סמינר מחלקתי

School of Mechanical Engineering Seminar
Wednesday, November 26, 2014 at 15:00
Wolfson Building of Mechanical Engineering, Room 206

Crack-arresting voided periodic materials

Or Hadar

MSc Student of Prof. Shmuel Ryvkin

Evaluation of the stress field around the tip of a semi-infinite crack embedded in a material with periodic microstructure is very difficult because it is necessary to carry out a large volume of calculations. This work presents and implements a novel method to perform this calculation. The conditions at the boundaries of a rectangular domain around the tip are formulated by the use of K-field for the homogeneous material possessing effective elastic properties and then the finite discrete Fourier transform is applied. This allows to replace standard analysis of a large periodic domain with many cells by the analysis of a single repetitive cell in the transform space which can be carried out by any numerical method. Consequently, the volume of calculations in comparison with the standard approach is reduced and the problem of a macrocrack embedded in a material with fine microstructure can be addressed without simplifying assumptions. The accuracy of the proposed approach is verified by a comparison with the analytical solution for a crack embedded in a homogeneous plane and with the known results for low-density voided material.

Application of the suggested method is given for a crack in a two-dimensional periodically voided material with triangular isotropic layout. The representative cell problem is resolved by the finite element method. It was assumed that the parent material is brittle and fracture toughness of the voided material is determined by the stress criterion for crack propagation, i.e. the crack will propagate when the maximal tensile stress around the tip will reach the tensile strength of the parent material. The dependence of the fracture toughness upon the material relative density is investigated for circular and hexagon voids, as well as its dependence on the shape of the voids for high density material. A comparison of the fracture toughnesses of the solid and voided materials has shown for which parameter combinations voided ones will provide better crack resistance. Results are given for materials commonly used: alumina 99.9%, silicon nitride, sapphire, boron nitride and mullite.