Finite Contact Area Research Articles

A Novel Approach Using Finite Element Modeling and Contact Area Parameter for Predicting Wire Bond Shear Strength Nondestructively

A Novel Approach Using Finite Element Modeling and Contact Area Parameter for Predicting Wire Bond Shear Strength Nondestructively

Hysteretic energy dissipation capacity of dual-steel welded-plate preloaded bolted T-stubs

With the high- and ultrahigh-strength steels applied in the construction industry, the seismic safety of their structural components is very concerned due to the inferior material ductility of those steels. The current studies on bolted high-strength steel T-stubs mainly focus on their monotonic loading behavior. There is limited research work conducted to study their cyclic loading behavior. In this study, cyclic tests of bolted dual-steel T-stubs were conducted. Their T-elements were produced by Q690 high-strength steel flanges and Q355 normal-strength steel webs, and class 10.9 high-strength bolts with pretension were used to connect the groove-welded T-elements. Failure modes, force-deformation hysteretic and backbone curves, cumulative plastic deformation and energy dissipation capacities were tested and analyzed. The test results indicated that an optimal β ratio between the plastic resistances of Mode 1 (neglecting the influence of bolt action on a finite contact area) and Mode 3 in Eurocode 3 Part 1–8, could be 0.3 for those bolted T-stubs to maximize hysteretic energy dissipation. Accordingly, predictive formulas with good precision were proposed for the low-cycle fatigue failure criterion and hysteretic energy dissipation capacity of those bolted T-stubs, respectively.

Friction-induced planar vibration of a two-rigid-disc system with a finite contact area subjected to uncertain friction

Friction-induced planar vibration of a two-rigid-disc system with a finite contact area subjected to uncertain friction

Full mechanism modeling of contact thermal resistance with stagnant fluids in thermal discrete element method

After reexamining three mechanisms of thermal resistance in packed bed: particle-particle conduction through a finite contact area (PPA), conduction through a contact point (PPP), and through stagnant fluids near the contact point (PFP), a full mechanism model of contact thermal resistance (CTR) and the effective thermal conductivity (ETC) of particles with stagnant interstitial fluid is proposed here for thermal discrete particle simulations (TDEM). The current model agrees with experimental data of various conductivity ratios and void fractions, and can be applied for both dense and dilute gas-particle systems. It shows that the PPA mechanism is dominating when the conductivity ratio of particle-to-fluid κ is greater than 104. Moreover, when κ < 2000, the PPP mechanism becomes dominant and the PPA mechanism can be neglected. All these mechanisms incorporated in current model can be naturally imbedded in thermal discrete thermal method (TDEM).

Interaction of metal dust adhered on castellated substrates with the ELMy H-mode plasmas of ASDEX-Upgrade

Castellated substrates with adhered micron dust have been exposed in the outer ASDEX-Upgrade divertor to ELMy H-mode discharges. Beryllium proxy (chromium, copper) and refractory metal (tungsten, molybdenum) dust has been deposited on the plasma-facing and plasma-shadowed sides of the monoblocks as well as the bottom of the gaps. Interaction with time-averaged transient heat loads up to 5 MW m−2 led to dust remobilization, clustering, melting and wetting-induced coagulation. The amount of dust released in the vessel has been quantified and remobilized dust trajectories inferred. Gaps can efficiently trap locally adhered dust, but dust detaching from adjacent monoblocks does not preferentially move inside the gaps implying that they do not constitute a dust accumulation site. Heat transfer simulations of melting events are also reported taking into account heat constriction due to the finite contact area and the presence of surface roughness.

Geometrical correction factors for finite-size probe tips in microscopic four-point-probe resistivity measurements

The sheet resistance of thin film structures is commonly measured using a four-point-probe setup and involves the application of geometrical correction factors depending on the sample geometry and electrode pitch. The characterization of small thin film structures in the micrometer range requires probe tip diameters and spacings that are of similar size. An experimental realization with micro-manipulators is possible as tip distances in a range of a few micrometers can be achieved. However, such a setup requires an additional correction factor accounting for the finite probe tip contact area. Neglecting such a correction leads to an underestimation of the sheet resistance when the electrode pitch is comparable to the probe contact area diameter. Based on numerical simulation results, we develop a simplified method applying a new phenomenological correction scheme which takes into account the finite contact area size for small probe distances. This method can be applied directly without any additional numerical simulations and corrects the underestimation due to the probe tip size significantly.

