Strain Measurements of Silicon Dioxide Microspecimens by Digital Imaging Processing

Silicon dioxide thin film is a common component in electronic devices and in MEMS, but its mechanical properties have rarely been studied. Techniques have been adapted and developed to conduct tensile tests on 1.0 μm thick silicon dioxide specimens that are 100, 150, and 200 μm wide and either 1 or 2 mm long. One end of the specimen remains fastened to the substrate, and the other is glued to a silicon carbide fiber attached to a 30 g load cell mounted on a piezoelectric translation stage. Strain is measured by digital imaging of two gold lines applied to the gage section of the transparent specimen. Twenty-five tests yield a Young’s modulus of 60.1 ± 3.4 GPa and a fracture strength of 364 ± 57 MPa.     

Comparison of experimental data with results of some drying models for regularly shaped products

This paper presents an experimental and theoretical investigation of drying of moist slab, cylinder and spherical products to study dimensionless moisture content distributions and their comparisons. Experimental study includes the measurement of the moisture content distributions of slab and cylindrical carrot, slab and cylindrical pumpkin and spherical blueberry during drying at various temperatures (e.g., 30, 40, 50 and 60°C) at specific constant velocity (U = 1 m/s) and the relative humidity φ = 30%. In theoretical analysis, two moisture transfer models are used to determine drying process parameters (e.g., drying coefficient and lag factor) and moisture transfer parameters (e.g., moisture diffusivity and moisture transfer coefficient), and to calculate the dimensionless moisture content distributions. The calculated results are then compared with the experimental moisture data. A considerably high agreement is obtained between the calculations and experimental measurements for the cases considered. The effective diffusivity values were evaluated between 0.741 × 10⁻⁵ and 5.981 × 10⁻⁵ m²/h for slab products, 0.818 × 10⁻⁵ and 6.287 × 10⁻⁵ m²/h for cylindrical products and 1.213 × 10⁻⁷ and 7.589 × 10⁻⁷ m²/h spherical products using the Model-I and 0.316 × 10⁻⁵–5.072 × 10⁻⁵ m²/h for slab products, 0.580 × 10⁻⁵–9.587 × 10⁻⁵ m²/h for cylindrical products and 1.408 × 10⁻⁷–13.913 × 10⁻⁷ m²/h spherical products using the Model-II.     

Experimental Investigation of Strain Rate Dependence of Nanocrystalline Pt Films

A new microscale uniaxial tension experimental method was developed to investigate the strain rate dependent mechanical behavior of freestanding metallic thin films for MEMS. The method allows for highly repeatable mechanical testing of thin films for over eight orders of magnitude of strain rate. Its repeatability stems from the direct and full-field displacement measurements obtained from optical images with at least 25 nm displacement resolution. The method is demonstrated with micron-scale, 400-nm thick, freestanding nanocrystalline Pt specimens, with 25 nm grain size. The experiments were conducted in situ under an optical microscope, equipped with a digital high-speed camera, in the nominal strain rate range 10⁻⁶–10¹ s⁻¹. Full field displacements were computed by digital image correlation using a random speckle pattern generated onto the freestanding specimens. The elastic modulus of Pt, E = 182 ± 8 GPa, derived from uniaxial stress vs. strain curves, was independent of strain rate, while its Poisson’s ratio was v = 0.41 ± 0.01. Although the nanocrystalline Pt films had the elastic properties of bulk Pt, their inelastic property values were much higher than bulk and were rate-sensitive over the range of loading rates. For example, the elastic limit increased by more than 110% with increasing strain rate, and was 2–5 times higher than bulk Pt reaching 1.37 GPa at 10¹ s⁻¹.     

Dynamical deformation of a flat liquid–liquid interface

The passage of solid spheres through a liquid–liquid interface was experimentally investigated using a high-speed video and PIV (particle image velocimetry) system. Experiments were conducted in a square Plexiglas column of 0.1 m. The Newtonian Emkarox (HV45 50 and 65% wt) aqueous solutions were employed for the dense phase, while different silicone oils of different viscosity ranging from 10 to 100 mPa s were used as light phase. Experimental results quantitatively reveal the effect of the sphere’s size, interfacial tension and viscosity of both phases on the retaining time and the height of the liquid entrained behind the sphere. These data were combined with our previous results concerning the passage of a rising bubble through a liquid–liquid interface in order to propose a general relationship for the interface breakthrough for the wide range of Mo ₁/Mo ₂ ∈ [2 × 10⁻⁵–5 × 10⁴] and Re ₁/Re ₂ ∈ [2 × 10⁻³–5 × 10²].     

