A complete elastic-plastic spherical asperity contact model with the effect of isotropic strain hardening

2020 ◽  
pp. 135065012092989 ◽  
Author(s):  
A Megalingam ◽  
KS Hanumanth Ramji
Keyword(s):  
Strain Hardening ◽  
Rough Surface ◽  
Contact Area ◽  
Poisson’S Ratio ◽  
Combined Effect ◽  
Contact Model ◽  
Poisson's Ratio ◽  
Contact Load ◽  
Asperity Contact ◽  
Strain Hardening Rate

Understanding the deformation behavior of rough surface contacts is essential to minimise the tribological consequences of contacts. Mostly, statistical, deterministic and fractal approaches are adopted to explore the contact of rough surfaces. In statistical approach, a single asperity contact model is developed and extended to the whole surface. In the present work, a deformable spherical asperity contact with a rigid flat is modeled and analysed by accounting the combined effect of Young’s modulus, Poisson’s ratio, yield strength and isotropic strain hardening rate using finite element method. The results reveal that the elastic, elastoplastic and plastic contact states are highly influenced by E/Y ratio and strain hardening rate followed by Poisson’s ratio. The dimensionless contact radius is an inadequate parameter to explore the combined effect of material properties. For all E/Y ratio and Poisson’s ratio, as the strain hardening rate increases, the dimensionless contact area decreases for the same dimensionless contact load at elastoplastic and fully plastic contact states. As the strain hardening rate increases, the fully plastic contact state is reached at low dimensionless interference compared to elastic perfectly plastic materials for all E/Y ratio and Poisson’s ratio. For a common elastic-plastic material, empirical relations are developed to calculate the contact load and contact area appropriately with E/Y ratio, Poisson’s ratio and interference ratio as input variables. It can be utilised to study the interaction of rough surface contacts for most of the practical materials.

Comparative Contact Analysis Study of Finite Element Method Based Deterministic, Simplified Multi-Asperity and Modified Statistical Contact Models

2012 ◽  
Vol 134 (1) ◽  
Author(s):  
A. Megalingam ◽  
M. M. Mayuram
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rough Surface ◽  
Contact Area ◽  
Model Analysis ◽  
Contact Model ◽  
Contact Load ◽  
Asperity Contact ◽  
Single Asperity ◽  
Contact Models

The study of the contact stresses generated when two surfaces are in contact plays a significant role in understanding the tribology of contact pairs. Most of the present contact models are based on the statistical treatment of the single asperity contact model. For a clear understanding about the elastic-plastic behavior of two rough surfaces in contact, comparative study involving the deterministic contact model, simplified multi-asperity contact model, and modified statistical model are undertaken. In deterministic contact model analysis, a three dimensional deformable rough surface pressed against a rigid flat surface is carried out using the finite element method in steps. A simplified multi-asperity contact model is developed using actual summit radii deduced from the rough surface, applying single asperity contact model results. The resultant contact parameters like contact load, contact area, and contact pressure are compared. The asperity interaction noticed in the deterministic contact model analysis leads to wide disparity in the results. Observing the elastic-plastic transition of the summits and the sharing of contact load and contact area among the summits, modifications are employed in single asperity statistical contact model approaches in the form of a correction factor arising from asperity interaction to reduce the variations. Consequently, the modified statistical contact model and simplified multi-asperity contact model based on actual summit radius results show improved agreement with the deterministic contact model results.

Elastic–Plastic Multi-Asperity Contact Analysis of Cylinder-on-Flat Configuration

2007 ◽  
Vol 129 (2) ◽  
pp. 292-304 ◽  
Author(s):  
V. Sabelkin ◽  
S. Mall
Keyword(s):  
Rough Surface ◽  
Contact Area ◽  
Plastic Material ◽  
Material Behavior ◽  
Contact Load ◽  
Graphical Form ◽  
Complex Nature ◽  
Asperity Contact ◽  
Elastic Plastic ◽  
Elastic Plastic Material

