Avalanche statistics and the intermittent-to-smooth transition in microplasticity

Plastic flow at small scales is generally observed to be intermittent, whereas the stress-strain behavior of bulk crystals is mostly smooth. Here we find that when the external deformation rate of small-scale crystals approaches the speed of the crystallographic slip velocity, an intermittent-to-smooth transition of plastic flow is observed. By defining a rate-dependent intermittency parameter, this phenomenon can be captured with a power law covering 5.5 orders of magnitude for Au and Nb micron-sized single crystals with experiments and via simulations for Nb crystals. Our results indicate that the transition to smooth flow is driven by a gradual truncation of the underlying truncated power law that describes the intermittently evolving system. This is caused by a competition of internal and external rates, which aligns with the well-known transitions from serrated to nonserrated flow in metallic glasses or materials with dynamic strain aging.

Figure 1

(a) Engineering stress-strain curves for Nb⟨011⟩ crystals obtained at $\dot{u}=6$ and $\dot{u}=6000$ nm/s. (b) Stress-integrated complementary cumulative distribution, $C\left(S\right),$ for all tested rates.

Figure 2

(a) Intermittency parameter, $IP$, for Nb⟨011⟩ and Au⟨001⟩ obtained from experiments (left ordinate and lower abscissa) and for Nb⟨001⟩ obtained from DDD simulations (right ordinate and upper abscissa). (b)–(e) Scanning electron microscopy images for micron-sized Nb⟨011⟩ crystals deformed at $\dot{u}=0.06,6,600$, and $30000$ nm/s.

Figure 3

Stress-strain curves obtained from DDD simulations for 2-μm and 500-nm large Nb⟨001⟩ crystals at 10 and $1000{\mathrm{s}}^{-1}$. Right-hand $y$ axis indicates the plastic strain rate and the horizontal dashed line is the applied strain rate.

Figure 4

(a)–(d) Microstructures at some specific plastic strains ${\varepsilon }^{\mathrm{p}}$ as indicated. Solid lines in different colors represent dislocations with different Burgers vectors. The darkness of the purple shaded regions is proportional to the local plastic strain. The yellow arrows in (a) and (c) indicate the bowing direction of dislocation sources.