Asperity Distribution Research Articles

On the role of trans-lithospheric faults in the long-term seismotectonic segmentation of active margins: a case study in the Andes

Abstract. Plate coupling plays a fundamental role in the way in which seismic energy is released during the seismic cycle. This process includes quasi-instantaneous release during megathrust earthquakes and long-term creep. Both mechanisms can coexist in a given subduction margin, defining a seismotectonic segmentation in which seismically active segments are separated by zones where ruptures stop, classified for simplicity as asperities and barrier, respectively. The spatiotemporal stability of this segmentation has been a matter of debate in the seismological community for decades. In this regard, we explore in this paper the potential role of the interaction between geological heterogeneities in the overriding plate and fluids released from the subducting slab towards the subduction channel. As a case study, we take the convergence between the Nazca and South American plates between 18–40° S, given its relatively simple convergence style and the availability of a high-quality instrumental and historical record. We postulate that trans-lithospheric faults striking at a high angle with respect to the trench behave as large fluid sinks that create the appropriate conditions for the development of barriers and promote the growth of highly coupled asperity domains in their periphery. We tested this hypothesis against key short- and long-term observations in the study area (seismological, geodetic, and geological), obtaining consistent results. If the spatial distribution of asperities is controlled by the geology of the overriding plate, seismic risk assessment could be established with better confidence.

Quantifying the morphology of rock joints and updating the JRC–JCS criterion considering the asperity distribution

Roughness ubiquitously prevails in rock joints and controls the shear behaviours, permeability and damage characteristics of rock joints. A plethora of investigations have focused on the description of joint roughness; however, a detailed method for quantifying joint roughness and evaluating the shear strength has not yet been established. In this study, within the framework of fractal theory, an optical measurement scale was defined to depict the fractal characteristics of joint roughness, and a boundary measurement scale was used to identify first- and second-order asperities. A composite indicator η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta$$\\end{document}, including the fractal roughness coefficient (RD\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$R_{D}$$\\end{document}), the coefficient describing the roughness order (μ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mu$$\\end{document}) and the anisotropy parameter (λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\lambda$$\\end{document}), was proposed to quantify the surface morphology, which takes the asperity distribution and roughness anisotropy into account. The relationship between η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta$$\\end{document} and JRC was established, and the JRC–JCS criterion was further updated. Moreover, representative examples were given to show the steps required to quantify the morphology of rough joint surfaces with the new quantitative parameter. Direct shear tests were conducted to validate the effectiveness of the proposed method in describing joint roughness and estimating joint shear strength; the results indicate that it is appropriate to use η\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\eta$$\\end{document} to estimate the joint roughness and that the proposed shear strength criterion can appropriately predict the shear strength within an acceptable error.

A Novel Contact Resistance Model for the Spherical–Planar Joint Interface Based on Three Dimensional Fractal Theory

In order to obtain the contact resistance of relay contacts more accurately, a novel contact resistance model for the spherical–planar joint interface is constructed based on the three-dimensional fractal theory. In this model, three-dimensional fractal theory is adopted to generate a rough surface at microscopic scale. Then, using contact mechanics theory, the deformation mechanism of asperities on rough surfaces is explored. Combined with the distribution of asperities, a contact resistance model for the planar joint interface is established. Furthermore, by introducing the surface contact coefficient, cross-scale coupling between the macro-geometric configuration and micro-surface topography is achieved, and a contact resistance model for the spherical–planar joint interface is constructed. After that, experiments are conducted to verify the accuracy of the proposed model, and the maximum relative error of the proposed model is 8.44%. Ultimately, combining numerical simulation analysis, the patterns of variation in contact resistance influenced by factors such as macroscopic configuration and microscopic topography are discussed, thereby revealing the influence mechanism of the contact resistance for the spherical–planar joint interface. The proposed model provides a solid theoretical foundation for the optimization of relay contact structures and improvements in manufacturing processes, which is of great significance for ensuring the safe and stable operation of power systems and electronic equipment.

