Evaluation of different approaches to 3d numerical model development of the contact zone between elementary asperities and flat surface

Abstract

This paper presents two triaxial finite element (FE) models: a “full model” and a “quarter model”, representing the contact between the specimen’s rough surface and the ideally smooth and flat surface of the punch. Models have a contact zone that represents the topography of the real surface and has elastoplastic properties close to those of the real contact. The contact zone was entirely modelled on the basis of roughness measurements performed on a real milled specimen made of 5083 aluminium alloy. The development of the FE models, the stages in their refinement and the interlinking of the contact zone with the material of the specimen are described. The results of the computed deformations occurring during the specimen contact loading with the punch were compared with the experimental results. The possible causes of the observed deviations of the computer simulation results from the experimental ones were discussed. The models were used to analyse the effect of the specimen’s material properties, i.e. Young’s modulus, yield strength, compressive strength and material hardening, on the deformations in the contact. On this basis a procedure for predicting the parameters describing the contact characteristic in cases of changes in the properties of the subsurface zone is proposed

Invariant differential generalizations in problems of the elasticity theory as applied to polar coordinates

“…Using the Cauchy-Riemann relations (43), one can show that the equations in (44) taken in parentheses are also equal to zero. This has already been shown in (19) To obtain the final solution to the continuity equation (33), it is necessary to show that functions I 1 and I 2 satisfy the Laplace equations (33) as well since they are part of the final result of (37) to (39). Substitute (35), (36) into (39) taking into account:…”

“…Differential relations in the problem [18] were applied but they are inapplicable to the generalizations using argument functions. General approaches were considered in [19] where conditions of coupling in the sample-punch interaction were taken into account. The analysis has shown that they (conditions) do not adequately reflect the possibility of finding a concrete solution to the problem taking into account the application of the argument functions.…”

Studying the stressed state of elastic medium using the argument functions of a complex variable

“…Publication [14] examines the contact interaction between a sample and a punch. Common approaches to the problem were complemented by the relationship conditions.…”

“…Operators in (14) that are adjacent to the exponents contain the same second derivatives for coordinates and non-linearity. If for some reason the operators are zero, then there is an identity.…”

“…By comparing (14) and 16, we make sure that the operators before the exponents are of the opposite sign in comparison to function θ, but, in terms of solution, they almost have not changed. We group By substituting derivatives in the continuity equation, we make sure that (14) turns into an identity.…”