Numerical Investigation of the Plastic Contact Deformation between Hemispheres: Variation of Radii Ratio and Normal Loads

2015 ◽  
Vol 1123 ◽  
pp. 16-19
Author(s):  
Rifky Ismail ◽  
T. Prasojo ◽  
Mohammad Tauviqirrahman ◽  
J. Jamari ◽  
D.J. Schipper
Keyword(s):  
Plastic Deformation ◽  
Normal Load ◽  
Asperity Contact ◽  
Frictionless Contact ◽  
Finite Element Software ◽  
Total Displacement ◽  
Perfectly Plastic ◽  
Deformation Ratio ◽  
Elastic Perfectly Plastic ◽  
Local Plastic Deformation

Investigation of local plastic deformation between rough surfaces in mechanical components such as gears, camshaft and bearings is very important. Contact between real surfaces occurs at the summits of the highest asperities which vary in height and radius. The plastic deformation of the contact between two asperities was studied in this paper. Asperity contact was modelled as a contact between hemispheres. The commercial finite element software, ABAQUS, was employed to perform the numerical contact analysis of the elastic perfectly-plastic deforming hemispheres with the ratios of radii (R2/R1) from 1 to 7. Normal loads of 5000 N, 8000 N and 11000 N were applied to the frictionless contact of the hemispheres. It was shown that the plastic deformation ratio (ωp1/ωp2) decreases as the radii ratio increases. The higher normal load showed a lower plastic deformation ratio for high radii ratio. The results indicate that the radii ratio contributes to the severity of the plastic deformation and the total displacement of the contacting asperities.

Crushing of an Elastic-Perfectly Plastic Ring or Tube Between Two Planes

1987 ◽  
Vol 54 (1) ◽  
pp. 159-164 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Plastic Deformation ◽  
Numerical Integration ◽  
Mathematical Problem ◽  
Plastic Ring ◽  
Perfectly Plastic ◽  
Analytical Approximations ◽  
Original Shape ◽  
Thin Ring ◽  
Elastic Perfectly Plastic

A thin ring is crushed between two rigid planes. Due to plastic deformation the ring does not recover its original shape when the compression is removed. For an elastic-perfectly plastic flexural material, the ring undergoes two to five different stages. The mathematical problem is formulated and solved by exact numerical integration and accurate analytical approximations.

Elasto-Plastic Asperity Contacts of Layered Media

2005 ◽  
Author(s):  
Qin Xie ◽  
Geng Liu ◽  
Tianxiang Liu ◽  
Ruiting Tong ◽  
Quanren Zeng
Keyword(s):  
Yield Criterion ◽  
Layered Media ◽  
Asperity Contact ◽  
Initial Stiffness ◽  
Programming Technique ◽  
Perfectly Plastic ◽  
Real Area Of Contact ◽  
Asperity Contacts ◽  
Elastic Perfectly Plastic ◽  
Von Mises

An elasto-plastic asperity contact model for layered media is developed in the work reported in this paper to analyze the influences of coating-substrate materials on contact when yielding and the strain-hardening properties of materials are taken into account. The finite element method, the initial stiffness method and the mathematical programming technique are employed to solve the model. The von Mises yield criterion is used to determine the inception of plastic deformation. The effects of different layer thickness and different coating-substrate materials on the contact pressure, real area of contact, average gap of rough surface, and stresses in layer and substrate under the elastic-perfectly-plastic and the elasto-plastic contact conditions are numerically investigated and discussed.

