ULTRASONIC DETECTION OF PLASTIC YIELDING IN STEEL SPECIMENS Z. Radakovic and K. Willam CEAE Department University of Colorado at Boulder Boulder, CO 80309-0428 L. J. Bond Center for Acoustics, Mechanics and Materials University of Colorado at Boulder Boulder, CO 80309-0427 INTRODUCTION In the case of localization the loss of ellipticity is synonymous with the formation of weak discontinuities, or jumps of the velocity gradients (strain rates). The singularity in the localization tensor indicates discontinuous bifurcation when jump conditions in static problems are examined. By analogy, the singularity in the acoustic tensor indicates loss of hyperbolicity, which is synonymous with zero wave propagation velocities in dynamic problems. It is this analogy between the localization tensor and the acoustic tensor which led us to examine zero wave propagation properties for characterizing localized failure processes. Ultrasonic measurements of signal arrival times and amplitudes were performed on flat steel specimens, loaded in direct tension into the plastic yield regime. The objective was the characterization of discontinuous failure modes using ultrasonic wave measurements. In this paper preliminary results from the longitudinal, shear, and Rayleigh wave experiments are presented. ANALOGY BETWEEN LOCALIZATION AND ACOUSTIC ANALYSIS In the following we review the background material of elastic and elasto-plastic analysis and its implications with regard to wave propagation. Linear Elasticity The general format of the localization/acoustic tensor in index notation is: (1) where Eijlcl denotes the elasticity tensor, and where the vector Nj, withj = 1,2,3, defines the normal of the discontinuity surface associated with plane acceleration waves. In the case of isotropic linear elastic solids, the expression in Eq. 1 reduces to the simplified form Qjl = p. + I')NiNIc + 1'6ilc which expands into: (2) In this expression A and I' denote the Lame's parameters, Nit N2, Na the components of the propagation direction, and 6 the Kronecker delta. Review of Progress in Quantitative Nondestructive Evaluation. Vol. 14 Edited by D.O. Thompson and D.E. Chimenti. Plenum Press. New Yark, 1995 1593 brought to you by CORE View metadata, citation and similar papers at core.ac.uk provided by Digital Repository @ Iowa State University