General framework for acoustic emission during plastic deformation

Abstract

Despite the long history, so far there is no general theoretical framework for calculating the acoustic emission spectrum accompanying any plastic deformation. We set up a discrete wave equation with plastic strain rate as a source term and include the Rayleigh-dissipation function to represent dissipation accompanying acoustic emission. We devise a method of bridging the widely separated time scales of plastic deformation and elastic degrees of freedom. While this equation is applicable to any type of plastic deformation, it should be supplemented by evolution equations for the dislocation microstructure for calculating the plastic strain rate. The efficacy of the framework is illustrated by considering three distinct cases of plastic deformation. The first one is the acoustic emission during a typical continuous yield exhibiting a smooth stress-strain curve. We first construct an appropriate set of evolution equations for two types of dislocation densities and then show that the shape of the model stress-strain curve and accompanying acoustic emission spectrum match very well with experimental results. The second and the third are the more complex cases of the Portevin-Le Chatelier bands and the Lüders band. These two cases are dealt with in the context of the Ananthakrishna model since the model predicts the three types of the Portevin-Le Chatelier bands and also Lüders-like bands. Our results show that for the type-C bands where the serration amplitude is large, the acoustic emission spectrum consist of well separated bursts of acoustic emission. At higher strain rates of hopping type-B bands, the burst type acoustic emission spectrum tends to overlap forming a nearly continuous background with some sharp acoustic emission bursts. The latter can be identified with the nucleation of new bands. The acoustic emission spectrum associated with the continuously propagating type-A band is continuous. These predictions are consistent with experimental results. More importantly, our study shows that the low amplitude continuous acoustic emission spectrum seen in both the type-B and A band regimes is directly correlated to small amplitude serrations induced by propagating bands. The acoustic emission spectrum of the Lüders-like band matches with recent experiments as well. In all of these cases, acoustic emission signals are burst-like reflecting the intermittent character of dislocation mediated plastic flow.

A Novel Approach to Modelling Nanoindentation Instabilities

“…Further support for this premise comes from the fact that similar time evolution equations for the volume averaged dislocation densities have been effectively used in the literature to explain the temporal aspects of several spatio-temporal plastic deformation instabilities and patterns [30,32,34,[40][41][42][43]. For example, the 'storage recovery' model for the evolution of the forest dislocation density (with respect to shear strain or time) has been used to obtain good insight into several characteristic features of dislocation cell pattern seen in stage III deformation of F.C.C materials [40].…”

“…[30,32,41,42]). Similar volume averaged dislocation densities have also been used to explain the stress-strain curve for a smooth yield phenomenon in the context of acoustic emission [34]. The same type of approach has been used to explain the inverse power law dependence of the yield stress on the diameter of nano-pillars [43].…”

“…As discussed in a number of earlier publications, two distinct types of short range interactions can be identified that act as the source for the growth of the forest density ρ f . These act as loss terms to the mobile density ρ m [28,30,33,34,42,49]. When two dislocations moving in nearby glide planes approach a minimum distance (typically a few nanometers), they can form dipoles.…”

“…Following our earlier publications [28][29][30][32][33][34]41,46], we develop the time evolution equations for the mobile ρ m and forest ρ f densities based on relevant dislocation mechanisms contributing to the plastic flow. Dislocation mechanisms can be broadly categorized into dislocation production and transformation mechanisms.…”

“…The purpose of this paper is to review the recently introduced dynamical approach and the models that predict the results for the DC and LC mode nanoindentation experiments [28,29]. The approach is based on our previous experience in modeling a significantly more complex spatio-temporal instability, namely, the Portevin-Le Chatelier (PLC) effect seen in bulk samples of dilute alloys under constant strain rate conditions [30][31][32][33][34]. The approach is applicable to ideal single crystals without any kind of defects.…”