Int J Fract
https://doi.org/10.1007/s10704-018-0292-9
ORIGINAL PAPER
Crack nucleation from a wedge disclination dipole with shift
of rotation axes
Mao S. Wu
Received: 3 November 2017 / Accepted: 22 May 2018
© Springer Science+Business Media B.V., part of Springer Nature 2018
Abstract This paper analyzes crack nucleation from
a wedge disclination dipole in the presence of a remote
stress, accounting for the shift of the rotation axes
within the dipole arm of the disclinations. A Zener–
Griffith crack is assumed and an energy method is
employed for the analysis. A single energy equation
determines the equilibrium crack lengths and the crack
head opening. Uniaxial and biaxial dipoles are com-
pared: in the former the disclinations share a common
rotation axis while in the latter the axes are separate.
The results show that stable and unstable cracks can
nucleate from the positive disclination of the dipole,
but some of them are energetically unfavorable. A uni-
axial dipole is stable against crack nucleation when
the axis is located away from the positive disclination.
Biaxial dipoles are more stable when the rotation axis of
each disclination approaches the defect line of the other
disclination. If the negative disclinations of a uniaxial
dipole and a biaxial dipole have the same axis shift, the
critical nucleation stress of the biaxial dipole is larger
if its positive disclination shift is more than that of the
uniaxial dipole. Stablecracklengthsgenerallyincrease,
while the crack head openings decrease, with the axis
shift of the positive disclination. The crack head open-
ing to crack length ratio is of the order of 0.001–0.01,
and can be higher if an applied stress is present.
M. S. Wu (
B
)
School of Mechanical and Aerospace Engineering,
Nanyang Technological University, Singapore 639798,
Singapore
e-mail: mmswu@ntu.edu.sg
Keywords Crack nucleation · Wedge disclination
dipole · Rotation axis shift · Zener–Griffith crack
1 Introduction
A disclination is a rotational defect, which may be
wedge or twist in character. A wedge disclination has
its line parallel to the Frank vector of rotation, whereas
a twist disclination has its line perpendicular to the vec-
tor, in analogy to screw and edge dislocations, respec-
tively. Conceptually, a positive wedge disclination can
be created by removing a wedge of material from a
circular cylinder, mending the cut faces and allowing
the cylinder to relax (Romanov and Vladimirov 1992).
Similarly, a negative wedge disclination can be visual-
ized in terms of inserting a wedge into a cylinder. On
its own, a disclination has a logarithmic stress singu-
larity at the defect line and at long range. For this rea-
son, disclinations usually exist in dipole or quadrupole
configurations containing both positive and negative
defects, with a screened stress at long range. Single
disclinations may also exist in objects with boundaries
that screen their stress field, such as a nanowire. More-
over, disclinations can be represented by dislocation
walls. A negative wedge disclination can be created by
the insertion of a wedge as mentioned above, or equiv-
alently by a succession of edge dislocations with small
Burgers vectors.
Disclination dipoles have been used to describe and
model rotational plastic deformation and microstruc-
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