Plastic Contact Research Articles

Normal Contact Model for Elastic and Plastic Mechanics of Rough Surfaces

An elastic and plastic mechanical model is proposed to characterize the normal contact of rough surfaces. The contact process is considered as three separated contact regimes, i.e., the fully elastic, mixed elastic–plastic and fully plastic ones. The Hertzian elastic contact solutions and the classical fully plastic contact model of Abbott and Firestone are used to model the contact behaviors of fully elastically deformed asperities and fully plastically deformed ones, respectively. For the mixed elastic–plastic regime, an improved Hermit interpolation method is applied to enforce the continuity and smoothness at the critical contact interference, and to decrease the interpolation waving effect by transforming the physical quantities of contact load into logarithmic coordinates. The contact model of rough surfaces is formulated by using the Greenwood and Williamson’s statistics analysis. Comparisons with the CEB, ZMC and KE models are then performed to examine the effects of plasticity index and mean separation. Agreeing well with the ZMC model, our results show that the total contact load of rough surfaces decreases with the increase in mean separation, and the difference between the prediction results of elastic models and the plastic ones also decreases, indicating that the contact behaviors mainly dominated by plastically deformed asperities have been changed to be controlled by elastically deformed ones. Larger plasticity index represents more plastically deformed asperities, inducing normal contact behaviors mainly dominated by plastic solutions.

Coupling fractal model for adhesive and three-body abrasive wear of AISI 1045 carbon steel spool valves

The coupling of adhesive wear with three-body abrasive wear exists in many mechanical systems. Traditional approaches consider either only a single-wear mechanism or cannot account for the self-similarity of worn surfaces at multiple scales. In this study, we develop a new fractal model to account for the coupling of adhesive wear with three-body abrasive wear of self-mated AISI 1045 carbon steel spool valves, and we use this model as a basis for product life design. First, the elastic–plastic contact behavior on the fractal surface is investigated; subsequently, a dual mode wear prediction model that also includes three-body abrasion is proposed. The adhesive wear calculation is derived based on the fractal distribution and the plasticity-induced adhesion between interacting asperities. The three-body abrasive wear is determined by a semi-empirical equation. The coupled wear mode calculation is illustrated using two time-varying fractal parameters: fractal dimension (D) and scaling coefficient (G) as the references of the adhesive wear calculation. Finally, a limited number of lubricated wear tests for self-mated AISI 1045 carbon steel spool valves were conducted to evaluate and verify the proposed model. The comparison between the model's prediction and laboratory test data demonstrates that the new model can reasonably explain the dual mode wear behavior and predict the wear rate of spool valves.

Effect of load on the tribological properties of Si3N4-hBN composite ceramics sliding against Si3N4

PurposeThe effect of the load on the tribological properties of Si3N4-hBN sliding against Si3N4 were investigated under dry and water lubrication condition.Design/methodology/approachUsing a MMU-5G type pin-on-disc friction and wear tester.FindingsUnder the dry friction, the wear mechanism was dominated by ploughing and abrasive wear, and the contact status was elastic contact under the load less than 25 N. With the increase of the load, the friction coefficient decreased; the main wear mechanism was fatigue fracture, and the contact status turned into plastic contact. Under water lubrication, effective lubrication film could be produced on the worn surface, and it had a function of fluid lubrication under the load less than 15 N. With the increase of the load, the pin and the disc came into direct contact, and the friction and wear of the pairs were aggravated; the wear mechanism changed from chemical wear into abrasive wear and brittle spalling.Originality/valueThe study on the effect of the load on the tribological properties of Si3N4-hBN sliding against Si3N4 was investigated under dry and water lubrication condition in the way of contact stress.

A generalized mechanics theory of idealized rough surfaces under dry and liquid-mediated plastic contact conditions

An upper-bound plasticity analysis based on volume conservation and presumed uniform surface rise of noncontact regions was used to develop analytical models of a rigid-perfectly plastic half-space with a flat surface indented by a sinusoidal rigid surface and a rigid-perfectly plastic half-space with a sinusoidal surface compressed by a rigid flat surface. The hydrodynamic effect of lubricant fluid pressurized in the surface grooves of the deformed half-space on the deformation process was analyzed by solving the Reynolds equation of a squeezed film using a perturbation method. Analytical solutions of the fractional contact area, normal approach, average surface rise, cavity volume, and surface roughness were obtained after plastic contact deformation. Numerical results of a finite element analysis of relatively compliant and stiff elastic-nearly perfectly plastic materials are shown to be in good agreement with analytical results. The hypothesis of uniform surface rise of noncontact regions is shown to be a reasonable assumption, leading to a good approximation of global deformation quantities and providing an accurate description of changes in the surface profile for relatively large contact areas. The results of the present study provide a basis for explaining the full plastic merger of asperity contacts in multi-scale rough (fractal) surfaces and elucidate the role of surface roughness in metal-working processes.

