Periodic Contact Problems in Plane Elasticity: The Fracture Mechanics Approach

2017 ◽  
Vol 140 (1) ◽  
Author(s):  
Yang Xu ◽  
Robert L. Jackson
Keyword(s):  
Fracture Mechanics ◽  
Contact Region ◽  
Contact Problems ◽  
Plane Elasticity ◽  
Partial Slip ◽  
Tangential Load ◽  
Normal Contact ◽  
Material Contact ◽  
Interfacial Gap ◽  
Simply Connected

In this study, the concept of the fracture mechanics is used to solve the: (i) frictionless purely normal contact and (ii) the similar material contact under the mutual actions of the normal and tangential load. Considering the contact region is simply connected, the out-of-contact regions can be treated as periodic collinear cracks. Through evaluating the stress intensity factor (SIF), we are able to obtain the size and location of the contact/out-of-contact region. Then, the normal traction, shear traction and interfacial gap can be directly determined by the Green's function of the periodic collinear crack. In the case of frictionless purely normal contact, the new approach is applied to two classic problems, namely, the Westergaard problem (sinusoidal waviness punch) and the periodic flat-end punch problem. Then, the sinusoidal waviness contact pair in the full stick and the partial slip conditions under the mutual actions of the normal and tangential loads are solved by the newly developed approach.

The Calculation and Analysis for the Independent Wheels of Tramcar

2014 ◽  
Vol 577 ◽  
pp. 297-300 ◽  
Author(s):  
He Ma ◽  
Jun Zhang ◽  
Xiu Juan Zhang
Keyword(s):  
Contact Region ◽  
Contact Problems ◽  
Attack Angle ◽  
Von Mises Stress ◽  
Wheel Wear ◽  
Normal Contact ◽  
Normal Contact Force ◽  
Straight Line ◽  
Contact Models ◽  
Von Mises

The wheel/rail profiles in different wear stages are measured using the apparatus of wheel-rail profile. The 3D elastic-plastic FEM contact models are established for the straight line and curves, in which attack angle is considered. Contact problems between the wheels in different wear stages and the worn rail are studied. Contact area, normal contact force, and equivalent Von Mises stress of different cases are analyzed. The obtained results show that the maximum equivalent Von Mises stress reduces and tends to be steady with the independent wheel wearing. Widening the track gauge can have an influence on the variation of wheel wear positions and the wear rules between wheel and rail. When the wheel with a certain attack angle contacts with rail, the maximum equivalent Von Mises stress appears at the contact region between the flange and rail side. The influence of attack angle on the wear between the wheel and rail is quite serious. It is very important to do the research for the further optimization and design of the wheel/rail profiles.

A New Approach to Calculation of Contact Characteristics

1999 ◽  
Vol 121 (1) ◽  
pp. 20-27 ◽  
Author(s):  
O. G. Chekina ◽  
L. M. Keer
Keyword(s):  
Rough Surfaces ◽  
Contact Region ◽  
Contact Problems ◽  
Surface Shape ◽  
Real Contact Area ◽  
Iteration Algorithm ◽  
Normal Contact Stress ◽  
Normal Contact ◽  
The Real ◽  
Integral Relations

A new method of calculation of contact characteristics for rough surfaces is proposed based on integral relations that express the normal contact stress as an explicit function of the surface shape. To produce calculations by this method, a region having a simple shape should be chosen first, where the contact is supposed to be nominally complete. An iterative procedure with regard to the shape is applied within the load-free surface portion, and allows the normal stresses, surface displacement and the real area of contact to be determined. The method is applicable to rough bodies of arbitrary shape for which the half-space formulation and equivalent roughness concepts apply; the real contact area should lie within the initially chosen contact region and can include a system of unconnected contact spots. Both 2D and 3D cases are considered in the present work. The 2D analysis is based on known integral relations for nonperiodic and periodic contact problems. In the 3D case, new analytical relations are obtained and their properties are analyzed. An iteration algorithm based on these relations and its efficient numerical implementation are described. Application of the method to the contact of real rough surfaces is discussed.

