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

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Hamid Ghaednia ◽  
Matthew R. W. Brake ◽  
Michael Berryhill ◽  
Robert L. Jackson
Keyword(s):  
Finite Element ◽  
Contact Force ◽  
Material Model ◽  
Real Contact Area ◽  
Contact Radius ◽  
Elastic Contact ◽  
Elastic Deformations ◽  
Real Contact ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

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.

A Finite Element Based Study on the Elastic-Plastic Transition Behavior in a Hemisphere in Contact With a Rigid Flat

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
S. Shankar ◽  
M. M. Mayuram
Keyword(s):  
Finite Element ◽  
Contact Area ◽  
Plastic Material ◽  
Plastic Region ◽  
Real Contact Area ◽  
Real Contact ◽  
Perfectly Plastic ◽  
The Difference ◽  
Elastic Perfectly Plastic ◽  
Green Model

An axisymmetrical hemispherical asperity in contact with a rigid flat is modeled for an elastic perfectly plastic material. The present analysis extends the work (sphere in contact with a flat plate) of Kogut–Etsion Model and Jackson–Green Model and addresses some aspects uncovered in the above models. This paper shows the critical values in the dimensionless interference ratios (ω∕ωc) for the evolution of the elastic core and the plastic region within the asperity for different Y∕E ratios. The present analysis also covers higher interference ratios, and the results are applied to show the difference in the calculation of real contact area for the entire surface with other existing models. The statistical model developed to calculate the real contact area and the contact load for the entire surfaces based on the finite element method (FEM) single asperity model with the elastic perfectly plastic assumption depends on the Y∕E ratio of the material.

Finite element analysis of cyclic indentation of an elastic-perfectly plastic half-space by a rigid sphere

2003 ◽  
Vol 217 (5) ◽  
pp. 505-514 ◽  
Author(s):  
S L Yan ◽  
L Y Li
Keyword(s):  
Finite Element ◽  
Pressure Distribution ◽  
Half Space ◽  
Contact Force ◽  
Contact Radius ◽  
Rigid Sphere ◽  
Perfectly Plastic ◽  
Contact Behaviour ◽  
Cyclic Indentation ◽  
Elastic Perfectly Plastic

This paper presents a numerical study on the cyclic indentation of an elastic-perfectly plastic half-space by a rigid sphere. The study is performed using non-linear finite element methods. Results of contact pressure distribution, relationships between contact force, displacement and contact radius during loading, unloading and reloading are presented. The results show that the deformation during unloading from a contact beyond the elastic limit is perfectly elastic. However, the pressure distribution returns to the Hertzian elliptical distribution only when the maximum pressure at the contact centre is below 1.6αy. The reloading curve is found to be exactly the same as the unloading curve and the pressure distributions in reloading and unloading are the same for the same contact force. The influence of the plastic permanent deformation and residual stresses on the contact behaviour during reloading is discussed.

scholarly journals Use of shakedown maps to assess plastic flow in railway curves

2019 ◽  
Vol 234 (4) ◽  
pp. 417-425
Author(s):  
SJ Hawksbee ◽  
GJ Tucker ◽  
M Burstow
Keyword(s):  
Finite Element Analysis ◽  
Plastic Deformation ◽  
Finite Element ◽  
Plastic Flow ◽  
Material Model ◽  
Element Analysis ◽  
Contact Conditions ◽  
Effective Measure ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Plastic deformation of rails can occur on tight curves, which can significantly reduce the rail life. This paper investigated the phenomena of gross plastic deformation, or plastic flow, using multibody vehicle–track interaction and simplified finite element analysis. The focus is on understanding the contact conditions on the low rail of curves and how these differ from those in shakedown maps. To this end, two trial sites are simulated using multibody vehicle–track software. The contact conditions are then compared against several criteria assumed in the derivation of the shakedown maps. A further assumption implicit in the shakedown maps is also investigated by a non-linear finite element analysis. In this case, a more realistic Chaboche material model is used as opposed to the simple linear elastic–perfectly plastic model in the shakedown theory. The results of the finite element analysis are combined with a bespoke indicator of plastic flow to assess the influence of distance to shakedown limits on the likely plastic flow. Finally, a simple interpolation scheme is used to map the finite element results back to the trial sites. The interpolated results for the sites are used to evaluate the influence of running speed and different levels of wheel profile wear. Results suggest that the bespoke indicator defined in this work can be used as an effective measure of plastic flow; this measure is then used to quantify the influence of cant excess on the rates of plastic flow.

Unloading Process in Elastic-Plastic Contact of a Rough Surface With a Flat

2008 ◽  
Author(s):  
A. Sepehri ◽  
K. Farhang
Keyword(s):  
Finite Element ◽  
Rough Surface ◽  
Contact Force ◽  
Contact Area ◽  
Three Dimensional ◽  
Integral Form ◽  
Real Contact Area ◽  
Elastic Plastic ◽  
Real Contact ◽  
Approximate Equations

Three dimensional elastic-plastic contact of a nominally flat rough surface and a flat is considered. The asperity level Finite Element based constitutive equations relating contact force and real contact area to the interference is used. The statistical summation of asperity interaction during unloading phase is derived in integral form. Approximate equations are found that describe in closed form contact load as a function of mean plane separation during unloading. The approximate equations provide accuracy to within 6 percent for the unload phase of the contact force.

