A three-dimensional numerical model based on a semi-analytical method in the framework of small strains and small displacements with respect of Hertz’s hypotheses is presented for solving an elastic-plastic dented contact with friction. The calculation of surface deformations and pressure distribution, which is the most time consuming step during the elastic-plastic algorithm, is obtained using a method based on a variational principle with a Fast Fourier Transform (FFT) and a Conjugate Gradient Method (CGM). The method is fast enough to allow investigating the effect of a small size surface defect, here a debris denting, on the subsurface elastic-plastic stress state, requiring a fine mesh with around 10 6 surface grid points. Further, the FFT approach is also involved in the calculation of internal stress state. The plasticity model is based on an incremental load and Von Mises yield criterion. The effects of the contact pressure distribution and residual strain on the geometry of the contacting surfaces yield from the Betti’s reciprocal theorem with initial strain. The code is used to compute a few smooth and dented contacts, with several types of contact interfaces conditions, including frictionless and Coulomb friction. The effects of surface dents and friction on the contact pressure and subsurface stress field are presented and discussed.

The process of unloading an elastic-plastic loaded sphere in contact with a rigid flat is studied by the Finite Element Method. The sphere material is assumed isotropic with elastic-linear hardening. The numerical simulations cover a wide range of loading interference deformation of various values of Young’s modulus and Poisson ratios of the sphere material. The contact loads, stresses, and deformations in the sphere during both loading and unloading, are calculated for the range of interferences. Empirical dimensionless expressions are presented for the unloading load-deformation relation, the residual axial displacement and the residual curvature of the sphere after complete unloading.

For faster signal propagation in integrated circuits, new materials with lower dielectric constant (low- k ) values are required with copper metal lines. Although integration of low- k materials ( k <3.0) has been demonstrated, but ultra low- k materials possess many challenges due to their poor mechanical integrity and weak adhesion to other interconnects. During chemical mechanical planarization (CMP) generation of several defects including delamination of low- k materials is severe problem in the integration of these materials. Different slurries and pad introduces different levels of defect and also batch-to-batch variation in consumables is often makes process more difficult. In this study we have investigated the tribological properties of CMP pad and wafer interface while monitoring coefficient of friction and acoustic emission data. Signals are analyzed in order to online defect monitoring, batch-to-batch consumable variations and different consumables effects.

An experimental investigation was conducted to study the nature of dynamic rupture caused by shear loading, through impact, of interfaces which are held together by friction under external pressure. The dynamic stress field developed during rupture propagation was recorded in real time by a high-speed camera in conjunction with a classical dynamic photoelasticity set-up. Visual evidences of different dynamic propagating rupture modes were recorded. Unlike classical shear cracks in coherent interfaces of finite strength, rupture in frictional interfaces seems to grow without noticeable acceleration phases and at various discreet speeds. At low impact velocities a crack-like rupture mode occurs which becomes super-shear with the increase of the impact speed and a shear Mach cone emanates from the rupture point. For higher impact speeds super-shear and super-sonic Mach lines are observed formatting an unstable slip pulse which subsequently vanishes whereas evidences for extended stick and slip regions are recorded. Increasing the external applied pressure the observed features are intensified.

An innovative RF-MEMS varactor has been developed for use in distributed RF-MEMS circuits such as phase shifters and tunable matching networks where the capacitance ratio between on- and off- state must be limited to 2–10. By fabricating standoffs on the bottom side of the beam, this device eliminates the intimate contact between the FR-MEMS and dielectric, that is found in typical RF-MEMS beam capacitive switches. These standoffs limit the range of motion, allowing the capacitance ratio to be set, and also greatly reduces the contact area thus preventing stiction from occurring. The RF-MEMS switch has been fabricated with initial measurements demonstrating a capacitance ratio of 2.5. Preliminary reliability testing results demonstrate that this RF-MEMS design is very robust.

In order to understand the mechanisms of micro-slip initiation and propagation at the contact interface, a visualization method of partial micro-slip at the contact interface was developed. The process of micro-slip initiation and propagation at the contact interface was successfully observed, and the relationship between tangential coefficient and partial slip distribution at the contact interface was analyzed by using the newly developed method. It was clarified that the partial slip distribution was affected by contact morphologies such as spherical ball, triangular stamp, rectangular stamp and concave stamp contact. The effect of uneven area of the contact surface on the micro-slip initiation and propagation was also clarified. It is confirmed from observed results that the visualization of the partial slip at the contact interface is useful for understanding the mechanism of the micro-slip initiation and the propagation at the contact interface.

It is well known that the conventional Coulomb friction condition can lead to non-uniqueness of solution in elastostatic solutions if the friction coefficient is sufficiently high. Interest in this field has centered on discrete formulations, particularly with reference to the finite element method. More recently Hild has demonstrated the existence of a multiplicity of non-unique solutions to a simple problem in two-dimensional continuum elasticity and showed how to determine the conditions for such states to exist by formulating an eigenvalue problem. Both the discrete and continuum examples of non-uniqueness seem to be related to the well known physical phenomenon whereby a frictional system can become locked or ‘wedged’ in a state of stress even when no external loads are applied (the homogeneous problem), but the equivalence is not complete because of the influence of unilateral inequalities in the physical problem. We shall discuss the relations between these concepts in the context of simple continuum and discrete problems in two-dimensional linear elasticity.

