Vol. 14, No. 1, 2019

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Effect of surface elasticity on stress intensity factors near mode-III crack tips

Xian-Fang Li

Vol. 14 (2019), No. 1, 43–60
Abstract

This paper studies a nanoscale mode-III crack in a homogeneous isotropic material. Classical elasticity, incorporating surface elasticity, is applied to solve a mixed boundary value problem. An emphasis is placed on the influence of surface elasticity on the stress intensity factors. Using the Fourier transform, the problem is reduced to a hypersingular integro-differential equation, then to a singular integro-differential equation with Cauchy kernel or a weakly singular integral equation with logarithmic kernel of the second kind. Using the Galerkin method, a solution of the resulting singular integro-differential equation is determined through expanding the out-of-plane displacement jump across crack faces as a series of Chebyshev polynomials. The influences of surface material properties on the stress intensity factor are examined and displayed graphically. For most materials, the surface effect decreases the stress intensity factors and enhances the effective fracture toughness of most nanoscale materials with a crack.

Keywords
nanoscale crack, surface elasticity, stress intensity factor, hypersingular integro-differential equation.
Milestones
Received: 18 July 2018
Revised: 29 November 2018
Accepted: 4 December 2018
Published: 7 April 2019
Authors
Xian-Fang Li
School of Civil Engineering
Central South University
Changsha, 410075
China