Full-field Thermal Deformation Measurements in a Scanning Electron Microscope by 2D Digital Image Correlation

Using recently developed methods for application of a nano-scale random pattern having high contrast during SEM imaging, baseline full-field thermal deformation experiments have been performed successfully in an FEI Quanta SEM using 2D-DIC methods. Employing a specially redesigned commercial heating plate and control system, with modified specimen attachment procedures to minimize unwanted image motions, recently developed distortion correction procedures were shown to be effective in removing both drift and spatial distortion fields under thermal heating. 2D-DIC results from heating experiments up to 125°C on an aluminum specimen indicate that (a) the fully corrected displacement components have nearly random variability and a standard deviation of 0.02 pixels (≈25 nm at 200× and ≈0.5 nm at 10,000×) in each displacement component and (b) the unbiased measured strain fields have a standard deviation ≈150 × 10⁻⁶ and a mean value that is in good agreement with independent measurements, confirming that the SEM-DIC based method can be used for both micro-scale and nano-scale thermal strain measurements.

Scanning Electron Microscopy for Quantitative Small and Large Deformation Measurements Part I: SEM Imaging at Magnifications from 200 to 10,000

A series of baseline displacement measurements have been obtained using 2D Digital Image Correlation (2D-DIC) and images from Scanning Electron Microscopes (SEM). Direct correlation of subsets from a reference image to subsets in a series of uncorrected images is used to identify the presence of non-stationary step-changes in the measured displacements. Using image time integration and recently developed approaches to correct residual drift and spatial distortions in recorded images, results clearly indicate that the corrected SEM images can be used to extract deformations with displacement accuracy of ±0.02 pixels (1 nm at magnification of 10,000) and mean value strain measurements that are consistent with independent estimates and have point-to-point strain variability of ±1.5 × 10⁻⁴.

Surfactant turbulent drag reduction in an enclosed rotating disk apparatus

An enclosed rotating disk apparatus (RDA) with rotational speed up to 5,500 rpm and with temperature control from −5 to 55°C was designed to screen the turbulent drag reducing effectiveness of small samples of newly synthesized drag reducing additives. First, the rotating disk was calibrated with water using both logarithmic and power law models. Then experiments were carried out to measure the frictional torque reduction for a drag reducing aqueous cationic surfactant system (5 mM Ethoquad O12 with 12.5 mM sodium salicylate) over a range of Re. The maximum drag reduction at 30°C was about 47% at Re = 1.90 × 10⁶. For the first time, results with the RDA were compared with those in a circular pipe flow system. They showed similar trends indicating it is a useful screening device for small samples, giving conservative estimates of surfactant effectiveness compared with pipe flow.

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Rosetta Stone Experiments

Dynamic failure events such as armor penetration and explosive fragmentation are too complex to be treated by classical single-crack continuum fracture mechanics. In such cases deformation and fracture result from multiple cracks, voids, and shear bands acting simultaneously and influencing one another’s evolution. An alternative “meso” fracture mechanics is needed that treats microfailure activity while permitting fast and inexpensive predictive computations. This paper discusses the approach and experiments that elucidate and quantify failure physics on the micron level. “Rosetta Stone” experiments that isolate a damage mode, produce statistical distributions of damage features, and “freeze in” damage at various stages of development are described and illustrated. The observations and data lead to equations describing nucleation and growth of cracks, voids, and shear bands. The resulting mesomechanical material failure models link the microworld with the macroworld and can be used in continuum hydrocodes for fast, efficient simulations of dynamic fracture scenarios.

Transient elongational viscosities of aqueous polyacrylamide solutions measured with an optical rheometer

An anionic polyacrylamide solution was characterized in elongational flow by combining laser-Doppler velocimetry to determine the strain rate in the flow direction and the two-color flow-induced birefringence method to measure the first normal stress difference along the axial centerline of a hyperbolic die. The elongational rate was constant along the axial centerline of the planar hyperbolic die as long as vortices at the die entrance did not occur. The transient elongational viscosity μ ⁺ was determined as a function of the elongational rate. The parameters varied are the Hencky strain rate and the polymer concentration. μ ⁺ showed a pronounced increase over the linear viscoelastic behavior above critical Hencky strains of 1.2 to 1.5; that is, a significant strain hardening could be observed for polyacrylamide solutions. This strain hardening is stronger the higher the elongational rate. A slight enhancement of strain hardening was found by increasing the concentration from 0.5 to 1 g/l. The stress optical coefficient was determined as 1.8 × 10⁻⁷ Pa⁻¹ (0.5 g/l) and 1.2 × 10⁻⁷ Pa⁻¹ (1 g/l).

