Asperity Model Research Articles

Development of Dynamic Asperity Models to Predict Surface Fault Displacement Caused by Earthquakes

Asperity models for ground motion prediction is widely used in Japan. Here we expand the application of these asperity models to predict fault displacement caused by surface rupture. The proposed approach is rather simple and practical for the use in fault displacement hazard analysis in nuclear installations and other critical infrastructures, as it is the emphasis of the current topical issue. The proposed method mainly consists of two steps. The first step consists in the characterization of asperities at the seismogenic zone based on the kinematic asperity source model following Irikura’s recipe (Irikura and Miyake in Pure Applied Geophysics, 168:85–104, 2011) for strong ground motion prediction. Since the kinematic model does not take into account surface rupture mechanism, this first step assumes that the fault is buried, and then by trial and error procedure the stress drop on the asperities are estimated, so that the average slip at each asperity be consistent with the ones from the kinematic model. At this stage, the dynamic model predicts strong ground motion consistent with those from the kinematic model. In the second step, the surface rupture is included by calibrating the shallow layer (SL) with stress drop, strength excess and critical slip distance, so that the final fault displacement along the fault be consistent with observations. The 2010 Mw 7.0 Darfield (New Zealand) earthquake is used to test the proposed method. Surface-rupturing was observed in several sites along the main fault reaching values of fault displacement larger than 5 m. The main fault of this earthquake is strike-slip, almost vertical. Therefore, a simplified planar fault asperity model to capture the main features of the fault displacement is assumed. The fault dimensions are assumed to have a length of 60 km and a width of 24 km with three asperities. The preferred model of the first step predicts average slip for each asperity of 2.7, 2.7, and 2 m corresponding, respectively, to stress drops of 6.0 MPa, 8.5 MPa, and 7.0 MPa. In the second step, the surface rupture is calibrated assuming a SL zone of 3 km depth. We found that negative stress drop is not necessary in the SL, because this strongly inhibits surface rupturing. Our preferred model produces fault displacement distribution closer to the observed ones, but average slip at each asperity increases to 3.4 m, 3.2 and 2.8 m. This increase in average slip is due to the contribution of surface rupturing. Ground motion differences between fault-surface rupturing and buried models are negligible, except at the very near-source. These differences are attributed to the SL rupture that mainly affect the ground motion at the very near-source. Overall, our simple asperity model captures the main features of the observed fault displacement and near-source ground motion, proving that the proposed simple and practical two step-procedure provides meaningful estimate of fault displacement and near-source ground motion consistent with observations, as such, this method has the potential to be used in practical fault displacement hazard analysis.

Micropitting Fatigue Wear Simulation in Conformal-Contact Under Mixed Elastohydrodynamic Lubrication

In this study, a physics-based fatigue wear model is proposed to evaluate the reliability and to predict the life of cumulative micropitting wear for lubricated conformal contacts on rough surfaces. The surface normal load, mean film thickness, and frictional shear traction are simulated by a mixed elastohydrodynamic lubrication (EHL) model for a stress prediction model to calculate the average maximum Hertzian pressure of contact asperities and unit with the statistical contact model and dynamic contact model to obtain the asperity stress cycle number. The wear formula is established through combining a micropitting life prediction model of surface asperities and a mean micropitting damage constant of asperities. The four dominant aspects affecting wear behaviors of the surface contact pairs, working conditions, structure and surface topographies, material properties and lubrication conditions are all taken into account in the model. It is a high-fidelity and comprehensive model that can be used to analyze and optimize the tribological design of rolling–sliding pairs in machinery. The micropitting fatigue wear modeling scheme is validated by comparison of theoretical calculations and available experimental wear data.

Contact of rough surfaces: Modeling adhesion in advanced multiasperity models

Surface roughness affects several tribological phenomena and in particular adhesion. For many years, multiasperity models have been the most used in the study of rough contacts notwithstanding their evident limitations. In this work, we propose a fair assessment of improved asperity models with adhesion modeled according to the Derjaguin, Muller and Toporov theory, which assumes attractive forces do not deform the surface profiles. Results are given for three enhanced asperity models: the discrete Greenwood and Williamson model, where the effective heights and curvatures of the surface asperities are used rather than a statistical description; the interacting Hertzian asperities model, where the elastic coupling effects are included; the interacting and coalescing Hertzian asperities model, where the coalescence of contact spots is also conveniently considered. A comparison with advanced contact mechanics theories shows that only the interacting and coalescing Hertzian asperities model correctly captures the physics of the problem at all roughness scales.