Modification of a single-molecule AFM probe with highly defined surface functionality.

Single-molecule force spectroscopy with an atomic force microscope has been widely used to study inter- and intramolecular interactions. To obtain data consistent with single molecular events, a well-defined method is critical to limit the number of molecules at the apex of an AFM probe to one or to a few. In this paper, we demonstrate an easy method for single-molecule probe modification by using the Cu-catalyzed alkyne–azide cycloaddition reaction. Excess terminal alkynes were covalently attached to the probe, and a bi-functional molecule containing an azide at one end and a carboxylic acid at the other was dissolved in the reaction solution. By simply contacting the probe and the Cu substrate, controlled carboxylation on the probe apex could be achieved, since the ‘click’ reaction requires the co-exist of alkyne, azide and Cu(I). The finite contact area would result in a highly defined surface functionality of the probe down to single molecule level with high reproducibility.

Size effect on the compression breakage strengths of glass particles

The quasi-static compression-breakage responses of the glass spheres with five different sizes (4–25mm) are investigated. The breakage strength data are found to be highly scattered. Based on the Weibull model, a statistical approach is proposed to interpret the characteristics in the breakage strength of the glass particles. The Weibull stress concept is introduced to accurately define the breakage stress of the particles considering the effects of finite contact area and breakage modes. It is observed that the relationship between the cumulative survival probability of the particles and the breakage stress follows the Weibull distribution reasonably well. Moreover, the scaling law between the breakage strength and the particle size is consistent with the theoretical predication by the Weibull model. Finally, the energy consumption during the particle breakage process is discussed with a three-parameter Weibull distribution. The relationship of the characteristic energy and the particle size also follows a power law.

Statistical model of nearly complete elastic rough surface contact

In the area of homogeneous, isotropic, linear elastic rough surface normal contact, many classic statistical models have been developed which are only valid in the early contact when real area of contact is infinitesimally small, e.g., the Greenwood–Williamson (GW) model. In this article, newly developed statistical models, built under the framework of the (i) GW, (ii) Nayak–Bush and (iii) Greenwood’s simplified elliptic models, extend the range of application of the classic statistical models to the case of nearly complete contact. Nearly complete contact is the stage when the ratio of the real area of contact to the nominal contact area approaches unity. At nearly complete contact, the non-contact area consists of a finite number of the non-contact regions (over a finite nominal contact area). Each non-contact region is treated as a mode-I “crack”. The area of each non-contact region and the corresponding trapped volume within each non-contact region are determined by the analytical solutions in the linear elastic fracture mechanics, respectively. For a certain average contact pressure, not only can the real area of contact be determined by the newly developed statistical models, but also the average interfacial gap. Rough surface is restricted to the geometrically-isotropic surface, i.e., the corresponding statistical parameters are independent of the direction of measurement. Relations between the average contact pressure, non-contact area and average interfacial gap for different combinations of statistical parameters are compared between newly developed statistical models. The relations between non-contact area and average contact pressure predicted by the current models are also compared with that by Persson’s theory of contact. The analogies between the classic statistical models and the newly developed models are also explored.

Nanoscale Contact-Radius Determination by Spectral Analysis of Polymer Roughness Images

In spite of the long history of atomic force microscopy (AFM) imaging of soft materials such as polymers, little is known about the detailed effect of a finite tip size and applied force on the imaging performance on such materials. Here we exploit the defined scaling of roughness amplitudes on amorphous polymer films to determine the transfer function imposed by the imaging tip. The finite indentation of the nanometer-scale tip into the comparatively soft polymer surface leads to a finite contact area, which in turn effectively acts as a moving average filter for the surface roughness. In the power spectral density (PSD), this leads to an attenuation of the roughness amplitudes related to the Airy pattern known from light diffraction of a circular aperture. This transfer function is affected by the roughness-induced local modulation of the tip height and contact area, which is studied by performing simulations of the polymer roughness and the imaging process. We find that for typical polymer parameters and sharp tips the contact radius of the tip-sample contact can be recovered from the roughness spectrum. We experimentally verify and demonstrate the method by measuring the nanoscale contact radius as a function of applied load and travel distance on a highly cross-linked model polymer. The data are consistent with the Johnson-Kendall-Roberts (JKR) contact model and verifies its applicability at the nanometer scale. Using the model, quantitative values of the elastic sample parameters can be determined.

