Numerical Simulations of Cracks in Polycrystalline Aggregates
Résumé
Finite Element Crystal Plasticity is now a well developped field of research that allows the researchers to investigate global and local material behaviour. The initial attempts were devoted to homogenization: the goal was to determine the global properties by means of a description of the microstructures in terms of morphology and crystal orientations. A crude model of the microstructure is well adapted in that case, as, after averaging process, the details of the local fields just vanish at the macroscale. Even non realistic geometries with a new crystal orientation in each element of a cubic mesh is an acceptable solution in some cases. Nevertheless, this approach is now obsolete, due to the development of the experimental characterization of the microstructures (automated mapping of a surface, EBSD, microtomography). These new techniques are able to provide a quantitative analysis of the aggregate, that can be reproduced directly as it is, or as a statistically equivalent synthetic aggregate generated by morphological operations. Having such a type of mesh in hand, one can have an access to local stress and strain fields on the microstructural level. The purpose is now to investigate the strain localisation scheme [1], surface or grain boundary effects [2], or the influence of specific microstructures like for bainitic steels [3]. In these approaches, one has an evaluation of local pertinent fields, ready to use in local damage models to predict degradation and failure of the material element. This is why the next step must be prepared: the modelling of craks in aggregates. This paper shows three applications where cracks have been introduced in realistic agggregates. The first one deals with intergranular crack propagation in presence of stress corrosion cracking [4]. Special elements are introduced to represent the grain boundary affected zone in the grains. The behaviour of these elements is inherited from the grain they belong to and includes also three additional variables to represent damage, opening and sliding of the grain boundaries. Opening and sliding simulate relative motion of the grains and allow crack propagation to occur. They are promoted by damage, which evolution is linked to the mechanical state and to the environment, namely the presence of iodine. On the other hand, iodine adsorption is made easier in grain boundaries by damage, producing a catastrophic process. The second case study introduces cyclic loadings. It aims to characterise short crack propagation in fatigue. During the fatigue process, cracks initiate in surface grains, following maximum shear planes. In this “stage I” period, many initiation sites are present in the material element, and the crack occurrence is totally linked to the crystallography. The “micropropagation” regime corresponds then to mechanisms where cracks interact with the microstructure. The macroscopic crack initiation used by engineers takes place when the crack is large enough (several grains) to impose its own stress field. The goal of the study is to explain the transition between the crack in one grain and a long crack crossing several grains. The way the crack interact with grain boundaries is then simulated, and several arguments are proposed to decide if it is trapped or if it can go through. The last example is an application to fretting. A previous work has shown that crystal plasticity enhances strain localisation under the contact [5]. The new study wants to characterise the propagation angle of the cracks that initiate on both sides of the contact zone, and try to determine the condition they have to fill for stopping [6]. References: [1] C. Gérard, F. N'Guyen, N. Osipov, G. Cailletaud, M. Bornert, and D. Caldemaison, “Finite element simulation of strain localisation scheme and comparison with experimental results under cyclic loading paths,” submitted, 2009. [2] A. Musienko, A. Tatschl, K. Schmidegg, O. Kolednik, R. Pippan, and G. Cailletaud, “3D finite element simulation of a polycrystalline copper specimen,” Acta Mat., vol. 55,pp. 4121–4136, 2007. [3] N. Osipov, A.-F. Gourgues-Lorenzon, B. Marini, V. Mounoury, F. Nguyen, and G. Cailletaud, “FE modelling of bainitic steels using crystal plasticity,” Philosophical Magasine, vol. 88, no. 30–32, pp. 3757–3777, 2008. [4] A. Musienko and G. Cailletaud, “Simulation of inter and transgranular crack propagation in polycrystalline aggregates due to stress corrosion cracking,” submitted, 2009. [5] T. Dick and G. Cailletaud, “Fretting modelling with a crystal plasticity model of Ti6Al4V,” Computational Materials Science, vol. 38, pp. 113–125, 2006. [6] L. Sun, H. Proudhon, S. Basseville, and G. Cailletaud, “Effet de la microstructure sur la propagation des fissures de fretting,” in 9e colloque national en calcul de structures (C. Rey et al ed.), (Giens, France), may 25–29, 2009.