Antiplane Deformation of a Bimaterial Containing an Interfacial Crack with the Account of Friction I. Single Loading

Abstract

The paper presents the exact analytic solution to the antiplane problem for a non-homogeneous bimaterial medium containing closed interfacial cracks, which faces can move relatively to each other with dry friction. The medium is subjected to the action of normal and arbitrary single loading in a longitudinal direction. Based on the discontinuity function method the problem is reduced to the solution of the system of singular integral-differential equations for stress and displacement discontinuities at the possible slippage zones. Influence of loading parameters and the effects of friction on the sizes of these zones is analyzed. The stress intensity factors, stress and displacement discontinuities, energy dissipation are determined for several characteristic types of external loading.

Antiplane Deformation Of A Bimaterial Containing An Interfacial Crack With The Account Of Friction 2. Repeating And Cyclic Loading

“…At excessive intensity the latter can sometimes cause unpredictable change in mechanical, physical and chemical properties of a material, distribution of physical fields, and consequently influence the diffusive processes, in particular hydrogen diffusion, and development of the fracture phenomena warned by tribofatigue (Sosnovskiy, 2005; Evtushenko and Kutsei, 2010, Pyriev et al, 2012). This paper continues previous authors' publication (Sulym et al, 2015) and develops the technique for studying the influence of friction in the antiplane problem for a solid with a closed crack under the applied quasi-static (inertia-free) repeatedly changing loading, including cyclic one. The most general case is considered, when at each step the loading can either increase (additional loading) or change sign (unloading) reaching sufficient magnitude, which causes development of slippage zones.…”

“…As well as in the previous work (Sulym et al, 2015), consider an infinite isotropic medium consisting of two half-spaces with elastic constants , , ( = 1,2), which are pressed to each other along their interface with normal stress = − ( = 1,2; ∈ ). Here the system of co-ordinates is used, with its origin at a plane of contact of half-spaces, where -coaxial strip cracks are localized at…”

“…Contact between the bimaterial medium components along a line ′′ = \ ′ is supposed to be mechanically perfect, and the contact along defects' (cracks') faces ′ is assumed to be performed according to the laws of tangential mechanic contact, at which bodies contact mechanically perfect until the moment, when relative sliding of crack faces may start in some areas ( ) ⊂ ′ at the material interface (Johnson, 1985;Sulym et al, 2015). Presence of such slippage zones (cracks with contacting faces) at each -th step of loading (cycle) is modeled with stress and displacement discontinuity vectors at ( ) ⊂ ′ (Bozhydarnyk and Sulym, 1999;Sulym, 2007;Piskozub and Sulim, 2008):…”

“…which provides straightness of the material interface at the infinity. The first (initial) step of loading and the SSS produced by it are considered in details in Ref [17], where the resulting system of singular integral equations (SSIE) is obtained…”

“…For definiteness it is assumed (other cases are studied similarly) that at the point * 2 = of the top half-space only one alternating monotonously changing concentrated force with magnitude 2 ( ) = ∑ 2( ) ( ) is applied, which increase at odd and decrease at even . SIF magnitude, the size of a slippage zone, displacement discontinuity and energy dissipation at the first step of such loading are studied in Ref [17]. Consider the second step (unloading), when 2(2) ( ) < 0 ( > (1) ).…”