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 |