A statistical model of elastic-plastic contact between rough surfaces

In a mechanical interface, the contact surface topography has an important influence on the contact stiffness. In the contact processes of asperities, elastic-plastic change can lead to discontinuity and lack of smoothness at a critical contact point. The result is a large difference between the elastic-plastic deformation and the actual asperity deformation. Based on Hertz contact theory, the heights of asperities on a rough surface obey a Gaussian distribution. To take into consideration the continuity of elastic-plastic asperity deformation, we divide the elastic-plastic deformation into three stages: pre-elastic-plastic, mid-elastic-plastic, and post-elastic-plastic deformation. This establishes an elastic-plastic contact model of asperity at a continuous critical point. The contact model of a single asperity fits well with the Kogut–Etsion model and the Zhao–Maietta–Chang model, and the variation trend is consistent. At a lower plastic index, the present model coincides with classical models of contact area and contact load. At a higher plastic index, the simulation results of the present model differ from the Greenwood–Williamson model and the Chang–Etsion–Bogy model but are similar to results from the Kogut–Etsion and Zhao–Maietta–Chang models. This study provides a more accurate microscopic contact model for rough surfaces and a theoretical framework for interface design and analysis.

Effect of Slip-Weakening Distance on Seismic\u2013Aseismic Slip Patterns

In order to explain the seismic–aseismic slip patterns observed on megathrust faults, numerical simulations were carried out using the quasi-dynamic asperity fault model with the slip-dependent friction and stress-dependent healing. Two friction law parameters, strength and slip-weakening distance, are interpreted in the subduction channel context. The parameters are treated as random fields with specified characteristics. Their distributions define heterogeneities of the interplate frictional coupling. The higher strength regions accumulate stresses, whereas the slip-weakening distance lengths control the stress release rates. The simulation results indicate that the slip-dependent asperity model reproduces key features of real megathrust fault behavior. First, stable and unstable slip movements can occur at the same locations, even if the friction parameters are fixed. Second, two rupture styles, single asperity breaks and wide, smooth, propagating rupture fronts, can be distinguished. The latter style is responsible for large slips near the free surface, where lower fault strengths are expected. The reason for these effects is that slip instabilities depend both on local friction and on the system stiffness, which is related to the slipping area size and distribution of slips. It is also shown that the high-strength interplate patches, such as subducted seamounts, can both promote and restrain large earthquakes, depending on the slip-weakening distance lengths.

Modeling of pad surface topography and material removal characteristics for computer-controlled optical surfacing process

Computer-controlled optical surfacing (CCOS) technology is an advantageous polishing process for producing optical surfaces with high convergence rates and high form accuracy, especially for fabricating hard and brittle materials. However, the optimum control of polishing parameters depends critically on the understanding of polishing mechanisms and modeling of material removal characteristics to achieve a deterministic process with high polishing efficiency. Removal analysis still requires further enhancement due to the multi-disciplinary, multi-scale complexity of the material removal mechanism involved in CCOS. Thus, this study presents a novel statistical asperity model and a material removal model to provide scientific and quantitative knowledge of the material removal mechanisms in CCOS. The model is developed on the basis of the research on statistical method, contact mechanics, iterative algorithm, abrasive wear mechanism, and cumulative removal process in CCOS. Practical experiments with different polishing parameters are performed to verify the theoretical model. Simulation results reasonably agree with measured data. Simulation experiments also show that the proposed model helps clarify the effect of pad surface topography on the micro-contact behavior and the material removal characteristics in CCOS and thus forms the theoretical basis for optimizing the polishing process.

Temperature rise of diamond-like carbon during sliding: Consideration of the real contact area

Abstract The real contact area based on modified Hertzian theory derived from sinusoidal asperity model is introduced and the measurement method for the real contact area is proposed. The real contact approach is compared with the Greenwood-Williamson theory showing good agreement between the two methods. The separation between the contact surfaces is estimated by taking into account the surface roughness. The temperature rise at the sliding interface between the DLC coating and E52100 steel is evaluated experimentally by the thermal indicator paint method, and the real contact area ratio is estimated from the temperature simulation data. The temperature rise is discussed from the entropy balance point of view induced from the real contact area and the frictional energy.

