Existence and numerical approximation of a solution to frictional contact problem for electro-elastic materials

In this paper,a frictional contact problem between an electro-elastic body and an electrically conductive foundation is studied.The contact is modeled by normal compliance with finite penetration and a version of Coulomb’s law of dry friction in which the coefficient of friction depends on the slip.In addition,the effects of the electrical conductivity of the foundation are taken into account.This model leads to a coupled system of the quasi-variational inequality of the elliptic type for the displacement and the nonlinear variational equation for the electric potential.The existence of a weak solution is proved by using an abstract result for elliptic variational inequalities and a fixed point argument.Then,a finite element approximation of the problem is presented.Under some regularity conditions,an optimal order error estimate of the approximate solution is derived.Finally,a successive iteration technique is used to solve the problem numerically and a convergence result is established.

A hybrid contact approach for modeling soil-structure interaction using the material point method

The grid-based multi-velocity field technique has become increasingly popular for simulating the Material Point Method(MPM)in contact problems.However,this traditional technique has some shortcomings,such as(1)early contact and contact penetration can occur when the contact conditions are unsuitable,and(2)the method is not available for contact problems involving rigid-nonrigid materials,which can cause numerical instability.This study presents a new hybrid contact approach for the MPM to address these limitations to simulate the soil and structure interactions.The approach combines the advantages of point-point and point-segment contacts to implement contact detection,satisfying the impenetrability condition and smoothing the corner contact problem.The proposed approach is first validated through a disk test on an inclined slope.Then,several typical cases,such as granular collapse,bearing capacity,and deformation of a flexible retaining wall,are simulated to demonstrate the robustness of the proposed approach compared with FEM or analytical solutions.Finally,the proposed method is used to simulate the impact of sand flow on a deformable structure.The results show that the proposed contact approach can well describe the phenomenon of soil-structure interaction problems.

Frictional contact analysis of a rigid solid with periodic surface sliding on the thermoelectric material

Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear,optimize lubrication,and enhance the overall performance and durability of mechanical systems.The sliding friction contact problem between a thermoelectric(TE)half-plane and a rigid solid with a periodic wavy surface is the focus of this investigation.To simplify the problem,we utilize mixed boundary conditions,leading to a set of singular integral equations(SIEs)with the Hilbert kernels.The analytical solutions for the energy flux and electric current density are obtained by the variable transform method in the context of the electric and temperature field.The contact problem for the elastic field is transformed into the second-kind SIE and solved by the Jacobi polynomials.Notably,the smoothness of the wavy contact surface ensures that there are no singularities in the surface contact stress,and ensures that it remains free at the contact edge.Based on the plane strain theory of elasticity,the analysis primarily examines the correlation between the applied load and the effective contact area.The distribution of the normal stress on the surface with or without TE loads is discussed in detail for various friction coefficients.Furthermore,the obtained results indicate that the in-plane stress decreases behind the trailing edge,while it increases ahead of the trailing edge when subjected to TE loads.

Arc erosion behaviors of AgSnO_2 contact materials prepared with different SnO_2 particle sizes

To clarify the effect of SnO2 particle size on the arc erosion behavior of AgSnO2 contact material, Ag?4%SnO2 (mass fraction) contact materials with different sizes of SnO2 particles were fabricated by powder metallurgy. The microstructure of Ag?4%SnO2 contact materials was characterized, and the relative density, hardness and electrical conductivity were measured. The arc erosion of Ag?4%SnO2 contact materials was tested, the arc duration and mass loss before and after arc erosion were determined, the surface morphologies and compositions of Ag?4%SnO2 contact materials after arc erosion were characterized, and the arc erosion mechanism of AgSnO2 contact materials was discussed. The results show that fine SnO2 particle is beneficial for the improvement of the relative density and hardness, but decreases the electrical conductivity. With the decrease of SnO2 particle size, Ag?4%SnO2contact material presents shorter arc duration, less mass loss, larger erosion area and shallower arc erosion pits.

