Asperity Size Research Articles

Numerical modelling of pressure solution deformation at axisymmetric asperities under normal load

Abstract We developed a numerical model of compression of asperities by pressure solution (PS). The dissolution rate along the contact was determined by (1) computing the normal stress distribution from the present shape of the asperities, and (2) solving the diffusion equation inside the fluid-saturated solid–solid interface, including local dissolution source terms corresponding to the stress field previously determined. The change in shape of the asperities during an infinitesimal time interval can then be calculated and the entire procedure repeated as many times as desired. We simulated PS compaction of axisymmetric asperities with different sizes and shapes under various temperatures and loads, and using different values of the interface diffusion coefficient. Our results show that as the contact flattens and grows during PS, the initial elastic deformation is partially relaxed and the stress transferred from the contact centre to the edge. Transient stress release remains significant during an extended period and could strongly influence the interpretation of laboratory experiments. In our model, dissolution and interface diffusion are not sequentially combined as is usually assumed, making it impossible to identify a single rate-limiting process. The convergence rate of the asperities was approximately proportional to the mean effective stress at the contact, and depended in a complex way on the contact radius, but was not sensitive to the asperity size. We also estimated the conditions under which undercutting at the contact edge is triggered.

Adhesion forces measured between particles and substrates with nano-roughness

This report briefly reviews the measurements and interpretation of adhesion forces between microscopic probes and substrates having micro- and nano-scaled roughness characteristics. The measurements were recently conducted at Michigan Technological University using atomic force microscopy. The laboratory study concentrated on both rigid and deformable materials, with the probes larger than the size of roughness features of interacting surfaces. For such systems, a detailed surface characterization, in terms of roughness parameters, asperity size and shape and spacing between asperities, as well as analysis of deformation of materials, is required. Analysis of the experimental data can be done using theoretical models suitable for rough surfaces, which would allow one to normalize the measured forces. Alternatively, loading of the probe during adhesion force measurements can be managed properly to control deformations of the nano-scaled surface irregularities. Controlling the deformation reduces and even eliminates the effects of nano-roughness on the probe-substrate contact area, promoting conditions described by the contact mechanics models for the sphere-smooth substrate system.

Crack Propagation under Compressive Stress Influenced by Crack Face Asperity

The influence of surface roughness in crack face on the behavior of crack growth is studied. Numerical results derived from two kinds of mechanical models representing the macroscopic and microscopic asperity supposed to exist in the face of an initial crack are compared. In macro-asperity model, the influence of location and size of single-triangular asperity on the stress intensity factor is evaluated. In this model, it is found that the mode-I stress singularity appears in certain circumstances even under overall compression. In micro-asperity model, influence of friction coefficient on the trajectory of crack path is discussed. There exists a tendency that a path of wing crack growth becomes more straight and parallel to axis of compression as the friction coefficient increases.

Adhesion as an interplay between particle size and surface roughness

Surface roughness plays an important role in the adhesion of small particles. In this paper we have investigated adhesion as a geometrical effect taking into account both the particle size and the size of the surface features. Adhesion is studied using blunt model particles on surfaces up to 10 nm root-mean-square (RMS) roughness. Measurements with particles both smaller and larger than surface features are presented. Results indicate different behavior in these areas. Adhesion of particles smaller than or similar in size to the asperities depend mainly on the size and shape of the asperities and only weakly on the size of the particle. For large particles also the particle size has a significant effect on the adhesion. A new model, which takes the relative size of particles and asperities into account, is also derived and compared to the experimental data. The proposed model predicts adhesion well over a wide range of particle/asperity length scales.

Capillarity and electromigration effects on asperity contact evolution in microelectromechanical systems switches

Morphology evolution of asperity contacts in microelectromechanical systems switches is examined in the framework of the phase field method. Surface mass diffusion, driven by capillarity, rapidly increases the asperity contact radius at early times, decreases it slowly at later times, and, possibly, pinches off the contact due to a Rayleigh instability. Electromigration accelerates this process but retards or prevents the pinch off at late times. The evolution occurs faster when the asperity size and/or density are smaller. Approximate analytical results for the evolution kinetics are provided.

