Tensile testing of polysilicon

Tensile specimens of polysilicon are deposited on a silicon wafer; one end remains affixed to the wafer and the other end has a relatively large paddle that can be gripped by an electrostatic probe. The overall length of the specimen is less than 2 mm, but the smooth tensile portion can be as small as 1.5×2m in cross section and 50m long. The specimen is pulled by a computer-controlled translation stage. Force is recorded with a 100-g load cell, whereas displacement is recorded with a capacitance-based transducer. Strain can be measured directly on wider specimens with laser-based interferometry from two small gold markers deposited on the smooth portion of the specimen. The strength of this linear and brittle material is measured with relative ease. Young's modulus measurement is more difficult; it can be determined from either the stress-strain curve, the record of force versus displacement or the comparison of the records of two specimens of different sizes. Specimens of different sizes—thicknesses of 1.5 or 3.5 m, widths from 2 to 50 m and lengths from 50 to 500 m—were tested. The average tensile strength of this polysilicon is 1.45±0.19 GPa (210 ±28 ksi) for the 27 specimens that could be broken with electrostatic gripping. The average Young's modulus from force displacement records of 43 specimens is 162±14 GPa (23.5 ±2.0×10³ ksi). This single value is misleading because the modulus values tend to increase with decreasing specimen width; that is not the case for the strength. The three methods for determining the modulus agree in general, although the scatter can be large.     

正常及骨关节炎软骨细胞黏弹性研究

采用前交叉韧带切断术造骨关节炎(OA)动物模型，并采用微管吸吮技术和标准线性 黏弹性固体模型研究正常及OA软骨细胞的黏弹性特性. 实验研究表明：OA软骨明显退变， 大体评分及Mankin's评分均明显高于正常软骨. 正常软骨细胞直径与OA软骨细胞直径的差异无显 著意义，而正常软骨细胞与OA软骨细胞的黏弹性特性存在明显差异，正常软骨 细胞的平衡模量E , 瞬间模量E0及表观黏性 明显高于OA软骨细胞. 除正常软骨细胞平衡模量E 仅与细胞直径有微弱 相关性且具有统计学意义外，其余黏弹性参数均与细胞直径以及其 直径和微管直径比率无相关性.     

On-Chip Electrostatically Actuated Bending Tests for the Mechanical Characterization of Polysilicon at the Micro Scale

The issue of mechanical characterization of polysilicon used in micro electro mechanical systems (MEMS) is discussed in this paper. An innovative approach based on a fully on-chip testing procedure is described; two ad hoc designed electrostatically actuated microsystems are here used in order to determine experimentally the Young’s modulus and the rupture strength of polysilicon. The first device is based on a rotational test structure actuated by a system of comb-finger capacitors which load up to rupture a couple of tapered beams under bending in the plane parallel to the substrate. The second microsystem is based on a large plate with holes. It constitutes with the substrate a parallel plate capacitor moving in the direction orthogonal to the substrate itself. A couple of tapered beams placed at the centre of the plate is loaded up to rupture in bending in the plane orthogonal to the substrate. By means of the two devices, experimental data are obtained: they allow for a careful determination of Young’s modulus and rupture strength. The rupture values are interpreted by means of the Weibull approach; statistical size effects and stress gradient effect are taken into account thus allowing for a direct comparison between the data obtained from the two test structures.     

A Sequential Tensile Method for Rapid Characterization of Extreme-value Behavior in Microfabricated Materials

A high-throughput sequential tensile test method has been developed to characterize the fracture strength distribution of microfabricated polycrystalline silicon, the primary structural material used in microelectromechanical systems (MEMS). The resulting dataset of over 1,000 microtensile tests reveals subtle extreme-value behavior in the tails of the distribution, demonstrating that the common two-parameter Weibull distribution is inferior to a three-parameter Weibull model. The results suggest the existence of a cut-off or threshold stress (1.446 GPa for this particular material) below which tensile failure will not occur. The existence of a cut-off stress suggests that the material’s flaw size distribution and toughness distribution are both also bounded. From an application perspective, the cut-off stress provides a statistically-sound basis for reliable design. While the sequential method is demonstrated here for tensile strength distributions in polycrystalline silicon MEMS, the technique could be extended to a wide range of mechanical tests (bending strength, elastic modulus, fracture toughness, creep, etc.) for both microsystem and conventional materials.     

