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Prediction of shear crack growth direction under compressive loading and plane strain conditions

Isaksson, P. and Ståhle, P. LU (2002) In International Journal of Fracture 113(2). p.175-194
Abstract
A directional crack growth prediction in a compressed homogenous elastic isotropic material under plane strain conditions is considered. The conditions at the parent crack tip are evaluated for a straight stationary crack. Remote load is a combined biaxial compressive normal stress and pure shear. Crack surfaces are assumed to be frictionless and to remain closed during the kink formation wherefore the mode I stress intensity factor K I is vanishing. Hence the mode II stress intensity factor K II remains as the single stress intensity variable for the kinked crack. An expression for the local mode II stress intensity factor k 2 at the tip of a straight kink has been calculated numerically with an integral equation using the solution scheme... (More)
A directional crack growth prediction in a compressed homogenous elastic isotropic material under plane strain conditions is considered. The conditions at the parent crack tip are evaluated for a straight stationary crack. Remote load is a combined biaxial compressive normal stress and pure shear. Crack surfaces are assumed to be frictionless and to remain closed during the kink formation wherefore the mode I stress intensity factor K I is vanishing. Hence the mode II stress intensity factor K II remains as the single stress intensity variable for the kinked crack. An expression for the local mode II stress intensity factor k 2 at the tip of a straight kink has been calculated numerically with an integral equation using the solution scheme proposed by Lo (1978) and refined by He and Hutchinson (1989). The confidence of the solution is strengthened by verifications with a boundary element method and by particular analytical solutions. The expression has been found as a function of the mode II stress intensity factor K II of the parent crack, the direction and length of the kink, and the difference between the remote compressive normal stresses perpendicular to, and parallel with, the plane of the parent crack. Based on the expression, initial crack growth directions have been suggested. At a sufficiently high non-isotropic compressive normal stress, so that the crack remains closed, the crack is predicted to extend along a curved path that maximizes the mode II stress intensity factor k 2. Only at an isotropic remote compressive normal stress the crack will continue straight ahead without change of the direction. Further, an analysis of the shape of the crack path has revealed that the propagation path is, according the model, required to be described by a function y=cx γ, where the exponent γ is equal to 3/2. In that case, when γ=3/2, predicts the analytical model a propagation path that is self-similar (i.e. the curvature c is independent of any length of a crack extension), and which can be described by a function of only the mode II stress intensity factor K II at the parent crack tip and the difference between the remote compressive normal stress perpendicular to, and parallel with, the parent crack plane. Comparisons with curved shear cracks in brittle materials reported in literature provide limited support for the model discussed. (Less)
Abstract (Swedish)
A directional crack growth prediction in a compressed homogenous elastic isotropic material under plane strain conditions is considered. The conditions at the parent crack tip are evaluated for a straight stationary crack. Remote load is a combined biaxial compressive normal stress and pure shear. Crack surfaces are assumed to be frictionless and to remain closed during the kink formation wherefore the mode I stress intensity factor K-I is vanishing. Hence the mode II stress intensity factor K-II remains as the single stress intensity variable for the kinked crack. An expression for the local mode H stress intensity factor k(2) at the tip of a straight kink has been calculated numerically with an integral equation using the solution scheme... (More)
A directional crack growth prediction in a compressed homogenous elastic isotropic material under plane strain conditions is considered. The conditions at the parent crack tip are evaluated for a straight stationary crack. Remote load is a combined biaxial compressive normal stress and pure shear. Crack surfaces are assumed to be frictionless and to remain closed during the kink formation wherefore the mode I stress intensity factor K-I is vanishing. Hence the mode II stress intensity factor K-II remains as the single stress intensity variable for the kinked crack. An expression for the local mode H stress intensity factor k(2) at the tip of a straight kink has been calculated numerically with an integral equation using the solution scheme proposed by Lo (1978) and refined by He and Hutchinson (1989). The confidence of the solution is strengthened by verifications