Influence of alloy components on arc erosion morphology of Ag/MeO electrical contact materials

Arc erosion morphologies of Ag/MeO（10） electrical contact materials after 50000 operations under direct current of 19 V and 20 A and resistive load conditions were investigated using scanning electron microscope（SEM） and a 3D optical profiler（3DOP）. The results indicated that 3DOP could supply clearer and more detailed arc erosion morphology information. Arc erosion resistance of Ag/SnO_2（10） electrical contact material was the best and that of Ag/CuO（10） was the worst. Arc erosion morphology of Ag/MeO（10） electrical contact materials mainly included three different types. Arc erosion morphologies of Ag/ZnO（10） and Ag/SnO_2（10） electrical contact materials were mainly liquid splash and evaporation, and those of Ag/CuO（10） and Ag/CdO（10） were mainly material transfer from anode to cathode. Arc erosion morphology of Ag/SnO_2（6）In_2O_3（4） electrical contact materials included both liquid splash, evaporation and material transfer. In addition, the formation process and mechanism on arc erosion morphology of Ag/MeO（10） electrical contact materials were discussed.

Constitutive modelling of idealised granular materials using machine learning method

Predicting the constitutive response of granular soils is a fundamental goal in geomechanics.This paper presents a machine learning(ML)framework for the prediction of the stress-strain behaviour and shearinduced contact fabric evolution of an idealised granular material subject to triaxial shearing.The MLbased framework is comprised of a set of mini-triaxial tests which provide a benchmark for the setup and validation of the discrete element method(DEM)model of the granular materials,a parametric DEM simulation programme of virtual triaxial tests which provides datasets of micro-and macro-mechanical information,as well as a multi-layer perceptron(MLP)neural network which is trained and tested using the DEM-based datasets.The ML model only requires the initial void ratio of the granular sample as the input for predicting its constitutive response.The excellent agreement between the ML model prediction and experimental test and DEM simulation results indicates that the MLebased modelling approach is capable of capturing accurately the effects of initial void ratio on the constitutive behaviour of idealised granular materials,bypassing the need to incorporate the complex micromechanics underlying the macroscopic mechanical behaviour of granular materials.Lastly,a detailed comparison between the used MLP model and long short-term memory(LSTM)model was made from the perspective of technical algorithm,prediction accuracy,and computational efficiency.

Influence of Metal Oxides on the Arc Erosion Behaviour of Silver Metal Oxides Electrical Contact Materials

In the present work investigations have been made to see the role of metal oxides on the performance of the silver metal oxides electrical contact materials. Silver metal oxide materials of three different compositions Ag-10CdO, Ag-7.6SnO2-2.3ln2O3 and Ag-10ZnO were prepared by internal oxidation process under identical processing conditions. These materials were tested for electrical conductivity, hardness, and erosion loss. Performing an accelerated test on the actual contactor assessed the electrical performance, involving erosion loss and temperature rise of the processed materials. The arc-eroded surface was characterized under scanning electron microscope. The study of the eroded surfaces of contacts indicates that the thermal stability of metal oxides depends on nature of silver-metal oxide interface and their mode of erosion. An attempt is made to correlate the surface features of the eroded contacts with the thermal stability of metal oxides.

Effect of sintering temperature on the physical properties and electrical contact properties of doped AgSnO_2 contact materials

AgSnO_ 2 electrical contact materials doped with Bi_2O_3,La_2O_3,and TiO_2 were successfully fabricated by the powder metallurgy method under different initial sintering temperatures.The electrical conductivity,density,hardness,and contact resistance of the Ag Sn O_2/Bi_2O_3,AgSnO_2/La_2O_3,and AgSnO_2/Ti O_2 contact materials were measured and analyzed.The arc-eroded surface morphologies of the doped AgSnO_2 contact materials were investigated by scanning electron microscopy(SEM).The effects of the initial sintering temperature on the physical properties and electrical contact properties of the doped AgSnO_2 contact materials were discussed.The results indicate that the physical properties can be improved and the contact resistance of the AgSnO_2 contact materials can be substantially reduced when the materials are sintered under their optimal initial sintering temperatures.

Microstructure and properties of Ag–Ti_3SiC_2 contact materials prepared by pressureless sintering

Ti3SiC2-reintbrced Ag-maJxix composites are expected to serve as eleclrical contacts. In this study, the wettability of Ag on a Ti3SiC2 subslxate was measured by the sessile drop melkod. The Ag-Ti3SiC2 composites were prepared from Ag mad Ti3SiC2 powder mix- tures by pressureless sintering. The effects of compacting pressure （100-800 MPa）, sintering temperature （850-950~C）, mad soaking time （0.5-2 h） on the microslxucture mad properties of the Ag-Ti3SiC2 composites were investigated. The experimental results indicated that Ti3SiC2 paxticulates were uniformly distxibuted in flae Ag matrix, wiflaout reactions at the interthces between flae two phases. The prepared Ag-10wt%Ti3SiC2 had a relative density of 95% mad an electrical resistivity of 2.76 x 10 3 m~）＇cm when compacted at 800 MPa mad sintered at 950~C for 1 h. The incorporation of Ti3SiC2 into Ag was found to improve its hardness without substantially compromising its electrical conductivity; INs behavior was attxibuted to the combination of ceramic and metallic properties of the Ti3SiC2 reinforcement, suggesting its potential application in electrical contacts.

