Unterschiede
Hier werden die Unterschiede zwischen zwei Versionen angezeigt.
| Beide Seiten der vorigen RevisionVorhergehende ÜberarbeitungNächste Überarbeitung | Vorhergehende Überarbeitung | ||
| en:grundlagenhandbuch:materialkenngroessen [2026/05/21 22:16] – [Tensile Strength] neelest | en:grundlagenhandbuch:materialkenngroessen [2026/09/04 08:25] (aktuell) – [Meaning] paal | ||
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| Zeile 24: | Zeile 24: | ||
| In this equation: | In this equation: | ||
| - | * $K$ = Power law co-efficient | + | * $K$ = Power-law coefficient |
| * $n$ = Exponent of the power law (n<1). | * $n$ = Exponent of the power law (n<1). | ||
| - | In double logarithmic scale, the viscosity over the shear rate yields a linear profile with gradient (n-1). The gradient of this straight line is dependent on the shear rate, therefore for the value of " | + | In double logarithmic scale, the viscosity over the shear rate yields a linear profile with gradient (n-1). The gradient of this straight line is dependent on the shear rate, therefore for the value of " |
| The simulation programme SIGMA offers two equations to describe the rheological behavior, firstly the **Carreau–WLF** (Williams, Landel-Ferry) equation and secondly the **Carreau-Arrhenius** equation. The equations differ in that they offer different descriptions in the temperature dependence of the viscosity | The simulation programme SIGMA offers two equations to describe the rheological behavior, firstly the **Carreau–WLF** (Williams, Landel-Ferry) equation and secondly the **Carreau-Arrhenius** equation. The equations differ in that they offer different descriptions in the temperature dependence of the viscosity | ||
| - | . This difference was introduced so that data from different origins (CAMPUS; BAYMAT; VISCOSITY) is able to be entered without any conversions. The evaluation of the viscosity function with the Carreau-estimation programme offers not only the zero viscosity $a$, but the reciprocal transitional shear rate $b$, the gradient $c$, the reference temperature \( T_B \)and the standard temperature \( T_S \) which are necessary for the equation: | + | . This difference was introduced so that data from different origins (CAMPUS; BAYMAT; VISCOSITY) is able to be entered without any conversions. The evaluation of the viscosity function with the Carreau-estimation programme offers not only the zero viscosity $a$, but the reciprocal transitional shear rate $b$, the gradient $c$, the reference temperature \( T_B \) and the standard temperature \( T_S \) which are necessary for the equation: |
| $$\eta = \frac{a \cdot a_T}{(1 + b \cdot a_T \cdot \dot{\gamma})^c} \tag{3}$$ | $$\eta = \frac{a \cdot a_T}{(1 + b \cdot a_T \cdot \dot{\gamma})^c} \tag{3}$$ | ||
| Zeile 66: | Zeile 66: | ||
| {{ : | {{ : | ||
| - | ==== Measuring Series with the High Pressure Capillary Rheometer ==== | + | ==== Measuring Series with the High-Pressure Capillary Rheometer ==== |
| To be able to define the necessary Carreau parameters, measurements have to be taken, for instance, the high pressure capillary rheometer. Usually the experimental series are performed at 3 different temperatures. | To be able to define the necessary Carreau parameters, measurements have to be taken, for instance, the high pressure capillary rheometer. Usually the experimental series are performed at 3 different temperatures. | ||
| - | In a high pressured capillary rheometer, pre-heated material flows through a capillary with a circular cross-section. During this process, practically the total area of the interesting viscosities is measured. For low viscous fluids, long thin capillaries are used and for high viscous fluids appropriately high pressures are used. By using this discontinual | + | In a high-pressured capillary rheometer, pre-heated material flows through a capillary with a circular cross-section. During this process, practically the total area of the interesting viscosities is measured. For low viscous fluids, long thin capillaries are used and for high viscous fluids appropriately high pressures are used. In the discontinuous |
| ===== Thermodynamic Material Parameters ===== | ===== Thermodynamic Material Parameters ===== | ||
| - | The calculation of both the melting behavior and the temperature development in power melts requires a comprehensive knowledge of the thermodynamic material behavior | + | The calculation of both the melting behavior and the temperature development in polymer |
| - | The following data is required for SIGMA: the crystalline melting temperature, | + | The following data is required for SIGMA: the crystalline melting temperature, |
| ==== General Principle of the DSC-Analysis ==== | ==== General Principle of the DSC-Analysis ==== | ||
| Zeile 85: | Zeile 85: | ||
| {{ : | {{ : | ||
