Probing Microplasticity in Small-Scale FCC Crystals via Dynamic Mechanical Analysis

In small-scale metallic systems, collective dislocation activity has been correlated with size effects in strength and with a steplike plastic response under uniaxial compression and tension. Yielding and plastic flow in these samples is often accompanied by the emergence of multiple dislocation avalanches. Dislocations might be active preyield, but their activity typically cannot be discerned because of the inherent instrumental noise in detecting equipment. We apply alternate current load perturbations via dynamic mechanical analysis during quasistatic uniaxial compression experiments on single crystalline Cu nanopillars with diameters of 500 nm and compute dynamic moduli at frequencies 0.1, 0.3, 1, and 10 Hz under progressively higher static loads until yielding. By tracking the collective aspects of the oscillatory stress-strain-time series in multiple samples, we observe an evolving dissipative component of the dislocation network response that signifies the transition from elastic behavior to dislocation avalanches in the globally preyield regime. We postulate that microplasticity, which is associated with the combination of dislocation avalanches and slow viscoplastic relaxations, is the cause of the dependency of dynamic modulus on the driving rate and the quasistatic stress. We construct a continuum mesoscopic dislocation dynamics model to compute the frequency response of stress over strain and obtain a consistent agreement with experimental observations. The results of our experiments and simulations present a pathway to discern and quantify correlated dislocation activity in the preyield regime of deforming crystals.

Figure 1

Dynamic mechanical analysis on Cu nanopillars. (a) Engineering stress vs strain during DMA measurements on a Cu sample at a frequency of 0.3 Hz; different colors separate data taken at different steps of stress-oscillation segments. The inset shows raw load vs displacement as a function of time in the preyield regime. The overlaying different color curves are sinusoidal fits for each data set of oscillation segments, using Eqs. (1a) and (1b). (b) SEM images of an as-fabricated (pre-) and compressed (post-) $\sim 500\mathrm{nm}$ diameter Cu pillar with a nominal aspect ratio of $3:1$.

Figure 2

Dynamic modulus vs stress. (a) The experimental DMA results on copper and fused silica (FS) 500 nm pillars. The amplitude $A$ and phase $\varphi$ of the dynamic modulus values are statistically analyzed from six samples for driving varying from 0.1 Hz to 10 Hz, both plotted versus the global stress, around which the oscillations were applied. This plot demonstrates that the dynamic modulus is not constant as the quasistatic load approaches the yield point, and the deviation gets larger with slower driving. (b) DMA results from the mesoscopic dislocation dynamics simulation.

Figure 3

Scaling analysis of the normalized strain-rate amplitude. (a) The normalized strain rate amplitude scaling over driving frequency analysis [28] using experimental DMA data and (b) simulation DMA data. The figures show explicitly the fitting for scaling parameter $\kappa$ using Eq. (6) at different quasistatic stress levels. The inset presents the measured $\kappa$ as a function of normalized stress.