with a boundary element method and by particular analytical solutions. The expression has been found as a function of the mode II stress intensity factor K-II of the parent crack, the direction and length of the kink, and the difference between the remote compressive normal stresses perpendicular to, and parallel with, the plane of the parent crack. Based on the expression, initial crack growth directions have been suggested. At a sufficiently high non-isotropic compressive normal stress, so that the crack remains closed, the crack is predicted to extend along a curved path that maximizes the mode II stress intensity factor k(2). Only at an isotropic remote compressive normal stress the crack will continue straight ahead without change of the direction. Further, an analysis of the shape of the crack path has revealed that the propagation path is, according the model, required to be described by a function y = cx(gamma), where the exponent y is equal to 3/2. In that case, when gamma = 3/2, predicts the analytical model a propagation path that is self-similar (i.e. the curvature c is independent of any length of a crack extension), and which can be described by a function of only the mode II stress intensity factor K-II at the parent crack tip and the difference between the remote compressive normal stress perpendicular to, and parallel with, the parent crack plane. Comparisons with curved shear cracks in brittle materials reported in literature provide limited support for the model discussed. (Less)
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author
and
publishing date
type
Contribution to journal
publication status
published
subject
in
International Journal of Fracture
volume
113
issue
2
pages
20 pages
publisher
Springer
external identifiers
  • wos:000173841600004
  • scopus:0036171354
ISSN
0376-9429
DOI
10.1023/a:1015581922242
language
English
LU publication?
no
additional info
Isaksson, P Stahle, P Stahle, Per/J-3590-2014
id
339202b3-6880-4109-80b9-d107aa00765d
date added to LUP
2019-06-25 19:10:02
date last changed
2022-01-31 22:39:43
@article{339202b3-6880-4109-80b9-d107aa00765d,
  abstract     = {{A directional crack growth prediction in a compressed homogenous elastic isotropic material under plane strain conditions is considered. The conditions at the parent crack tip are evaluated for a straight stationary crack. Remote load is a combined biaxial compressive normal stress and pure shear. Crack surfaces are assumed to be frictionless and to remain closed during the kink formation wherefore the mode I stress intensity factor K I is vanishing. Hence the mode II stress intensity factor K II remains as the single stress intensity variable for the kinked crack. An expression for the local mode II stress intensity factor k 2 at the tip of a straight kink has been calculated numerically with an integral equation using the solution scheme proposed by Lo (1978) and refined by He and Hutchinson (1989). The confidence of the solution is strengthened by verifications with a boundary element method and by particular analytical solutions. The expression has been found as a function of the mode II stress intensity factor K II of the parent crack, the direction and length of the kink, and the difference between the remote compressive normal stresses perpendicular to, and parallel with, the plane of the parent crack. Based on the expression, initial crack growth directions have been suggested. At a sufficiently high non-isotropic compressive normal stress, so that the crack remains closed, the crack is predicted to extend along a curved path that maximizes the mode II stress intensity factor k 2. Only at an isotropic remote compressive normal stress the crack will continue straight ahead without change of the direction. Further, an analysis of the shape of the crack path has revealed that the propagation path is, according the model, required to be described by a function y=cx γ, where the exponent γ is equal to 3/2. In that case, when γ=3/2, predicts the analytical model a propagation path that is self-similar (i.e. the curvature c is independent of any length of a crack extension), and which can be described by a function of only the mode II stress intensity factor K II at the parent crack tip and the difference between the remote compressive normal stress perpendicular to, and parallel with, the parent crack plane. Comparisons with curved shear cracks in brittle materials reported in literature provide limited support for the model discussed.}},
  author       = {{Isaksson, P. and Ståhle, P.}},
  issn         = {{0376-9429}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{175--194}},
  publisher    = {{Springer}},
  series       = {{International Journal of Fracture}},
  title        = {{Prediction of shear crack growth direction under compressive loading and plane strain conditions}},
  url          = {{http://dx.doi.org/10.1023/a:1015581922242}},
  doi          = {{10.1023/a:1015581922242}},
  volume       = {{113}},
  year         = {{2002}},
}