An Elliptical Microcontact Model Considering Elastic, Elastoplastic, and Plastic Deformation

2003 ◽  
Vol 125 (2) ◽  
pp. 232-240 ◽  
Author(s):  
Yeau-Ren Jeng ◽  
Pei-Ying Wang
Keyword(s):  
Plastic Deformation ◽  
Contact Pressure ◽  
Contact Area ◽  
Contact Model ◽  
Real Area Of Contact ◽  
Elliptical Contact ◽  
The Mean ◽  
Elliptic Contact ◽  
Circular Contact ◽  
Real Area

This study developed an elastic-plastic microcontact model that considers the elliptical contact of surface asperities. In the elastoplastic regime, the relations of the mean contact pressure and contact area of asperity to its contact interference are modeled considering the continuity and smoothness of variables across different modes of deformation. Results obtained from this model are compared with other existing models such as that calculated by the GW, CEB, Zhao and Horng models. The elliptic contact model and circular contact model can deviate considerably in regard to the separation and real area of contact.

Experimental and Theoretical Study of the Contact Mechanics of Five Total Knee Joint Replacements

1995 ◽  
Vol 209 (4) ◽  
pp. 225-231 ◽  
Author(s):  
T Stewart ◽  
Z M Jin ◽  
D Shaw ◽  
D D Auger ◽  
M Stone ◽  
...  
Keyword(s):  
Plastic Deformation ◽  
Knee Joint ◽  
Contact Pressure ◽  
Contact Stress ◽  
Linear Elasticity ◽  
Contact Area ◽  
Elasticity Analysis ◽  
Joint Replacements ◽  
Total Knee ◽  
Maximum Contact

The tibio-femoral contact area in five current popular total knee joint replacements has been measured using pressure-sensitive film under a normal load of 2.5 kN and at several angles of flexion The corresponding maximum contact pressure has been estimated from the measured contact areas and found to exceed the point at which plastic deformation is expected in the ultra-high molecular weight polyethylene (UHMWPE) component particularly at flexion angles near 90°. The measured contact area and the estimated maximum contact stress have been found to be similar in magnitude for all of the five knee joint replacements tested. A significant difference, however, has been found in maximum contact pressure predicted from linear elasticity analysis for the different knee joints. This indicates that varying amounts of plastic deformation occurred in the polyethylene component in the different knee designs. It is important to know the extent of damage as knees with large amounts of plastic deformation are more likely to suffer low cycle fatigue failure. It is therefore concluded that the measurement of contact areas alone can be misleading in the design of and deformation in total knee joint replacements. It is important to modify geometries to reduce the maximum contact stress as predicted from the linear elasticity analysis, to below the linear elastic limit of the plastic component.

Analysis of the Real Area of Contact Between a Polymeric Magnetic Medium and a Rigid Surface

1984 ◽  
Vol 106 (1) ◽  
pp. 26-34 ◽  
Author(s):  
Bharat Bhushan
Keyword(s):  
Complex Modulus ◽  
Critical Value ◽  
Computer Applications ◽  
Hard Material ◽  
Rigid Surface ◽  
Magnetic Medium ◽  
The Real ◽  
Real Area Of Contact ◽  
The Mean ◽  
Real Area

The statistical analysis of the real area of contact proposed by Greenwood and Williamson is revisited. General and simplified equations for the mean asperity real area of contact, number of contacts, total real area of contact, and mean real pressure as a function of apparent pressure for the case of elastic junctions are presented. The critical value of the mean asperity pressure at which plastic flow starts when a polymer contacts a hard material is derived. Based on this, conditions of elastic and plastic junctions for polymers are defined by a “polymer” plasticity index, Ψp which depends on the complex modulus, Poisson’s ratio, yield strength, and surface topography. Calculations show that most dynamic contacts that occur in a computer-magnetic tape are elastic, and the predictions are supported by experimental evidence. Tape wear in computer applications is small and decreases Ψp by less than 10 percent. The theory presented here can also be applied to rigid and floppy disks.

Human Joint Performance and the Roughness of Articular Cartilage

1980 ◽  
Vol 102 (1) ◽  
pp. 50-56 ◽  
Author(s):  
T. R. Thomas ◽  
R. S. Sayles ◽  
I. Haslock
Keyword(s):  
Articular Cartilage ◽  
Heel Strike ◽  
Height Distribution ◽  
Normal Walking ◽  
Cartilage Surface ◽  
Real Area Of Contact ◽  
The Mean ◽  
Human Joints ◽  
Human Joint ◽  
Real Area

