Statistics of avalanches in martensitic transformations. I. Acoustic emission experiments

Challenges and Accomplishments in Mechanical Testing Instrumented by In Situ Techniques: Infrared Thermography, Digital Image Correlation, and Acoustic Emission

A current trend in mechanical testing technologies is to equip researchers and industrial practitioners with the facilities for non-destructive characterisation of the deformation and fracture processes occurring on different scales. The synergistic effect of such a combination of destructive and non-destructive techniques both widens and deepens existing knowledge in the field of plasticity and fracture of materials and provides the feedback sought to develop new non-destructive testing approaches and in situ monitoring techniques with enhanced reliability, accuracy and a wider scope of applications. The macroscopic standardised mechanical testing is still dominant in the research laboratories and industrial sector worldwide. The present paper reviews multiple challenges commonly faced by experimentalists, aiming at enhancing the capability of conventional mechanical testing by a combination of contemporary infrared thermography (IRT), rapid video imaging (RVI) with non-contact strain mapping possibilities enabled by the digital image correlation (DIC) method, and the acoustic emission (AE) technique providing unbeatable temporal resolution of the stochastic defect dynamics under load. Practical recommendations to address these challenges are outlined. A versatile experimental setup uniting the unique competencies of all named techniques is described alone with the fascinating possibilities it offers for the comprehensive characterisation of damage accumulation during plastic deformation and fracture of materials. The developed toolbox comprising practical hardware and software solutions brings together measuring technologies, data, and processing in a single place. The proposed methodology focuses on the characterisation of the thermodynamics, kinematics and dynamics of the deformation and fracture processes occurring on different spatial and temporal scales. The capacity of the proposed combination is illustrated using preliminary results on the tensile and fatigue behaviour of the fcc Inconel-625 alloy used as a representative example. Dissipative processes occurring in this alloy are assessed through the complex interplay between the released heat, acoustic emission waves, and expended and stored elastic energy.

Acoustic Emissions during Structural Changes in Shape Memory Alloys

Structural changes (martensitic transformation, rearrangements of martensitic variants) in shape memory alloys have an intermittent character that is accompanied by the emission of different (thermal, acoustic, and magnetic) noises, which are fingerprints of the driven criticality, resulting in a damped power-law behaviour. We will illustrate what kinds of important information can be obtained on the structural changes in shape memory alloys. It was established that the power exponents of distributions of acoustic emission (AE) parameters (energy, amplitude, etc.), belonging to martensitic transformations, show quite a universal character and depend only on the symmetry of the martensite. However, we have shown that the asymmetry of the transformation (the exponents are different for the forward and reverse transformations) results in as large differences as those due to the martensite symmetry. We will also demonstrate how the recently introduced AE clustering method can help to identify the different contributions responsible for the asymmetry. The usefulness of the investigations of time correlations between the subsequent events and correlations between acoustic and magnetic noise events in ferromagnetic shape memory alloys will be demonstrated too. Finally, examples of acoustic and magnetic emissions during variant rearrangements (superplastic or superelastic behaviour) in the martensitic state will be described.

Increasing power-law range in avalanche amplitude and energy distributions

Power-law-type probability density functions spanning several orders of magnitude are found for different avalanche properties. We propose a methodology to overcome empirical constraints that limit the range of truncated power-law distributions. By considering catalogs of events that cover different observation windows, the maximum likelihood estimation of a global power-law exponent is computed. This methodology is applied to amplitude and energy distributions of acoustic emission avalanches in failure-under-compression experiments of a nanoporous silica glass, finding in some cases global exponents in an unprecedented broad range: 4.5 decades for amplitudes and 9.5 decades for energies. In the latter case, however, strict statistical analysis suggests experimental limitations might alter the power-law behavior.

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

Scale-invariant power-law distributions for acoustic emission signals are ubiquitous in several plastically deforming materials. However, power-law distributions for 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 have been no models that predict the power-law statistics for 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 a 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 with 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 have a maximum spread for the type C bands and decreasing with types B and A. We further show that the acoustic emission signals associated with Lüders-like band also exhibit a power-law distribution and multifractality.

Avalanches in strained amorphous solids: does inertia destroy critical behavior?

Simulations are used to determine the effect of inertia on athermal shear of amorphous two-dimensional solids. In the quasistatic limit, shear occurs through a series of rapid avalanches. The distribution of avalanches is analyzed using finite-size scaling with thousands to millions of disks. Inertia takes the system to a new underdamped universality class rather than driving the system away from criticality as previously thought. Scaling exponents are determined for the underdamped and overdamped limits and a critical damping that separates the two regimes. Systems are in the overdamped universality class even when most vibrational modes are underdamped.

Analysis of power-law exponents by maximum-likelihood maps

Maximum-likelihood exponent maps have been studied as a technique to increase the understanding and improve the fit of power-law exponents to experimental and numerical simulation data, especially when they exhibit both upper and lower cutoffs. The use of the technique is tested by analyzing seismological data, acoustic emission data, and avalanches in numerical simulations of the three-dimensional random field Ising model. In the different examples we discuss the nature of the deviations observed in the exponent maps and some relevant conclusions are drawn for the physics behind each phenomenon.

Acoustic emission and shape memory effect in the martensitic transformation

Acoustic emission signals are known to exhibit a high degree of reproducibility in time and show correlations with the growth and shrinkage of martensite domains when athermal martensites are subjected to repeated thermal cycling in a restricted temperature range. We show that a recently introduced two dimensional model for the martensitic transformation mimics these features. We also show that these features are related to the shape memory effect where near full reversal of morphological features are seen under these thermal cycling conditions.

Power-law statistics for avalanches in a martensitic transformation

We devise a two-dimensional model that mimics the recently observed power-law distributions for the amplitudes and durations of the acoustic emission signals observed during martensitic transformation [Vives et al., Phys. Rev. Lett. 72, 1694 (1994)]. We include a threshold mechanism, long-range interaction between the transformed domains, inertial effects, and dissipation arising due to the motion of the interface. The model exhibits thermal hysteresis and, more importantly, it shows that the energy is released in the form of avalanches with power-law distributions for their amplitudes and durations. Computer simulations also reveal morphological features similar to those observed in real systems.