DIGITAL MICROSTRUCTURES (1 day)

R.E. Logé, P.R. Dawson, M. Bernacki, D. Boyce, E. Busso, A. Borbély, L. Delannay
Dr. Roland Logé,

Groupe Métallurgie, Structure et Rhéologie
Centre de Mise en Forme des Matériaux
Ecole des Mines de Paris
BP 207
06904 Sophia Antipolis, France

The concept of Digital Microstructures has become more and more useful to a better understanding of complex microstructure evolutions taking place in engineering materials as a result of thermal, mechanical, or even electromagnetic solicitations.

Digital Microstructures are representative volume elements which have been constructed either as a close replicate of a real microstructure (e.g. measured with diffraction microscopy), or as a statistical equivalent of it. The statistical equivalence must be ensured on selected features/properties of the microstructure. In the case of metallic materials, the building bricks of microstructures are the grains. Further divisions of the grains are possible, for example to define subgrains or dislocation cells. Precipitates can also be materialized by smaller cells. A topology results from the microstructure construction, and is composed of a hierarchy of sub-volumes. A convenient way of constructing a large number of volumes or sub-volumes is given by the Voronoï tessellation. Physical properties can then be sampled among the constructed geometric features according to experimental data. The data should be stored in an appropriate/organized way, e.g. using databases.

After construction of a digital microstructure, any property—geometric or physical—can be probed, to check the correspondence with experiment. Many distinct virtual samples can be created based on the same statistical experimental information: while being individually different, they obey overall the measured statistics.

A DIGIMICRO software is under development, allowing to construct digital microstructures, and to probe them after their construction. Probing is done using characterization methods that are to a large extent similar to the ones used in real experiments. Besides the digital characterization experiments, digital experiments (mechanical testing, thermal treatment, etc.) can also be performed on the digital samples, using appropriate modelling. The most natural approach is the finite element method, as long as the virtual samples can be converted into suitable meshes. Constitutive laws at the relevant scales are also needed, plus adequate boundary conditions.

The ATLAS software is used as a database containing all microstructural informations for different materials, coming from experiments or simulations. Plugins can be used to interrogate the database and provide the needed data for microstructure examination or construction, the latter being done for example with the DIGIMICRO software.

The objective of the course is to address some of the methods used to numerically build, represent and analyze microstructures/textures of materials, and to model their evolutions under the action of external or internal forces. The participants will be able to generate and analyze microstructures themselves, based on experimental or computed data, using both ATLAS and DIGIMICRO softwares. The conversion of the digital microstructures into finite element meshes will be detailed, with a focus on special meshing procedures allowing to conform the mesh to chosen microstructural features.

Finally, three examples of digital experiment will be presented, each time with the necessary constitutive framework within the finite element method. The first type of experiment, mechanical testing, will emphasize constitutive behaviours for crystal and polycrystal plasticity, including the physical basis, the computational aspects, and the experimental validation. The second type of experiment, thermal treatment, will lead to a framework allowing the prediction of geometrical evolutions of the microstructure, using the level set method. Nucleation and growth phenomena will be discussed, in the context of recrystallization phenomena. A third example of digital experiment will then focus on the evolving distribution of lattice strains and the progressive formation of a substructure resulting from large plastic deformation of a titanium alloy.

Outline
1. Concept of digital microstructures – Introduction and philosophy (35 min.)
2. Microstructural data organization – Database and repository layout (30 min.)
3. Digital specimens instantiation [includes hands-on work]
3.1. From statistical analysis (50 min.)
3.2. From 3D experimental data using diffraction microscopy (50 min.)
4. Meshing strategies and boundary conditions (60 min.)
5. Digital experiments
5.1. Mechanical testing – constitutive modelling and numerical approaches for crystal and polycrystal plasticity. Experimental validation. Finite element implementation (50 min.)
5.2. Thermal treatment – finite element framework for moving boundaries problems using the level set method. Nucleation and growth phenomena (50 min.)
5.3. Large plastic deformation in a titanium alloy – analysis of lattice strains evolutions and substructure formation (40 min.)
6. Microstructure examination – database plugins/visualization [includes hands-on work] (60 min.)
7. Summary and conclusions (15 min.)

NOTE: ATLAS will need Macs while DIGIMICRO will need PCs. People will need to work in groups, using PCs for section 3 and Macs for section 6.

Back to Course List