Contact Analysis of Tire Tread Rubber on Flat Surface with Microscopic Roughness3

2006 ◽  
Vol 34 (4) ◽  
pp. 237-255 ◽  
Author(s):  
M. Kuwajima ◽  
M. Koishi ◽  
J. Sugimura
Keyword(s):  
Surface Roughness ◽  
Finite Element ◽  
Sliding Friction ◽  
Tangential Force ◽  
Partial Slip ◽  
Real Contact Area ◽  
Element Analysis ◽  
Real Contact ◽  
Local Slip ◽  
Tread Rubber

Abstract This paper describes experimental and analytical studies of the dependence of tire friction on the surface roughness of pavement. Abrasive papers were adopted as representative of the microscopic surface roughness of pavement surfaces. The rolling∕sliding friction of tire tread rubber against these abrasive papers were measured at low slip velocities. Experimental results indicated that rolling∕sliding frictional characteristics depended on the surface roughness. In order to examine the interfacial phenomena between rubber and the abrasive papers, real contact length, partial slip, and apparent friction coefficient under vertical load and tangential force were analyzed with two-dimensional explicit finite element analysis in which slip-velocity-dependent frictional coefficients were considered. Finite element method results indicated that the sum of real contact area and local partial slip were larger for finer surfaces under the same normal and tangential forces. In addition, the velocity-dependent friction enhanced local slip, where the dependence of local slip on surface roughness was pronounced. It proved that rolling∕sliding friction at low slip ratio was affected by local frictional behavior at microslip regions at asperity contacts.

Elasto-Plastic Coupled Temperature-Displacement Finite Element Analysis of Two-Dimensional Rolling-Sliding Contact With a Translating Heat Source

1991 ◽  
Vol 113 (1) ◽  
pp. 93-101 ◽  
Author(s):  
S. M. Kulkarni ◽  
C. A. Rubin ◽  
G. T. Hahn
Keyword(s):  
Finite Element ◽  
Half Space ◽  
Plastic Material ◽  
Element Model ◽  
Rolling Contact ◽  
Two Dimensional ◽  
Element Analysis ◽  
Element Mesh ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

The present paper, describes a transient translating elasto-plastic thermo-mechanical finite element model to study 2-D frictional rolling contact. Frictional two-dimensional contact is simulated by repeatedly translating a non-uniform thermo-mechanical distribution across the surface of an elasto-plastic half space. The half space is represented by a two dimensional finite element mesh with appropriate boundaries. Calculations are for an elastic-perfectly plastic material and the selected thermo-physical properties are assumed to be temperature independent. The paper presents temperature variations, stress and plastic strain distributions and deformations. Residual tensile stresses are observed. The magnitude and depth of these stresses depends on 1) the temperature gradients and 2) the magnitudes of the normal and tangential tractions.

A limit load solution for a thick-walled cylinder with a fully circumferential crack under axial tension

2009 ◽  
Vol 44 (6) ◽  
pp. 407-416 ◽  
Author(s):  
P J Budden ◽  
Y Lei
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Yield Criterion ◽  
Limit Load ◽  
Cylinder Wall ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Von Mises ◽  
Inside Radius ◽  
Walled Cylinder

Limit loads for a thick-walled cylinder with an internal or external fully circumferential surface crack under pure axial load are derived on the basis of the von Mises yield criterion. The solutions reproduce the existing thin-walled solution when the ratio between the cylinder wall thickness and the inside radius tends to zero. The solutions are compared with published finite element limit load results for an elastic–perfectly plastic material. The comparison shows that the theoretical solutions are conservative and very close to the finite element data.

scholarly journals A 3D study of the contact surface developed by the contact between the tires and the structural pavements

Exacta ◽  
2009 ◽  
Vol 6 (2) ◽  
pp. 197-208
Author(s):  
Alex Alves Bandeira ◽  
Rita Moura Fortes ◽  
João Virgílio Merighi
Keyword(s):  
Finite Element ◽  
Contact Mechanics ◽  
Contact Area ◽  
Augmented Lagrangian Method ◽  
Numerical Results ◽  
Real Contact Area ◽  
The Real ◽  
Real Contact ◽  
Commercial Program ◽  
Contact Surfaces

The basic aim in this work is to present a new technique to analyze the contact surfaces developed by the contact between the tires and the structural pavements by numerical simulations, using 3D finite element formulations with contact mechanics. For this purpose, the Augmented Lagrangian method is used. This study is performed just putting the tires on the structural pavement. These tires and the structural pavement are discretized by finite elements under large 3D elastoplastic deformation. The real loads (of aircrafts, trucks or cars) are applied directly on each tire and by contact mechanics procedures, the real contact area between the tires and the pavement surface is computed. The penetration conditions and the contact interfaces are investigated in details. Furthermore, the pressure developed at the contact surfaces is automatically calculated and transferred to the structural pavement by contact mechanics techniques. The purpose of this work research is to show that the contact area is not circular and the finite element techniques can calculate automatically the real contact area, the real geometry and its stresses and strains. In the end of this work, numerical results in terms of geometry, stress and strain are presented and compared to show the ability of the algorithm. These numerical results are also compared with the numerical results obtained by the commercial program ANSYS.

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