A stochastic crystal plasticity model with size-dependent and intermittent strain bursts characteristics at micron scale

Abstract

Please cite this article as: Lin, P., Liu, Z., Cui, Y., Zhuang, Z., A stochastic crystal plasticity model with sizedependent and intermittent strain bursts characteristics at micron scale, International Journal of Solids and Structures (2015), doi: http://dx.Abstract: Size effect and strain bursts are widely observed in the plastic deformation of micron-sized single crystals. In this paper, a stochastic crystal plasticity model is established by importing these two dislocation-source-controlled characteristics into the conventional crystal plasticity theory. The plastic strain is composed of a series of strain bursts instead of formulated as a continuous function. The size of each strain burst follows a power-law distribution function and the rate of strain bursts is determined by a constitutive equation. On the other hand, size effect is accounted for by dislocation-source-controlled slip resistance. The effective dislocation source length is derived as a function of sample size by a statistical analysis and experimental data. Uniaxial compression of single crystal Ni micron-sized pillars, with diameters ranging from 5 to 40 µm, are investigated by the model. The results show that this model well captures the significant features of plastic deformation at micron scale: 1) Strain bursts are strongly affected by sample size. For large pillars (e.g. 40 µm), the stress-strain curves are almost continuous and predictable. But as sample size decreases, strain bursts become more and more evident and the stress-strain curves are unpredictable. 2)The yield strength increases significantly as sample size decreases. For diameter larger than 40 µm, the strengthening effect still exists but is not evident anymore. All these results match well with the experimental observations.

Influence of loading control on strain bursts and dislocation avalanches at the nanometer and micrometer scale

“…Various parameters have been used, as summarized in Table III, to quantify the statistics of strain bursts. The plastic strain increment produced by a dislocation avalanche has been selected in references 3,17 , because the related results can give information to develop stochastic crystal plasticity models 37 . Other investigations used the displacement magnitude and stress drop magnitude corresponding to each burst 2,38 , because they are easy to be experimentally measured.…”

Implementation of annihilation and junction reactions in vector density-based continuum dislocation dynamics

“…After all dislocations satisfying the collinear annihilation criteria have annihilated, loop expansion dominates the density evolution again (red line). The latter stage is sensitive to the critical angle for collinear annihilation as depicted by the green line, see equation (8).…”

Low‐temperature failure mechanism of [001] niobium micropillars under uniaxial tension

“…Flow strength can increase readily, up to a factor of 10, by reducing the sample dimension down to the micrometer scale [11,12,13]. Additionally, jerky plastic flow is observed due to intermittent source operation of dislocations [14,15,16,17]. More surprisingly, dislocation multiplication can be completely suppressed if the sample volume is sufficiently small enough, for instance, a sub-micrometer dimension [18,19].…”