Translated Abstract
The extreme miniaturization of metallic crystals in microelectromechanical systems (MEMS) and microelectronic devices calls for deeper insights into their non-conventional mechanical behaviors at small scales. Distinct from their bulk counterparts, micron/sub-micron metallic samples exhibit external-size enhanced yield strength and strain hardening rate, however, corrupted by intermittent strain bursts as a result of dislocation avalanches, which compromises the forming processes and endangers the structural stability. Despite many observations showing that alloying can suppress plastic fluctuations, this effect has not been quantified in terms of avalanche statistics. Consequently, the theoretical framework, as well as the possible correlations between the typical features of micro-plasticity, have not been established yet, thus imposing severe restrictions on utilizing such strategy in practice, particularly in the structural analysis and design of MEMS. Focusing on this challenge, the micro-pillar compression tests were performed on five different model Al alloys in present study, which disclosed the fundamental aspects underlying the effects of external size and alloying on micro-plasticity. A theoretical framework based on a mean-field model was also established. The main conclusions are listed below.
The correlation between the material strengths at macro and micro/sub-micro scales was analysed based on the tests of micro-pillar compression and bulk tension. The yield strength of Al alloy micro-pillar was found to be a linear superposition of the pinning strength of quenched disorder and the activation stress of single-armed dislocation source. This simple relation prevails in various kinds of Al alloys containing precipitate of different size (from micron to nanometer), morphology (sphere or plate-like) and interaction mechanism with dislocation (by-passing or shearing). This finding can promote the usage of the micro-pillar compression methodology in bulk alloy, with a special advantage of extracting the strength of a particular structure or phase from average property.
The compression tests were performed on the micro-pillars of Al alloy strengthening by nano-size disorders. The results show that the plastic flow proceeds through a combination of two fundamentally different manners, i.e., the mild plasticity with Gaussian distributed fluctuations, and the wild plasticity with power-law distributed fluctuations. Based on this observation, an objective data mining procedure was proposed, giving not only the power-law exponent of fluctuation distribution ??, but also the fraction of plastic deformation accommodated through power-law distributed fluctuations ??. This quantification of plastic intermittency allows to make the following general conclusions. Diminishing the external length scale (miniaturization) intensifies fluctuations and contributes to criticality (?? → 1, ?? → 1.5), leading to wild plasticity with jerky deformation curve, on the contrary, enlarging the external size drives dislocation system towards equilibrium (?? → 0, ?? ≫ 1.5), thus leading to mild plasticity. Introducing quenched disorder shifts the transition from wild to mild plasticity towards smaller external length scales, as well as increases the power law exponent, hence lowering the probability of large dislocation avalanches. A single non-dimensional parameter ?? is constructed to unify the coupling effects of external size and quenched disorder (alloying) in all tested materials: wild plasticity dominates when ?? ＜ 5, while mild plasticity dominates when ?? ＞ 5. The correlation analysis shows that the dislocation-source exhaustion hardening, strain localization and wild plasticity are highly linked with each other, hitting towards their common origination, i.e., the lacking of dislocation short-range reactions.
A mean field model of intermittent plasticity was established by introducing the mean-free path of dislocation, external size, pinning strength and external stress into a stochastic equation of mobile dislocation density. The non-constant power-law exponent observed in experiments can be recovered, and the physical meaning of the controlling parameter ?? was deduced based on the dislocation theory. The model rationalizes the competition between external (size related) and internal (disorder related) length scales on plastic fluctuations in a semi-quantitative manner, and verifies that the size effects on strength and intermittent plasticity, which seem to be two independent phenomena, are tightly linked with each other.
The mechanical behaviors were investigated in Al-Cu alloy micro-pillars, where the plate-like θ′-Al2Cu precipitates have diameters commensurate with the external size. In the micro-pillar only a few times larger than precipitate, the dislocation source can be activated and then move inside the precipitate array before getting pinned. This breakdown of the mean-field pinning landscape weakens its taming effect on intermittency, but does not affect the strengthening of the precipitate. Over an intermediate range of sample sizes allowing the precipitates to cross the entire micro-pillar, an enhanced strain hardening and a sharp decrease of wildness were observed, in association with slip along non-close-packed planes {100}, identified for the first time in Al-alloys at room temperature. This novel slip mode is a result of the cross-slip of {111} matrix dislocation onto {100} θ′-Al2Cu/Al matrix coherent interface for the stress concentration at the tip of dislocation pile-up. Moreover, the ab-initio calculation shows that θ′- Al2Cu/Al matrix coherent interface can significantly lower the lattice fraction on {100} plane, thus promoting the slip along {100} interface. The in-situ compression tests demonstrated that the plastic intermittency can be stabilized effectively by using plate-like precipitates cutting the entire micro-pillar, suggesting a new approach to mitigate “smaller is wilder”effect in MEMS.
At last, this study identified a universal relation between the wildness ?? and the power-law exponent ??, irrelevant to the material microstructure, external size, and even the deformation mechanism. The distribution of dislocation avalanches is solely determined by the wildness, and vice versa. Our mean field model recovers this universal relation theoretically.
Translated Keyword
[Plasma resonance, Precious metal nanostructures, Sensitive sensing, SERS]
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