Abstract
In linear elastic fracture mechanics the path-independent J-integral is a loading quantity equivalent to stress intensity factors (SIF) or the energy release rate. Concerning plane crack problems, \(J_k\) is a 2-dimensional vector with its components \(J_1\) and \(J_2\). These two parameters can be related to the mode-I and mode-II SIFs \(K_{\mathrm{I}}\) and \(K_{\mathrm{II}}\). To guarantee path-independence for curved crack geometries, an integration path along the crack faces must be considered. This paper deals with problems occurring at the numerical calculation of the J-integral in connection with the FE-method. Two new methods for accurately calculating values of \(J_2\) for arbitrary cracks are presented.
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Appendix
Appendix
Angular trigonometric functions of the n-th eigenfunction according to Eq. (3), (Kuna 2010):
Angular trigonometric functions of the n-th eigenfunction according to Eq. (3), (Kuna 2010):
Complex potentials for the Griffith crack problem under mode-I and mode-II loading with the spatial coordinate \(z=x_1+i\,x_2\), (Kuna 2010):
Kolosov’s equations, (Kuna 2010):
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Judt, P.O., Ricoeur, A. Accurate loading analyses of curved cracks under mixed-mode conditions applying the J-integral. Int J Fract 182, 53–66 (2013). https://doi.org/10.1007/s10704-013-9857-9
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DOI: https://doi.org/10.1007/s10704-013-9857-9