The contact interaction between a rough cylindrical body (i.e., with asperities) and a deformable smooth flat was investigated using the finite-element analysis. Analysis included both elastic–plastic deformation and friction. Further, the effects of several parameters of rough surface on the evolution of the contact area with increasing contact load were investigated. These were radius, number, constraint, and placement of asperities. Contact area of rough surface is smaller than its counterpart of smooth surface, and this decrease depends on number, radius, constraint, and placement of asperities. The elastic material behavior results in considerably smaller contact area than that from elastic–plastic material behavior. The evolution of contact area with increasing contact load is of the complex nature with elastic–plastic material deformation since the yielded region widens and/or deepens with increasing load depending on number, radius, and constraint of asperities. The effect of constraint on the asperity depends upon its nature (i.e., from either sides or one side) and radius of the asperity. The effects of these several parameters on the contact area versus applied load relationships are expressed in the graphical form as well as in terms of equations wherever possible.

A Reexamination of the Extraction of Material Properties Using Nanoindentation

2008 ◽  
Author(s):  
B. Poon ◽  
D. Rittel ◽  
G. Ravichandran
Keyword(s):  
Contact Area ◽  
Material Properties ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Nanoindentation Test ◽  
Displacement Curve ◽  
Elastic Solids ◽  
Ratio Effect ◽  
Elastic Plastic ◽  
Tip Radius

The paper reexamines the extraction of material properties using nanoindentation for linearly elastic and elastic-plastic materials. The paper considers indentation performed using a rigid conical indenter, as follows. Linearly elastic solids: The reduction of nanoindentation test data of elastic solids is usually processed using Sneddon’s relation [1], which assumes a linearly elastic infinite half space and an infinitely sharp indenter tip. These assumptions are violated in practical indentation experiments. Since most of the research on the extraction of material properties relies heavily on numerical simulations, we used them to investigate the specimen dimensions required for it to qualify as an infinite body, and the indentation conditions for finite tip radius effect to be negligible. The outcome of this part is firstly, the definition of a “converged” 2D geometry so that additional magnification of the numerical model does not influence the load-displacement curve, and secondly, an explicit relationship between the measured load and displacement that takes into account the finite tip radius. Elastic-plastic solids: Here, the main data reduction technique was proposed by Pharr et al. [2], assuming elastic unloading of a plastic nanoindentation. We investigated the effects of finite tip radius in elastic-plastic indentations and found that the accuracy of the prediction is currently limited by the accurate determination of the projected contact area. This point will be discussed and a new experimental technique to measure the projected contact area will be proposed. The Poisson’s ratio effect in elastic-plastic indentations is found to be different from the linearly elastic case. This leads to the discussion on the applicability of the correction factor (for Poisson’s ratio effect) derived in linear elastic indentations, on elastic-plastic indentations. Finally, a technique to obtain an upper bound estimate of the yield stress for the indented elastic-plastic material (which is an exact estimation for non-hardening materials), will be presented.

Elastic-Plastic Microcontact Analysis of a Sphere and a Flat Plate

2007 ◽  
Vol 23 (4) ◽  
pp. 341-352 ◽  
Author(s):  
J. L. Liou ◽  
J. F. Lin
Keyword(s):  
Surface Roughness ◽  
Flat Plate ◽  
Contact Pressure ◽  
Contact Area ◽  
Normal Load ◽  
Contact Load ◽  
Asperity Contact ◽  
Elastic Plastic ◽  
Deformation Regime ◽  
Maximum Contact

ABSTRACTThe elastic-plastic microcontact model of a sphere in contact with a flat plate is developed in the present study to investigate the effect of surface roughness on the total contact area and contact load. From the study done by the finite element method, the dimensionless asperity contact area, average contact pressure, and contact load in the elastoplastic regime are assumed to be a power form as a function of dimensionless interference (δ/δec). The coefficients and exponents of the power form expressions can be determined by the boundary conditions set at the two ends of the elastoplastic deformation regime. The contact pressures evaluated by the present model are compared with those predicted by the Hertz theory, without considering the surface roughness and the reported model, including the roughness effect, but only manipulating in the elastic regime. The area of non-zero contact pressure is enlarged if the surface roughness is considered in the microcontact behavior. The maximum contact pressure is lowered by the presence of surface roughness if the contact load is fixed. Under a normal load, both the contact pressure and the contact area are elevated by raising the plasticity index for the surface of the same surface roughness.