In this extended abstract, we briefly describe a thermodynamic model to treat capillary adhesion energies in MEMS. We first determine the constitutive laws of a capillary pendular ring bridging an asperity to a substrate. We find that the work of adhesion, W , depends on the surface separation rate. For the constant volume case (rapid surface separation), W = 2γ (where γ is the surface energy per unit area of the liquid-air interface), but if thermodynamic equilibrium is maintained (slow surface separation), W = γ. Thermodynamic analysis indicates that heat from the system walls can lower the work of adhesion at slow separation rates. We extend these constitutive laws to a simple multi-asperity surface in which the asperities are all of constant height. At low vapor partial pressures ( p/p sat ), adhesion can be several orders of magnitude below γ because of incomplete wetting. As vapor partial pressure increases, condensing liquid fills in the geometric irregularities of the surface. As this filling takes place, W approaches 2γ for both the slow and rapid separation rates.

This paper investigates the dynamic contact between an axi-symmetric rigid paraboloid and a standard solid (Zener) viscoelastic half-space. The load consists of a pulse cosine applied over a step function. Following the theory developed by Ting, analytical expression of contact radius for an advancing contact is derived. For receding contact, contact radius is numerically obtained. Contact pressures for increasing and decreasing contacts are derived. The influence of load frequency is evidenced. At low frequencies, contact pressure has an initial Hertz shape and then, as the contact increases, a relaxed one. As the contact reaches its maximum, the pressure tends again to an elastic pattern. Experimental tests were carried out on a contact between a polymeric sphere and a glass plate. A good agreement is found with theoretical results by measuring contact radius.

A recent theorem due to Barber shows an analogy between conductance and incremental stiffness of a contact, implying bounds on conductance based on peak-to-peak roughness. This shows that even a fractal roughness, with bounded amplitude, has a finite conductance. The analogy also permits a simple interpretation of classical results of rough contact models based on independent asperities such as Greenwood-Williamson and developments. For example, in the GW model with exponential distribution of asperity heights, the conductance is found simply proportional to load, and inversely proportional to a roughness amplitude parameter which does not depend greatly on resolution, contrary to parameters of slopes and curvatures. However, for the Gaussian distribution or for more refined models also considering varying curvature of asperities (such as Bush Gibson and Thomas), there is dependence on sampling interval and the conductance grows unbounded. An alternative choice of asperity definition (Aramaki-Majumdar-Bhushan) is suggested, which builds on the geometrical intersection of the rough surface, with the consequence of a finite contact area, and converging load-separation and load-conductance relationship. A discussion follows, also based on numerical results.

Previous models and measurements of MEMs adhesion have focused on steady-state adhesion behavior. This approach is inadequate for micromachined switches (such as RF MEMS switches) because it gives no information about the time required for contact opening, an important specification. We propose a technique to measure the switch opening time and present substantial experimental data for switches with gold-gold contacts. The data demonstrate that contact opening time increases dramatically as contact dimple area increases or as pull-apart force or contact resistance decrease. A model of opening time is also presented with model parameters that fit the experimental data.

A numerical procedure for the surface deformation and adhesion between elastic half-spaces interacting by the Lennard-Jones surface potential is presented. The problem is solved based on the superposition of Boussinesq solutions for a half-space, with an iteration procedure to incorporate the nonlinear surface force-depression relation. First the axisymmetric contact between a sphere and a plane surface is demonstrated to show the validity of the procedure for a wide range of the Tabor parameter. The method is then applied to the contact between a sphere and a wavy surface, and the influence of the surface waviness on the adhesive behavior is illustrated.

Microball bearings can potentially provide robust and low friction support in micromachines such as micromotors and microgenerators. Their microtribological behavior needs to be investigated for design and control of such micromachines. In this paper a vision-based, non-intrusive measurement method is presented for characterization of friction in linear microball bearings. Infrared imaging is used to directly observe the dynamics of microballs and track the motion of bearing components. It is verified that microballs roll most of the time with occasional sliding or bumping resulting from fabrication nonuniformity. The friction-velocity curve demonstrates evident hysteresis. The dependence of frictional behavior on several factors is studied.

In laser display applications, the necessity to create images free of distortions imposes specific requirements on the motion of scanning devices. We present an approach of a scanning micromirror operation that is aimed to fulfill the requirements of motion linearity, high operational frequency and low actuation voltages. The operational mode incorporates a contact event between the mirror and an elastic constraint followed by a bouncing event and a subsequent inversion of motion. A stable limit cycle with voltage-dependent frequency and triangular response signal is obtained by the application of an actuation voltage which is piecewise constant in time. Approximate expressions relating the frequency and amplitude of the response with the actuating voltage are obtained by energy balance method. The influence of contact losses on the response as well as the stability of the limit cycle are studied numerically.

