Showing papers in "Experimental Mechanics in 2003"

A Critical Review of Microscale Mechanical Testing Methods Used in the Design of Microelectromechanical Systems

Abstract: Microelectromechanical systems (MEMS) technologies are evolving at a rapid rate with increasing activity in the design, fabrication, and commercialization of a wide variety of microscale systems and devices. The importance of accurate mechanical property measurement for successful design was realized early on in the development of this field. Consequently, there exist many different techniques to measure quantities such as the Young's modulus (E), yield strength (σ Y ), fracture strength (σ F ), residual stress (σ F ), and residual stress gradient (∇σ R ) of microscale structures and materials. We review and critically compare several of the important techniques including the microtension test, axisymmetric plate bend test, microbeam bend test, M-test, wafer curvature measurements, dynamic (resonant) tests, fabrication of passive strain sensors, and Raman spectroscopy. We discuss the characteristics of typical test structures, and the common sources of structure-related errors in measurement. A rational approach for the selection of test techniques for the design of microsystems is suggested.

A review of MEMS-based microscale and nanoscale tensile and bending testing

Abstract: Thin films at the micrometer and submicrometer scales exhibit mechanical properties that are different than those of bulk polycrystals. Industrial application of these materials requires accurate mechanical characterization. Also, a fundamental understanding of the deformation processes at smaller length scales is required to exploit the size and interface effects to develop new and technologically attractive materials. Specimen fabrication, small-scale force and displacement generation, and high resolution in the measurements are generic challenges in microscale and nanoscale mechanical testing. In this paper, we review small-scale materials testing techniques with special focus on the application of microelectromechanical systems (MEMS). Small size and high force and displacement resolution make MEMS suitable for small-scale mechanical testing. We discuss the development of tensile and bending testing techniques using MEMS, along with the experimental results on nanoscale aluminum specimens.

Piezoelectric-Wafer Active-Sensor Embedded Ultrasonics in Beams and Plates

Abstract: In this paper we present the results of a systematic theoretical and experimental investigation of the fundamental aspects of using piezoelectric wafe active sensors (PWASs) to achieve embedded ultrasonics in thin-gage beam and plate structures. This investigation opens the path for systematic application of PWASs forin situ health monitoring. After a comprehensive review of the literature, we present the principles of embedded PWASs and their interaction with the host structure. We give a brief review of the Lamb wave principles with emphasis on the understanding the particle motion wave speed/group velocity dispersion. Finite element modeling and experiments on thin-gage beam and plate specimens are presented and analyzed. The axial (S 0) and flexural (A 0) wave propagation patterns are simulated and experimentally measured. The group-velocity dispersion curves are validated. The use of the pulse-echo ultrasonic technique with embedded PWASs is illustrated using both finite element simulation and experiments. The importance of using high-frequency waves optimally tuned to the sensor-structure interaction is demonstrated. In conclusion, we discuss the extension of these results toin situ structural health monitoring using embedded ultrasonics.

Dynamic small strain measurements of a metal specimen with a split Hopkinson pressure bar

Abstract: When a conventional split Hopkinson pressure bar (SHPB) is used to investigate the dynamic flow behavior of ductile metals, the results at small strains (ɛ≲2%) are not considered valid owing to fluctuations associated with the early portion of the reflected signal and the nonequilibrated stress state in the specimen. When small-strain behavior is important, such as in the case of determining the elastic behavior of materials, the accuracy of a conventional SHPB is not acceptable. Using a pulse-shaping technique, the dynamic elastic properties can be determined with a SHPB, as well as the dynamic plastic flow. We present a description of the experimental technique and the experimental results for a mild steel. The dynamic compressive stress-strain curve is composed of a lower strain-rate elastic portion and a high strain-rate plastic flow portion.

Digital speckle correlation for strain measurement by image analysis

Abstract: This paper is concerned with small strain measurement utilizing the numerical processing of digital images. The proposed method has its theoretical basis in digital signal analysis and, from a methodological point of view, it can be considered as an extension to digital images of the wellknown white light speckle photography technique. That conventional method is based on the analysis of photographic plates that are exposed twice (before and after the specimen deformation) with the image of a random speckle pattern that has been previously printed on the test piece surface. The digital speckle correlation advantages consist of requiring a very simple specimen preparation and, mainly, of allowing the strain field computation just by numerical elaboration of the acquired images. In this paper, the theoretical basis of the technique and some valuable improvements to the known analogous methodologies are presented. Finally, test results for an application of digital speckle correlation are shown and advantages and disadvantages of the technique are elaborated. In addition, further developments in this area are discussed.

