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.     

Ultra High Speed DIC and Virtual Fields Method Analysis of a Three Point Bending Impact Test on an Aluminium Bar

This paper deals with the analysis of an aluminium beam impacted in a three point bending configuration using a Hopkinson bar device. Full-field deformation measurements were performed using Digital Image Correlation on images captured with an ultra high speed camera (16 frames at a time resolution of 10 μs). The performance of the deformation and strain measurements were evaluated and the data were then used quantitatively to analyse the very complex dynamic behaviour of the beam. It was shown that the deformation of the beam was controlled by the interaction between the striker and the flexural bending wave triggered by the initial impact. The principle of virtual work was used to reconstruct the impact force from the shear strains and to analyze how this impact force relates to the acceleration of the specimen (inertia forces) and the development of the bending stresses. The results are in good agreement with expectations. This opens up new perspectives in the quantitative use of full-field measurements to extract elasto-plastic constitutive parameters from such impact tests.     

Time-dependent thermoelastic creep analysis of rotating disk made of Al–SiC composite

Time-dependent creep stress redistribution analysis of rotating disk made of Al–SiC composite is investigated using Mendelson’s method of successive elastic solution. All mechanical and thermal properties except Poisson’s ratio are radial dependent based on volume fraction percent of SiC reinforcement. The material creep behavior is described by Sherby’s constitutive model using Pandey’s experimental results on Al–SiC composite. Loading is an inertia body force due to rotation and a distributed temperature field due to steady-state heat conduction from inner to outer surface of the disk. Using equations of equilibrium, stress strain, and strain displacement, a differential equation, containing creep strains, for displacement is obtained. History of stresses and deformations are calculated using method of successive elastic solution. It is concluded that the uniform distribution of SiC reinforcement does not considerably influence on stresses. However, the minimum and most uniform distribution of circumferential and effective thermoelastic stresses belongs to composite disk of aluminum with 0% SiC at inner surface and 40% SiC at outer surface. It has also been found that the stresses, displacement, and creep strains are changing with time at a decreasing rate so that after almost 50 years the solution approaches the steady-state condition.     

Bearing Load Measurement in a Hydropower Unit Using Strain Gauges Installed Inside Pivot Pin

To determine a machine’s mechanical condition it is of importance to know the radial bearing forces in the machine. Radial forces are caused by magnetic pull forces in the generator, clamped shafts, mass unbalance and flow properties around the turbine. Measuring the shaft displacement in the bearing or the bearing housing acceleration is not sufficient for status determination of a vertical hydropower unit. It is the magnitude and frequencies of the radial forces in combination with structure properties which give information as to whether a measured value is harmful or not. This paper presents an alternative method for measurement of radial bearing load in a hydropower unit. The method presented in this paper is based on strain measurements on pivot pins. The pivot pins are placed behind the bearing pad and the radial loads acting on the pad propagate through the pivot pin. New pivot pins were purchased and equipped with strain gauges. The new pivot pins were calibrated and a transfer function between applied load and measured output voltage was identified for each pivot pin. After calibration the pivot pins were installed in a vertical hydropower unit. Measurements were performed for several different operating modes of the hydropower unit. To verify that the measured load levels were of right order of magnitude, the radial bearing loads were calculated from numerical simulations of bearing properties and shaft eccentricity measurements. The two methods for determining bearing load showed almost the same results. This indicates that either method can be used to determine bearing load.     

A Procedure for Accurate One-Dimensional Strain Measurement Using the Grid Method

This paper deals with the accurate calculation of strain using the grid method. The strain field is first directly deduced from the fringe pattern without calculating the displacement field. This procedure is validated with two numerical examples. Two types of experiment are then carried out: a translation and a tensile test. It is observed that some additional fictitious strains appear in both cases. They are due to two main reasons which interact with each other: the grid defects and the displacement of the grid lines during testing. A suitable procedure is proposed to cancel out these fictitious strains. This procedure is successfully applied in two cases of fringe patterns.     

