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Scale invariant power law distributions for acoustic emission signals areubiquitous to several plastically deforming materials. However, power lawdistributions for the acoustic emission energies are reported in distinctlydifferent plastically deforming situations such as in hcp and, fcc single andpolycrystalline samples exhibiting smooth stress-strain curves, and in dilutemetallic alloys exhibiting discontinuous flow. This is surprising since theunderlying dislocation mechanisms in these two types of deformations are verydifferent. So far, there has been no models that predict the power lawstatistics for the discontinuous flow. Furthermore, the statistics of theacoustic emission signals in jerky flow is even more complex requiringmultifractal measures for a proper characterization. There has been no modelthat explains the complex statistics either. Here, we address the problem ofstatistical characterization of the acoustic emission signals associated withthe three types of Portevin-Le Chatelier bands. We set-up a wave equation forelastic degrees of freedom with plastic strain rate as a source term. Using theplastic strain rate obtained from the Ananthakrishna model for the Portevin-LeChatelier effect, we compute the acoustic emission spectrum corresponding tothe three Portevin-Le Chatelier bands, which is used for further statisticalcharacterization. Our results show that the model predicts power law statisticsfor all the three types of Portevin-Le Chatelier bands with the exponent valuesincreasing with increasing strain rate. The calculated multifractal spectracorresponding to the acoustic emission signals associated with these three bandtypes has a maximum spread for the type C decreasing with type B and A. Wefurther show that the acoustic emission signals associated with L\"uders likeband also exhibits power law distribution and multifractality.

Modeling the complexity of acoustic emission spectra during intermittent plastic deformation: Power laws and multifractal spectra