A Molecular Dynamics Model for Single Adhesive Contact

The normal adhesive contact between a pair of asperities is performed using molecular dynamics. To simplify the problem, the equivalent contact problem of sphere–plane interaction is solved. Displacements in the contact zone are very small compared to the asperity size, therefore, the computational model is focused on the neighborhood of the contact area. The adhesion between the asperity and the plane is calculated as a sum of interactions between atoms of the asperity and the plane. A computational experiment of pull-on and pull-off is carried out to study the influence of the adhesion on the formation of the contact forces and deformations. The numerical results are compared with theoretical predictions.

Stress and cracking behavior of plasma sprayed thermal barrier coatings using an advanced constitutive model

A finite element simulation of a plasma sprayed thermal barrier coating (TBC) system represented as a three-layer structure with an interface asperity is presented. Loading due to thermal expansion mismatch and geometry changes from oxide growth are included. A realistic viscoplastic model is used to represent the behavior of the ceramic layer, which includes both time dependent behavior and strong yield stress asymmetry. Predicted stresses can be up to three orders of magnitude lower than those based on elastic analysis. Elastic–plastic analysis using symmetric yield stresses result in errors up to a factor of 5 on the stress and hence inclusion of tension compression yield asymmetry is essential if better than order of magnitude stress estimates are required. It is shown that residual stresses at room temperature never become large enough to propagate asperity size cracks based on linear elastic fracture mechanics. Instead, failure may need to be described in terms of volumetric damage. A simple representative approach based on Rankine failure theory is presented.

Extended DLVO interactions between spherical particles and rough surfaces

An “extended DLVO” approach that includes Lifshitz–van der Waals, Lewis acid–base, and electrostatic double layer interactions is used to describe interaction energies between spherical particles and rough surfaces. Favorable, unfavorable, and intermediate deposition conditions are simulated using surface properties representing common aquatic colloids and polymeric membranes. The surface element integration (SEI) technique and Derjaguin's integration method are employed to calculate interaction energy. Numerical simulations using SEI demonstrate that nanometer scale surface roughness features can produce a distribution of interaction energy profiles. Local interaction energies are statistically analyzed to define representative interaction energy profiles—minimum, average, and maximum—for various combinations of simulated particles and surfaces. In all cases, the magnitude of the average interaction energy profile is reduced, but the reduction of energy depends on particle size, asperity size, and density of asperities. In some cases, a surface that is on average unfavorable for deposition (repulsive) may possess locally favorable (attractive) sites solely due to nanoscale surface roughness. A weighted average of the analytical sphere–sphere and sphere–plate expressions of Derjaguin reasonably approximates the average interaction energy profiles predicted by the SEI model, where the weighting factor is based on the fraction of interactions involving asperities.

Adhesion force between fine particles with controlled surface properties

AbstractThe adhesion force between previously consolidated polymer particles is affected by the use of additives that modify relevant surface parameters, such as the contact hardness and size of asperities at contact. Both the size of silica nanoparticles uniformly coating the particle surfaces, and their surface coverage have been investigated. The effects of the presence of other additives, such as wax and cross‐linking polymer were tested. The experimental results are compared with predictions from theoretical models. Our measurements are shown to be in semi‐quantitative agreement with the theoretical expectations built on the hypothesis of plastic flow of interparticle contacts. Moreover, the results indicate that the aggregation of individual particles in the fluidlike regime must play a relevant role in how bulk stresses distribute among interparticle contacts when the powder transits to the solid state. This work highlights the need of considering particle aggregation and contact plasticity as central features, mostly obviated so far, to deal with real problems on cohesive powders. © 2006 American Institute of Chemical Engineers AIChE J, 2006

Designing for Optimum Liquid Repellency

In the current state-of-the-art, most super repellent surfaces are not sufficiently robust to move out of the laboratory into the commercial realm. With the hope of creating super repellent surfaces that could be employed in a wider variety of commercial applications, means to improve the robustness of ultralyophobic surfaces have been explored theoretically. Suspension pressures and drop retention forces were examined in terms of asperity shape, size, and spacing. The findings from this study suggest a strategy for creating surfaces that maintain their liquid repellency even after exposure to large hydrostatic pressures associated with liquid columns or jets.

