copper. The relative change in the wave speed △V/V is usually small: one part per thousand for a strain of a few parts per thousand. In the present paper, we examine the effect of plastic deformation on the propagation of ultrasonic plane waves and then exoplore the propagation in the plastically deformed region near a crack.