Mechanical Properties of Ultrananocrystalline Diamond Thin Films Relevant to MEMS/NEMS Devices

Abstract: The mechanical properties of ultrananocrystalline diamond (UNCD) thin films were measured using microcantilever deflection and membrane deflection techniques. Bending tests on several free-standing UNCD cantilevers, 0.5 μm thick, 20 μm wide and 80 μm long, yielded elastic modulus values of 916–959 GPa. The tests showed good reproducibility by repeated testing on the same cantilever and by testing several cantilevers of different lengths. The largest source of error in the method was accurate measurement of film thickness. Elastic modulus measurements performed with the novel membrane deflection experiment (MDE), developed by Espinosa and co-workers, gave results similar to those from the microcantilever-based tests. Tests were performed on UNCD specimens grown by both micro and nano wafer-seeding techniques. The elastic modulus was measured to be between 930–970 GPa for the microseeding and between 945–963 GPa for the nanoseeding technique. The MDE test also provided the fracture strength, which for UNCD was found to vary from 0.89 to 2.42 GPa for the microseeded samples and from 3.95 to 5.03 for the nanoseeded samples. The narrowing of the elastic modulus variation and major increase in fracture strength is believed to result from a reduction in surface roughness, less stress concentration, when employing the nanoseeding technique. Although both methods yielded reliable values of elastic modulus, the MDE was found to be more versatile since it yielded additional information about the structure and material properties, such as strength and initial stress state.

Determination of dynamic fracture-initiation toughness using three-point bending tests in a modified Hopkinson pressure bar

Abstract: We present a procedure for measuring the dynamic fracture-initiation toughness of materials. The method is based on three-point bending tests at high loading rates, performed in an experimental device which is a modification of the classical split Hopkinson pressure bar. Coupled with the loading device, a high-speed photography system was used to measure the crack mouth opening displacement (CMOD) directly on the specimen. The stress intensity factor was calculated by three different simplified methods and the time to fracture was obtained from an appropriate specimen instrumentation. To evaluate the results derived from the simplified methods, a two-dimensional full-numerical analysis of the dynamic bending fracture test was made. The model includes the specimen, the input bar, the impacting projectile and the supporting device and takes into account the possible loss of contact during the experiment between the input bar and the specimen and between the specimen and its supports. From the tests and numerical results, it can be concluded that the CMOD procedure, together with the knowledge of the time to fracture determined using crack gages, seems to be the best method for measuring dynamic fracture-initiation toughness.

Fourier and wavelet analyses for fatigue assessment of concrete beams

Abstract: We investigate damage detection in a simply-supported pre-stressed beam. A crack was propagated by fatigue loads, which were applied up to two million cycles. Both fast Fourier transform (FFT) and continuous wavelet transform (CWT) are used in the analysis of the structural response to impulse loads. The acceleration response of the full-scale beam was measured each time a certain number of cycles of fatigue loads were applied. The results of this study show that both methods can clearly identify the crack growth induced by fatigue loads. The natural frequencies found by FFT are sensitive to the crack progression. The results from the CWT analysis show a clear difference in structural responses between the initial and damaged states of the structure. The response accelerations are de-noised by a soft-thresholding method before they are analyzed by CWT. In addition to the frequency components, the CWT shows the moment in time when particular frequencies occur. Therefore, wavelet analysis has the potential of becoming an effective tool for damage detection and health monitoring of structures for which the natural frequencies are irregularly changing. As the crack grows, the magnitude of ridges obtained by CWT analysis decreases significantly, which indicates the reduction in structural stiffness.

Murray Lecture Tensile Testing at the Micrometer Scale: Opportunities in Experimental Mechanics

Abstract: The measurement of mechanical properties using specimens whose minimum dimensions are of the order of micrometers is an important new area of experimental solid mechanics. One obvious application is in the area of micro-electromechanical systems (MEMS) where the final product is on the millimeter or micrometer scale.

