Acoustic Emission from Plastic Sources

Abstract

Monitoring of structures which may be subjected to overloads can be based on observing signals emitted in the course of developing defects. Ductile structures react on overloads by the formation of (small scale) plastic zones. Within the linear elastic background concept such an event is considered by the formation of sources of eigenstress. Since a direct description of the source characteristics is rather cumbersome we choose the time convolution of the imposed plastic strains with the complementary Green's stress dyadic to describe the signal of the acoustice mission. Thus, the dynamic generalization of Maysel's formula of thermo-elasticity, to include all kinds of eigenstrains, enters the field of computational acoustics. In that context, the novel contribution of this paper to acoustic emission and monitoring of (layered) structures is the formulation of the full 3-D problems and the introduction of the generalized rays in the background considering an instantaneous oblique force point source at the transducer's location. That means, all the information on the wave guide is contained in the Green's stress dyadic. The expansion into plane waves of cylindrical or spherical waves propagating in a layered elastic half-space or plate proves to be quite efficient for short observation times. Even the divergence effects of dipping interfaces of wedge-type layers are perfectly included by proper coordinate rotations and the exact seismograms are observed at a point receiver (where the localized plastic source is assumed to develop, commonly buried and often localized at an interface) from any source located at the hypo center (the site of the transducer in receiving mode, commonly placed at the outer surface). This nontrivial technique relies on the invariance of the phase function (arrival time) and of the infinitesimal amplitude of the plane waves in the ray expansion. The concept of the elastic background is illustrated by elastic-viscoplastic waves propagating in thin rods and subsequently extended to the 3-D problem of spherical waves with point symmetry. In that context and in an incremental formulation, the notion of plastic sources is introduced, which emit elastic waves in the background. Finally, the full 3-D problem in a layered half space or layered plate is solved in terms of generalized rays to be received at a transducer in receiving mode. Taking into account the progress in symbolic manipulation with integrated numeric capabilities (e.g., of Mathematica), such a formulation seems timely and may prove to be competitive to the entirely computational Finite Element Method of analysis of signals received from plastic sources. Time signatures of Green's displacement components at the surface of a half-space are illustrated when produced by a vertical, horizontal and inclined line load with a triangular time source function, respectively.