Unterschiede

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--- en:berechnungen:materialabbau [2024/04/12 13:41] – angelegt admin
+++ en:berechnungen:materialabbau [2025/07/03 13:35] (aktuell) – cschall
@@ Zeile 1: / Zeile 1: @@
 ======Material degradation======
+-> [[en:grafische_darstellung_der_ergebnisse:materialabbau|Graphical representation of the material degradation]]
+===== Theoretical principles =====
+Material degradation describes progressive damage to polymers at a molecular level. Among other things, this can change the rheological material behaviour as well as the mechanical and optical properties, usually unintentionally.
+The degradation behaviour during processing can be simulated in REX/PSI. In particular, high shear stress and high temperatures, in conjunction with a corresponding dwell time, lead to breaks in the polymer chains and thus to a decreasing average molecular weight. The shorter molecular chains can slide better against each other, whereby the viscosity decreases as the material damage progresses.
+Material degradation in REX/PSI is characterised by the decrease in [[en:materialdaten:rheologische_materialdaten|zero viscosity]]. Simulation requires a material characterisation and the corresponding [[en:materialdaten:molekulargewicht|material parameters for the degradation behaviour]].
+The material degradation is calculated according to the following equation:
+$\frac{\eta_{0,sch}}{\eta_0} = (1-\eta_\infty^*) * exp \left[ -\left( \left( \frac{T}{K_T}\right)^{n_T} \left( \frac{\dot \gamma}{K_{\dot \gamma}}\right)^{n_{\dot \gamma}} \right) * \frac{t}{1s} \right]+\eta_\infty^*$
+The material parameters $\eta_\infty^*$, $K_T$, $K_{\dot \gamma}$, $n_T$ and $n_{\dot \gamma}$ must be defined in the [[en:materialdaten:molekulargewicht|material data]].
+The following figure shows how material degradation can look under the influencing variables of temperature, shear rate and dwell time.
+{{ :berechnungen:materialabbau:abb_materialabbau_en.svg?nolink&600 |}}
+===== Calculation in REX =====
+Based on the values calculated by REX (shear rate, temperature, dwell time), the material degradation can be analysed. The following assumptions are made for this:
+  * Material degradation only takes place in the melt
+  * If the degree of melting increases in one of the intervals, a new isolated mass flow starts in each case
+  * Each mass flow starts with a degradation level of 0 %
+  * Die Abbaugeschwindigkeit ist geringer, solange neu aufgeschmolzenes Material in die Schmelze eingemischt wird
+The assumptions are explained in more detail below.
+The first assumption describes the simplification that no material degradation takes place below the melting temperature, and therefore in the non-melted plastic.
+This can be justified by the fact that only low temperatures and no shear are present in the solid material and therefore the degradation mechanisms that occur are negligible.
+The second and third assumptions for calculating the material degradation are based on the idea that an individual melt mass flow starts each time the degree of melting increases within the intervals calculated by REX/PSI.
+If the melting degree for an exemplary process with a throughput of 100 kg/h increases from 0 % in interval 20 to 2 % in interval~21, the first mass flow considered starts with 2 kg/h and a degradation degree of 0 %.
+In the next interval~22 the degree of melting increases from 2 % to 3 %.
+A second mass flow now starts with a throughput of 1~kg/h and again an initial degree of degradation of 0 %.
+However, the first mass flow of 2~kg/h is damaged in this screw section, so that the degree of degradation increases.
+A new mass flow starts in each interval until the interval where the plastic is completely melted.
+If the degree of melting in the described example extrusion process increases to 100 % in the interval~90, a total of 70 mass flows are started, which in total correspond to the total throughput of 100~kg/h. The melt stream that melted first has the longest damage history and therefore has the highest degree of degradation. The last mass flow to be melted, on the other hand, has the lowest degree of degradation and therefore the least damage. The degree of degradation of all melt streams can be weighted with the respective throughputs to calculate an average degree of degradation.
+In the calculation, however, the fourth assumption is added, namely that the load in the melt and thus also the material degradation takes place more slowly if the material has not yet completely melted. If only solid material is present, no material degradation takes place. If only melt is present, material degradation takes place according to the above mathematical description. In the area in between, the material degradation in REX/PSI is additionally throttled. This is achieved by multiplying the theoretical material degradation by the degree of melting. With an exemplary melting degree of 20 %, the degradation rate is therefore only 20 % of the actual value. This can be explained by the fact that only individual, separate mass flows are considered. Mathematically, these are completely isolated and without interaction. In the real process, however, the mass flows mix, so that the average degradation rate is lower than when isolated mass flows are considered, especially in the melting area, where freshly melted plastic constantly joins the melt phase.
+The visualisation of the material degradation is explained in the chapter [[en:grafische_darstellung_der_ergebnisse:materialabbau|Graphical representation of the results]].
+<details><summary>Source</summary>
+  * Schall, Christoph: Materialschonende Verarbeitung von Thermoplasten auf Wave-Schnecken, Dissertation, Universität Paderborn, 2023
+</details>
+===Further topics===
+  * [[en:berechnungen:einfache_berechnung|]]
+  * [[en:berechnungen:prozess_iterieren]]
+  * [[en:berechnungen:durchsatz|]]
+  * [[en:berechnungen:druckverlauf|]]
+  * [[en:berechnungen:aufschmelzverlauf|]]
+  * [[en:berechnungen:temperaturverlauf|]]
+  * [[en:berechnungen:leistung_und_schubspannungen|]]
+  * [[en:berechnungen:schergeschwindigkeit]]
+  * [[en:berechnungen:verweilzeit|]]
+  * [[en:berechnungen:verweilzeitverteilung|]]
+  * [[en:berechnungen:materialabbau|]]
+  * [[en:berechnungen:faserlaengenabbau|]]
+  * [[en:berechnungen:entgasungskennzahlen|]]
+  * [[en:berechnungen:festigkeitsberechnung|]]
+  * [[en:berechnungen:schlepp-druckstroemung|]]
+  * [[en:berechnungen:feststofffoerderung|]]
+  * [[en:berechnungen:verarbeitung_von_mischungen|]]
+  * [[en:berechnungen:wandgleitende_materialien|]]
+  * [[en:berechnungen:nutbuchsenberechnung|]]
+  * [[en:berechnungen:kompressionsverhaeltnisse|]]