Non-Hertzian contact stress analysis for an elastic half space—normal and sliding contact

1983 ◽  
Vol 19 (4) ◽  
pp. 357-373 ◽  
Author(s):  
N. Ahmadi ◽  
L.M. Keer ◽  
T. Mura
Keyword(s):  
Stress Analysis ◽  
Half Space ◽  
Contact Stress ◽  
Elastic Half Space ◽  
Sliding Contact ◽  
Hertzian Contact ◽  
Hertzian Contact Stress

Sliding Contact Stress Field Due to a Spherical Indenter on a Layered Elastic Half-Space

1988 ◽  
Vol 110 (2) ◽  
pp. 235-240 ◽  
Author(s):  
T. C. O’Sullivan ◽  
R. B. King
Keyword(s):  
Friction Coefficient ◽  
Stress Field ◽  
Contact Problem ◽  
Half Space ◽  
Contact Stress ◽  
Single Layer ◽  
Elastic Half Space ◽  
Spherical Indenter ◽  
Sliding Contact ◽  
Iterative Approach

The quasi-static sliding contact stress field due to a spherical indenter on an elastic half-space with a single layer is studied. The contact problem is solved using a least-squares iterative approach and the stress field in the layer and substrate is determined using the Papkovich-Neuber potentials. The resulting stresses are discussed for different values of the layer stiffness relative to the substrate and also for different values of the friction coefficient.

Subsurface and Surface Cracking Due to Hertzian Contact

1982 ◽  
Vol 104 (3) ◽  
pp. 347-351 ◽  
Author(s):  
L. M. Keer ◽  
M. D. Bryant ◽  
G. K. Haritos
Keyword(s):  
Crack Propagation ◽  
Half Space ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Numerical Results ◽  
Hertzian Contact ◽  
Vertical Crack ◽  
Subsurface Crack ◽  
Surface Cracking ◽  
Crack Geometry

Numerical results are presented for a cracked elastic half-space surface-loaded by Hertzian contact stresses. A horizontal subsurface crack and a surface breaking vertical crack are contained within the half-space. An attempt to correlate crack geometry to fracture is made and possible mechanisms for crack propagation are introduced.

Plane Strain Sliding Contact Between a Rigid Cylinder and a Pseudoelastic Shape Memory Alloy Half-Space

2018 ◽  
Author(s):  
Ralston Fernandes ◽  
James G. Boyd ◽  
Dimitris C. Lagoudas ◽  
Sami El-Borgi
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Half Space ◽  
Maximum Stress ◽  
Transformation Strain ◽  
Elastic Half Space ◽  
Sliding Contact ◽  
Temperature Dependent ◽  
Rigid Cylinder ◽  
Parametric Studies

This study uses the finite element method to analyze the sliding contact behavior between a rigid cylinder and a shape memory alloy (SMA) semi-infinite half-space. An experimentally validated constitutive model is used to capture the pseudoelastic effect exhibited by these alloys. Parametric studies involving the maximum recoverable transformation strain and the transformation temperatures are performed to analyze the effects that these parameters have on the stress fields during indentation and sliding contact. It is shown that, depending on the amount of recoverable transformation strain possessed by the alloy, a reduction of almost 40 % of the maximum stress in the pseudoelastic half-space is achieved when compared to the maximum stress in a purely elastic half-space. The studies also reveal that the sliding response is strongly temperature dependent, with significant residual stress present in the half-space at temperatures below the austenitic finish temperature.

Description of the Nanoindentation Unloading Behavior of Brittle Ceramics with a Modified Surface

2007 ◽  
Vol 336-338 ◽  
pp. 2422-2425
Author(s):  
Zong Huai Li ◽  
Jiang Hong Gong ◽  
Zhi Jian Peng ◽  
He Zhuo Miao
Keyword(s):  
Half Space ◽  
Contact Stress ◽  
Physical Meaning ◽  
Elastic Half Space ◽  
Quadratic Polynomial ◽  
Modified Surfaces ◽  
Modified Surface ◽  
Force Displacement

The nanoindentation unloading behavior of some brittle ceramics with modified surfaces was analyzed. It was found that the unloading data may be described well with a quadratic polynomial. The physical meaning of the quadratic polynomial in describing the nanoindentation unloading behavior was then discussed by considering the effect of residual contact stress on the force-displacement relationship. It was suggested that the quadratic polynomial may be considered as a modified form of the basic forcedisplacement relationship for the contact of an isotropic elastic half-space by a rigid conical punch.