It is known that the surface of articular cartilage is rough and it has been suggested that this is likely to affect the lubrication of human joints. This paper describes the direct measurement of a cartilage surface with a stylus instrument. It is found that the height distribution is Gaussian with an inverse-square power spectrum. It is thus possible to calculate the elastic deflection of the surface under normal walking loads and it is shown that the mean separation of the cartilage surfaces in a human joint varies rather slowly with load. In one particular hip joint at heel strike the real area of contact was calculated to be about 1.3 cm2, the mean gap to be about 60 μm and the trapped volume to be about 80 percent of that when standing.

scholarly journals Experimental Investigation of Fully Plastic Contact of a Sphere Against a Hard Flat

2005 ◽  
Vol 128 (2) ◽  
pp. 230-235 ◽  
Author(s):  
J. Jamari ◽  
D. J. Schipper
Keyword(s):  
Experimental Investigation ◽  
Contact Pressure ◽  
Contact Area ◽  
Measurement Method ◽  
Contact Load ◽  
Model Predictions ◽  
The Mean

In this paper we report the experimental investigation to evaluate the published models for the contact of a deformable sphere against a hard flat in the fully plastic contact regime. A new measurement method has been used to measure the contact area. The behavior of the mean contact pressure and the contact area as a function of the contact load are presented. Substantial differences are found between the measurements and the model predictions. A constant value of the mean contact pressure as the load increases is observed, however, the value is lower than the hardness, as often reported. The contact area is found to be a simple truncation of the sphere by a hard flat.

A Numerical Study of the Partial Slip Elliptical Contact under Fretting Conditions

2013 ◽  
Vol 371 ◽  
pp. 576-580 ◽  
Author(s):  
Sergiu Spînu ◽  
Dorin Gradinaru
Keyword(s):  
Contact Area ◽  
State Of The Art ◽  
Numerical Study ◽  
Partial Slip ◽  
Elastic Materials ◽  
Elastic Mismatch ◽  
Numerical Tools ◽  
Elliptical Contact ◽  
Contact Parameters ◽  
Circular Contact

The technologically important elliptical contact undergoing fretting is simulated using previously advanced state-of-the-art numerical tools. The influence of contact ellipse eccentricity on various contact parameters is assessed. An analogy with the circular contact is found when tractions equations are written in dimensionless coordinates in case of similarly elastic materials. However, when an elastic mismatch is introduced, the stick area no longer follows proportionally the established contact area.

A Study of the Average Real Contact Pressure Between Rough Surfaces

2008 ◽  
Author(s):  
Robert L. Jackson ◽  
W. Everett Wilson ◽  
Santosh Angadi
Keyword(s):  
Fatigue Life ◽  
Contact Resistance ◽  
Contact Pressure ◽  
Current Work ◽  
The Real ◽  
Real Contact ◽  
Real Area Of Contact ◽  
Deterministic Methods ◽  
The Relationship ◽  
Real Area

It is well known that the friction, wear, fatigue life, and contact resistance (electrical and thermal) are dependent on the contact between the rough profiles of the surfaces. Several different techniques have been used to model this contact (fractal, wavelet, statistical, multiscale, and deterministic methods). Several of these methods have found that the relationship between the real area of contact and load is linear. This suggests that there is a constant contact pressure between two surfaces (the average real contact pressure). Somewhat surprisingly, several works have found that this pressure may be greater than traditional hardness, even when the contact is heavily loaded and the contacts are deforming plastically. This mechanism is often called the asperity persistence. The current work uses a recent multiscale contact model and other theories to explain this mechanism and to help predict the average real contact pressure, especially during heavily loaded contacts.

Normal and Angular Motions at Rough Planar Contacts During Sliding With Friction

1992 ◽  
Vol 114 (3) ◽  
pp. 567-578 ◽  
Author(s):  
D. P. Hess ◽  
A. Soom
Keyword(s):  
Nonlinear Equations ◽  
Contact Force ◽  
Contact Area ◽  
Normal Contact ◽  
Frictional Contacts ◽  
Normal Contact Force ◽  
The Real ◽  
Real Area Of Contact ◽  
Real Area ◽  
Contact Vibrations

The planar dynamics of a rough block in nominally stationary or sliding contact with a counter-surface is studied in this work. Starting with the Greenwood-Williamson model of a rough surface, the analysis of elastic contact deflections is extended to accommodate angular as well as normal motions. The real area of contact and the normal contact force are obtained in terms of the relative approach and orientation of the surfaces. It is shown that angular and normal motions at frictional contacts are generally coupled. The contact area and normal contact force are shown to be nonlinearly related to the normal and angular motions. However, the contact area remains proportional to the normal load, even in the presence of angular motions. When the friction force is assumed to be proportional to the real area of contact, the coefficient of sliding friction will be unchanged by small relative rotations between the sliding bodies. Based on this contact and friction model, the nonlinear equations of motion that describe the planar contact vibrations of a sliding block can be written directly. Although a detailed analysis of the stability and response characteristics of these nonlinear equations is beyond the scope of the present work, a limited comparison of calculations and measurements taken on both stationary and sliding blocks indicate that the small amplitude contact vibrations are reasonably well captured by the model developed in this work.

