An equilibrium internal transverse crack in a composite elastic half-plane

Rashidova, E. V.; Sobol, B. V.

doi:10.1016/j.jappmathmech.2017.08.016

Cited by 5 publications

(4 citation statements)

References 17 publications

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“…Paper [2] considers the problem of stress concentration in the neighborhood of the crack vertices for a crack of the finite length, located perpendicular to the interface of two elastic bodies -the half-plane and strip. Using the method of generalized integral transformations, the problem is reduced to solving a singular integral equation with the Cauchy nucleus.…”

Section: Literature Review and Problem Statementmentioning

confidence: 99%

Determining patterns in thermoelastic interaction between a crack and a curvilinear inclusion located in a circular plate

Zelenyak

Klapchuk

Kolyasa

et al. 2021

EEJET

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A two-dimensional mathematical model of the thermoelastic state has been built for a circular plate containing a curvilinear inclusion and a crack, under the action of a uniformly distributed temperature across the entire piece-homogeneous plate. Using the apparatus of singular integral equations (SIEs), the problem was reduced to a system of two singular integral equations of the first and second kind on the contours of the crack and inclusion, respectively. Numerical solutions to the system of integral equations have been obtained for certain cases of the circular disk with an elliptical inclusion and a crack in the disk outside the inclusion, as well as within the inclusion. These solutions were applied to determine the stress intensity coefficients (SICs) at the tops of the crack. Stress intensity coefficients could later be used to determine the critical temperature values in the disk at which a crack begins to grow. Therefore, such a model reflects, to some extent, the destruction mechanism of the elements of those engineering structures with cracks that are operated in the thermal power industry and, therefore, is relevant. Graphic dependences of stress intensity coefficients on the shape of an inclusion have been built, as well as on its mechanical and thermal-physical characteristics, and a distance to the crack. This would make it possible to analyze the intensity of stresses in the neighborhood of the crack vertices, depending on geometric and mechanical factors. The study's specific results, given in the form of plots, could prove useful in the development of rational modes of operation of structural elements in the form of circular plates with an inclusion hosting a crack. The reported mathematical model builds on the earlier models of two-dimensional stationary problems of thermal conductivity and thermoelasticity for piece-homogeneous bodies with cracks.

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Section: Literature Review and Problem Statementmentioning

confidence: 99%

Determining patterns in thermoelastic interaction between a crack and a curvilinear inclusion located in a circular plate

Zelenyak

Klapchuk

Kolyasa

et al. 2021

EEJET

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“…The solution of the problem consists in solving the system of two integral equations (8) and (9) of the heat conduction problem with respect to functions ( 1 ), ′ ( 2 ) and substituting them into the system of two equations (11) and (12) of the thermoelasticity problem for the determination of functions ( ), = 1, 2 . Then we calculate the SIFs ± , ± , which are the real quantities that characterise the stress-deformed state in the vicinity of the crack tips, according to formula (13). The numerical solution of the system of equations (8), (9), (12) and (13) is found using the method of mechanical quadrature (Erdogan et.…”

Section: Fig 2 a Periodic System Of Elliptic Inclusions And Rectilimentioning

confidence: 99%

“…The problem of the stress concentration in the vicinity crack tips for a crack of finite length located perpendicular to the interface of two elastic bodies -a half-plane and a strip -is considered. Using the method of generalised integral transforms, the problem reduces to the solution of an SIE with a Cauchy kernel (Rashidova and Sobol, 2017). Local frictional heating of surface of a layered plate with inclusion was investigated in Havrysh (2017Havrysh ( , 2015.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Modelling of Stationary Thermoelastic State for a Plate with Periodic System of Inclusions and Cracks

Zelenyak

2019

Acta Mechanica Et Automatica

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Two-dimensional stationary problem of heat conduction and thermoelasticity for infinite elastic body containing periodic system of inclusions and cracks is considered. Solution of the problem is constructed using the method of singular integral equations (SIEs). The numerical solution of the system integral equations are obtained by the method of mechanical quadrature for a plate heated by a heat flow, containing periodic system elliptic inclusions and thermally insulated cracks. There are obtained graphic dependences of stress intensity factors (SIFs), which characterise the distribution of intensity of stresses at the tops of a crack, depending on the length of crack, elastic and thermoelastic characteristics inclusion, relative position of crack and inclusion.

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“…A system of singular integral equations is obtained with the distribution dislocation function as unknown, and the traction applied on the crack faces and the right hand terms in the paper [1]. In the paper [2], the problem of the stress concentration in the vicinity of the crack tips for a crack of finite length located perpendicular to the interface of two elastic bodies -a half plane and a strip is considered. Using the method of generalized integral transform, the problem reduces to solution of a singular integral equation with a Cauchy kernel.…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of stationary thermoelastic state in a half plane containing a periodic system of cracks due to periodic local heating by a heat flux

Zelenyak¹,

Kolyasa²,

Klapchuk³

2019

Ukr. j. mech. eng. mater. sci.

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Purpose. To determine the two-dimensional thermoelastic state in a semi-infinite solid (half-plane), weakened by a system of periodic internal cracks under conditions of local heating on the edge of the half plane. Heat flux due to frictional heating on the local area of the body, causes changes in temperature and stresses in the body, which significantly affects its strength, as it can lead to crack growth and local destruction. Therefore, the study of the problem of frictional heat is of a practical interest. This paper proposes to investigate the stress-deformed state in the vicinity of the crack tip, depending on the period of cracks placement. Methodology. The methods for studying two-dimensional thermoelastic state of a body with crack as stress concentrators are based on the method of complex variable function. Reducing the problem of stationary heat conduction and thermoelasticity to singular integral equations (SIE) of the first kind, the numerical solution by the method of mechanical quadrature was obtained. Findings. In this paper, we present graphical dependencies of stress intensity factors (SIF) at the crack tip on the angle of orientation and on the relative position of cracks. The obtained results will be used later to determine the critical value of the intensity of the local heat flux from equations of limit equilibrium at which crack growth and the local destruction of the body occur. Originality. The originality of our solution lies in the fact that the new two-dimensional problems of heat conduction and thermoelasticity for a half plane containing a periodic cracks due to local heating by a heat flux are obtained. Practical value. The practical value is the ability to extend our knowledge of the real situation in the thermoelastic elements of engineering structures with cracks that operate under conditions of heat stress (frictional heat) in various industries, particularly in mechanical engineering. The results of specific values of SIF at the crack tip in graphs may be useful in the development of sustainable modes of structural elements in terms of preventing the growth of cracks.

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An equilibrium internal transverse crack in a composite elastic half-plane

Cited by 5 publications

References 17 publications

Determining patterns in thermoelastic interaction between a crack and a curvilinear inclusion located in a circular plate

Determining patterns in thermoelastic interaction between a crack and a curvilinear inclusion located in a circular plate

Mathematical Modelling of Stationary Thermoelastic State for a Plate with Periodic System of Inclusions and Cracks

Mathematical modeling of stationary thermoelastic state in a half plane containing a periodic system of cracks due to periodic local heating by a heat flux

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