Adhesion of micro-cantilevers subjected to mechanical point loading: modeling and experiments

This paper presents experimental and theoretical results that characterize the adhesion of MEMS cantilevers by means of mechanical actuation. Micro-cantilever beams are loaded at various locations along the freestanding portion of the beam using a nanoindenter. Transitions between three equilibrium configurations (freestanding, arc-shaped, and s-shaped beams) and the response to cyclic loading are studied experimentally. The resulting mechanical response is used to estimate the interface adhesion energy (using theoretical models), and to quantify the energy dissipated during cyclic loading. The experiments reveal interesting behaviors related to adhesion: (i) path dependence during mechanical loading of adhered beams, (ii) history dependence of interfacial adhesion energy during repeated loading, and (iii) energy dissipation during cyclic loading, which scales roughly with estimated cyclic changes in the size of the adhered regions. The experimental results are interpreted in the context of elementary fracture-based adhesion and contact models, and briefly discussed in terms of their implications regarding the nature of adhesion and future modeling to establish adhesion mechanisms.     

Energy method solution for the postbuckling response of an axially loaded bilaterally constrained beam

Bistable and multistable structures have shown great usefulness in many applications such as MEMS actuation and energy harvesting. Bistability of structures can be achieved through buckling. Confining a buckled beam between two lateral constraints allows it to buckle into higher modes as the axial load increases. This paper presents a theoretical study of the postbuckling response of a bilaterally constrained elastica subjected to gradually increased axial load. Equilibrium states are determined using an energy method. Under small deformation assumptions, the total potential energy is minimized under the defined constraints. The presented model allows for an accurate representation of the flatting behavior and the increase in the length of contact areas with the lateral constraints before the sudden snapping between equilibrium states. Mode transitions are manifested by jumps in the response curves. Previously developed models based on geometry and symmetries overestimate the required forces for higher equilibrium modes and do not match experimental observations. Results are validated with experimental force–displacement measurements under both force- and displacement-control. The kinetic energy released during buckling mode transitions is determined by a dynamic analysis.     

Mechanics of energy transfer and failure of ductile microscale beams subjected to dynamic loading

The mechanical response of microelectromechanical systems (MEMS) under impulse loading conditions has not been thoroughly studied to date, partially because of the lack of means to provide such extreme loading rates to miniature devices. However, the increasing use of MEMS-based sensors and actuators in adverse environments, which include extreme strain rate loading, has motivated the investigation of the response of MEMS components under these conditions. In this work, basic and mostly commonly employed Au MEMS components were subjected to impulse loads of 40 ns in duration, which were generated by a high power pulsed laser in order to achieve acceleration levels on the order of 10⁹g. This allowed for the microdevice mechanical/structural response to be investigated at time scales that were of the order of wave transit times in the substrate and the devices. Basic microscale structures, such as cantilevers and fixed-fixed beams of uniform cross-section, were employed to facilitate comparisons with companion finite element simulations in order to gain insight into the mechanisms responsible for impulsive deformation at the microscale. The simulations investigated the effect of loading rate, boundary conditions, beam length, material constitutive response, and damping on the final deformed shapes of the beams. It was found that contact and momentum transfer mechanisms were responsible for the large permanent beam deflections which were measured postmortem. Additionally, the effects of both damping and material property rate dependence were found to be dominant in determining the final deformed shape of the beams. In fact, our observations suggest that the contributions of material rate dependence and damping are not simply additive, but rather involve a coupling between them that affects the final structure response.     

循环加卸载损伤大理岩的动力学特性

利用MTS 815电液伺服岩石实验系统进行上限应力为80%、85%、90%、95%单轴抗压强度的大理岩单轴压缩循环加卸载实验,每种上限应力条件分别设置20、40、60、80次循环。再利用分离式Hopkinson压杆对损伤岩样进行动力学实验。分析了循环加卸载上限应力及循环次数对大理岩塑性应变的影响,揭示了大理岩动态力学参数和破碎吸收能随损伤变量的演化规律。实验结果表明:塑性应变与循环次数呈正相关,且上限应力越大,塑性应变趋于稳定所需的循环次数也会增大;动态单轴抗压强度、动态弹性模量随损伤变量增加呈指数衰减;破碎吸能占比以损伤变量D=0.343为临界点分为两个阶段,D<0.343时,破碎吸能占比稳定在10%左右,数值约为13 J,当D>0.343时破碎吸能占比随损伤变量增加不断增大。研究结果可为岩体工程的设计、施工及支护参数的选取提供参考。     

Rail-end bolt hole fatigue crack in three dimensions

This work is concerned with subcritical crack growth in rail-end bolt hole caused by fatigue. Included in the analysis are the mechanical wheel loads and thermal fluctuations experienced by the rail. The interaction of cyclic loading with the rail geometry is considered to be essential. Finite element stress analysis is coupled with the strain energy density criterion for determining the subcritical crack growth steps. The crack can grow and follow any arbitrary surface in the three-dimensional space depending on the symmetry or antisymmetry conditions of the load and geometry. Results on crack shapes and growth rates compare favorably with those observed experimentally.     