Formulas for Moderately Elliptical Hertzian Contacts

1985 ◽  
Vol 107 (4) ◽  
pp. 501-504 ◽  
Author(s):  
J. A. Greenwood
Keyword(s):  
Contact Pressure ◽  
Contact Area ◽  
Hertzian Contact ◽  
Radius Of Curvature ◽  
Asymptotic Equation ◽  
Equivalent Radius ◽  
Circular Contact

For small ellipticities the Hertzian contact pressure and approach can be obtained to a good approximation by using the formulae for circular contact with an equivalent radius of curvature (AB) −1/2, where A and B are the principal relative curvatures. For higher ellipticities (AB(A + B)/2)−1/3 should be used to find the contact area and pressure; an equivalent radius for finding the approach is also given. The ellipticity of the contact can be estimated from the asymptotic equation (a/b) ≈ (B/A)2/3.

On the plastic contact of rough surfaces

1972 ◽  
Vol 327 (1569) ◽  
pp. 159-173 ◽  
Keyword(s):  
Flat Surface ◽  
Rough Surfaces ◽  
Material Constant ◽  
Unexpected Result ◽  
Height Distribution ◽  
Real Area Of Contact ◽  
Soft Surface ◽  
The Mean ◽  
Load Separation ◽  
Real Area

The treatment of plastic contact developed in this paper is based on three physical observations: that the total volume of metal is not changed by plastic deformation; that the mean indentation pressure is a well-defined material constant applicable to the whole range of likely asperity shapes; and that the displaced material reappears as a uniform rise in the non-contacting surface. An energy-balance argument is used to obtain dimensionless relations between the load, separation, and degree of contact, in terms of the height distribution of the surface. A fourth observation is then added: that the height distributions of many engineering surfaces are, to a good approximation, Gaussian. The relations are worked out in detail for this height distribution and compared with experimental observations. The treatment accurately predicts the behaviour up to extremely high loads; and accounts for the remarkable persistence of asperities on rough surfaces in plastic contact. The argument, and the main supporting experiments, were conceived in terms of the contact of a uniformly loaded nominally flat surface, but the extention to local indentations is quite straightforward. It is shown that for local indentations in homogeneous bodies the real area of contact is always one half of the nominal area. This unexpected result is in fact accurately confirmed by experiment. The treatment also discusses the effect of a hard or soft surface layer on the indented body, and again the predictions are supported by practical measurements.

scholarly journals Evaluation of Different Forces for Super Finishing the Internal Surface of Ballizing process

2012 ◽  
Vol 9 (2) ◽  
pp. 197-205
Author(s):  
PAWAN K. UPADHYAY ◽  
H. JOSHI ◽  
PANKAJ AGARWAL
Keyword(s):  
Plastic Deformation ◽  
Fatigue Strength ◽  
Contact Pressure ◽  
Contact Area ◽  
Testing Machine ◽  
Hardened Steel ◽  
Surface Plastic ◽  
Cold Plastic Deformation ◽  
Pressure Force ◽  
Hardened Steels

This paper is an attempt towards comparing experimental and theoretically results of forces obtained by varying interference. with of contact of the Tool and materials , calculated theoretically, may also be helpful for many production and design calculations. The fatigue strength can be increased by 50 to 100% or even more as a result of cold surface plastic deformation. Cold plastic deformation completely eliminates the unwanted stress raisers. Fatigue strength of machine components can be increased by plastic deformation. Various steels, cast irons and non ferrous alloys, all undergo favorable changes in their surface layers form fatigue strength view point as a result of cold plastic deformation. Surface of work piece hardening, perhaps the most effective method of increasing the fatigue strength of machine components. Use of cold plastic deformation increases the wear resistance of machine components. The explanation is that the relationship between the contact area and the force is near linear for these materials, and therefore the contact pressure force as a ratio of force to area is practically constant. In the case of hard metals (for example hardened steels) the significant elasticity causes the contact area to increase more slowly than the force. Therefore the contact pressure force for hardened steels increases with the Ballizing force. As the forces required are excessive, Tensile testing machine .The material of the ball is so selected that it is not suggests 2 to 3 percent interference between the ball and the hole. In the experience Hardened steel balls were used for low carbon, or medium carbon steel bushes. Aluminium bushed and the same hardened steel ball combinations were also used. Ball Ballizing is a mass production process for improving the accuracy and surface finish of holes.

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