The 2016 Mw 5.9 earthquake off the southeastern coast of Mie Prefecture as an indicator of preparatory processes of the next Nankai Trough megathrust earthquake

Megathrust earthquakes have occurred repeatedly at intervals of 100 to 150 years along the Nankai Trough, situated in the southwest of Japan. Given that it has been 70 years since the last event, the occurrence of the next devastating earthquake is anticipated in the near future. On April 1, 2016, a moderate earthquake (Mw 5.9, MJMA 6.5) occurred off the southeastern coast of Mie Prefecture in the source region of the 1944 Tonankai earthquake (Mw 8.2). In this study, we investigated the influence of the 2016 earthquake on future megathrust earthquakes. We first determined the hypocenter distributions using a precise velocity structure obtained from seismic surveys in the source region. Using data obtained from the DONET ocean-bottom observation network, we found that this earthquake occurred along the plate boundary fault, which is also believed to have slipped during past megathrust earthquakes. We then performed a preliminary numerical simulation to reproduce the occurrence of a moderate earthquake in the middle of a megathrust earthquake cycle. We used a hierarchical asperity model, in which smaller asperities causing moderate earthquakes are embedded in a hyper-asperity that serves as the source region of megathrust earthquakes. The simulation shows that moderate earthquakes, caused by ruptures of a smaller asperity, occur as a result of shrinkage of strongly coupled areas in the hyper-asperity. This result is consistent with the observation that the hypocenter of the 2016 earthquake was located at the edge of a strongly coupled region along the plate boundary. The simulation also reproduced postseismic slip (afterslip/slow slip) along the plate boundary updip of the hyper-asperity, which is consistent with the observations of slow slip events and very-low-frequency earthquakes after the 2016 earthquake. Thus, the occurrence of the moderate earthquake offshore southeastern Mie Prefecture in the middle of the megathrust earthquake cycle implies that the shrinkage of the strongly coupled area along the plate boundary is occurring as a preparatory process for the next megathrust earthquake in the region.

Elastic Contact Mechanics of Randomly Rough Surfaces: An Assessment of Advanced Asperity Models and Persson’s Theory

In this work, we discuss important improvements of asperity models. Specifically, we assess the predictive capabilities of a recently developed multiasperity model, which differs from the original Greenwood and Williamson model by (i) including the coupling between the elastic fields generated by each contact spot, and (ii) taking into account the coalescence among the contact areas, occurring during the loading process. Interaction of the elastic field is captured by summing the contributions, which are analytically known, of the elastic displacements in a given point of the surface due to each Hertzian-like contact spot. The coalescence is instead considered by defining an equivalent contact spot in such a way to guarantee conservation of contact area during coalescence. To evaluate the accuracy of the model, a comparison with fully numerical ‘exact’ calculations and Persson’s contact mechanics theory of elastic rough surfaces is proposed. Results in terms of contact area versus load and separation versus load show that the three approaches give almost the same predictions, while traditional asperity models neglecting coalescence and elastic coupling between contact regions are unable to correctly capture the contact behavior. Finally, very good results are also obtained when dealing with the probability distribution of interfacial stresses and gaps.

A spherical conformal contact model considering frictional and microscopic factors based on fractal theory

Spherical conformal contact is widely used in engineering structures. The existing solution of the spherical conformal contact problem always ignores the microscopic characteristics or friction of the spherical surfaces. Therefore, the current paper presents a spherical fractal model to characterize the contact state of spherical pairs considering the microscopic topography of rough spherical surface and the factor of friction. Firstly, a method of characterizing the microscopic topography of rough spherical surface is proposed based on three-dimensional Weierstrass–Mandelbrot function. The fractal contact model of the single asperity is developed by Hertz theory in combination with elasticity. Then, the macroscopic parameters are introduced to construct the contact surface coefficient. The area distribution function under conformal contact region is obtained. Considering the friction factor of the conformal contact region, the microcontact model of the spherical conformal contact is developed based on fractal theory. Finally, the formula between (elastic, elastic-plastic, plastic) contact area, (elastic, elastic-plastic, plastic) contact load and the key parameters (fractal parameters and macro parameters) are derived based on the proposed model. The relationship between the actual contact area and the normal load of the contact region is established. Numerical results show that the proposed model is more accurate for the analysis of the spherical surface contact area and contact load.