Oscillations of the Body with Consideration of the Formation of Finite Contact Area

Small free and forced vibrations of a roller bearing have been investigated taking into account the finite contact area between the rolling body surface and the base bearing surface. It is shown that a decrease in the amplitude of free oscillations of the rolling body leads to free vibration frequency growing to infinity that represents a dynamic effect known as rattling. It is also stated that investigated bearing is a kind of filter to those external harmonic impacts whose frequencies are below a certain threshold value of the circular frequency ρ0.

Origin of piezoelectric response under a biased scanning probe microscopy tip across a 180∘ferroelectric domain wall

The piezoelectric response of a material under a nanoscale biased tip scanned across a sample in piezoelectric force microscopy (PFM) provides insight into the structure and dynamics of domain walls in ferroelectrics. While the vertical displacements of the tip under piezoelectric deformations of the sample have been reasonably explained, the origin of the lateral twisting of the tip remains unclear. This poses a serious problem when combining vertical and lateral signals to create vector PFM maps of polarization distribution in ferroelectrics. Using a combination of finite element modeling and analytical theory, and by comparison with prior experimental work across a single antiparallel domain wall on the (0001) surface of LiNbO${}_{3}$, we unequivocally show that the lateral signal originates from a shear displacement of the surface. We show that there are two types of lateral signals, one arising from the ${d}_{15}$ shear deformation, and the other from the ${d}_{22}$ lateral deformation. The vertical PFM signal surprisingly shows equal contributions from the ${d}_{33}$ (leading to normal displacements) and ${d}_{15}$ (leading to shear displacement) coefficients. We also show that an averaging of the PFM signal over a finite contact area of the tip, as experimentally observed, is essential to understanding the line shape of the PFM responses across the wall. After clarifying the origin of the nanoscale PFM signals, we conclude that, in general, a vertical signal does not automatically indicate a polarization component out of the surface, while a lateral signal does not automatically indicate an in-plane polarization component. Without a detailed theory or simulation especially in materials with nanoscale domain structures, ferroelectric relaxors, and morphotropic compositions, such assumptions may lead to incorrect domain and wall interpretations. The proposed model and numerical simulation method could be applied to all piezoelectric materials.

Exploring atomic-scale lateral forces in the attractive regime: a case study on graphite (0001)

A non-contact atomic force microscopy-based method has been used to map the static lateral forces exerted on an atomically sharp Pt/Ir probe tip by a graphite surface. With measurements carried out at low temperatures and in the attractive regime, where the atomic sharpness of the tip can be maintained over extended time periods, the method allows the quantification and directional analysis of lateral forces with piconewton and picometer resolution as a function of both the in-plane tip position and the vertical tip–sample distance, without limitations due to a finite contact area or to stick-slip-related sudden jumps of tip apex atoms. After reviewing the measurement principle, the data obtained in this case study are utilized to illustrate the unique insight that the method offers. In particular, the local lateral forces that are expected to determine frictional resistance in the attractive regime are found to depend linearly on the normal force for small tip–sample distances.

Dynamic instability of a thin circular plate with friction interface and its application to disc brake squeal

The mathematical formulation for determining the dynamic instability due to transverse doublet modes in the self-excited vibration of a thin annular plate is presented in this paper. An analytical approach is developed to obtain the stability results from the eigenvalue problem of a stationary disc with a finite contact area. The approach uses the eigenfunctions of transverse doublet modes in classical plate theory and establishes the formulation of modal instability due to the modal-interaction of a doublet mode pair. The one-doublet mode model of a disc and a discrete model equivalent to the one-doublet mode model are proposed for providing a more fundamental understanding of the onset of squeal. The analytical models are validated through a comparison of results from a modal expansion model obtained from finite element component models. Throughout the analytical investigation, the pad arc length is found to be a critical design parameter in controlling squeal propensity.

Theory of organization in nature: pulsating physiological processes

This paper shows that thermodynamic optimization provides a common theoretical basis for the existence of the finely tuned frequencies of pulsating processes of animals. In respiration and circulation, the minimization of mechanical power consumption subject to finite contact area and mass transfer (metabolic) rate constraints also explains why frequencies decrease as the body size ( M ) increases. For example, it is shown that the optimal breathing and heartbeat time intervals should increase as M 0.24 , which is in excellent agreement with experimental data. It is also shown that the breathing and heartbeat time intervals should be of the same order of magnitude. In ejaculation, the maximization of the mechanical power transmitted to the ejected seminal fluid explains the existence of an optimal bursting time interval. The deterministic method of thermodynamic optimization predicts temporal organization in Nature, and extends thermodynamics to the field of biology.

