Electromechanical Characterization of Au Thin Films using Micro-tensile Testing

This paper presents the test technique about measurement of electrical resistance changes of thin films during tensile testing. In this work, we used a real-time digital image correlation strain measurement system coupled with micro-tensile testing unit and voltage/current sourcemeter. This system has the advantage of real time displacement monitoring with a resolution of 50 nm during the micro-tensile testing, with the ability to measure the variation in electrical resistance of the specimen at the same time. We obtained the complete testing data for the stress–strain curve and associated electrical resistance-strain curve for 1 and 2 μm-thick freestanding gold films. Young’s modulus was about 61~69 GPa and 0.2% offset yield strength was about 361~402 MPa. In case of the electrical resistance, rapid change was observed under the elastic regime, while less obvious under the plastic regime. We also conducted finite element analysis, and this result implied that the electrical resistivity would not be constant during micro-tensile testing.     

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.     

Microscale Experiments at Elevated Temperatures Evaluated with Digital Image Correlation

The methods of uniform heating and resistive (Joule) heating for microscale freestanding surface-micromachined thin metal film specimens were evaluated by a combination of full-field strain measurements by optical microscopy/Digital Image Correlation (DIC) and microscopic infrared (IR) imaging. The efficacy of each method was qualitatively and quantitatively evaluated with the aid of strain fields and IR-obtained temperature distributions along 850 nm thick freestanding microscale specimens subjected to uniaxial tension while heated by each method. The strain and temperature fields were quite uniform in experiments carried out with uniform specimen heating except for minor end-effects at the specimen grips. However, the resistively heated specimens showed highly uneven temperature distribution varying by 50°C along the 1,000 μm specimen gauge length. This high temperature gradient resulted in strain localization and 40% reduction in yield and ultimate tensile strengths of resistively heated specimens compared to the uniformly heated ones. Therefore, it is concluded that resistive heating is not a reliable method for conducting microscale temperature experiments with metallic films.     

An Investigation of Fatigue Characteristics of Copper Film

Tensile and fatigue behaviors of the copper film coated by tin (Sn) were investigated considering S-N relationships and scanning electron microscope (SEM) observation of fracture surfaces. The fatigue behavior was investigated considering the effect of load ratio, R. The specimen of 2000 μm width, 8000 μm length and 15.26 μm thickness was fabricated by etching process. Tensile properties were measured using the micro-tensile testing system and in-plane electronic speckle pattern interferometric (ESPI) system for measuring the tensile strain during the test. The fatigue tests of the film were carried out in load-control mode with 40 Hz at three different stress ratios of 0.05, 0.3 and 0.5. The S-N curves, including the slope of the curve and fatigue limit, at the respective stress ratios were obtained. These curves were dependent on the load ratio. Empirical relationships indicating the dependency of the fatigue limit and S-N curve on the load ratio were suggested in this study. SEM observation of the tensile fracture surface showed that the cross-sectional area of the testing section was necked in the direction of the film thickness (i.e. parallel to the substrate surface normal) and some ductile dimples in the fracture surface were present. The fracture of the copper film under cyclic loading was progressed in the transgranular fracture mode.     

Mechanical properties of ultrananocrystalline diamond thin films relevant to MEMS/NEMS devices

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.     

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.     

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.     

New Explicit Expression of Barnett-Lothe Tensors for Anisotropic Linear Elastic Materials