An approximate JKR solution for a general contact, including rough contacts

In the present note, we suggest a simple closed form approximate solution to the adhesive contact problem under the so-called JKR regime. The derivation is based on generalizing the original JKR energetic derivation assuming calculation of the strain energy in adhesiveless contact, and unloading at constant contact area. The underlying assumption is that the contact area distributions are the same as under adhesiveless conditions (for an appropriately increased normal load), so that in general the stress intensity factors will not be exactly equal at all contact edges. The solution is simply that the indentation is δ=δ1−2wA′/P″ where w is surface energy, δ1 is the adhesiveless indentation, A′ is the first derivative of contact area and P′′ the second derivative of the load with respect to δ1. The solution only requires macroscopic quantities, and not very elaborate local distributions, and is exact in many configurations like axisymmetric contacts, but also sinusoidal waves contact and correctly predicts some features of an ideal asperity model used as a test case and not as a real description of a rough contact problem. The solution permits therefore an estimate of the full solution for elastic rough solids with Gaussian multiple scales of roughness, which so far was lacking, using known adhesiveless simple results. The result turns out to depend only on rms amplitude and slopes of the surface, and as in the fractal limit, slopes would grow without limit, tends to the adhesiveless result – although in this limit the JKR model is inappropriate. The solution would also go to adhesiveless result for large rms amplitude of roughness hrms, irrespective of the small scale details, and in agreement with common sense, well known experiments and previous models by the author.

研磨パッド・アスペリティ内のミクロなスラリー循環流れ

Chemical mechanical polishing (CMP) is used in a wide range of processes in semiconductor production. However, the polishing mechanism of CMP is not completely understood. The behavior of the abrasive particles and chemical species in the slurry is believed to play a critical role in the polishing mechanism. Therefore, in this study, we observed the slurry flow occurring in the polishing pad asperities experimentally. Because in situ observation of the slurry flow is exceptionally difficult, an enlarged visualization model of the pad asperities was made, based on the scaling laws of fluid dynamics. A refractive index matching technique and a particle suspension method were applied to visualize the scaled-up slurry flow. As a result, the circulation flows in the vertical direction to the wafer surface have been observed at the openings of the pad pores, and at the valleys of the undulations formed by the pad conditioning. The size of the biggest circulation flow observed in this study is approximately 200 μm. This result suggests that, similar to the pad pores, the valleys of undulations of the pad have the function of aiding the slurry transport to the entire wafer surface.

活断層で発生する地震のアスペリティモデルの設定に用いる断層面積の算定方法の違いが断層パラメータと予測強震動に及ぼす影響

活断層で発生する地震のアスペリティモデルの設定に用いる断層面積の算定方法の違いが断層パラメータと予測強震動に及ぼす影響

On the Sensitivity of Adhesion between Rough Surfaces to Asperity Height Distribution

There has been a long debate about the validity of asperity models in the contact between rough surfaces, much of it concentrated on relatively minor aspects of the solution for the special case of Gaussian random processes for roughness, like the exact value of the area-load slope or the extent of the linear regime. It is shown here that in the case of adhesion, the behavior is extremely sensitive to the shape of the height distribution. We show for example results for Weibull distributions, which has been suggested in a number of practical cases from macroscopic to nanoscopic roughness. Pull-off force is found to vary by several orders of magnitude both lower and higher than in the Gaussian case, whereas the "stickiness" criterion on the adhesion parameter changes by an order of magnitude. Additionally, in some operations like chemical-mechanical polishing, tails are almost completely removed and a sharp peak develops instead of a tail: modeling this with contact on the bounded side of the Weibull distribution, stickiness seems to occur for any level of roughness. Pome qualitative comparison with recent numerical experiments is attempted.

A Generalized Johnson Parameter for Pull-Off Decay in the Adhesion of Rough Surfaces

There is no simple theory at present to predict accurately the decay of pull-off in the adhesion of randomly rough surfaces. The asperity model of Fuller and Tabor has shown significant error in recent numerical investigations by Pastewka and Robbins of self-affine random roughness from micrometer to atomic scale which corresponds to low values of Tabor parameter. For sinusoidal contact, the Johnson parameter, originally introduced for the JKR regime (from Johnson-Kendall-Roberts) is the dominant parameter ruling the pull-off at intermediate Tabor values. Hence, we define a generalized Johnson parameter as the ratio between the adhesive energy to the elastic strain energy to flatten the surface in the case of multiscale roughness and find that it correlates very well with the data of Pastewka and Robbins spanning almost five orders of magnitude of reduction from theoretical strength, improving significantly with respect to other possible single parameter criteria. For the most important case in practice, that of low fractal dimensions, this suggests the product of amplitude and slope of the largest wavelength components of roughness dominate pull-off decay, and not small scales features like slopes and curvatures, as suggested by Pastewka and Robbins.

