# QUELQUES PROBLEMES TRIDIMENSIONNELS DE MECANIQUE DE LA RUPTURE FRAGILE

Abstract : The first part of this thesis deals with crack paths in mixed (I+II+III) mode. First, the expansion of the stress intensity factors in powers of the crack extension length established by Mouchrif, is completed by the determination of some universal operator (independent of the problem) describing the influence of the variation of the crack extension length along the front. This operator is determined by using a matched asymptotic expansion technique and by combining Muskhelishvili formalism with conformal mapping. Second, we present crack paths actually observed in the presence of mode III and introduce some criterions able to predict the value of the kink angle along the front when it gradually twists around the propagation direction to reach a situation of pure mode I. The results agree with values of experiments performed, for a part, by ourselves.
In the second part, we calculate the three-dimensional crack-face weight functions for the semi-infinite interface crack in an infinite body. The method employed is new and avoids the full solution of the elasticity problems implied. First, the expression of the variation of the stress intensity factors arising from an infinitesimal coplanar perturbation of the front is derived. Then this result is applied to those special loadings which define the crackface weight functions and to a special perturbation which preserves the crack shape. The result consists in some integrodi erential equations which are transformed into ordinary di erential ones through Fourier transform in the crack front direction. The solution is obtained in closed form to first order in the bimaterial constant "$\epsilon$". As an application, the problem of the stability of the straight configuration of the crack front versus small in-plane perturbations is examined.
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Theses

Cited literature [39 references]

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• HAL Id : tel-00273453, version 1

### Citation

Veronique Lazarus. QUELQUES PROBLEMES TRIDIMENSIONNELS DE MECANIQUE DE LA RUPTURE FRAGILE. Mécanique [physics.med-ph]. Université Pierre et Marie Curie - Paris VI, 1997. Français. ⟨tel-00273453⟩

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