Microscopic defect dynamics during a brittle-to-ductile transition

Abstract

Deformation of all materials necessitates the collective propagation of various microscopic defects. On Earth, fracturing gives way to crystal-plastic deformation with increasing depth resulting in a "brittle-to-ductile" transition (BDT) region that is key for estimating the integrated strength of tectonic plates, constraining the earthquake cycle, and utilizing deep geothermal resources. Here, we show that the crossing of a BDT in marble during deformation experiments in the laboratory is accompanied by systematic increase in the frequency of acoustic emissions suggesting a profound change in the mean size and propagation velocity of the active defects. We further identify dominant classes of emitted waveforms using unsupervised learning methods and show that their relative activity systematically changes as the rocks cross the brittle-ductile transition. As pressure increases, long-period signals are suppressed and short-period signals become dominant. At higher pressures, signals frequently come in avalanche-like patterns. We propose that these classes of waveforms correlate with individual dominant defect types. Complex mixed-mode events indicate that interactions between the defects are common over the whole pressure range, in agreement with postmortem microstructural observations. Our measurements provide unique, real-time data of microscale dynamics over a broad range of pressures (10 to 200 MPa) and can inform micromechanical models for semi-brittle deformation.

Keywords: brittle–ductile transitions; defect dynamics; rock deformation; ultrasound probes.

Fig. 1.

Mechanical and acoustic data. (A and B) Cumulative AE hits coplotted with stress–strain curves and v_p evolution for samples deformed under confining pressures of 10 and 200 MPa. Size of the circles indicates the maximum local amplitude of the AEs. The color of individual circles as well as the color bar by AE count visualizes the occurrence of AE classes with respect to the mechanical data. Only classes with >1% of AEs are shown. (C and D) Clustering of data reveals characteristic waveforms. Note the decrease in duration and increase in frequency of the AEs as pressure increases (triggered time window x axis shrinks from 70 µs to 5 µs).

Fig. 2.

Hierarchical clustering of acoustic data. (A) Representative waveforms for 5 global clusters further grouped into 3 types. (B) Occurrence of individual clusters at different confining pressures. The red dashed line indicates the location of the BDT in our experiments (C) Distance matrix and cluster dendrogram of all waveforms. The 1:1 diagonal is a correlation of a wave with itself. Several clusters of waveforms that occur under common conditions emerge as squares in the diagram. Red numbers in circles show characteristic clusters in the dendrogram; red squares highlight these clusters in the distance matrix. Each cluster can be further refined by higher-order differences between individual waveforms that are visualized as smaller squares within a larger cluster square and progressively finer branching in the dendrogram. Δσ–differential stress, Pc–confining pressure, ε–strain, Vp–longitudinal wave velocity.

Fig. 3.

Frequency Evolution of AEs and inferred defect size–propagation velocity relationships. (A) Cumulative distribution of frequencies indicates a progressive increase in mean frequency of acoustic waves with increasing pressure. The black dashed line shows the typical upper sensitivity limit of AE recordings in conventional rock mechanics experiments. (B) Observed frequency and inferred defect size–front propagation velocity relationship based on the Savage source model. Propagation velocity increases, and/or the mean source size decreases, with increasing confining pressure. Vs – transverse wave velocity. (C) Mean stress, $\begin{array}{ccc}\left({\sigma }_1+{\sigma }_2+{\sigma }_3\right)\hfill & /& 3\end{array}$ vs. spectral power at frequency. Note the progressive shift to higher frequencies with increasing mean stress. The red dashed line shows the location of the BDT in our experiments. (D) Flow of clusters in amplitude, A, propagation velocity, $v_f$ and effective source dimension, $d_{\mathit{source}}$ parameter space. The measured amplitudes and frequencies are used to infer effective source size and mean front velocity. The observed inflection point hints at the transition to a regime where the spread of clusters (in this space) becomes smaller, i.e., the characteristics of energy dissipation sources become more homogenous.

Fig. 4.

Summary of observations. (A–C) The final appearance of the sample after deformation at a fixed pressure. At higher pressures, the deformation is dispersed through the sample and no faults formed. (D–F). Characteristic microstructures. Note how defect density increases and crystal plastic defects become more abundant with increasing mean stress. Gray–grain boundaries, red–crystal plastic defects (slip lines and twins), black–brittle defects (microcracks and pores). (G) Schematic of microstructural processes occurring during deformation and their postulated ultrasound signatures (H–J).