Representation of Half-Plane Contact Edge Behaviour by Asymptotes

2021 ◽  
pp. 125-141
Author(s):  
David A. Hills ◽  
Hendrik N. Andresen
Keyword(s):  
Half Plane ◽  
Plane Contact

scholarly journals Half-plane contacts subject to remote tension

2021 ◽  
pp. 030932472098844
Author(s):  
Nils Cwiekala ◽  
David A Hills
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Asymptotic Form ◽  
Fretting Fatigue ◽  
The State ◽  
Partial Slip ◽  
Practical Relevance ◽  
Plane Contact ◽  
State Of Stress ◽  
Plane Contact Problem

The state of stress present in an elastic half-plane contact problem, where one or both bodies is subject to remote tension has been investigated, both for conditions of full stick and partial slip. The state of stress present near the contact edges is studied for different loading scenarios in an asymptotic form. This is of practical relevance to the study of contacts experiencing fretting fatigue, and enables the environment in which cracks nucleate to be specified.

scholarly journals Consideration of wear in plane contact of rectangular punch and elastic half-plane

2019 ◽  
pp. 138-141
Author(s):  
V. M. Onyshkevych ◽  
G. T. Sulym
Keyword(s):  
Half Plane ◽  
Integral Transformation ◽  
Initial Approximation ◽  
Vertical Displacement ◽  
Fourier Integral ◽  
Mean Value ◽  
Theory Of Elasticity ◽  
Contact Stresses ◽  
Dual Integral Equations ◽  
Plane Contact

The plane contact problem on wear of elastic half-plane by a rigid punch has been considered. The punch moves with constant velocity. Arising thermal effects are neglected because the problem is investigated in stationary statement. In this case the crumpling of the nonhomogeneities of the surfaces and abrasion of half-plane take place. Out of the punch the surface of half-plane is free of load. The solution for problem of theory of elasticity is constructed by means of Fourier integral transformation. Contact stresses are found in Fourier series which coefficients satisfy the dual integral equations. It leads to the system of nonlinear algebraical equations for unknown coefficients by a method of collocations. This system is reduced to linear system in the partial most interesting cases for computing of maximum and minimum wear. The iterative scheme is considered for investigation of other nonlinear cases, for initial approximation the mean value of boundary cases is used. The evolutions of contact stresses, wear and abrasion in the time are given. For both last cases increase or invariable of vertical displacement correspondently is obtained. In the boundary cases coincidence of results with known is obtained.

Flamant solution of a half-plane with surface flexural resistibility and its applications to nanocontact mechanics

2019 ◽  
Vol 25 (3) ◽  
pp. 664-681 ◽  
Author(s):  
Xiaobao Li ◽  
Lijian Jiang ◽  
Changwen Mi
Keyword(s):  
Contact Problem ◽  
Half Plane ◽  
Contact Problems ◽  
Plane Boundary ◽  
Material Surface ◽  
Surface Model ◽  
Surface Traction ◽  
Bending Rigidity ◽  
Plane Contact ◽  
Plane Contact Problem

This article presents a semianalytical solution to a half-plane contact problem subjected to an arbitrarily distributed surface traction. The half-plane boundary is treated as a material surface of the Steigmann–Ogden type. Under the assumption of plane strain condition, the problem is formulated by coupling the methods of an Airy stress function and Fourier integral transforms. Stresses and displacements in the form of semi-infinite integrals are derived. A non-classical Flamant solution that is able to simultaneously account for the surface tension, membrane stiffness, and bending rigidity of the half-plane boundary is derived through limit analysis on the half-plane contact problem owing to a uniform surface traction. The fundamental Flamant solution is further integrated for tackling two half-plane contact problems owing to classical contact pressures corresponding to a rigid cylindrical roller and a rigid flat-ended punch. The resultant semi-infinite integrals are integrated by the joint use of the Gauss–Legendre numerical quadrature and the Euler transformation algorithm. Extensive parametric studies are conducted for comparing and contrasting the effects of Gurtin–Murdoch and Steigmann–Ogden surface mechanical models. The major observations and conclusions are two-fold. First, the introduction of either surface mechanical model results in size-dependent elastic fields. Second, the incorporation of the curvature-dependent nature of the half-plane boundary leads to bounded stresses and displacements in the fundamental Flamant solution. This is in contrast to the otherwise singular classical and Gurtin–Murdoch solutions. For all four case studies, the Steigmann–Ogden surface model also results in much smoother displacement and stress variations, indicating the significance of surface bending rigidity in nanoscale contact problems.

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