Plastic Contact Research Articles

Theoretical and experimental analysis of compressive residual stress field on 6061 aluminum alloy after ultrasonic surface rolling process

Ultrasonic surface rolling process is a mechanical surface treatment used for improving fatigue life by introducing a compressive residual stress field into the surface of metallic components. This paper develops a simplified theoretical analysis model of compressive residual stress field induced by ultrasonic surface rolling process. Explicit dynamic solution in ABAQUS is used for calculating the plastic contact radius ap and velocity V0 of the tool tip. Afterward, compressive residual stress field is predicted by using MATLAB on the basis of this theoretical model. Additionally, ultrasonic surface rolling process experiments are conducted to verify the calculated results of compressive residual stress field. The influence of ultrasonic surface rolling process parameters on compressive residual stress field, such as static force F0, spindle speed n, vibration amplitude B, and ultrasonic frequency f, are examined by using theoretical analysis and experiments. The calculated results of compressive residual stress field are in relatively good agreement with the experimental results. Furthermore, ap essentially determines the distribution of compressive residual stress field. Other parameters indirectly affect the distribution of compressive residual stress field through changing ap. Finally, static force and vibration energy simultaneously applied to the tool tip can significantly affect the distribution of compressive residual stress field compared with only static force.

A Fourier-accelerated volume integral method for elastoplastic contact

The contact of solids with rough surfaces plays a fundamental role in physical phenomena such as friction, wear, sealing, and thermal transfer. However, its simulation is a challenging problem due to surface asperities covering a wide range of length-scales. In addition, non-linear local processes, such as plasticity, are expected to occur even at the lightest loads. In this context, robust and efficient computational approaches are required. We therefore present a novel numerical method, based on integral equations, capable of handling the large discretization requirements of real rough surfaces as well as the non-linear plastic flow occurring below and at the contacting asperities. This method is based on a new derivation of the Mindlin fundamental solution in Fourier space, which leverages the computational efficiency of the fast Fourier transform. The use of this Mindlin solution allows a dramatic reduction of the memory imprint (as the Fourier coefficients are computed on-the-fly), a reduction of the discretization error, and the exploitation of the structure of the functions to speed up computation of the integral operators. We validate our method against an elastic–plastic FEM Hertz normal contact simulation and showcase its ability to simulate contact of rough surfaces with plastic flow.

A numerical elastic–plastic contact model for a half-space with inhomogeneous inclusions and cracks

The elastic–plastic contact problem plays an important role in predicting the mechanical properties of materials. In this paper, a semi-analytic solution is developed to investigate the plastic behaviors of a half-space with inhomogeneous inclusions and cracks under contact loading. In this solution, the plastic zones are determined based on the stress field equations and the von Mises yield criterion. The contact area and surface pressure distribution are obtained by solving a set of governing equations via a modified conjugate gradient method. The inhomogeneous inclusions are modeled as homogeneous inclusions with the initial eigenstrains plus unknown equivalent eigenstrains according to the Eshelby’s equivalent inclusion method. The cracks are treated as a collection of distributions of unknown dislocation densities according to the distributed dislocation technique. The case studies of a cylinder loaded against a half-space with inhomogeneous inclusions and vertical or horizontal cracks are conducted to explore the effects of the Young’s moduli and positions of the inhomogeneous inclusions on the plastic behavior of materials.

Characteristics analysis of rotor model with support–foundation looseness fault considering elastic–plastic contact

In this paper, the nonlinear response characteristics of a single degree of freedom lumped mass model with a new support looseness fault are analyzed. In this model, a new nonlinear contact stiffness model between the support and foundation is considered, which considers the elastic–plastic deformation of the contact parts. The nonlinear response of the system is obtained by numerical integration methods. The nonlinear results are compared with an asymmetric model and a piece-wise contact model. By comparing three different looseness fault models, the mechanism of generating multi-frequencies and fractional frequencies is analyzed. The result shows that plastic deformation makes the displacement amplitude increase rapidly; odd harmonics appear in symmetric stiffness model due to the modulation of symmetric shock forces; however, harmonic response appears in asymmetric stiffness model; when the contact number is odd, the frequency components contain odd or even order fractional frequencies at supercritical speeds due to the incompatibility of contacts on the upper and lower surfaces; when the contact number is even, multiple frequency components appear at subcritical frequencies.