Frictional characteristics of sheet metals with superimposed ultrasonic vibrations

The forming performance of sheet metals in the deep-drawing process with ultrasonic vibrations can be improved by the surface effect between the sheet metal and the die. A sheet metal friction test with ultrasonic vibrations is performed to explore the cause of the surface effect. The frictional characteristics are investigated, and the corresponding friction expressions are established based on the contact mechanics and the elastic—plastic contact model for rough surfaces. Friction is caused by the elastic—plastic deformation of contacting asperities under normal loads. The actual contacting region between two surfaces increases with normal loads, whereas the normal distance decreases. The normal distance between the contacting surfaces is changed, asperities generate a tangential deformation with ultrasonic vibrations, and the friction coefficient is eventually altered. Ultrasonic vibrations are applied on a 40Cr steel punch at the frequency of 20 kHz and the amplitude of 4.2 μm. In the friction tests, the punch is perpendicular to the surface of the magnesium alloy AZ31B sheet metals and is sliding with a relative velocity of 1 mm/s. The test results show that the friction coefficient is decreased by approximately 40% and the theoretical values are in accordance with the test values; Ultrasonic vibrations can clearly reduce wear and improve the surface quality of parts.

Investigation on surface morphology and tribological property generated by vibration assisted strengthening on aviation spherical plain bearings

The extreme and complex working conditions require aviation spherical plain bearings not only to have high machining accuracy and low surface roughness, but also to possess high surface microhardness and lubricant retaining capability. This paper presents a vibration assisted strengthening approach to achieving the synergistic effects of the surface property-improving and appearance-improving. The research attempts to answer how vibration assisted strengthening technique can improve the surface tribological properties of aviation spherical plain bearing components particularly in light of proposing the flat-headed asperity distribution model and the corresponding elastic–plastic contact modelling for the special processed surface morphology. Subsequently, the models are corroborated by the experimental results of characterizing the surface morphology produced by vibration assisted strengthening with different parameters such as rolling times and rolling static force. The surface tribological properties of spherical plain bearing specimens were studied by employing the UMT-TriboLab platform. The theoretical analysis and experimental results indicate that the surface asperities of spherical plain bearing components processed with repeated high frequency strikes present a flat-headed distribution but not Gauss distribution. It characterizes with a marked majority of produced small asperities with similar height, which is beneficial to frictional couple contacts and a lot of original valleys retaining lubricants. The processing technique contributes to increasing the surface microhardness by 20% and decreasing the surface roughness from about Ra 0.4 µm to below Ra 0.1 µm. The ball-on-flat friction tests demonstrate that both the special flat-headed surface structure and the elevated microhardness can attribute the improvement of tribological properties and wear resistance performance of spherical plain bearings.

Model for Elastic–Plastic Contact Between Rough Surfaces

This paper studies elastic–plastic contact between Greenwood–Williamson (GW) rough surfaces, on which there are many asperities with the same radius whose height obeys the Gaussian distribution. A new plasticity index is defined as the ratio of the standard deviation of the height of asperities on the rough surface to the single-asperity critical displacement (the transition point from the elastic to the elastic-fully plastic deformation regime), which is linearly proportional to the GW plasticity index to the power of 2. The equations for the load/area–separation relationship of rough surfaces are presented based on Wang and Wang's smooth model of singe-asperity elastic–plastic contact, which is an improvement of the Kogut–Etsion (KE) empirical model based on finite element analysis (FEA) data. The load/area–separation relationship can be described by empirical Gaussian functions. The load–area relationship of rough surfaces is approximately linear. The average pressure is only function of the new plasticity index. According to Wang and Wang's conclusion that Etsion et al. single-asperity elastic–plastic loading (EPL) index is approximately equal to the ratio of the single-asperity residual plastic contact displacement to the single-asperity total elastic–plastic contact displacement, the equations for the relationship between Kadin et al. modified plasticity index (MPI) and separation of rough surfaces are also presented. In addition, the MPI is approximately linearly proportional to the separation between rough surfaces for a given new plasticity index ranging from 5 to 30. When the new plasticity index is smaller than 5, due to the large proportion of the elastic deformation in the total deformation, the MPI slightly deviate from linearity.

