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Effect of Strain Hardening on Elastic-Plastic Contact of a Deformable Sphere against a Rigid Flat under Full Stick Contact Condition

DOI: 10.1155/2012/472794

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The present study considers the effect of strain hardening on elastic-plastic contact of a deformable sphere with a rigid flat under full stick contact condition using commercial finite element software ANSYS. Different values of tangent modulus are considered to study the effect of strain hardening. It is found that under a full stick contact condition, strain hardening greatly influences the contact parameters. Comparison has also been made between perfect slip and full stick contact conditions. It is observed that the contact conditions have negligible effect on contact parameters. Studies on isotropic and kinematic hardening models reveal that the material with isotropic hardening has the higher load carrying capacity than that of kinematic hardening particularly for higher strain hardening. 1. Introduction Surface interactions are dependent on the contacting materials and the shape of the contacting surfaces. The shape of the surface of an engineering material is a function of both its production process and the nature of the parent material. When studied carefully on a very fine scale, all solid surfaces are found to be rough. So when two such surfaces are pressed together under loading, only the peaks or the asperities of the surface are in contact and the real area of contact is only a fraction of the apparent area of contact. In such conditions the pressure in those contact spots are high. Accurate calculation of contact area and contact load are of immense importance in the field of tribology and lead to an improved understanding of friction, wear, and thermal and electrical conductance between surfaces. However, it is a difficult task as rough surfaces consist of asperities having different radius and height. The problem is simplified when Hertz [1] provides the contact analysis of two elastic solids with geometries defined by quadratic surfaces. From then, the assumption of surfaces having asperities of spherical shape is adopted to simplify the contact problems. Greenwood and Williamson [2] used the Hertz theory and proposed an asperity-based elastic model where asperity heights follow a Gaussian distribution. Hertz assumed frictionless surfaces and his theory is restricted for perfectly elastic solids. Later on, researchers have attempted to investigate the effect of material properties beyond the Hertz restriction and the elastic plastic contact of a sphere with a flat became a fundamental problem in contact mechanics. The plastic model introduced by Abbot and Firestone [3], neglects volume conservation of the plastically deformed sphere.

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