The Development of a High Rate Tensile Testing System for Micro Scaled Single Crystal Silicon Specimens

Structures have been built at micro scales with unique failure mechanisms that are not yet understood, in particular, under high-rate loading conditions. Consequently, microelectromechanical systems (MEMS) devices can suffer from inconsistent performance and insufficient reliability. This research aims to understand the failure mechanisms in micro-scaled specimens deforming at high rates. Single-crystal silicon (SCS) micro specimens that are 4 μm thick are subjected to tensile loading at an average strain rate of 92 s^?1 using a miniature Hopkinson tension bar. A capacitance displacement system and piezoelectric load cell are incorporated to directly measure the strain and stress of the silicon micro specimens. The average dynamic elastic modulus of the silicon micro specimens is measured to be 226.8?±?18.50 GPa and the average dynamic tensile strength of the silicon is measured to be 1.26?±?0.310 GPa. High-speed images show that extensive fragmentation of the specimens occurs during tensile failure.     

Comparison of tensile and bulge tests for thin-film silicon nitride

The mechanical properties of thin-film, low-pressure chemical vapor deposited silicon nitride were measured in uniaxial tension and by a bulge test method suitable for wafer-level testing. This research compares the two approaches and presents additional data on silicon nitride. The common property from the two test methods is the Young's modulus. Tensile tests performed at the Johns Hopkins University provided a value of 257±5 GPa. Bulge tests conducted by Exponent, Inc., an engineering and scientific consulting firm, yielded a value of 258±1 GPa. It is concluded that this bulge test is a valid wafer-level test method. These tensile results, when added to earlier results, yield the following properties for low-stress silicon nitride: Young's modulus =255±5 GPa, Poisson ratio=0.23±0.02, and fracture strength=5.87±0.62 GPa.     

Research on viscosity of metal at high pressure

A new experimental technique, the flyer-impact method, is proposed in this article to investigate the viscosity coefficient of shocked metals. In this technique, a shock wave with a sinusoidal perturbation on the front is induced by the sinusoidal profile of the impact surface of the sample by use of a two-stage light-gas gun, and the oscillatory damping process of the perturbation amplitude is monitored by electric pins. The damping processes of aluminum at 78 and 101 GPa and iron at 159 and 103 GPa are obtained by this technique, which supplement the existing data by measuring the viscosity coefficient via a dynamic high-pressure method. Applying the formula of Miller and Ahrens to fit the experimental data, the shear viscosity coefficients of aluminum at 78 and 101 GPa are \(1350\,\pm \,500\) and \(1200\,\pm \,500~\hbox {Pa}\,\hbox {s}\), respectively, and those of iron at 159 and 103 GPa are \(1150\,\pm \,1000\) and \(4800\,\pm \,1000~\hbox {Pa}\,\hbox {s}\), respectively. The values measured by the flyer-impact method, approximately \(10^{3}~\hbox {Pa}\, \hbox {s}\), are consistent with those measured by Sakharov’s method, while still greatly differing from those measured by static high-pressure methods. In dynamic high-pressure experiments, the shear viscosity is related to dislocation motion in the solid material, while that in static high-pressure experiments is related to the diffusion motion of atoms or molecules in liquids. Therefore, there are different physical meanings of shear viscosity in dynamic and static high-pressure experiments, and there is no comparability among these results.     