Repeated loading model for elastic–plastic contact of geomaterial

A new nonlinear hysteretic model with considering the loading, unloading, and reloading processes is developed based on Drucker–Prager yield criterion and finite-element analysis. This model can be used for multiple repeated elastic–plastic normal direction contact problems between two identical spherical geomaterials. After examining the influence of material properties, strain hardening, and loading histories, we found that the hysteretic phenomena (represented by residual displacement and plastic work) become weak after the first cycle, and the subsequent cycles step into elastic shakedown state eventually. A critical number of cycles can be used to estimate the state of ratchetting, plastic shakedown, as well as elastic shakedown. It also found that the subsequent curves will be stiffer than the previous ones, especially when the yield strength is high and ratchetting effect is not strong. This new model can be used for a wide range of geomaterials under different loading levels, and it can also be extended to describe the constitutive behavior of spheres under earthquake as well as aftershocks.

Investigation on the uncertain factors of the elastic–plastic contact characteristics of the planetary roller screw mechanism

The scatter of uncertain factors of the planetary roller screw mechanism, which originated from the manufacturing process, has a significant influence on its serving performance. However, this influence remains insufficiently studied. Further, the elastic–plastic contact analysis of the planetary roller screw mechanism with considering the uncertainties needs large numbers of repetitive calculations by traditional finite element method, which is labor intensive and often impractical. In this paper, an uncertain model of the planetary roller screw mechanism, including parameterization and finite element calculation, is established to conduct the elastic–plastic contact analysis automatically. Besides, the finite element method results can be also obtained automatically with the self-compiled flow program and the secondary development platform using the design of experiment method. Then, a mathematic model is applied to value the influence of the uncertain factors on the contact characteristics. The Pareto graphs are plotted to clearly show this sequence of the percent effects of all the uncertain factors. The present work, for the first time, developed an automatic modeling method for analyzing efficiently the uncertain factors of planetary roller screw mechanism, which is worthy in industrial application.

Numerical Simulations and Validation of Contact Mechanics in a Granodiorite Fracture

Numerous rock engineering applications require a reliable estimation of fracture permeabilities to predict fluid flow and transport processes. Since measurements of fracture properties at great depth are extremely elaborate, representative fracture geometries typically are obtained from outcrops or core drillings. Thus, physically valid numerical approaches are required to compute the actual fracture geometries under in situ stress conditions. Hence, the objective of this study is the validation of a fast Fourier transform (FFT)-based numerical approach for a circular granodiorite fracture considering stress-dependent normal closure. The numerical approach employs both purely elastic and elastic–plastic contact deformation models, which are based on high-resolution fracture scans and representative mechanical properties, which were measured in laboratory experiments. The numerical approaches are validated by comparing the simulated results with uniaxial laboratory tests. The normal stresses applied in the axial direction of the cylindrical specimen vary between 0.25 and 10 MPa. The simulations indicate the best performance for the elastic–plastic model, which fits well with experimentally derived normal closure data (root-mean-squared error = 9 µm). The validity of the elastic–plastic model is emphasized by a more realistic reproduction of aperture distributions, local stresses and contact areas along the fracture. Although there are differences in simulated closure for the elastic and elastic–plastic models, only slight differences in the resulting aperture distributions are observed. In contrast to alternative interpenetration models or analytical models such as the Barton–Bandis models and the “exponential repulsion model”, the numerical simulations reproduce heterogeneous local closure as well as low-contact areas (< 2%) even at high normal stresses (10 MPa), which coincides with findings of former experimental studies. Additionally, a relative hardness value of 0.14 for granitic rocks, which defines the general resistance to non-elastic deformation of the contacts, is introduced and successfully applied for the elastic–plastic model.

