Full-frame simulation of micro-structural failure using a multi-grid finite difference method

International audienceSince the development of X-ray tomography, it has been possible to obtain 3D images of the micro-structure of materials. These data are extremely useful for analysing of the morphology of heterogeneous materials. More recently, using diffraction contrast tomography in polycrystalline materials, not only the morphology of grains but also their orientation can be measured. Using these data for building numerical models of materials at the microstructure scale is extremely promising. For finite element based simulations, mesh generation reveals very tedious and time consuming, sometimes more than the simulation by itself. As an alternative approach, we propose a multi-grid finite-difference method. This approach has the following advantages: 1. no mesh is required, the voxel grid of the tomography images is directly used as the finite difference grid 2. thanks to the multi-grid algorithm, stiffness ratio between different material constituents as high as 10 billions can be simulated. 3. the memory cost compared to finite element is really low and the method can be run massively in parallel with a good scalability. To illustrate the capability of the proposed approach we analyse low cycle fatigue experimental data on glass/epoxy laminate. In this material, depending on the stacking sequence, free edge effect may induce early initiation of delamination at the interfaces between plies of different orientation. We were able to show how the actual repartition of the glass fibres influence the stress distribution compared to an ideal microstructure. To analyse failure, we have developed a phase field damage model that can be implemented within a multi-grid finite-difference context. This makes possible the analysis of quasi-brittle failure at the microstructure scale in heterogeneous materials based on X-ray tomography images. In a near future, we plan to incorporate in the damage model anisotropy and directionality effect for the analysis of crystalline materials