Incipient plasticity and fully plastic contact behavior of copper coated with a graphene layer

Cu coated with a graphene layer increases the elastic modulus from 163.4 GPa to 176.7 GPa, as analyzed for the initial elastic loading during nanoindentation by the Hertzian contact theory. This is attributed to stiffening, due to the ultra-high elastic modulus of the graphene layer, and the compressive in-plane residual stresses in the Cu surface volume introduced by the lattice mismatch between graphene and Cu. The graphene layer induces incipient plasticity, manifested by pop-in events during nanoindentation loading, at shallower indentation depths. This could be due to the compressive in-plane residual stress in the Cu surface volume; however, this compressive stress does not significantly change the critical resolved shear stress for the incipient plasticity. Even in the fully plastic contact region, at an indentation depth of 100 nm, the graphene layer affects the stress distribution underneath the indenter, resulting in a lower pile-up height. When considering this reduced pile-up height, the graphene layer is found to enhance elastic modulus by 5%, whereas it has no effect on hardness.

On the numerical prediction of the torque-to-turn-value of a blind rivet nut

In the present paper, finite element simulations are used to gain a better understanding of the setting process of a blind rivet nut. A blind rivet nut is a mechanical fastener capable of clinching materials whilst providing a threaded solution without the need for thread forming. The technique relies on plastic deformation introduced by axial compression of the rivet nut in such a way that a counter head is formed on the opposite side of the work piece. For certain applications, stresses in the plate material induced by the setting process are detrimental for the fastener’s integrity. Hence an improved design of the fastener is desired. To embark on such a redesign, an appropriate numerical model to reveal the influence of several parameters is indispensable. In this work, a strategy is presented to simulate the setting process involving large plastic strains and contact pressures. An FE based inverse method was used to identify the local plastic material properties of the blind rivet nut. The forming simulation was validated in terms of predicted shape of the rivet nut and the evolution of the setting force. A quasi-static FE model using the shape and solution variables of the deformed rivet nut was used to reproduce the torque-to-turn resistance as a function of the setting force. The strategy was successfully applied on two blind rivet nuts, different in geometry and base material. Finally, three industrial case studies confirmed the viability of the model.

Microstructure and Mechanical Properties of an Ultrasonic Spot-Welded Aluminum-to-Aluminum Joint: Response to Interlayer Thickness.

To enhance the mechanical strength of an ultrasonic spot-welded Al/Al joint, an Al 2219 particle interlayer was placed between the two Al sheets during the ultrasonic spot welding process. The effects of the interlayer thickness on the microstructure and mechanical performances of the joints were systematically investigated. The results showed that, the optimum thickness of the Al 2219 particle interlayer was 10 μm, which was beneficial to enhance the weld interface temperature up to 402 °C. The bonding interface of Al/Al 2219 with a wave-like shape was sound, and no significant diffusion layer occurred. The peak lap shear tensile strength (~84.8 MPa) was obtained, which was 36% higher than that (~67.3 MPa) for the joint without the Al 2219 particle interlayer. The strengthening mechanism is caused by the increase of plastic deformation and contact areas in the weld interface.

Numerical analysis of contact plastic bodies made by aluminium alloy with taking account of micro-roughness surfaces

The following article describes selected aspects of numerical modeling of the process of bonding metal alloys with consideration for micro-roughness. Plastic contact between two deformable bodies is studied within a DEFROM FEM environment. The paper presents selected numerical analysis results for an aluminum alloy. The mathematical model of surface roughness has been created on the basis of the surface real profile. The dependence between the tool lathe angle and the feed has been used to build a numerical model of roughness after completion of the turning process. The article investigates the impact of wave roughness in respect to the size effect and the possibility of cold welding as well as the simplification process of real surface roughness.

An Experimental and Theoretical Study of the Normal Coefficient of Restitution for Marble Spheres

The normal coefficient of restitution (NCOR) is a useful index to quantify the energy dissipation during impact. This study presents experimental tests of marble spheres impacting a plate. The effects of the sphere diameter, elastic properties of the plate, impact velocity, and repeated impacts on the NCOR were investigated. Three fracture phases were observed: no macrocrack, macrocrack, and fragmentation. A clear influence of the propagation of the macrocracks on the NCOR was observed. Macrocracks also cause increased NCOR variability. The cumulative damage caused by macrocracks can affect the propagation of macrocracks and fragmentation. In the no macrocrack phase, the NCOR decreases with increasing velocity and with decreasing diameter, and the velocity effect of the NCOR is also related to the size of the marble sphere. The proposed average rate of contact stress correlates well with the NCOR and can describe fully the velocity and size effects of the NCOR, which provides a simple way to consider the complex velocity and size effects in rockfall simulations. The dissipation caused by microcracks and viscosity can be considered simultaneously through the average rate of contact stress. The marble sphere NCOR decreases with increasing elasticity modulus of the plate, and this conclusion is verified by the elastic-perfectly plastic contact theory. Finally, viscoelastic contact theory is used to describe the NCOR, which proves that the decrease in the NCOR with decreasing diameter is reasonable and can be used to predict a decrease in the NCOR with an increase in velocity.

