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

Abstract

The paper presents the exact solution of the antiplane problem for an inhomogeneous bimaterial with the interface crack exposed to the normal load and cyclic loading by a concentrated force in the longitudinal direction. Using discontinuity function method the problem is reduced to the solution of singular integral equations for the displacement and stress discontinuities at the domains with sliding friction. The paper provides the analysis of the effect of friction and loading parameters on the size of these zones. Hysteretic behaviour of the stress and displacement discontinuities in these domains is observed.

Effect of the Transverse Functional Gradient of the Thin Interfacial Inclusion Material on the Stress Distribution of the Bimaterial under Longitudinal Shear

“…Successful attempts were made in [ 17 , 33 , 42 , 43 , 44 , 45 ] to apply it to consider the influence of various physical and contact nonlinearities in the antiplane problem of elasticity theory for two compressed half-spaces with interfacial defects. The frictional slip with possible heat generation for contacting bodies [ 34 , 44 , 46 , 47 , 48 , 49 ] and the boundary element approach [ 50 , 51 , 52 ] were also considered here. Inhomogeneity of the mechanical properties of structural materials can be both designed for a specific purpose (FGM) and a consequence of technological processes of obtaining new materials and their processing (FSW, ball-burnishing process, etc.)…”

An Interface Crack with Mixed Electro-Magnetic Conditions at it Faces in a Piezoelectric / Piezomagnetic Bimaterial under Anti-Plane Mechanical and In-Plane Electric Loadings

“…Also the case of a moving interface crack between magnetoelectroelastic and functionally graded elastic layers was studied by Hu and Chen (2014). An exact analytic solution to the anti-plane problem for a non-homogeneous bimaterial medium containing closed interfacial cracks, which faces can move relatively to each other with dry friction under the action of arbitrary single loading and also cyclic loading was considered by Sulym et al, (2015aSulym et al, ( , 2015b. A more detailed review of anti-plane crack problem investigation in piezoelectric/piezomagnetic bimaterials is presented in Govorukha et al, (2016).…”

The problem of the partial delamination of the elastic interface thin inclusion in the conditions of longitudinal shear of the bimaterial

“…Спроби врахувати різноманітну геометричну нелінійність у антиплоскій задачі для двох стиснених півпросторів із міжфазними дефектами було зроблено різними авторами в працях [14 -19], в т.ч. розглядалися фрикційне проковзування контактуючих тіл [14 -16], гранично-елементний підхід [17,19].…”

“…приймаємо умови дотикового тертьового контакту [16,17], які передбачають, що в усіх точках L  дотичні напруження (зусилля тертя) дорівнюють…”

“…Величини, зазначені далі індексом "0" зверху, відповідають НДС масиву без модельованих неоднорідностей (включень, тріщин тощо) за відповідного зовнішнього навантаження (однорідний розв'язок). Тут і далі використані позначення [15,17]:…”