The three Barnett-Lothe tensors H, L, S appear often in the Stroth formalism of two-dimensional deformations of anisotropic elastic materials [1–3]. They also appear in certain three-dimensional problems [4, 5]. The algebraic representation of H, L, S requires computation of the eigenvalues p^v(v=1,2,3) and the normalized eigenvectors (a, b). The integral representation of H, L, S circumvents the need for computing p ^v(v=1,2,3) and (a, b), but it is not simple to integrate the integrals except for special materials. Ting and Lee [6] have recently obtained an explicit expression of H for general anisotropic materials. We present here the remaining tensors L, S using the algebraic representation. They key to our success is the obtaining of the normalization factor for (a, b) in a simple form. The derivation of L and S then makes use of (a, b) but the final result does not require computation of (a, b), which makes the result attractive to numerical computation. Even though the tensor H given in [6] is in terms of the elastic stiffnesses C^μ v while the tensors L, S presented here are in terms of the reduced elastic compliances s′ _μv , the structure of L, S is similar to that of H. Following the derivation of H, we also present alternate expressions of L, S that remain valid for the degenerate cases p ₁ p ₂ and p₁=p₂ = p ₃. One may want to compute H, L, S using either C _μv or s′ _μv v, but not both. We show how an expression in C^μ v can be converted to an expression in s′ _μv v, and vice versa. As an application of the conversion, we present explicit expressions of the extic equation for p in C^μ v and s′ _μv v. This revised version was published online in August 2006 with corrections to the Cover Date.     

微纳米材料及其结构的界面强度的实验研究

介绍了近年来微纳米材料强度实验测试研究方面的最新进展,重点综述了可用于微纳米材料及其结构中界面强度测试的实验系统、测试方法及结果.主要内容包括:测试微纳米薄膜界面端分层裂纹启裂的夹层悬臂梁方法,测试纳米岛/衬底间界面结合强度的改进AFM (atomic force microscopy)方法, 测试裂纹沿界面扩展的预裂纹法,可实现纳米薄膜界面裂纹原位观察的实验测试方法,测试薄膜在疲劳、蠕变条件下界面裂纹扩展的改进4点弯曲法等.除了总结分析测试结果,还讨论了上述实验方法的优缺点和适用范围,并指出了微纳米材料界面强度实验研究方面的一些挑战与难点,最后提出了若干需要继续研究的课题.      

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.     

Tensile and Tensile-Mode Fatigue Testing of Microscale Specimens in Constant Humidity Environment

A tensile and tensile-mode-fatigue tester has been developed for testing microscale specimens in high humidity environments in order to investigate the fracture mechanisms of microelectromechanical materials. A humidity control system was installed on a tensile-mode fatigue tester equipped with an electrostatic force grip. A specimen and a griping device were inserted into a small chamber and the humidity was controlled by air flow from a temperature and humidity chamber. The humidity stability was within ±2%RH for humidities in the range 25–90%RH for eight hours of testing. Fatigue tests were performed on single-crystal silicon (SCS) specimens in constant humidity environments and laboratory air for up to 10⁶ cycles. The gauge length, width, and thickness of the SCS specimens were 100 or 500 μm, 13.0 μm, and 3.3 μm, respectively. The average tensile strength was 3.68 GPa in laboratory air; this value decreased in high humidity environments. Fatigue failure was observed during cyclic loading at stresses lower than the average strength. A reduction in the fatigue strength was observed at high relative humidities. Different fracture origins and fracture behaviors were observed in tensile tests and fatigue tests, which indicates that the water vapor in air affects the fatigue properties of SCS specimens.     

A new direct biaxial testing machine for anisotropic materials

A screw-driven new biaxial testing machine for the realization of experimental investigations on anisotropic sheet materials, such as composite plates or rolled sheet metals, is presented. The described mechanical concept and servocontrol system allow cruciform specimens to be subjected to large strain biaxial tensile and compressive tests without kinematic incompatibilities. Moreover, for the proper implementation of biaxial tensile tests, the specific problems linked to the anisotropic properties of the investigated materials are taken into account; therefore, for the first time, the biaxial machine is supplied with the original ‘off-axes testing device,’ consisting of hinged fixtures with knife-edges at each arm of the cruciform specimen. A recently developed optimization method for the optimal design of flat tensile cruciform specimens is shortly reviewed. Numerical simulations illustrate the decisive superiority of the optimized specimen compared with specimen designs proposed in the literature, as well as the necessity to use the ‘off-axes’ testing technique in biaxial tests on anisotropic materials.     

