Biaxial Bending of an Isotropic Plate with Through Rectilinear Crack with Regard for the Width of the Contact Zone of its Edges and in the Presence of Plastic Zones Near its Tips

Opanasovych, V. K.; Slobodyan, Mikhail

doi:10.1007/s10958-017-3613-z

Cited by 3 publications

(6 citation statements)

References 7 publications

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“…It should be noted that for the case when we have only biaxial bending, i.e. = = 0, we will get the results obtained in the article (Opanasovych, 2015).…”

Section: Construction Of the Solution Of The Problemsupporting

confidence: 52%

“…which takes place, as shown in publications of Opanasovych et al (2008Opanasovych et al ( , 2015 in a case, when there are no plastic zones in the crack tips. Crack opening displacement in the crack tips on the lower base of the plate we will find by the formula:…”

Section: Construction Of the Solution Of The Problemmentioning

confidence: 71%

“…To determine the contact force between the crack banks we take into account formulas (6), (7), (11) and (30). After the appropriate transformations we will get:…”

Section: Construction Of the Solution Of The Problemmentioning

confidence: 99%

“…If we take into account (7), (8), (11), (19), (30), then after transformations from (33) we will get:…”

Section: Construction Of the Solution Of The Problemmentioning

confidence: 99%

“…In the work of García-Collado et al (2017) a numerical analysis of influence of plasticity, caused by crack closure, that uses the method of crack propagation in combination with cyclic plasticity in the crack tip. Research of stress-strain state at biaxial bending or combined bending and tension of isotropic plate with through-crack considering crack faces contact both on the crack line and in the region of constant width near one of the basis of the plate, without considering the plastic zones in the crack tip are represented in the works of Shackyj et al (1989Shackyj et al ( , 1995Shackyj et al ( , 2004aShackyj et al ( , 2004b, Slepyan et al (1995), Papargyri-Pegiou et al (1995), Opanasovych (2007Opanasovych ( , 2008, excluding papers of Alfavicka (2015) and Opanasovych et al (2015), where such consideration is done. In this article is studied the case of combined bending and tension of isotropic plate with through crack, faces of which are in contact on the area of constant width under the action of distributed forces and bending moments, applied at infinity, the vectors of which, are parallel and perpendicular to the crack faces, and considering plastic zones in the crack tip, where Treska plasticity conditions in the form of surface layer or the plastic hinge are satisfied.…”

Section: Introductionmentioning

confidence: 99%

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Combined Bending with Tension of Isotropic Plate with Crack Considering Crack Banks Contact and Plastic Zones at its Tops

Sulym

Opanasovych

Слободян

et al. 2018

Acta Mechanica Et Automatica

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Stress-strain state of isotropic plate with rectilinear through-crack at combined action of bending and tension, realized by applying distributed forces and bending moments at infinity, the vectors of which are parallel and perpendicular to the crack, is investigated. Under the influence of the internal stress the crack faces contacts on area of constant width near the upper base of plate, and plastic zones forms in its tips. Using methods of the theory of complex variables, complex potentials plane problem of elasticity theory and the classical theory of plates bending, solving of the problem is reduced to the set of linear conjugation problems and their analytical solution is built in a class of functions of limited plastic zones in the crack tips. The conditions of existence of the solution of the problem in these terms are determined. Using Treska plasticity conditions in the form of surface layer or the plastic hinge, the length of plastic zone and crack opening displacement are found analytically. Their numerical analysis for various parameters of the problem is conducted.

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“…It should be noted that for the case when we have only biaxial bending, i.e. = = 0, we will get the results obtained in the article (Opanasovych, 2015).…”

Section: Construction Of the Solution Of The Problemsupporting

confidence: 52%

Section: Construction Of the Solution Of The Problemmentioning

confidence: 71%

“…To determine the contact force between the crack banks we take into account formulas (6), (7), (11) and (30). After the appropriate transformations we will get:…”

Section: Construction Of the Solution Of The Problemmentioning

confidence: 99%

“…If we take into account (7), (8), (11), (19), (30), then after transformations from (33) we will get:…”

Section: Construction Of the Solution Of The Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Combined Bending with Tension of Isotropic Plate with Crack Considering Crack Banks Contact and Plastic Zones at its Tops

Sulym

Opanasovych

Слободян

et al. 2018

Acta Mechanica Et Automatica

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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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Bending of a piecewise homogeneous plate with a circular interfacial materials separation zone and radial crack considering the strip contact of its edges

Slobodian,

Zvizlo,

Bilash

et al. 2024

Vib. proced.

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The work presents a solution to the bending problem of an infinite piecewise homogeneous isotropic plate with an elastic circular washer and a radial through straight crack. It was assumed that under the action of an external loads at infinity, the edges of the crack are smoothly contacted on area of constant width (strip contact) on the upper base of the plate. The solution of the problem is built using the methods of the theory of functions of a complex variable and complex potentials and is reduced to a system of singular integral equations, which is numerically solved using the method of mechanical quadrature A numerical analysis of the problem is conducted and graphic dependencies of contact force, coefficients of intensity of moments and forces at various parameters of the problem were constructed.

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Biaxial Bending of an Isotropic Plate with Through Rectilinear Crack with Regard for the Width of the Contact Zone of its Edges and in the Presence of Plastic Zones Near its Tips

Cited by 3 publications

References 7 publications

Combined Bending with Tension of Isotropic Plate with Crack Considering Crack Banks Contact and Plastic Zones at its Tops

Combined Bending with Tension of Isotropic Plate with Crack Considering Crack Banks Contact and Plastic Zones at its Tops

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

Bending of a piecewise homogeneous plate with a circular interfacial materials separation zone and radial crack considering the strip contact of its edges

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