Rapid determination of 13 ultraviolet absorbents in plastic food contact materials by ultra-performance convergence chromatography

A rapid method based on ultra-performance convergence chromatography (UPC2) was developed for the analysis of 13 ultraviolet (UV) absorbents in plastic food contact materials. The UV absorbents were extracted from plastic food contact materials by supersonic extraction with methanol, purified by C18 solid phase extraction column, and analyzed via UPC2 before filtration with an organic filtration membrane (0.22 μm). An ACQUTY UPC2 HSS C18 SB chromatographic column (150 mm×3.0 mm, 1.8 μm) was used for the detection of the UV absorbents. An effective separation was achieved within 4 min under the optimized conditions. The mobile phases were supercritical carbon dioxide and isopropanol as a modifier. The results showed that the 13 UV absorbents exhibited good linear relationships in the respective linear ranges with the correlation coefficients no less than 0.9985. The limits of detection (S/N=3) were in the range of 0.05-0.15 mg/kg. The recoveries were from 86.8% to 115.7%, and the relative standard deviations were between 0.73% and 5.61%. This method is rapid, convenient, accurate and reliable, and can be used for the rapid determination of the 13 UV absorbents in plastic food contact materials.

Rapid analysis of the specific migration of seven terephthalates and benzoates from plastic food contact material and products by high performance liquid chromatography-ultraviolet detection

A method based on high-performance liquid chromatography-ultraviolet (HPLC-UV) detection was developed for the rapid analysis of the specific migration of seven terephthalates and benzoates (TPBAs) in seven food simulants (10% (v/v) ethanol, 3% (m/v, i. e. 3 g/100 mL) acetic acid, 4% (v/v) acetic acid, 20% (v/v) ethanol, 50% (v/v) ethanol, 95% (v/v) ethanol, or olive oil)). Detailed comparisons were made on the extraction or purification of the seven TPBAs in olive oil food simulants by solvents, QuEChERS dSPE EMR-Lipid technology, and Captiva EMR-Lipid technology. The seven TPBAs were separated completely within 17 min by gradient elution on a phenyl column using water and methanol as the mobile phase. The detection wavelength was set at 237 nm. The injection volume was 10 μL. The linearities of the seven TPBAs were good, with r≥0.9998 at 1-80 mg/L or 8-160 mg/kg in the seven food simulants. The average recoveries of the seven TPBAs were between 91.7% and 106%, with relative standard deviations (RSDs) between 0.1% and 3.1% (n=6). The limits of quantification were 0.2-8.1 mg/kg. This method is simple, with convenient pretreatments, good chromatographic separation and linear relationships, as well as satisfactory recoveries and RSDs. The method has been applied to detect the specific migration of the seven TPBAs in real samples.

Experimental verification of a numerical surface roughness model for metallic bodies under large plastic strain

The present work describes selected aspects of numerical modelling of the process of bonding metal alloys with consideration for micro-roughness, as well as experimental verification. The plastic-elastic contact between two deformable bodies was investigated in a DEFROM FEM environment, and verified at the test stand. The present paper demonstrates selected results of contact modelling investigated using aluminium-copper samples, in relation to their elastic-plastic range. The real surface profile helped to create a mathematical model of surface roughness measured using a laser microscope. Dependency between a blade of a tool and a feed was used to build a numerical model of roughness based on the arithmetic average value of the roughness profile. The work presents also a process of simplification of real surface roughness for the needs of numerical calculations. The paper investigates an impact of wave roughness at obtained values on effective plastic strain and stress. Additionally, numerical analysis shows a need to enter a new roughness wave correction factor assuming a zero value of the coefficient of friction. This is due to the interaction of metallic surfaces within the plastic contact zone. The obtained results allow the estimation of the impact of surface force interaction expressed by the wave coefficient factor. The experimental verification of numerical calculations allowed the estimation of the actual impact of the micro-cutting process in the entire friction process. Further analysis of obtained results permits the author to explain the surface phenomena occurring during the friction process, such as adhesion or diffusion, and outline the development direction of numerical methods.