Numerical model of the locomotion of oscillating ‘robots’ with frictional anisotropy on differently-structured surfaces

In engineering materials, surface anisotropy is known in certain textured patterns that appear during the manufacturing process. In biology, there are numerous examples of mechanical systems which combine anisotropic surfaces with the motion, elicited due to some actuation using muscles or stimuli-responsive materials, such as highly ordered cellulose fiber arrays of plant seeds. The systems supplemented by the muscles are rather fast actuators, because of the relatively high speed of muscle contraction, whereas the latter ones are very slow, because they generate actuation depending on the daily changes in the environmental air humidity. If the substrate has ordered surface profile, one can expect certain statistical order of potential trajectories (depending on the order of the spatial distribution of the surface asperities). If not, the expected trajectories can be statistically rather random. The same presumably holds true for the artificial miniature robots that use actuation in combination with frictional anisotropy. In order to prove this hypothesis, we developed numerical model helping us to study abovementioned cases of locomotion in 2D space on an uneven terrain. We show that at extremely long times, these systems tends to behave according to the rules of ballistic diffusion. Physically, it means that their motion tends to be associated with the “channels” of the patterned substrate. Such a motion is more or less the same as it should be in the uniform space. Such asymptotic behavior is specific for the motion in model regular potential and would be impossible on more realistic (and complex) fractal reliefs. However, one can expect that in any kind of the potential with certain symmetry (hexagonal or rhombic, for example), where it is still possible to find the ways, the motion along fixed direction during long (or even almost infinite) time intervals is possible.

(Dielectric Science and Technology Division Poster Award, 1st Place) The Influence of Pad Micro-Features on Chemical Mechanical Polishing (CMP) Performance: Insights from Computational Fluid Dynamics (CFD)

With semiconductor chip dimensions shrinking below 7 nanometers, Chemical Mechanical Planarization (CMP) becomes more critical [1], [2]. To meet the increasing demand for precision and uniformity in the fabrication of wafers and chips, enhancements in CMP consumables and operating conditions are necessary. To address these requirements, novel pad designs have been developed, particularly those that do not require conditioning [3]. It is known that the CMP polishing rate depends on pressure, pad wafer relative velocity, and the distribution of pad asperities [4]. As conventional pads provide small and random contact areas, the external pressure applied by the head determines the material removal rate (MRR) [5] Advanced pads with micro-features provide more contact areas and help deliver consistent pressure and slurry distribution during Chemical Mechanical Polishing (CMP) [6], [7]. This study uses computational fluid dynamics (CFD) to simulate the flow between pad and wafer surfaces to determine how pad surface micro-features affect the CMP process. The abrasive residence time, total fluid pressure, and slurry flow velocity are evaluated for four distinct pad micro-feature geometries: square, square-circle, circle, and ellipse. Increasing the number of edges in the pad micro-feature patterns increases pressure drop, leading to more interaction between pad and slurry and enhancement of MRR. The findings of this study confirm the effectiveness of micro-featured pads in optimizing CMP processes and provide valuable insights into the influence of microfeature geometries on critical parameters for improving the semiconductor fabrication process.[1] J. Seo, Journal of Materials Research, 36, 235–257, Jan, 2021.[2] B. Suryadevara, Advances in Chemical Mechanical Planarization (CMP). Woodhead Publishing, 2021.[3] S. Lee and E. Hwang, “Smart pad fabrication for CMP,” LMA Res Rep, vol. 10, pp. 100–104, 2002.[4] G. Ahmadi and X. Xia, J Electrochem Soc, 148, G99, 2001.[5] X. Xia and G. Ahmadi, Particulate Science and Technology, 20, 187–196, 2002.[6] S. Lee, G. Kim, M. Mcgahay, H. Kim, and H. Cho, “Pad Designs-To navigate the fundamentals of CMP.”[7] M. Mcgahay, G. Kim, S. Lee, H. Cho, and H. Kim, “Critical Feature Size of Polishing Pad and Its Performance.”

Research on Plunging Resistant Force of Drive-Shaft Systems Based on Fractal Methods

When drive-shaft systems move axially, the friction between rollers and raceways inside tripod joints will generate a plunging resistant force (PRF). Excessive PRF causes significant noise in vehicles. To reveal the generation mechanism, an analytical model of the PRF is proposed by analyzing the axial motion mechanism of a drive-shaft system. Based on the analytical model and fractal methods, a fractal model of the PRF is proposed to reveal influencing factors of the PRF more comprehensively. An effective method for correcting distribution of asperities between rollers and raceways is proposed to describe the contact state accurately. The fractal model shows that influencing factors of the PRF include the fractal dimension and the characteristic scale coefficient related to the roughness of contact surfaces, the material parameters, the working angle, and the correction coefficient for distribution of asperities. A measurement method for the PRF is subsequently proposed, and the fractal dimension and the characteristic scale coefficient are measured and determined. The effectiveness of the fractal model is verified based on the measurement of the PRF and the determined fractal dimension and characteristic scale coefficient. Numerical analysis results show that reducing Poisson’s ratio, the yield strength, and the working angle, increasing the characteristic scale coefficient, the elastic modulus, and the correction coefficient, and selecting a fractal dimension lower than 1.544 or higher than 1.782 can effectively reduce the PRF, thereby reducing the noise caused by the PRF.

