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--- en:materialdaten:rheologische_materialdaten [2024/07/13 18:04] – neelest
+++ en:materialdaten:rheologische_materialdaten [2026/09/17 09:23] (aktuell) – gelöscht - Externe Bearbeitung (Unbekanntes Datum) 127.0.0.1
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-======Rheological material data======
-FIXME
-===== Flow behaviour of plastics =====
-Fluids can be divided into two groups on the basis of their flow characteristics:
-  * Newtonian fluids
-  * Non-Newtonian fluids
-For Newtonian fluids the following law applies:
-\[τ=η\cdot\dotγ\]
-with shear stress $τ$, the viscosity $η$ and the shear rate $\dotγ$.
-This law states that the shear stress and the shear rate are proportional to each
-other, with viscosity being the proportionality factor. In the case of polymeric fluids
-respectively melts this flow behavior occurs at a very low shear rate and occasionally
-with very high ones. Deviations are manifested in so-called structural viscosity,
-dilatancy or the presence of a flow limit.
-The flow behavior of polymer melts is characterised in the shear rate ranges that
-exist in practice by structural viscosity. This describes a flow behavior which deviates
-from that of Newtonian fluids, where the viscosity is no longer constant but highly
-dependent on the shear rate.
-{{ :materialdaten:abb_stoffverhalten_en.svg |}}
-The following illustration shows the basic profile of the viscosity against the shear rate. Where the
-shear rate range is not too large it is possible to describe this behavior through the
-empirically established power flow law according OSTWALD und DE WAELE:
-\[τ=K\cdot\dotγ^n\]
-$n$ is the exponent of the flow lay and $K$ is the flow lay coefficient.
-{{ :materialdaten:abb_viskositaetsverlauf_en.svg |}}
-With the simple setup of this law nearly all flow problems, which are ascertainable for
-Newtonian fluids, can be treated analytically. In the double logarithmic depiction there
-is also for the power law model a straight line. As shown in the next figure, each curve
-segment has to be calculated with the corresponding flow exponent $n$. The
-consistency factor $K$ is described by:
-\[K = K_{0T}\cdot e^{-β(T-T_0)}\]
-The constant $K_{0T}$ corresponds to the viscosity at the shear rate and the reference
-temperature $T_0=0°C$; the temperature dependence of the viscosity is described.
-{{ :materialdaten:abb_potenz_naeherung_en.svg |}}
-A better description of further areas of the viscosity function is offered by the
-CARREAU-law, especially with materials which show a pronounced transition from
-the Newtonian to the low viscosity area:
-\[η = \frac {Aa_T} {(1+a_TB\dotγ)^C}\]
-Here, $A$ is the zero viscosity, $B$ the reciprocal transition shear rate and $C (= 1-n)$ the
-pitch.
-{{ :materialdaten:abb_carreau_en.svg |}}
-==== Temperature shift factor α ====
-The temperature dependence is considered by the temperature shift factor aT which
-can be determined from the WLF-relation:
-Carreau-WLF ($T_B$, $T_S$):
-\[lg(a_T) = \frac {C_1\cdot(T_B-T_S)} {C_2+(T_B-T_S)} - \frac {C_1\cdot(T-T_S)} {C_2+(T-T_S)}\]
-$T_B$, $T_S$ are given, $C_1 = 8,86$, $C_2 = 101,6$
-o r
-Carreau-WLF ($C_1$, $C_2$):
-\[ln(a_T) = - \frac {C_1 \cdot (T-T_B)} {C_2+(T-T_B)}\]
-$C_1$, $C_2$, $T_B$ are given
-**with**: $T_B$ = reference temperature, $T_S$ = standard temperature, $T$ = current temperature
-Carreau-Arrhenius ($E$, $T_B$):
-\[K = K_{0T}exp[\frac{\Delta E}{R} (\frac{1}{T}-\frac{1}{T_0})]\]
-**with**: $E$ = activating energy, $R$ = gas constant, $K_{0T}$ = physical size at the temperature $T_0$, $T_0$ = reference temperature
-With the Carreau-law the polymer specific material behavior can be described over
-large shear rate and temperature areas.
-==== Pressure shift factor β ====
-The pressure shift factor beta considers the pressure’s influence on the viscosity. The value refers to an average material specific temperature from PAM
-and to a reference pressure of 100 bar. The pressure dependent viscosity is
-calculated with the following equation.
-\[y(p) = (p_0)\cdot e^{β(p-p_0)}\]
-{{ :materialdaten:abb_viskositaet_druckabhaengig_en.svg |}}
-The value beta can be imported directly from PAM or entered manually. If 0 is
-entered as the value for beta, the viscosity is calculated without considering the
-pressure.
-As the law can only be used analytically to a limited extent, from this function the
-corresponding coefficients of the power law model are calculated internally for the
-occurring shear rates and temperatures. You can choose between three different
-laws in the input mask **Rheology**. All of them describe the rheological behavior of
-polymer melts. The difference of the laws is their description of the temperature shift
-function. This distinction has been introduced to guarantee an easy input despite different sources of the data (CAMPUS, BAYMAT, VISCOSITY). If the Carreau-WLF
-data is taken for example from the BASF database VISCOSITY, the setting CarreauWLF ($C_1$, $C_2$) has to be chosen. If you want to calculate with a material from BAYER,
-the data can be taken from the BAYMAT file and entered with the help of the setting
-Carreau-WLF ($T_B$, $T_S$). Both constants $C_1$ and $C_2$ are here internally set to 8.86 or
-rather to 101.6 and cannot be edited.
-If you want to calculate a wall-slipping material with **REX/PSI**, you have to
-characterize the flow law with the help of the Carreau or the Arrhenius parameter. In
-addition you have to enter two pairs of variates, consisting of a test temperature and
-the critical wall shear stress determined at this test temperature.
-Additionally, with the material parameter $k_{mat}$ the increase of the dimensionless
-sliding speed $V_{sl}^*$ in dependence of the dimensionless shear stress $τ^*$ can be
-described. The determination of the necessary material data, like the sliding speed
-$v_{sl}$ in dependence of the wall shear stress $τ$, occurs during the viscosity
-measurement (e.g. with a high pressure capillary rheometer).
-At measuring the pressure in dependence of the volume flow, with wall-slipping melts
-discontinuities occur in the double-logarithmic diagram as opposed to wall-adhering
-melts.
-{{ :materialdaten:abb_krit_wandschubspannung_en.svg |}}
-From the critical pressure $Δp_{krit}$ at which this discontinuity occurs, with the following
-formula the critical wall shear stress $τ_{krit}$ can be calculated for rectangular
-capillaries:
-\[τ_{krit} = \frac{\Delta p_{krit}}{2} \frac{h}{l}\]
-These critical shear stresses can be indicated approximately as straight line
-equations in dependence of temperature. Thus, you have to enter two pairs of variates in REX/PSI for the critical shear stresses and the temperature belonging to it.
-**Platzhalter Abbildung 5.9: Rheologische Materialdaten**