Pressure sensitivity of cemented granular materials

Abstract In this paper, we explore the mechanical contact interaction of two identical elastic spheres uniformly coated with thin layers of a different elastic material. These two coating layers intersect over a finite contact area thus bonding the spheres. The normal contact stiffness and the shear contact stiffness increase when the spheres are axially pressed together, due to the increasing contact area. The dependence of these stiffnesses on the axial load is calculated by using a new approximate analytical solution. The solution also gives the distributions of the normal and shear stress components on the cemented contact. We use this solution to calculate the pressure dependence of the effective elastic moduli of a random pack of identical cemented spheres. This pressure dependence may be large if the initial contact radius is small. It is insignificant for large contact radii. If the spheres are in direct contact and the initial contact radius is small, the elastic properties of the cement have little effect on the pack's elastic moduli. However, if the spheres are separated by even a small cemented gap, the elastic properties of the cement may have a considerable effect on the pack's elastic moduli.

Efficient calculation of forces and stresses due to transverse impact of polycrystalline graphite beams

A new method is described for the calculation of the time-dependent forces and stresses in a polycrystalline graphite beam subjected to transverse impact. Unlike earlier methods, which consider the contact area to be infinitesimal, the present method takes account of the effect of the time-dependent finite contact area, and is therefore more realistic. It has the effect of limiting the high-frequency modes of response of the beam, which has the computational advantage of improving the convergence of the summation for stresses.

A mechanics model of the compression of cells with finite initial contact area

The effect of intercellular bonding on the stress-strain behavior of soft plant tissue is considered. In our mechanical model, a conglomerate of identical cells is arranged in a regular array. Each cell is pressurized and bonded across flat contact areas with adjacent cells in the direction of the applied load. The cell wall is a finitely-deformed mechanical membrane bounding an incompressible fluid (the cytoplasm). A nonlinear elastic constitutive law is presented that describes data for apple parenchyma. Results show that intercellular bonding has a strong effect on the macroscopic properties of the whole tissue. A larger intercellular contact area increases tissue stiffness and magnifies the effect of initial turgor pressure on tissue stiffness.

Effect of finite contact area on impact stresses in polycrystalline graphite beams

Theoretical work is reported on the determination of the stresses produced by a single impact load in rod specimens of polycrystalline graphites, typically 0.1 m long and 0.015 m diameter, simply supported at the ends. The impact force function was calculated from the theory of Timoshenko, the effects of a finite area between rod and impactor being included by varying the radius of curvature of the impactor. Results have been obtained for the maximum tensile stress as a function of time produced by an impactor of mass 0.29 kg striking with a velocity of 1.3 ms −1. Compared with some previous calculations for a point impact force, the effect of a larger contact area was found to reduce the contributions of the higher order vibrational modes. However, even for the largest radius of cuvature of the impactor studied, 1 m, the net effect on the predicted stresses was to reduce their values by only a few per centage from those obtained for a point contact force.

Further consideration of the DMT model for elastic contact

One of the early models for the contact of an elastic sphere on a rigid flat, which took account of the action of surface forces, was developed by Derjaguin et al. Making the assumption that the deformed profile of the sphere is Hertzian, they calculated the force of attraction due to surface forces by a “thermodynamic” method. This approach is now shown to be incorrect, and is replaced by a direct “force” method of calculation. The new analysis shows that the adhesional behaviour depends on the sphere radius, elastic modulus and the surface energy of the sphere. For small, fairly rigid spheres with low surface energy, the contact behaviour is the same as that originally predicted by Derjaguin et al., that is, as the sphere and the flat are pulled apart, separation occurs at point contact. However, for larger, more elastic spheres with high surface energy, separation of the sphere and flat occurs at a finite area of contact even though the deformation is still assumed to be Hertzian. The behaviour resembles that predicted by Johnson et al. where a different mode of deformation is assumed. However, in the present work, the instability at a finite contact area is not due to infinite tensile stresses around the contact periphery as in the Johnson—Kendall—Roberts model, but arises from the sharp fall in surface forces as the contact area decreases.