A Novel Contact Stiffness Model for Grinding Joint Surface Based on the Generalized Ubiquitiformal Sierpinski Carpet Theory

A novel analytical model based on the generalized ubiquitiformal Sierpinski carpet is proposed which can more accurately obtain the normal contact stiffness of the grinding joint surface. Firstly, the profile and the distribution of asperities on the grinding surface are characterized. Then, based on the generalized ubiquitiformal Sierpinski carpet, the contact characterization of the grinding joint surface is realized. Secondly, a contact mechanics analysis of the asperities on the grinding surface is carried out. The analytical expressions for contact stiffness in various deformation stages are derived, culminating in the establishment of a comprehensive analytical model for the grinding joint surface. Subsequently, a comparative analysis is conducted between the outcomes of the presented model, the KE model, and experimental data. The findings reveal that, under identical contact pressure conditions, the results obtained from the presented model exhibit a closer alignment with experimental observations compared to the KE model. With an increase in contact pressure, the relative error of the presented model shows a trend of first increasing and then decreasing, while the KE model has a trend of increasing. For the relative error values of the four surfaces under different contact pressures, the maximum relative error of the presented model is 5.44%, while the KE model is 22.99%. The presented model can lay a solid theoretical foundation for the optimization design of high-precision machine tools and provide a scientific theoretical basis for the performance analysis of machine tool systems.

Novel Probability Density Function of Pad Asperity by Wear Effect over Time in Chemical Mechanical Planarization.

Chemical mechanical planarization (CMP) reduces film thickness, eliminates step height, and achieves high levels of planarity in semiconductor manufacturing. However, research into its mechanisms is still in progress, and there are many issues to be resolved. To solve problems in CMP, it is necessary to understand the contact phenomenon that occurs at the pad-wafer interface, especially pad asperity. Moreover, understanding the non-uniform distribution of pad asperity, such as height and radius, is essential for predicting the material removal rate (MRR). In this study, based on the existing Greenwood-Williamson (GW) theory and probability density function (PDF), a modified mathematical model that includes changes in asperity distribution was developed and validated experimentally. The contact model proposed in this study included functions that calculated the time-dependent height and radius wear of the pad asperities. Specifically, the experimentally obtained values were compared with the values obtained by the model, and the comparison results were analyzed. Thereby, it was found that the contact model and MRR model considering the change in asperity wear and distribution due to CMP proposed in this study are in better agreement with the experimental results than the existing model, which shows that the MRR can be predicted by a mathematical model using the change in asperity distribution.

Reverse calculation and quantitative estimation of JRC3D for rough rock fracture surfaces in various shear directions

The quantitative evaluation of the three-dimensional roughness feature of natural rock fracture surface is essential for predicting shear strength. This article presents an effective approach to estimate the three-dimensional roughness of natural fracture surfaces from the two-dimensional roughness of fracture profile. Firstly, four types of rough fracture samples were created using rock-like materials, followed by conducting direct shear tests of the fracture surfaces under 4 different normal pressures and 4 shear directions. The results of the shear strength tests exhibited a distinct discrete pattern and consistently increased with higher normal pressures. Furthermore, the distribution of the damage area on the fracture surface after shear was significantly impacted by the distribution and size of asperities, as well as the shear direction. The three-dimensional roughness of four fracture surfaces in different directions was first reverse calculated using the shear strength model. Using the weighted positive angle, the estimation of the three-dimensional roughness in different directions of the fracture surface was then determined from the two-dimensional roughness of fracture profiles using both the arithmetic mean method and the weighted average method. The weighted average method effectively captures the contribution of the two-dimensional roughness of fracture profiles to the three-dimensional roughness of fracture surfaces, and exhibits a lower estimation error compared to the arithmetic mean method. Compared to other roughness indicators, the three-dimensional roughness evaluated through the weighted positive angle indicator are closest to the experimental result. Finally, the influence of transverse spacing on the estimated three-dimensional roughness was discussed.

