Vol. 14, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 19
Issue 4, 541–572
Issue 3, 303–540
Issue 2, 157–302
Issue 1, 1–156

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN (electronic): 1559-3959
ISSN (print): 1559-3959
Author index
To appear
Other MSP journals
Effect of surface elasticity on stress intensity factors near mode-III crack tips

Xian-Fang Li

Vol. 14 (2019), No. 1, 43–60

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.

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