Corrosion fatigue of welded offshore steels and tubular connections

This work is concerned with subcritical crack growth in rail-end bolt hole caused by fatigue. Included in the analysis are the mechanical wheel loads and thermal fluctuations experienced by the rail. The interaction of cyclic loading with the rail geometry is considered to be essential. Finite element stress analysis is coupled with the strain energy density criterion for determining the subcritical crack growth steps. The crack can grow and follow any arbitrary surface in the three-dimensional space depending on the symmetry or antisymmetry conditions of the load and geometry. Results on crack shapes and growth rates compare favorably with those observed experimentally.     

Flexural contact in MEMS stiction

Adhesive force between two solid surfaces can lead to stiction failure of the micro-electro-mechanical systems (MEMS) device. The competition between the adhesive force and the beam restoring force determines whether the stiction occurs or not. Previous models assume that the stuck beam deforms either as the arc-shape or the S-shape, which causes significant differences in the measurements of adhesion and disputations among researchers. The contact mechanics model presented in this paper shows that the assumptions of the arc-shape and S-shape on the beam deformation over-simplify the problem; both the arc-shaped deformation and S-shaped deformation significantly deviate from the real ones. The previous theories are shown to be incompatible with the recent experimental results. The model presented in this paper attempts to explain those new experimental results and resolve some disputations on the previous models. The instabilities of jump-in during loading process and jump-off during unloading process are also incorporated in this model.     

Using Micro-Raman Spectroscopy to Assess MEMS Si/SiO2 Membranes Exhibiting Negative Spring Constant Behavior

We introduce a novel micro-mechanical structure that exhibits two regions of stable linear positive and negative stiffness. Springs, cantilevers, beams and any other geometry that display an increasing return force that is proportional to the displacement can be considered to have a “Hookean” positive spring constant, or stiffness. Less well known is the opposite characteristic of a reducing return force for a given deflection, or negative stiffness. Unfortunately many simple negative stiffness structures exhibit unstable buckling and require additional moving components during deflection to avoid deforming out of its useful shape. In Micro-Electro-Mechanical Systems (MEMS) devices, buckling caused by stress at the interface of silicon and thermally grown SiO₂ causes tensile and compressive forces that will warp structures if the silicon layer is thin enough. The 1 mm² membrane structures presented here utilizes this effect but overcome this limitation and empirically demonstrates linearity in both regions. The Si/SiO₂ membranes presented deflect ~17 μm from their pre-released position. The load deflection curves produced exhibit positive linear stiffness with an inflection point holding nearly constant with a slight negative stiffness. Depositing a 0.05 μm titanium and 0.3 μm layer of gold on top of the Si/SiO₂ membrane reduces the initial deflection to ~13.5 μm. However, the load deflection curve produced illustrates both a linear positive and negative spring constant with a fairly sharp inflection point. These results are potentially useful to selectively tune the spring constant of mechanical structures used in MEMS. The structures presented are manufactured using typical micromachining techniques and can be fabricated in-situ with other MEMS devices.     

Micromechanics of substrate-supported thin films

The mechanical properties of metallic thin films deposited on a substrate play a crucial role in the performance of micro/nano-electromechanical systems (MEMS/NEMS) and flexible electronics. This article reviews ongoing study on the mechanics of substrate-supported thin films, with emphasis on the experimental characterization techniques, such as the rule of mixture and X-ray tensile testing. In particular, the determination of interfacial adhesion energy, film deformation, elastic properties and Bauschinger effect are discussed.     

微梁与基底间的毛细粘附作用

在表面微型机械结构的制造过程中,强的毛细相互作用常常使得组成这些结构的微桥、微梁与基底粘附而导致失效。而在微尺度实验中,微桥与微梁又是微尺度材料常数和性能检测的常用的试件样式,如果实验中加载端与被检测的微尺度试件发生毛细粘附,将直接影响检测数据的准确性。本文应用微悬臂梁试件,讨论微梁与基底间的毛细粘附作用,并通过能量原理计算其粘附力的大小和试件几何尺寸、粘附面距离、粘附液体特性之间的关系。最后应用微散斑干涉,检测粘附平衡态时微桥和微梁的粘附力以及由毛细粘附所导致的弯曲变形,并与理论计算结果进行比较。     

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

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.     