Contact mechanics of open-cell foams with macroscopic asperities

Poroelastic materials mounted against rigid surfaces often result in partial contact between the two, affecting their mechanical interaction. The surface roughness of cellular materials introduces complexity in predicting their behavior due to the interface with partial contact. This interface exhibits a stiffness distinct from the bulk material, which is driven by the surface asperities and the preload. This study conducts compression experiments on an open-cell poroelastic melamine foam, and compares them to finite elements simulations and analytic predictions. The material’s intrinsic stress–strain nonlinearity is accounted for, and an original hyperelastic aging model is proposed to achieve accurate predictions of its compression stiffness across multiple time scales. Predicting the compression stiffness of a macroscopic pyramidal asperity demonstrates a good agreement with the simple analytic solution for an elastic pyramidal geometry. Using a Greenwood–Williamson-like model based on the distribution of asperities of different heights, we propose a method to predict the contact stiffness of a rough surface. Our findings have important implications for understanding and optimizing efficient vibration barriers, resulting from the simple stacking of layers and screens of raw poroelastic materials, a configuration widely adopted in the transportation and civil engineering industries.

Transient and Steady‐State Friction in Non‐Isobaric Conditions

AbstractThe frictional properties of faults control the initiation and propagation of earthquakes and the associated hazards. Although the ambient temperature and instantaneous slip velocity controls on friction in isobaric conditions are increasingly well understood, the role of normal stress on steady‐state and transient frictional behaviors remains elusive. The friction coefficient of rocks exhibits a strong dependence on normal stress at typical crustal depths. Furthermore, rapid changes in normal stress cause a direct effect on friction followed by an evolutionary response. Here, we derive a constitutive friction law that consistently explains the yield strength of rocks from atmospheric pressure to gigapascals while capturing the transient behavior following perturbations in normal stress. The model explains the frictional strength of a variety of sedimentary, metamorphic, and igneous rocks and the slip‐dependent response upon normal stress steps of Westerly granite bare contact and synthetic gouges made of quartz and a mixture of quartz and smectite. The nonlinear normal stress dependence of the frictional resistance may originate from the distribution of asperities that control the real area of contact. The direct and transient effects may be important for induced seismicity by hydraulic fracturing or for naturally occurring normal stress perturbations within fault zones in the brittle crust.

Effect of roughness on shear behavior of interface between cemented paste backfill and rock

The interaction between cemented paste backfill (CPB) and rock at their interface plays a crucial role in the stability of underground backfill structures. Considering the interface roughness could have a significant influence on the shear behavior and mechanical properties of the interface, a series of laboratory direct shear tests were carried out on the CPB-rock interface with various roughnesses. The results indicates that the interface roughness and normal stresses have a remarkable effect on the interfacial shear behavior, with typical stress-shear displacement curves that could be classified into three types depending on the peak and post-peak characteristics. Compared to the smooth interface, the shear strength increases with increasing roughness, owing to the enhancing interlocking effect, which is confirmed by digital image correlation (DIC) in micro views. In addition, the shear contraction observed at the smooth interface changes to shear dilatation at the rough interface, which is caused by wider distribution and higher adhesion of CPB asperities, as observes by using 3D laser scanning technology. Furthermore, a theoretical model for the shear strength, taking into account the influence of interface roughness, is developed to assess its effect on shear strength. The experimental results and the theoretical model presented in this paper will contribute to better understand the interaction mechanism and predict the shear strength of the interface.

Analysis, Modeling and Experimental Study of the Normal Contact Stiffness of Rough Surfaces in Grinding

Grinding is the most important method in machining, which belongs to the category of precision machining processes. Many mechanical bonding surfaces are grinding surfaces. Therefore, the contact mechanism of grinding a joint surface is of great significance for predicting the loading process and dynamic characteristics of precision mechanical products. In this paper, based on the collected grinding surface roughness data, the profile parameters and topography characteristics of the asperity were analyzed, the rough surface data were fitted, the asperity profile was reconstructed, and the parabola y = nx2 + mx + l of the cylindrical asperity model was established. After analyzing the rough surface data of the grinding process, the asperity distribution height was fitted with a Gaussian distribution function, which proved that asperity follows the Gaussian distribution law. The validity of this model was confirmed by the non-dimensional processing of the assumed model and the fitting of six plasticity indices. When the pressure is the same, the normal stiffness increases with the decrease in the roughness value of the joint surface. The experimental stiffness values are basically consistent with the fitting stiffness values of the newly established model, which verifies the reliability and effectiveness of the new model established for the grinding surface. In this paper, a new model for grinding joint surface is established, and an experimental platform is set up to verify the validity of the model.

