Open Access
Table 2
Summary of all parameters used in the modelling approach.
| Symbol | Parameter | Units | Values from literature | Values used in the model | |
|---|---|---|---|---|---|
| General | vd | Debye frequency constant | s−1 | 2 ∙ 1012 | 2 ∙ 1012 |
| kB | Boltzmann constant | J.K−1 | 1.381 ∙ 10−23 | 1.381 ∙ 10−23 | |
| R | Gas constant | J.mol−1.K−1 | 8.314 | 8.314 | |
| General − Ferrite | b | Burgers’ vector | m | 2.48 ∙ 10−10 | 2.48 ∙ 10−10 |
| G | Shear modulus | GPa | 77.5 | 77.5 | |
| E | Young’s modulus | GPa | 200 | ||
| VFe | Molar volume | m3.mol−1 | 7.11 ∙ 10−6 | 7.11 ∙ 10−6 | |
| Nv | Number of atoms per unit volume Nv = 6.022.1023/VFe |
#.m−3 | 8.5 ∙ 1028 | ||
| MT | Taylor factor | ∼3.15 (γ-fiber) − ∼2.1 (α and θ-fibers) in plane strain compression [12] 2.3–3.2 [5] |
3.2 (HSE) 2.3 (LSE) |
||
| Recovery | Uα | Activation energy for recovery | kJ mol−1 | 170–210 [9] 286 [2] 245–290 [5] |
250 (LSE-binary) 255 (LSE-ternary) 225 (HSE-binary) 240 (HSE-ternary) |
| Vα | Activation volume for recovery | 5-100b3 [13] | 12b3 | ||
| αrec | Recovery constant | 0.15 [2] 0.20–0.27 [5] |
0.2 (LSE-binary) 0.2 (LSE-ternary) 0.24 (HSE-binary) 0.27 (HSE-ternary) |
||
| Mobility | λ | Migrating grain boundary width | m | 1 ∙ 10−9 [2] | 1 ∙ 10−9 |
| γgb | Grain boundary energy | J m−2 | 0.5 [3] 1.3115–0.0005T [2] |
1.0 | |
 |
Pre-exponential factor for grain boundary migration | m2 s−1 | 1.5 ∙ 10−4 [14] | 8 ∙ 102 | |
| Qgb | Activation energy for grain boundary migration | kJ mol−1 | 148 [14] 290 [1] |
290 | |
 |
Trans interface diffusion coefficient for Sn | m2 s−1 | 2 ∙ 10−1 | ||
| Qtrans | Activation energy for trans interface diffusion of Sn | kJ mol−1 | 290 | ||
| E0 | Binding energy between grain boundary and solute atoms | kJ mol−1 | (−26)–(−29) [6] | −28 | |
| Recrystallization | NREX | Nucleation density of recrystallisation calculated using the approach proposed in [15],  where A is a parameter that depends on grain shape-size distribution, A = 0.426 for tetrakaidecahedra and  the average grain size. |
m−3 | 5 ∙ 1014 [14] | 4 ∙ 1014 |
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