1Cr18Ni9Ti不锈钢的非比例循环强化性能

对1Cr18Ni9Ti不锈钢进行了各种比例和非比例循环本构实验,其中包括圆路径、正方形、正菱形、蝶形、三角形和两种十字形应变路径。表明其具有明显的非比例循环附加强化。在相同的等效应变幅值上,材料的附加强化与路径密切相关。对于圆路径,其附加强化度最大可达60％。通过对不同应变历史的实验研究表明,先前小的非比例度的加载历史对后继大的非比例度路径的强化没有影响;而先前大非比例度的加载路径对后继小非比例度路径的循环强化有较大影响。     

考虑路径相关性的非比例循环塑性本构模型

根据非比例加载下金属材料响应的延迟特性及加载路径相关性,选取沿应力迹法向的塑性应变的累积量作为非比例加载影响的度量,相应给出反映非比例附加强化的变量,并假设其模量和强化率与加载路径的几何参数相关．为反映由于非比例加载而引起的材料强化的异向效应,在Valanis的塑性内时响应方程中引入与加载路径几何性质有关的应力项,构成非比例循环塑性本构关系．对316和304不锈钢材料在一些典型非比例循环加载路径下的应力响应进行了理论预测,与Benallal等及McDowell的实验结果取得了良好的一致．     

A constitutive model for the Mullins effect with changes in material symmetry

When an unfilled or particle reinforced rubber is subjected to cyclic loading–unloading with a fixed amplitude from its natural reference configuration, the stress required on reloading is less than on the initial loading for a deformation up to the maximum value of the stretches achieved. The stress differences in successive loading cycles are largest during the first and second cycles and become negligible after about 4–6 cycles. This phenomenon is known as the Mullins effect. In this paper new experimental data are reported showing the change in material symmetry for an initially undamaged and isotropic material subjected to uniaxial and biaxial extension tests. The effect of preconditioning in one direction on the mechanical response when loaded in a perpendicular direction is discussed. A simple phenomenological model is derived to account for stress softening and changes in material symmetry. The formulation is based on the theory of pseudo-elasticity, the basis of which is the inclusion of scalar variables in the energy function. When active, these variables modify the form of the energy function during the deformation process and therefore change the material response. The general formulation is specialized to pure homogeneous deformation in order to fit the new data. The numerical results are in very good agreement with the experimental data.     

SRRs Embedded with MEMS Cantilevers to Enable Electrostatic Tuning of the Resonant Frequency

A microelectromechanical systems (MEMS) cantilever array was monolithically fabricated in the gap region of a split ring resonator (SRR) to enable electrostatic tuning of the resonant frequency. The design consisted of two concentric SRRs each with a set of cantilevers extending across the split region. The cantilever array consisted of five beams that varied in length from 300 to 400 μm, with each beam adding about 2 pF to the capacitance as it actuated. The entire structure was fabricated monolithically to reduce its size and minimize losses from externally wire bonded components. The beams actuate one at a time, longest to shortest with an applied voltage ranging from 30–60 V. The MEMS embedded SRRs displayed dual resonant frequencies at 7.3 and 14.2 GHz or 8.4 and 13.5 GHz depending on the design details. As the beams on the inner SRR actuated the 14.2 GHz resonance displayed tuning, while the cantilevers on the outer SRR tuned the 8.4 GHz resonance. The 14.2 GHz resonant frequency shifts 1.6 GHz to 12.6 GHz as all the cantilevers pulled-in. Only the first two beams on the outer cantilever array pulled-in, tuning the resonant frequency 0.4 GHz from 8.4 to 8.0 GHz.     

The Effect of Edge Compliance on the Contact between a Spherical Indenter and a High-Aspect-Ratio Rectangular Fin

In the last two decades, significant progress has been made on developing new nanoscale mechanical property measurement techniques including instrumented indentation and atomic force microscopy based techniques. The changes in the tip-sample contact mechanics during measurements uniquely modify the displacement and force sensed by a measurement sensor and much effort is dedicated to correctly retrieve the sample mechanical properties from the measured signal. It turns out that in many cases, for the sake of simplicity, a simple contact mechanics model is adopted by overlooking the complexity of the actual contact geometry. In this work, a newly developed matrix formulation is used to solve the stress and strain equations for samples with edge geometries. Such sample geometries are often encountered in today’s nanoscale integrated electronics in the form of high-aspect-ratio fins with widths in the range of tens of nanometers. In the matrix formulation, the fin geometries can be easily modeled as adjacent overlapped half-spaces and the contact problem can be solved by a numerical implementation of the conjugate gradient method. This method is very versatile in terms of contact geometry and contact interaction, either non-adhesive or adhesive. The discussion will incorporate a few model examples that are relevant for the nanoscale mechanics investigated by intermittent contact resonance AFM (ICR-AFM) on low-k dielectric fins of high-aspect-ratio. In such ICR-AFM measurements, distinct dependence of the contact stiffness was observed as a function of the applied force and distance from the edges of the fins. These dependences were correctly predicted by the model and used to retrieve the mechanical changes undergone by fins during fabrication and processing.     