The influence of surface topography on thermal contact resistance of 7075-T6/beryllium bronze

The calculation of thermal contact resistance is crucial for studying heat transfer between solids. Surface topography has a significant impact on thermal contact resistance, however, the influence of surface topography parameters on thermal resistance is still limited to the parameters such as roughness. The effect of other topography parameters still lacks. Therefore, in this paper, randomly non-Gaussian rough surfaces with specified root mean square roughness value, kurtosis, skewness, and wave lengths are generated by two-dimensional digital filtering method combined with Johnson transformation system. The contact mechanical deformation, heat transfer performance and thermal contact resistance between 7075-T6 and beryllium bronze QBe2 are studied using ABAQUS. The results show that thermal contact resistance is correlated with real contact area. The thermal contact resistance decreases with the increase of pressure, and gradually gets a rise with the increase of root mean square roughness value. Normal distribution of asperities, the isotropic surface, and zero or a low negative value of skewness all can enhance heat transfer efficiency. Our results provide guidance for designing surface topography when heat transfer need be considered in application.

Numerical modeling of Van der Waals interaction between a spherical particle and rough surfaces with different planar asperity distributions

Roughness and microstructures at the micro and the nano scales have significant influence on the van der Waals forces between the adhering particles and the surface. Previous theoretical models may treat the particle-asperity interactions in an unprecise manner, which may result in inaccurate estimations of the van der Waals force especially when the sphere is much larger than the asperities. In this paper, we proposed a numerical model to calculate the van der Waals force between a spherical particle and a rough surface with periodic nanostructures. The 3D sinusoidal rough surfaces are simplified with their asperities modelled as hemispheres, and the contact is within the Derjaguin-Muller-Toporov (DMT) regime. The proposed model calculates the van der Waals forces between the sphere and all the asperities in the contact surface, which will provide more accurate estimations of the van der Waals force. Moreover, the effect of the planar distribution of asperities on the van der Waals forces is considered, which includes the cases when asperities have close-packed hexagonal lattice, square, and hollow-centered hexagonal packing distributions. The theoretical results calculated using the proposed model are verified by comparing the results to previous theoretical and experimental results and the comparison shows that the proposed numerical model predicts the van der Waals force accurately.

Numerical and experimental study of the preload induced period-1 and chaotic vibration of a rotor system considering contact effects

Contact effects are one of the primary nonlinear sources of vibrations in the gas turbine rotor systems. Specifically, the nonlinear stiffness between the disk interface from the contact effects has an important influence on the vibration characteristics. In this study, a contact model that accounts for the elastoplastic deformation of asperity is established based on the contact theory. To improve the macroscopic contact model of the bolted structure, we integrate the tested morphology results and modified the skewed distribution function. Subsequently, a dynamic model of the rod fastened rotor-bearing system that incorporates the nonlinear oil film force is established. The influence of the preload on the vibration characteristics of the rotor bearing system is analyzed. The results demonstrate that the improved contact model accurately describes the distribution of asperities on rough surface. The contact effects weaken the rotor lateral stiffness to a certain extent. According to the numerical results and experimental results, it can be found that changes in preload significantly affects the occurrence conditions from periodic vibration to chaotic vibration, a higher preload is conducive to maintaining the stable period-1 motion state at high speed. Additionally, as the preload is decreased, the speed range with obvious periodic-doubling frequencies gradually increases and the amplitude of vibration response decreases. This work provides a practical guidance for the dynamic design and preload adjustment of gas turbine rod-fastened rotor considering contact effects.

Modeling the adhesion of spherical particles on rough surfaces at nanoscale

In this paper, the Van der Waals force acting between a spherical nanoparticle and a surface with random distribution of asperities has been simulated using the Johnson-Kendall-Roberts (JKR) contact mechanics model. To predict the adhesion force in different mediums and under different contact conditions, it is necessary to calculate the adhesion force in micro/nano systems. For this purpose, four different cases of surface roughness have been studied. The geometries of these rough surfaces have been defined taking into account the two key parameters of asperity radius and asperity height, and the necessary equations to determine the contact area and the magnitude of the adhesion force have been derived. Based on the geometries of the surface cap/trough, the interaction force between a spherical nanoparticle and a rough substrate has been obtained by applying Van der Waals theory. Then, the adhesion force for spherical nanoparticle has been modeled with respect to its height above the rough surface. Finally, the behavior of nanoparticles with different radii on four different rough substrates have been simulated and analyzed. The simulation results show that more precise adhesion forces can be obtained by modelling the surface roughness at the nanoscale. For small distances between spherical nanoparticle and the substrate, the adhesion force determined with the new roughness models is larger for rough substrates than for smooth ones.