Micro-blast waves using detonation transmission tubing

Micro-blast waves emerging from the open end of a detonation transmission tube were experimentally visualized in this study. A commercially available detonation transmission tube was used (Nonel tube, M/s Dyno Nobel, Sweden), which is a small diameter tube coated with a thin layer of explosive mixture (HMX $+$ traces of Al) on its inner side. The typical explosive loading for this tube is of the order of 18 mg/m of tube length. The blast wave was visualized using a high speed digital camera (frame rate 1 MHz) to acquire time-resolved schlieren images of the resulting flow field. The visualization studies were complemented by computational fluid dynamic simulations. An analysis of the schlieren images showed that although the blast wave appears to be spherical, it propagates faster along the tube axis than along a direction perpendicular to the tube axis. Additionally, CFD analysis revealed the presence of a barrel shock and Mach disc, showing structures that are typical of an underexpanded jet. A theory in use for centered large–scale explosions of intermediate strength $(10\, < \Delta {p}/{p}_0 \lesssim \, 0.02)$ gave good agreement with the blast trajectory along the tube axis. The energy of these micro-blast waves was found to be $1.25 \pm 0.94$ J and the average TNT equivalent was found to be $0.3$ . The repeatability in generating these micro-blast waves using the Nonel tube was very good $(\pm 2~\%)$ and this opens up the possibility of using this device for studying some of the phenomena associated with muzzle blasts in the near future.     

The mechanical strength of polysilicon films: Part 2. Size effects associated with elliptical and circular perforations

A systematic study of failure initiation in small-scale specimens has been performed to assess the effect of size scale on “failure properties” by drawing on the classical analysis of elliptically perforated specimens. Limitations imposed by photolithography restricted the minimum radii of curvature of the specimen perforations to one micron. By varying the radius of curvature and the size of the ellipses, the effects of domain size and stress concentration amplitude could be assessed separately to the point where the size of individual grains becomes important. The measurements demonstrate a strong influence of the domain size under elevated stress on the “failure strength” of MEMS scale specimens, while the amplitude, or the variation, of the stress concentration factor is less significant. In agreement with probabilistic considerations of failure, the “local failure strength” at the root of a notch clearly increases as the radius of curvature becomes smaller. Accordingly, the statistical scatter also increases with decreasing size of the (super)stressed domain. When the notch radius becomes as small as the failure stress increases on average by a factor of two relative to the tension values derived from unnotched specimens. This effect becomes moderate for larger radii of curvature, up to a radius of (25 times the grain size), for which the failure stress at the notch tip closely approaches the value of the tensile strength for un-notched tensile configurations. We deduce that standard tests, performed on micron-sized, non-perforated, tension specimens, provide conservative strength values for design purposes. In addition, a Weibull analysis shows for surface-micromachined specimens a dependence of the strength on the specimen length, rather than the surface area or volume, which implies that the sidewall geometry, dimensions and surface conditions can dominate the failure process.     

Prediction of bond failure and deflection of carbon fiber-reinforced plastic reinforced concrete beams

Carbon fiber-reinforced plastic (CFRP) reinforced concrete beams can fail due to interface debonding, due to the high tensile strength of such rebars. A set of 16 concrete beams reinforced with different amounts of CFRP reinforcement was subject to static three-point bending. The beam dimensions and CFRP reinforcements used were selected to demonstrate a transition from compression failure to bond failure with decreasing reinforcement ratio. It is shown that accurate bond strength data to predict such failures can be obtained from a “hinged-beam” test configuration, rather than the conventional direct “pull-out” tests. Deflection under service loads can also be predicted more accurately using a proposed equation that includes the reinforcement ratio and the elastic modulus of the reinforcement.     

