Nontrivial scaling exponents of dislocation avalanches in microplasticity

Crystal plasticity causes structural fluctuations that can be scale-free and therefore admit power-law distributions. Numerous experiments, modeling, and theory have reported a scaling exponent that is in good agreement with mean-field predictions or a jamming-unjamming scenario. Via experiments on pure single crystals, we show here that the scaling exponent of a stress-integrated distribution for dislocation-avalanche sizes is nontrivial and can be in agreement with both models by admitting values between 1.0 and 2.3. This range is dictated by the structure and orientation of the deforming crystal, as long as the applied rate is below a critical value. For the highest symmetry tested, plastic strain can drive a change from truncated power-law scaling to pure exponential scaling. These findings show how the same crystal may yield different scaling exponents depending on intrinsic and extrinsic factors.

Figure 1

(a) Probability density distribution $P_{\mathrm{int}}\left(S\right)$ for Au microcrystals of various orientations. The full lines are truncated power-law fits obtained from MLE analysis. The inset in (a) shows the resolved shear stress as a function of resolved shear strain for different orientations of Nb. Each curve is an average of 7–12 stress-strain curves. (b) $C_{\mathrm{int}}\left(S\right)$ constructed from (a) with corresponding truncated power-law fits for differently oriented Au- and Nb microcrystals. In the case of $\mathrm{Nb}\langle 001\rangle$ for $\gamma >0.03$, an exponential distribution fits the data best. ${\dot{u}}_{\mathrm{Au}}=60$ nm/s and ${\dot{u}}_{\mathrm{Nb}}=0.6$ nm/s.

Figure 2

$C_{\mathrm{int}}\left(S\right)$ for $\mathrm{Nb}\langle 011\rangle$ (a) and $\mathrm{Au}\langle 111\rangle$ (b) as a function of applied displacement rate $\dot{u}$. Above a critical rate, ${\dot{u}}_{\mathrm{crit}}$, the scaling exponent depends on $\dot{u}$. Full lines are truncated power-law fits.

Figure 3

Avalanche peak velocity as a function of avalanche size for Au and Nb of various orientations, and cold-rolled $\mathrm{Au}\langle 011\rangle$ and $\mathrm{Nb}\langle 011\rangle$. All data were obtained at ${\dot{u}}_{\mathrm{crit}}$.

Figure 4

$C_{\mathrm{int}}\left(S\right)$ for $\mathrm{Au}\langle 111\rangle$ and $\mathrm{Nb}\langle 011\rangle$ after cold rolling, revealing identical scaling exponents, but increasing dominance of the exponential truncation. All data were obtained at ${\dot{u}}_{\mathrm{crit}}$.