Asperity Distribution Research Articles

Tangential Contact Stiffness of Rough Cylindrical Faying Surfaces Based on the Fractal Theory

The tangential contact stiffness of cylindrical asperities is investigated using macro- and micro-mechanisms in this study. A microanalysis model is developed and the tangential contact stiffness of elliptically parabolic asperities on the contact surface is determined. The shape influence coefficient of the cylindrical contact is defined, and its rationality is evaluated. The influence of asperity distribution on the rough surface is determined, and the tangential contact stiffness macroanalysis model is constructed based on fractal theory. The mathematical expression to determine the tangential contact stiffness of the macroscopically cylindrical contact is generated, and the effects of influential factors on tangential contact stiffness are explicitly evaluated. Numerical results show that the tangential contact stiffness of asperities is determined by several factors, such as material properties, applied loads, fractal dimension, and surface shape.

Distribution of discrete seismic asperities and aseismic slip along the Ecuadorian megathrust

A dense GPS network deployed in Ecuador reveals a highly heterogeneous pattern of interseismic coupling confined in the first 35 km depth of the contact between the subducting oceanic Nazca plate and the North Andean Sliver. Interseismic models indicate that the coupling is weak and very shallow (0–15 km) in south Ecuador and increases northward, with maximum found in the rupture areas of large (Mw>7.0) megathrust earthquakes that occurred during the 20th century. Since the great 1906 Mw=8.8 Colombia–Ecuador earthquake may have involved the simultaneous rupture of three to six asperities, only one or two asperities were reactivated during the large seismic sequence of 1942 (Mw=7.8), 1958 (Mw=7.7), 1979 (Mw=8.2) and 1998 (Mw=7.1). The axis of the Carnegie Ridge, which is entering the subduction zone south of the Equator, coincides well with the location of a 50 km wide creeping corridor that may have acted as persistent barrier to large seismic ruptures. South of this creeping region, a highly locked asperity is found right below La Plata Island. While this asperity may have the potential to generate an Mw∼7.0–7.5 earthquake and a local tsunami, until now it is unknown to have produced any similar events. That region is characterized by the presence of slow slip events that may contribute significantly to reduce the long-term moment deficit accumulated there and postpone the failure of that asperity. At the actual accumulation rate, a characteristic recurrence time for events such as those in 1942, 1958 and 1979 is 140±30 yr, 90±20 yr, 153±80 yr respectively. For the great 1906 event, we find a recurrence time of at least 575±100 yr, making the great 1906 earthquake a rare super cycle event.

Effect of surface parameters on finite element method based deterministic Gaussian rough surface contact model

Three-dimensional rough surface contact models enrich the understanding of the influence of surface texture in rough surface contacts. Most of the existing contact models did not consider the effect of elasto-plastic deformation and neighboring asperity interactions for the rough surface contact analysis, or only to a limited extent. In the present work, three-dimensional contact analyses of Gaussian rough surfaces are carried out using finite element method. By fast Fourier transform approach, Gaussian rough surfaces having auto-correlation lengths of 0.5, 2.0, 5.0, and 10 µm and surface roughness of 0.001, 0.01, and 0.1 µm are generated. The generated rough surfaces are transferred to finite element method based ANSYS package for micro-contact analysis. The continuity of elastic, elasto-plastic, and plastic deformations of near realistic feature-based asperities and effects of asperity interactions are inherently included in the present analysis. Each rough surface contact analysis is carried out in such a manner to cover the entire asperity distribution with incremental displacements. The contact load, real area of contact, and contact pressure are extracted from each analysis. The results showed that the surface having low surface roughness, the asperities deform mostly elastically whereas in medium and high surface roughness surfaces, the elasto-plastic and plastic deformation of asperities are significant and also in low auto-correlation length surface, the intensification of sub surface stresses cause the mean contact pressure ratio to reach peak value whereas in high auto correlation length surface, the larger size of asperities and the neighboring asperity interaction keep the mean contact pressure ratio at low level.

Transient Heat Conduction Between Rough Sliding Surfaces

When two rough bodies slide against each other, asperities on the opposing surfaces interact with each other, defining a transient contact and heat conduction problem. We represent each body by a Greenwood and Williamson asperity model with a Gaussian height distribution of identical spherical asperities. The heat transfer during a typical asperity interaction is analyzed, and the results are combined with the height distributions to determine the mean heat flux and the mean normal contact pressure as functions of the separation between reference planes in the two surfaces. We find that the effective thermal conductance is an approximately linear function of nominal contact pressure, but it also increases with the square root of the sliding speed and decreases with the 3/4 power of the combined RMS roughness. The results can be used to define an effective thermal contact resistance and division of frictional heat in macroscale (e.g., finite element) models of engineering components, requiring as input only the measured roughness and material properties.

