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{{Language_sel|LANG=ger|ARTIKEL=Relaxationsverhalten Ermittlung}}
{{PSM_Infobox}}
Relaxation behaviour determination
__FORCETOC__

==Types of stress for stress relaxation experiments==

The [[Relaxation Plastics|relaxation behaviour]] of [[Plastics|plastics]] can be determined under [[Tensile Test|tensile]], [[Bend Test|bending]] and [[Compression Test|compressive stress]] [1] or using [[Instrumented Hardness Measurement – Creep|instrumented hardness measurement]] [2–4]. This requires the measurement of time-dependent force and the measurement of [[Deformation|deformation]] to check the consistency of the test conditions. The load on the test [[Specimen|specimen]], expressed as the constant strain ''ε''0, should be variable for different deformation levels. To achieve these stress levels, [[Creep Behaviour – Tensile Creep Test|creep test benches]] or simple [[Material Testing Machine|universal testing machines]] can be used, which should be equipped with temperature control chambers to ensure constant test conditions. From an economic and time perspective, at least 10 individual test benches should be available, which are operated either with variable [[Deformation|deformation]] at identical temperatures or with the same deformation level but staggered temperatures. To determine the [[Relaxation Plastics|stress relaxation]] at specified times, each test system must be equipped with [[Electro-mechanical Force Transducer|electro-mechanical force measuring cells]] that are queried via a connected computer in multiplex mode ('''Fig. 1'''). Modern test software can also query the data from the force measuring cells (see: [[Piezoelectric Force Transducer|piezoelectric force transducer]]) at shorter intervals (variable sampling rate) at the start of the experiments and shortly before the test specimen [[Fracture|fracture]], ensuring a higher data density at these stages of the test.

[[File:RelaxBehavDet_-_Fig-1.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 1''':
|width="600px" |Schematic representation of the recording of time-dependent stress relaxation in plastics under tensile stress a), bending stress b) and compressive stress c)
|}

==Evaluation of stress relaxation tests==

Since the evaluation algorithm is identical regardless of the type of [[Stress|stress]] applied ([[Tensile Test|strain]], [[Peripheral Fibre Strain|peripheral fibre strain]] or [[Compression Test|compression]]), only the general procedure after registration of the time–stress curves is explained here. The evaluation of stress relaxation experiments is based on the registration of the force decrease up to a specified point in time or until the test specimen [[Fracture|breaks]], which is significantly influenced by the set deformation and the test temperature of the testing device ('''Fig. 2''').

[[File:RelaxBehavDet_-_Fig-2.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 2''':
|width="600px" |Technical version of the creep test device for determining stress relaxation behaviour [1]
|}

One problem in investigating creep relaxation behaviour is that there is currently no standard available for testing [[Plastics|plastics]]. The evaluation algorithm can therefore only be presented on the basis of the withdrawn standard DIN 53441 [5]. From the recorded time-stress curves, which are plotted on a double logarithmic scale, the relaxation modulus Er is calculated according to the general '''Eq. (1)''' from the time-dependent stress and the specified strain for the tensile and compressive loads. '''Eq. (2)''' is then to be applied for the [[Bend Test#The Tree-point bending test method|three-point bending stress]].

[[File:R_ermittlung_3.jpg]]
{|
|- valign="top"
|width="50px"|'''Fig. 3''':
|width="600px" |Diagram of time–stress curves a) and relaxation modulus–time curves b) in the tensile relaxation test [1]
|}

{|
|-
|width="20px"|
|width="500px" | <math>E_{r}(t)=\frac{\sigma (t)}{\varepsilon }</math>
|width="50px" |(1)
|}

{|
|-
|width="20px"|
|width="500px" | <math>E_{r}(t)=\frac{F (t) L^{3}}{4bh^{3}s}</math>
|width="50px" |(2)
|}

Similar to the creep modulus ''E''c, the relaxation modulus ''E''r is important as a design parameter because it takes into account the reduction in [[Stiffness|stiffness]] due to the duration of loading and time. However, since the differences between the two [[Elastic Modulus – Examples and Material Values|moduli]] are small due to identical molecular processes, the creep modulus can be used as an approximation for dimensioning tasks, especially since its determination is standardised. Further information on the relaxation modulus can be found in [6].

==See also==

* [[Relaxation Plastics|Relaxation plastics]]
* [[Instrumented Hardness Measurement – Relaxation|Instrumented hardness measurement – relaxation]]
* [[Tensile Test Overlapping Creep Relaxation|Tensile test overlapping creep relaxation]]
* [[MAXWELL Model|MAXWELL model]]

==References==

{|
|-valign="top"
|[1]
|Höninger, H.: Long-therm Static Behavior. In: [[Grellmann,_Wolfgang|Grellmann, W.]], [[Seidler,_Sabine|Seidler, S.]] (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3rd Edition, pp. 167–177 (ISBN 978-1-56990-806-8; E-Book: ISBN 978-1-56990-806-5; see [[AMK-Library]] under A 22)
|-valign="top"
|[2]
|Fröhlich, F., Grau, P., [https://www.researchgate.net/profile/Wolfgang-Grellmann Grellmann, W.]: Performance and Analysis of Recording Microhardness Tests. Phys. stat. sol. (a) 42 (1977) 79–89, DOI: https://doi.org/10.1002/pssa.2210420106
|-valign="top"
|[3]
|[https://de.wikipedia.org/wiki/Wolfgang_Grellmann Grellmann, W.]: Ermittlung der Härte von Gläsern und Keramiken. Dissertation, Martin-Luther-Universität Halle-Wittenberg (1978) ([https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/Diss_Grellmann_Inhaltsverzeichnis.pdf Content as pdf])
|-valign="top"
|[4]
|May, M., Fröhlich, F., Grau, P., Grellmann, W.: Anwendung der Methode der registrierenden Mikrohärteprüfung für die Ermittlung von mechanischen Materialkennwerten an Polymerwerkstoffen. Plaste und Kautschuk 30 (1983) H. 3 pp. 149–153 [https://www.polymerservice-merseburg.de/fileadmin/inhalte/psm/veroeffentlichungen/May_Anwendung_der_registrierenden_Mikrohaertepruefung.pdf Download as pdf]
|-valign="top"
|[5]
|DIN 53441 (1984): Testing of Plastics – Stress Relaxation Test (withdrawn)
|-valign="top"
|[6]
|[[Bierögel,_Christian|Bierögel, C.]], Grellmann, W.: Long-term Loading Test. In: Grellmann, W., Seidler, S. (Eds.): Mechanical and Thermomechanical Properties of Polymers. Landoldt Börnstein. Volume VIII/6A3, Springer, Berlin (2014) pp. 286−331 (ISBN 978-3-642-55165-9; see [[AMK-Library]] under A 16)
|}

[[Category:Deformation]]

Relaxation Behaviour Determination - Revision history