Concurrent tracking of strain and noise bursts at ferroelastic phase fronts

The study investigates how martensitic phase transformations in ferroelastic materials proceed through intermittent, bursty dynamics and how these relate to acoustic emission. Martensitic transformations are first-order, diffusionless transitions that generate complex microstructures and exhibit strain avalanches with associated AE bursts. These intermittent events affect functional performance (e.g., elastocaloric refrigeration, energy harvesting, sensing/actuation), yet direct visualization and correlation of strain and AE at relevant scales have been challenging. The authors aim to concurrently monitor full-field strain evolution and AE during a stress-induced martensitic transformation in a CuZnAl shape-memory alloy, to uncover detailed interface dynamics (formation, propagation, jamming, arrest) and quantify correlations between strain bursts and AE in space and time.

Prior work established the intermittent (avalanche) character of martensitic transformations with AE bursts and strain avalanches, and reported scale-free statistics for these events. AE techniques offer excellent time resolution and have been used to image martensitic dynamics and quantify avalanche energies and critical exponents. Full-field optical methods like the grid method have separately captured strain intermittency in SMAs. However, simultaneous, spatially resolved strain imaging and AE localization had not been implemented together. Previous studies in SMAs reported AE energy power-law exponents within a similar range (~1.8). The present work bridges these approaches by combining full-field strain mapping with AE localization and energy measurement to directly correlate both signals during transformation.

Material and specimen: Single-crystal Cu68.13Zn15.74Al16.13 (at.%) grown by Bridgman method. Geometry: thin elongated parallelepiped with cylindrical heads; central part approximately 3.85 × 35 × 1.12 mm. Vertical y-axis along specimen length, near [001] direction of bcc austenite. Heat treatment ensured ordered state with minimal internal stresses and low vacancy concentration. The specimen was cycled (>20 loading-unloading cycles) to reach a stationary transformation path. Mechanical loading: Gravity-based uniaxial loading device providing strictly monotonic low-rate load. Test at room temperature 25.7 ± 0.5 °C. Preload: 81.92 MPa; then constant loading rate 109.7 Pa/s up to 88.97 MPa. Total duration ~64,200 s (~8 h). Transformation plateau nearly horizontal, duration ~27 min; loading stopped shortly after elastic response resumed to preserve specimen. Grid method (GM) for strain mapping: Bidimensional grid (pitch 0.2 mm) printed (50,800 dpi) on polymeric sheet, transferred with white E504 Epotecny adhesive; grid slightly rotated to avoid aliasing. Imaging: Sensicam QE camera, 12-bit, 1040 × 1376 pixels, 105 mm Tokina lens; shutter 10 ms; ~17 Hz acquisition; pixel size on sample ~0.0274 mm (≈7 pixels per grid pitch). Direct-current LED illumination. Processing via Localised Spectrum Analysis with Gaussian window (7-pixel std). Motion compensation to remove local grid defects. Spatial resolution for strain ~42 pixels (~1.15 mm). Strain components obtained: in-plane εxx, εyy, εxy and in-plane rotation ω. For analysis focused on εyy due to 1D AE localization along y and higher SNR. Strain-rate computation: Differences between consecutive strain maps separated by 64 images (~3.8 s), divided by 3.8 s to get rates in s^-1. Plateau considered from t=62,400 s to 64,000 s (duration 1,600 s), yielding ~420 strain-increment maps. Noise characterization: using 15 consecutive y-profiles during a still period with x-averaging over N=50 pixels gave noise standard deviation 6.70 × 10^-5 s^-1; threshold set at 4.5× this value ≈ 3 × 10^-4 s^-1 for reliable strain-rate burst detection. AE detection and localization: Two Micro-80 piezoelectric transducers (Europhysical Acoustics), flat response 0.2–1 MHz, acoustically coupled to upper and lower grips on the face opposite the camera. Preamplification 60 dB; acquisition via two-channel Europhysical Acoustics PCI2 at 40 MHz, 18-bit A/D. Hit definition per channel: start at t0 when |V(t)| crosses threshold 21 dB (≈11.22 mV preamplified), end at t_fin when |V(t)| remains below threshold until t_fin + 100 µs. Amplitude defined from peak in first 100 µs: A(dB) = 20 log10(Vmax/1 µV) − 60; thus 60 dB corresponds to 1 V peak at preamplifier (1 mV at transducer). Hit energy E = ∫ V(t)^2 dt. Recorded hits: N1 = 108,471 (upper), N2 = 60,357 (lower); asymmetry due to coupling differences. 1D AE event localization along y: Events defined from consecutive hits in opposite channels within tx = 0.038 ms; location y = 0.5 L (1 − Δt/L) with L = 35 mm (length of central region) and Δt the inter-channel delay. Located events: 37,540 along y; of these, 26,266 within the 25-mm averaging strip used for x-averaging. Source energy estimate for located events: E_source ≈ sqrt(E1 E2) to approximately correct for attenuation (assumed constant exponential damping). Source amplitude A ≈ (A1 + A2)/2. Event extraction and pairing: 1D strain events defined on each y-profile of εyy rate where contiguous y-intervals exceed the threshold 3×10^-4 s^-1. For each event, extracted interval size, epicenter (y of maximum εyy rate), and magnitude (sum of squared εyy rate over the interval). Identified approximately 1,058–1,100 1D strain bursts on the plateau. AE hits binned in time (3.8 s) and space (0.7 mm) for density maps; strain-burst epicenters superposed on AE density for correlation analyses.

