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.