Source model of the 2005 west off Fukuoka prefecture earthquake estimated from the empirical Green’s function simulation of broadband strong motions

AbstractWe estimated strong motion generation area (SMGA) source model which is responsible for broadband (0.2, 0.3–10 Hz) strong motions of the 2005 west off Fukuoka prefecture earthquake and its largest aftershock using the empirical Green’s function (EGF) method. The estimated SMGAs are almost corresponding to the large slip area deduced by kinematic waveform inversion. The SMGA rupture for the mainshock propagated mainly upward and toward the northwest with rupture velocity of 3.15 km/s. The size of the SMGA follows the self-similar empirical formula of the asperity size derived by Somervilleet al.(1999). The stress drop of the mainshock SMGA is calculated to be 10.7 MPa, which is larger than those of the largest aftershock SMGA and the aftershocks used as EGF.

Wetting of rough three-dimensional superhydrophobic surfaces

Wetting of rough three-dimensional periodic surfaces is studied. The contact angle of liquid with a rough surface (θ) is different from that with a smooth surface (θ0) due to the difference in the contact area and effect of the air pockets. For non-wetting liquids (θ0>π/2), the contact angle increases with roughness and may approach the value of π (superhydrophobic surface). For high θ0, a homogeneous solid-liquid interface, as well as a composite solid-liquid-air interface with air pockets at the valleys of rough surface are possible. These two interfaces correspond to different states of equilibrium and result in different θ. A probability-based approach is introduced to handle the multiple states of equilibrium and to calculate θ. It is found also that increasing droplet size has the same effect as increasing period of roughness (size of asperities). For larger droplets and for larger asperities, the composite interface is less likely. For applications involving liquid’s transport near rough walls of a channel, an analogy between a droplet of non-wetting liquid and a gas bubble in wetting liquid is proposed. In order to increase bubbles mobility, the contact angle and the contact angle hysteresis should be minimized. Practical recommendations for design of superhydrophobic surfaces are formulated.

Evaluation of asperity-scale temperature effects during seismic slip

For the common rock-forming minerals, the Joule–Thompson effect produces cooling on compression and heating on decompression. Experimental rock friction studies and seismological evidence suggest that the strength of faults is controlled by high-stress asperities that represent a small fraction of the total fault area. During seismic rupture, the area immediately beneath asperities is inferred to undergo adiabatic compressions and decompressions on the order of 1–2.8 GPa. Joule–Thompson coefficients are in the range 261–372 °C/GPa, resulting in temperature changes of ±336–880 °C. Quartz asperities with a compressive strength of 2.8 GPa can produce a heating or cooling of 880 °C immediately beneath an asperity. By comparison, frictional heating ‘flash temperatures’ are less than 1000 °C for asperity contact areas <300 μm 2. The Joule–Thompson effect is independent of asperity size and may augment or counteract frictional heating. The paucity of pseudotachylytes in the geologic record and the absence of localized heat flow anomalies on active faults might be explained by the Joule–Thompson cooling effect.

Dry particle coating for improving the flowability of cohesive powders

Several dry processing techniques are used to coat cohesive cornstarch powder with different size silica particles. For nanosized silica guest particles, FESEM images show that both the magnetic assisted impaction coater (MAIC) and the hybridizer (HB) produce particles that are significantly more uniformly coated than using either a V-shape blender or simple hand mixing. Image analysis confirms that MAIC and HB provide higher surface coverage for the amount of guest material (flow aid) used. The improvement in flowablity of coated cornstarch is determined from angle of repose measurements using a Hosokawa powder tester. These measurements show that nanosized silica provides the best flowability enhancement, whereas mono-dispersed 500-nm silica does not improve the flow properties of cornstarch at all. This observation agrees with a simple theoretical derivation based on the original Rumpf model, which shows that the flowability improvement is inversely proportional to the guest particle size for a given host particle size or size of surface asperities. Experimental results also indicate that surface-treated hydrophobic silica is more effective in improving the flowability of cornstarch particles than untreated hydrophilic silica. An increase in processing time using MAIC and the V-blender also improves the flowability of the cornstarch since the guest particles are more deagglomerated and better dispersed, the longer the processing time.