Investigation of contact and friction at multiple length scales is necessary for the design of surfaces in sliding microelectromechanical system (MEMS). A method is developed to investigate the geometry of asperities at different length scales. Analysis of density, height, and curvature of asperities on atomic force microscopy (AFM) images of actual silicon MEMS surfaces show these properties have a power law relationship with the sampling size used to define an asperity. This behavior and its similarity to results for fractal Weierstrass-Mandelbrot (W-M) function approximations indicate that a multiscale model is required to properly describe the surfaces.

A polarization vector of the piezoceramic element and location of excitation electrodes on its surface determine the resonance modes of the high frequency vibration exciter. In its turn the modes of vibration play a key role in the functionality of ultrasonic motor. Two different regimes of operation are analyzed — when the contact zone of the resonator performs elliptic and unidirectional motions. Though the mechanical characteristics of the ultrasonic motor in both cases are comparable, detailed analysis of the contact surface shows very different wears. Computational simulation and experimental investigations are used to analyze the contact zone of ultrasonic motor. Laser holography is used to identify and control the regimes of motion. Atomic force microscopy is used for analysis of contact surfaces.

Adhesion plays an important role in microelectromechanical systems (MEMS). It is a major concern in MEMS reliability and oftentimes excessive adhesion forces lead to permanent adherence of MEMS surfaces resulting in microdevice failure. The role of residual stresses in the adhesive contact between a pre-stressed membrane and a rigid flat-ended cylindrical punch is studied. Breaking the contact can be achieved under either fixed-load or fixed-grips configuration. The influence of the residual stress on the pull-off force, punch displacement, and contact area at pull-off is studied. It is shown that residual stresses have significant influence on interfacial contact behavior in MEMS and, hence, should be taken into consideration in formulating the adhesion contact mechanics.

Microelectromechanical systems (MEMS) technology employed to generate switches and relays has the potential to replace traditional solid-state devices due to broader operating temperature range, higher breakdown voltage, and much higher off-state resistance. Interest in MEMS switches and relays has surged recently, principally due to the demonstrated performance in switching radio-frequency signals. The role of surface topography in the performance and lifetime of MEMS switches and relays is the objective of this review paper. Special emphasis is given to an approach that accounts for effect of roughness and to the role of surface topography in the pull-in voltage and contact bouncing. A critical assessment of emerging topics where experimental and theoretical studies are still required in order to obtain better insight into the role of surface topography in MEMS switches and relays is presented.

Many state-of-art microelectronic, photonic and MEMS devices are based upon or created using small-scale contacts. These include, for example, high frequency, microscale electromechanical switches and nanopatterning of organic optoelectronic materials by contact adhesion, cold welding, and lift-off. The initial stages of contact occur between asperities of micro- and/or nano-scopic dimensions. As a consequence, understanding the processes that occur at the atomic level when two rough surfaces are bought into contact is fundamentally important for a wide range of problems including adhesion, contact formation, contact resistance, materials hardness, friction, wear, and fracture. The centrality of single asperities in the fundamental micromechanical response of contact between two rough surfaces has long been recognized. A wide range of experiments has shown that the conductance of small contacts changes abruptly as a function of contact size. In some cases, the conductance through individual asperities increases in a stepwise manner as the two surfaces are pressed into contact. These jumps conductance appear to be correlated with jumps in the force. The observed force-displacement relation appears to be poorly described by JKR theory during loading, while JKR provides a reasonable description of the behavior in unloading. In this presentation (see Acta Materialia 52 , 3983 (2004) for more details), we report the results of molecular dynamics simulations of single asperity contact during multiple cycles of loading and unloading at room temperature. We focus on the mechanisms by which contact deformation occurs and the relationship between contact conductance (and contact area) and the deformation. These simulations account for adhesion, elastic deformation, dislocation generation and migration, the formation of other types of defects and morphology evolution. In order to study the elastic and plastic deformation of the asperities on a rough surface, we set up a model system, as shown in Fig. 1. For simplificity, we consider a single deformable asperity on a deformable substrate that interacts with a flat, rigid plate. We calculate the conductance of the contact during loading and unloading through the modified Sharvin model [12]. To our knowledge, this study represents the first dynamic, atomistic simulation of the elastic and plastic deformation behavior of a single asperity and the corresponding evolution of the contact area and contact conductance. The present simulation results reproduce a large body of existing nano-contact experimental results, including the stepwise variation of contact area and conductance with displacement and the hysteresis in the contact radius and contact resistance versus force curves.

The behavior of a nano-scale cylindrical body (e.g. a fiber), lying on a substrate and acted upon by a combination of normal and tangential forces, is the subject of this investigation. As the scale decreases to the nano level, adhesion becomes an important issue in this contact problem. Thus this investigation treats the two-dimensional plane strain elastic deformation of both the cylinder and the substrate during a rolling/sliding motion, including the effect of adhesion using the Maugis model. For the initiation of sliding, the Mindlin approach is used, whereas for rolling, the Carter approach is utilized. Each case is modified for nano-scale effects by including the effect of adhesion on the contact area and by using the adhesion theory of friction for the friction stress. Analytical results are given for the normal and tangential loading problems, including the initiation of sliding and rolling in terms of dimensionless quantities representing adhesion, cylinder size, and applied forces.