| - | A heat flow $\dot{Q}$, drifts from the oven over a sensor (thermal resistor) to the sample pot and to the reference pot, which are usually very similar (equal in dimension and composed of the same material). The heat flow to the reference $\dot{Q}_R$ is caused due to the heat capacity of the pot material and the heat flow losses. This applies to equal pot materials, symmetry of the measuring cell and also to the specimen pot $\dot{Q}_S = \dot{Q}_R$. The specimen substance that is embedded | + | A heat flow $\dot{Q}$, drifts from the oven over a sensor (thermal resistor) to the sample pot and to the reference pot, which are usually very similar (equal in dimension and composed of the same material). The heat flow to the reference $\dot{Q}_R$ is caused due to the heat capacity of the pot material and the heat flow losses. This applies to equal pot materials, symmetry of the measuring cell and also to the specimen pot $\dot{Q}_S = \dot{Q}_R$. The sample material enclosed |
| $$\dot{H} = \dot{Q}_S - \dot{Q}_R = \frac{T_p - T_S}{R_t} - \frac{T_p - T_R}{R_t} = \frac{T_S - T_R}{R_t} = -\frac{\Delta T}{R_t} \tag{6}$$ | $$\dot{H} = \dot{Q}_S - \dot{Q}_R = \frac{T_p - T_S}{R_t} - \frac{T_p - T_R}{R_t} = \frac{T_S - T_R}{R_t} = -\frac{\Delta T}{R_t} \tag{6}$$ | ||
| - | Where is $\dot{H}$ = heat flow of the specimen substance $\dot{Q}_S$, | + | Where is $\dot{H}$ = heat flow of the specimen substance $\dot{Q}_S$, |
| - | Partially crystalline thermoplastics do not have a fixed melting point but rather a melting range. This is due to them having different sized crystal lamellas in comparison to metals. Smaller, irregular crystallites melt at a lower temperature than larger crystallites. Characteristic for every partially crystalline polymer is the melting temperature resp. the crystallite peak temperature TK. The position of the peak on the temperature axis is identified by the start temperature ($T_A$), the peak temperature ($T_K$) and the final temperature ($T_E$) that is also important for other thermodynamical | + | Partially crystalline thermoplastics do not have a fixed melting point but rather a melting range. This is due to them having different sized crystal lamellas in comparison to metals. Smaller, irregular crystallites melt at a lower temperature than larger crystallites. Characteristic for every partially crystalline polymer is the melting temperature resp. the crystallite peak temperature TK. The position of the peak on the temperature axis is identified by the start temperature ($T_A$), the peak temperature ($T_K$) and the final temperature ($T_E$) that is also important for other thermodynamic |
| {{ : | {{ : | ||
| Zeile 198: | Zeile 198: | ||
| * $V_0$= volume of the tank. | * $V_0$= volume of the tank. | ||
| - | The solid densities can be determined according to DIN 53 479. This method (lift method) compares the value of a certain sample mass of air with a fluid medium (here: distillate water $\rho_{H_2O}$=1, | + | The solid densities can be determined according to DIN 53 479. This method (buoyancy |
| {{ : | {{ : | ||
| Zeile 219: | Zeile 219: | ||
| {{ : | {{ : | ||
| - | Another option is to determine the granule diameter $d$ from a total of $n$ samples using the solid density $r$ and the total weight of the samples $m_{total}$. The following applies to the total of $n$ samples: | + | Another option is to determine the granule diameter $d$ from a total of $n$ samples using the solid density $\rho$ and the total weight of the samples $m_{total}$. The following applies to the total of $n$ samples: |
| $$V_{ges} = \frac{m_{ges}}{\rho} \tag{15}$$ | $$V_{ges} = \frac{m_{ges}}{\rho} \tag{15}$$ | ||
| Zeile 251: | Zeile 251: | ||
| The volume or mass of the discharged polymer melt (the so-called extrudate) is determined as a function of time [[en: | The volume or mass of the discharged polymer melt (the so-called extrudate) is determined as a function of time [[en: | ||
| - | The melt flows out mass is determined by the deposition of the liquid strand at predetermined time intervals and weighing. As modified melt index the increased volume flow index MVI / MVR is strongly used indicating the extruded melt volume in 10 minutes. A major advantage of the melt volume flow rate MVR is the simple measurement of the piston travel at a known piston diameter to determine the treat out melt volume. In contrast, for the melt mass-flow rate MFR the detached molten strands have to be weighed and as result it is an additional expense for the handling. For this reason, the measurement of the mass flow rate is only used when the determination of the melt volume in case of problems during the reaction is not workable. | + | {{ : |
| + | |||
| + | The melt flows out mass is determined by the deposition of the liquid strand at predetermined time intervals and weighing. As modified melt index the increased volume flow index MVI / MVR is strongly used indicating the extruded melt volume in 10 minutes. A major advantage of the melt volume flow rate MVR is the simple measurement of the piston travel at a known piston diameter to determine the extruded | ||