Axisymmetric partial slip contact of a functionally graded piezoelectric coating under a conducting punch

2016 ◽  
Vol 28 (14) ◽  
pp. 1925-1940 ◽  
Author(s):  
Jie Su ◽  
Liao-Liang Ke ◽  
Yue-Sheng Wang
Keyword(s):  
Electric Charge ◽  
Contact Region ◽  
Functionally Graded ◽  
Partial Slip ◽  
Perfect Conductor ◽  
Stick Slip ◽  
Normal Contact ◽  
Functionally Graded Piezoelectric Materials ◽  
Slip Region ◽  
Functionally Graded Piezoelectric

This article considered the axisymmetric partial slip contact problem of a functionally graded piezoelectric coated half-space indented by a rigid spherical punch subjected to a normal load. It is assumed that the punch within the contact region is a perfect conductor with a constant electric potential. The electro-mechanical properties of the functionally graded piezoelectric materials vary exponentially along the thickness direction. The whole contact region consists of an inner circular stick region surrounded by an outer annular slip region obeying Coulomb’s law of friction. The problem is reduced to a set of coupled Cauchy singular integral equations by employing the Hankel integral transform. An iterative method is used to determine the unknown stick/slip region, normal contact pressure, electric charge, and radial tangential traction. The effects of the resultant electric charge, friction coefficient, and gradient index on the surface electro-mechanical fields are presented in detail.

On Some Unbonded Contact Problems in Plane Elasticity Theory

1976 ◽  
Vol 43 (2) ◽  
pp. 263-267 ◽  
Author(s):  
G. M. L. Gladwell
Keyword(s):  
Integral Equation ◽  
Elasticity Theory ◽  
Contact Pressure ◽  
Chebyshev Polynomials ◽  
Contact Region ◽  
Contact Problems ◽  
Elastic Cylinder ◽  
Plane Elasticity ◽  
Elastic Strip ◽  
Plane Elasticity Theory

Paper considers plane, frictionless, unbonded contact problems. It is shown that the integral equation relating the unknown contact pressure to the specified displacement in the contact region may be solved approximately by using an expansion in terms of Chebyshev polynomials. Three examples are chosen, a beam resting on a half plane, a rigid cylinder pressed into an elastic strip, and an elastic cylinder pressed between rigid planes. Graphs of results are presented.

Modeling Tangential Contact of Rough Surfaces With Elastic- and Plastic-Deformed Asperities

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Dong Wang ◽  
Chao Xu ◽  
Qiang Wan
Keyword(s):  
Rough Surface ◽  
Normal Load ◽  
Experimental Results ◽  
Partial Slip ◽  
Tangential Load ◽  
Stick Slip ◽  
Normal Contact ◽  
Tangential Contact ◽  
Bilinear Relation ◽  
Proposed Model

A new tangential contact model between a rough surface and a smooth rigid flat is proposed in this paper. The model considers the contribution of both elastically deformed asperities and plastically deformed asperities to the total tangential load of rough surface. The method combining the Mindlin partial slip solution with the Hertz solution is used to model the contact formulation of elastically deformed asperities, and for the plastically deformed asperities, the solution combining the fully plastic theory of normal contact with the bilinear relation between the tangential load and deformation developed by Fujimoto is implemented. The total tangential contact load is obtained by Greenwood and Williamson statistical analysis procedure. The proposed model is first compared to the model considering only elastically deformed asperities, and the effect of mean separation and plasticity index on the relationship between the tangential load and deformation is also investigated. It is shown that the present model can be used to describe the stick–slip behavior of the rough surface, and it is a more realistic-based model for the tangential rough contact. A comparison with published experimental results is also made. The proposed model agrees very well with the experimental results when the normal load is small, and shows an error when the normal load is large.

scholarly journals Viscoelastic Effects during Tangential Contact Analyzed by a Novel Finite Element Approach with Embedded Interface Profiles

Lubricants ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 107
Author(s):  
Jacopo Bonari ◽  
Marco Paggi
Keyword(s):  
Finite Elements ◽  
Contact Problem ◽  
Finite Thickness ◽  
Viscoelastic Model ◽  
Contact Problems ◽  
Partial Slip ◽  
Viscoelastic Layer ◽  
Model Approximation ◽  
Normal Contact ◽  
Viscoelastic Effects