Thin-layer drying of tomato (<Emphasis Type="Italic">Lycopersicum esculentum Mill. cv. Rio Grande</Emphasis>) slices in a convective hot air dryer

The effects of different drying temperatures on the drying kinetics of tomato slices were investigated using a cabinet-type dryer. The experimental drying data were fitted best to the to the Page and Modified Page models apart from other theoretical models to predict the drying kinetics. The effective moisture diffusivities varied from 1.015 × 10⁻⁹ to 2.650 × 10⁻⁹ m² s⁻¹over the temperature range studied, and activation energy was 22.981 kJ mol⁻¹.     

Scanning Electron Microscopy for Quantitative Small and Large Deformation Measurements Part II: Experimental Validation for Magnifications from 200 to 10,000

A combination of drift distortion removal and spatial distortion removal are performed to correct Scanning Electron Microscope (SEM) images at both ×200 and ×10,000 magnification. Using multiple, time-spaced images and in-plane rigid body motions to extract the relative displacement field throughout the imaging process, results from numerical simulations clearly demonstrate that the correction procedures successfully remove both drift and spatial distortions with errors on the order of ±0.02 pixels. A series of 2D translation and tensile loading experiments are performed in an SEM for magnifications at ×200 and ×10,000, where both the drift and spatial distortion removal methods described above are applied to correct the digital images and improve the accuracy of measurements obtained using 2D-DIC. Results from translation and loading experiments indicate that (a) the fully corrected displacement components have nearly random variability with standard deviation of 0.02 pixels (≈25 nm at ×200 and ≈0.5 nm at ×10,000) in each displacement component and (b) the measured strain fields are unbiased and in excellent agreement with expected results, with a spatial resolution of 43 pixels (≈54 μm at ×200 and ≈1.1 μm at ×10,000) and a standard deviation on the order of 6 × 10⁻⁵ for each component.

Thin-layer drying characteristics of sweet potato slices and mathematical modelling

The effect of blanching and drying temperature (50, 60 and 70°C) on drying kinetics and rehydration ratio of sweet potatoes was investigated. It was observed that both the drying temperature and blanching affected the drying time and rehydration ratio. The logarithmic model showed the best fit to experimental drying data. The values of effective moisture diffusivity and activation energy ranged from 9.32 × 10⁻¹¹ to 1.75 × 10⁻¹⁰ m²/s, and 22.7–23.2 kJ/mol, respectively.     

Stereoscopic micro particle image velocimetry

A stereoscopic micro-PIV (stereo-μPIV) system for the simultaneous measurement of all three components of the velocity vector in a measurement plane (2D–3C) in a closed microchannel has been developed and first test measurements were performed on the 3D laminar flow in a T-shaped micromixer. Stereomicroscopy is used to capture PIV images of the flow in a microchannel from two different angles. Stereoscopic viewing is achieved by the use of a large diameter stereo objective lens with two off-axis beam paths. Additional floating lenses in the beam paths in the microscope body allow a magnification up to 23×. The stereo-PIV images are captured simultaneously by two CCD cameras. Due to the very small confinement, a standard calibration procedure for the stereoscopic imaging by means of a calibration target is not feasible, and therefore stereo-μPIV measurements in closed microchannels require a calibration based on the self-calibration of the tracer particle images. In order to include the effects of different refractive indices (of the fluid in the microchannel, the entrance window and the surrounding air) a three-media-model is included in the triangulation procedure of the self-calibration. Test measurement in both an aligned and a tilted channel serve as an accuracy assessment of the proposed method. This shows that the stereo-μPIV results have an RMS error of less than 10% of the expected value of the in-plane velocity component. First measurements in the mixing region of a T-shaped micromixer at Re = 120 show that 3D flow in a microchannel with dimensions of 800 × 200 μm² can be measured with a spatial resolution of 44 × 44 × 15 μm³. The stationary flow in the 200 μm deep channel was scanned in multiple planes at 22 μm separation, providing a full 3D measurement of the averaged velocity distribution in the mixing region of the T-mixer. A limitation is that this approach requires a stereo-objective that typically has a low NA (0.14–0.28) and large depth-of-focus as opposed to high NA lenses (up to 0.95 without immersion) for standard μPIV.     

