On the Tangential Displacement of a Surface Point Due to a Cuboid of Uniform Plastic Strain in a Half-Space

Abstract

The elastic solution of a tangentially loaded contact is known as Cerruti’s solution. Since the contact surfaces could be easily discretized in small rectangles of uniform shear stress the elastic problem is usually numerically solved by summation of well known integral solution. For soft metallic materials, metals at high temperature, rough surfaces, or dry contacts with high friction coefficient, the yield stress within the material could be easily exceeded even at low normal load. This paper presents the effect of a cuboid of uniform plastic strain in a half-space on the tangential displacement of a surface point. The analytical solutions are first presented. All analytical expressions are then validated by comparison with the finite element method. It is found that the influence coefficients for tangential displacements are of the same order of magnitude as the ones describing the normal displacement (Jacq et al., 2002, “Development of a Three-Dimensional Semi-Analytical Elastic-Plastic Contact Code,” ASME J. Tribol., 124(4), pp. 653–667). This result is of great importance for frictional contact problem when coupling the normal and tangential behaviors in the elastic-plastic regime, such as stick-slip problems, and also for metals and alloys with low or moderate yield stress.

Contact analysis in presence of spherical inhomogeneities within a half-space

“…Note that for dissimilar elastic materials in frictional contact the tangential displacements of the surface points, given elsewhere in an analytical form by Fulleringer and Nélias (2010) for a cuboid of uniform eigenstrain, should not be neglected any more.…”

A methodology to predict the roughness of shot peened surfaces

“…In the present investigation only normal effects will be considered and hence impacts will be assumed frictionless. However the coupling between normal and tangential effects has already been implemented in the contact solver -see Gallego et al (2010) and Fulleringer and Nelias (2010).…”

Modelling of multiple impacts for the prediction of distortions and residual stresses induced by ultrasonic shot peening (USP)

“…When the convergence is reached, the final contact force is used to update the velocity of the ball and the next rigid body displacement can be calculated. For more details on SAM as developed to solve inelastic contact problems or contact problem with heterogeneous materials the reader may refer to Boucly et al (2007), Fulleringer and Nelias (2010), Leroux and Nélias (2011) or . The reader may also refer to the recent work of Wang, Keer and coauthors from Northwestern University Chen and Wang, 2008;Zhou et al, 2009), Bosman and Schipper at the University of Twente (Bosman and Schipper, 2011), and Wang et al from Tsinghua Univ.…”

“…In most commercial FE packages it is not possible to import an inelastic strain tensor as initial state, whereas equivalent thermal strains can be used to represent the original state as presented by Fulleringer and Nelias (2010). The mesh is set up by 8-node linear bricks.…”