Упрощенное аналитическое решение контактной задачи о вдавливании конического штампа в полупространство с покрытием

Abstract

The present paper is devoted to the construction of the approximate solution of the contact problem on a conical punch indentation into an elastic isotropic half-space with coating. The solution is suitable for both homogeneous (when elastic moduli are constant) and multilayered or functionally-graded coatings (when elastic moduli change with depth). The solution was obtained using the bilateral asymptotic method in the analytical form. The kernel trans-form approximation was obtained as the ratio of two quadratic functions and contains only one parameter. Thus, the scheme of the approximate analytical solution was constructed in a significantly simplified manner in comparison with the general case in which the product of fractional-quadratic functions is used. Such an approach allowed us to obtain explicit analytical expressions for the distribution of contact stresses and the force-displacement dependences in a simplified form, convenient for engineering calculations. The influence of the parameter characterizing the relative Young's modulus of the coating on the characteristics of contact interaction was analyzed. The accuracy of the obtained solution was studied depending on the ratio of the elastic moduli of the coating and the substrate using a series of homogeneous coatings as an example. Particular attention was paid to the investigation of the indentation stiffness - the most important characteristic used in experimental researches. The results of the work can be used to describe an experiment on nanoindentation of materials with coatings using either a conical or a Berkovich indenter.