Semi-Analytic Iterative Solution for the Adhesive Contact Between a Micro-Indenter and a Graded Elasticity Coating

Volume 4: 19th Design for Manufacturing and the Life Cycle Conference; 8th International Conference on Micro- and Nanosystems ◽

10.1115/detc2014-35110 ◽

2014 ◽

Author(s):

Stewart J. Chidlow ◽

William W. F. Chong ◽

Mircea Teodorescu

Keyword(s):

Stress Field ◽

Analytic Solution ◽

Superposition Principle ◽

Elastic Solid ◽

Iterative Solution ◽

Normal Pressure ◽

Adhesive Contact ◽

Collocation Methods ◽

Subsurface Stress ◽

The Fourier Transform

This paper proposes a hybrid (semi-analytic) solution for determining the contact footprint and subsurface stress field in a two-dimensional adhesive problem involving a multi-layered elastic solid loaded normally by a rigid indenter. The subsurface stress field is determined using a semi-analytic solution and the footprint using a fast converging iterative algorithm. The solid to be indented consists of a graded elasticity coating with exponential increase of decay of its shear modulus bonded on a homogeneously elastic substrate. By applying the Fourier Transform to the governing boundary value problem, we formulate expressions for the stresses and displacements induced by the application of line forces acting both normally and tangentially at the origin. The superposition principle is then used to generalize these expressions to the case of distributed normal pressure acting on the solid surface. A pair of coupled integral equations are further derived for the parabolic stamp problem which are easily solved using collocation methods.

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The Effect of Two Rigid Spherical Inclusions on the Stresses in an Infinite Elastic Solid

Journal of Applied Mechanics ◽

10.1115/1.3625027 ◽

1966 ◽

Vol 33 (1) ◽

pp. 68-74 ◽

Cited By ~ 23

Author(s):

Joseph F. Shelley ◽

Yi-Yuan Yu

Keyword(s):

Stress Field ◽

Uniaxial Tension ◽

Elastic Solid ◽

Displacement Function ◽

Hydrostatic Tension ◽

Series Form ◽

Spherical Inclusions ◽

Spherical Cavities ◽

In Series ◽

The Common

Presented in this paper is a solution in series form for the stresses in an infinite elastic solid which contains two rigid spherical inclusions of the same size. The stress field at infinity is assumed to be either hydrostatic tension or uniaxial tension in the direction of the common axis of the inclusions. The solution is based upon the Papkovich-Boussinesq displacement-function approach and makes use of the spherical dipolar harmonics developed by Sternberg and Sadowsky. The problem is closely related to, but turns out to be much more involved than, the corresponding problem of two spherical cavities solved by these authors.

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Relating Surface Roughness to Subsurface Stress

World Tribology Congress III, Volume 1 ◽

10.1115/wtc2005-63090 ◽

2005 ◽

Author(s):

A. Martini ◽

S. B. Liu ◽

B. Escoffier ◽

Q. Wang

Keyword(s):

Surface Roughness ◽

Stress Field ◽

Point Contact ◽

Surface Characteristics ◽

Operating Conditions ◽

Surface Design ◽

Dry Contact ◽

Subsurface Stress ◽

The Relationship ◽

Machined Surfaces

Understanding and anticipating the effects of surface roughness on subsurface stress in the design phase can help ensure that performance and life requirements are satisfied. The specific approach taken in this work to address the goal of improved surface design is to relate surface characteristics of real, machined surfaces to subsurface stress fields for dry contact. This was done by digitizing machined surfaces, simulating point contact numerically, calculating the corresponding subsurface stress field, and then relating stress results back to the surface. The relationship between surface characteristics and subsurface stress is evaluated using several different approaches including analyses of trends identified through stress field visualization and extraction of statistical data. One such approach revealed a sharp transition between cases in which surface characteristics dominated the stress field and those in which bulk, or global contact effects dominated the stress. This transition point was found to be a function of the contact operating conditions, material properties, and most interestingly, the roughness of the surface.

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Plane Deformations of an Inhomogeneity–Matrix System Incorporating a Compressible Liquid Inhomogeneity and Complete Gurtin–Murdoch Interface Model

Journal of Applied Mechanics ◽

10.1115/1.4041469 ◽

2018 ◽

Vol 85 (12) ◽

Cited By ~ 9

Author(s):

Ming Dai ◽

Min Li ◽

Peter Schiavone

Keyword(s):

Analytic Solution ◽

Elastic Solid ◽

Compressible Liquid ◽

External Loading ◽

Interface Model ◽

Interface Tension ◽

Soft Solids ◽

Remote Loading ◽

Interface Elasticity ◽

Plane Deformations

We consider the plane deformations of an infinite elastic solid containing an arbitrarily shaped compressible liquid inhomogeneity in the presence of uniform remote in-plane loading. The effects of residual interface tension and interface elasticity are incorporated into the model of deformation via the complete Gurtin–Murdoch (G–M) interface model. The corresponding boundary value problem is reformulated and analyzed in the complex plane. A concise analytical solution describing the entire stress field in the surrounding solid is found in the particular case involving a circular inhomogeneity. Numerical examples are presented to illustrate the analytic solution when the uniform remote loading takes the form of a uniaxial compression. It is shown that using the simplified G–M interface model instead of the complete version may lead to significant errors in predicting the external loading-induced stress concentration in gel-like soft solids containing submicro- (or smaller) liquid inhomogeneities.

