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en:materialdaten:rheologische_materialdaten [2025/05/15 15:45] – [Temperature shift factor a${}_T$] cschallen:materialdaten:rheologische_materialdaten [2025/05/15 15:49] (aktuell) – [Pressure shift factor β] cschall
Zeile 70: Zeile 70:
 \[log(a_T) = \frac {C_1\cdot(T_B-T_S)} {C_2+(T_B-T_S)} - \frac {C_1\cdot(T-T_S)} {C_2+(T-T_S)}\]  \[log(a_T) = \frac {C_1\cdot(T_B-T_S)} {C_2+(T_B-T_S)} - \frac {C_1\cdot(T-T_S)} {C_2+(T-T_S)}\] 
  
-$T_B$, $T_S$ are to be defined, $C_1 = 8,86$, $C_2 = 101,6$+$T_B$, $T_S$ must be provided, $C_1 = 8,86$, $C_2 = 101,6$
  
 with: $T_B$ = reference temperature, $T_S$ = standard temperature, $T$ = current temperature with: $T_B$ = reference temperature, $T_S$ = standard temperature, $T$ = current temperature
Zeile 78: Zeile 78:
 \[ln(a_T) = - \frac {C_1 \cdot (T-T_B)} {C_2+(T-T_B)}\]  \[ln(a_T) = - \frac {C_1 \cdot (T-T_B)} {C_2+(T-T_B)}\] 
  
-$C_1$, $C_2$, $T_B$ are given +$C_1$, $C_2$, $T_B$ must be provided
  
-**with**: $T_B$ = reference temperature, $T_S$ = standard temperature, $T$ = current temperature+**with**: $T_B$ = reference temperature, $T$ = current temperature
  
 === Carreau-Arrhenius (E, T_B) === === Carreau-Arrhenius (E, T_B) ===
Zeile 86: Zeile 86:
 $$ln(a_T)=\frac{E}{R} (\frac{1}{T}-\frac{1}{T_B}) $$ $$ln(a_T)=\frac{E}{R} (\frac{1}{T}-\frac{1}{T_B}) $$
  
-**with**: $E$ = activating energy, $R$ = gas constant, $K_{0T}$ = physical size at the temperature $T_0$, $T_0$ = reference temperature (in kelvin) +**with**: $E$ = activating energy, $R$ = gas constant, $T_B$ = reference temperature (in kelvin), $T$ = current temperature (in kelvin) 
- +
-With the Carreau-law the polymer specific material behavior can be described over +
-large shear rate and temperature areas. +
  
 ==== Pressure shift factor β ==== ==== Pressure shift factor β ====
Zeile 97: Zeile 94:
 $$ a_p = exp(\beta \cdot (p-p_B))$$ $$ a_p = exp(\beta \cdot (p-p_B))$$
  
-with the pressure displacement factor $\beta$, the pressure $p$ and the reference pressure $p_B$.+with the pressure shift factor $\beta$, the pressure $p$ and the reference pressure $p_B$.
  
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