Statistical aspects of microplasticity: experiments, discrete dislocation simulations and stochastic continuum models

Abstract

The plastic deformation properties of microscale and nanoscale specimens differ from those of their macroscopic counterparts as the discrete nature of the elementary processes governing plastic flow becomes directly visible. In such specimens, details of the initial defect microstructure may exert a strong influence on the recorded deformation behaviour, which accordingly exhibits significant scatter even amongst specimens that share an identical preparation history. The plasticity of microsamples appears as a sequence of spatially and temporally localised events and not as the smooth and continuous flow process envisaged by classical continuum elastoplasticity. These observations pose a significant challenge to constitutive modelling. In this feature article, we discuss the statistics of fluctuations in microscale and nanoscale plasticity and discuss the implications for computational modelling of plastic deformation processes on microscale and nanoscales. We propose a new type of constitutive models that combine a classical continuum description of the elastic problem with a stochastic description of the dynamics of plastic flow.

Origin of scale-free intermittency in structural first-order phase transitions

“…From Eq. (19) we then conclude that R (1) MA (r|τ ) is negligible. This means that during cooling runs elements do not become unstable with respect to the inverse transition from martensite to austenite.…”

“…shape memory alloys, in applications [14,15]. The study of intermittency in such systems is important because the rearrangements of microstructural morphologies associated with avalanches [16] can perilously interfere with material and structural response at sub-micron scale preventing reliable control of the pseudo-plastic deformation [17][18][19].Avalanche dynamics with power-law statistics [20, 21] is an inherent feature of a broad variety of natural systems from neural networks [22] and animal herds [23] to tectonic faults [24] and stellar flares [25]. To explain the mechanism responsible for scale-free regimes in such systems, a number of general paradigms have been proposed, including implicit external tuning [26,27], the involvement of nonlocal restoring fields [28,29], the inherent complexity of the quenched energy landscapes [30], and the multiplicative structure of the endogenous noise [31].Controversy surrounds, in particular, the scale-free intermittent response of solid materials undergoing firstorder phase transitions.…”

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

“…Recent investigations of plastic deformation of microscale materials reveal that the stress-strain relationship is not smooth, and that plastic strain is released in intermittent "bursts" [1][2][3][4] . Because of the generality of this behavior and similarity with many branches of statistical mechanics, this observation has quickly become a topic that continues to receive considerable experimental and theoretical attention [5][6][7][8][9][10] . Moreover, and from a purely technical point of view, such strain burst behavior makes it difficult to control microscale plastic forming, and may even induce catastrophic collapse of microdevices.…”

Plate-like precipitate effects on plasticity of Al-Cu alloys at micrometer to sub-micrometer scales

“…These experiments demonstrated that diminishing the external length scale intensifies fluctuations (higher degree of wildness, ), shifting the collective dislocation dynamics towards criticality, with a progressively smaller exponent for the power law-tailed distribution of burst sizes X, ( )~ . From the engineering viewpoint, the external size related plastic fluctuations are unwelcome due to their unpredictable nature and the possibility for large avalanches to span the whole system size [19,34]. Giving a practical example, the mass production of metallic patterns with high resolution and quality (e.g., ultra-smooth surfaces) represents a substantial challenge, partly limited by undesired morphological fluctuations resulting from stochastic dislocation avalanches [35].…”