A new method for the biaxial testing of cellular solids

Abstract: Commercial cellular solids such as metal foams and honeycombs exhibit deformation and failure responses that are dependent on specimen size during testing. For foams, this size dependence originates from the fabrication-induced material and structural inhomogeneities, which cause the uncontrolled localization of deformation during the testing of foam cubes. Different peak loads and failure modes are observed in honeycomb specimens in the plate-shear configuration depending on specimen height. This size dependence causes difficulty in obtaining a more representative constitutive behavior of the material. It has recently been established that the size dependence under uniaxial compression can be eliminated with tapered cellular specimens, which enable controlled deformation at a given region of the specimen. This concept is extended in this paper to the biaxial testing of butterfly-shaped cellular specimens in the Arcan apparatus, which focuses deformation at the central section of the specimen. The Arcan apparatus has been modified such that all displacements at the boundaries of the specimen could be controlled during testing. As a consequence of this fully displacement controlled Arcan apparatus, a force perpendicular to that applied by the standard universal testing machine is generated and becomes significant. Thus, an additional load cell is integrated on the apparatus to measure this load. Example responses of butterfly-shaped specimens composed of aluminum alloy honeycomb, aluminum alloy foam and hybrid stainless-steel assembly are presented to illustrate the capabilities of this new testing method.

Overview of optical techniques that measure displacements: Murray lecture

Abstract: Optical techniques that measure displacements play a very important role in current experimental mechanics, material sciences and metrology. This paper presents a survey of developments in these techniques from a personal experience point of view. Three main aspects are considered. Mathematical and numerical models used in the interpretation of fringe information and the corresponding data processing techniques. Optical and electro-optical developments that have taken place to improve the sensitivity, and the efficiency of these methods to make them competitive with purely numerical methods. Applications that have arisen from the synergy between advanced computational capabilities and optics are also presented.

Processing and characterization of epoxy/clay nanocomposites

Abstract: Nanocomposite materials consisting of an epoxy matrix and silicate clay particles have been processed and characterized mechanically. The clay material used was a modified natural montmorillonite. The clay particles consisted of 1 nm thick layers with aspect ratios in the range of 100–1000. The clay particles were mixed with acetone and sonicated, then mixed with the polymer, deaerated and cured. The ultimate objective of processing was to produce a polymer/clay nanocomposite with separated (exfoliated) platelets, dispersed as uniformly as possible. Samples were prepared with clay concentrations of up to 10 wt%. The process used resulted in limited exfoliation but mostly intercalation, i.e., infusion of polymer between the silicate layers and increase of interlayer spacing. The characteristics of the nanocomposite were assessed by transmission electron microscopy and x-ray diffraction. Results from these observations show that the basal spacing of clay platelets increased from an initial pre-processing value of 1.85 nm to 4.5 nm. Enhancement of mechanical properties was measured by tensile testing of coupons. Stiffness increases of up to 50% over that of the unfilled epoxy were measured for clay concentrations of 5 wt%. Strength increases were also measured for low clay concentrations and low strain rate loading. Micromechanics modeling of mechanical behavior is discussed as a function of clay platelet dispersion.

A novel instrument for transient photoelasticity

Abstract: A new instrument has been developed for the photoelastic analysis of transient events. The instrument is based on the Phase-Stepped Images Obtained Simultaneously (PSIOS) system developed by Patterson and Wang, which enables four phase-stepped photoelastic images to be collected simultaneously. Where the new instrument differs is that the original instrument requires four cameras to collect the four images, whereas the new instrument requires only one camera. This makes the use of phase-stepping viable for events, in which the fringe order varies with time. Three examples are given of the use of the instrument in static and dynamic photoelasticity to generate full field maps of isochromatic fringes. The instrument has been found to work well and significantly increases the potential for the use of photoelasticity to study transient and possibly dynamic events.

Residual stress distribution on surface-treated Ti-6Al-4V by X-ray diffraction

Abstract: The x-ray diffraction technique has been used to measure surface residual stress in Ti-6Al-4V samples subjected to shot peening (SP), laser shock peening (LSP) and low plasticity burnishing (LPB). The magnitude, spatial and directional dependence and uniformity of the surface residual stresses have been investigated. The results show that residual stresses due to SP are uniform and independent of direction. LSP has been observed to produce non-uniform residual stress varying from one region to another, and also within a single laser shock. In the case of LPB, residual stresses have uniform spatial distribution but have been observed to be direction-dependent. Various components of the residual stress tensor in the LPB sample have been determined following the Dolle-Hauk method. The results of the residual stress due to three surface treatments are compared, and possible reasons for spatial and directional dependence are discussed.