Planar Tooth Profile Synthesis for Relative Curvature

2017 ◽  
Author(s):  
Zhiyuan Yu ◽  
Kwun-Lon Ting
Keyword(s):  
Contact Stress ◽  
Tooth Profile ◽  
Hertzian Contact ◽  
Rolling Motion ◽  
Special Cases ◽  
Systematic Methodology ◽  
Hertzian Contact Stress ◽  
Curvature Theory ◽  
The Given ◽  
Tooth Pair

This paper is the first that uses the new conjugation curvature theory [1] to directly synthesize conjugate tooth profiles with the given relative curvature that determines the Hertzian contact stress. Conjugation curvature theory offers a systematic methodology to synthesize the relative curvature for a tooth pair. For any given relative curvature between the contact tooth profiles, a generating point can be located on an auxiliary body. Under the rolling motion among the pinion pitch, the gear pitch and the pitch on the auxiliary body, the generating point will trace fully conjugate profiles on the pinion and gear bodies with the given relative curvature at the instant of the contact. Full conjugation throughout the contact of the profiles is guaranteed with the three instant centers remaining coincident [1]. The methodology is demonstrated with a planar tooth profile synthesis with given relative curvature. One may find that the Wildhaber-Novikov tooth profile, which is known to have low relative curvature and Hertzian contact stress, and its variations become special cases under such methodology.

A Unified Treatment of Axisymmetric Adhesive Contact on a Power-Law Graded Elastic Half-Space

2013 ◽  
Vol 80 (6) ◽  
Author(s):  
Fan Jin ◽  
Xu Guo ◽  
Wei Zhang
Keyword(s):  
Half Space ◽  
Power Law ◽  
Contact Region ◽  
Adhesive Contact ◽  
Elastic Half Space ◽  
Hertzian Contact ◽  
Contact Radius ◽  
Abel Transformation ◽  
Numerical Solution Methods ◽  
Special Cases

In the present paper, axisymmetric frictionless adhesive contact between a rigid punch and a power-law graded elastic half-space is analytically investigated with use of Betti's reciprocity theorem and the generalized Abel transformation, a set of general closed-form solutions are derived to the Hertzian contact and Johnson–Kendall–Roberts (JKR)-type adhesive contact problems for an arbitrary punch profile within a circular contact region. These solutions provide analytical expressions of the surface stress, deformation fields, and equilibrium relations among the applied load, indentation depth, and contact radius. Based on these results, we then examine the combined effects of material inhomogeneities and punch surface morphologies on the adhesion behaviors of the considered contact system. The analytical results obtained in this paper include the corresponding solutions for homogeneous isotropic materials and the Gibson soil as special cases and, therefore, can also serve as the benchmarks for checking the validity of the numerical solution methods.

Hertzian Contact-Stress Deformation Coefficients

1969 ◽  
Vol 36 (2) ◽  
pp. 296-303 ◽  
Author(s):  
Duane H. Cooper
Keyword(s):  
Contact Stress ◽  
Digital Computer ◽  
Approximate Calculation ◽  
Transcendental Equation ◽  
Contact Stresses ◽  
Elliptic Integrals ◽  
Hertzian Contact ◽  
Stress Deformation ◽  
Hertzian Contact Stress

Formulations are given for the coefficients λ, μ, ν defined by Hertz in terms of the solution of a transcendental equation involving elliptic integrals and used by him to describe the deformation of bodies subjected to contact stresses. Methods of approximate calculation are explained and errors in the tables prepared by Hertz are noted. For the purpose of providing a more extensive and more accurate tabulation, using an automatic digital computer, these coefficients are reformulated so that a large part of the variation is expressed by means of easily interpreted elementary formulas. The remainder of the variation is tabulated to 6 places for 100 values of the argument. Graphs of the coefficients are also provided.

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