Numerical simulation of elastoplastic contact of heavy-loaded spiroid gears

The paper presents the analysis of heavy-loaded low-speed multi-pair spiroid gears under the effect of elastic contact, bending and shearing, and elastoplastic contact interaction of spiroid gearwheel teeth and spiroid worm threads. The main stages of the developed algorithm for analysis of load distribution and plastic strain of flanks with account of elastic and elastoplastic contact conditions, multi-pair contact and macro-roughnesses on flanks are described in short. At elastoplastic contact the zones of plastic contact on flanks of spiroid gearwheel teeth are determined and the value of plastic strain is analyzed. The flanks of the spiroid gearwheel teeth and worm threads are represented in the algorithm as the set of segments (cells) with coordinates of centers determined with account of the analyzed factors that influence the load distribution in spiroid gearing. These factors are the errors of manufacturing and (or) assembly, micro-roughnesses, and deformations of spiroid gear supports. The paper gives the numerical results of research of the real spiroid gears of gearboxes for pipeline valves (PV) at elastic and elastoplastic contact represented as summary tables and diagrams of contact stress distribution along contact areas and of plastic strain, that show the workability of the algorithm. The presented numerical results of the algorithm functioning are well agreed with the experience of operation of spiroid gears and can be applied for analysis of load-carrying capacity of spiroid gears.

Mechanical model of single abrasive during chemical mechanical polishing: Molecular dynamics simulation

Abstract The loading process among the silicon substrate, silica cluster and polyurethane pad was performed by molecular dynamics simulations. The results showed that the interaction force between the cluster and pad did not change with the working pressure at low load stage due to strong fluidity of pad atoms. But at high load stage, the interaction force would increase with increase of the working pressure owing to the reduction of pad fluidity. These demonstrate that the contact status between the abrasives and pad will change from an elastic contact to plastic contact with increase of working pressure for a chemical mechanical polishing (CMP) process. Finally, a unified mechanical model for the single abrasive during CMP under different loads was established.

Shear thinning in non-Brownian suspensions explained by variable friction between particles

We propose to explain shear-thinning behaviour observed in most concentrated non-Brownian suspensions by variable friction between particles. Considering the low magnitude of the forces experienced by the particles of suspensions under shear flow, it is first argued that rough particles come into solid contact through one or a few asperities. In such a few-asperity elastic–plastic contact, the friction coefficient is expected not to be constant but to decrease with increasing normal load. Simulations based on the force coupling method and including such a load-dependent friction coefficient are performed for various particle volume fractions. The results of the numerical simulations are compared to viscosity measurements carried out on suspensions of polystyrene particles ($40~\unicode[STIX]{x03BC}\text{m}$in diameter) dispersed in a Newtonian silicon oil. The agreement is shown to be satisfactory. Furthermore, the comparison between the simulations conducted either with a constant or a load-dependent friction coefficient provides a model for the shear-thinning viscosity. In this model the effective friction coefficient$\unicode[STIX]{x1D707}^{eff}$is specified by the effective normal contact force which is simply proportional to the bulk shear stress. As the shear stress increases,$\unicode[STIX]{x1D707}^{eff}$decreases and the jamming volume fraction increases, leading to the reduction of the viscosity. Finally, using this model, we show that it is possible to evaluate the microscopic friction coefficient for each applied shear stress from the rheometric measurements.

Fractal modeling of normal contact stiffness for rough surface contact considering the elastic–plastic deformation

In this work, a new formulation of elastic–plastic contact model for the normal contact between rough surfaces is proposed based on the fractal theory. The surface topography is described using the modified one-variable Weierstrass–Mandelbrot fractal function. A new elastoplastic asperity contact model is developed based on the contact mechanics combined with the continuity and smoothness of mean contact pressure and contact load across different deformation regimes from elastic to elastoplastic, and from elastoplastic to fully plastic. The contact stiffness of a single asperity in the three deformation regimes of fully plastic, elastoplastic and elastic is derived, which changes smoothly at transit points between different deformation modes and overcomes the shortcoming of discontinuity derived from previous model. The contact stiffness and contact load of the whole surface in the three deformation regimes are formulated by integrating the micro-asperity contact. The difference between contact stiffness calculated from the plastic–elastoplastic–elastic three contact regimes and plastic–elastic two contact regimes is not obvious for surface with rougher topograph; however, for surface with smoother topograph, the two contact regimes predict a much smaller contact stiffness. The relationship of the normal contact stiffness and the normal contact force follows a power law function for the fractal surface contact considering three deformation regimes. The power exponent is nonlinearly dependent on the fractal dimension, which is different from the linear relationship for the purely elastic contact.

Detection and quantification analysis of chemical migrants in plastic food contact products.

