# MODELING CRACK INITIATION IN A COMPOSITE UNDER BENDING

 DOI https://doi.org/10.15407/pmach2018.02.025 Journal Journal of Mechanical Engineering – Problemy Mashynobuduvannia Publisher A. Podgorny Institute for Mechanical Engineering Problems National Academy of Science of Ukraine ISSN 0131-2928 (Print), 2411-0779 (Online) Issue Vol. 21, no. 2, 2018 (June) Pages 25-31 Cited by J. of Mech. Eng., 2018, vol. 21, no. 2, pp. 25-31

Author

Sh. G. Hasanov, Azerbaijan Technical University (25, H. Cavid ave., Baku, AZ 1073, Azerbaijan), e-mail: hssh3883@gmail.com

Abstract

It is known that multi-component structures are more reliable and durable than homogeneous ones. At the design stage of new structures from composite materials, it is necessary to take into account the cases when cracks may appear in the material. The purpose of this paper is to construct a computational model for a binder-inclusion composite body, which makes it possible to calculate the limiting external bending loads at which cracking occurs in a composite. A thin plate of elastic isotropic medium (matrix) and inclusions (fibers) from other elastic material, distributed in the plate under bending, is considered. A mathematical description of a crack initiation model in a binder composite under bending is carried out. The theory of analytic functions and the method of power series are used. The determination of the unknown parameters characterizing an initial crack reduces to solving a singular integral equation. A closed system of nonlinear algebraic equations is constructed, whose solution helps to predict cracks in a composite under bending, depending on the geometric and mechanical characteristics of both the binder and the inclusions. The criterion of crack initiation in a composite under the influence of bending loads is formulated. The size of the limiting minimum pre-fraction zone, at which crack initiation occurs is recommended to be considered as a design characteristic of a binder material.

Keywords: binder, inclusion, composite plate, bending, pre-fracture zone, crack formation

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