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.

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.

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.     

Full Field Strain Measurement in Compression and Tensile Split Hopkinson Bar Experiments

The 3D image correlation technique is used for full field measurement of strain (and strain rate) in compression and tensile split Hopkinson bar experiments using commercial image correlation software and two digital high-speed cameras that provide a synchronized stereo view of the specimen. Using an array of 128 × 80 (compression tests) and 258 × 48 (tensile tests) pixels, the cameras record about 110,000 frames per second. A random dot pattern is applied to the surface of the specimens. The image correlation algorithm uses the dot pattern to define a field of overlapping virtual gage boxes, and the 3-D coordinates of the center of each gage box are determined at each frame. The coordinates are then used for calculating the strains throughout the surface of the specimen. The strains determined with the image correlation method are compared with those determined from analyzing the elastic waves in the bars, and with strains measured with strain gages placed on the specimens. The system is used to study the response of OFE C10100 copper. In compression tests, the image correlation shows a nearly uniform deformation which agrees with the average strain that is determined from the waves in the bars and the strains measured with strain gages that are placed directly on the specimen. In tensile tests, the specimen geometry and properties affect the outcome from the experiment. The full field strain measurement provides means for examining the validity and accuracy of the tests. In tests where the deforming section of the specimen is well defined and the deformation is uniform, the strains measured with the image correlation technique agree with the average strain that is determined from the split Hopkinson bar wave records. If significant deformation is taking place outside the gage section, and when necking develops, the strains determined from the waves are not valid, but the image correlation method provides the accurate full field strain history.     

Sensitivity of in-Plane Strain Measurement to Calibration Parameter for out-of-Plane Specimen Rotations

In practice, out-of-plane motions usually are not avoidable during experiments. Since 2D–DIC measurements are vulnerable to parasitic deformations due to out-of-plane specimen motions, three-dimensional digital image correlation (StereoDIC or 3D–DIC) oftentimes is employed. The StereoDIC method is known to be capable of accurate deformation measurements for specimens subjected to general three-dimensional motions, including out-of-plane rotations and displacements. As a result, there has been limited study of the deformation measurements obtained when using StereoDIC to measure the displacement and strain fields for a specimen subjected only to out-of-plane rotation. To assess the accuracy of strain measurements obtained using stereovision systems and StereoDIC when a specimen undergoes appreciable out of plane rotation, rigid body out-of-plane rotation experiments are performed in the range ?40⁰?≤?θ?≤?40⁰ using a two-camera stereovision system. Results indicate that (a) for what would normally be considered “small angle” calibration processes, the measured normal strain in the foreshortened specimen direction due to specimen rotation increases in a non-linear manner with rotation angle, with measurement errors exceeding ±1400με and (b) for what would normally be considered “large angle” calibration processes, the magnitude of the errors in the strain are reduced to ±300με. To theoretically assess the effect of calibration parameters on the measurements, two separate analyses are performed. First, theoretical strains due to out-of-plane rigid body rotation are determined using a pinhole camera model to project a series of three-dimensional object points into the image plane using large angle calibration parameters and then re-project the corresponding sensor plane coordinates back into the plane using small angle calibration parameters. Secondly, the entire imaging process is also simulated in order to remove experimental error sources and to further validate the theory. Results from both approaches confirmed the same strain error trends as the experimental strain measurements, providing confidence that the source of the errors is the calibration process. Finally, variance based sensitivity analyses show that inaccuracy in the calibrated stereo angle parameter is the most significant factor affecting the accuracy of the measured strain.     

Identification of Heterogeneous Constitutive Parameters in a Welded Specimen: Uniform Stress and Virtual Fields Methods for Material Property Estimation

Local strain data obtained throughout the entire weld region encompassing both the weld nugget and heat affected zones (HAZs) are processed using two methodologies, uniform stress and virtual fields, to estimate specific heterogeneous material properties throughout the weld zone. Results indicate that (a) the heterogeneous stress–strain behavior obtained by using a relatively simple virtual fields model offers a theoretically sound approach for modeling stress–strain behavior in heterogeneous materials, (b) the local stress–strain results obtained using both a uniform stress assumption and a simplified uniaxial virtual fields model are in good agreement for strains ɛ _xx < 0.025, (c) the weld nugget region has a higher hardening coefficient, higher initial yield stress and a higher hardening exponent, consistent with the fact that the steel weld is overmatched and (d) for ɛ _xx > 0.025, strain localization occurs in the HAZ region of the specimen, resulting in necking and structural effects that complicate the extraction of local stress strain behavior using either of the relatively simple models.

