Modeling dislocation sources and size effects at initial yield in continuum plasticity

Size effects at initial yield (prior to stage II) of idealized micron-sized specimens are modeled within a continuum model of plasticity. Two different aspects are considered: specification of a density of dislocation sources that represent the emission of dislocation dipoles, and the presence of an initial, spatially inhomogeneous excess dislocation content. Discreteness of the source distribution appears to lead to a stochastic response in stress-strain curves, with the stochasticity diminishing as the number of sources increases. Variability in stress-strain response due to variations of source distribution is also shown. These size effects at initial yield are inferred to be due to physical length scales in dislocation mobility and the discrete description of sources that induce internal-stress-related effects, and not due to length-scale effects in the mean-field strain-hardening response (as represented through a constitutive equation)

Active colloidal particles in emulsion droplets: A model system for the cytoplasm

In living cells, molecular motors create activity that enhances the diffusion of particles throughout the cytoplasm, and not just ones attached to the motors. We demonstrate initial steps toward creating artificial cells that mimic this phenomenon. Our system consists of active, Pt-coated Janus particles and passive tracers confined to emulsion droplets. We track the motion of both the active particles and passive tracers in a hydrogen peroxide solution, which serves as the fuel to drive the motion. We first show that correcting for bulk translational and rotational motion of the droplets induced by bubble formation is necessary to accurately track the particles. After drift correction, we find that the active particles show enhanced diffusion in the interior of the droplets and are not captured by the droplet interface. At the particle and hydrogen peroxide concentrations we use, we observe little coupling between the active and passive particles. We discuss the possible reasons for lack of coupling and describe ways to improve the system to more effectively mimic cytoplasmic activity

Using the Discrete Dipole Approximation and Holographic Microscopy to Measure Rotational Dynamics of Non-spherical Colloidal Particles

We present a new, high-speed technique to track the three-dimensional translation and rotation of non-spherical colloidal particles. We capture digital holograms of micrometer-scale silica rods and sub-micrometer-scale Janus particles freely diffusing in water, and then fit numerical scattering models based on the discrete dipole approximation to the measured holograms. This inverse-scattering approach allows us to extract the the position and orientation of the particles as a function of time, along with static parameters including the size, shape, and refractive index. The best-fit sizes and refractive indices of both particles agree well with expected values. The technique is able to track the center of mass of the rod to a precision of 35 nm and its orientation to a precision of 1.5$^\circ$, comparable to or better than the precision of other 3D diffusion measurements on non-spherical particles. Furthermore, the measured translational and rotational diffusion coefficients for the silica rods agree with hydrodynamic predictions for a spherocylinder to within 0.3%. We also show that although the Janus particles have only weak optical asymmetry, the technique can track their 2D translation and azimuthal rotation over a depth of field of several micrometers, yielding independent measurements of the effective hydrodynamic radius that agree to within 0.2%. The internal and external consistency of these measurements validate the technique. Because the discrete dipole approximation can model scattering from arbitrarily shaped particles, our technique could be used in a range of applications, including particle tracking, microrheology, and fundamental studies of colloidal self-assembly or microbial motion.Comment: 11 pages, 9 figures, 2 table

Noninvasive imaging of three-dimensional micro and nanostructures by topological methods

We present topological derivative and energy based procedures for the imaging of micro and nano structures using one beam of visible light of a single wavelength. Objects with diameters as small as 10 nm can be located and their position tracked with nanometer precision. Multiple objects dis-tributed either on planes perpendicular to the incidence direction or along axial lines in the incidence direction are distinguishable. More precisely, the shape and size of plane sections perpendicular to the incidence direction can be clearly determined, even for asymmetric and nonconvex scatterers. Axial resolution improves as the size of the objects decreases. Initial reconstructions may proceed by gluing together two-dimensional horizontal slices between axial peaks or by locating objects at three-dimensional peaks of topological energies, depending on the effective wavenumber. Below a threshold size, topological derivative based iterative schemes improve initial predictions of the lo-cation, size, and shape of objects by postprocessing fixed measured data. For larger sizes, tracking the peaks of topological energy fields that average information from additional incident light beams seems to be more effective

Random-subset fitting of digital holograms for fast three-dimensional particle tracking

