Bending of an Isotropic Plate with Two Identical Coaxial Through Cracks Depending on the Width of the Contact Zone of Their Faces and in the Presence of Plastic Zones Near Their Tips

Opanasovych, V. K.; Slobodyan, Mikhail

doi:10.1007/s10958-018-3677-4

Cited by 3 publications

(3 citation statements)

References 7 publications

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“…The experiments carried out by J. Kalthof, I. Shatsky and A. Burgel [6] testify to the significant influence of the contact of crack faces on stress-strain state of the plate under bending. The model of smooth contact of crack faces along a line along the entire length of cracks (linear contact) was used in works [7][8][9]. The model of smooth contact of crack faced along a region of constant width (strip contact) is used in works [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Bending of a plate with circular rigid inclusion and system of cracks on the assumption of strip crack face contact

Слободян

Bilash

Seliverstov

et al. 2023

IOP Conf. Ser.: Mater. Sci. Eng.

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The article presents a solution to the bending problem for an infinite isotropic plate with a circular rigid inclusion and arbitrarily oriented straight through cracks. It is assumed that under the action of an external load at infinity, the faces of all cracks are in smooth contact along a region of constant width near the upper surface of the plate. The solution is obtained using methods of the theory of functions of complex variable and complex potentials and is reduced to a system of singular integral equations, which is numerically solved by the mechanical quadrature method. On the basis of numerical analysis, the graphical dependences of the contact force, forces and moments intensity factors are constructed at various parameters of the problem.

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Section: Introductionmentioning

confidence: 99%

Bending of a plate with circular rigid inclusion and system of cracks on the assumption of strip crack face contact

Слободян

Bilash

Seliverstov

et al. 2023

IOP Conf. Ser.: Mater. Sci. Eng.

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“…This approach was developed by Shatskii (1989), Shatsky (1998), Liu et al (1999), Shat'skyi and Perepichka (2004), Shats'kyi and Makoviichuk (2005), Shatskyi et al (2017) to study the behavior of closable cracks under combined tension and bending. Certain problems for arrays of rectilinear contact cracks in plates and shells have been solved in the papers by Shatskii (1990Shatskii ( , 1991, Shatsky (1998), Perepichka (1998), Shats'kyi and Dalyak (2000), Perepichka and Shats'kyi (2002), Dalyak (2004Dalyak ( , 2019, Opanasovych and Selivestrov (2006), Opanasovych et al (2008), Shats'kyi and Makoviichuk (2009), Shatskii and Makoviichuk (2011), Syasky and Muzychuk (2012), Dovbnya and Shevtsova (2014), Shats'kyi (2015), Dovbnya and Hryhorchuk (2016), Opanasovych and Slobodyan (2018). In the article by Shats'kyi and Dalyak (2002), the elastic equilibrium of the bent plate containing the rectilinear cracks, connected with coaxial slits, was addressed.…”

Section: Introductionmentioning

confidence: 99%

Interference of Closable Cracks and Narrow Slits in an Elastic Plate Under Bending

Dalyak¹,

Shatskyi²

2020

JSSCM

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The problem of bending of an infinite plate containing an array of trough closable cracks and narrow slits is considered in a two-dimensional statement. A crack is treated as a mathematical cut, the edges of which are able to contact along the line on the plate outside. A slit is referred to as a cut with contact stress-free surfaces and the negative jump of normal displacement can occur on this cut. The crack closure caused by bending deformation was studied based on the classical hypothesis of direct normal and previously developed model of the contact of edges along the line. A new boundary problem for a couple of biharmonic equations of plane stress and plate bending with interconnected boundary conditions in the form of inequalities on the cuts is formulated. The method of singular integral equations was applied in order to develop approximate analytical and numerical solutions to the problem. The forces and moments intensity factors near the peaks of defects and contact reaction on the closed edges of the cracks are calculated. A detailed analysis was carried out for parallel rectilinear crack and slit, depending on their relative location. Presented results demonstrate qualitative differences in the stress concentration near the defects of different nature.

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“…Shatsky [11] was the first to investigate the cracks closure effect in the simultaneous extension and bending of a plate. As to the problem of reciprocal influence of contact cracks, the most studied cases are those of collinear defects in plates [12][13][14][15] and shells [16][17][18][19][20]. The periodical problems for parallel defects were obtained, taking into account crack closure in infinite [21] and half-infinite [22] plates.…”

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confidence: 99%

Investigation of the interaction of two parallel shifted cracks in plate bending adjusted for their closure

Dalyak

2019

Theor appl mech (Belgr)

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The problem of interaction of two parallel shifted cracks in plate bending is considered. The cracks closure has been investigated in the classical two-dimensional statement, using the model of smooth contact along a line. The influence of the relative position of cracks and of the contact of their edges on the forces and moment intensity factors has been studied by the singular integral equations method.

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Bending of an Isotropic Plate with Two Identical Coaxial Through Cracks Depending on the Width of the Contact Zone of Their Faces and in the Presence of Plastic Zones Near Their Tips

Cited by 3 publications

References 7 publications

Bending of a plate with circular rigid inclusion and system of cracks on the assumption of strip crack face contact

Bending of a plate with circular rigid inclusion and system of cracks on the assumption of strip crack face contact

Interference of Closable Cracks and Narrow Slits in an Elastic Plate Under Bending

Investigation of the interaction of two parallel shifted cracks in plate bending adjusted for their closure

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