Michael D. Uchic

Scale-Free Intermittent Flow in Crystal Plasticity

Under stress, crystals irreversibly deform through complex dislocation processes that intermittently change the microscopic material shape through isolated slip events. These underlying processes can be revealed in the statistics of the discrete changes. Through ultraprecise nanoscale measurements on nickel microcrystals, we directly determined the size of discrete slip events. The sizes ranged over nearly three orders of magnitude and exhibited a shock-and-aftershock, earthquake-like behavior over time. Analysis of the events reveals power-law scaling between the number of events and their magnitude, or scale-free flow. We show that dislocated crystals are a model system for studying scale-free behavior as observed in many macroscopic systems. In analogy to plate tectonics, smooth macroscopic-scale crystalline glide arises from the spatial and time averages of disruptive earthquake-like events at the nanometer scale.

Estimating the strength of single-ended dislocation sources in micron-sized single crystals

Three-dimensional (3D) discrete dislocation dynamics simulations were used to calculate the effects of anisotropy of dislocation line tension (increasing Poissons ratio, ν) on the strength of single-ended dislocation sources in micron-sized volumes with free surfaces and to compare them with the strength of double-ended sources of equal length. Their plastic response was directly modelled within a 1 µm3 volume composed of a single crystal fcc metal. In general, double-ended sources are stronger than single-ended sources of an equal length and exhibit no significant effects from truncating the long-range elastic fields at this scale. The double-ended source strength increases with ν, exhibiting an increase of about 50% at ν = 0.38 (value for Ni) as compared to the value at ν = 0. Independent of dislocation line direction, for ν greater than 0.20, the strengths of single-ended sources depend upon the sense of the stress applied. The value for α in the expression for strength, τ = α(L)µb/L is shown to vary from 0.4 to 0.84 depending on the character of the dislocation and the direction of operation of the source at ν = 0.38 and L = 933b. By varying the lengths of the sources from 933 to 233b, it was shown that the scaling of the strength of single-ended and double-ended sources with their length both follow a ln(L/b)/(L/b) dependence. Surface image stresses are shown to have little effect on the critical stress of single-ended sources at a length of ∼250b or greater. This suggests that for 3D discrete dislocation dynamics simulations of the plastic deformation of micron-sized crystals in the size range 0.5–20 µm, image stresses making the surface traction-free can be neglected. The relationship between these findings and a recent statistical model for the hardening of small volumes is discussed.

Overview of experiments on microcrystal plasticity in FCC-derivative materials: selected challenges for modelling and simulation of plasticity

An important frontier in both metallurgy and mechanics is the development of a modelling framework that accurately represents length-scale effects and dislocation structure. Emerging mechanics formulations incorporate a length scale tied to distortion gradients aimed at modelling the effects from geometrically necessary dislocations (GND). However, recent experimental studies show important intrinsic size effects exist separately from an evolving GND structure at a mesoscopic scale. The present studies probed for intrinsic size effects at this scale using experimental methods that more closely approach the size scales accessible via discrete dislocation simulation (DDS) in 3d. Uniaxial compression tests of single crystals of pure Ni, Ni3Al alloys, Ni superalloys and fine grained polycrystalline Ni showed material-unique size-dependent responses. Notable among these are a range of strengths and clear intermittency of flow that reveals self-organization. Mechanistically self-consistent simulation of such results, by either discrete dislocation or continuum methods, stands as an unsolved challenge for emerging materials modelling approaches.

Quasi-periodic events in crystal plasticity and the self-organized avalanche oscillator

When external stresses in a system—physical, social or virtual—are relieved through impulsive events, it is natural to focus on the attributes of these avalanches. However, during the quiescent periods between them, stresses may be relieved through competing processes, such as slowly flowing water between earthquakes or thermally activated dislocation flow between plastic bursts in crystals. Such smooth responses can in turn have marked effects on the avalanche properties. Here we report an experimental investigation of slowly compressed nickel microcrystals, covering three orders of magnitude in nominal strain rate, in which we observe unconventional quasi-periodic avalanche bursts and higher critical exponents as the strain rate is decreased. Our experiments are faithfully reproduced by analytic and computational dislocation avalanche modelling that we have extended to incorporate dislocation relaxation, revealing the emergence of the self-organized avalanche oscillator: a novel critical state exhibiting oscillatory approaches towards a depinning critical point. This theory suggests that whenever avalanches compete with slow relaxation—in settings ranging from crystal microplasticity to earthquakes—dynamical quasi-periodic scale invariance ought to emerge.