Structural and tribo-mechanical characterization of nitrogen plasma treated titanium for bone implants

Bioactive layers produced on titanium to induce osseointegration may not be mechanically stable and/or attend to the requirement for the bone-matching elastic modulus. The previous surface modification by ion nitriding can eventually improve adhesion and mechanical properties of such bioactive coatings. Titanium samples were DC plasma nitrided in low conditions of temperature (673K and 873K) and time (1h and 3h). The surfaces were studied by grazing-incidence X-ray diffraction, micro-Raman spectroscopy, atomic force microscopy, scanning electron microscopy, instrumented indentation and nanoscratch tests. The treatments at 873K produced a stratified surface containing δ-TiN, ε-Ti2N and N-solid solution Ti(N), whereas the 673K samples presented Ti(N) and evidence of nitride precipitates at a very shallow depth, as suggested by micro-Raman (depth of analysis≤25nm). The asperity degree and distribution increased with the treatment temperature and time, whose effects on hardness and elastic modulus were corrected by the contact stiffness analysis. The most significant changes in the near surface hardness (5 to 15GPa) and elastic modulus (170 to 200GPa) profiles in respect to the pristine Ti were observed for 873K treatments. However, the 673K – 3h sample presented scratch hardness twice as high as the substrate value, even if the ductile-like tribological response was preserved. Afterwards, Ca–P containing titania coatings were produced by anodic oxidation on selected samples. The layers presented reduced brittleness under normal loading if grown on the previously nitrided surfaces, whereas elastic modulus profiles (75–90GPa) were kept lower than bulk Ti. We conclude that Ti surfaces can be tailored by plasma nitriding to improve their load bearing capacity for deposition of bioactive layers.

Effect of substrate curvature on residual stresses and failure modes of an air plasma sprayed thermal barrier coating system

Abstract A set of aerofoil shaped air plasma sprayed thermal barrier coated (APS-TBC) specimens were adopted in this paper to investigate the stress distributions in the ceramic top coat (TC) and the thermally grown oxide (TGO), the mechanism of local crack generation and propagation at the TC/BC (bond coat) interface. The failure mode of the TBC system, the distribution of asperities at TC/BC interface, thickness of the TC and BC, and the TC microstructure were found to be influenced by substrate curvature. Residual stress was therefore measured across the thickness of the TC, along the undulating TGO and mapped at locations of asperities where failure tended to occur to interpret the initiation of local failure. The role of the TGO was investigated via its chemical bonding with the TC and the decohesion occurring at the TGO/BC interface. The crack propagation at the interface has been discussed with respect to the macro-failure of the TBC system.

Non–Amontons-Coulomb local friction law of randomly rough contact interfaces with rubber

We report on measurements of the local friction law at a multi-contact interface formed between a smooth rubber and statistically rough glass lenses, under steady-state friction. Using contact imaging, surface displacements are measured, and inverted to extract both distributions of frictional shear stress and contact pressure with a spatial resolution of about . For a glass surface whose topography is self-affine with a Gaussian height asperity distribution, the local frictional shear stress is found to vary sub-linearly with the local contact pressure over the whole investigated pressure range. Such sub-linear behavior is also evidenced for a surface with a non-Gaussian height asperity distribution, demonstrating that, for such multi-contact interfaces, Amontons-Coulomb's friction law does not prevail at the local scale.

절리면의 거칠기 변화가 전단강도에 미치는 영향

Multi-stage shear test has been performed using joint specimens of gneiss, granite and shale to investigate the influence of micro-scale asperity change on the shear strength of joint plane. For each shear test asperity degradation characteristics of joint specimens of different joint surface strength have been analyzed by utilizing the optimum asperity parameter which can reflect the sequential asperity degradation. Elevation of joint surface profile has been measured and both the changes of asperity parameters and micro-scale asperity distribution have been investigated. Two distinctive variation modes of cohesion and friction angle have been delineated and major cause of shear strength parameter change has been analyzed by considering the micro-scale asperity angle change resulting from the abrasion, fracturing and regeneration of micro-scale asperities. Effects of micro-scale asperity variation on the joint shear strength have been also investigated.