<Emphasis Type="BoldItalic">In-Situ</Emphasis> Mechanical Testing for Characterizing Strain Localization During Deformation at Elevated Temperatures

An experimental methodology has been developed to characterize local strain heterogeneities in alloys via in-situ scanning electron microscope (SEM) based mechanical testing. Quantitative measurements of local strains as a function of grain orientation, morphology and neighborhood are crucial for mechanistic understanding and validation of crystal plasticity models. This study focuses on the technical challenges associated with performing creep tests at elevated temperatures ≤700°C in an SEM. Samples of nickel-based superalloy Rene 104 were used for this study, but the technique is applicable to testing of any metal samples at elevated temperature. Electron beam lithography was employed to produce a suitable surface speckle pattern of hafnium oxide to facilitate full field displacement measurements using a commercial software package. The speckle pattern proved to have good thermal stability and provided excellent contrast for image acquisition using secondary electron imaging at elevated temperature. The speckle pattern and microscope magnification were optimized to obtain the resolution necessary to discern strain localizations within grain interiors and along grain boundaries. Minimum strain resolution due to SEM image distortions was determined prior to tensile testing, and image integration methods were utilized to minimize imaging artifacts. Limitations due to the present specimen heating method and potential solutions to these limitations are also addressed.     

In-situ tensile testing of nano-scale specimens in SEM and TEM

We present a new experimental method for the mechanical characterization of freestanding thin films with thickness on the order of nanometers to micrometers. The method allows, for the first time, in-situ SEM and TEM observation of materials response under uniaxial tension, with measurements of both stresses and strains under a wide variety of environmental conditions such as temperature and humidity. The materials that can be tested include metals, dielectrics, and multi-layer composites that can be deposited/grown on a silicon substrate. The method involves lithography and bulk micromachining techniques to pattern the specimen of desired geometry, release the specimen from the substrate, and co-fabricate a force sensor with the specimen. Co-fabrication provides perfect alignment and gripping. The tensile testing fits an existing TEM straining stage, and a SEM stage. We demonstrate the proposed methodology by fabricating a 200 nm thick, 23.5 μm wide, and 185 μm long freestanding sputter deposited aluminum specimen. The testing was done in-situ inside an environmental SEM chamber. The stress-strain diagram of the specimen shows a linear elastic regime up to the yield stress σ _y MPa, with an elastic modulusE=74.6 GPa.     

Carrier fringe method of moiré interferometry for tiny strain measurements in micro-field

In this paper, we demonstrate a new optical method for tiny strain measurements based on the principle of carrier fringes of moire interferometry. A cross-line grating with frequency of 1200 lp/mm is replicated on the specimen surface, and the strain can be deduced from the changes in carrier fringes before and after the deformation of an object. Four coherent laser beams are used to obtain the carrier fringe patterns of field U and V. Both theoretical analysis and numerical simulation indicate that the ideal accuracy of strain can be controlled within a range of ±1με. Case study of a plane extension experiment shows that the measurement accuracy of strain can be controlled within the range of ±10με. The average strain values of every row of field U and every column of field V can be obtained by using this method, and approximated strain of every pixel in the whole-field can be further acquired, and thus it is possible to measure tiny strains occurred in a micro-field. The technology in this paper can provide comprehensive information for analyzing related mechanical content in the field of MEMS.     

The rheological characterisation of bread dough using capillary rheometry

An Australian hard wheat flour–water dough has been characterised using parallel plate and capillary rheometers over an extensive range of apparent shear rates (10^− 3–10³ s^− 1) relevant to process conditions. Torsional measurements showed that the shear viscosity of the dough increased with strain to a maximum value and then decreased, suggesting a breakdown of the dough structure. Both torsional and capillary experiments revealed the shear-thinning behaviour of the dough. The wall slip phenomenon in capillary rheometry was investigated and found to be diameter dependent and occurred at a critical shear stress of approximately 5–10 kPa. A two-regime power law behaviour was observed, with the power law index approximately 0.3 in the low shear rate range increasing to 0.67 in the high shear rate range. Pressure fluctuation was observed in the capillary data and increased with shear rate, in particular, at shear rates approaching 10⁴ s^− 1. The results demonstrate that capillary rheometry is a viable means of rheologically testing dough at high shear rates provided pressure fluctuation is carefully monitored and capillary rheometry corrections, including wall slip, are accounted for.     

