# Table 4 Exemplary evolution of reference strain for a cyclic, partial remelting of solid phase assuming $$\varvec{\varepsilon }- \varvec{\varepsilon }_T$$ is constant in all phase change intervals
time temperature reference strain $$r_s$$ $$r_m$$
$$t^0$$ $$T < T_s$$ $$\varvec{\varepsilon }_\text {ref}^0 = 0$$ 1.0 0.0
$$t^1$$ $$T = 0.5(T_l+T_s)$$ $$\varvec{\varepsilon }_\text {ref}^1 = 0$$ 0.5 0.5
$$t^2$$ $$T < T_s$$ $$\varvec{\varepsilon }_\text {ref}^2 = \frac{1}{1} (0.5 \varvec{\varepsilon }_\text {ref}^1 + 0.5 (\varvec{\varepsilon }- \varvec{\varepsilon }_T)) = \frac{1}{2} (\varvec{\varepsilon }- \varvec{\varepsilon }_T)$$ 1.0 0.0
$$t^3$$ $$T = 0.5(T_l+T_s)$$ $$\varvec{\varepsilon }_\text {ref}^3 = \frac{1}{0.5} 0.5 \varvec{\varepsilon }_\text {ref}^2 = \varvec{\varepsilon }_\text {ref}^2$$ 0.5 0.5
$$t^4$$ $$T < T_s$$ $$\varvec{\varepsilon }_\text {ref}^4 = \frac{1}{1} (0.5 \varvec{\varepsilon }_\text {ref}^3 + 0.5(\varvec{\varepsilon }- \varvec{\varepsilon }_T)) = \frac{3}{4}(\varvec{\varepsilon }- \varvec{\varepsilon }_T)$$ 1.0 0.0
$$t^5$$ $$T = 0.5(T_l+T_s)$$ $$\varvec{\varepsilon }_\text {ref}^5 = \frac{1}{0.5} 0.5 \varvec{\varepsilon }_\text {ref}^4 = \varvec{\varepsilon }_\text {ref}^4$$ 0.5 0.5
$$t^6$$ $$T < T_s$$ $$\varvec{\varepsilon }_\text {ref}^6 = \frac{1}{1} (0.5 \varvec{\varepsilon }_\text {ref}^5 + 0.5(\varvec{\varepsilon }- \varvec{\varepsilon }_T)) = \frac{7}{8}(\varvec{\varepsilon }- \varvec{\varepsilon }_T)$$ 1.0 0.0