Dislocation layers applied to moving cracks in orthotropic crystals

Abstract

A B S T R A C TIn this paper, we consider loaded Griffith-type strip cracks moving in orthotropic crystals using the powerful method of dislocation layers. Expressions.for the components of the stress fields created are obtained in closed forms and some representative numerical results are given. The applications of the method to the BCS model of moving cracks with plastic flow are briefly discussed. RI~SUM/~Dans cet article, nous traitons des fissures sur ruban charg~ de type Griffith se d6placant en cristaux orthotropiques utilisant la puissante m6thode de couches de dislocation.Des formules pour les composantes des domaines charg6s qui sont cr6s, sont obtenues en formes ferm~es et quelques r~sultats num6riques repr6sentatifs sont donn~s. Les applications, au module BCS, de cette m~thode de fissures mobiles avec ~coulement plastique sont bri~vement discut6es. Z U S A M M E N F A S S U N GIn diesem Referat handelt es sich um geladene B/inderrisse des Griffith-Typus, die sich unter Anwendung der kraftvollen Methode der Schichtenverschiebung in orthotropischen Kristallen bewegen. Ausdrticke fiir die Bestandteile der erzeugten Kraftfelder werden in geschlossenen Formen ermittelt und einige typische, zahlenmfissige Ergebnisse angegeben. Die Anwendungen der Methode auf das BSC-Modell der sich bewegenden Risse mit plastischem Fluss werden auch kurz er6rtert.

A note on arbitrarily loaded penny-shaped cracks in hexagonal crystals

“…Then we obtain, either from t.he above integral formulae or directly from the results in [1] for the unidirectional shear case, that [4]. Tupholme [5,6] found that the behaviour of a stationary or moving strip crack in a strongly anisotropic material, such as graphite, is significantly different from in an isotropic material as far as the angular distribution of stress about the crack-tip is concerned. However, when the present tabulated values are compared with those of an isotropic material for which typically v =¼ or ½, so that (l-v) -~ and tan ~ (l-v) ~ are 1.33 or 1.50 and 55.13 or 56.31 , respectively, we see that the strength of anisotropy does not greatly affect the distribution of the stress singularity in the plane of the crack for a penny-shaped crack under a unidirectional shear traction.…”