Interseismic Coupling, Asperity Distribution, and Earthquake Potential on Major Faults in Southeastern Tibet

AbstractSoutheastern (SE) Tibet is one of the most seismically active regions in mainland China, but the spatial distribution of interseismic coupling that quantifies seismic hazard is unknown along most major faults. In this study, we constructed an elastic block model to invert Global Positioning System data for slip rates and locking coefficients along 20 major faults in SE Tibet. Our results identify 27 strongly coupled fault segments with locking coefficients >0.5, defined as potential seismogenic asperities, extending laterally for 36–330 km. Quantitative calculations of seismic moment budgets on these seismogenic asperities indicate that they are capable of generating Mw 6.4–7.7 earthquakes in the next few decades, of which the Anninghe, Daliangshan and Red River faults have the potential for Mw ≥ 7.5 earthquakes. The interseismic coupling model provides a component for probabilistic analysis of future seismic hazards in densely populated Southwest China.

Chemically-induced active micro-nano bubbles assisting chemical mechanical polishing: Modeling and experiments

The material loss caused by bubble collapse during the micro-nano bubbles auxiliary chemical mechanical polishing (CMP) process cannot be ignored. In this study, the material removal mechanism of cavitation in the polishing process was investigated in detail. Based on the mixed lubrication or thin film lubrication, bubble-wafer plastic deformation, spherical indentation theory, Johnson-Cook (J-C) constitutive model, and the assumption of periodic distribution of pad asperities, a new model suitable for micro-nano bubble auxiliary material removal in CMP was developed. The model integrates many parameters, including the reactant concentration, wafer hardness, polishing pad roughness, strain hardening, strain rate, micro-jet radius, and bubble radius. The model reflects the influence of active bubbles on material removal. A new and simple chemical reaction method was used to form a controllable number of micro-nano bubbles during the polishing process to assist in polishing silicon oxide wafers. The experimental results show that micro-nano bubbles can greatly increase the material removal rate (MRR) by about 400% and result in a lower surface roughness of 0.17 nm. The experimental results are consistent with the established model. In the process of verifying the model, a better understanding of the material removal mechanism involved in micro-nano bubbles in CMP was obtained.

An Analytical Model for the Normal Contact Stiffness of Mechanical Joint Surfaces Based on Parabolic Cylindrical Asperities.

The analytical results of normal contact stiffness for mechanical joint surfaces are quite different from the experimental data. So, this paper proposes an analytical model based on parabolic cylindrical asperity that considers the micro-topography of machined surfaces and how they were made. First, the topography of a machined surface was considered. Then, the parabolic cylindrical asperity and Gaussian distribution were used to create a hypothetical surface that better matches the real topography. Second, based on the hypothetical surface, the relationship between indentation depth and contact force in the elastic, elastoplastic, and plastic deformation intervals of the asperity was recalculated, and the theoretical analytical model of normal contact stiffness was obtained. Finally, an experimental test platform was then constructed, and the numerical simulation results were compared with the experimental results. At the same time, the numerical simulation results of the proposed model, the J. A. Greenwood and J. B. P. Williamson (GW) model, the W. R. Chang, I. Etsion, and D. B. Bogy (CEB) model, and the L. Kogut and I. Etsion (KE) model were compared with the experimental results. The results show that when roughness is Sa 1.6 μm, the maximum relative errors are 2.56%, 157.9%, 134%, and 90.3%, respectively. When roughness is Sa 3.2 μm, the maximum relative errors are 2.92%, 152.4%, 108.4%, and 75.1%, respectively. When roughness is Sa 4.5 μm, the maximum relative errors are 2.89%, 158.07%, 68.4%, and 46.13%, respectively. When roughness is Sa 5.8 μm, the maximum relative errors are 2.89%, 201.57%, 110.26%, and 73.18%, respectively. The comparison results demonstrate that the suggested model is accurate. This new method for examining the contact characteristics of mechanical joint surfaces uses the proposed model in conjunction with a micro-topography examination of an actual machined surface.