Vol. 10, No. 3, 2015

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ISSN: 1559-3959
On the strong influence of imperfections upon the quick deviation of a mode I+III crack from coplanarity

Jean-Baptiste Leblond and Véronique Lazarus

Vol. 10 (2015), No. 3, 299–315
DOI: 10.2140/jomms.2015.10.299

This work explores the possibility that quick deviations of cracks loaded in mode I+III from coplanarity may be greatly facilitated by inevitable fluctuations of the fracture toughness. The idea is that such fluctuations must induce in-plane undulations of the crack front resulting, because of the presence of the mode III load, in nonzero values of the local stress intensity factor of mode II, implying future local out-of-plane deviations of the crack which might be “unstable” in Cotterell and Rice’s sense if the local nonsingular stress parallel to the direction of propagation is positive.

Exploration of this idea implies evaluation of the variations of the local stress intensity factors and nonsingular stresses arising from a slight but otherwise arbitrary in-plane perturbation of a semi-infinite crack. These quantities were calculated in works of Gao and Rice, but the evaluation of the nonsingular stresses was incomplete, and is supplemented here by using the theory of 3D weight functions due to Rice and Bueckner.

Inspection of the results shows that for in-plane sinusoidal undulations of the crack front of sufficient (though still small) amplitude, the conditions of nonzero local stress intensity factor of mode II and positive local nonsingular stress parallel to the direction of propagation are simultaneously met on some parts of the front, implying the possibility of future local deviations of the crack from coplanarity that are “unstable” in Cotterell and Rice’s sense, and thus confirming the idea investigated.

imperfections, deviation from coplanarity, mode I+III crack, nonsingular stresses, Cotterell and Rice's directional stability criterion
Received: 13 January 2014
Accepted: 12 October 2014
Published: 26 August 2015
Jean-Baptiste Leblond
Institut Jean Le Rond d’Alembert
Sorbonne Universités UPMC Université Paris 06, CNRS
UMR 7190
75005 Paris 06
Véronique Lazarus
Université Paris-Sud 11
UMR 7608
91405 Orsay