On the strong influence of imperfections upon the quick deviation of a mode I+III crack from coplanarity - Sorbonne Université Access content directly
Journal Articles Journal of Mechanics of Materials and Structures Year : 2015

On the strong influence of imperfections upon the quick deviation of a mode I+III crack from coplanarity

Abstract

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 non-zero 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 (1980)'s sense if the local non-singular 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 non-singular stresses arising from a slight but otherwise arbitrary in-plane perturbation of a semi-infinite crack. These quantities were calculated in works of Rice (1985), Gao and Rice (1986) and Gao (1992) but the evaluation of the non-singular stresses was incomplete, and is supplemented here by using the theory of 3D weight functions (Rice, 1985; Bueckner, 1987). 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 non-singular 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 " unstable " in Cotterell and Rice (1980)'s sense, and thus confirming the idea investigated.
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Dates and versions

hal-01436389 , version 1 (16-01-2017)

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Jean-Baptiste Leblond, Veronique Lazarus. On the strong influence of imperfections upon the quick deviation of a mode I+III crack from coplanarity. Journal of Mechanics of Materials and Structures, 2015, 10 (3), pp.299 - 315. ⟨10.2140/jomms.2015.10.299⟩. ⟨hal-01436389⟩
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