Modeling of water transport in roof tiles by removal of moisture at isothermal conditions

The main objective of this article is to describe the drying process of ceramic roof tiles, shaped from red clay, using diffusion models. Samples of the product with initial moisture content of 0.24 (db) were placed inside an oven in the temperatures of 55.6, 69.7, 82.7 and 98.6°C; and the data of the drying kinetics were obtained. The analytical solutions of the diffusion equation for the parallelepiped with boundary conditions of the first and third kinds were used to describe the drying processes. The process parameters were determined using an optimization algorithm based on inverse method coupled to the analytical solutions. The analysis of the results makes it possible to affirm that the boundary condition of the third kind satisfactorily describes the drying processes. The values obtained for the convective mass transfer coefficient were between 8.25 × 10⁻⁷ and 1.64 × 10⁻⁶ m s⁻¹, and for the effective water diffusivity were between 9.21 × 10⁻⁹ and 1.80 × 10⁻⁸ m² s⁻¹.     

A three-scale FE approach to reliability analysis of MEMS sensors subject to impacts

In this paper the effects of accidental impacts on polysilicon MEMS sensors are investigated within the framework of a three-scale finite element approach. By allowing for the very small ratio (on the order of 10⁻⁴) between the inertia of the MEMS and the inertia of the whole device, macro-scale analyses at the package length-scale are run to obtain the loading conditions at the sensor anchor points. These loading conditions are successively adopted in meso-scale analyses at the MEMS length-scale to detect where the stress level tends to be amplified by sensor layout. To foresee failure of polysilicon in these domains, as caused by the propagation of inter- as well as trans-granular cracks up to percolation, representative crystal topologies are handled in micro-scale analyses. In case of a uni-axial MEMS accelerometer falling from a reference drop height, results show that the crystal structure within the failing sensor detail can have a remarkable effect on the failure mode and on the time to failure. Conversely, through comparison with simulations where the MEMS is assumed to fall anchored to the naked die, it is assessed that packaging only slightly modifies failure details, without significantly reducing the shock loading on the sensor. F. Fachin is currently with: Technology Laboratory for Advanced Materials and Structures, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307 (USA). F. Cacchione is currently with: ABB SACE, Viale dell’Industria 18, Vittuone, 20010 (Italy).     

Microscale 3D flow mapping with μDDPIV

Three-dimensional (3D) quantitative flow visualization by tracking microscale particles has become an invaluable tool in microfluid mechanics. Defocusing digital particle image velocimetry (DDPIV) can recover spatial coordinates by calculating the separation between defocused images generated by an aperture mask with a plurality of pinholes. In this paper, a high-speed 3D micro-DDPIV (μDDPIV) system was devised based on this technique to achieve microscale velocity field measurements. A micro-volume of 400 × 300 μm² with a depth of 150 μm has been mapped using an inverted microscope equipped with a 20× objective lens. The proposed technique was successfully applied to 3D tracking of 2-μm fluorescent particles inside an evaporating water droplet.     

Freon R141b flow boiling in silicon microchannel heat sinks: experimental investigation

This paper presents experimental investigations on Freon R141b flow boiling in rectangular microchannel heat sinks. The main aim is to provide an appropriate working fluid for microchannel flow boiling to meet the cooling demand of high power electronic devices. The microchannel heat sink used in this work contains 50 parallel channels, with a 60 × 200 (W × H) μm cross-section. The flow boiling heat transfer experiments are performed with R141b over mass velocities ranging from 400 to 980 kg/(m² s) and heat flux from 40 to 700 kW/m², and the outlet pressure satisfying the atmospheric condition. The fluid flow-rate, fluid inlet/outlet temperature, wall temperature, and pressure drop are measured. The results indicate that the mean heat transfer coefficient of R141b flow boiling in present microchannel heat sinks depends heavily on mass velocity and heat flux and can be predicted by Kandlikar’s correlation (Heat Transf Eng 25(3):86–93, 2004). The two-phase pressure drop keeps increasing as mass velocity and exit vapor quality rise.     

