REPUBLIC OF SERBIA

MINISTRY OF DEFENCE

www.mod.gov.rs

MINISTRY OF DEFENCE

Material Resources Sector

Defensive Technologies Department

Military Technical Institute

www.vti.mod.gov.rs

An adAptive remeshing technique for 3D crack growth simulations

Vincent Chiaruttini

The presence of cracks is unsafe for many critical industrial parts, such as rotors in aircraft engines. For this reason, manufacturers carry routine inspections, using non-destructive methods of detection. But the  limitations of these methods, and the growing need for lean, cost-efficient structures in a wide range of industrial applications (aeronautic, automotive industry, civil engineering, etc.), have led to new approaches of damage tolerance design. Conservative lifetime computations give way to increasingly sophisticated, realistic simulations of crack propagation. The goal of manufacturers is to correctly define the time  between inspections, by modelling how small, undetectable cracks would propagate due to fatigue loading.

 The physical theory of fracture and description of cracks have existed for a long time, dating back to the works of Griffith and Irwin in the first half of the 20th century. Crack propagation and structure lifetime have first been described by Paris and Erdogan. Yet, many computations found in the literature take into account simple cases, that can be solved  analytically; these are usually only relevant to a precise industrial case, that allows for approximations (2D structures, specific crack geometries...). The need for generic loading and geometries of both crack and structure remained, and, since the last decades, many new  approaches have been developed (mostly based on the X-FEM/Levelset methods [1] or efficient remeshing techniques [2]). These methods have made finite element computations an efficient tool, that can predict accurate crack paths and stress intensity factors for complex 3D crack growth simulation under fatigue loading.

The present study encompasses the work done in Z-Cracks, a crack-propagation tool for the FEM analysis code Z-Set [3], developed at  Onera - the French Aerospace Lab - and at the Centre des Materiaux of the Ecole des Mines de Paris - Paristech. Our objective is to provide a tool for industrial use, which has to be robust, accurate, and with low  computation time. Two methods are implemented at the present time: one is based on the G-theta method [4], another uses an adaptative meshing of cohesive zone element. We will describe in particular the G-theta method, which relies on stress intensity factors and remeshing techniques for updating the structure’s geometry. The algorithms will be described, and  their efficiency shown on some particular complex cases.

 References:

 [1]  N. Moes, J. Dolbow, T. Belytschko, A finite element method method for crack

       growth without remeshing, Int. Journal for Num. Meth. In Engrg, vol.  46, p. 131-

       150, 1999.

 [2]  V. Chiaruttini, F. Feyel, J.L. Chaboche, A robust meshing algorithm for complex

       3D crack growth simulation, ECCM 2010, Paris.

 [3]  J. Besson and R. Foerch, Large Scale Object-Oriented Finite Element Code

       Design, Comp. Meth. in Appl. Mech. and Eng., vol. 142, p. 165-187, 1997.

 [4]  P. Destuynder, A. Djaoua, S. Lescure, Quelques remarques sur la mecanique

      de la rupture elastique, Journal de mecanique theorique et applique, 1983.