Synchronous Full-Field Strain and Temperature Measurement in Tensile Tests at Low,Intermediate and High Strain Rates

Tensile tests with simultaneous full-field strain and temperature measurements at the nominal strain rates of 0.01, 0.1, 1, 200 and 3000 s^?1 are presented. Three different testing methods with specimens of the same thin and flat gage-section geometry are utilized. The full-field deformation is measured on one side of the specimen, using the DIC technique with low and high speed visible cameras, and the full-field temperature is measured on the opposite side using an IR camera. Austenitic stainless steel is used as the test material. The results show that a similar deformation pattern evolves at all strain rates with an initial uniform deformation up to the strain of 0.25–0.35, followed by necking with localized deformation with a maximum strain of 0.7–0.95. The strain rate in the necking regions can exceed three times the nominal strain rate. The duration of the tests vary from 57 s at the lowest strain rate to 197 μs at the highest strain rate. The results show temperature rise at all strain rates. The temperature rise increases with strain rate as the test duration shortens and there is less time for the heat to dissipate. At a strain rate of 0.01 s^?1 the temperature rise is small (up to 48 °C) but noticeable. At a strain rate of 0.1 the temperature rises up to 140 °C and at a strain rate of 1 s^?1 up to 260 °C. The temperature increase in the tests at strain rates of 200 s^?1 and 3000 s^?1 is nearly the same with the maximum temperature reaching 375 °C.     

Strain Separation on a Nonplanar Object Using a Luminescent Photoelastic Coating

This paper presents the theoretical modeling and corresponding experimental results of the oblique incidence response of a luminescent photoelastic coating (LPC) applied to a cylinder under load. LPC is a measurement technique to acquire full-field maximum shear strain and its principal strain direction. The technique uses an absorption dye and a luminescent dye within a photoelastic coating, and the coating is applied on the surface of the specimen using conventional aerosol techniques. On 3D objects, the response of the emission field is dependent on the excitation orientation due to the surface inclination of the structural component and the out-of-plane strain component within the coating. Full-field strain separated results have been previously demonstrated on a 2D specimen. The extension of the strain separation technique to a 3D specimen—a cylinder in bending—is the focus of this investigation. Two different responses were obtained from normal and oblique excitation. As a result, the principal strain was separated over ±56° of circumference of the cylinder with RMS error relative to the theoretical result of 87 μɛ for maximum principal strain and 78 μɛ for minimum.     

The Image-Based Inertial Release (IBIR) Test: A New High Strain Rate Test for Stiffness Strain-Rate Sensitivity Identification

A key limitation of current moderate and high strain rate test methods is the need for external force measurement. For high loading rate hydraulic machines, ringing in the load cell corrupts the force measurement. Similarly, the analysis of split-Hopkinson bar tests requires the assumption that the specimen is in a state of quasi-static equilibrium. Recently, image-based inertial test methods have shown that external force measurement is not required if full-field measurements are available and inertial effects are significant enough. In this case the load information is provided by the acceleration fields which are derived from full-field displacement measurements. This article describes a new image-based inertial test method that can be used for simultaneous quasi-static and high strain rate stiffness identification on the same test sample. An experimental validation of the new test method is provided using PMMA samples. A major advantage of this new test method is that it utilises a standard tensile test machine and the only specialist equipment that is required is an ultra-high speed camera.

     

On the instability of steady motion

This paper deals with the instability of steady motions of conservative mechanical systems with cyclic coordinates. The following are applied: Kozlov’s generalization of the first Lyapunov’s method, as well as Rout’s method of ignoration of cyclic coordinates. Having obtained through analysis the Maclaurin’s series for the coefficients of the metric tensor, a theorem on instability is formulated which, together with the theorem formulated in Furta (J. Appl. Math. Mech. 50(6):938–944, 1986), contributes to solving the problem of inversion of the Lagrange-Dirichlet theorem for steady motions. The cases in which truncated equations involve the gyroscopic forces are solved, too. The algebraic equations resulting from Kozlov’s generalizations of the first Lyapunov’s method are formulated in a form including one variable less than was the case in existing literature.     

Identification of Elasto-Plastic Constitutive Parameters from Statically Undetermined Tests Using the Virtual Fields Method

This paper presents an experimental validation of the use of the virtual fields method to identify the elasto-plastic behaviour of an iron specimen from full-field measurements with the grid method and a simple heterogeneous test configuration. The experimental procedure is carefully detailed since it is of primary importance to obtain good identification results. In particular, the use of two back-to-back cameras has proved essential to eliminate out-of-plane effects. Then, the procedure for extracting the elastic parameters and the parameters of a Voce’s hardening model using the virtual fields method is presented. The results are very convincing and encouraging for future developments using more complex test geometries leading to fully multi-axial stress states. It is a first step towards the development of such inverse procedures as an alternative to difficult and costly methods involving homogeneous tests using multi-axial testing machines.     