Determination of residual stresses by an optical correlative hole-drilling method

Abstract: In conjunction with the incremental hole-drilling method, a new evaluation procedure is presented for determining the residual stress state in components. In contrast to the classical method, the whole displacement field around the drilled hole is measured using the electronic speckle pattern interferometry technique. The displacement patterns, measured without contact to the surface, are then correlated with those obtained by finite-element simulations using statistical methods. The simulated displacement patterns, used for calibration purposes, result from the application of properly defined basic loads. In this way, the values and the orientation of the residual stresses can be determined by superposition of these properly scaled and shifted basic loads. Even complex states of stress can be evaluated. The theoretical background and experimental results are presented.

Mixed-mode failure of thin films using laser-generated shear waves

Abstract: A new test method is developed for studying mixed-mode interfacial failure of thin films using laser generated stress waves. Guided by recent parametric studies of laser-induced tensile spallation, we successfully extend this technique to achieve mixed-mode loading conditions. By allowing an initial longitudinal wave to mode convert at an oblique surface, a high amplitude shear wave is generated in a fused silica substrate and propagated toward the thin-film surface. A shear wave is obtained with amplitude large enough to fail an Al film/fused silica interface and the corresponding shear stress calculated from high-speed interferometric displacement measurements. Examination of the interfaces failed under mixed-mode conditions reveals significant wrinkling and tearing of the film, in great contrast to blister patterns observed in similar Al films failed under tensile loading.

Strain analysis for moiré interferometry using the two-dimensional continuous wavelet transform

Abstract: In this paper, we introduce the two-dimensional continuous wavelet transform for the automated strain analysis of the moire interference fringe pattern. The Fourier transform method has been widely used for automated analysis of an optical interference fringe pattern. However, this method is hardly applicable to the analysis of the fringe pattern, which includes large displacement range or discontinuities. We show the advantages of the wavelet transform method by applying it to experimental results on composite laminates.

Thin film cracking modulated by underlayer creep

Abstract: In devices that integrate dissimilar materials in small dimensions, crack extension in one material often accompanies inelastic deformation in another. In this paper we analyze a channel crack advancing in an elastic film, while an underlayer creeps. The film is subject to a tensile stress. As the underlayer creeps, the stress field in the film relaxes in the crack wake, and intensifies around the crack tip. In a blanket film, the crack can attain a steady velocity, set by two rate processes: subcritical decohesion at the crack tip, and creep in the underlayer. In a thin-film microbridge over a viscous stripe, the crack cannot grow when the bridge is short, and can grow at a steady velocity when the bridge is long. We use a two-dimensional shear lag model to approximate the three-dimensional fracture process, and an extended finite element method to simulate the moving crack with an invariant, relatively coarse mesh. On the basis of the theoretical findings, we propose new experiments to measure fracture toughness and creep laws in small structures. As a byproduct, an analytical formula is found for the growth rate per temperature cycle of a channel crack in a brittle film, induced by ratcheting plastic deformation in a metal underlayer.

Dynamic torsion testing of nanocrystalline coatings using high-speed photography and digital image correlation

Abstract: The strength and ductility of microcrystalline and nanocrystalline tungstsen carbide-cobalt (WC-Co) cermets have been evaluated by employing a stored energy Kolsky bar apparatus, high-speed photography and digital image correlation. The test specimens were thin-walled tubular AI7075-T6 substrates 250 μm thick, coated with a 300 μm thick microcrystalline or nanocrystalline WC-Co layer with an average grain size of about 3 μm and 100 nm, respectively. Dynamic torsion experiments reported in this paper reveal a shear modulus of 50 GPa and a shear strength of about 50 MPa for both microcrystalline and nanocrystalline WC-Co coatings.