Plastic food contact materials (FCM)-based products were widely used in everyday life. These products were normally imposed to strict regulations in order to pass the enforcement tests of compliance as a prefix condition. However, even in these “qualified” materials, unknown chemical substances, not involving in legislation lists, could migrate from FCM. In this perspective, the present work aims to thoroughly analyze by means of Gas Chromatography-Mass Spectrometry (GC-MS) the different substances/migrants in 120 qualified FCM plastic products. Unexpectedly, among the identified compounds (nearly 100), only 13% was included in the permitted list of Commission Regulation EU No 10/2011. All the identified compounds were classified into 11 categories according to their chemical structure and the FCM type, whereas toxicology data were in addition analyzed. Each plastic type exhibited different preferences of chemical migrants. Fortunately, most of the compounds identified were of low toxicity, and only 4 chemicals were included in priority lists and previous literature reports as potential risk factors. Subsequently, the accurate amount of these 4 chemicals was determined. The amount of Bis(2-ethylhexyl) adipate (DEHA) and Bis(2-ethylhexyl) phthalate (DEHP) were lower than the SML in Commission Regulation EU No 10/2011, and that of stearamide was under the recommended use quantity. The 2,4-di-tert-butylphenol (2,4-DTBP) was widely exist in the investigated FCM products. Among them, the highest level is obtained in polypropylene/low density polyethylene (BOPP/LDPE) materials, up to 45.568±31.513 mg/kg. In summary, a panel of unlisted chemical migrants were discovered and identified by GS-MS screening. The results implied that plastic FCMs were not so “inert” as they usually considered, and further safety evaluation should be performed toward the complete identification of new substances in FCM products.

Plastic food contact articles—food chemical safety unwrapped

Plastic food contact articles—food chemical safety unwrapped

Evaluation of contact fatigue life of a wind turbine carburized gear considering gradients of mechanical properties

Case hardening processes such as carburizing are extensively applied in heavy-duty gears used in wind turbines, ships, high-speed rails, etc. Contact fatigue failure occurs commonly in engineering practice, thus reduces reliabilities of those machines. Rolling contact fatigue life of a carburized gear is influenced by factors such as the gradients of mechanical properties and profile of initial residual stress. In this regard, the study of contact fatigue life of carburized gears should be conducted with the consideration of those aspects. In this study, a finite element elastic–plastic contact model of a carburized gear is developed which takes the gradients of hardness and initial residual stress into account. Initial residual stress distribution and the hardness profile along the depth are obtained through experimental measurements. The effect of the hardness gradient is reflected by the gradients of yield strength and fatigue parameters. The modified Fatemi–Socie strain-life criterion is used to estimate the rolling contact fatigue life of the heavy-duty carburized gear. Numerical results reveal that according to the Fatemi–Socie fatigue life criterion, rolling contact fatigue failure of the carburized gear will first initiate at subsurface rather than surface. Compared with the un-carburized gear, the rolling contact fatigue lives of the carburized gear under all load conditions are significantly improved. Under heavy load conditions, the carburized layer significantly reduces the fatigue damage mainly due to the benefit to inhibit the accumulation of plasticity. Influence of the residual stress is also investigated. Under the nominal load condition, compared with the residual stress-free case, the existence of the tensile residual stress causes remarkable deterioration of the rolling contact fatigue life while the compressive residual stress with the same magnitude leads to a moderate growth of the rolling contact fatigue life. As the load becomes heavier when plasticity becomes notable, the influence of the initial residual stress on the life is somewhat weakened.

Strain Hardening From Elastic–Perfectly Plastic to Perfectly Elastic Flattening Single Asperity Contact

For elastic contact, an exact analytical solution for the stresses and strains within two contacting bodies has been known since the 1880s. Despite this, there is no similar solution for elastic–plastic contact due to the integral nature of plastic deformations, and the few models that do exist develop approximate solutions for the elastic–perfectly plastic material model. In this work, the full transition from elastic–perfectly plastic to elastic materials in contact is studied using a bilinear material model in a finite element environment for a frictionless dry flattening contact. Even though the contact is considered flattening, elastic deformations are allowed to happen on the flat. The real contact radius is found to converge to the elastic contact limit at a tangent modulus of elasticity around 20%. For the contact force, the results show a different trend in which there is a continual variation in forces across the entire range of material models studied. A new formulation has been developed based on the finite element results to predict the deformations, real contact area, and contact force. A second approach has been introduced to calculate the contact force based on the approximation of the Hertzian solution for the elastic deformations on the flat. The proposed formulation is verified for five different materials sets.