Fissuration polymodale dans les matériaux viscoélastiques orthotropes

Rostand Moutou Pitti (1) , Frédéric Dubois (2)

1 IP - Institut Pascal
2 GEMH - Groupe d'Etudes des Matériaux Hétérogènes

Ce travail présente un algorithme numérique de l'amorçage et de la propagation de fissure en mode mixte dans un milieu viscoélastique orthotrope. Le modèle numérique couple la résolution par éléments finis du comportement viscoélastique au calcul de l'intégrale Mθ permettant le découplage des modes de rupture en termes de facteur d'intensité de contrainte et de taux de restitution d'énergie. L'application proposée utilise une éprouvette 2MCG permettant conjointement l'obtention des différents taux de mixités et une stabilité de la propagation de fissure. L'algorithme éléments finis permet de modéliser la propagation du front de fissure en simulant la décohésion progressive des lèvres dans la zone d'élaboration. L'ensemble est piloté par une fonction de charge intégrant les performances énergétiques à la rupture des différents modes (I et II) en configuration plane. La zone d'élaboration est définie via un champ de contrainte en mode mixte défini dans la zone singulière. Pour citer cet article : R. Moutou Pitti, F. Dubois, C. R. Mecanique 337 (2009). Abstract Polimodal fracture in orthotropic viscoelastic media. This Note deals with an algorithmic approach about the crack initiation and the crack growth in a viscoelastic media for mixed mode configurations. This numerical model couples a finite element resolution of viscoelastic behavior and the Mθ integral calculus allowing a mixed mode separation in terms of stress intensity factors and energy release rate. The numerical application uses a 2MCG specimen allowing, in the same time, different mixed mode ratios and a crack growth stability. The finite element algorithm allows us to model the crack tip advance by taking into account the crack lip uncohesion in the process zone. It size is defined by taking into account stress field in the crack tip vicinity. 749 Abridged English version The important use of polymers or composites in engineering structures required the best understanding of their fracture mechanical behavior. Also, these materials are often characterized by a viscoelastic response and orthotropic or anisotropic characters. In the most cases, these structures are submitted to complex solicitations modifying their mechanical properties and leading to the important damaging and the local micro-crack. In the durability context, it appears very important to drive the evolution speed of the different defaults. That way, new numerical and experimental approaches enable us to understand the crack initiation and the crack growth process in viscoelastic orthotropic materials is required. This work is based on the coupling of the non-path-dependent integral Mθ generalized for vis-coelastic media and crack growth process [3], Eq. (1) and a complex finite element algorithm about the crack growth process in time-dependent material, Fig. 2. This work allows us to compute the crack growth process by taking into account the time uncohesion of the crack lips in the process zone. The time step advance is calculated according to a dichotomy algorithm. Its criterion is based on the use of a functional formed by critical time values of energy release rate separated in terms of opening mode and shear mode parts, Eq. (5). A numerical application is based on a creep test using a timber mixed mode crack growth specimen. Results put in evidence the algorithm capacities to separate fracture mode during the crack growth and to compute the crack tip speed versus time. This model can be employed for other complex loadings like ramp tests and fatigue in force or displacements under different loading speeds.

Mots clés: Mixed modes; Path-independent integrals; Crack growth process

Mots clés: Rupture; Modes mixtes; Intégrales indépendantes; Propagation de fissure

Domaines: Matériaux; Structures; Matériaux composites et construction; Construction durable

Rostand Moutou Pitti, Frédéric Dubois. Fissuration polymodale dans les matériaux viscoélastiques orthotropes. Comptes Rendus Mécanique, 2009, 337 (11-12), pp.748 - 754. ⟨10.1016/j.crme.2009.10.008⟩. ⟨hal-01616909⟩