Effects of silver powder particle size on the microstructure and properties of Ag-Yb_2O_3 electrical contact materials prepared by spark plasma sintering

mg-Yb203 electrical contact materials were fabricated by spark plasma sintefing （SPS）. The effects of silver powder particle size on the microstructure and properties of the samples were investigated. The surface morphologies of the sintered samples were examined by optical microscope （OM）, and the fracture morphologies were observed by scanning electron microscopy （SEM）. The physical and mechanical properties such as density, electrical resistivity, microhardness, and tensile strength were also tested. The results show that the silver powder particle size has evident effects on the sintered materials. Comparing with coarse silver powder （5 ktm）, homogeneous and fme microstmcture was obtained by fine silver powder （_〈0.5-1am）. At the same time, the electrical conductivity, microhardness, and tensile strength of the sin- tered samples with fine silver powder were higher than those of the samples with coarse silver powder. However, silver powder particle size has little influence on the relative densities, which of all samples （both by free and coarse silver powders） is more than 95%. The fracture characteristics are ductile.

Testing results analysis of contact materials’electrical contact performance

Because of the different ways in which contact materials work, the basic requirements for silver metal oxide contact materials are different. They are anti-welded and anti-erosion when closed, anti-erosion when broken, and arc easily moved and have smaller contact resistance. In this paper, La2O3 is used as a stable oxide in contact material to replace CdO. A new type of Ag/SnO2-La2O3-Bi2O3 contact material is first obtained through using powder metallurgical method. Then electrical contact material parameter tester is used to test the electrical contact performance of the contact material. Through experiments, the arcing voltage and current curves, arcing energy curves, fusion power curves while broken and contact resistance while closed were obtained. Analysis of the results showed that the addition of La2O3 makes the contact material have the following advantages: smaller electrical wear, smaller arc energy, smaller contact resistance and arc is more easily extinguished.

Study of the Material Transfer Characteristics and Surface Morphology Due to Arc Erosion of PtIr Contact Materials

By means of breaking tests on PtIr contact materials via a JF04C contact material testing machine, it was attempted to elucidate the characteristics of the various surface morphology and material transfer after the arc erosion process caused by break arc. The material transfer characteristics appeared in the experiments were concluded and analyzed. Meanwhile, the morphology of the anode and cathode surface were observed and analyzed by SEM.

Influence of operation number on arc erosion behavior of Ag/Ni electrical contact materials

Arc erosion behavior of Ag/Ni materials with different operation numbers was investigated by OM,3DOP and SEM.The results indicated that the arc erosion of Ag/10Ni electrical contact material fabricated by sintering−extrusion technology was more and more serious with the operation numbers increasing from 1000 to 40000.With the same operation numbers,the arc erosion on anode was more serious than that on cathode.Besides,the pores preferred to emerge around the arc effect spot during the first 10000 operations.And the morphology of the molten silver on cathode and anode was different due to the action of gravity and arc erosion.Furthermore,the relationships among arc energy,arc time,welding force,electric resistivity,temperature and mass change on contacts were discussed,which indicated that the mass loss on cathode was mainly caused by the fracture of molten bridge.

Research on arc erosion of silver-based alloy contact materials under low voltage,resistive load and small current at 400 Hz and 50 Hz

By using a self-developed IF power and a ASTM contact material experimental system of small-capacity and variable frequency,the value of arcing characteristics and the welding force of the silver-based contact material are acquired under low voltage,resistive load and small current at 400 Hz and 50 Hz. By means of an electricity-ray analytical balance,SEM and EDAX,the weighing values of the contact materials and the changes of AgCdO,AgNi,AgC and AgW contact material surface profile and micro-area constituent are obtained and analyzed. The arc erosion causes of silver-based alloy contact materials at 400 Hz and 50 Hz are also discussed.