Spatial resolution of the Stereo PIV technique

A theoretical analysis of the spatial resolution in terms of modulation transfer function of the Stereo PIV technique with and without the correction of the misalignment error is performed, and the results show that some wavelengths of the flow field can be significantly dephased and modulated. A performance assessment has been conducted with both synthetic and real images and shows a good agreement with the theoretical analysis. The reconstruction of the three-dimensional displacement field is achieved using both the methods proposed by Soloff et al. (Meas Sci Technol 8:1441–1454, 1997) and by Willert (Meas Sci Technol 8:1465–1479, 1997).

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Two- and three-dimensional flows in nearly rectangular cavities driven by collinear motion of two facing walls

Two- and three-dimensional flows in nearly cuboidal cavities are investigated experimentally. A tight cavity is formed in the gap between two long and parallel cylinders of large radii by adding rigid top, bottom, and end walls. The cross-section perpendicular to the axes of the cylinders is nearly rectangular with aspect ratio Γ. The axial aspect ratio Λ > 10 is large to suppress end-wall effects. The fluid motion is driven by independent and steady rotation of the cylinders about their axes which defines two Reynolds numbers Re _1,2. Stability boundaries of the nearly two-dimensional steady flow have been determined as functions of Re _1,2 for Γ = 0.76 and Γ = 1. Up to six different three-dimensional supercritical modes have been identified. The critical thresholds for the onset of most of the three-dimensional modes, three of which have been observed for the first time, agree well with corresponding linear-stability calculations. Particular attention is paid to the flow for Γ = 1 under symmetric and parallel wall motion. In that case the basic flow consists of two mirror symmetric counter-rotating parallel vortices. They become modulated in span-wise direction as the driving increases. Detailed LDV measurements of the supercritical three-dimensional velocity field and the bifurcation show an excellent agreement with numerical simulations.

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Dependence of the zero shear-rate viscosity and the viscosity function of linear high-density polyethylenes on the mass-average molar mass and polydispersity

Linear high-density polyethylenes with molar masses M _w between 240 and 1,000,000 g/mol, obtained by metallocene catalysts, were characterized in shear using oscillatory and creep tests. The polydispersities of the molar mass distributions (MMDs) lay between 1 and 16. The resulting zero shear-rate viscosities η₀ covered a range from 2.5×10⁻³ to around 10⁸ Pas. Above a critical molar mass of M _c≈2,900 g/mol, the experimental results can be described by the relation η₀ ∼ M _w^3.6, independently of the MMD. The oscillatory data were fitted with a Carreau–Yasuda equation. The resulting parameters were correlated to molecular structure. The parameter a, being a quantity for the width of the transition between the Newtonian and the non-Newtonian regime, showed a dependence on the molar mass M _w but not on M _w/M _n. The parameter λ of the Carreau-Yasuda equation was found to be the reciprocal crossover frequency for all samples with a log-Gaussian MMD. λ depends on the molar mass M _w and also on M _w/M _n.

Microscale Synthetic Schlieren

We develop the axisymmetric Synthetic Schlieren technique to study the wake of a microscale sphere settling through a density stratification. A video-microscope was used to magnify and image apparent displacements of a micron-sized random-dot pattern. Due to the nature of the wake, density gradient perturbations in the horizontal greatly exceed those in the vertical, requiring modification of previously developed axisymmetric techniques. We present results for 780 and 383 μm spheres, and describe the limiting role of noise in the system for a 157 μm sphere. This technique can be instrumental in understanding a range of ecological and environmental oceanic processes on the microscale.

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Measurement of the gradient field of a turbulent free surface

We study the free surface above a turbulent channel flow. We describe a laser scanning technique that can be used to measure the space–time turbulent surface gradient field along a line. A harmonically swiveling laser beam is focused on the surface and its angle of refraction is measured using a position sensing device. The registered signals can be converted easily to the desired gradient field, and spectra and correlations can be measured. Examples of measured spectra and correlation functions of the surface above a turbulent channel flow (Reynolds number R _λ ≈ 250) demonstrate the viability of the technique. We further assess the validity of Taylor’s frozen turbulence hypothesis that implies that time-dependent signals measured along a line that is oriented perpendicularly to the mean channel velocity can be interpreted as 2D measurements of the surface slope. While Taylor’s hypothesis works for a turbulent velocity field, it does not work for its free surface.