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Growth of a short fatigue crack - A long term simulation using a dislocation technique

Bjerkén, Christina LU and Melin, Solveig LU (2009) In International Journal of Solids and Structures 46(5). p.1196-1204
Abstract
In this study, the growth of a short edge crack during more than 14 000 cycles of fatigue loading is investigated in detail. An edge crack, in a semi-infinite body with no pre-existing obstacles present, is modelled in a boundary element approach by a distribution of dislocation dipoles. The fatigue cycles are fully reversed (R = -1), and the load range is well below the threshold for long fatigue cracks. The developing local plasticity consists of discrete edge dislocations that are emitted from the crack tip. The movements of discrete dislocations are restricted to slip along preferred slip planes. The present model is restricted to a 2D plane strain problem with a through-thickness crack, assuming no 3D irregularities. A remote load is... (More)
In this study, the growth of a short edge crack during more than 14 000 cycles of fatigue loading is investigated in detail. An edge crack, in a semi-infinite body with no pre-existing obstacles present, is modelled in a boundary element approach by a distribution of dislocation dipoles. The fatigue cycles are fully reversed (R = -1), and the load range is well below the threshold for long fatigue cracks. The developing local plasticity consists of discrete edge dislocations that are emitted from the crack tip. The movements of discrete dislocations are restricted to slip along preferred slip planes. The present model is restricted to a 2D plane strain problem with a through-thickness crack, assuming no 3D irregularities. A remote load is applied perpendicular to the crack extension line, and the material parameters are those of a BCC crystal structure. The competition between influence of the global loading on and local shielding of the crack tip governs the crack growth. The growth rate increases in discrete steps with short periods of retardation, from approximately the size of Burgers vector, b, up to 25 b per cycle as the length of the crack is tripled. The plastic zone changes from having an elongated, slender form to include a low angle grain boundary, which, eventually, divides into two parts. The crack growth is found to change from constant acceleration to constant growth rate as the event of the low-angle grain boundary split is approached. The results are compared to long crack characteristics, for which linear elastic fracture mechanics and Paris law can be used to predict fatigue crack growth. The exponent in Paris law varies between 1 and 0 in the present study, i.e. smaller than typical values for ductile BCC materials. The ratio between static and cyclic plastic zone sizes is found to increase during crack growth, and the angle of the general plastic zone direction increases, showing a tendency towards long crack values. The characteristics of the simulated crack growth, found in the present study, are typical for below-threshold growth, with slow acceleration, constant growth rate. and, eventually, either arrest or transition to long crack growth behaviour, as reported in the literature. (c) 2008 Elsevier Ltd. All rights reserved. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Boundary element method, Plastic zone, Long term simulation, Dislocation dynamics, Fatigue, Crack growth
in
International Journal of Solids and Structures
volume
46
issue
5
pages
1196 - 1204
publisher
Elsevier
external identifiers
  • wos:000263422500020
  • scopus:58249130169
ISSN
0020-7683
DOI
10.1016/j.ijsolstr.2008.10.023
language
English
LU publication?
yes
id
6f13c893-89f0-4bff-b46f-66c99564fc04 (old id 1372182)
date added to LUP
2009-05-08 14:17:07
date last changed
2017-01-01 06:02:50
@article{6f13c893-89f0-4bff-b46f-66c99564fc04,
  abstract     = {In this study, the growth of a short edge crack during more than 14 000 cycles of fatigue loading is investigated in detail. An edge crack, in a semi-infinite body with no pre-existing obstacles present, is modelled in a boundary element approach by a distribution of dislocation dipoles. The fatigue cycles are fully reversed (R = -1), and the load range is well below the threshold for long fatigue cracks. The developing local plasticity consists of discrete edge dislocations that are emitted from the crack tip. The movements of discrete dislocations are restricted to slip along preferred slip planes. The present model is restricted to a 2D plane strain problem with a through-thickness crack, assuming no 3D irregularities. A remote load is applied perpendicular to the crack extension line, and the material parameters are those of a BCC crystal structure. The competition between influence of the global loading on and local shielding of the crack tip governs the crack growth. The growth rate increases in discrete steps with short periods of retardation, from approximately the size of Burgers vector, b, up to 25 b per cycle as the length of the crack is tripled. The plastic zone changes from having an elongated, slender form to include a low angle grain boundary, which, eventually, divides into two parts. The crack growth is found to change from constant acceleration to constant growth rate as the event of the low-angle grain boundary split is approached. The results are compared to long crack characteristics, for which linear elastic fracture mechanics and Paris law can be used to predict fatigue crack growth. The exponent in Paris law varies between 1 and 0 in the present study, i.e. smaller than typical values for ductile BCC materials. The ratio between static and cyclic plastic zone sizes is found to increase during crack growth, and the angle of the general plastic zone direction increases, showing a tendency towards long crack values. The characteristics of the simulated crack growth, found in the present study, are typical for below-threshold growth, with slow acceleration, constant growth rate. and, eventually, either arrest or transition to long crack growth behaviour, as reported in the literature. (c) 2008 Elsevier Ltd. All rights reserved.},
  author       = {Bjerkén, Christina and Melin, Solveig},
  issn         = {0020-7683},
  keyword      = {Boundary element method,Plastic zone,Long term simulation,Dislocation dynamics,Fatigue,Crack growth},
  language     = {eng},
  number       = {5},
  pages        = {1196--1204},
  publisher    = {Elsevier},
  series       = {International Journal of Solids and Structures},
  title        = {Growth of a short fatigue crack - A long term simulation using a dislocation technique},
  url          = {http://dx.doi.org/10.1016/j.ijsolstr.2008.10.023},
  volume       = {46},
  year         = {2009},
}