PSI - Issue 71

Manan Ghosh et al. / Procedia Structural Integrity 71 (2025) 445–452

449

3. Verification with Single Time Scale Solution To evaluate the accuracy and efficiency of the multi-time scale method, a microstructure of a BCC crystal lattice with 8 grains is analysed. The material properties used for the CPFEM simulations are detailed in Venkatramani and Ghosh (2007). A representative polycrystalline volume of 1 x 1 x 1 is constructed as shown in Fig. 1 with random orientation. The volume is discretized using linear tetrahedral elements, resulting in 2021 elements and 464 nodes. Initial position and Euler angles of the grain’s details can be found in table 1. Table 1. Grain position and orientation. Grain Number Grain Position (x min ≤ x ≤ x max , y min ≤ y ≤ y max , z min ≤ z ≤ z max ) Euler angles (Radian) Grain 1 (0.0 ≤ x ≤0.5, 0.0 ≤ y ≤0.5, 0.0 ≤ z ≤0.5) (0.847, 0.249, 1.203) Grain 2 (0.5 ≤ x ≤1.0, 0.0 ≤ y ≤0.5, 0.0 ≤ z ≤0.5) (0.442, 1.312, 0.158) Grain 3 (0.5 ≤ x ≤1.0, 0.5 ≤ y ≤1.0, 0.0 ≤ z ≤0.5) (0.734, 1.299, 0.954) Grain 4 (0.0 ≤ x ≤0.5, 0.5 ≤ y ≤1.0, 0.0 ≤ z ≤0.5) (0.535, 0.270, 0.804) Grain 5 (0.0 ≤ x ≤0.5, 0.0 ≤ y ≤0.5, 0.5 ≤ z ≤1.0) (0.453, 0.583, 1.285) Grain 6 (0.5 ≤ x ≤1.0, 0.0 ≤ y ≤0.5, 0.5 ≤ z ≤1.0) (0.896, 1.201, 1.453) Grain 7 (0.5 ≤ x ≤1.0, 0.5 ≤ y ≤1.0, 0.5 ≤ z ≤1.0) (0.491, 0.498, 0.447) Grain 8 (0.0 ≤ x ≤0.5, 0.5 ≤ y ≤1.0, 0.5 ≤ z ≤1.0) (0.609, 1.011, 0.676) The microstructure is subjected to a triangular load on the z-face, with S max = 500 MPa and S min = 0 MPa, and displacement boundary conditions are applied to restrict rigid body modes such that (i) at z=0 surface motion is restricted in the z direction or w = 0; (ii) the corner node at x = y = z = 0 is restricted from motion in all directions or u = v = w = 0, and (iii) the motion of nodes on the line y = 0 and z = 0 are restricted in y direction or v = 0. Single time scale simulation is performed for 2000 cycles due to the high computational cost when compared with the multi-time scale method. From the single time scale analysis, the evolution of normal component of 0 in the loading direction at a point with its maximum value is chosen for comparison. This point corresponds to x = 0.067, y = 0.975 and z = 0.890 in the domain. Similarly, 0 on a slip system at a point is chosen and is located at x = 0.108, y = 0.975 and z = 0.932. Both the points belonged to the same grain with Euler angles (0.609, 1.011, 0.676) radians.