Insensitivity to small defects of the rupture of materials governed by the Dugdale model

Ann. Solid Struct. Mech.

Weller

2010

We propose a construction of fatigue laws from cohesive forces models in the case of a crack submitted to a mode I cyclic loading. Taking the cumulated opening as the memory variable and the surface energy density associated with Dugdale's model, we explicitly construct the fatigue law which gives the crack growth rate by cycle d'/dN in terms of the stress intensity factor K I . In particular, we recover a Paris law with an exponent 4, i.e., d'/dN = CK I 4 , when K I is small, the coefficient C being explicitly expressed in terms of the material parameters. Furthermore, the law can be applied in the full range of values of K I and can be extended to non simple cycles.

Section: Introductionmentioning

confidence: 98%

Construction and justification of Paris-like fatigue laws from Dugdale-type cohesive models

Abdelmoula

Ann. Solid Struct. Mech.

Weller

2010

“…An important step will be to apply the MAM in the case of a cohesive crack [Barenblatt 1962;Dugdale 1960;Del Piero and Raous 2010], which automatically contains a critical stress and even a characteristic length. The goal will be to study the influence of the critical stress and characteristic length on the nucleation and the propagation of a crack in the spirit of the previous works based on the variational approach to fracture [Abdelmoula et al 2010;Bourdin et al 2008;Charlotte et al 2006;Del Piero and Truskinovsky 2009;Ferdjani et al 2007;Giacomini 2005;Jaubert and Marigo 2006;Marigo and Truskinovsky 2004].…”

Section: Discussionmentioning

confidence: 99%

Asymptotic analysis of small defects near a singular point in antiplane elasticity, with an application to the nucleation of a crack at a notch

Dang

Halpern

Math. Mech. Compl. Sys.

2014

We use matching asymptotic expansions to treat the antiplane elastic problem associated with a small defect located at the tip of a notch. In a first part, we develop the asymptotic method for any type of defect and present the sequential procedure which allows us to calculate the different terms of the inner and outer expansions at any order. This requires in particular separating in each term its singular part from its regular part. In a second part, the asymptotic method is applied to the case of a crack of variable length located at the tip of a given notch. We show that the first two nontrivial terms of the expansion of the energy release rate are sufficient to well approximate the dependence of the energy release rate on the crack length in the range of values of the length which are sufficient to treat the problem of nucleation. This problem is considered in the last part where we compare the nucleation and the propagation of a crack predicted by two different models: the classical Griffith law and the Francfort-Marigo law based on an energy minimization principle. Several numerical results illustrate the interest of the method.

“…Ce résultat est identique au résultat obtenu par Ferdjani et al (2006a), Ferdjani et al (2006b) et Ferdjani et al (2007 dans le cas du modèle de Dugdale. Par contre, la charge limite de la structure est très sensible à la taille du défaut, mais peu à sa forme.…”

Section: Conclusion Généraleunclassified

Etude de l’influence des défauts de petite taille sur le comportement à rupture avec le modèle de Dugdale régularisé

Ferdjani

Abdelmoula

European Journal of Computational Mechanics

2008

Le but du travail est de montrer, dans le cadre de la mécanique de la rupture avec le modèle de Dugdale régularisé des forces cohésives, que les défauts de petite taille devant la longueur caractéristique du matériau ont pratiquement peu d'influence sur les capacités de résistance d'une structure. On traite pour cela deux exemples : le cas d'une plaque préfissurée, puis le cas d'une plaque contenant une cavité circulaire. Les calculs sont effectués avec la méthode des éléments finis. ABSTRACT. The goal of this work is to prove that, within the framework of Fracture Mechanics with the regularized Dugdale's model of cohesive forces, the defects the size of which are small compared to the material characteristic length are practically without influence on the limit loads of structures. For that, we treat two examples : the case of a precracked plate, then the case of a plate with a circular hole. The calculations are made with the finite element method. MOTS-CLÉS : rupture, modèle de Dugdale régularisé, effet d'échelle, charges limites.