Deterministic Contact Model of a Rough Surface Against a Flat-Layered Surface

2004 ◽  
Author(s):  
H. R. Pasaribu ◽  
D. J. Schipper
Keyword(s):  
Mechanical Properties ◽  
Rough Surface ◽  
Contact Area ◽  
Indentation Depth ◽  
Normal Load ◽  
Contact Model ◽  
Real Contact Area ◽  
Single Asperity ◽  
Real Contact ◽  
Effective Mechanical Properties

The effective mechanical properties of a layered surface vary as a function of indentation depth and the values of these properties range between the value of the layer itself and of the substrate. In this paper, a layered surface is modelled like a solid that has effective mechanical properties as a function of indentation depth by assuming that the layer is perfectly bounded to the substrate. The normal load as a function of indentation depth of sphere pressed against a flat layered surface is calculated using this model and is in agreement with the experimental results published by El-Sherbiney (1975), El-Shafei et al. (1983), Tang & Arnell (1999) and Michler & Blank (2001). A deterministic contact model of a rough surface against a flat layered surface is developed by representing a rough surface as an array of spherically shaped asperities with different radii and heights (not necessarily Gaussian distributed). Once the data of radius and height of every single asperity is obtained, one can calculate the number of asperities in contact, the real contact area and the load carried by the asperities as a function of the separation.

Compliance of Elastic Bodies in Contact

1949 ◽  
Vol 16 (3) ◽  
pp. 259-268
Author(s):  
R. D. Mindlin
Keyword(s):  
Contact Area ◽  
Contact Surface ◽  
Poisson’S Ratio ◽  
Tangential Force ◽  
Normal Component ◽  
Poisson's Ratio ◽  
Elastic Bodies ◽  
Complete Elliptic Integrals ◽  
Elliptic Contact ◽  
Circular Contact

Abstract A small tangential force and a small torsional couple are applied across the elliptic contact surface of a pair of elastic bodies which have been pressed together. If there is no slip at the contact surface, considerations of symmetry and continuity lead to the conclusion that there is no change in the normal component of traction across the surface and, aside from warping of the surface, there is no relative displacement of points on the contact surface. The problem is thus reduced to a “problem of the plane” in which the tangential displacements and normal component of traction are given over part of the boundary and the three components of traction are given over the remainder. In the case of the tangential force it is observed that, when Poisson’s ratio is zero, the problem is a simple one, in potential theory, which is then generalized by means of a special device. An expression for tangential compliance is found as a linear combination of complete elliptic integrals. In general, the compliance is greater in the direction of the major axis of the elliptic contact surface than in the direction of the minor axis. Both components of tangential compliance increase as Poisson’s ratio decreases and become equal when Poisson’s ratio is zero. Over the practical range of Poisson’s ratio, the tangential compliance is greater than the normal compliance, but never more than twice as great as long as there is no slip. The tangential traction on the contact surface is everywhere parallel to the applied force. Contours of constant traction are ellipses homothetic with the elliptic boundary. The magnitude of the traction rises from one half the average at the center of the contact surface to infinity at the edge. Due to this infinity, there will be slip, the effect of which is studied for the circular contact surface. In the case of the torsional couple, the solution is obtained by generalizing a solution by H. Neuber pertaining to a hyperbolic groove in a twisted shaft. The torsional compliance is expressed in terms of complete elliptic integrals and, for the circular contact area, reduces to that found by E. Reissner and H. F. Sagoci. The resultant traction at a point rises from zero at the center to infinity at the edge of the contact surface, but is constant along and parallel to homothetic ellipses only in the case of the circular contact area.

scholarly journals Fractal Loading Model of the Joint Interface Considering Strain Hardening of Materials

