PSI - Issue 71

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

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Fig. 1: Unit cube with 8 grains having random orientations used to demonstrate the accuracy and efficiency of the multi-time scale method Fig. 2 compares the evolution of the loading direction normal component of the plastic deformation gradient 0 and one of the slip system resistances 0 between two scales at these material points. As can be seen from the figure, the coarse scale results align closely with the single time scale response. Furthermore, as the response saturates, the multi time scale method can use larger cycle jumps which increases the efficiency further.

Fig. 2: Comparison of evolution of variables (a) 0 , 3 3 and (b) 0 between single and multi-time scale methods

4. Application of the Method for HCF Simulation The cycle scale simulation using the multi-time scale method was extended to 100,000 cycles which is typical of HCF condition. The evolution of the loading direction normal component of the plastic deformation gradient ( 0 ) and a slip system resistance ( 0 ) with cycles are depicted in Fig. 3. As the number of load cycles increases, the response saturates, allowing for larger cycle steps in accordance with the criterion (Chakraborty and Ghosh (2013). To assess the computational efficiency of the multi-time scale method for 100,000 cycles of simulation, the required time for a single time scale method was extrapolated from 2000 cycles, revealing a scale-up of approximately 100 times.