Dynamic material properties of wood subjected to low-velocity impact

This article studied the effects of low-velocity impact on the failure stresses and stiffness using a pendulum test. The specimens were of variable depth (20, 30, and 40 mm), a width of 50 mm, length of 650 mm, and span-length of 480 mm. The smallest specimen depth was similar to specimen sizes tested in the literature used to create the duration of load curve, while the largest specimen depth are considered structural size specimens. The impact was predicted using a numerical approach with Euler–Bernoulli beam, as well as Timoshenko beam theory, with a plastic contact law. The models were validated for impact from a low release-angle (where the beam remained elastic), but could use improvement for the force prediction at a high incidence velocity. The measured force signals were used as forcing functions to obtain the dynamic failure stresses for all of the evaluated specimens, and the Timoshenko–Goens–Hearmon Method to derive the dynamic E. The resulting strain rates ranged from 9.11 × 10−5 s−1 for the quasi-static specimens up to 25 s−1 for the greatest incidence velocity. The results from this study suggest different duration of load factors than the Madison Curve, influencing the design of structures subjected to dynamic loading.

The relationship between plastic zone and contact radius during indentation experiment for strain-hardened materials

ABSTRACTIn this study, the ratio f of the plastic zone radius, , to the contact radius, , for different material properties and at various indentation depths was investigated using a three-dimensional finite element model for strain hardening materials. The effective indentation radius and f were determined via the statistical volume of plastic zone. It was found that f is significantly influenced by material properties, such as yield strength, Young’s modulus, strain hardening exponent and Poisson’s ratio, and less influenced by the indentation depth. A relationship between f and the material properties was proposed.

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.

Investigation into the Normal Contact Stiffness of Rough Surface in Line Contact Mixed Elastohydrodynamic Lubrication

ABSTRACT In this work, the statistical asperity microcontact models in combination with the acoustic spring model and the load sharing concept are utilized to study the interfacial normal contact stiffness for a rough surface in line contact elastohydrodynamic lubrication (EHL). Two different statistical microcontact models of Greenwood and Williamson (GW) and Kogut and Etsion (KE) are employed to derive the normal contact stiffness expressions for a dry rough line contact considering the purely elastic contact and the multiple regimes elastic–elastoplastic–fully plastic contact, respectively. The liquid film stiffness is calculated based on the relationship between film thickness and bulk modulus of the lubricant. The lubricant film thickness equations are employed in conjunction with the load sharing concept and the empirical formulas for the maximum contact pressure in a dry rough contact are fitted for the GW model and the KE model, to evaluate the relationship between film thickness and motion velocity for the purely elastic GW microcontact model and the multiregime KE microcontact model, respectively. The comparison with experimental results shows that the KE model predicts closer total contact stiffness results than the GW model. The stiffness contributions from the solid asperity contact and lubricant film are obtained and effects of surface roughness, applied load, motion velocity, and type of lubricant on the normal contact stiffness are analyzed.

Fractal modeling of elastic-plastic contact between three-dimensional rough surfaces

PurposeThis paper aims to propose a semi-analytical model to investigate the elastic-plastic contact between fractal rough surfaces. Parametric studies have been performed to analyze the dependencies between the contact properties and the scale-independent fractal parameters.Design/methodology/approachA modified two-variable Weierstrass-Mandelbrot function has been used to build the geometrical model of rough surfaces. The computation program was developed using software MATLAB R2015a. The results have been qualitatively validated by the existing theoretical and experimental results in the literature.FindingsIn most cases, a nonlinear relation between the load and the displacement of the rigid plane is found. Only under the condition of larger loads, an approximate linear relation can be seen for great D and small G values. (D: fractal dimension and G: fractal roughness).Originality/valueThe contact model of the cylindrical joints (conformal contact) with radial clearance is constructed by using the fractal theory and the Kogut-Etsion elastic-plastic contact model, which includes purely elastic, elastic-plastic and fully plastic contacts. The present method can generate a more reliable calculation result as compared with the Hertz contact model and a higher calculation efficiency as compared with the finite element method for the conformal contact problem.

Deformation processes within wheel-rail adhesion in contact area

The study of working surface deformation during interaction of open-pit locomotive tires allowed defining outstanding features of phenomena occurring in the contact area of interacting surfaces. It was found that processes typical for plastic saturated contact occur in the area of wheel-rail interaction of industrial railway transport. In case of plastic deformation exposed to heavy loads typical for open-pit locomotives, upon all rough surfaces of the contour contact area being fully deformed, the frame on which they are found is exposed to plastic deformation. Plastic deformation of roughness within the contact area of interacting surfaces leads to the increase in the actual area of their contact and, therefore, increases the towing capacity of mining machines. Finally, the available data on deformation characteristics with regard to processes occurring in the contact area of wheel-rail interaction will allow making theoretical forecasts on the expected design value of friction coefficient and, therefore, the towing capacity of open-pit locomotives.