A brick model for asperity sintering and creep of APS TBCs

A micromechanical model is developed for the microstructural evolution of an air plasma sprayed (APS), thermal barrier coating: discrete, brick-like splats progressively sinter together at contacting asperities and also undergo Coble creep within each splat. The main microstructural features are captured: the shape, orientation and distribution of asperities between disc-shaped splats, and the presence of columnar grains within each splat. Elasticity is accounted for at the asperity contacts and within each splat, and the high contact compliance explains the fact that APS coatings have a much lower modulus (and thermal conductivity) than that of the parent, fully dense solid. The macroscopic elastic, sintering and creep responses are taken to be transversely isotropic, and remain so with microstructural evolution. Despite the large number of geometric and kinetic parameters, the main features of the behaviour are captured by a small number of characteristic material timescales: these reveal the competition between the deformation mechanisms and identify the rate controlling processes for both free and constrained sintering. The evolution of macroscopic strain, moduli and asperity size is compared for free and constrained sintering, and the level of in-plane stress within a constrained coating is predicted.

Computational modelling of constrained sintering in EB-PVD thermal barrier coatings

A micromechanical model is developed to simulate the evolution of microstructure during in-service sintering and eventual inter-columnar cracking in coatings made using electron beam vapour deposition (EB-PVD) route. The coating is idealized with a discrete distribution of axisymmetric asperities across interfaces between columnar grains. The model assumes that inter-columnar sintering is driven by changes in interface free energy of columns and the potential energy of the applied stress. Much faster diffusion that occurs over the free surfaces of the asperities is neglected. It is further assumed that the rate of sintering of the contacting asperities is determined by diffusion along the interface between the contacting asperities. Time evolution of contact modulus of the coating is accounted for as a function of sintering strain. The developed macroscopic constitutive model is employed to evaluate the sensitivity of the sintering response to imperfections and examine the conditions under which inter-columnar cracks can develop within the coating.

Biased geodetic inference on asperity distribution on a subducted plate interface: a quantitative study

The asperity model was developed to explain plate boundary behavior such as interplate earthquakes. Asperity is defined as a strongly-coupled region on the plate interface. Since interplate earthquakes are considered to occur on asperities, it is important to know the asperity distribution, which can be inferred from interseismic crustal deformation through estimation of the slip deficit distribution. Slip deficit is the difference between the long-term plate convergence rate and the actual relative displacement rate of the plate interface. It is a kinematic description of plate interaction. The relation between the estimated slip deficit and the asperity is still not clearly understood. We have conducted a quantitative comparison between them by combining a forward simulation of crustal deformation, as a result of plate subduction, and a geodetic data inversion. We found that the seismic moment accumulation rate is likely to be overestimated in most cases. The degree of overestimation increases in the case of small asperity areas. Conversely, if no slip deficit is detected by geodetic data inversion, it is highly probable that no asperity exists. Such a misinference may lead to an incorrect estimation of strong ground motion in future earthquakes, and appropriate measures should be taken to allow for this.

Stress switching in subduction forearcs: Implications for overpressure containment and strength cycling on megathrusts

Abstract Seismogenic megathrusts contained within subduction interface shear zones (SISZ) appear generally to be overpressured to near-lithostatic values (λv > 0.9) below forearc hanging-walls. Solution transfer within fine-grained material along the deeper interface (150 Husen and Kissling (2001) proposed massive trans-megathrust discharge of fluids across the interface. Such discharges are a form of ‘fault-valve’ action where the megathrust itself acts as a seal to overpressured fluids derived from within the SISZ and from dehydration of the descending slab. Brittle failure or fault reactivation limits fluid overpressure which is highest at low differential stress under a compressional stress regime. Over much of the forearc hanging-wall of the 2011 Mw9.0 Tohoku-Oki megathrust rupture, focal mechanisms show that the stress-state switched from compressional reverse-slip faulting prefailure to extensional normal-slip faulting postfailure. Mean stress and fault-normal stress thus changed from being greater than vertical stress prefailure, to less than vertical stress postfailure. Reductions in overpressure are expected from a combination of poroelastic effects and fluid loss through fault–fracture networks enhancing postfailure permeability in the changing stress field. Local drainage across the subduction interface increases frictional strength significantly, giving rise to a postfailure distribution of strength asperities. The amplitude of strength variations from such fluid discharge is potentially large (