Modelling the influence of velocity on wet friction-element friction in clutches

PurposeThis study aims to establish a friction coefficient model relative to the rotation speed of a wet clutch engagement, which can predict friction coefficient under different stages of slipping velocity and different load pressures. In particular, the model has been improved by accounting the speed effect for the perdition of wet friction-element boundary friction, which is significant for understanding the friction mechanisms and for supporting the development of more efficient and related products.Design/methodology/approachThis research investigated the mechanism of wet friction in a wet clutch engagement. A mixed friction model is established based on the asperity model and Newton’s law of viscosity. To obtain a friction coefficient computed by the model, the normal load shared by both asperities and lubrication fluid needs to be determined. Therefore, rough surface contact mechanism is analysed; a surface topography model is established; and surface parameters are obtained by means of surface topography measurement and reconstruction. Finally, verification of the mixed friction model is achieved.FindingsFriction will be generated by both the asperity contact and the lubrication film shear relative to the rotation speed. And, the higher the relative speed, the larger the shearing power of lubrication film. It is caused by decrease in contact area of asperity. Surface morphology of a sintered bronze friction disk was obtained by a Laser-Micro-Test. The predicted results by the established model show that the total friction coefficient slightly reduced and then increased suddenly with speed. The surface topography model is responsible for the nonlinear behaviour of the asperity friction. Results of the simulation model are in agreement with those of the wet clutch engagement experiments.Originality/valueThis research is original and it is supported by the national defence project. The wet friction element which is applied on tracked vehicles is analysed for the first time. Through the model, the trend of the friction coefficient can be more accurately predicted. The problem of the wet friction plate modelling difficult is solved by using the mixed friction model.

Contact stiffness of regularly patterned multi-asperity interfaces

Contact stiffness is a fundamental mechanical index of solid surfaces and relevant to a wide range of applications. Although the correlation between contact stiffness, contact size and load has long been explored for single-asperity contacts, our understanding of the contact stiffness of rough interfaces is less clear. In this work, the contact stiffness of hexagonally patterned multi-asperity interfaces is studied using a discrete asperity model. We confirm that the elastic interaction among asperities is critical in determining the mechanical behavior of rough contact interfaces. More importantly, in contrast to the common wisdom that the interplay of asperities is solely dictated by the inter-asperity spacing, we show that the number of asperities in contact (or equivalently, the apparent size of contact) also plays an indispensable role. Based on the theoretical analysis, we propose a new parameter for gauging the closeness of asperities. Our theoretical model is validated by a set of experiments. To facilitate the application of the discrete asperity model, we present a general equation for contact stiffness estimation of regularly rough interfaces, which is further proved to be applicable for interfaces with single-scale random roughness.

Tribological behavior anisotropy in sliding interaction of asperities on single-crystal α-iron: A quasi-continuum study

Abstract Fundamental understanding of interfacial phenomena in asperity interactions at the nanoscale is prompted by advances in tribology. In this work, we established a multiscale model of asperity–asperity sliding interaction to study the effects of both crystalline anisotropy and crystallographic orientation matching degree on the tribological behavior. Asperity pairs in cases of both mismatched and matched crystallographic orientations were considered. The results revealed that the crystallographic orientation and its matching degree had a tremendous influence on tribological characteristics. The combination effects of internal defect generation and interfacial adhesion anisotropies were found to be responsible for the anisotropic tribological properties. Wear mechanism for the matched case behaved as adhesion wear, whereas wear mechanism for the mismatched case was identified as abrasive wear.

Numerical Modeling Describing the Effects of Heterogeneous Distributions of Asperities on the Quasi-static Evolution of Frictional Slip

A better understanding of how slip accumulates along faults and its relation to the breakdown of shear stress is beneficial to many engineering disciplines, such as, hydraulic fracture and understanding induced seismicity (among others). Asperities forming along a preexisting fault resist the relative motion of the two sides of the interface and occur due to the interaction of the surface topographies. Here, we employ a finite element model to simulate circular partial slip asperities along a nominally flat frictional interface. Shear behavior of our partial slip asperity model closely matched the theory described by Cattaneo. The asperity model was employed to simulate a small section of an experimental fault formed between two bodies of polymethyl methacrylate, which consisted of multiple asperities whose location and sizes were directly measured using a pressure sensitive film. The quasi-static shear behavior of the interface was modeled for cyclical loading conditions, and the frictional dissipation (hysteresis) was normal stress dependent. We further our understanding by synthetically modeling lognormal size distributions of asperities that were randomly distributed in space. Synthetic distributions conserved the real contact area and aspects of the size distributions from the experimental case, allowing us to compare the constitutive behaviors based solely on spacing effects. Traction-slip behavior of the experimental interface appears to be considerably affected by spatial clustering of asperities that was not present in the randomly spaced, synthetic asperity distributions. Estimates of bulk interfacial shear stiffness were determined from the constitutive traction-slip behavior and were comparable to the theoretical estimates of multi-contact interfaces with non-interacting asperities.

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.