The determination of monomers and oligomers from polyester-based can coatings into foodstuffs over extended storage periods

ABSTRACTThe polymeric coating used in metal packaging such as cans for foods and beverages may contain residual amounts of monomers used in the production of the coating, as well as unreacted linear and cyclic oligomers. Traditionally, although designed for use with plastic food contact materials, food simulants have been used to determine the migration of monomers from coatings into foodstuffs. More recently, food simulants have also been used to determine oligomeric species migrating from can coatings. In the work reported here, the migration of both monomers and oligomers from polyester-based can coatings into food simulants and foodstuffs, some of which were towards the end of their shelf-life, is compared. The concentrations of monomers and selected oligomers in canned foods at the end of their shelf life were found to be significantly lower than those in food simulants, which in turn was lower than those in the extraction solvent acetonitrile.

Modeling tangential contact based on non-Gaussian rough surfaces

A stick-slip tangential contact model between rough surfaces was proposed in this paper. The Mindlin partial slip solution for elastic contact and the double linear formulation developed by Fujimoto for plastic contact in conjunction with the Coulomb dry friction law were used to derive tangential contact formulas. Pearson system of frequency curves was used to generate non-Gaussian random surfaces. Effects of skewness and kurtosis on normal and tangential contact responses were studied independently. The results showed that negative skewness predicted lower mean separation for a given normal force and greater tangential stiffness, while for positive skewness, there exist different trends from negative skewness. With the increase of kurtosis, the load capacity and tangential stiffness decreased. The practical significance of these findings is that it can help engineers to design proper surface textures based on their requirements. A comparison of initial tangential stiffness between predicted results and published experimental results was made. The results well agreed with the experimental results when the non-Gaussian surface effects were taken into consideration.

Safety assessment of the active substances carboxymethylcellulose, acetylated distarch phosphate, bentonite, boric acid and aluminium sulfate, for use in active food contact materials.

This scientific opinion of the EFSA Panel on Food Contact Materials, Enzymes, Flavourings and Processing Aids (CEF Panel) deals with the safety evaluation of the active substances carboxymethylcellulose, acetylated distarch phosphate (FCM substance No 1071), bentonite, boric acid and aluminium sulfate (FCM substance No 1072). The mixture is intended to be used as a liquid absorber in the packaging of perishable foods to extend their shelf‐life. All substances have been evaluated and approved for use as additives in plastic food contact materials and/or as food additives. Migration of boron into foods was up to 0.7 mg/kg food. Migration of aluminium was not detected (limit of detection (LOD) of 0.001 mg/kg). The CEF Panel concludes that the substances carboxymethylcellulose, acetylated distarch phosphate, bentonite, boric acid and aluminium sulfate are not of safety concern for the consumer when used as active components in moisture and liquid absorbers. The absorbent pads must be used under conditions in which direct contact between the active mixture and the food is avoided and the fluid absorption capacity of the absorber is not exceeded.

A loading fractal prediction model developed for dry-friction rough joint surfaces considering elastic–plastic contact

In the microscopic view, the contact between two solid surfaces is reckoned to be the contact among asperities indeed. These asperities loaded which contact with each other are to experience three stages of deformation in succession: elastic deformation, elastic–plastic deformation, and plastic deformation, not the direct transition from elastic deformation to plastic deformation. In addition, these asperities should be distributed on the three-dimensional surface topography, and the corresponding fractal dimension is $$2<D<3$$ . In this study, firstly, based on the fractal theory and Hertz contact theory, the loading fractal model of rough dry-friction joint surfaces is established in consideration of elastic–plastic deformation of asperities and three-dimensional surface topography. Secondly, two important fractal parameters, fractal dimension D and fractal roughness G, can be calculated according to sampled surface topography of 45 steel and power spectrum density function method. Then, the effects of friction factor $$\mu $$ , fractal dimension D, and fractal roughness G on the loading fractal model are analyzed by numerical simulation. Finally, the present model is compared with experimental data and other models, which indicates that their trends are the same. The elastic–plastic loading modeling provides a certain theoretical reference for the accurate solution of contact among rough surfaces.