A Finite Element Study of Elasto-Plastic Hemispherical Contact

2003 ◽  
Author(s):  
Robert L. Jackson ◽  
Itzhak Green
Keyword(s):  
Finite Element ◽  
Yield Strength ◽  
Constant Factor ◽  
Elastic Model ◽  
Asperity Contact ◽  
Finite Element Study ◽  
Perfectly Plastic ◽  
Wide Range ◽  
Elastic Perfectly Plastic ◽  
Element Study

This work presents a finite element study of elasto-plastic hemispherical contact. The results are normalized such that they are valid for macro contacts (e.g., rolling element bearings) and micro contacts (e.g., asperity contact). The material is modeled as elastic-perfectly plastic. The numerical results are compared to other existing models of spherical contact, including the fully plastic case (known as the Abbott and Firestone model) and the perfectly elastic case (known as the Hertz contact). At the same interference, the area of contact is shown to be larger for the elasto-plastic model than that of the elastic model. It is also shown, that at the same interference, the load carrying capacity of the elasto-plastic modeled sphere is less than that for the Hertzian solution. This work finds that the fully plastic average contact pressure, or hardness, commonly approximated to be a constant factor (about three) times the yield strength, actually varies with the deformed contact geometry, which in turn is dependant upon the material properties (e.g., yield strength). The results are fit by empirical formulations for a wide range of interferences and materials for use in other applications.

scholarly journals Thermo-Mechanical Modeling of Distortions Promoted during Cooling of Ti-6Al-4V Part Produced by Superplastic Forming

2016 ◽  
Vol 838-839 ◽  
pp. 196-201
Author(s):  
Maxime Rollin ◽  
Vincent Velay ◽  
Luc Penazzi ◽  
Thomas Pottier ◽  
Thierry Sentenac ◽  
...  
Keyword(s):  
Finite Element ◽  
Thermal Stresses ◽  
Superplastic Forming ◽  
Model Material ◽  
Material Behavior ◽  
Mechanical Modeling ◽  
Temperature Dependent ◽  
Finite Element Software ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

In AIRBUS, most of the complex shaped titanium fairing parts of pylon and air inlets are produced by superplastic forming (SPF). These parts are cooled down after forming to ease their extraction and increase the production rate, but AIRBUS wastes a lot of time to go back over the geometric defects generated by the cooling step. This paper investigates the simulations of the SPF, cooling and clipping operations of a part on Abaqus® Finite element software. The different steps of the global process impact the final distortions. SPF impacts the thickness and the microstructure/behavior of material, cooling impacts also the microstructure/behavior of material and promotes distortions through thermal stresses and finally, clipping relaxes the residual stresses of the cut part. An elastic-viscoplastic power law is used to model material behavior during SPF and a temperature dependent elastic perfectly plastic model for the cooling and clipping operations.

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.

Nonuniqueness in Contained Plastic Deformation

1980 ◽  
Vol 47 (2) ◽  
pp. 273-277 ◽  
Author(s):  
P. G. Hodge ◽  
D. L. White
Keyword(s):  
Plastic Deformation ◽  
Boundary Value Problem ◽  
Yield Point ◽  
Displacement Field ◽  
Point Load ◽  
Point Of View ◽  
Computational Point ◽  
Plastic Structure ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

It is well known that in a well-defined load-controlled boundary-value problem for an elastic/perfectly-plastic structure the displacements are unique if the structure is everywhere elastic, and they are not unique at the yield-point load when the structure becomes a mechanism. The present paper is concerned with the range of contained plastic deformation between these two extremes. Several examples are given in which more than one displacement field exists for loads less than the yield-point load. The significance of this phenomenon is commented on from a physical, mathematical, and computational point of view.

Causes and Consequences of Nonuniqueness in an Elastic/Perfectly-Plastic Truss

1986 ◽  
Vol 53 (2) ◽  
pp. 235-241 ◽  
Author(s):  
P. G. Hodge ◽  
K.-J. Bathe ◽  
E. N. Dvorkin
Keyword(s):  
Plastic Deformation ◽  
Plastic Material ◽  
Complete Solution ◽  
Physical Modelling ◽  
Equilibrium Equations ◽  
First Order ◽  
Perfectly Plastic ◽  
Points Of View ◽  
Elastic Perfectly Plastic

A complete solution to collapse is given for a three-bar symmetric truss made of an elastic/perfectly-plastic material, using linear statics and kinematics, and the solution is found to be partially nonunique in the range of contained plastic deformation. The introduction of a first-order deviation from symmetry and/or the inclusion of first-order nonlinear terms in the equilibrium equations is found to restore uniqueness. The significance of these effects is analyzed and discussed from mathematical, physical, modelling, computational, and engineering points of view.