A Tensile Split Hopkinson Bar for Testing Particulate Polymer Composites Under Elevated Rates of Loading

A tensile split Hopkinson bar apparatus is developed for testing high strain rate behavior of glass-filled epoxy. The apparatus uses a specimen gripping configuration which does not require fastening and/or gluing and can be readily used for castable materials. Details of the experimental setup, design of grips and specimen, specimen preparation method, benchmark experiments, and tensile responses are reported. Also, the effects of filler volume fraction (0–30%) and particle size (11–42 μm) are examined under high rates of loading and the results are compared with the ones obtained from quasi-static loading conditions. The results indicate that the increase in the loading rate contributes to a stiffer and brittle material response. In the dynamic case lower ultimate stresses are seen with higher volume fractions of filler whereas in the corresponding quasi-static cases an opposite trend exists. However, the absorbed specific energy values show a decreasing trend in both situations. The results are also evaluated relative to the existing micromechanical models. The tensile response for different filler sizes at a constant volume fraction (10%) is also reported. Larger size filler particles cause a reduction in specimen failure stress and specific energy absorbed under elevated rates of loading. In the quasi-static case, however, the ultimate stress is minimally affected by the filler size.     

A new hybrid technique for in-plane characterization of orthotropic materials

In this paper we present a novel hybrid procedure for the in-plane mechanical characterization of orthotropic materials. The material identification reverse engineering problem is solved by combining speckle interferometry and numerical optimization. The rationale behind the entire process is the following: for any specimen to be characterized and which has been subjected to some loading condition, it is possible to express the difference between experimental data and analytical/numerical predictions by means of an error function ψ, which depends on the elastic constants of the material. The ψ error will decrease as the elastic constants come close to their target values. Here, we build the ψ function as the difference between the displacement field measured with speckle interferometry and its counterpart computed by means of finite element analysis. Since the ψ function is highly non-linear, it has to be optimized with a global optimization algorithm, which perform a random search in the elastic constants design space. The hybrid material identification process finally allows us to determine values of the elastic constants. In order to prove the feasibility of the present approach, we have determined the in-plane elastic properties of an eight-ply composite laminate (woven fiberglass-epoxy) used as a substrate for printed circuit boards. The results indicate that the procedure proposed in this paper was able to accurately characterize the material under investigation. Remarkably, the elastic constants found by the identification procedure were less than 0.7% different from their target values, while the residual error between the displacements measured by speckle interferometry and those computed at the end of the optimization process was less than 3%. L. Lamberti is an Assistant Professor, and C. Pappalettere (SEM Member and President of the Italian Society of Stress Analysis) is Professor of Mechanical Engineering and Experimental Mechanics, Politecnico di Bari, Dipartimento di Ingegneria Meccanica e Gestionale, Viale Japigia 182, 70126 Bari, Italy     

An Experimental–Numerical Methodology for a Rapid Prototyped Application Combined with Finite Element Models in Vertebral Trabecular Bone

In the present study, a novel evaluation method involving rapid prototyped (RP) technology and finite element (FE) analysis was used to study the elastic mechanical characteristics of human vertebral trabecular bone. Three-dimensional (3D) geometries of the RP and FE models were obtained from the central area of vertebral bones of female cadavers, age 70 and 85. RP and FE models were generated from the same high-resolution micro-computed tomography (μCT) scan data. We utilized RP technology along with FE analysis based on μCT for high-resolution vertebral trabecular bone specimens. RP models were used to fabricate complex 3D objects of vertebral trabecular bone that were created in a fused deposition modeling machine. RP models of vertebral trabecular bone are advantageous, particularly considering the repetition, risks, and ethical issues involved in using real bone from cadaveric specimens. A cubic specimen with a side length of 6.5 mm or a cylindrical specimen with a 7 mm diameter and 5 mm length proved better than a universal cubic specimen with a side length of 4 mm for the evaluation of elastic mechanical characteristics of vertebral trabecular bones through experimental and simulated compression tests. The results from the experimental compression tests of RP models closely matched those predicted by the FE models, and thus provided substantive corroboration of all three approaches (experimental tests using RP models and simulated tests using FE models with ABS and trabecular bone material properties). The RP technique combined with FE analysis has potential for widespread biomechanical use, such as the fabrication of dummy human skeleton systems for the investigation of elastic mechanical characteristics of various bones.     