Full-Field Surface 3D Shape and Displacement Measurements Using an Unfocused Plenoptic Camera

Full-field surface 3D shape and displacement measurements using a single commercial unfocused plenoptic camera (Lytro Illum) are reported in this work. Before measurements, the unfocused plenoptic camera is calibrated with two consecutive steps, including lateral calibration and depth calibration. Each raw image of a checkerboard pattern recorded by Lytro Illum is first extracted to an array of sub-aperture images (SAIs), and the center sub-aperture images (CSAIs) at diverse poses are used for lateral calibration to determine intrinsic and extrinsic parameters. The parallax maps between the CSAI and the remaining SAIs at each pose are then determined for depth parameters estimation using depth calibration. Furthermore, a newly developed physical-based depth distortion model is established to correct the serious distortion of the depth field. To realize shape and deformation measurements, the raw images of a test sample with speckle patterns premade on its surface are captured by Lytro Illum and extracted to arrays of SAIs. The parallax maps between the CSAI and the target SAIs are obtained using subset-based digital image correlation. Based on the pre-computed intrinsic and depth parameters and the disparity map, the full-field surface 3D shape and displacement of a test object are finally determined. The effectiveness and accuracy of the proposed approach are evaluated by a set of experiments involving the shape reconstruction of a cylinder, in-plane and out-of-plane displacement measurements of a flat plate and 3D full-field displacement measurements of a cantilever beam. The preliminary results indicate that the proposed method is expected to become a novel approach for full-field surface 3D shape and displacement measurements.     

Nano-meter Displacement Measurement by Phase Analysis of Fringe Patterns Obtained by Optical Methods

0Introduction Inordertomonitorthehealthofstructures,straingagesanddisplacementtransducersare usuallyused.Thereasonisthatmanyrulesorcodesforinspectionofstructuresrequiretousestrain gagesanddisplacementtransducers,anditiseasytousethem.However,thesemethodsarebasically one pointmeasurementmethods.Theyareexpensiveandtime consumingfordistributionanalysis.Opticalmethodssuchasgrating projection,geometricmoir啨,moir啨interferometry,holographic interferometryandspeckleinterferometryareusefultomeasuredi…     

A Load-Based Multiple-Partial Unloading Micro-Indentation Technique for Mechanical Property Evaluation

A load-based multiple-partial unloading micro-indentation technique has been developed for evaluating mechanical properties of materials. Comparing to the current prevailing nano/micro-indentation methods, which require precise measurements of the indentation depth and load, the proposed technique only measures indentation load and the overall indentation displacement (i.e. including displacement of the loading apparatus). Coupled with a multiple-partial unloading procedure during the indentation process, this technique results in a load-depth sensing indentation system capable of determining Young’s modulus of metallic alloys with flat, tubular, or curved architectures. Test results show consistent and correct elastic modulus values when performing indentation tests on standard alloys such as steel, aluminum, bronze, and single crystal superalloys. The proposed micro-indentation technique has led to the development of a portable load-depth sensing indentation system capable of on-site, in-situ material property measurement.     

利用光学干涉条纹图相位分析测量纳米位移

Optical methods such as Twyman-Green interferometry, moiré interferometry, holographic interferometry and speckle interferometry are useful to measure displacement and strain in the full-field of structures. Recently phase analysis method of fringe patterns obtained by these optical methods becomes popular, and it provides accurate quantitative results in the full-field. In this paper, in order to measure displacement and strain, real-time or high-speed nano-meter displacement measurement methods developed by the authors are introduced. That is, (1) out-of-plane displacement analysis by Twyman-Green interferometry using integrated phase-shifting method using Fourier transform phase-shifting method, (2) simultaneous two-dimensional in-plane displacement analysis by moiré interferometry and (3) out-of-plane displacement analysis by phase-shifting digital holographic interferometry. The theories and applications are shown.     

