Fig. 3: Overall flow chart of the numerical computation
The numerical algorithm is depicted in Fig. 3 using a flow chart. First, the material parameters in Table 1 are read by our self-written MATLAB script. Afterwards, Δt is read from input, ρ andσ n are set to zero, and the iteration begins at the time section k =1. Within each iteration, T andσ s at time k Δt are read first, thenσ n can be calculated by Eq.. Next, the nucleation rate is computed by Eq., from which the initial ρ that does not consider the sintering effect can be worked out. After this step, the script enters into the sintering module, which is ruled by Eq.. Note that the flag variable will be updated with a value of 0 if the considered cavity group is found to be as sintered using the criterion given in Eq.. Afterwards, the cavitated GB area fraction f can be calculated by Eq.. At the end of each iteration, time section kis updated by k +1, and a new iteration begins. Refer to Appendix C for the limited numerical error generated by using the forward Euler method together with Δt =0.5 s.