- The stress-induced austenite-to-martensite transformation predominantly proceeded via two diverging, triangular austenite–martensite fronts propagating along the specimen length. Martensite nucleated at a localized high-stress fluctuation site. - Strain evolution was jerky: average εyy evolved smoothly, but the average strain-rate showed intermittent spikes, strongly correlated with AE hit density during the plateau. - Quantitative correlation at global scale (3.8 s bins): Pearson correlation ≈ -0.90; Spearman ≈ -0.85 between normalized strain-rate and AE hit density (negative sign due to normalization conventions). Decoupling occurred when a phase front exited the imaged grid region near the end of the test. - Located AE events: ~37,540 along y (26,266 within the central 25 mm). Total recorded AE hits: 108,471 (upper transducer) and 60,357 (lower transducer). - Strain events: ~1,058–1,100 1D strain avalanches identified on the plateau using a strain-rate threshold of ~3 × 10^-4 s^-1 (time step 3.8 s). Plateau duration analyzed: 1,600 s (from t=62,400 to 64,000 s). - Spatial-temporal maps showed two high-activity bands corresponding to the advancing phase fronts; additional smaller events occurred away from fronts, especially within the martensitic region. - Cross-technique concordance at local scale: strain-burst epicenters and magnitudes align with AE event density in space-time; inset correlation (paired along y at each t) showed Pearson ≈ -0.42; Spearman ≈ -0.79 for normalized magnitudes/energies. - Statistical distributions exhibited heavy tails: AE avalanche energy and strain-avalanche magnitude follow power-law-like behavior with exponent ~1.8 (guideline line), consistent with prior SMA AE exponents. - Observed detailed dynamical features: low-activity intervals, pauses suggestive of strong pinning, and rapid sequences of large bursts; evidence of interface jamming and arrest at pinning sites.

By concurrently applying full-field strain mapping (grid method) and AE localization/energy measurement, the study directly connected local strain avalanches to AE bursts in space and time during a reversible martensitic transformation. The strong correlations at both global and local scales confirm that the same transformational mechanisms underlie both signals. Space-time activity maps elucidated the dynamics of two moving interfaces (triangle-shaped fronts), capturing their formation, propagation, intermittent advancement, jamming, and arrest at pinning points. The identification of heavy-tailed statistics (power-law-like with exponent ~1.8) aligns with the view of scale-free avalanche dynamics in ferroelastic transitions. These insights advance the understanding of how microstructural evolution under slow, steady forcing gives rise to bursty behavior, informing the design and reliability assessment of SMA-based functional devices where such intermittency impacts performance and stability.

The work demonstrates a combined experimental methodology that synchronizes full-field strain-burst detection with AE-based localization and energy quantification to track ferroelastic transformation dynamics. In a CuZnAl single-crystal, the approach revealed highly correlated, intermittent strain and AE activity associated with the motion of two triangular phase fronts and highlighted interface jamming and pinning. Statistical analyses confirmed scale-free behavior consistent with previous reports. The methodology is broadly applicable to varied specimen geometries and loading conditions and can be extended to study analogous bursty phenomena in plasticity, fracture, metallic glasses, and porous media. Future research could refine temporal resolution of strain-rate measurements, enable full 2D/3D AE localization, investigate different materials and microstructural compatibilities, and explore the effects of loading rate, temperature, and sample geometry on avalanche statistics and interface dynamics.

- Temporal resolution mismatch: strain-rate maps used a 3.8 s time step, much larger than typical AE avalanche durations, so each detected strain event aggregates many microscale bursts. - Spatial coverage and 1D reductions: strain mapping was limited to the imaged grid area on one surface and x-averaged to a central strip for 1D analysis; the 1D AE localization was along the y-axis only. These reductions may overlook lateral heterogeneity and out-of-plane sources. - Grid exit effect: near the test end, a phase front moved out of the imaged grid region, causing decoupling between ongoing AE activity and strain detection. - Transducer coupling asymmetry led to differing hit counts in the two channels and could influence localization and energy estimation, despite attenuation corrections. - The study focused on a single material/composition/specimen geometry and near-adiabatic, very low-rate loading; generalization to other conditions may require additional validation.