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Computing the Stresses Induced Within Multi-Layered Elastic Media That Result From Sliding Contact With a Rigid Punch

Volume 1: 15th International Conference on Advanced Vehicle Technologies; 10th International Conference on Design Education; 7th International Conference on Micro- and Nanosystems ◽

10.1115/detc2013-12605 ◽

2013 ◽

Author(s):

Stewart Chidlow ◽

Mircea Teodorescu

Keyword(s):

Contact Problem ◽

Elastic Solid ◽

Maximum Principal Stress ◽

Functionally Graded ◽

Material Failure ◽

Rigid Punch ◽

Vertical Displacements ◽

The Fourier Transform ◽

Graded Interlayer ◽

Selection Of

This paper is concerned with the solution of the contact problem that results when a rigid punch is pressed into the surface of an inhomogeneously elastic solid comprising three distinct layers. The upper and lower layers of the solid are assumed to be homogeneous and are joined together by a functionally graded interlayer whose material properties progressively change from those of the coating to those of the substrate. By applying the Fourier transform to the governing boundary value problem (BVP), we may write the stresses and displacements within the solid in terms of indefinite integrals. In particular, the expressions for the horizontal and vertical displacements of the solid surface are used to formulate a coupled pair of integral equations which may be solved numerically to approximate the solution of the stamp problem. A selection of numerical results are then presented which illustrate the effects of friction on the contact problem and it is found that the presence of friction within the contact increases the magnitude of the maximum principal stress and changes its location. These observations indicate that material failure is much more likely to occur when friction is present within the contact as expected.

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Stress in an Elastic Bedrock Hump Due to Glacier Flow

Journal of Glaciology ◽

10.1017/s0022143000021523 ◽

1977 ◽

Vol 18 (78) ◽

pp. 67-75 ◽

Cited By ~ 10

Author(s):

L. W. Morland ◽

E. M. Morris

Keyword(s):

Stress Field ◽

Applied Load ◽

Pore Water Pressure ◽

Water Pressure ◽

Normal Pressure ◽

Cohesive Stress ◽

Coulomb Failure ◽

Gravity Effects ◽

Coulomb Failure Criterion ◽

Glacier Flow

Abstract The stress field in an isotropic elastic hump representing a typical bedrock feature is obtained for plane strain conditions. Gravity effects are included and the applied load is a normal pressure distribution deduced from an idealized model of glacier flow. A Coulomb failure criterion is applied, including the effective stress change due to pore-water pressure, and stresses on the predicted failure planes determined for different pressure amplitudes and relative gravity contributions. The latter make little difference to the maximum “failure stress" but influence the regions where such stress levels occur. Levels of cohesive stress required to inhibit Coulomb failure are obtained, and are low in general, implying that coherent rock in the adopted hump profile, subject to the model pressure, would not fail. That is, this profile is stable unless jointing introduces an easier failure mechanism.

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Stress field in an isotropic elastic solid containing a circular hard or soft inclusion under uniaxial tensile stress

Materials Today Proceedings ◽

10.1016/j.matpr.2019.03.024 ◽

2019 ◽

Vol 11 ◽

pp. 657-666

Author(s):

Amit Kumar Rana ◽

Surajit Kumar Paul ◽

P.P. Dey

Keyword(s):

Stress Field ◽

Tensile Stress ◽

Elastic Solid ◽

Uniaxial Tensile ◽

Soft Inclusion ◽

Uniaxial Tensile Stress

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Travel-Time Difference Extracting in Experimental Study of Rayleigh Wave Acoustoelastic Effect

ISRN Mechanical Engineering ◽

10.1155/2014/349020 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7

Author(s):

Hu Eryi ◽

Ying Shao

Keyword(s):

Experimental Study ◽

Rayleigh Wave ◽

Travel Time ◽

Correlation Method ◽

Experimental System ◽

Time Difference ◽

Acoustoelastic Effect ◽

Digital Oscilloscope ◽

Subsurface Stress ◽

The Fourier Transform

In order to identify the travel-time difference accurately in the experimental study of Rayleigh wave acoustoelastic effect, an experimental system is constructed by the ultrasonic pulser-receiver, digital oscilloscope, Rayleigh wave transmitter and receiver, and a personal computer. And then, the digital correlation method and the Fourier transform frequency analysis method are used to obtain the travel-time difference of the Rayleigh wave corresponding to different subsurface stress conditions. Furthermore, the simulated ultrasonic signals are used to verify the reliability of the two kinds of ultrasonic signal information extracting algorithms, respectively. Finally, the proposed signal processing methods are applied to extract the time delay between different Rayleigh wave signals corresponding to different subsurface stress level.

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Adhesive Contacts for Graded-Elastic Coatings Using Fourier Series Decomposition

ASME/STLE 2011 Joint Tribology Conference ◽

10.1115/ijtc2011-61112 ◽

2011 ◽

Author(s):

S. J. Chidlow ◽

W. W. F. Chong ◽

M. Teodorescu ◽

N. D. Vaughan

Keyword(s):

Fourier Series ◽

Analytic Solution ◽

Adhesive Contact ◽

Solution Technique ◽

Control Case ◽

Principal Stresses ◽

Pressure Distributions ◽

Surface Deflection ◽

Elastic Layers ◽

Adhesive Contacts

We propose a semi-analytic solution technique to determine the subsurface stresses and local deflections resulting in an adhesive contact of graded elastic layers. Identical pressure distributions, typical for a Maugis parameter λ = 1, were applied to a range of graded elastic coatings. The principal stresses and surface deflection in both regions (graded elastic layer and substrate) are computed in terms of Fourier series. This control case has the advantage that the response of different coatings can be easily monitored and compared.

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