Experimental Evidence of Accelerated Seismic Release without Critical Failure in Acoustic Emissions of Compressed Nanoporous Materials

The total energy of acoustic emission (AE) events in externally stressed materials diverges when approaching macroscopic failure. Numerical and conceptual models explain this accelerated seismic release (ASR) as the approach to a critical point that coincides with ultimate failure. Here, we report ASR during soft uniaxial compression of three silica-based (${\mathrm{SiO}}_2$) nanoporous materials. Instead of a singular critical point, the distribution of AE energies is stationary, and variations in the activity rate are sufficient to explain the presence of multiple periods of ASR leading to distinct brittle failure events. We propose that critical failure is suppressed in the AE statistics by mechanisms of transient hardening. Some of the critical exponents estimated from the experiments are compatible with mean field models, while others are still open to interpretation in terms of the solution of frictional and fracture avalanche models.

Figure 1

Histograms (color-coded) of AE events in the duration-energy ($D_{\mathrm{AE}}$, $E_{\mathrm{AE}}$) space. Blue dots: Conditional averages $⟨D_{\mathrm{AE}}⟩(E_{\mathrm{AE}})$. Green triangles: Numerical solutions of $E_{\mathrm{AE}}(D_{\mathrm{AE}})$ consistent with Eq. (4) (see main text for details), with $\gamma =3.0(4)$ for V32, $\gamma =3.4(4)$ for G26, and $\gamma =3.2(4)$ for SR2.

Figure 2

Mechanical response and AE sequence for experiment on Vycor (V32). (a) Cumulative number of events $N$ (dark red) and height evolution $h$ (light green) in experiment V32 as a function of uniaxial pressure $P$. The size of the circles depends on the AE energy (size $\sim E_{\mathrm{AE}}^{0.25}$). (b) Mean AE activity rate $dN/dt$ (dark red histograms) and strain rate $dh/dt$ (light green histograms) in intervals of $\mathrm{\Delta }P=100\mathrm{kPa}$. Vertical gray lines: $P_c^k$.

Figure 3

Statistical variations with distance to strain drops $P_c^k$. The color scheme identifies the index $k$. (a)–(c) Exponent $\widehat{ϵ}(f_k)$ from Eq. (2) estimated within the interval (1.0–1000 aJ). (d)–(f) Mean energy per signal $⟨E_{\mathrm{AE}}⟩(f_k)$; expected mean value according to $D\mathbf{(}E;E_m,E_c,\widehat{ϵ}(f_k)\mathbf{)}$ (triangles) with $E_c={10}^6\mathrm{aJ}$ ($10^4\mathrm{aJ}$ for SR2); expected value from the global exponent (gray line). (g)–(i) Rate of AE energy $d{E}_{\mathrm{AE}}/dt$. Thin gray line: Exponent $m$ fitted by least squares within ${10}^{-6}<f_k<{10}^{-1}$. Thick gray line: A correction as expected by critical failure $D\mathbf{(}E;E_m,E_m{f}_k^{\beta (\widehat{ϵ},\widehat{m})},\widehat{ϵ}(f_k)\mathbf{)}$ with global $\widehat{ϵ}$ and estimated $\widehat{m}$. The $f_k$ intervals of evaluation grow exponentially and have an imposed minimum size of $n=100$ signals ($n=50$ for G26). $X$-error bars: Integration interval. $Y$-error bars: 90% bootstrap interval in (d)–(i) and likelihood standard deviation in (d)–(f). Hard lower threshold imposed at $E_m=1.0\mathrm{aJ}$.