Abstract. Time sequences of 3D images of an Al-Cu alloy in the mushy state are obtained using in situ and real-time X-ray microtomography during a tensile test. Surface meshes of phase interfaces are built from these images with the help of a Marching Cubes algorithm. The signed distance to the surface meshes is then computed on a finite element mesh of the volume of the phases. These signed distance functions enable to track the interfaces between the phases in an implicit way. A numerical representation of the real microstructure is thus obtained, allowing to perform a numerical tensile test which is compared with the experimental tensile test. Results retrieve the general dynamic behaviour of the strain field evolution and opens promising perspectives for further interpretations of experimental results based on numerical simulations.
IntroductionNowadays, numerical simulations of complex systems are mandatory in many fields. The first aspect to consider for performing analyses on such system is the creation of a realistic numerical representation of the object under study. This is the case in phase transformations taking place in the context of materials science. Several phases may coexist in a given material, delimited by interfaces. A mesh of the structure of the phases is then needed to study the heat, mass and momentum transfers taking place at phase interfaces and in the bulk phases. Results of such analyses for the entire material are not trivial because of the various phase properties and interface behaviours.When it is not possible to consider a numerical representation of the real specimen, statistical representative elementary volumes (REV) can be used. Advantages lead in the possibility to easily change the morphology of the REV. The sample behaviour can then be studied with respect to various parameters. For instance, by using a modified Voronoi tessellation, Phillion et al. showed the effect of microstructural features on the semi-solid tensile deformation of an aluminium alloy such as solid fraction, porosity and grain size [1].During the last decade, X-ray microtomography has considerably developed [2][3][4]. This imaging technique gives access to in situ three-dimensional (3D) morphology of a multiphase sample. Thus, Terzi et al. obtained a set of 3D images showing morphological evolutions in a few millimeters sample of an aluminium copper alloy during tensile testing [5]. It is currently possible to reach a spatial and time resolution of less than 1 µm and 1 s, respectively, on millimeters domain size [4].The ambition of this paper is to describe a way to transform data coming from X-ray microtomography into a finite element (FE) representation and to use it to run numerical simulations. In section 2, the approach chosen to obtain the FE representation is explained. Section 3 presents the model equations for the numerical tensile test and the way to solve them. Finally, results on the real morphology are presented and compared to the experimental data in section 4.