LONGITUDINAL SHIFT OF THE BINDER AND INCLUSIONS OF A COMPOSITE WEAKENED BY TWO-PERIODIC RIGHT LINEAR CRACKS

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Published: Sunday, 04 April 2021 20:08
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Volume 6 (2), April 2021, Pages 23-35

1Rafail Mehdiev, 2Alekber Mehdiev

1Assistant Professor, Department of “Materials Technology”, Azerbaijan Technical University, Candidate of Physical and Mathematical Sciences, Azerbaijan. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

2Associate Professor, Department of “Mathematics”, Azerbaijan State Oil and Industry University, Candidate of Physical and Mathematical Sciences, Azerbaijan. E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

 Аbstract

In this paper, we consider antiplane deformation for an isotropic elastic material consisting of an infinite system of parallel identical circular cylindrical fibers covered with a uniform cylindrical film uniformly covering the surface of each fiber and a bonding medium weakened by a doubly periodic system of rectilinear cracks. Each washer has a centrally located crack that is less than the diameter of the washer. The presented stresses and their displacements are expressed in terms of an analytical function.

For the solution, the well-known position is used that the displacement in the case of an antiplane shear is a harmonic function. A known representation of the solution in each area is applied through the corresponding complex analytical function. Three analytic functions are represented by Laurent series. Satisfying the boundary condition on the contours of holes and crack faces, the problem is reduced to two infinite algebraic systems with respect to the sought coefficients and to two singular integral equations with a Cauchy-type kernel. Then the singular integral equation is reduced to a finite algebraic system of equations by the Multopp – Kalandia method. The procedure for calculating the stress intensity coefficients is given. The numerical implementation of the described method is given at IBM. The results of calculations of the critical load depending on the crack length and elastic geometric parameters of the perforated medium are presented.

Keywords: isotropically elastic material, doubly periodic lattice, rectilinear cracks, stress intensity factor, mean stresses, critical load, circular hole, longitudinal shear.