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2 Acta Mechanica et Automatica

2 2020

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Pure bending of strip (beam) with crack in strip of tensile stress with allowance for plastic strips near crack tips

Sulym Heorgij, Opanasovych Viktor, Slobodian Mykola, Bilash Oksana

Acta Mechanica et Automatica

2020

Vol. 14, no. 1

44--49

In the article, the pure bending problem for strip (beam) with straight, perpendicular to its axis crack located in the zone of tensile stresses is investigated on the assumption of narrow plastic strips near crack tips. Using methods of the theory of functions of a complex variable and complex potentials, the problem is reduced to the several linear conjunction problems. The solutions of latter problems are ob-tained in the class of functions confined in the edges of plastic strips. Formulas for the calculation of their lengths are derived. Expressions for the determination of crack tip opening values are written. Numerical analysis of the problem is performed.

A circular inclusion and two radial coaxial cracks with contacting faces in a piecewise homogeneous isotropic plate under bending

Sulym Heorhiy, Opanasovych Viktor, Zvizlo Ivan, Seliverstov Roman, Bilash Oksana

Acta Mechanica et Automatica

2020

Vol. 14, no. 1

16--21

The bending problem of an infinite, piecewise homogeneous, isotropic plate with circular interfacial zone and two coaxial radial cracks is solved on the assumption of crack closure along a line on the plate surface. Using the theory of functions of a complex variable, complex potentials and a superposition of plane problem of the elasticity theory and plate bending problem, the solution is obtained in the form of a system of singular integral equations, which is numerically solved after reducing to a system of linear algebraic equations by the mechanical quadrature method. Numerical results are presented for the forces and moments intensity factors, contact forces between crack faces and critical load for various geometrical and mechanical task parameters.