Fatigue damage evolution in silicon films for micromechanical applications

Abstract: In this paper we examine the conditions for surface topography evolution and crack growth/fracture during the cyclic actuation of polysilicon microelectromechanical systems (MEMS) structures. The surface topography evolution that occurs during cyclic fatigue is shown to be stressassisted and may be predicted by linear perturbation analyses. The conditions for crack growth (due to pre-existing or nucleated cracks) are also examined within the framework of linear elastic fracture mechanics. Within this framework, we consider pre-existing cracks in the topical SiO2 layer that forms on the Si substrate in the absence of passivation. The thickening of the SiO2 that is normally observed during cyclic actuation of Si MEMS structures is shown to increase the possibility of stable crack growth by stress corrosion cracking prior to the onset of unstable crack growth in the SiO2 and Si layers. Finally, the implications of the results are discussed for the prediction of fatigue damage in silicon MEMS structures.

Performance evaluation of accelerometers used for penetration experiments

Abstract: We present a Hopkinson bar technique to evaluate the performance of accelerometers that measure large amplitude pulses, such as those experienced during projectile penetration tests. An aluminum striker bar impacts a thin Plexiglas or copper disk placed on the impact surface of an aluminum incident bar. The Plexiglas or copper disk pulse shaper produces a nondispersive stress wave that propagates in the aluminum incident bar and eventually interacts with a tungsten disk at the end of the bar. A quartz stress gage is placed between the aluminum bar and tungsten disk, and an accelerometer is mounted to the free end of the tungsten disk. An analytical model shows that the rise time of the incident stress pulse in the aluminum bar is long enough and the tungsten disk length is short enough that the response of the tungsten disk can be accurately approximated as rigid-body motion. We measure stress at the aluminum bar-tungsten disk interface with the quartz gage and we calculate rigid-body acceleration of the tungsten disk from Newton's Second Law and the stress gage data. In addition, we measure strain-time at two locations on the aluminum incident bar to show that the incident strain pulse is nondispersive and we calculate rigid-body acceleration of the tungsten disk from a model that uses this strain-time data. Thus, we can compare accelerations measured with the accelerometer and accelerations calculated with models that use stress gage and strain gage measurements. We show that all three acceleration-time pulses are in very close agreement for acceleration amplitudes to about 20,000 G.

A polymeric split Hopkinson pressure bar instrumented with velocity gages

Abstract: Polymeric split Hopkinson pressure bars are often used to test low-impedance materials at elevated strain rates. However, they tend to be viscoelastic, and a viscoelastic wave propagation model is required to analyze the data. This considerably complicates the analysis over the more common linear elastic split Hopkinson bar. In this research, a polymeric split Hopkinson bar is instrumented with electromagnetic velocity gages. The gages are placed at the interfaces between the bars and the specimen. By using this arrangement, viscoelastic effects in the bars are negligible and the need for a viscoelastic correction is eliminated. The method is applied by testing low-density foams.

An Experimental/Computational Approach to Identify Moduli and Residual Stress in MEMS Radio-Frequency Switches

Abstract: In this paper, we identify the Young's modulus and residual stress state of a free-standing thin aluminum membrane, used in MEMS radio-frequency (rf) switches. We have developed a new methodology that combines a membrane deflection experiment (MDE) and three-dimensional numerical simulations. Wafer-level MDE tests were conducted with a commercially available nanoindenter. The accuracy and usefulness of the MDE is confirmed by the repeatability and uniformity of measured load-deflection curves on a number of switches with both wedge and Berkovich tips. It was found that the load-deflection behavior is a function of membrane elastic properties, initial residual stress state and corresponding membrane shape. Furthermore, it was assessed that initial membrane shape has a strong effect on load-deflection curves; hence, its accurate characterization is critical. Through an iterative process and comparison between MDE data and numerical simulations, the Young's modulus and residual stress state, consistent with measured membrane shape, were identified. One important finding from this investigation is that variations in membrane elastic properties and residual stress state affect the load-deflection curve in different regimes. Changes in residual stress state significantly affect the load-deflection slope at small values of deflection. By contrast, variations in Young's modulus result in changes in load-deflection slope at large deflections. These features are helpful to decouple both effects in the identification process.