A microsystem for the fracture characterization of polysilicon at the micro-scale

To characterize the effective fracture energy G_IC of polysilicon wafers at room temperature, an on-chip MEMS test structure has been designed and fabricated. The device can provide fatigue pre-cracking at the notch apex and subsequently impose a monotonical load up to failure. The proposed procedure combines the experimental data with outcomes of numerical simulations. A continuously monitored decrease in stiffness of the system is linked to the crack length and the effective fracture energy for the non-standard geometry of the testing device. An average value of G_IC = 12.0 ± 1.8 N m^?1 is found. These values are then used in numerical micro-scale fracture analyses taking into account the material heterogeneity due to the grain structure and reproducing the crack propagation process with a cohesive approach.     

Competitive Methane Desorption by Supercritical CO2 Injection in Coal

A large diameter (∼70 mm) dry coal sample was used to study the competitive displacement of CH₄ by injection of supercritical CO₂, and CO₂–CH₄ counter-diffusion in coal matrix. During the test, a staged loading procedure, which allows the calibration of the key reservoir modelling parameters in a sequential and progressive manner, was employed. The core-flooding test was history matched using an Enhanced Coalbed Methane (ECBM) simulator, in which Fick’s Law for mixed gas diffusion and the extended Langmuir equations are implemented. The system pressure rise during the two loading stages and the CO₂ breakthrough time in the final production stage were matched by using the pair of constant sorption times (9 and 3.2 days) for CH₄ and CO₂, respectively. The corresponding diffusion coefficients for CH₄ and CO₂ were estimated to be 1.6 ×  10⁻¹² and 4.6 ×  10⁻¹² m²/s, respectively. Comparison was made with published gas diffusion coefficients for dry ground samples (ranging from < 0.063 to ∼3 mm) of the same coal at relatively low pressures (< 4 MPa). The CO₂/CH₄ gas diffusion coefficient ratio was well within the reported range (2–3), whereas the CH₄ diffusion coefficient obtained from history matching of the core-flooding test is approximately 15 times smaller than that arrived by curve-fitting the measured sorption uptake rate using a unipore diffusion model. The calibrated model prediction of the effluent gas composition was in good agreement with the test data for CO₂ mole fraction of up to 20%.     

Spatiotemporal Thermal Inhomogeneities During Compression of Highly Textured Zirconium

Using a focal plane array infrared camera, the heat generated during large strain compression (at a rate of 1 s⁻¹) is used to study the characteristics of plastic flow for hcp zirconium. Heat generation during plastic flow in a reference material, copper, was seen to develop uniformly both at the lower (40 μm/pixel) and higher (8 μm/pixel) magnifications used in this study. The thermomechanical response of Zr, however, was seen to depend on the loading direction with respect to the specimen texture. Highly textured zirconium compressed along nonbasal oriented grains results in a homogeneous thermal response at both scales. However, compression along basal (0001) oriented grains shows evidence of inhomogeneous deformation at small strains that lead to macroscale localization and failure at large strains. The conversion of plastic work into heat is observed to be a dynamic process, both in the time-dependent nature of the energy conversion, but also in the passage of waves and ‘bursts’ of plastic heating. Basal compression also showed evidence of small scale localization at strains far below macroscale localization, even below 10%. These localizations at the lower strain levels eventually dominate the response, and form the shear band that is responsible for the softening of the macroscopic stress–strain curve.     