Mechanical annealing under low-amplitude cyclic loading in micropillars

Mechanical annealing has been demonstrated to be an effective method for decreasing the overall dislocation density in submicron single crystal. However, simultaneously significant shape change always unexpectedly happens under extremely high monotonic loading to drive the pre-existing dislocations out of the free surfaces. In the present work, through in situ TEM experiments it is found that cyclic loading with low stress amplitude can drive most dislocations out of the submicron sample with virtually little change of the shape. The underlying dislocation mechanism is revealed by carrying out discrete dislocation dynamic (DDD) simulations. The simulation results indicate that the dislocation density decreases within cycles, while the accumulated plastic strain is small. By comparing the evolution of dislocation junction under monotonic, cyclic and relaxation deformation, the cumulative irreversible slip is found to be the key factor of promoting junction destruction and dislocation annihilation at free surface under low-amplitude cyclic loading condition. By introducing this mechanics into dislocation density evolution equations, the critical conditions for mechanical annealing under cyclic and monotonic loadings are discussed. Low-amplitude cyclic loading which strengthens the single crystal without seriously disturbing the structure has the potential applications in the manufacture of defect-free nano-devices.     

Minimum energy consumption of soil working cyclic processes

Analysis of some experimental studies concerning the processes of soil penetration and cutting indicates that the loading stages of both these processes as well as their unloading stages are respectively analogous. This means that the relationships between the frontal resistance forces of soil and tool displacement for penetration and cutting can be characterized by an identical mathematical model of soil.An analytical investigation of energy consumption for a generalized cyclic soil working process is carried out. This investigation shows that the minimum energy consumption can be reached if, on the loading stage, the tool displacement is equal to a so-called optimum displacement per cycle, which can be calculated according to the formulas derived in this analysis.The necessary and sufficient conditions of existence of optimum displacements per cycle are determined. These conditions are expressed by a definite correlation between some mechanical characteristics of soil.It is shown that the energy consumption of a corresponding quasistatic soil working process considerably exceeds the minimum energy consumption of a cyclic process.     

Effects of static electric field on the fracture behavior of piezoelectric ceramics

The paper gives an overview on experimental observations of the failure behavior of electrically insulating and conducting cracks in piezoelectric ceramics. The experiments include the indentation fracture test, the bending test on smooth samples, and the fracture test on pre-notched (or pre-cracked) compact tension samples. For electrically insulating cracks, the experimental results show a complicated fracture behavior under electrical and mechanical loading. Fracture data are much scattered when a static electric field is applied. A statistically based fracture criterion is required. For electrically conducting cracks, the experimental results demonstrate that static electric fields can fracture poled and depoled lead zirconate titanate ceramics and that the concepts of fracture mechanics can be used to measure the electrical fracture toughness. Furthermore, the electrical fracture toughness is much higher than the mechanical fracture toughness. The highly electrical fracture toughness arises from the greater energy dissipation around the conductive crack tip under purely electric loading, which is impossible under mechanical loading in the brittle ceramics. The project supported by an RGC grant from the Research Grant Council of the Hong Kong Special Administrative Region, China     

Snap transitions in adhesion

Equilibrium adhesion states are analyzed for nonlinear spherical caps adhered to a rigid substrate under the influence of adhesive tractions that depend on the local separation between the shell and substrate. Transitions between bistable snapped-in and snapped-out configurations are predicted as a function of four nondimensional parameters representing the adhesive energy, the undeformed shell curvature, the range of the adhesive interactions, and the magnitude of an externally applied load. Nonuniform energy and traction fields associated with free-edge boundary conditions are calculated to better understand localized phenomena such as the diffusion of impurities into a bonded interface and the diffusion of receptors in the cell membrane. The linear Griffith approximations commonly used in the literature are shown to be limited to shells with a small height to thickness ratio and short-range adhesive interactions. External loading is found to alter the adhered configurations and the spatial distributions of both adhesive and elastic energies. An important implication of the latter analysis is the theoretical prediction of the pull-off force, which is shown to depend not only on the interface properties, but also on the geometric and material parameters of the shell and on both the magnitude and type of external loading.