Critical strain

${\epsilon }_c=8.87\times {10}^{-4}{d}_0{}^{0.2}{Z}^{0.099}$

when

$\dot{\epsilon }\ge 0.01{\text{s}}^{-1}$

${\epsilon }_c=9.57\times {10}^{-6}{d}_0{}^{0.196}{Z}^{0.167}$

when

$\dot{\epsilon }<0.01{\text{s}}^{-1}$

Dynamic recrystallization

$X_{dyn}=1-\exp (-\ln 2{(\frac{\epsilon }{{\epsilon }_{0.5}})}^{1.68}$ when $T\le {1038}^{\circ }C,{\epsilon }_{0.5}=0.037d_0{}^{0.2}{Z}^{0.058}$

$X_{dyn}=1-\exp (-\ln 2{(\frac{\epsilon }{{\epsilon }_{0.5}})}^{1.90}$ when $T>{1038}^{\circ }C,{\epsilon }_{0.5}=0.029d_0{}^{0.2}{Z}^{0.058}$

$d_{dyn}=1301\times Z^{-0.124}$

Grain growth

$d^3-d_0{}^3=9.8\times {10}^{19}t\exp (-43700/RT)$