Date
2020-11-23Metadata
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The J-integral for mixed-mode loaded cracks with cohesive zones
Abstract
The J-integral quantifies the loading of a crack tip, just as the crack tip opening displacement (CTOD) emanating from the cohesive zone model. Both quantities, being based on fundamentally different interpretations of cracks in fracture mechanics of brittle or ductile materials, have been proven to be equivalent in the late 60s of the previous century, however, just for the simple mode-I loading case. The relation of J and CTOD turned out to be uniquely determined by the constitutive law of the cohesive zone in front of the physical crack tip. In this paper, a J-integral vector is derived for a mixed-mode loaded crack based on the cohesive zone approach, accounting for the most general case of a mode-coupled cohesive law. While the J1-coordinate, as energy release rate of a straight crack extension, is uniquely related to the cohesive potential at the physical crack tip and thus to the CTOD, the J2-coordinate depends on the solution of the specific boundary value problem in terms of stresses and displacement gradients at the cohesive zone faces. The generalized relation is verified for the Griffith crack, employing solutions of the Dugdale crack based on improved holomorphic functions.
Citation
In: International Journal of Fracture Volume 227 / Issue 1 (2020-11-23) , S. 79-94 ; EISSN 1573-2673Sponsorship
Gefördert im Rahmen des Projekts DEALCitation
@article{doi:10.17170/kobra-202102113184,
author={Scheel, Johannes and Schlosser, Alexander and Ricoeur, Andreas},
title={The J-integral for mixed-mode loaded cracks with cohesive zones},
journal={International Journal of Fracture},
year={2020}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2020$n2020 1500 1/eng 2050 ##0##http://hdl.handle.net/123456789/12516 3000 Scheel, Johannes 3010 Schlosser, Alexander 3010 Ricoeur, Andreas 4000 The J-integral for mixed-mode loaded cracks with cohesive zones / Scheel, Johannes 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/http://hdl.handle.net/123456789/12516=x R 4204 \$dAufsatz 4170 5550 {{Jot Integral}} 5550 {{Rissspitze}} 5550 {{Bruchmechanik}} 5550 {{Dugdale-Riss}} 5550 {{Rissbildung}} 7136 ##0##http://hdl.handle.net/123456789/12516
2021-02-16T15:02:50Z 2021-02-16T15:02:50Z 2020-11-23 doi:10.17170/kobra-202102113184 http://hdl.handle.net/123456789/12516 Gefördert im Rahmen des Projekts DEAL eng Namensnennung 4.0 International http://creativecommons.org/licenses/by/4.0/ J-Integral crack tip opening displacement cohesive zones Griffith crack Dugdale crack cohesive potential 620 The J-integral for mixed-mode loaded cracks with cohesive zones Aufsatz The J-integral quantifies the loading of a crack tip, just as the crack tip opening displacement (CTOD) emanating from the cohesive zone model. Both quantities, being based on fundamentally different interpretations of cracks in fracture mechanics of brittle or ductile materials, have been proven to be equivalent in the late 60s of the previous century, however, just for the simple mode-I loading case. The relation of J and CTOD turned out to be uniquely determined by the constitutive law of the cohesive zone in front of the physical crack tip. In this paper, a J-integral vector is derived for a mixed-mode loaded crack based on the cohesive zone approach, accounting for the most general case of a mode-coupled cohesive law. While the J1-coordinate, as energy release rate of a straight crack extension, is uniquely related to the cohesive potential at the physical crack tip and thus to the CTOD, the J2-coordinate depends on the solution of the specific boundary value problem in terms of stresses and displacement gradients at the cohesive zone faces. The generalized relation is verified for the Griffith crack, employing solutions of the Dugdale crack based on improved holomorphic functions. open access Scheel, Johannes Schlosser, Alexander Ricoeur, Andreas doi:10.1007/s10704-020-00496-6 Jot Integral Rissspitze Bruchmechanik Dugdale-Riss Rissbildung publishedVersion EISSN 1573-2673 Issue 1 International Journal of Fracture 79-94 Volume 227 false
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