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Dissertation

Analyse des efforts à l'interface entre les couches des matériaux composites à l'aide de modèles multiparticulaires de matériaux multicouches (M4)

24 Jun 1997-
TL;DR: In this paper, a modelisation multiparticulaires (M4) is presented, in which champs de contraintes tridimensionnels approches ecrits sous forme de polynomes de Legendre en z par couche.
Abstract: La these a pour but de concevoir un outil simple d'utilisation, pour l'ingenieur, capable d'analyser les champs de contraintes tridimensionnels responsables de delaminage au bord ou de fissuration transverse dans les materiaux multicouches. Dans la premiere partie du memoire, nous construisons des modelisations multiparticulaires (M4) a partir de champs de contraintes tridimensionnels approches ecrits sous forme de polynomes de Legendre en z par couche. Les coefficients de ces polynomes sont des champs en (x,y) relies aux efforts generalises. Nous utilisons la formulation d'Hellinger-Reissner pour en deduire les deplacements et les deformations generalisees associees. Par stationnarite de la fonctionnelle, nous donnons les equations d'equilibre, les conditions aux limites et le comportement ecrit en souplesse. La richesse plus ou moins grande des champs de contraintes approches ainsi construit mene a 7n, 5n, 3n et (2n+1) (n: nombre de couches) equations d'equilibre dans le plan. Dans la seconde partie de la these, nous testons quatre modeles sur le probleme de la traction simple pour des stratifies non troues d'empilement quelconque et troues d'empilement (0°, 90°)s. Nous posons analytiquement les systemes d'equations qui par combinaison se condensent en un systeme d'equations differentielles de degre 2 en y et dont la resolution se fait par le logiciel de calcul formel MATHEMATICA. Sur le cas du stratifie (0°, 90°)s non troue, nous montrons que l'energie due aux efforts manquants dans les modeles reduits ne disparait pas completement mais est transferee sur celles des efforts restants. Dans le cas du modele multiparticulaire M4_(2n+1)M (M: pour membrane) le plus simple, pour assurer l'equilibre global de la plaque, nous proposons un concept, generalisable, d'effort lineique de type Dirac dont l'intensite est relie au maximum des cisaillements au bord. Nous pensons que l'intensite du Dirac peut servir de base a un critere sur le delaminage.
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TL;DR: In this paper, the authors used two models called Multiparticle Models of Multilayered Materials (M4) to calculate the interfacial stresses in composite laminate in the vicinity of a free edge or micro-cracks.
Abstract: The mechanical problem discussed in this paper focuses on the stress state estimation in a composite laminate in the vicinity of a free edge or microcracks. To calculate these stresses, we use two models called Multiparticle Models of Multilayered Materials (M4). The first one can be considered as a stacking sequence of Reissner-Mindlin plates (5 kinematic fields per layer), while the second is a membranar superposition (2 fields per layer plus a global one). These simplified models are able to provide finite values of interfacial stresses, even on the free edges of a structure. The current paper consists of validating the M4 by a finite element analysis through describing the stress fields in both a (0,90)s laminate in tension (free-edge problem) and a transversally microcracked (0,90)s laminate. A comparison of the various energy contributions helps yield a mechanical perspective: it appears possible to define an interply energy as well as a layer energy, these energies expressing the FE 3D reality.

62 citations

Journal ArticleDOI
TL;DR: In this article, the exact beam theory is used to calculate the characteristic operators involved in beam's structural behavior and the Saint Venant solution is derived from the solutions of six characteristic beam elasticity problems.

59 citations

Journal ArticleDOI
TL;DR: In this paper, the authors used two models called multiparticle models of multilayered materials (M4) to calculate the interfacial stresses of a composite laminate in the vicinity of a free edge or micro-cracks.

57 citations


Cites background or methods from "Analyse des efforts à l'interface e..."

  • ...3 number of authors (Wang & Choi (1982a) , Leguillon (1998)), etc.) and has often been identified using a logarithmic expression. Shah & Murty (1991) modelled the laminate as a combination of three distinct regions: quasi-3D elements close to the free edge, linear elements over the entire plate, and transitional elements between these two regions....

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  • ...After integration in each ply with respect to z, these associated generalised displacements are then deduced (see Chabot (1997) for more details)....

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  • ...The various studies of Caron & Ehrlacher (1997), Chabot (1997), Naciri et al. (1998), 1998), Caron et al. (1999), Carreira (1998), (referring to the M4) take their inspiration from Pagano’s model (1978)....

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  • ...The complete expressions for i d α Φ , 1 , + α i i D and 1 , 3 + i i D can be found in Chabot (1997)....

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  • ...The M4 construction method (Chabot (1997)) is based upon the four steps described below....

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Journal ArticleDOI
TL;DR: In this article, a laminate theory which considers a kinematic field per layer (particle) is used to approach the three-dimensional stress state in multi-layered composites, and some relevant criteria able to predict delamination initiation in some angle-ply laminates based on the model results.

56 citations

Journal ArticleDOI
TL;DR: In this paper, a multilayered medium with as many particles in each point of the surface as the number of layers in the medium is modeled as a multiparticle model of multi-layered materials (M4 in the following text).

47 citations


Cites background from "Analyse des efforts à l'interface e..."

  • ...The internal virtual power can be written as follows: (4)...

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  • ...Composites Science and Technology, Elsevier, 1998, 58 (3-4), pp....

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