Effects of strain rate and notch on acoustic emission during the tensile deformation of a discontinuous yielding material

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.

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“…2(c) of Ref. [19]. It is clear that the overall shape of the model AE spectrum is quite similar to the experimental AE spectrum.…”

Section: B Acoustic Emission Spectrumsupporting

confidence: 63%

“…2 along with experimental points extracted from Fig. 2(c) of [19]. It is clear that the model σ − curve matches the experimental σ − quite well.…”

Section: A Numerical Solution Of Model Equations For Continuous Yieldmentioning

confidence: 53%

General framework for acoustic emission during plastic deformation

2015

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“…Equations (5)(6)(7)(8) are solved by using an adaptive step size differential equation solver (ode15s MATLAB solver). The model parameters fall into two types, one experimental and the other theoretical.…”

Section: B the Ananthakrishna Model For The Portevin-lementioning

confidence: 99%

“…For instance, AE studies on the smooth homogeneous yield phenomenon exhibit intermittent AE signals with its overall envelope exhibiting a peak just beyond the elastic regime decaying for larger strains [5,6]. Recent AE studies for this case throw light on the origin of the pulse like character of AE signals [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

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

Kumar

Ananthakrishna

2018

Phys. Rev. E

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Scale invariant power law distributions for acoustic emission signals are ubiquitous to several plastically deforming materials. However, power law distributions for the acoustic emission energies are reported in distinctly different plastically deforming situations such as hcp and, fcc single and polycrystalline samples exhibiting smooth stress-strain curves, and in dilute metallic alloys exhibiting discontinuous flow. This is surprising since the underlying dislocation mechanisms in these two types of deformations are very different. So far, there has been no models that predict the power law statistics for the discontinuous flow. Furthermore, the statistics of the acoustic emission signals in jerky flow is even more complex requiring multifractal measures for a proper characterization. There has been no model that explains the complex statistics either. Here, we address the problem of statistical characterization of the acoustic emission signals associated with the three types of the Portevin-Le Chatelier bands. Following our recently proposed general framework for calculating acoustic emission, we set-up a wave equation for the elastic degrees of freedom with plastic strain rate as a source term. The energy dissipated during acoustic emission is represented by the Rayleigh-dissipation function. Using the plastic strain rate obtained from the Ananthakrishna model for the Portevin-Le Chatelier effect, we compute the acoustic emission signals associated the three Portevin-Le Chatelier bands and the Lüders like band. The so calculated acoustic emission signals are used for further statistical characterization. Our results show that the model predicts power law statistics for all the acoustic emission signals associated with the three types of Portevin-Le Chatelier bands with the exponent values increasing with increasing strain rate. The calculated multifractal spectra corresponding to the acoustic emission signals associated with the three band types has a maximum spread for the type C decreasing with type B and A. We further show that the acoustic emission signals associated with Lüders like band also exhibits power law distribution and multifractality.

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“…Han et al [8], for example, related the yield stress in tensile tests with wave forms, while Niknam et al [18] related AE signals with a statistical approach to lubrication conditions. However, in these investigations absolute measurement is not used nor do they relate signal and source directly to each other.…”

Section: Introductionmentioning

confidence: 99%

Absolute Measurement of Elastic Waves Excited by Hertzian Contacts in Boundary Restricted Systems

et al. 2016

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In most applied monitoring investigations using acoustic emission, measurements are carried out relatively, even though that limits the use of the extracted information. The authors believe acoustic emission monitoring can be improved by instead using absolute measurements. However, knowledge about absolute measurement in boundary restricted systems is limited. This article evaluates a method for absolute calibration of acoustic emission transducers and evaluates its performance in a boundary restricted system. Absolute measured signals of Hertzian contact excited elastic waves in boundary restricted systems were studied with respect to contact time and excitation energy. Good agreement is shown between measured and calculated signals. For contact times short enough to avoid interaction between elastic waves and initiating forces, the signals contain both resonances and zero frequencies, whereas for longer contact times the signals exclusively contained resonances. For both cases, aGreen's function model and measured signals showed good agreement.

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Effects of strain rate and notch on acoustic emission during the tensile deformation of a discontinuous yielding material

Cited by 40 publications

References 26 publications

General framework for acoustic emission during plastic deformation

General framework for acoustic emission during plastic deformation

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

Absolute Measurement of Elastic Waves Excited by Hertzian Contacts in Boundary Restricted Systems

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