A Computational Study of Dry Static Friction Between Elastoplastic Surfaces Using a Statistically Homogenized Microasperity Model

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Bhargava Sista ◽  
Kumar Vemaganti
Keyword(s):  
Computational Model ◽  
Computational Study ◽  
Normal Load ◽  
Static Friction ◽  
Parametric Representation ◽  
Physical Parameters ◽  
Additional Parameter ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic ◽  
Adhesive Forces

Friction is a complex phenomenon that arises from the interaction of deforming surface microasperities and adhesive forces at very small length scales. In this work, we use a computational model to understand the effects of various physical parameters on the friction response between two similar linearly elastic-perfectly plastic surfaces. The main ingredients of the computational model are a statistical model of the surface based on a Gaussian autocorrelation function (ACF), a parametric representation of the normal and shear responses of a single microasperity, and a statistical homogenization procedure to compute the overall friction response. The surfaces are assumed to be isotropic in nature. We employ this computational model to develop constitutive relationships for the friction force and coefficient of friction for Aluminum 6061 and stainless steel surfaces. We study the effects of various quantities such as surface roughness, material properties, normal load, and adhesive forces on the overall friction response. Our results show that the model is able to capture a wide variety of friction responses. Our results also suggest that the root mean squared (RMS) roughness of the surface alone is insufficient to describe the friction characteristics of a surface, and that an additional parameter is needed. We propose one such parameter, the aspect ratio, which is the ratio of the RMS roughness to the correlation length.

Mechanical and Thermodynamic Considerations of an Assemblage of Homogeneous Elastic-Plastic States

1968 ◽  
Vol 35 (3) ◽  
pp. 596-603 ◽  
Author(s):  
David Rubin
Keyword(s):  
Plastic Deformation ◽  
Mechanical Behavior ◽  
Strain Energy ◽  
Material Behavior ◽  
Free State ◽  
Elastic Plastic ◽  
Elastic Range ◽  
Perfectly Plastic ◽  
Stress Free State ◽  
Elastic Perfectly Plastic

The mechanics and the thermodynamics of plastic deformation are considered in terms of a general assemblage or continuum of elastic, perfectly plastic elements or states. Such models not only match the external mechanical behavior of real materials structures and continua, but they also afford a simple thermodynamic definability. A consideration of the internal behavior shows that the stress-free state has the maximum elastic range. Hardening in the sense of an increasing macroscopic elastic range is accompanied by a release of stored strain energy; the stress-free state always is restorable. This behavior is appropriate for real structures and continua. However, it is precisely these continuum characteristics which make the assemblages inappropriate models of material behavior. Barriers to continuing plastic deformation are required which do exist on the microscale, but lie outside of the scope of the most complex of these thermodynamically well-defined assemblages.

Finite Element Based Unloading of an Elastic Plastic Spherical Stick Contact for Varying Tangent Modulus and Hardening Rule

2013 ◽  
Vol 1 (1) ◽  
pp. 13-32
Author(s):  
Biplab Chatterjee ◽  
Prasanta Sahoo
Keyword(s):  
Finite Element ◽  
Plastic Material ◽  
Kinematic Hardening ◽  
Tangent Modulus ◽  
Isotropic Hardening ◽  
Finite Element Software ◽  
Perfectly Plastic ◽  
Hardening Models ◽  
Qualitative Similarity ◽  
Elastic Perfectly Plastic

Loading-unloading behavior of a deformable sphere with a rigid flat under full stick contact condition is investigated for varying strain hardening. The study considers various tangent modulus using the finite element software ANSYS. Both the bilinear kinematic hardening and isotropic hardening models are considered. Numerical simulation reveals the qualitative similarity between kinematic and isotropic hardening regarding the variation of interfacial parameters during loading-unloading for various tangent modulus. It is found that the material with kinematic hardening dissipates more energy than the material with isotropic hardening during unloading. However for elastic perfectly plastic material, the loading-unloading behavior is insensitive to hardening model.

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