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.