On the use of simulated experiments in designing tests for material characterization from full-field measurements

The present paper deals with the use of simulated experiments to improve the design of an actual mechanical test. The analysis focused on the identification of the orthotropic properties of composites using the unnotched Iosipescu test and a full-field optical technique, the grid method. The experimental test was reproduced numerically by finite element analysis and the recording of deformed grey level images by a CCD camera was simulated trying to take into account the most significant parameters that can play a role during an actual test, e.g. the noise, the failure of the specimen, the size of the grid printed on the surface, etc. The grid method then was applied to the generated synthetic images in order to extract the displacement and strain fields and the Virtual Fields Method was finally used to identify the material properties and a cost function was devised to evaluate the error in the identification. The developed procedure was used to study different features of the test such as the aspect ratio and the fibre orientation of the specimen, the use of smoothing functions in the strain reconstruction from noisy data, the influence of missing data on the identification. Four different composite materials were considered and, for each of them, a set of optimized design variables was found by minimization of the cost function.     

A Multi-step Method for <Emphasis Type="Italic">In Situ</Emphasis> Mechanical Characterization of 1-D Nanostructures Using a Novel Micromechanical Device

A novel micromechanical device was developed to convert the compressive force applied by a nanoindenter into pure tensile loading at the sample stages inside a scanning electron microscope or a transmission electron microscope, in order to mechanically deform a one-dimensional nanostructure, such as a nanotube or a nanowire. Force vs. displacement curves for samples with Young’s modulus above a threshold value can be obtained independently from readings of a quantitative high resolution nanoindenter with considerable accuracy, using a simple conversion relationship. However, in-depth finite element analysis revealed the existence of limitations for the device when testing samples with relatively low Young’s modulus, where forces applied on samples derived from nanoindenter readings using a predetermined force conversion factor will no longer be accurate. In this paper, we will demonstrate a multi-step method which can alleviate this problem and make the device capable of testing a wide range of samples with considerable accuracy.     

Use of 3-D Digital Image Correlation to Characterize the Mechanical Behavior of a Fiber Reinforced Refractory Castable

Refractory castables exhibit very low fracture strain levels when subjected to tension or bending. The main objective of this work is to show that 3-D digital image correlation (3-D DIC) allows such low strain levels to be measured. Compared to mechanical extensometer measurements, 3-D DIC makes it possible to reach similar strain resolution levels and to avoid the problem of position dependance related to the heterogeneous nature of the strain and to strain localization phenomena. First, the 3-D DIC method and the experimental set-up are presented. Secondly, an analysis of the 3-D DIC method is performed in order to evaluate the resolution, the standard uncertainty and the spatial resolution for both displacement and strain measurements. An optimized compromise between strain spatial resolution and standard uncertainty is reached for the configuration of the experimental bending test. Finally, the macroscopic mechanical behavior of a fiber reinforced refractory castable (FRRC) is studied using mechanical extensometry and 3-D DIC in the case of tensile and four-point bending tests. It is shown that similar results are obtained with both methods. Furthermore, in the case of bending tests on damaged castable, 3-D DIC results demonstrate the ability to determine Young’s modulus from heterogeneous strain fields better than by using classical beam deflection measurements.     

3D Strain measurement from gratings on both surfaces of sheet metal

Summary  The deformation of thick sheet metal is analyzed using 3D coordinates of cross-gratings on both sides of a specimen. The basic equations are presented for evaluating the 3D strain tensor from displacement functions. Provided the grating coordinates are measured in the undeformed and the deformed states, the difference of the coordinates yields displacement vectors. These are used to determine polynomial displacement functions, which approximate the displacement vectors in a least-squares sense. The condition of volume invariance at plastic deformation implies the strain in the direction of the thickness. The whole procedure is tested by a radial symmetric forming of a rectangular sheet metal into a half-tube, because it can be evaluated analytically, too. Finally, a real forming process of a plane circular sheet metal into a cup-like object is analyzed. Received 10 May 1999; accepted for publication 22 September 1999     

Effect of magneto-thermo-viscoelasticity in an unbounded body with a spherical cavity subjected to a harmonically varying temperature without energy dissipation

The present work is devoted to study effects of the thermally induced vibration, magnetic field and viscoelasticity in an isotropic homogeneous unbounded body with a spherical cavity. The GN model of thermoelasticity without energy dissipation is applied. The closed form solutions for distributions of displacement, temperature and radial and hoop stresses are illustrated. The boundary conditions for the temperature and mechanical and Maxwell’s stresses are employed. The solutions valid in the case of small frequency are deduced and the results are compared with the corresponding results obtained in other generalized thermoelasticity theories. The results obtained are calculated for a copper material and presented graphically. It’s deduced that the magnetic field, viscosity and thermally induced vibration are very pronounced on displacement, temperature and stresses.