PSI - Issue 71

Ayub Khan et al. / Procedia Structural Integrity 71 (2025) 461–468

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1.3. Biased mesh generation from EBSD data A biased meshing technique (Thondiraj et al. (2024)) is used in the simulations to reduce the computational effort. The criteria involves using relatively smaller elements in the region of higher gradients of strain, which are assumed to be near the grain boundaries, and larger elements in the bulk where gradients of strain are assumed to be relatively low. First, a fine regular mesh is constructed, then grain IDs are assigned to all the elements. Based on these element grain Ids, nodal grain Ids are evaluated as, =∑ =1 / , with as the number of elements surrounding the respective node in a finite region controlled by a tolerance ( = ∗ ). is the radius factor (taken as 2) and is the minimum element size after coarsening. Grain weights for each element are calculated as, = / , with as number of elements belonging to a certain grain. Element grain weights quantify the influence of each surrounding grain on the element. Coarsening of an element is done based on the difference in the nodal grain Ids as, | − | of the nodes in a specified region decided by coarsening tolerance . The tolerance decides a minimum region required for the calculation of and and decides the thickness of the GB region. To further make an efficient biased mesh, multi-step coarsening is done that generates very fine elements near GB and very coarse elements in the grain bulk (Fig. 2(a)). We have obtained the EBSD data for polycrystalline pure iron and processed it first using an In-house code developed in MATLAB to generate a uniformly discretized mesh. A cubic RVE is then extracted from it (Fig. 2(b)), which is again 2 step coarsened to obtain a biased mesh to reduce simulation time.

Fig. 2. (a) A three-step coarsening of the uniformly discretised mesh using the biased mesh generation technique. (b) A 13 grain polycrystalline RVE of pure iron extracted from the EBSD data. The biased mesh is generated by two-step coarsening of elements. 1.4. Computational procedure A fully-implicit time-integration scheme (Kalidindi et al. (1992)) has been implemented in our In-house FE solver to simulate the micromechanical response of polycrystals. At the start of an iteration, it is assumed that ( ), ( ), ( ), ( ), ( ) at the previous time step ′ ′ are known. Using Eqs. 4, 5, and 6, ( ) can be obtained as ( ) = { + ∑ =1 ∑ =1 ( ( ), ( )) ̃ } ( ) (11) We have used a two-level iterative procedure for the convergence of stress and slip system resistance . In the First Level , the stress at the end of a time step is computed by substituting Eqs. 2 & 3 in Eq. 1 as ( ) = [(1/2){ − ( ) ( ) ( ) − 1 ( )}] (12) Using Eq. 11, Eq. 12 is further reduced to ( ) = −∑ =1 ∑ =1 ( ( ), ( )) (13) where = [(1/2){ − }] = [(1/2) ] = ̃ + ̃