16MnR钢缺口试样解理断裂行为研究

研究了低合金热轧钢16MnR缺口试样在$-196\,{^\circ}$C和$-130\,{^\circ}$C的解理断裂机 理. 拉伸试验、单、双缺口四点弯曲实验、断口形貌观察以及有限元分析结果表明, 缺口试 样发生解理断裂时均起裂于夹杂物粒子, 一种位于缺口根部前端(IC型), 另一种位于距缺口 根部较远的条形裂纹前端(SIC型); 且随温度升高, 起裂源的类型从$-196\,{^\circ}$C下的IC 型转变为$-130\,{^\circ}$C下的SIC型. 微裂纹均形核于夹杂物, 最终的断裂由铁素体晶粒尺 寸的微裂纹扩展控制. 缺口试样IC型解理断裂遵循裂纹形核条 件$\varepsilon_{\rm p} \ge \varepsilon_{\rm pc}$和裂纹扩展条件$\sigma_{yy} \ge \sigma_{f}$, 而SIC型解理断裂条件则演化为$\varepsilon_{\rm p}+\varepsilon_{\rm ps} \ge \varepsilon_{\rm pc}$和$\sigma_{yy} +\sigma_{yy{\rm s}} \ge \sigma_{f}$.     

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.     

On strain-rate sensitivity and size effect of brittle solids: transition from cooperative phenomena to microcrack nucleation

An idealized brittle microscale system is subjected to dynamic uniaxial tension in the medium-to-high strain-rate range $(\dot \varepsilon \in \;[100\;s^{-1},\;1 \times 10^{7} \;s^{-1}])$ to investigate its mechanical response under constrained spatial and temporal scales. The setup of dynamic simulations is designed to ensure practically identical in-plane stress conditions on a system of continuum particles forming a two-dimensional, geometrically and structurally disordered, lattice. The rate sensitivity of size effects is observed as well as the ordering effect of kinetic energy. A simple phenomenological expression is developed to account for the tensile strength sensitivity of the small-sized brittle systems to the strain-rate and extrinsic size effects, which may serve as a guideline for formulation of constitutive relations in the MEMS design. The representative sample is defined as a square lattice size for which the tensile strength becomes rate-insensitive and an expression is proposed to model its evolution between two asymptotes corresponding to the limiting loading rates. The dynamics of damage accumulation is analyzed as a function of sample size and loading rate.     

Characterization of crack-tip strain singularity in brittle-microcracking materials by means of the photoelastic-coating method

The strain fields ahead of crack tips in rock, mortar, and graphite were measured using a photoelastic coating method. A transparent ferroelectric ceramic was used as a coating material to observe the photoelastic fringe pattern. A coating plate of 110–150 μm thick was placed on single-edge-notch specimens, and photoelasticity experiments were conducted in three-point bending under a polarizing microscope. The results show that the principal-strain difference ahead of the crack tip is given by $$\Delta \in = \Delta \in _o [(J/\sigma _{ult} )/r]^m $$ whereσ _ult is the ultimate tensile strength,r is the distance from the crack tip, and9? _o andm are material constants. Based on this observation, the use of theJ _Ic concept in determining the fracture toughness of brittle-microcracking materials is discussed.     

THE SURFACE EFFECT ON THE TENSILE STRENGTH OF MICROMACHINED POLYSILICON FILMS FOR MEMS

In order to accomplish reliable mechanical design of MEMS, the influences of surface roughness and octadecyltrichlorosilane (OTS) self-assembled monolayers (SAMs) on the mechanical properties of micromachined polysilicon films for MEMS are investigated. Surface effect on the fracture properties of micromachined polysilicon films is evaluated with a new microtensile testing method using a magnet-coil force actuator. Statistical analysis of the surface roughness effects on the tensile strength predicated the surface roughness characterization of polysilicon films being tested and the direct relation of the mechanical properties with the surface roughness features. The fracture strength decreases with the increase of the surface roughness. The octadecyltrichlorosilane self-assembled monolayers coating leads to an increase of the average fracture strength up to 32.46%. Surface roughness and the hydrophobic properties of specimen when coated with OTS films are the two main factors influencing the tensile strength of micromachined polysilicon films for MEMS.     

