Asperity Model Research Articles

A Physical Model for Interseismic Erosion of Locked Fault Asperities

AbstractThe conventional “asperity model” posits that faults are partitioned into fixed velocity‐weakening (VW) patches (asperities) that are locked interseismically and velocity‐strengthening (VS) regions that creep stably without accumulating stress. However, studies of GPS‐derived deformation in northern Japan have shown that interseismic strain in the Tohoku region did not accumulate at a constant rate (as expected) but gradually decreased from 1996 to 2011. This change in strain rate is consistent with locked asperities shrinking by ∼75% in area during this period. Here we consider a modification to the conventional asperity model, such that thermal pressurization (TP) is active over an area that encompasses a VW region and part of the surrounding VS region. In our quasi‐dynamic simulations, TP causes shear stress during rapid slip to decrease to very low levels. During the interseismic period, stress gradually recovers to steady state friction at the plate rate, at which point stable creep initiates. The creep front propagates inward, effectively eroding the locked asperity. For uniform properties, the locked area shrinks roughly linearly in time through the VS region. Locked asperities shrink more slowly with higher nominal friction coefficient or background effective normal stress in the VS region, lower hydraulic diffusivity, and larger TP zones. Lateral heterogeneity in properties can give rise to nonlinear erosion. Predictions from this model can be compared against GPS data to test whether the model can explain the observed changes in interseismic strain rate in Tohoku.

Effects of friction reduction of micro-patterned array of rough slider bearing

Complex micro-scale patterns have attracted interest because of the functionality that can be created using this type of patterning. This study evaluates the frictional reduction effects of various micro patterns on a slider bearing surface which is operating under mixed lubrication. Due to the rapid growth of contact area under mixed lubrication, it has become important to study the phenomenon of asperity contact in bearings with a heavy load. New analysis using the modified Reynolds equation with both the average flow model and the contact model of asperities is conducted for the rough slider bearing. A numerical analysis is performed to determine the effects of surface roughness on a lubricated bearing. Several dented patterns such as, dot pattern, dashed line patterns are used to evaluate frictional reduction effects. To verify the analytical results, friction test for the micro-patterned samples are performed. From comparing the frictional reduction effects of patterned arrays, the design of them can control the frictional loss of bearings. Our results showed that the design of pattern array on the bearing surface was important to the friction reduction of bearings. To reduce frictional loss, the longitudinal direction of them was better than the transverse direction.

Fractal Model for Wettability of Rough Surfaces.

This paper presents a fractal model to describe wettability on multiscale randomly rough surfaces. Hydrophobic or superhydrophobic surfaces, produced by processes such as electrodeposition and etching, lead to the creation of random roughness at multiple length scales on the surface. This paper considers the description of such surfaces with a fractal asperity model based on the Weierstrass-Mandelbrot (W-M) function, where the fractal parameters are uniquely determined from a power spectrum of the surface. By use of this description, a model is presented to evaluate the apparent contact angle in the different wetting regimes. The model is predictive in that it does not use any empirical or correlatory fitting of parameters to experimental data. Experimental validation of the model predictions is presented on various hydrophobic and superhydrophobic surfaces generated on several materials under different processing conditions. The contact angle is found be strongly dependent on the range of asperity length scale and weakly dependent on the fractal dimension for a surface with stable Cassie state. Based on the fractal description, desired surface roughness characteristics for generating superhydrophobicity on a particular substrate are also derived.

A random process asperity model for adhesion between rough surfaces

A simple asperity model using random process theory is developed in the presence of adhesion, using the Derjaguin, Muller and Toporov model for each individual asperity. A new adhesion parameter is found, which perhaps improves the previous parameter proposed by Fuller and Tabor which assumed identical asperities – the model in all his variants for the radius always gives a finite pull-off force, as in Fuller and Tabor, and contrary to the exponential asperity height distribution, where the force is either always compressive, or always tensile. It is shown that a model with spheres having a radius only dependent on height is a reasonable approximation with respect to models having also a distribution of radius curvatures – the three models differ considerably, as opposed to the adhesionless case where these details did not matter. The important surface parameters in the theory determining the pull-off force are the three moments m0, m2, m4. The asymptotic form of the model at large separation is solved in closed form. As the theoretical pull-off of aligned asperities having the same radius (the average value) increases with the square root of the Nayak bandwidth of the roughness, and as asperity models are known to describe less well the surface at large bandwidth parameters, the limit behavior at large bandwidths remains uncertain.