Shear Failure of Inconel 718 under Dynamic Loads

Kinetics of deformation and fracture of nickel–iron alloy Inconel 718 under dynamic shear loading was measured using a split torsional Hopkinson bar facility and high-speed photography. Tubular specimens with a reduced gage length and a starter notch were sheared at strain rates up to 6 × 10³ s⁻¹. High-speed photographs of fiducial lines scribed on the specimen surface showed the development of local strains and cracking. This paper describes the experimental and analytical procedures, illustrates average and local plastic strain evolution, and presents shear crack initiation times and propagation speeds.     

Velocity measurements of flow through a step stenosis using Magnetic Resonance Imaging

 Magnetic resonance imaging (MRI) is a versatile noninvasive tool for achieving full-field quantitative visualization of complex fluid flows. The MRI signal results from the interaction of radio-frequency (RF) pulses with nuclear spins exposed to a strong static magnetic field. The two main techniques of MRI velocimetry are time-of-flight and phase contrast techniques. Time-of- flight techniques involve tagging and tracking a material volume of fluid, whereas phase contrast techniques use magnetic field gradients to encode velocity information into the phase of the MRI signal. In this study, both techniques are used to probe the pressure-driven steady flow of water in a pipe with a step stenosis. The velocity measurements were then compared with computational results obtained using the FIDAP software package. The experiments show that the phase contrast method gives more accurate results, with 90% of the measurements within 10% of the local computational fluid dynamics (CFD) velocity predictions at Re = 100 and 94% of the measurements within 10% of the local CFD predictions at Re = 258. Although the time-of-flight experiments were not as accurate, they provide a good qualitative image of the flow field. Sources of the discrepancies between the MRI data and the CFD results are also discussed, including acceleration and spin flow-through artifacts. Received: 7 April 1999/Accepted: 20 December 1999     

Novel Microtensile Method for Monotonic and Cyclic Testing of Freestanding Copper Thin Films

This paper presents the results of new microtensile tests conducted to investigate the mechanical properties of submicron-thick freestanding copper films. The method, used in this study, allows the observation of materials response under uniaxial tensile loads with measurements of stress at strain rates up to 5.5 × 10⁻⁴/s. It also facilitates tension–tension fatigue experiments under a variety of mean stress conditions at cyclic loading frequencies to 20 Hz. The sample processes involve fabrication of a supporting frame with springs and alignment beams all made of electroplated nickel. Electroplating took place on top of a previously deposited sample rather than creating a structure by subtractive fabrication. Tensile sample loading is applied using a piezoelectric actuator. Load was measured using a capacitance gap sensor with a novel mechanical coupling to the sample. Tension–tension fatigue experiments were carried out with feedback to give load control. Fatigue tests were conducted on sputter-deposited 500 and 900 nm copper films with grain sizes ∼50 nm. Fatigue life reached 10⁵ cycles at low mean load, which decreased with an increase in the mean load. The results indicate decreasing plasticity with increasing mean load.     

Design of an Impact Loading Machine Based on a Flywheel Device: Application to the Fatigue Resistance of the High Rate Pre-straining Sensitivity of Aluminium Alloys

This paper presents a device that has been designed for tensile loading at medium impact rates (up to 10³ s^–1) and for performing either interrupted or failure tests. This machine allows us to apply prescribed pre-straining to the specimen, and then apply subsequent loading histories such as impact fatigue. Two specimen loading systems are considered, which make it possible to carry out tests with various ranges of force and various durations of time. A multi-CCD camera system is triggered by a chosen threshold from the force signal. The system is dedicated to the displacement measurement and gives both qualitative and quantitative information about the stretching mechanism leading to fracture. To illustrate the performance of the device, experimental results concerning impact tensile tests at a strain rate of about 300 s^–1 are presented, as well as consecutive impact-fatigue tests on two aluminium alloys.     