Resonant-Based Identification of the Poisson’s Ratio of Orthotropic Materials

The resonant-based identification of the in-plane elastic properties of orthotropic materials implies the estimation of four principal elastic parameters: E ₁ , E ₂ , G ₁₂ , and ν ₁₂ . The two elastic moduli and the shear modulus can easily be derived from the resonant frequencies of the flexural and torsional vibration modes, respectively. The identification of the Poisson’s ratio, however, is much more challenging, since most frequencies are not sufficiently sensitive to it. The present work addresses this problem by determining the test specimen specifications that create the optimal conditions for the identification of the Poisson’s ratio. Two methods are suggested for the determination of the Poisson’s ratio of orthotropic materials: the first employs the resonant frequencies of a plate-shaped specimen, while the second uses the resonant frequencies of a set of beam-shaped specimens. Both methods are experimentally validated using a stainless steel sheet.     

A new microtensile tester for the study of MEMS materials with the aid of atomic force microscopy

An apparatus has been designed and implemented to measure the elastic tensile properties (Young's modulus and tensile strength) of surface micromachined polysilicon specimens. The tensile specimens are “dog-bone” shaped ending in a large “paddle” for convenient electrostatic or, in the improved apparatus, ultraviolet (UV) light curable adhesive gripping deposited with electrostatically controlled manipulation. The typical test section of the specimens is 400 μm long with 2 μm×50 μm cross section. The new device supports a nanomechanics method developed in our laboratory to acquire surface topologies of deforming specimens by means of Atomic Force Microscopy (AFM) to determine (fields of) strains via Digital Image Correlation (DIC). With this tool, high strength or non-linearly behaving materials can be tested under different environmental conditions by measuring the strains directly on the surface of the film with nanometer resolution.     

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.

Heat transfer,pressure drop and flow patterns during flow boiling of R407C in a horizontal microfin tube

The heat transfer, pressure drop and flow patterns during flow boiling of R407C in a horizontal microfin tube have been investigated. The microfin tube is made of copper with a total fin number of 55 and a helix angle of 15°. The fin height is 0.24 mm and the inner tube diameter at fin root is 8.95 mm. The test tube is 1 m long. It is heated electrically. The experiments have been performed at saturation temperatures between −30°C and +10°C. The mass flux was varied between 25 and 300 kg/m²/s, the heat flux from 20,000 W/m² down to 1,000 W/m². The vapour quality was kept constant at 0.1, 0.3, 0.5, 0.7 at the inlet and 0.8, 1.0 at the outlet, respectively. The measured heat transfer coefficient is compared with the correlations of Cavallini et al., Shah as well as Zhang et al. Cavallini’s correlation contains seven experimental constants. After fitting these constants to our measured values, the correlation achieves good agreement. The measured pressure drop is compared to the correlations of Pierre, Kuo and Wang as well as Müller-Steinhagen and Heck. The best agreement is achieved with the correlation of Kuo and Wang. Almost all values are calculated within an accuracy of ±30%. The flow regimes were observed. It is shown, that changes in the flow regime affect the heat transfer coefficient significantly.     

Influence of elastic material compressibility on parameters of an expanding spherical stress wave

We investigated the influence of elastic material compressibility on parameters of an expanding spherical stress wave. The material compressibility is represented by Poisson’s ratio, ν, in this paper. The stress wave is generated by a pressure produced inside a spherical cavity surrounded by the isotropic elastic material. The analytical closed form formulae determining the dynamic state of the mechanical parameters (displacement, particle velocity, strains, stresses, and material density) in the material have been derived. These formulae were obtained for surge pressure p(t) = p ₀ = const inside the cavity. From analysis of these formulae, it is shown that the Poisson’s ratio substantially influences the course of material parameters in space and time. All parameters intensively decrease in space together with an increase of the Lagrangian coordinate, r. On the contrary, these parameters oscillate versus time around their static values. These oscillations decay in the course of time. We can mark out two ranges of parameter ν values in which vibrations of the parameters are “damped” at a different rate. Thus, Poisson’s ratio in the range below about 0.4 causes intense decay of parameter oscillations. On the other hand in the range 0.4 < ν < 0.5, i.e. in quasi-incompressible materials, the “damping” of parameter vibrations is very low. In the limiting case when ν = 0.5, i.e. in the incompressible material, “damping” vanishes, and the parameters harmonically oscillate around their static values. The abnormal behaviour of the material occurs in the range 0.4 < ν < 0.5. In this case, an insignificant increase of Poisson’s ratio causes a considerable increase of the parameter vibration amplitude and decrease of vibration “damping”.