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Yanhui Wang ◽  
Xueliang Zhang ◽  
Shuhua Wen ◽  
Yonghui Chen
Keyword(s):  
Strain Hardening ◽  
Contact Area ◽  
Elastoplastic Deformation ◽  
Contact Load ◽  
Joint Interface ◽  
Normal Contact ◽  
Deformation Stage ◽  
Deformation Phase ◽  
Deformation State ◽  
The Relationship

Based on fractal geometry theory, the deformation state of the four stages of the asperity elastic, first elastoplastic, second elastoplastic, and fully plastic deformation and comprehensively considering the hardness of the asperity changes with the amount of deformation in elastoplastic deformation stage due to strain hardening are considered, thereby establishing a single-loading model of the joint interface. By introducing the pushing coefficient and the asperity frequency exponent, each critical frequency exponents of asperity is obtained, and the relationship between the normal contact load and the contact area of the first elastoplastic deformation phase and the second elastoplastic deformation phase of the single asperity in the case of taking into account the change in hardness is inferred, eventually deducing the relationship between the total contact load of the joint interface and the contact area. The analysis results show that in the elastoplastic deformation stage, when the deformation is constant, the asperity load considering the hardness change is smaller than the unconsidered load, and the difference increases with the increase of the deformation amount. The establishment of the model provides a theoretical basis for further research on the elastoplastic contact of joint interfaces.

scholarly journals On a method for determination of Poisson’s ratio and Young modulus of a material

2018 ◽  
Vol 226 ◽  
pp. 03027 ◽  
Author(s):  
Vladimir B. Zelentsov ◽  
Evgeniy V. Sadyrin ◽  
Aleksandr G. Sukiyazov ◽  
Nataliya Yu. Shubchinskaya
Keyword(s):  
Contact Problem ◽  
Young’S Modulus ◽  
Contact Area ◽  
Poisson’S Ratio ◽  
Young's Modulus ◽  
Young Modulus ◽  
Theory Of Elasticity ◽  
Poisson's Ratio ◽  
Parabolic Cylinder ◽  
And Control

On the base of modernized NanoTest 600 Platform 3 indentation method is proposed to determine elastic parameters – Poisson’s ratio and Young’s modulus – of a material while loading in an elastic region. The experiment is based on procedure: lateral surface of indenter tip with the shape of parabolic cylinder penetrates into the specimen. NanoTest 600 was equipped by additional optics, backlight and device for spatial orientation of the specimen. This modernization allows to control the process of the indenter penetration both along its length and from the edges, so that one can observe and measure the width of the contact area and control the depth of the indentation area in a sample material. Mathematical modeling of the indentation process was conducted within the framework of plane theory of elasticity. This required solution of the contact problem on indentation of a rigid indenter with a parabolic shape into an elastic strip coupled with a non-deformable substrate. The fulfilment of condition of zeroing the contact stresses at the edges of the indenter with a known width of the contact area allows to determine the Poisson’s ratio, and condition of static equilibrium of the contact problem helps to find Young’s modulus of a strip material.

An Improved Elastic Contact Model Accounting for Asperity Interaction and Bulk Substrate Deformation

2009 ◽  
Author(s):  
Jungkyu Lee ◽  
Chang-Dong Yeo ◽  
Andreas A. Polycarpou
Keyword(s):  
Rough Surface ◽  
Contact Stiffness ◽  
Elastic Half Space ◽  
Contact Model ◽  
Asperity Contact ◽  
Single Asperity ◽  
Surface Contact ◽  
In Series ◽  
Bulk Substrate ◽  
Rough Surface Contact

An improved rough surface contact model is proposed accounting for bulk substrate deformation and asperity interaction. The asperity contact stiffness is based on Hertzian solution for spherical contact, and the bulk substrate stiffness on the solution of Hertzian pressure on a circular region of the elastic half-space. The contact behavior of a single asperity composed of hemi-spherical asperity deformation as well as bulk substrate deformation is calculated by introducing the concept of spring-in-series. Based on the single asperity model, the contact stiffness for the rough surface is calculated including the effect of asperity interaction. Analytical simulation results using the proposed rough surface contact model were compared with the CEB model and experimental measurements.

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