A Combined Theoretical/Experimental Approach for Reducing Ringing Artifacts in Low Dynamic Testing with Servo-hydraulic Load Frames

One of the most challenging tasks facing computer-aided engineering (CAE) analysis is the acquisition of accurate tensile test data that spans quasi-static to low dynamic (10^?5/s?≤ $ \overset{.}{\varepsilon } $ ≤5?×?10²/s) strain rates ( $ \overset{.}{\varepsilon } $ ). Critical to the accuracy of data acquired over the low dynamic range is the reduction of ringing artifacts in flow data. Ringing artifacts, which are a consequence of the inertial response of the load frame, are spurious oscillations that can obscure the desired material response (i.e. load vs. time or load vs. displacement) from which flow data are derived. These oscillations tend to grow with increasing strain rate and peak at the high end of the low dynamic range on servo-hydraulic tensile test frames. Common practices for addressing ringing are data filtering, which is often problematic since filtering introduces distortion in smoothed material data, or trial-and-error design of test specimen geometries. This renders techniques for reducing ringing based upon the mechanics of the load frame and optimization of tensile specimen geometry quite attractive. In the present paper, relationships between load, stress wave propagation, and specimen geometries are addressed, to both quantify ringing and to develop specimen designs that will reduce ringing. A combined theoretical/experimental approach for tensile specimen design was developed for reducing ringing in flow data over the low dynamic range of strain rates (10^?5/s≤ $ \overset{.}{\varepsilon } $ ≤5?×?10²/s). The single camera digital image correlation (DIC) method was used to measure the displacement fields and strain rates with specimens resulting from the combined theoretical/experimental approach. While the approach was developed on a specific commercial load frame with a TRIP steel subject to a two-step quenching and partitioning heat treatment (Q&P980), it is readily adaptable to other servo-hydraulic load frames and metallic alloys. The developed approach results in a 90 % reduction in ringing artifact (with no filtering) in a tensile flow curve for Q&P980 at $ \overset{.}{\varepsilon}\kern-4pt $ = 5?×?10²/s. Results from split Hopkinson bar tests of Q&P980 were performed at $ \overset{.}{\varepsilon } $ = 500/s and compare favorably with the test data generated by the developed testing approach. Since the Q&P980 steel represents a new generation of advanced high strength steels, we also evaluated its strain rate sensitivity over the low dynamic range.     

Murray lecture tensile testing at the micrometer scale: Opportunities in experimental mechanics

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. This paper describes techniques developed at Johns Hopkins University for tensile testing of materials used in MEMS. Polycrystalline silicon is currently the most widely used material; its modulus has been measured as 158±10 GPa, and its Poisson's ratio as 0.22±0.01, with fracture strengths ranging from 1.2 to 3.0 GPa depending upon the manufacturer. The properties of silicon nitride, silicon carbide, and electroplated nickel have also been measured and are presented. In addition to the quasi-static tensile tests, new techniques and procedures for measuring strengths at stress concentrations in brittle thin-film materials, fatique testing, and high-temperature testing are described.     

岩石断裂尺寸效应测试装置研制及实验研究

面向岩石断裂尺寸效应研究的实验装置需求,针对现有技术中三点弯曲装置对多组尺寸岩石试件适应性差、最小跨距的测试量程不足等问题,研制了一种可灵活用于岩石断裂尺寸效应测试的三点弯曲装里.装置采用"两体分离式"的设计,三种不同型号的滚子与压头体、支座体配合使用,有效避免了不同尺寸试件采用同一直径滚子测试带来的实验精度问题;同时...     

Elastic modulus of human cementum

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Bending stresses in out-of-round uni- and multi-axial internally pressurized strength specimens

A derivation is presented for the bending stresses in internally pressurized slightly elliptical tubular or ring specimens used in the testing of uni- and multiaxial strength. The solution obtained shows that the bending stresses are directly proportional to Young's modulus of elasticity of the material being tested. A numerical example applicable to strength testing of aluminum oxide demonstrates, that a slight out-of-round-ness can result in bending stresses which are an appreciable percentage of the observed values of the fracture strength. It is concluded that strength testing by means of the internal pressurization of tubular or ring specimens requires close dimensional control in specimen manufacture.