Inspection of interfaces between corroded steel bars and concrete using the combination of a piezoelectric zirconate-titanate transducer and an electromagnetic acoustic transducer

Abstract: We have conducted an inspection of the interface between a steel bar and concrete using the combination of a piezoelectric zirconate-titanate transducer (PZT) and an electromagnetic acoustic transducer (EMAT). The PZT is used for generating elastic waves by mechanical vibration and then the EMAT is used for receiving the transmitted ultrasonic guided waves. This arrangement is made in order to overcome the major shortcomings of the PZT, i.e., the requirement of a couplant, and of the EMAT, i.e., relatively low transmitted ultrasonic energy. To investigate the applicability of this technique in the field, outside the laboratory environment, the experiments are conducted on different types of steel bars: corrosion-free, naturally corroded, and zinc-coated as well as corroded bars. It is shown that the PZT-EMAT combination is very effective for inspecting the steel bar-concrete interface. Using this technique, small separation at the steel bar-concrete interface can be effectively detected for corroded as well as corrosion-free specimens. This method can be applied in the field to pre-stressed tendons and soil nails, where one side of the reinforcement is exposed.

On the Use of Stereolithography for the Manufacture of Photoelastic Models

Abstract: Three-dimensional photoelasticity using the stress-freezing technique is dependent on the production of resin models that do not possess any residual stresses from the manufacturing process. The traditional methods of production involve casting to shape or machining from solid blocks using thermo-setting resins. These methods are expensive and time-consuming, with models typically requiring days for preparation. The rapid-prototyping technique of stereolithography employs similar resins and allows complex components to be built in a matter of hours. However, the residual birefringence associated with the stereolithographic process has so far inhibited its routine use in photoelasticity. A four-centre study has been conducted in an attempt to understand the mechanisms generating this birefringence and to investigate methodologies for producing models free of stress and birfringence. The mechanical behavior of stereolithographic and thermo-setting resins have been compared at room temperature and under stress-freezing conditions.

Process pathway inference via time series analysis

Abstract: Motivated by recent experimental developments in functional genomics, we construct and test a numerical technique for inferring process pathways, in which one process calls another process, from time series data. We validate using a case in which data are readily available and we formulate an extension, appropriate for genetic regulatory networks, which exploits Bayesian inference and in which the present-day undersampling is compensated for by prior understanding of genetic regulation.

Elastic-plastic contact mechanics of indentations accounting for phase transformations

Abstract: A contact mechanics model is developed which takes into account possible phase transformations in materials induced by hydrostatic and shear stresses associated with indentation. The proposed model allows prediction of the average thickness and approximate shape of the phase transformation zone in semiconductors and ceramics under various types of diamond indenters. The results of theoretical calculation are in good agreement with the available experimental data.

Measurement techniques in the testing of thin-walled structural members

Abstract: The paper describes methods for measuring displacements and end moments in the testing of thin-walled columns. The complete spatial deformation of a column can be captured by using local and overall deformation measurement frames. The local frame involves spring-loaded levers and roller bearings to mount the frame on to the specimen. The overall frame slides along high-precision shafts using linear ball bearings. Fixed-ended bearings are used to measure minor and major axis bending moments as well as the applied load. The bearings allow the line of action of the applied force to be determined.

Reduction of KI and KII by the shape-memory effect in a TiNi shape-memory fiber-reinforced epoxy matrix composite

Abstract: Shape-memory TiNi fiber-reinforced/epoxy matrix composites have been fabricated, and the suppression of crack-tip stress intensity and the change in fracture toughness have been systematically investigated. Stress-strain data for these composite specimens with notches at various angles and different crack lengths in the transverse direction have been measured in tensile tests. The stress intensity factor at the crack tip is experimentally determined from photoelastic fringe patterns. The decreases inK values are attributed to the compressive stress field in the matrix induced when the pre-strains of the TiNi fiber contract to their initial length upon heating above the austenitic final temperature. We present the influences of the pre-strain of TiNi fibers and the compressive domain size between a crack tip and fiber on theK value.

Strain measurements in the nanometer range in a particulate composite using computer-aided moiré

Abstract: When using metals and polymers in structural applications the macroscopic behavior depends on events taking place at levels in micrometer and nanometer ranges. At this range, material behavior, phenomena such as plasticity and fracture are size-dependent. We discuss these phenomena with regards to the case analyzed in this paper. Continuum mechanics flow theory of plasticity cannot explain the failure behavior of a particle-reinforced aluminum composite. An experimental study of the strain field in the micrometer range provides an explanation of the earlier than expected failure of the composite. We give a detailed description of the optical technique used to make the experimental mechanics measurements.