Emanuel Diaconescu

Visualization and measurement of contact area by reflectivity

Surface deformations measured by laser profilometry in a contact model metal punch-sapphire window yield pressure distribution if the contact area is known. This paper advances a new method to assess this area by reflectivity. The contact model possesses higher reflectivity outside the contact area than inside, the step evidencing contact contour. A correction for interference effects is derived. Experimental results on circular Hertz contacts agree well with theoretical predictions.

A New Experimental Technique to Measure Contact Pressure

A new technique to measure the pressure in a real contact is proposed. One of contacting surfaces is covered, prior to contact establishment, by a special gel. The contact closing removes the excess gel and, during a certain time interval, the contact pressure transforms the entrapped substance in an amorphous solid. In each point, the refractive index of this solid depends on the pressure acting during transformation. After contact opening, the reflectivity of this coating depends on the former contact pressure and it is mapped by aid of a laser profilometer and becomes an indicator of contact pressure. Theoretical considerations show that the gel must possess certain optical parameters for the method to work. Several experimental reported results offer a clear image upon pressure distribution in Hertz point contacts, end effects in finite length line contacts, pressure distribution between rough surfaces and indicate the onset of plastic deformation.Copyright

A Boussinesq Type Problem for the Elastic Layer

This paper derives an analytical solution to the Boussinesq problem for the elastic layer. This is found by adding supplementary displacements to half-space displacements. The corresponding integral interference condition is established and this is useful for solving elastic layer contacts.Copyright

Numerical Simulation of Elastic-Plastic Non-Conforming Contact

A fast algorithm for elastic-plastic non-conforming contact simulation is presented in this work. While the elastic response of a material subjected to load application is reversible, plasticity theory describes the irreversible behavior of the material in reaction to loading beyond the limit of elastic domain. Therefore, elastic-plastic response of contacting bodies to loading beyond yield strength is needed to assess the load-carrying capacity of the mechanical contact. The modern approach in simulating elastic-plastic contact is based on the algorithm originally proposed by Mayeur, (Mayeur, 1996), employing Betti’s reciprocal theorem. Although Mayeur developed a model for the three-dimensional problem, numerical implementation was restricted to two-dimensional case, due to lack of formulas for the influence coefficients. Problem generalization is due to Jacq, (Jacq, 2001), and to Jacq et al. (Jacq et al., 2002), who advanced a complete semi-analytical formulation for the three-dimensional elastic-plastic contact. The algorithm was later refined by these authors, (Wang & Keer, 2005), who improved the convergence of residual and elastic loops. The main idea of their Fast Convergence Method (FCM) is to use the convergence values for the current loop as initial guess values for the next loop. This approach reduces the number of iterations if the loading increments are small. Nelias, Boucly, and Brunet, (Nelias et al., 2006), further improved the convergence of the residual loop. They assessed plastic strain increment with the aid of a universal algorithm for integration of elastoplasticity constitutive equations, originally proposed by Fotiu and Nemat-Nasser, (Fotiu & Nemat-Nasser, 1996), as opposed to existing formulation, based on Prandtl-Reuss equations, (Jacq, 2001). As stated in (Nelias et al., 2006), this results in a decrease of one order of magnitude in the CPU time. Influence of a tangential loading in elastic-plastic contact was investigated by Antaluca, (Antaluca, 2005). Kinematic hardening was added by Chen, Wang, Wang, Keer, and Cao, (Chen et al.,2008), who advanced a three-dimensional numerical model for simulating the repeated rolling or sliding contact of a rigid sphere over an elastic-plastic half-space. The efficiency of existing elastic-plastic contact solvers, (Jacq et al., 2002; Wang & Keer, 2005) is impaired by two shortcomings. Firstly, the algorithms are based on several levels of iteration, with the innermost level having a slow convergence. Secondly, the effect of a three-dimensional distribution in a three-dimensional domain, namely residual stresses related to plastic strains, is computed using two-dimensional spectral algorithms.

