Complex variable formulation for non-slipping plane strain contact of two elastic solids in the presence of interface mismatch eigenstrain

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:49

Article

Ma, Lifeng¹  Korsunsky, Alexander M.² 

[1] Xi An Jiao Tong Univ, S&V Lab, Dept Engn Mech, Xian 710049, Peoples R China

[2] Univ Oxford, Dept Engn Sci, Oxford OX1 3PJ, England

关键词: Contact mechanics;    Non-slipping contact;    Adhesion;    JKR theory;   

DOI  :  10.1016/j.ijsolstr.2012.02.002

来源: Elsevier

【 摘 要 】

In this paper, the problems of non-slipping contact, non-slipping adhesive contact, and non-slipping adhesive contact with a stretched substrate are sequentially studied under the plane strain theory. The main results are obtained as follows: (i) The explicit solutions for a kind of singular integrals frequently encountered in contact mechanics (and fracture mechanics) are derived, which enables a comprehensive analysis of non-slipping contacts. (ii) The non-slipping contact problems are formulated in terms of the Kolosov-Muskhelishvili complex potential formulae and their exact solutions are obtained in closed or explicit forms. The relative tangential displacement within a non-slipping contact is found in a compact form. (iii) The spatial derivative of this relative displacement will be referred to in this study as the interface mismatch eigenst rain. Taking into account the interface mismatch eigenstrain, a new non-slipping adhesive contact model is proposed and its solution is obtained. It is shown that the pull-off force and the half-width of the non-slipping adhesive contact are smaller than the corresponding solutions of the JKR model (Johnson et al., 1971). The maximum difference can reach 9% for pull-off force and 17% for pull-off width, respectively. In contrast, the new model may be more accurate in modeling the non-slipping adhesion. (iv) The non-slipping adhesions with a stretch strain (S-strain) imposed to one of contact counterparts are re-examined and the analytical solutions are obtained. The accurate analysis shows that under small values of the S-strain both the natural adhesive contact half-width and the pull-off force may be augmented, but for the larger S-strain values they are always reduced. It is also found that Dundurs' parameter beta may exert a considerable effect on the solution of the pull-off problem under the S-strain. These solutions may be used to study contacts at macro-, micro-, and nano-scales. (C) 2012 Elsevier Ltd. All rights reserved.

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