Immersion interferometer for microscopic moiré interferometry

The basic sensitivity of moiré interferometry has been increased beyond the previously conceived theoretical limit. This is accomplished by creating the virtual reference grating inside a refractive medium instead of air, thus shortening the wavelength of light. Various optical configurations of moiré interferometry for operation in a refractive medium are introduced and one of them has been put into current practice. A very compact four-beamimmersion interferometer has been developed for microscopic viewing, which produces a basic sensitivity of 4.8 fringes per μm displacement (contour interval of 0.208 μm per fringe order), corresponding to moiré with 4800 lines per mm. Its configuration makes it inherently stable and relatively insensitive to environmental disturbances. An optical microscope is employed to obtain high spatial resolution. The method is demonstrated for deformation of a thick graphite/epoxy composite at the 0/90-deg ply interface. Paper was presented at the 1991 SEM Spring Conference on Experimental Mechanics held in Milwaukee, WI on June 9–13, 1991.     

Flexure-based micromechanical testing machines

The successful design and fabrication of structures and systems at the small scale require robust methods for characterizing the mechanical behavior of materials at the same scale. In this paper we describe the design of two flexure-based micromechanical testers capable of measuring forces with an accuracy of 25 μN over a range of 1–30 N, and specimen extensions with an accuracy of 20 nm over a range of 1–5 mm. These force and displacement resolutions and ranges are required in a wide variety of material characterization applications, such as microtensile testing of micrometer-dimensioned films, foils and wires, bending of millimeter-sized beams, as well as micro-indentation. The novel feature of our machines is that they are based on the use of two compound flexures in an integrated monolithic frame: one flexure functioning as a precision guide for actuation, and the other fexure as a linear spring for force measurement. Two machines, one with a maximum load capacity of 1.5 N and the other of 30 N, have been constructed based on this concept. Details of their design, construction, and typical test results are presented in this paper.     

Material Property Differentiation in Indentation Testing Using Secondary Sensors

Current in vivo and in situ testing procedures are dominated by indentation. The major challenge for this testing technique is in finding a unique solution to the “inverse problem” i.e., defining an appropriate constitutive framework and obtaining material properties consistent with the indentation force–displacement data. Much of the information related to the interplay between shear and bulk compliance in the deformation field beneath the indenter is lost when capturing this single output. We propose a material testing method that follows the well proven path of conventional indentation methods, but enriches the signal by acquiring displacement data not only for the actuated indenter, but also for a set of offset, passive secondary sensors. We use finite element (FE) simulations involving three cases of materials: (a) linear elastic, (b) hyperelastic and (c) time-dependent to demonstrate the benefit of these additional sensors. The results indicate that the addition of these secondary sensors can help to discern between materials with varying degrees of compressibility.     

High-magnification moiré interferometer for crack tip analysis of steels

A high-magnification moiré interferometer, particularly suitable for near-tip field analysis in cracked materials, is described. It has a submillimeter field of view, a high-resolution image sensor (1.4 million pixels), X-Y-Z translation stage and an optical fiber light delivery system. These features enable the microscope head to observe the crack tip while the specimen is loaded in a standard tensile test machine. Automated fringe pattern analysis, using temporal phase shifting and spatial phase unwrapping, enables thex ory displacement component to be measured and the corresponding in-plane strain component computed. The displacement placement accuracy is better than 40 nm, and the effective strain gage dimension is ∼ 25 μm. Furthermore, the interferometer has a built-in white light microscope that allows the observation of the specimen granular microstructure in exact registration with the displacement field. The interferometer has hence been employed to investigate the near-tip fields of a precracked stainless steel specimen under load. The influence of the grain boundaries on the measured displacement fields was relatively minor. The near-tip strain field shows a significant asymmetrical behavior despite pure mode lloading conditions.