| In order to compare MFI values among themselves, whose value must always be specified in addition to the weight used and the respective test temperature. Specifying MFI 190/2,16 for example, means that the melt index was determined at 190 ° C and a piston mass of 2,16 kg [[en: | In order to compare MFI values among themselves, whose value must always be specified in addition to the weight used and the respective test temperature. Specifying MFI 190/2,16 for example, means that the melt index was determined at 190 ° C and a piston mass of 2,16 kg [[en: | ||
| Zeile 351: | Zeile 353: | ||
| $$c_{MIX} = w_1 \cdot c_1 + w_2 \cdot c_2 \tag{37}$$ | $$c_{MIX} = w_1 \cdot c_1 + w_2 \cdot c_2 \tag{37}$$ | ||
| - | Where the weight content | + | Where the weight content |
| The specific heat capacity $c_{0,MIX}$ of the blend is set to: | The specific heat capacity $c_{0,MIX}$ of the blend is set to: | ||
| Zeile 644: | Zeile 646: | ||
| Porosity is defined using the ratio of void volume to total volume: | Porosity is defined using the ratio of void volume to total volume: | ||
| - | $$\psi = \frac{V_H}{V_{ges}} \tag{1}$$ | + | $$\psi = \frac{V_H}{V_{ges}} \tag{81}$$ |
| with: | with: | ||
| Zeile 659: | Zeile 661: | ||
| In the loose fill of agglomerates one can find the bulk porosity $\psi_b$, which is the relationship between the agglomerates and the total volume of the loose fill within the mold cavity. The total porosity $\psi$ is composed of individual porosities. It considers: | In the loose fill of agglomerates one can find the bulk porosity $\psi_b$, which is the relationship between the agglomerates and the total volume of the loose fill within the mold cavity. The total porosity $\psi$ is composed of individual porosities. It considers: | ||
| - | $$(1 - \psi) = (1 - \psi_p)(1 - \psi_a)(1 - \psi_b) \tag{2}$$ | + | $$(1 - \psi) = (1 - \psi_p)(1 - \psi_a)(1 - \psi_b) \tag{82}$$ |
| {{ : | {{ : | ||
| Zeile 667: | Zeile 669: | ||
| From measurements one cannot not distinguish between the porosity of the primary particles $\psi_p$, the porosity of the agglomerates $\psi_a$ and the bulk porosity $\psi_b$. Densities are also usually measured. A porous material has a smaller density than the solid material $\rho_f$. The density of the individual particle $\rho_p$ is related to the porosity as follows: | From measurements one cannot not distinguish between the porosity of the primary particles $\psi_p$, the porosity of the agglomerates $\psi_a$ and the bulk porosity $\psi_b$. Densities are also usually measured. A porous material has a smaller density than the solid material $\rho_f$. The density of the individual particle $\rho_p$ is related to the porosity as follows: | ||
| - | $$\rho_p = (1 - \psi_p) \cdot \rho_f \tag{3}$$ | + | $$\rho_p = (1 - \psi_p) \cdot \rho_f \tag{83}$$ |
| The agglomerate density is: | The agglomerate density is: | ||
| - | $$\rho_a = (1 - \psi_p) \cdot (1 - \psi_a) \cdot \rho_f \tag{4}$$ | + | $$\rho_a = (1 - \psi_p) \cdot (1 - \psi_a) \cdot \rho_f \tag{84}$$ |
| Appropriately considered for the bulk density $\rho_b$: | Appropriately considered for the bulk density $\rho_b$: | ||
| - | $$\rho_b = (1 - \psi_p) \cdot (1 - \psi_a) \cdot (1 - \psi_b) \cdot \rho_f \tag{5}$$ | + | $$\rho_b = (1 - \psi_p) \cdot (1 - \psi_a) \cdot (1 - \psi_b) \cdot \rho_f \tag{85}$$ |
| Besides the different pore types there are also various pore sizes to be considered. In the figure, the distribution density curve of the pore radius is represented for a fill of agglomerates. Generally speaking, pore sizes can be distinguished into: single particle pores, agglomerate pores and loose material pores. In the ideal case they yield various maximums of the distribution density (multi-modal). | Besides the different pore types there are also various pore sizes to be considered. In the figure, the distribution density curve of the pore radius is represented for a fill of agglomerates. Generally speaking, pore sizes can be distinguished into: single particle pores, agglomerate pores and loose material pores. In the ideal case they yield various maximums of the distribution density (multi-modal). | ||
| Zeile 699: | Zeile 701: | ||
| Through known solid densities, the agglomerate density yields corresponding to DIN 53193 or DIN 51057 from the displaced volume and the difference in mass. In dependence of the pressure needed, the mercury penetrates the small pores, corresponding to the Gauß-Laplace equation: | Through known solid densities, the agglomerate density yields corresponding to DIN 53193 or DIN 51057 from the displaced volume and the difference in mass. In dependence of the pressure needed, the mercury penetrates the small pores, corresponding to the Gauß-Laplace equation: | ||
| - | $$p = \frac{2\sigma \cos(\Theta)}{r} \tag{1}$$ | + | $$p = \frac{2\sigma \cos(\Theta)}{r} \tag{86}$$ |
| with: | with: | ||