Intergranular or intragranular deformation dominates?

[CsatiZoltan]

Physics

From the modelling viewpoint, it is of importance to know whether the strain localizes to the grain boundaries (also called interfaces) or it is dominant within the grains as well. Indeed, the cohesive zone/band model can largely speed up the computations in the first case. To decide whether the localization is intergranular or intragranular in a given microstructure, we can make use of experimental data (if available). From now on, we will assume that thanks to full-field measurement (e.g. digital image correlation - DIC), we have access to the strain field at every point¹ in the microstructure.

Algorithm

Things to do:

1. [x] Define a band on the interfaces. The thickness of the band is a parameter of the model. ce6c499

2. [x] Be able to compute

   • [x] a strain measure (tensor) from the displacement field 7eaa0b5
   • [x] an equivalent strain from the strain tensor 2b9b0be

   on the whole domain (where the displacement field exists)

3. [x] Take the grain microstructure and the (equivalent) strain field and

   • [x] localize the strain field on the band a74f954
   • [x] possibly return a histogram of the magnitude of the equivalent strain in the band a74f954
   • [x] determine what portion of the large strain values lie in the band, compared to the rest of the domain (i.e. the internal regions of the grains) a74f954

4. [x] The ratio of inter/intragranular deformation should be

   • [x] executed for different time steps, as the deformation evolves 13576f7; and
   • [x] the data above should be visualized somehow 13576f7

5. [ ] Once the methodology works properly, create a Jupyter notebook from it.

Expected results

For many microstructures, the strain localization is dominantly intergranular. If that is the case,

1. Device a model to allow simplifications (e.g. no need to account plastic deformation in the grain interiors)
2. Allow extracting the generated mesh on the interfaces (they will be a set of 1D elements)

Footnotes

¹ I.e. in every pixel. Use subpixel interpolation if you need a value at an arbitrary position.

[CsatiZoltan]

For now, I don't create a Jupyter notebook. Reason: as the example script run_simulation_geometry clearly shows the workflow, there is no need to repeat it. Moreover, similarly to the script, the online notebook also wouldn't have access to the large HDF5 file.