Fitting scattering solutions to time series of digital holograms is a precise way to measure three-dimensional dynamics of microscale objects such as colloidal particles. However, this inverse-problem approach is computationally expensive. We show that the computational time can be reduced by an order of magnitude or more by fitting to a random subset of the pixels in a hologram. We demonstrate our algorithm on experimentally measured holograms of micrometer-scale colloidal particles, and we show that 20-fold increases in speed, relative to fitting full frames, can be attained while introducing errors in the particle positions of 10 nm or less. The method is straightforward to implement and works for any scattering model. It also enables a parallelization strategy wherein random-subset fitting is used to quickly determine initial guesses that are subsequently used to fit full frames in parallel. This approach may prove particularly useful for studying rare events, such as nucleation, that can only be captured with high frame rates over long times.Engineering and Applied SciencesPhysic

Yielding and irreversible deformation below the microscale: Surface effects and non-mean-field plastic avalanches

Nanoindentation techniques recently developed to measure the mechanical response of crystals under external loading conditions reveal new phenomena upon decreasing sample size below the microscale. At small length scales, material resistance to irreversible deformation depends on sample morphology. Here we study the mechanisms of yield and plastic flow in inherently small crystals under uniaxial compression. Discrete structural rearrangements emerge as series of abrupt discontinuities in stress-strain curves. We obtain the theoretical dependence of the yield stress on system size and geometry and elucidate the statistical properties of plastic deformation at such scales. Our results show that the absence of dislocation storage leads to crucial effects on the statistics of plastic events, ultimately affecting the universal scaling behavior observed at larger scales.Comment: Supporting Videos available at http://dx.plos.org/10.1371/journal.pone.002041

A Simple, Inexpensive Holographic Microscope

We have built a simple holographic microscope completely out of consumer components. We obtain at least 2.8 micrometer resolution and depth of field greater than 200 micrometers from an instrument costing less than $1000.Engineering and Applied SciencesPhysic

Microstructural evolution of a delta containing nickel-base superalloy during heat treatment and isothermal forging

The next generation of aerospace gas turbine engines need to operate at higher temperatures and stresses to improve their efficiency and reduce emissions. These operating conditions are beyond the capability of existing nickel-base superalloys, requiring the development of new high temperature materials. Controlling the microstructures of these new materials is key to obtaining the required properties and, therefore, it is critical to understand how these alloys respond to processing and heat treatment. Here, the microstructural evolution of V207M, a new δ containing, nickel-base superalloy, has been investigated following heat treatment and forging. The solvus temperatures of the γ′ and δ phases, determined by differential scanning calorimetry and microscopy, were found to be ~985 and ~1060 °C respectively. Isothermal forging of the alloy was conducted at 1000, 1050 and 1100 °C, corresponding to different volume fractions of retained δ. Considerable softening was observed prior to steady state flow when forging at 1000 °C, whilst only steady state flow occurred at 1050 and 1100 °C. The steady state flow process was believed to be dominated by dynamic recovery in the γ phase, with an activation energy of 407 kJmol−1. Samples that exhibited flow softening also showed a significant change in the orientation of the δ precipitates, preferentially aligning normal to the forging axis, and this reorientation was thought to be the cause of the observed flow softening

On the critical nature of plastic flow: one and two dimensional models

Steady state plastic flows have been compared to developed turbulence because the two phenomena share the inherent complexity of particle trajectories, the scale free spatial patterns and the power law statistics of fluctuations. The origin of the apparently chaotic and at the same time highly correlated microscopic response in plasticity remains hidden behind conventional engineering models which are based on smooth fitting functions. To regain access to fluctuations, we study in this paper a minimal mesoscopic model whose goal is to elucidate the origin of scale free behavior in plasticity. We limit our description to fcc type crystals and leave out both temperature and rate effects. We provide simple illustrations of the fact that complexity in rate independent athermal plastic flows is due to marginal stability of the underlying elastic system. Our conclusions are based on a reduction of an over-damped visco-elasticity problem for a system with a rugged elastic energy landscape to an integer valued automaton. We start with an overdamped one dimensional model and show that it reproduces the main macroscopic phenomenology of rate independent plastic behavior but falls short of generating self similar structure of fluctuations. We then provide evidence that a two dimensional model is already adequate for describing power law statistics of avalanches and fractal character of dislocation patterning. In addition to capturing experimentally measured critical exponents, the proposed minimal model shows finite size scaling collapse and generates realistic shape functions in the scaling laws.Comment: 72 pages, 40 Figures, International Journal of Engineering Science for the special issue in honor of Victor Berdichevsky, 201