On non-symmetrical plane contacts

doi:10.1016/S0020-7403(98)00105-2

International Journal of Mechanical Sciences

Volume 41, Issue 12, December 1999, Pages 1533-1550

https://doi.org/10.1016/S0020-7403(98)00105-2 Get rights and content

Abstract

Plane elastic contact problems are considered, with particular emphasis on asymmetrical punch profiles, in the case of ‘complete’, ‘partially complete’ and ‘incomplete’ contact. An explicit, analytical solution is presented for the case of a single area of contact where the overlap is described by a generic spline function, and examples presented. The interior stress field and strength of the contact, under full or partial slip conditions, are also discussed, and some example shown for representative cases. It is found also that the direction of sliding has a significant effect for the strength of non-symmetrical contacts.

References (0)

Cited by (25)

Study on the edge rounding with consulting contact mechanics
2023, Tribology International
Present work concerns the radius of an edge rounding of mechanical components consulting contact mechanics. A design formula for the size of the minimum radius is derived. A contact of a punch with edge rounding parts and a half plane, both are elastically similar, is used for the analysis model. A condition of the slip region being within the rounding parts is found to derive the formula. The allowance of a step is also examined. As a result, the minimum radius of the edge rounding is found extremely tiny, and thus it is not a critical concern. It is required to completely remove the step to avoid a peak traction which is likely to initiate a failure.
Extending the Mossakovskii method to contacts supporting a moment
2020, Journal of the Mechanics and Physics of Solids
In this article, we extend the Mossakovskii approach to half-plane contacts supporting a moment. Since the method relies on approximating the punch geometry by a series of flat punches, we choose the load path in (P, M)-space that fixes the body tilt, which allows us to reduce the standard Cauchy singular integral formulation to a non-symmetric Abel integral equation. We use the formulation to derive simple expressions for the applied normal force and necessary applied moment as functions of the contact extent and indenter tilt, while also deriving the coefficients of the square-root terms in the contact pressure expansion at the edges of the contact. These results are analysed in detail for two specific examples: the tilted wedge and the tilted flat-and-rounded punch. We conclude by briefly discussing the equivalent tangential problem when an applied shear force and differential bulk tensions are present.
Analysis of effective parameters for stress intensity factors in the contact problem between an asymmetric wedge and a half-plane using an experimental method of photoelasticity
2013, Materials and Design
Citation Excerpt :
Persson [5] showed that minor surface roughness can have a substantial effect on the contact between solids. Ciavarella et al. [6–11] investigated the contact problem for rounded apex wedges and also compared theory, experiment, and numerical methods for slipping contact problems. Chamoret et al. [12] improved numerical contact simulations by developing a smoothing procedure.
Photoelasticity was utilized as an experimental stress analysis tool to determine the stress intensity factors for the contact problem between a half-plane with an edge crack and an asymmetric tilted wedge. The effect of contact force magnitude as well as the angle, length, and position of the crack on mode I and II stress intensity factors were studied and discussed. Analysis of the experimental results is based on fracture mechanics, optical properties of materials, and the correlation between fringe patterns and the distribution of stress in transparent materials (i.e., polycarbonate). Image processing was utilized to extract details from the images acquired from the plate under loading. The finite element method was also used to calculate the stress intensity factors. Experimental and finite element results were in good agreement; however, there are some limitations on the application of photoelasticity method.
Contact of an asymmetrical rounded apex wedge with a half plane
2012, International Journal of Engineering Science
Citation Excerpt :
All problems which were solved by Hills, Nowell, and Sackfield (1993) have symmetrical profiles, nevertheless Hills’ group have been interested in the asymmetrical wedge with sharp apex and utilized asymptotic method to solve the problem (Hills, Churchman, & Mugaudu, 2003; Hills, Mugaudu, Barber, & Sackfield, 2004). Ciavarella and Demelio (1999) considered nonsymmetrical plane contacts. Although his method is useful to resolve any asymmetrical contact profiles, it rather complicates the calculation of Muskhelishvili’s potential function.
Two-dimensional elastic contact problem of an asymmetrical rounded apex wedge with a half plane is considered and an analytical solution is presented for vertical and horizontal external loading in the presence of coulomb friction. The pressure and shear distribution functions are found in closed form under partial slip condition. Further by utilizing a new relation Muskhelishvili’s potential function is obtained and results are analyzed. Designing better cutting tools, selecting fretting fatigue test pads and deeper lap joint analyzing are several practical applications of the outcomes.
Singular integral equation method for contact problem for rigidly connected punches on elastic half-plane
2011, Applied Mathematics and Computation
Citation Excerpt :
Indentation with adhesion of a symmetrical punch into elastic half-plane was studied [7]. A problem for non-symmetrical plane contacts was investigated [8]. A frictional punch problem was studied [9].
In the contact problem of a rigid flat-ended punch on an elastic half-plane, the contact stress under punch is studied. The angle distribution for the stress components in the elastic medium under punch is achieved in an explicit form. From obtained singular stress distribution, the punch singular stress factor (abbreviated as PSSF) is defined. A fundamental solution for the multiple flat punch problems on the elastic half-plane is investigated where the punches are disconnected and the forces applied on the punches are arbitrary. The singular integral equation method is suggested to obtain the fundamental solution. Further, the contact problem for rigidly connected punches on an elastic half-plane is considered. The solution for this problem can be considered as a superposition of many particular fundamental solutions. The resultant forces on punches are the undetermined unknowns in the problem, which can be evaluated by the condition of relative descent between punches. Finally, the resultant forces on punches can be determined, and the PSSFs at the corner points can be evaluated. Numerical examples are given.
What features are needed in a fretting fatigue test?
2009, Tribology International
This paper looks at the essential features of a fretting fatigue test arrangement by first classifying the possible geometries which can occur in practice. It then ascribes to each class a local solution for the contact tractions, which can then be used to scale most complex prototypical problems into a simplified laboratory test. In this way the qualities of the contact in the critical region may be well represented whilst keeping the overall geometry quite simple.

View all citing articles on Scopus

View full text