Frequency-dependent rupture process, stress change, and seismogenic mechanism of the 25 April 2015 Nepal Gorkha M w 7.8 earthquake

On 25 April 2015, an M w 7.8 earthquake occurred on the Main Himalaya Thrust fault with a dip angle of ~ 7° about 77 km northwest of Kathmandu, Nepal. This Nepal Gorkha event is the largest one on the Himalayan thrust belt since 1950. Here we use the compressive sensing method in the frequency domain to track the seismic radiation and rupture process of this event using teleseismic P waves recorded by array stations in North America. We also compute the distribution of static shear stress changes on the fault plane from a coseismic slip model. Our results indicate a dominant east-southeastward unilateral rupture process from the epicenter with an average rupture speed of ~3 km s‒1. Coseismic radiation of this earthquake shows clear frequency-dependent features. The lower frequency (0.05–0.3 Hz) radiation mainly originates from large coseismic slip regions with negative coseismic shear stress changes. In comparison, higher frequency (0.3–0.6 Hz) radiation appears to be from the down-dip part around the margin of large slip areas, which has been loaded and presents positive coseismic shear stress changes. We propose an asperity model to interpret this Nepal earthquake sequence and compare the frequency-dependent coseismic radiation with that in subduction zones. Such frequency-dependent radiation indicates the depth-varying frictional properties on the plate interface of the Nepal section in the main Himalaya thrust system, similar to previous findings in oceanic subduction zones. Our findings provide further evidence of the spatial correlation between changes of static stress status on the fault plane and the observed frequency-dependent coseismic radiation during large earthquakes. Our results show that the frequency-dependent coseismic radiation is not only found for megathrust earthquakes in the oceanic subduction environment, but also holds true for thrust events in the continental collision zone.

Effect of surface asperities on the capacitances of capacitive RF MEMS switches

The effects of surface asperities on the up- and down-state capacitances of the capacitive radio frequency (RF) micro electromechanical system (MEMS) switches were studied in this paper based on the single asperity model and statics. The research results demonstrated that surface asperities effects on the up-state capacitance could be neglected, whereas surface asperities must be taken into consideration at the down-state position in the RF MEMS switches because the surface asperities significantly affected the down-state capacitance. The down-state capacitance typically decreased as the root mean square (RMS) roughness and asperity radius increased. The down-state capacitance was approximately 26% of the theoretical value when the RMS roughness was 20 nm, and 32% of the theoretical value when the asperity radius was 100 nm. The experimental results were in good agreement with the simulation results.

Tribological effects of a rough surface bearing using an average flow analysis with a contact model of asperities

To evaluate the effects of surface roughness for a slider bearing operating under partial or boundary lubrication, a new approach with both stochastic and contact characteristics is proposed. It has become important to study the phenomenon of asperity contact in bearings because the growth of contact area under heavy load conditions induces severe changes in their performance. In this study, average flow factors derived according to Patir and Cheng were used and a model for multi-asperities contact was incorporated to calculate the tribological performance of a bearing with random surface roughness. An analysis using the modified Reynolds equation with both the average flow model and the contact model of asperities was conducted and compared with previous findings. The results showed that the influence of roughness parameters on friction and load capacity increased rapidly upon application of asperities contact.

Theoretical Prediction of Mixed Frictional Heat of Mechanical Seals Based on Shoulder-shoulder Contact Model of Asperities

Theoretical Prediction of Mixed Frictional Heat of Mechanical Seals Based on Shoulder-shoulder Contact Model of Asperities

On Pastewka and Robbins' Criterion for Macroscopic Adhesion of Rough Surfaces

Pastewka and Robbins (2014, “Contact Between Rough Surfaces and a Criterion for Macroscopic Adhesion,” Proc. Natl. Acad. Sci., 111(9), pp. 3298–3303) recently have proposed a criterion to distinguish when two surfaces will stick together or not and suggested that it shows quantitative and qualitative large conflicts with asperity theories. However, a comparison with asperity theories is not really attempted, except in pull-off data which show finite pull-off values in cases where both their own criterion and an asperity based one seem to suggest nonstickiness, and the results are in these respects inconclusive. Here, we find that their criterion corresponds very closely to an asperity model one (provided we use their very simplified form of the Derjaguin–Muller–Toporov (DMT) adhesion regime which introduces a dependence on the range of attractive forces) when bandwidth α is small, but otherwise involves a root-mean-square (RMS) amplitude of roughness reduced by a factor α. Therefore, it implies that the stickiness of any rough surface is the same as that of the surface where practically all the wavelength components of roughness are removed except the very fine ones.

