Time Temperature Reference strain $$r_p$$ $$r_s$$ $$r_m$$
$$t^0$$ $$T < T_s$$ $$\varvec{\varepsilon }_\text {ref}^0 = 0$$ 1.0 0.0 0.0
$$t^1$$ $$T = 0.5(T_l+T_s)$$ $$\varvec{\varepsilon }_\text {ref}^1 = 0$$ 0.5 0.0 0.5
$$t^2$$ $$T < T_s$$ $$\varvec{\varepsilon }_\text {ref}^2 = \frac{1}{0.5} 0.5 (\varvec{\varepsilon }^{1} - \varvec{\varepsilon }_T^{1})$$ 0.5 0.5 0.0
$$t^3$$ $$T = 0.25T_l +0.75T_s$$ $$\varvec{\varepsilon }_\text {ref}^3 = \frac{1}{0.25} 0.25 \varvec{\varepsilon }_\text {ref}^2 = \varvec{\varepsilon }_\text {ref}^2$$ 0.5 0.25 0.25
$$t^4$$ $$T < T_s$$ $$\varvec{\varepsilon }_\text {ref}^4 = \frac{1}{0.5} (0.25 \varvec{\varepsilon }_\text {ref}^3 + 0.25(\varvec{\varepsilon }^3 - \varvec{\varepsilon }_T^3)) =$$ $$\frac{1}{2}\varvec{\varepsilon }_\text {ref}^3 +\frac{1}{2}(\varvec{\varepsilon }^3 - \varvec{\varepsilon }_T^3)$$ 0.5 0.5 0.0
$$t^5$$ $$T = 0.75T_l +0.25T_s$$ $$\varvec{\varepsilon }_\text {ref}^5 = \lim _{r_s \rightarrow 0}\frac{r_s}{r_s}\varvec{\varepsilon }_\text {ref}^4 = \varvec{\varepsilon }_\text {ref}^4$$ 0.25 0.0 0.75
$$t^6$$ $$T < T_s$$ $$\varvec{\varepsilon }_\text {ref}^6 = \frac{1}{0.75}(0\cdot \varvec{\varepsilon }_\text {ref}^5 + 0.75(\varvec{\varepsilon }^5 - \varvec{\varepsilon }_T^5)) = \varvec{\varepsilon }^5 - \varvec{\varepsilon }_T^5$$ 0.25 0.75 0.0