Equistrong hole shape for crack growth deceleration under longitudinal shear

Authors

  • Н. М. Калантарлы Institute of Mathematics and Mechanics of NAS of Azerbaijan, Azerbaijan

Keywords:

crack, longitudinal shear, optimal hole, principle of equal strength

Abstract

The problem of finding an equistrong hole shape in crack tip and its effect on crack development is considered. A criterion and method for the problem solution to prevent brittle fracture of solid weakened by longitudinal shear crack is proposed. Using the perturbation method and the conformal mapping to parametric plane, the problem in each approximation is reduced to boundary value problem for analytic function. In each approximation, the solution of the boundary value problem for analytic function in the class of everywhere bounded functions (stresses) is obtained in closed form. The reduction of the stress concentration on the hole’s contour in the crack tip is done by the method of least squares. To determine expansion coefficients of the Fourier series of the required hole shape function and the optimal value of circumferential tangential stress in surface layer of the hole an infinite linear system of algebraic equations is obtained for elastic material. The condition of brittle fracture is obtained.

Author Biography

Н. М. Калантарлы, Institute of Mathematics and Mechanics of NAS of Azerbaijan

Doctor of Physical and Mathematical Sciences

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Published

2018-01-22

Issue

Vol. 20 No. 4 (2017)

Section

Dynamics and Strength of Machines

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Copyright (c) 2018 Н. М. Калантарлы

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