Surface contact behavior of functionally graded thermoelectric materials indented by a conducting punch

The contact problem for thermoelectric materials with functionally graded properties is considered.The material properties,such as the electric conductivity,the thermal conductivity,the shear modulus,and the thermal expansion coefficient,vary in an exponential function.Using the Fourier transform technique,the electro-thermoelastic problems are transformed into three sets of singular integral equations which are solved numerically in terms of the unknown normal electric current density,the normal energy flux,and the contact pressure.Meanwhile,the complex homogeneous solutions of the displacement fields caused by the gradient parameters are simplified with the help of Euler’s formula.After addressing the non-linearity excited by thermoelectric effects,the particular solutions of the displacement fields can be assessed.The effects of various combinations of material gradient parameters and thermoelectric loads on the contact behaviors of thermoelectric materials are presented.The results give a deep insight into the contact damage mechanism of functionally graded thermoelectric materials(FGTEMs).

Influence of graphite content on sliding wear characteristics of CNTs-Ag-G electrical contact materials

CNTs-Ag-G electrical contact composite material was prepared by means of powder metallurgical method. The influence of the graphite content on sliding wear characteristics of electrical contact levels was examined. In experiments, CNTs content was retained as 1% (mass fraction), and graphite was added at content levels of 8%, 10%, 13%, 15% and 18%, respectively. The results indicate that with the increase of graphite content, the contact resistance of electrical contacts is enhanced to a certain level then remains constant. Friction coefficient decreases gradually with the increase of graphite content. Wear mass loss decreases to the minimum value then increases. With the small content of graphite, the adhesive wear is hindered, which leads to the decrease of wear mass loss, while excessive graphite brings much more worn debris, resulting in the increase of mass loss. It is concluded that wear mass loss reaches the minimum value when the graphite mass fraction is about 13%. Compared with conventional Ag-G contact material, the wear mass loss of CNTs-Ag-G composite is much less due to the obvious increase of hardness and electrical conductivity, decline of friction surface temperature and inhibition of adhesive wear between composites and slip rings.

Numerical investigation on interface enhancement mechanism of Ag-SnO_(2) contact materials with Cu additive

The electrical contact and mechanical performances of Ag-SnO_(2) contact materials are often improved by additives,especially Cu and its oxides.To reveal the improvement mechanism of metal additive,the effects of Cu nanoparticles on the interface strength and failure behavior of the Ag-SnO_(2) contact materials are investigated by numerical simulations and experiments.Three-dimensional representative volume element(RVE)models for the Ag-SnO_(2) materials without and with Cu nanoparticles are established,and the cohesive zone model is used to simulate the interface debonding process.The results show that the stress−strain relationships and failure modes predicted by the simulation agree well with the experimental ones.The adhesion strengths of the Ag/SnO_(2) and Ag/Cu interfaces are respectively predicted to be 100 and 450 MPa through the inverse method.It is found that the stress concentration around the SnO_(2) phase is the primary reason for the interface debonding,which leads to the failure of Ag-SnO_(2) contact material.The addition of Cu particles not only improves the interface strength,but also effectively suppresses the initiation and propagation of cracks.The results have an reference value for improving the processability of Ag based contact materials.

Properties of CuCr contact materials with low chromium content and fine particles

The voltage withstanding capability and electric conductivity of CuCr contact materials with low chromium content and fine Cr particles were studied. The results show that the withstanding voltage has little relation with the Cr content for the melted casting CuCr alloy within 15%29% Cr content, and that the electric conductivity of the alloy increases with the decreasing of Cr content.

CONTACT MATERIALS FOR GaSb AND InSb: A PHASE DIAGRAM APPROACH

The development of well defined and thermally stable ohmic contacts for Ⅲ- Ⅴ semi-conductors like InSb and GaSb is still a challenging problem in semiconductor devicetechnology. As device processing usually includes the exposure to elevated tempera-tures, interface reactions often occur during metallization and further heat treatment.It is thus important to understand the respective phase equilibria of the involved el-ements. From the thermodynamic point of view, binary and ternary compounds inequilibrium with the respective compound semiconductor would be the best choice forcontact materials as these contacts will be stable even after long exposure to elevatedtemperatures. These possible candidates for contact materials may be directly obtainedfrom the phase diagrams.During the last years we investigated several phase diagrams of transition metals withGaSb and InSb. Experimental results in the systems Ga-Ni-Sb, Ga-Pd-Sb, Ga-Pt-Sb,In-Ni-Sb and In-Pd-Sb are summarized and are discussed in the context of contactchemistry.

INFILTRATION MECHANISM AND QUALITY CONTROL OF CONTACT MATERIALS

The infiltration mechanism, which has great significance for the quality control of electrieal contact material made from W-Cu, W-Ag alloys with high content of tungsten, has been studied. And a directive infiltration technology for improving the product quality and gaining a better economic benefit has been developed.