Evidence for self‐similar, triangular slip distributions on earthquakes: Implications for earthquake and fault mechanics

We characterize average slip distributions on earthquakes beyond their individual heterogeneity. For that, we analyze a large number of seismic slip distributions both measured at the surface after earthquakes (44 profiles) and derived from slip inversion models (76 models). Investigating the overall shape of these slip profiles, we find that they are roughly triangular both along strike and dip, and most of them (70–80%) are asymmetric. Long linear slopes and high slip gradients therefore are the key ingredients to describe earthquake slip profiles. The scaling relations between maximum displacement and length (or width) suggest furthermore that the triangular slip profiles are self‐similar. Such slip patterns make earthquakes dominated by one major zone of maximum slip hence one major “asperity.” Analyzing the position of hypocenters with respect to these “asperities,” we find that earthquakes nucleate at a distance from them that averages 20–30% of their total length. Compiling observations on 56 earthquakes, we show that this distance (i.e., the asperity size) is structurally defined. We then compare the earthquake slip profiles to cumulative slip profiles measured on long‐term faults of various ages and sizes and find that all profiles have a similar shape, triangular and asymmetric. Hence combining data for a large number of earthquakes leads to point out average, generic characteristics of the coseismic slip that are similar to those that emerge from the accumulation of events with time on a single fault. This suggests that these characteristics result from robust physical properties.

Shear behaviour of idealized rock joints - microscale analysis

Reliable estimation of shear strength of rock mass is important for design of tunnels or underground structures. Especially, the assessment of shear strength of a rock joint is critical because a rock joint is one of the weakest points of rock masses due to its discontinuity. Until now, numerous works have been performed through experimental tests, but it is hard to find a microscale study focusing on asperity geometry or asperity size of a rock joint surface and its spatial distribution. This paper explores the effects of microscale characteristics of joint asperities on rock joint shear behaviours through theoretical and numerical analyses. First, the shear strength and failure mode of a rectangular asperity are theoretically obtained from force equilibrium analysis and its basic mechanism is experimentally verified with idealized rock joints. Rectangular-shaped asperities can reflect the microscale asperity of a rough joint surface and evolve its shear behaviour in small deformation regime. Two failure modes of a rectangular asperity can be determined depending on its shape and critical aspect ratio: one mode is a dilative failure with an inclination of 45 - /f/2 and the other is a non-dilative failure with shearing of asperity. The critical aspect ratio, which is used as a failure mode criterion, is a function of peak friction angle, cohesion, and normal stress, and is the most sensitive to peak friction angle. The range of critical aspect ratio is 0.15-0.32 for general rocks. The shear strength of a rectangular asperity also can be determined with peak friction angle, cohesion, basic friction angle, aspect ratio, and normal stress. Upon this basic analysis, the effect of asperity size distribution, asperity shape distribution, normal stress, and specimen size are discussed on the shear behaviour of idealized rock joints. Asperity size distribution has a significant influence on the shear behaviour of rock joints, altering peak shear strength and shear displacement at peak. Numerical analysis results show that the joint of different asperity sizes experiences progressive failure in order of asperity size, while the joint of an identical asperity size approaches failure simultaneously. The joint of more various asperity sizes renders the more ductile shear behaviour. Asperity shape distribution also affects the shear strength. Although joints have the same average aspect ratio, their shear strength can vary depending on the variation of asperity shape. Numerical simulation shows that surface roughness alone may not be appropriate for reliable estimation of rock joint shear strength. Thus, a parameter for characterization of joint surface roughness should be able to reflect the effect of asperity shape distribution. Smaller-sized asperities contribute to peak shear strength at lower normal stresses while larger-sized asperities do at higher normal stresses. Thus, the increase of normal stress alters the evolution of rock joint shear behaviour due to the progressive failure of joint asperities and makes the joint shear behaviour ductile (or deformation-hardening). The mechanism of hardening behaviour of a rock joint with the increase of normal stress is related to reduction of cohesion effect relative to normal stress. Smaller specimens cause much bigger variation of shear strength and their shear behaviours become uniform when the number of asperity approaches or is greater than 100. The effect of specimen size worsens with the increase of variation of asperity size. Therefore, when the rock joint specimen is sampled for reliable estimation of shear strength, the specimen size has to be longer than a minimum required length (i.e., 100 times greater than mean asperity size). (A). Reprinted with permission from Elsevier. For the covering abstract see ITRD E124500.