Size effects in LiF micron-scale single crystals of low dislocation density

This study examines the size-dependent deformation response of pure LiF single crystals using microcompression testing. Microcrystals with an 〈001〉 orientation and sample diameter D ranging from 1 to 20 μm were fabricated by focused ion beam (FIB)-milling from bulk crystals having a low initial dislocation density. Both as-grown and γ-irradiated crystals were examined to characterize the effect of an increased point defect density on the size-affected plastic flow response. Similar to previously studied face-centered cubic (FCC)-derivative metals, both types of LiF microcrystals exhibit typical size-dependent plastic flow behavior: a dramatic size-dependent and statistically varying flow stress, atypically high strain hardening rates at small plastic strains, and fast intermittent strain bursts. The size-dependent strengthening obeys a power law, σ ∼ D − m , where m ≈ 0.8, and this rapid hardening results in engineering flow stresses of 650 MPa in 1-μm samples. The findings are evaluated against possible dislocation mechanisms that could be responsible for the observed size effects.

Strain rate sensitivity and activation volume of Cu/Ni metallic multilayer thin films measured via micropillar compression

Micropillar compression testing with repeated jumps in strain rate is used to circumvent inherent difficulties associated with nanoindentation and tensile testing of free-standing films. Application to sputtered 21 nm/21 nm Cu/Ni multilayer thin films with a cube-on-cube texture reveals an average strain rate sensitivity (m = 0.014) and activation volume (V = 17 b3), comparable to nanocrystalline face-centered cubic metals. Yet, m increases by ∼50% and V decreases by 70% with increasing strain, opposite to trends reported for nanotwinned Cu. The large, strain-dependent shifts in m and V are dependent on the underlying misfit dislocation structure of Cu/Ni interfaces.

Exploring specimen size effects in plastic deformation of Ni 3 (Al, Ta)

In this paper we present a mechanical test methodology to explore specimen size effects in Ni 3 Al, where the overall test sample dimensions artificially limit the volume for substructure evolution and hence the availability of jogs/kinks along individual dislocation lines. The test methodology consists of using Focused Ion Beam milling to micromachine cylindrical compression samples that have diameters ranging from 5 to 20 microns into the surface of a bulk sample, which is followed by nanoindentation using a flat-ended tip to measure the mechanical properties of the microsamples in uniaxial compression. The initial test results show that there is a strong increase in the flow stress with decreasing sample size, although misfit between the flat indenter tip and the top surface of the compression samples complicates complete interpretation of the mechanical test results at this time.

Serial Sectioning Methods for Generating 3D Characterization Data of Grain- and Precipitate-Scale Microstructures

This chapter provides an overview of the current state-of-the-art for experimental collection of microstructural data of grain assemblages and other features of similar scale in three dimensions (3D). The chapter focuses on the use of serial sectioning methods and associated instrumentation, as this is the most widely available and accessible technique for collecting such data for the foreseeable future. Specifically, the chapter describes the serial sectioning methodology in detail, focusing in particular on automated systems that can be used for such experiments, highlights possibilities for including crystallographic and chemical data, provides a concise discussion of the post-experiment handling of the data, and identifies current shortcomings and future development needs for this field.

Atomistic simulations of cross-slip nucleation at screw dislocation intersections in face-centered cubic nickel

The Escaig model for thermally activated cross-slip in face-centered cubic (fcc) materials assumes that cross-slip preferentially occurs at obstacles that produce large stress gradients on the Shockley partials of the screw dislocations. However, it is unclear as to the source, identity and concentration of such obstacles in single-phase fcc materials. Embedded atom potential, molecular-statics simulations of screw character dislocation intersections with 120° forest dislocations in fcc Ni are described that illustrate a mechanism for cross-slip nucleation. The simulations show how such intersections readily produce cross-slip nuclei and thus may be preferential sites for cross-slip. The energies of the dislocation intersection cores are estimated and it is shown that a partially cross-slipped configuration for the intersection is the most stable. In addition, simple three-dimensional dislocation dynamics simulations accounting for Shockley partials are shown to qualitatively reproduce the atomistically determined core structures for the same dislocation intersections.

An experimental investigation of intermittent flow and strain burst scaling behavior in LiF crystals during microcompression testing

The first experimental statistical study is reported of intermittent plastic deformation of LiF microscopic samples having low initial dislocation densities, in both as-grown and gamma-irradiated conditions. The investigations used the microcompression testing method. Data sets were evaluated independently for the loading and flow deformation stages for each material. Investigations selectively examined evolution of the strain-burst response in both the spatial and temporal domains. A revised analysis technique provided advances in quantitative evaluations of the statistical experimental data relative to previous studies. Platen displacement event cumulative probability distributions exhibited both Gaussian regimes at small displacements and power law regimes for event displacement, duration and average velocity at larger sizes. However, the observed event size scaling exponents did not follow the expectation from mean-field theory, revealing scaling exponents in the range 1.8–2.9. Additionally, extraordinarily large displacement events were observed that exceeded the sizes of those found in previous studies by at least 10 times. Quantitative clarification of the power-law exponent values and their dependence on deforming sample conditions demands both further experimental studies with larger numbers of samples and a wider range of sample conditions. Such studies would benefit from better matching of the time scales of dislocation processes and observation and, still further improvements to the data analysis methods.