A computational approach that is based on interface finite elements with eMbedded Profiles for Joint Roughness (MPJR) is exploited in order to study the viscoelastic contact problems with any complex shape of the indenting profiles. The MPJR finite elements, previously developed for partial slip contact problems, are herein further generalized in order to deal with finite sliding displacements. The approach is applied to a case study concerning a periodic contact problem between a sinusoidal profile and a viscoelastic layer of finite thickness. In particular, the effect of using three different rheological models that are based on Prony series (with one, two, or three arms) to approximate the viscoelastic behaviour of a real polymer is investigated. The method allows for predicting the whole transient regime during the normal contact problem and the subsequent sliding scenario from full stick to full slip, and then up to gross sliding. The effects of the viscoelastic model approximation and of the sliding velocities are carefully investigated. The proposed approach aims at tackling a class of problems that are difficult to address with other methods, which include the possibility of analysing indenters of generic profile, the capability of simulating partial slip and gross slip due to finite slidings, and, finally, the possibility of simultaneously investigating dissipative phenomena, like viscoelastic dissipation and energy losses due to interface friction.

On the Static-Kinetic Friction Transition in Dry Contact of Rough Surfaces

2011 ◽  
Author(s):  
K. Farhang ◽  
D. Segalman ◽  
M. Starr
Keyword(s):  
Large Scale ◽  
Rough Surfaces ◽  
Tangential Force ◽  
Static Friction ◽  
Partial Slip ◽  
Small Scale ◽  
Asperity Contact ◽  
Kinetic Friction ◽  
Tangential Load ◽  
Asperity Contacts

This paper shows that the Mindlin problem involving two spheres in contact under the action of oscillating tangential force can lead to the account of static-kinetic friction transition. In Mindlin’s problem two spheres experience partial slip as a result of application of oscillating tangential load. When the problem is extended to multi-sphere contact, i.e. two rough surfaces, the application of tangential oscillating load results in partial slip for some asperity contacts while others experience full slip. Increase in the amplitude of the oscillating tangential force results in more contacts experiencing full slip, thereby decreasing the number of contacts in parial slip. Constitutive relation proposed by Mindlin at small scale, governing asperity interaction, is used to obtain the large scale slip function through a statistical summation of asperity scale events. The slip function establishes the fraction of asperity contact in full slip. The complement of the slip parameter is a fraction of asperities in partial slip. Through slip function it is shown that it is possible to define a slip condition for the entire surface. The derivation of the slip function allows the account of transition between static friction and kinetic friction.

Interaction Model for “Shelled Particles” and Small-Strain Modulus of Granular Materials

2018 ◽  
Vol 85 (10) ◽  
Author(s):  
Shun-hua Zhou ◽  
Peijun Guo ◽  
Dieter F. E. Stolle
Keyword(s):  
Elastic Modulus ◽  
Contact Stiffness ◽  
Scaling Law ◽  
Interaction Model ◽  
Contact Problems ◽  
Hertzian Contact ◽  
Spherical Particles ◽  
Thin Coating ◽  
Normal Contact ◽  
Laboratory Test Results

The elastic modulus of a granular assembly composed of spherical particles in Hertzian contact usually has a scaling law with the mean effective pressure p as K∼G∼p1/3. Laboratory test results, however, reveal that the value of the exponent is generally around 1/2 for most sands and gravels, but it is much higher for reclaimed asphalt concrete composed of particles coated by a thin layer of asphalt binder and even approaching unity for aggregates consisting of crushed stone. By assuming that a particle is coated with a thin soft deteriorated layer, an energy-based simple approach is proposed for thin-coating contact problems. Based on the features of the surface layer, the normal contact stiffness between two spheres varies with the contact force following kn∼Fnm and m∈[1/3,  1], with m=1/3 for Hertzian contact, m=1/2 soft thin-coating contact, m=2/3 for incompressible soft thin-coating, and m=1 for spheres with rough surfaces. Correspondingly, the elastic modulus of a random granular packing is proportional to pm with m∈[1/3,  1].

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