Asperity map along the subduction zone in northeastern Japan inferred from regional seismic data

In an attempt to examine the characteristic behavior of asperities, we studied the source processes of large interplate earthquakes offshore of the Tohoku district, northeastern Japan, over the past 70 years. In this area, earthquakes of M7 class have a recurrence interval of about 30 years. Seismic observation using a strong‐motion seismometer has been carried out by the Japan Meteorological Agency since the beginning of the 1900s. We collected these seismograms in order to make a waveform inversion. On the basis of the derived heterogeneous fault slip, we identified large slip areas (asperities) for eight earthquakes which occurred after 1930, and we constructed an asperity map. The typical size of individual asperities in northeastern Japan is M7 class, and an M8 class earthquake can be caused when several asperities are synchronized. We propose that the patterns of asperity distribution beneath offshore Tohoku fall into three different categories. In the northern part (40°–41.3°N) the seismic coupling in the asperity is almost 100%, and the size is large. In the central part (39°–40°N), little seismic moment has been released by large earthquakes, and the asperity size is small. In the southern part (37.8°–39°N) the seismic coupling is medium. The weak seismic coupling may be related to submarine topographical features and to the sediment and water along the subducting plate. Our results also suggest a general tendency for the asperities to be located away from the hypocenters (initial break), with aftershocks occurring in the area surrounding the asperity.

Scaling Laws for Opening Partially Adhered Contacts in MEMS

MEMS switches represent a promising technology for a wide range of communications applications. They operate at high frequency, opening and closing the contact between metal pads. Surfaces are rough in nature, therefore a predictive description of contact switching requires understanding of asperity contact and adhesion. A simple model is presented to estimate adhesion forces in MEMS switches and the total forces required to detach the pads. The interface between two rigid pads is modeled as an array of uniformly distributed elastic asperities mimicking the interface roughness. Two types of asperities are considered: bonded asperities and adhered asperities, as described by the JKR adhesion model. The effects of asperity size, density, and load-displacement relationship are analyzed as a function of the loading conditions (i.e., tensile load and bending moment). The minimum force for detachment is proportional to the asperity size and asperity density, except when bending moments and tensile forces are combined (which leads to a more complex relationship). The results are summarized in a loading-detachment map. The most effective method to detach the contacts is through a combination of a bending moment and a tensile force. The implication of these results to MEMS designs are discussed and approaches to modifying the moment and tensile force ratio are suggested.

Time-Dependent Diffusion and Surface-Enhanced Relaxation in Stochastic Replicas of Porous Rock

Understanding the connection between pore structure and NMR behavior of fluid-saturated porous rock is essential in interpreting the results of NMR measurements in the field or laboratory and in establishing correlations between NMR parameters and petrophysical properties. In this paper we use random-walk simulation to study NMR relaxation and time-dependent diffusion in 3D stochastic replicas of real porous media. The microstructures are generated using low-order statistical information (porosity, void–void autocorrelation function) obtained from 2D images of thepore space. Pore size distributions obtained directly by a 3D pore space partitioning method and indirectly by inversion of NMR relaxation data are compared for the first time. For surface relaxation conditions typical of reservoir rock, diffusional coupling between pores of different size is observed to cause considerable deviations between the two distributions. Nevertheless, the pore space correlation length and the size of surface asperity are mirrored in the NMR relaxation data for the media studied. This observation is used to explain the performance of NMR-based permeability correlations. Additionally, the early time behavior of the time-dependent diffusion coefficient is shown to reflect the average pore surface-to-volume ratio. For sufficiently high values of the self-diffusion coefficient, the tortuosity of the pore space is also recovered from the long-time behavior of the time-dependent diffusion coefficient, even in the presence of surface relaxation. Finally, the simulations expose key limitations of the stochastic reconstruction method, and allow suggestions for future development to be made.

Analytical and finite element modelling of roughness induced crack closure

Crack closure is an established component of fatigue understanding, however, significant confusion remains in both experimental determination and micromechanical modelling. Analytical and finite element models of roughness induced crack closure (RICC) are developed in the present paper. A novel interpretation of RICC is explored where shear strains causing asperity contact arise explicitly from residual plastic deformation in the wake of a propagating crack, in a manner that is essentially analogous to plasticity induced crack closure (PICC). The analytical model estimates the crack opening along a simple deflected crack path, defined by a crack deflection angle and length, and residual shear at each asperity interfering with this opening to generate closure. The results from the analytical model are compared to finite element modelling and experimental results, with insight being provided into a controlling influence of the ratio of asperity size to plastic zone size on closure levels.