Abstract
A critical analysis was made on the relationship between the energy release rate G and the stress intensity factors for non-coplaner crack extension under combined Mode I, II and III loading. Developing a method different from the application of Bueckner's equation, the equation of G was derived as % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0Jf9crFfpeea0xh9v8qiW7rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4raiabg2% da9iaacUfacaGGOaGaeuOUdSMaey4kaSIaaGymaiaacMcacaGGVaGa% aGioaiabfY7aTjaac2facaGGOaGabm4sayaaiaWaa0baaSqaaiaabM% eacaWGIbaabaGaaGOmaaaakiabgUcaRiqadUeagaacamaaDaaaleaa% caqGjbGaaeysaiaadkgaaeaacaaIYaaaaOGaaiykaiabgUcaRiaacI% cacaaIXaGaai4laiaaikdacqqH8oqBcaGGPaGaey4kaSIabm4sayaa% iaWaa0baaSqaaiaabMeacaqGjbGaaeysaiaadkgaaeaacaaIYaaaaa% aa!5988!\[G = [(\kappa + 1)/8\mu ](\tilde K_{{\text{I}}b}^2 + \tilde K_{{\text{II}}b}^2 ) + (1/2\mu ) + \tilde K_{{\text{III}}b}^2 \], where % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGak0dh9WrFfpC0xh9vqqj-hEeeu0xXdbba9frFj0-OqFf% ea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs0dXdbPYxe9vr0-vr% 0-vqpWqaaeaabaGaciaacaqabeaadaqaaqaaaOqaaGqaciqa-Teaga% acamaaBaaaleaaieaacaGFjbGaa4NyaaqabaGccaqGGaGab83sayaa% iaWaaSbaaSqaaiaa+LeacaGFjbGaa4NyaiaabccaaeqaaKaaajaa+f% gacaGFUbGaa4hzaOGaa4hiaiqa-TeagaacamaaBaaaleaacaGFjbGa% a4xsaiaa+LeacaGFIbGaaeiiaaqabaaaaa!477C!\[\tilde K_{Ib} {\text{ }}\tilde K_{IIb{\text{ }}} and \tilde K_{IIIb{\text{ }}} \] are the stress intensity factors at the tip of an infinitesimal kink as formed by non-coplaner crack extension. Among the three existing equations of G which are mutually contradictory, Nuismer's equation and Wang's equation disagree with the present result. In the case where Mode III loading is not involved, Hussain et al's equation agrees with the present result, although their analysis seems to contain questionable points.
Résumé
On a procédé à une analyse critique de la relation entre la vitesse de relaxation de l'énergie G et les facteurs d'intensité de contrainte dans le cas de l'extension d'une fissure non coplanaire sous des modes de chargement I, II et III. En développant une méthode différente de l'application de l'équation de Bueckner, on a obtenu une équation pour G fonction des facteurs d'intensité de contrainte à l'extrémité d'un ressaut infinitésimal tel que formé par l'extension d'une fissure non coplanaire. Parmi les trois équations de G existantes qui se trouvent être mutuellement contradictoires l'équation de Nuismer et l'équation de Wang ne sont pas en accord avec les résultats obtenus dans le mémoire. Dans le cas où un mode de sollicitation III n'est pas pris en considération, l'équation de Hussain et al. est en accord avec les résultats obtenus bien que leur analyse semble contenir des points discutables.
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Ichikawa, M., Tanaka, S. A critical analysis of the relationship between the energy release rate and the stress intensity factors for non-coplanar crack extension under combined mode loading. Int J Fract 18, 19–28 (1982). https://doi.org/10.1007/BF00034825
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DOI: https://doi.org/10.1007/BF00034825