Double and multiple contacts of similar elastic materials

Narayan K Sundaram, Purdue University

Abstract

Ongoing fretting fatigue research has focussed on developing robust contact mechanics solutions for complicated load histories involving normal, shear, moment and bulk loads. For certain indenter profiles and applied loads, the contact patch separates into two disconnected regions. Existing Singular Integral Equation (SIE) techniques do not address these situations. A fast numerical tool is developed to solve such problems for similar elastic materials for a wide range of profiles and load paths including applied moments and remote bulk-stress effects. This tool is then used to investigate two problems in double contacts. The first, to determine the shear configuration space for a biquadratic punch for the generalized Cattaneo-Mindlin problem. The second, to obtain quantitative estimates of the interaction between neighboring cylindrical contacts for both the applied normal load and partial slip problems up to the limits of validity of the halfspace assumption. In double contact problems without symmetry, obtaining a unique solution requires the satisfaction of a condition relating the contact ends, rigid-body rotation and profile function. This condition has the interpretation that a rigid-rod connecting the inner contact ends of an equivalent frictionless double contact of a rigid indenter and halfspace may only undergo rigid body motions. It is also found that the ends of stick-zones, local slips and remote-applied strains in double contact problems are related by an equation expressing tangential surface-displacement continuity. This equation is essential to solve partial-slip problems without contact equivalents. Even when neighboring cylindrical contacts may be treated as non-interacting for the purpose of determining the pressure tractions, this is not generally true if a shear load is applied. The mutual influence of neighboring contacts in partial slip problems is largest at small shear load fractions. For both the pressure and partial slip problems, the interactions are stronger with increasing strength of loading and contact proximity. A new contact algorithm is developed and the SIE method extended to tackle contact problems with an arbitrary number of contact patches with no approximations made about contact interactions. In the case of multiple contact problems determining the correct contact configuration is significantly more complicated than in double contacts, necessitating a new approach. Both the normal contact and partial slip problems are solved. The tool is then used to study contacts of regular rough cylinders, a flat with rounded punch with superimposed sinusoidal roughness and is also applied to analyze the contact of an experimental rough surface with a halfspace. The partial slip results for multiple-contacts are generally consistent with Cattaneo-Mindlin continuum scale results, in that the outermost contacts tend to be in full sliding. Lastly, the influence of plasticity on frictionless multiple contact problems is studied using FEM for two common steel and aluminum alloys. The key findings are that the plasticity decreases the peak pressure and increases both real and apparent contact areas, thus ‘blunting’ the sharp pressures caused by the contact asperities in pure elasticity. Further, it is found that contact plasticity effects and load for onset of first yield are strongly dependent on roughness amplitude, with higher plasticity effects and lower yield-onset load at higher roughness amplitudes.

Degree

Ph.D.

Advisors

Farris, Purdue University.

Subject Area

Mechanics|Aerospace engineering

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