Characterization of Asphalt Pavement Surface Texture

This paper presents improved analysis methods for characterizing asphalt pavement surface texture and focuses on the use of laser profiling techniques to estimate friction characteristics. Derived from signal processing theories, texture spectral analysis methods show promise for improving characterization of the tire–pavement interface. Texture parameters measured with spectral analysis techniques represent a means for quantifying surface properties. Current methods to analyze frictional properties rely on the mean profile depth (MPD) and mean texture depth (MTD) texture parameters. Although these parameters are used widely, they do not capture the range and distribution of surface asperities on the pavement surface. Knowing the distribution of surface asperities is critical for assessing friction characteristics. Thus, texture spectral analysis methods are anticipated to improve on the MPD and MTD parameters by capturing relevant texture-level distributions. This study investigates the applicability of laser profiling systems for measuring pavement surface texture and subsequent relationships to friction. Models accounting for aggregate and mixture properties are developed and related to texture parameters through analysis of constructed field sections and corresponding laboratory samples. Results indicate that stationary laser profiling systems can capture the microtexture and macrotexture spectrum and suggest that a comprehensive friction characterization of asphalt mixtures can be obtained in a laboratory setting. With this analysis system, it is believed that asphalt mixture designers will have an improved tool by which to estimate pavement surface texture and frictional properties.

Structural-thermal finite element simulation of vibrothermography applied to cracked steel plates

One of the major drawbacks of ultrasound excited thermography applied to metal components manifests in the pronounced frequency dependence of crack detectability. This leads to an uncertainty in the application of the method. In order to investigate the crack face interaction by which it is constituted whether a certain crack can be detected or not a structural-thermal Finite Element simulation of a massive steel plate is conducted. The roughness of the crack faces is taken into account by generating a random asperity distribution. With this type of modelling the achieved numerical results are in a good agreement with experimental data of a performed ultrasonic sweep thermography (UST). Further investigation of the crack face morphology after repeated ultrasound excitation reveals that the true contact area is very small compared to the apparent contact area. The FE simulation approach allows for a realistic hot-spot size from which frictional heat is generated.

A Basic Theoretical Model for Friction Process at Microasperity Level

This article presents a theoretical model for dry, low-velocity, and wear-less friction based on a single asperity interaction with arbitrary assumed adhesion forces and elastic deformations of the microasperities. Simulations of friction behavior according to the single asperity interaction, as well as the interaction of multiplied single models, are presented. The multiplied model assumes a regular distribution of the single asperities, arbitrarily chosen geometrical properties (based on harmonic function), and elastomechanical properties of the cooperating materials. In the proposed model, the adhesion as a function of asperity deformation is introduced. This enables the simulation of an expedient local coefficient of friction. The model assumes no breaking of the contact between single asperities; however, the proposed model enables detection of such a situation. The results obtained by simulation of the model show both qualitative and quantitative agreement with the known types of friction force dynamic behavior, in particular, nonlinearity of the friction coefficient. At this level of investigation, the model assumes the most important relations connected with its properties, which need further refinement and elaboration, especially according to assumed asperity properties.

Micromechanics of asperity rupture during laboratory stick slip experiments

[1] Acoustic emissions and tremor-like signals are widely recorded in laboratory experiments. We are able to isolate the physical origins of these signals using high resolution nanoseismic analysis. The use of a picometer-sensitive, wide-band sensor array permits us to determine force-time functions and focal mechanisms for discrete events found amid the “noise” of friction, similar to how low frequency earthquakes are found buried within tremor. We interpret these localized events to be the rupture of μm-sized contacts, known as asperities. We performed stick-slip experiments on plastic/plastic and rock/rock interfaces and found a systematic difference between the nano earthquakes: the rock interface produces very rapid (<1 μs) implosive forces indicative of brittle failure and fault gouge formation, while rupture on the plastic interface releases only shear force and produces a nano quake more similar to earthquakes commonly recorded in the field. The difference between the mechanisms is attributed to the vast differences in the hardness and melting temperatures of the two materials, which affect the distribution of asperities as well as their failure behavior. With proper scaling, the strong link between material properties and laboratory earthquakes will aid in our understanding of fault mechanics and the generation of earthquakes and tectonic tremor.

Statistical model for normal and tangential contact parameters of rough surfaces

A new statistical model was developed for the normal and tangential contact parameters of rough surfaces based on the elastic—plastic contact theory of asperity. Four deformed regimes of fully elastic, first elastoplastic, second elastoplastic, and fully plastic of an asperity contacting with a rigid surface were taken into account by this model. The present model reveals that the normal and tangential contact parameters of rough surfaces are determined by the material properties of rough surface, statistical parameters for surface topography, and loading. Based on the results comparison and analysis, the present model is shown to be more complete than the GW, CEB, ZMC, and CEB friction models in describing the elastic—plastic contact problems between the rough surfaces. The effects of height distribution of asperities, plasticity index, and loading on contact parameters were simulated and discussed. In addition, the Gaussian numerical results predicted by the present model were researched emphatically.