Nano-Pattern Recognition and Correlation Technique for Sub-Nanometer In-Plane Displacement Measurement

An experimental technique to measure sub-nanometer scale in-plane deformations on a micron scale region of interest is proposed. The proposed Nano-Pattern Recognition and Correlation Technique (N-PRCT) utilizes regularly oriented patterns. Displacements are obtained by tracking the movement of each pattern on the images before and after loading through pattern recognition and correlation. The regularity offers a special benefit, relative to the random markings used in the existing techniques, which makes the proposed technique less sensitive to the random noise inherent in digital images at extreme magnifications (a region of interest less than 10 μm). The method is implemented to document thermally-induced deformations of a microelectronics circuit. E-beam lithography is implemented using a standard SEM to fabricate regularly oriented patterns required for N-PRCT. The patterns are produced on a polished cross-section of a flip-chip package, and the package is subsequently subjected to a temperature excursion inside the SEM chamber. Thermal deformations are obtained in a region of interest of approximately 7 × 6 μm.     

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.     

Laboratory measurement of suspended sediment concentration using an Acoustic Concentration Profiler (ACP)

Vertical profiles of suspended sediment concentration have been gathered in a laboratory flume using a 2.25 MHz acoustic transducer. The acoustic concentration profiler (ACP) was calibrated in a vertical duct for homogeneous concentrations of two uniformly sized sediments. The transducer was then transferred to a 6 m horizontal flume where concentration profiles were measured in steady and unsteady flows. For the steady flow tests, concentration measurements made with the ACP and with suction samplers are compared. The results demonstrate that the ACP provides an accurate method of non-intrusively measuring sediment concentrations of more than 2.5% by volume. Received: 24 September 1998/Accepted: 12 April 1999     

Evaluation Using Digital Image Correlation of Stress Intensity Factors in an Aerospace Panel

The fracture behavior of a crack propagating in a large (4.8 m × 1.4 m) aircraft panel was investigated quantitatively by experiment for the first time using digital image correlation. Mixed mode (I+II) stress intensity factors were evaluated using a methodology, which combined digital image correlation with the multi-point over-deterministic method to fit displacement field equations to the experimental data from around a crack tip. More than 800 images were taken during a 10-minute time period as the fracture of the panel occurred under monotonic loading. It was observed that the crack propagated through the skin of the panel at a relatively low speed, with an average crack tip velocity of 0.014 mm/s, and changed its propagation direction at particular points due to the reinforcement of the structure. In the later stages of the test, substantial shear lips were observed indicating a state of plane stress as would be expected in a thin, wide panel and the size of the plastic zone increased substantially. The value of the mode I stress intensity factor obtained from the measured displacement fields initially increased linearly to around 50 MPa√m (K_Ic = 37 MPa√m) and afterwards non-linearly reaching 300 to 400 MPa√m for crack extensions of the order of 100 mm. It is proposed that these high values of stress intensity factor do not represent an unrealistically high material fracture toughness but rather are indicative of the high resistance to crack growth of the structural assemblage of ribs, stringers and hole reinforcements in the panel which allow the skin to sustain a strain level that would otherwise cause unstable crack growth. Digital image correlation is demonstrated to be particularly powerful in elucidating this structural behavior.     

Design of Modified Tabs for Testing of Symmetric Composite Thin Walled Tubes Under Pure Torsional and Tensile Loadings

This paper is mainly concerned with designing modified tabbing systems for testing of composite thin-walled tubes with symmetric layup. The modified tabs are presented based on the concept of iso-displacement points—the points of the specimen that move together and behave similarly during a test. Numerical solutions are carried out for tubular specimens in order to find the displacement field and hence the iso-displacement points. The analyses are carried out for two loading cases: pure torsion and pure tension. Finite element analyses are conducted for both cases, to estimate the displacement fields of thin-walled tubular specimens and then predictive equation were determined using multiple nonlinear regression models. The accuracy of these models is evaluated using a multiple coefficient of determination, R ², where 0 ≤ R ² ≤ 1, coupled with predicted squared error (PSE) and mean squared error (MSE). R ² is found to be greater than or equal to 0.98 for all cases considered in this study while PSE and MSE values are minimized, demonstrating the reliability of the model. Comparison between the modified tabs, based on the iso-displacement points determined by predictive equations, with conventional tabs indicates an improvement in the uniformity of stress and strain distribution (which is an important factor in order to have a successful test) within the specimen for both load cases. It is also demonstrated that due to the elimination of the stress and strain non-uniformities, the measured permissible maximum load of the specimens is significantly increased during the test.