Contact Stress State in Elastic Layers

This paper presents the discrete counterpart of an existing continuous formulation for an elastic layer loaded symmetrically. The influence coefficients based numerical approach allows for computing contact stresses induced in the elastic layer by arbitrary shaped indenters. The newly developed code is validated against existing pressure distributions in layer contact for quadratic form punches.Copyright

Effect of Body Lateral Extension Upon the Elastic Contact

Half-space contact theory cannot be applied when either contacting bodies are thin or they possess small transversal dimensions. The former situation is often dealt with, but the latter seems to be neglected. This paper investigates the effect of outer radius of cylindrical bodies upon the contact stress field. The method consists in adding supplementary displacements and stresses to the half-space solution in order to fulfill the boundary conditions and the force balance equation on load direction. It is found that the half-space theory is applicable if transversal radius exceeds contact radius.Copyright

Elliptic Elastic Contact Between High Order Symmetrical Surfaces

This paper proves that a generalized Hertz pressure (the product of Hertz square root and an even polynomial of degree 2n with respect to coordinates) applied over elastic half-space boundary generates a polynomial normal displacement of degree 2n+2. Polynomial surface coefficients are combinations of elliptical integrals. The equation of rigid punch surface generating this pressure is derived, as well as the conditions in which an elliptical contact occurs. For second order surfaces, n=0, these results yield all Hertz formulas, whereas new formulas are derived for contact parameters between fourth, sixth, and eight order surfaces.

Improvement of Punch Profiles for Elastic Circular Contacts

Machine design and electrical contacts involve frequently elastic circular contacts subjected to normal loads. Depending on geometry, these may be Hertzian or surface contacts. Both possess highly nonuniform pressure distributions which diminish contact load carrying capacity. The achievement of a uniform pressure distribution would be ideal to improve the situation, but this violates stress continuity. Instead, the generation of a uniform pressure over most of contact area can be sought. Generally, equivalent punch profile which generates this pressure is found by numerical evaluation of double integrals. This paper simplifies the derivation of punch profile by using an existing correspondence between a polynomial punch surface and elastically generated pressure. First, an improved pressure profile is proposed seeking to avoid high Huber-Mises-Hencky stresses near contact surface. Then, this is approximated by the product between typical Hertz square root and an even polynomial, which yields directly the punch profile. Formulas for normal approach and central pressure are derived.

New Investigations of Finite Length Line Contact

Important end effects occur in Hertz-like finite length line contacts. If the length of shorter contacting cylinder is bounded by flat surfaces, the pressure tends to infinity at both ends. Many design measures were advanced to reduce or attenuate these pressure riser effects. These imply modification of contact geometry and, in most cases, numerical investigations. Few experiments were performed to check the actual contact between modified surfaces. Applying a previous proposal, contact area between a modified steel roller and a sapphire window is measured by scanning the reflectivity of metallic surface. A typical “dog bone” shape for this area is found. Lateral extensions of contact area, measured experimentally for a roller with rounded edges, agree well with numerical results obtained by a new, refined numerical procedure.Copyright

Improved Pressure Distribution in Elliptic Elastic Contacts between High-Order Surfaces

The improvement of mechanical contacts or microcontacts seeks a nearly uniform current density over most of contact area. When microtopography is homogeneous, this aim is achieved if nominal shape of contacting surfaces yields a nearly uniform central pressure which decreases monotonously to zero in contour points. These authors derived recently this shape for circular contacts by employing high-order surfaces. This paper extends this result to elliptical contacts. Some results are used to this end, derived for elliptical elastic contacts between high-order surfaces. As homogeneous high order surfaces lead to a highly nonuniform pressure distribution, central pressure is flattened by making the first derivatives of pressure vanish in contact center. Then, the contacts between fourth, sixth, and eighth, order surfaces are analyzed and recurrence relations for pressure distribution and contact parameters are proposed.