New methods for estimating the spatial distribution of locked asperities and stress‐driven interseismic creep on faults with application to the San Francisco Bay Area, California

We introduce new forward and inverse methods for inferring long‐term fault slip rates, interseismic fault creep rates, and distribution of locked and creeping patches on faults using geodetic and geologic data. The forward model consists of fault‐bounded blocks in an elastic crust overlying a Maxwell viscoelastic mantle. Interseismic elastic distortion of the blocks is modeled due to periodic locking and unlocking of faults throughout the earthquake cycle. Patches on the fault are assumed to be either locked during the interseismic period or creeping at constant shear stress. We utilize a Bayesian, probabilistic inversion method to infer the posterior probability distribution of long‐term interseismic fault slip rates, distribution of locked and creeping patches, and relative weighting of multiple data sets. We illustrate the method with an inversion of a synthetic data set. We apply the method to estimate fault slip rates and the distribution of interseismic creep on faults in the San Francisco Bay Area, CA, using GPS‐derived velocities and geologic measurements of fault slip rates. We show that the inferred fault slip rates and areas of the locked regions of faults are sensitive to the assumed viscosity of the upper mantle and the timing of past earthquakes and can be significantly different from values inferred from elastic models that do not include viscous flow. Considering models with different viscosities, inferred fault slip rates on major Bay Area faults can differ by factors of 1.5–4.0 and the inferred moment accumulation rate can differ by factors of 2–13.

An earthquake model with interacting asperities

SUMMARY A model is presented that treats an earthquake as the failure of asperities in a manner consistent with modern concepts of sliding friction. The mathematical description of the model includes results for elliptical and circular asperities, oblique tectonic slip, static and dynamic solutions for slip on the fault, stress intensity factors, strain energy and second-order moment tensor. The equations that control interaction of asperities are derived and solved both in a quasi-static tectonic mode when none of the asperities are in the process of failing and a dynamic failure mode when asperities are failing and sending out slip pulses that can trigger failure of additional asperities. The model produces moment rate functions for each asperity failure so that, given an appropriate Green function, the radiation of elastic waves is a straightforward calculation. The model explains an observed scaling relationship between repeat time and seismic moment for repeating seismic events and is consistent with the properties of pseudo-tachylites treated as fossil asperities. Properties of the model are explored with simulations of seismic activity that results when a section of the fault containing a spatial distribution of asperities is subjected to tectonic slip. The simulations show that the failure of a group of strongly interacting asperities satisfies the same scaling relationship as the failure of individual asperities, and that realistic distributions of asperities on a fault plane lead to seismic activity consistent with probability estimates for the interaction of asperities and predicted values of the Gutenberg–Richter a and b values. General features of the model are the exterior crack solution as a theoretical foundation, a heterogeneous state of stress and strength on the fault, dynamic effects controlled by propagating slip pulses and radiated elastic waves with a broad frequency band.

Delineating the rupture planes of an earthquake doublet using Source-Scanning Algorithm: application to the 2005 March 3 Ilan Doublet, northeast Taiwan

SUMMARY Correct identification of the fault plane(s) associated with an earthquake doublet is a very challenging problem because the pair of events often occurs in close space and time with almost the same magnitude. Most long-period waveforms of an earthquake doublet are severely tangled and thus unsuitable for conventional waveform inversion methods. In this study, we try to resolve this issue by utilizing the recently developed Source-Scanning Algorithm (SSA). The SSA systematically searches the model space for seismic sources whose times and locations are most compatible with the observed arrivals of large amplitudes on seismograms. The identification of a seismic source is based on the brightness function, which is defined as the summation of the normalized waveform amplitudes at the predicted arrival times at all stations. By illuminating the spatiotemporal distribution of asperities during an earthquake's source process, we are able to constrain the orientation of the rupture propagation that, in turn, leads to the identification of the fault plane. A series of synthetic experiments are performed to test SSA's resolution under various scenarios including different directions of rupture propagation, imperfect station coverage and short origin time difference between the two events of a doublet. Because only short-period records are needed in the analysis, the proposed method is best suited for an earthquake doublet with a short time gap between the two events. Using the 2005 Ilan doublet (the origin time difference is only 70 s) that occurred in northeast Taiwan as an example, we show that the trace of the brightest spots moves towards the west and infer the E–W-striking plane to be the actual fault plane.