Coupling Diffraction Contrast Tomography with the Finite Element Method

Abstract

This paper explains how to turn full three dimensional (3D) experimental grain maps into a finite elements (FE) mesh suitable for mechanical analysis. Two examples from diffraction contrast tomography characterizations are presented. Deformation of a pure titanium sample with 1400 grains is computed using elastic anisotropy and accurate boundary conditions allows to correctly capture the grain to grain elastic strain variations. In the second example a significantly large zone of a polycrystalline Al-Li sample is meshed and computed using elastoplastic finite strain calculation. Mean lattice reorientations and intra-grain lattice orientation spread are obtained as a function of deformation.

Optimal polyhedral description of 3D polycrystals: Method and application to statistical and synchrotron X-ray diffraction data

“…This is at the expense of morphology simplification (as opposed to direct meshing [27,28]); however, for the materials under investigation, a good agreement was obtained with an intersection rate of about 90%, comparable to experimental uncertainties. This level of agreement would somewhat drop for more complex (non-convex) grain shapes as those generally encountered in more highly alloyed metals [57].…”

“…Moreover, the microstructures are in general complex, as they can include general (non-convex) grain shapes which can only be described on grids of voxels, which is not adapted to standard, conformal meshing [26]. Such is also the case for polycrystal images provided by synchrotron X-ray diffraction [8,9], which motivated the development of dedicated meshing procedures [27,28]. In contrast, geometrical models such as Voronoi or Laguerre tessellations can be described in a compact, scalar fashion, using sets of points, lines, surfaces and volumes.…”

Simulation of Short Fatigue Crack Propagation in a 3D Experimental Microstructure

“…First, the full image data is meshed as described in Proudhon et al [25] to obtain a tetrahedron-based representation of the gage length of the specimen. First, the full image data is meshed as described in Proudhon et al [25] to obtain a tetrahedron-based representation of the gage length of the specimen.…”

“…Indeed, the general way to look at this problem is to compute some fatigue indicator parameters (FIP), which are to be regarded as crack formation driving forces. Meshing complex microstructural 3D images is also considerably easier, thanks to the development of new tools, see Proudhon et al and Spear et al, [25,26] for examples. Using extensive sets of calculations with single crystals containing cracks, Castelluccio and McDowell showed that computed FIPs are directly proportional to the crack sliding displacement, which is one of the principal driving forces for stage I crack growth.…”

“…The 3D characterization of millimetric polycrystalline microstructure is now available using serial sectioning techniques (destructive) or near-field synchrotron X-ray diffraction imaging (non-destructive and in a close future using laboratory sources [24] ). Meshing complex microstructural 3D images is also considerably easier, thanks to the development of new tools, see Proudhon et al and Spear et al, [25,26] for examples. Using adequate remeshing routines, it is possible to study the propagation of short cracks based on some FIP indicator.…”