Characteristics of subevents and three-stage rupture processes of the 2015 Mw 7.8 Gorkha Nepal earthquake from multiple-array back projection

On 25 April 2015 an Mw 7.8 earthquake occurred in Nepal and caused about 9000 casualties. This earthquake ruptured part of the Main Himalaya Thrust fault, which is due to the convergence of the subducting Indian plate to the overriding Eurasian plate, and showed thrust mechanism with a very small fault dip angle (about 7–10°). We apply teleseismic multiple-array back projection analysis to study the rupture process of this earthquake and find 6 clear high frequency radiation sources (subevents). Our results illustrate a simple unilateral eastward rupture of ∼160km with relative stable rupture speed of ∼2.8km/s and a duration of 56s. The entire rupture processes can be divided into 3 stages. The high frequency radiation appears to be mainly located at the edge of the large slip area, but the subevents have different characteristics in the western and eastern rupture areas. For this 2015 Nepal earthquake, the scales of asperities appear to be mainly controlled by depth, which dominates the overall patterns of slip and high frequency radiation. We finally propose a multiple-scale asperity model with stress and structural heterogeneities along the rupture direction to explain the distribution of high frequency subevents, co-seismic slip, and aftershocks.

On the Significance of Asperity Models Predictions of Rough Contact With Respect to Recent Alternative Theories

Recently, it has been shown that while asperity models show correctly qualitative features of rough contact problems (linearity in area–load, negative exponential dependence of load on separation which means also linearity of stiffness with load), the exact value of the coefficients are not precise for the idealized case of Gaussian distribution of heights. This is due to the intrinsic simplifications, neglecting asperity coalescence, and interaction effects. However, the issue of Gaussianity has not been proved or experimentally verified in many cases, and here, we show that, for example, assuming a Weibull distribution of asperity heights, the area–load linear coefficient is not much affected, while the relationships load–separation and, therefore, also stiffness–load do change largely, particularly when considering bounded distributions of asperity heights. It is suggested that Gaussianity of surfaces should be further tested in the experiments, before applying the most sophisticated rough contact models based on the Gaussian assumption.

Elastoplastic contact mechanics model of rough surface based on fractal theory

Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ϕ, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.

Adhesive friction based on finite element study and n-point asperity model

The present work considers analysis of adhesive friction of rough surfaces using n- point asperity concept for statistical definition of surface roughness features, and accurate finite element analysis of elastic-plastic deformation of single asperity contact. Well defined adhesion index and plasticity index are used to study the prospective contact situations arising out of variation in material properties and surface roughness features. From the present results it is possible to locate the combinations of adhesion index and plasticity index that may yield very low coefficient of friction. Thus suitable choice of surface and material parameters for the contact of two rough surfaces can be made in order to minimize friction typically at low load and micro scale roughness situations.

Validation of the Recipe for Broadband Ground‐Motion Simulations of Japanese Crustal Earthquakes

The robustness of broadband ground‐motion simulation can promote seismic‐hazard assessment. A broadband ground‐motion simulation technique called “the recipe” is used in the scenario earthquake shaking maps of the National Seismic Hazard Maps for Japan. The recipe represents a fault rupture based on a multiple asperity model referred to as the characterized source model. Broadband ground‐motion time histories on the engineering bedrock are computed by a hybrid approach of the 3D finite‐difference method and the stochastic Green’s function method for the long‐ (>1 s) and short‐period ( 70 km); such conditions are outside of the target range of the recipe. Simulations using a 1D velocity structure model were also examined. The simulation results for the 1D and 3D velocity structure models indicated that the 3D velocity structure models are important in reproducing PGV and the later phases with long duration, especially on deep sediment sites.

Surface specific asperity model for prediction of friction in boundary and mixed regimes of lubrication

Machine downsizing, increased loading and better sealing performance have progressively led to thinner lubricant films and an increased chance of direct surface interaction. Consequently, mixed and boundary regimes of lubrication are prevalent with ubiquitous asperity interactions, leading to increased parasitic losses and poor energy inefficiency. Surface topography has become an important consideration as it influences the prevailing regime of lubrication. As a result a plethora of machining processes and surface finishing techniques have emerged. The stochastic nature of the resulting topography determines the separation at which asperity interactions are initiated and ultimately affect the conjunctional load carrying capacity and operational efficiency. The paper presents a procedure for modelling of asperity interactions of real rough surfaces, from measured data, which do not conform to the usually assumed Gaussian distributions. The model is validated experimentally using a bench top reciprocating sliding test rig. The method demonstrates accurate determination of the onset of mixed regime of lubrication. In this manner, realistic predictions are made for load carrying and frictional performance in real applications where commonly used Gaussian distributions can lead to anomalous predictions.

