Relaxation Behaviour Determination

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Relaxation behaviour determination

Types of stress for stress relaxation experiments

The relaxation behaviour of plastics can be determined under tensile, bending and compressive stress [1] or using instrumented hardness measurement [2–4]. This requires the measurement of time-dependent force and the measurement of deformation to check the consistency of the test conditions. The load on the test specimen, expressed as the constant strain ε₀, should be variable for different deformation levels. To achieve these stress levels, creep test benches or simple 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 at identical temperatures or with the same deformation level but staggered temperatures. To determine the stress relaxation at specified times, each test system must be equipped with 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) at shorter intervals (variable sampling rate) at the start of the experiments and shortly before the test specimen fracture, ensuring a higher data density at these stages of the test.

Fig. 1:

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 applied (strain, peripheral fibre strain or 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 breaks, which is significantly influenced by the set deformation and the test temperature of the testing device (Fig. 2).

Fig. 2:

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. 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 three-point bending stress.

Fig. 3:

Diagram of time–stress curves a) and relaxation modulus–time curves b) in the tensile relaxation test [1]

$E_{r}(t)={\frac {\sigma (t)}{\varepsilon }}$

(1)

$E_{r}(t)={\frac {F(t)L^{3}}{4bh^{3}s}}$

(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 due to the duration of loading and time. However, since the differences between the two 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
• Instrumented hardness measurement – relaxation
• Tensile test overlapping creep relaxation
• MAXWELL model

References

[1]	Höninger, H.: Long-therm Static Behavior. In: Grellmann, W., 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)
[2]	Fröhlich, F., Grau, P., 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
[3]	Grellmann, W.: Ermittlung der Härte von Gläsern und Keramiken. Dissertation, Martin-Luther-Universität Halle-Wittenberg (1978) (Content as pdf)
[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 Download as pdf
[5]	DIN 53441 (1984): Testing of Plastics – Stress Relaxation Test (withdrawn)
[6]	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)