Slip statistics of dislocation avalanches under different loading modes

Slowly compressed microcrystals deform via intermittent slip events, observed as displacement jumps or stress drops. Experiments often use one of two loading modes: an increasing applied stress (stress driven, soft), or a constant strain rate (strain driven, hard). In this work we experimentally test the influence of the deformation loading conditions on the scaling behavior of slip events. It is found that these common deformation modes strongly affect time series properties, but not the scaling behavior of the slip statistics when analyzed with a mean-field model. With increasing plastic strain, the slip events are found to be smaller and more frequent when strain driven, and the slip-size distributions obtained for both drives collapse onto the same scaling function with the same exponents. The experimental results agree with the predictions of the used mean-field model, linking the slip behavior under different loading modes.

Figure 1

(a) Force-displacement curves for two 1-μm Au⟨001⟩ microcrystals deformed with different loading conditions (0.5 nm/s for strain driven, and 0.4μN/s for stress driven). The inset in (a) shows the correlation between slip-induced force-drop magnitude, $\Delta F$, and slip-size magnitude, $S$. Linear fits are displayed by dashed lines. Close-up views on a slip event during stress-driven compression (b) and strain-driven compression (c) demonstrate the different slip dynamics in terms of $\Delta F$.

Figure 2

Stress-integrated complementary cumulative distributions $C_{\mathrm{int}}(S,F_{\max }$) for the 1-μm-sized crystals. The slope of −1 is the predicted exponent for $C_{\mathrm{int}}(S,F_{\max })$. The red curves are from stress-driven experiments, and the blue curves are from strain-driven experiments. The shift to the right of the stress-driven experiments results from the fact that stress-driven conditions produce effectively larger slips.

Figure 3

Complementary cumulative avalanche size distributions from quasistatic compressions of 3-μm Au microcrystals. The colors correspond to different stress bins with different values for the average avalanche size ($\langle S\rangle$); the insets show scaling collapses according to Eq. (3), using the mean-field exponents (a) for strain-driven compression at 0.4 nm/s, (b) for stress-driven compression at 0.3 μN/s, (c) scaling collapse for strain driven (blue circles) and stress driven (red triangles). The black curve corresponds to the mean-field scaling function.

Figure 4

Force versus displacement for typical experiments on 3-μm-diameter Au crystals (a) for strain-driven compression at 0.4 nm/s, (b) for stress-driven compression at 0.3 μN/s. The histograms represent the slip frequency, which is the number of avalanche events within each force bin. The increase in the slip frequency with stress is more pronounced for strain-driven than for stress-driven compressions. In the strain-driven conditions the slip frequency grows exponentially with force as predicted by the model. The upper $x$ axes indicate the number of events per stress bin.

Figure 5

Plastic part of the force-displacement data for all-3-μm microcrystals deformed in both strain-driven [0.4 nm/s, Fig. 5] and stress-driven [0.3 μN/s, Fig. 5] steering mode. The alternating colored parts of the curves represent different displacement bins that are later grouped according to their corresponding $\langle S\rangle$ values into different $\langle S\rangle$ bins. Large gaps in the stress-driven curves in Fig. 5 are due to large slip events during plastic deformation.