Friction analysis at elastic-plastic contact of rough surfaces using n-point asperity model

The paper describes a theoretical study of friction at elastic-plastic contact of rough surfaces in n-point asperity model framework and based on accurate finite element analysis of elastic-plastic deformation of single asperity contact. Plasticity index, a well-defined nondimensional parameter is used to study the prospective situations arising out of variation in material properties and surface roughness. Using practical values of material properties and surface roughness parameters, results are obtained for the behavior of applied load, friction force, and coefficient of friction as a function plasticity index and mean separation of surfaces. It is observed that with increase in amount of plastic deformation, the load required to be applied for maintaining a particular level of separation between contacting surfaces increases while the frictional force decreases. Coefficient of friction is independent of applied load in predominantly plastic domain of deformation but varies nonlinearly in other domains of deformation. Also, for the same applied load the coefficient of friction increases with increase in elastic deformation.

Small interseismic asperities and widespread aseismic creep on the northern Japan subduction interface

AbstractThe canonical model of fault coupling assumes that slip is partitioned into fixed asperities that display stick‐slip behavior and regions that creep stably. We show that this simple asperity model is inconsistent with GPS‐derived deformation in northern Japan associated with interseismic coupling on the subduction interface and the transient response to Mw 6.3–7.2 earthquakes during 2003–2011. Comparisons of GPS data with simulations of earthquakes on asperities and associated velocity‐strengthening afterslip require that afterslip overlaps areas of the fault that ruptured in previous earthquakes, including the 2011 Mw 9 Tohoku‐oki earthquake. Whereas about 55% of the plate interface ruptured in earthquakes during 2003–2011, we infer that only 9% of the plate interface was fully locked between earthquakes. Inferred locked asperities are roughly 25% the size of rupture areas determined by seismic source inversions. These smaller asperities are consistent with interseismic strain accumulation in 2009, although more extensive locking is required a decade earlier in 1998.

Adhesive Wear Based on Accurate FEA Study of Asperity Contact and n-Point Asperity Model

The paper describes a theoretical study of adhesive wear based on accurate finite element analysis (FEA) of elastic-plastic contact of single asperity and n-point asperity model. The wear model developed considers wear particle generation in whole range of deformation, ranging from fully elastic through elastic-plastic to fully plastic. Well defined adhesion index and plasticity index are used to study the prospective situations arising out of variation in load, material properties, and surface roughness. It is observed that the wear volume at particular level of separation increases with increase in plastic deformation and adhesion effect. Materials having higher tendency to adhesion show higher wear rate. Trend of the results obtained is found in line with the existing solutions which are modeled with conventional asperity concept. Inclusion of separate formulations for intermediate state of deformation of asperities which are based on accurate FEA study gives complete solution.

Can clay minerals account for the behavior of non-asperity on the subducting plate interface?

Seismicity along the subducting plate interface shows regional variation, which has been explained by the seismic asperity model where large earthquakes occur at strongly coupled patches that are surrounded by weakly coupled regions. This suggests that the subduction plate interface is heterogeneous in terms of frictional properties; however, the mechanism producing the difference between strong and weak couplings remains poorly understood. Here, we propose that the heterogeneity of the fluid pathway and of the spatial distribution of clay minerals plays a key role in the formation of non-asperity at the subducting plate interface. We use laboratory measurements of frictional properties to show that clay minerals on a simulated fault interface are characterized by weak and slow recovery, whereas other materials such as quartz show relatively quick recovery and thereby strong coupling on the fault surface. Aqueous fluids change the mineralogy at the plate interface by producing clay minerals due to hydrate reactions, suggesting that the hydrated weakly coupled regions act as a non-asperity and form a barrier to rupture propagation along the plate boundary at the depths of seismogenic zone.

Rough contacts near full contact with a very simple asperity model

Recently, asperity theories in contact mechanics of rough surfaces have been extended in the range near full contact by elaborating on the idea of searching a corrective solution to the tensile regions of the full contact solution. The full contact solution defines a “surface” on which asperity theory can be applied. It is here shown that a very simple prediction can be made for the non-contact area, improving the accuracy near full contact with respect to the other simple solution available, that of Persson.