M4F 5.1.2: Full-field homogenization accounting for channeling

1. Multiscale Modelling for Fusion and Fission Materials (M4F) M4F 5.1.2: Full-field homogenization accounting for channeling I. Simonovski, T. Yalçinkaya (Middle East Technical University) Status update January 2019 Simonovski, M4F plenary meeting, Paris, February 13-14 2019

2. Task • Develop non-convex SGCP const. law (+non-convex free energy term to enable patterning of the deformation field). • Model channeling in 2D polycrystalline aggregates of different sizes (scale effect): • Different loads and BC. • ABAQUS UEL fortran subroutine. • Full-field homogenization on polycrystalline aggregates. Simonovski, M4F plenary meeting, Paris, February 13-14 2019

3. Status • Contract for further development of SGCP (Yalçinkaya) published. • Fortran and C++ routines for conversion of the ABAQUS *.odb file improved: • Aggregates with 1032 grain models can now be computed. • Memory allocation issue resolved. • 1000+ grain models require >256GB of memory for converting the *.odb file. • Our compute nodes have ‘only’ 256GB of memory. • Statistical analysis completed: • Aggregates with 14, 110, 214, 525, 1032 grains, R/Davg = 0.016, 0.025 and 0.05. • Tensile displacement load applied =0.2 s-1). • Soft and hard boundary conditions. • 100 sets of random grain orientations for each of the above cases. • Average tensile response computed (+standard deviation). Material length scale parameter Average grain size Simonovski, M4F plenary meeting, Paris, February 13-14 2019

4. Aggregates 110 grains • Voronoi tessellations 14 grains 525 grains Crystallographic orientations (random) 212 grains Simonovski, M4F plenary meeting, Paris, February 13-14 2019

5. Strain Gradient Crystal Plasticity[1] • Additive decomposition of the strain into elastic and plastic components • Plastic slip field evolution governed by the slip law Resolved Schmid stress on the slip system Symmetrized Schmid tensor Unit normal vector on slip system a Unit slip direction vector on slip system a Micro-stress vector, bringing the plastic slip gradients into the plasticity formulation Young modulus Internal length scale parameter , A=ER2/[16(1-n)] Length scale for dislocation interactions Poisson ratio [1] Yalçinkaya et. al, 2012, https://doi.org/10.1016/j.ijsolstr.2012.05.029 Simonovski, M4F plenary meeting, Paris, February 13-14 2019

6. Model • ABAQUS FEM • Geometry: Voronoi tessellation • Constitutive model: SGCP, user defined element in a fortransubroutine • 3 slip systems per grain • Mat. param. [1] used to demonstrate the strain gradient effects • Parallel execution • User define element: writing of results into standard *.odb file not fully[2] supported by ABAQUS: • C++ and Fortran subroutines used to write the SGCP results into the *.odb [1] Yalçinkaya et. al, 2012, https://doi.org/10.1016/j.ijsolstr.2012.05.029 [2] Only results from the first integration point are written. Simonovski, M4F plenary meeting, Paris, February 13-14 2019

7. Equivalent strain at <e11>=0.1. Hard boundary conditions (no slip at GB) R/Davg=1.6% Hard boundary conditions (no slip at GB) Soft boundary conditions (slip at GB) R/Davg=2.5% R/Davg=5% 525 grain aggregate, =0.2s-1, <e11>=0.1 Simonovski, M4F plenary meeting, Paris, February 13-14 2019

8. Equivalent stress at <e11>=0.1. Hard boundary conditions (no slip at GB) R/Davg=1.6% Hard boundary conditions (no slip at GB) Soft boundary conditions (slip at GB) R/Davg=2.5% R/Davg=5% 525 grain aggregate, =0.2s-1, <e11>=0.1 Simonovski, M4F plenary meeting, Paris, February 13-14 2019

9. Equivalent macroscopic response One set of crystallographic orientation only! Higher R/Davg, harder response More grains, softer response Simonovski, M4F plenary meeting, Paris, February 13-14 2019

10. Equivalent macroscopic response One set of crystallographic orientation only! Higher R/Davg, harder response More grains, softer response Simonovski, M4F plenary meeting, Paris, February 13-14 2019

11. Equivalent macro response Hard boundary conditions (no slip at GB) AVERAGE values: 100 sets of crystallographic orientation for each grain count R/Davg=0.05 One month of computing Higher R/Davg, harder response, cf next slides More grains, softer response Each line is an average of 100 different cases. 1 case is one set of crystallographic orientations. Simonovski, M4F plenary meeting, Paris, February 13-14 2019

12. Equivalent macro response Hard boundary conditions (no slip at GB) AVERAGE values: 100 sets of crystallographic orientation for each grain count R/Davg=0.025 Each line is an average of 100 different cases. 1 case is one set of crystallographic orientations. Simonovski, M4F plenary meeting, Paris, February 13-14 2019

13. Equivalent macro response Hard boundary conditions (no slip at GB) AVERAGE values: 100 sets of crystallographic orientation for each grain count R/Davg=0.016 Each line is an average of 100 different cases. 1 case is one set of crystallographic orientations. Simonovski, M4F plenary meeting, Paris, February 13-14 2019

14. Equivalent macro response Soft boundary conditions (slip at GB) AVERAGE values: 100 sets of crystallographic orientation for each grain count R/Davg=0.05 Each line is an average of 100 different cases. 1 case is one set of crystallographic orientations. Simonovski, M4F plenary meeting, Paris, February 13-14 2019

15. Equivalent macro response Soft boundary conditions (slip at GB) AVERAGE values: 100 sets of crystallographic orientation for each grain count R/Davg=0.025 Each line is an average of 100 different cases. 1 case is one set of crystallographic orientations. Simonovski, M4F plenary meeting, Paris, February 13-14 2019

16. Equivalent macro response Soft boundary conditions (slip at GB) AVERAGE values: 100 sets of crystallographic orientation for each grain count R/Davg=0.016 Each line is an average of 100 different cases. 1 case is one set of crystallographic orientations. Simonovski, M4F plenary meeting, Paris, February 13-14 2019

17. Channeling At initial stage, hard boundary conditions (no slip at GB) Further steps to be discussed with MaximeSauzay, TuncayYalçinkaya. Simonovski, M4F plenary meeting, Paris, February 13-14 2019

18. Coming work • SGCP development: • Finish setting-up the contract with TuncayYalçinkaya (contract already published) • Upgrade the hardening equations • Include non-convex formulation • 3D • 1000+ grain models: upgrade the memory on the compute nodes. • Further define channeling model Simonovski, M4F plenary meeting, Paris, February 13-14 2019

19. This project has received funding from the Euratom research and training programme 2014-2018 under grant agreement No 755039 Simonovski, M4F plenary meeting, Paris, February 13-14 2019