Thermal Expansion Coefficient

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Thermal expansion coefficient

General principles

As the loading temperature increases, plastics undergo lengthwise expansion, which is generally significantly greater than that of metallic materials.

This thermal expansion (see also: thermomechanical analysiss) is described by the plastic’s mean linear (α) or cubic (β) thermal expansion coefficient (see also: thermomechanical analysis) and also provides information about important phase-transition phenomena during heating.

The thermal expansion coefficient α_Th, also known as the thermal expansion number, describes the change in length ΔL of a body for a temperature increase of 1 °C and is expressed in K⁻¹ [1]. Within a limited temperature range, the linear expansion for a temperature increase of ΔT is given by Eq. (1).

$\Delta L_{Th}=\alpha _{Th}\ L\ \Delta T\!$

(1)

Over a wider temperature range, non-linearities may occur in various plastics, caused by local movements of small groups of molecules (secondary relaxation) and cooperative movements of entire molecular segments (main relaxation), whereby the expansion coefficients may also change abruptly when phase transition regions are reached.

Methods for determining the thermal expansion coefficient

The linear coefficient of expansion can be determined on very small specimens using the dilatometer method or thermomechanical analysis (TMA) [1], or on multipurpose test specimens using thermal strain analysis [2–4]. It should be noted that the first heating cycle of a TMA or thermal strain analysis is influenced by the specimen’s thermo-mechanical history. During this process, volatile components may escape, or the breakdown of orientations and residual stresses may be initiated at higher temperatures; in semi-crystalline plastics (see: crystallinity), post-crystallisation processes may occur. These processes cause shrinkage (see also: shrinkage test) and distort the absolute value of the thermal expansion coefficient. In thermosetting plastics, post-curing processes may occur, and in reinforced or filled plastics, anisotropy effects resulting from the manufacturing process can cause the expansion coefficient to vary depending on the direction.

Example of the temperature dependence of the expansion coefficient

Thermal stresses must be taken into account when designing and dimensioning plastic components. This is particularly important in the case of hybrid components made from plastics and other materials that have significantly different expansion coefficients. Large-area plastic components, such as panels for façade design, can, depending on their colour, exhibit very severe warping or distortion of their geometry under thermal stress, which is due to the temperature-dependent nature of thermal expansion (Fig. 1). If thermal expansion is restricted due to the installation conditions, the build-up of internal stresses gives rise to so-called thermal stresses, which, if the component is overloaded, can lead to cracks or component failure (see: component failure). Depending on external temperature differences, tensile or compressive stresses (see: tensile test and compression test) may then occur, particularly in force-fit or form-fit connections.

Fig. 1:

Thermal expansion behaviour and expansion coefficient of PMMA (a) and PVC (b) as determined by thermal strain analysis

A comprehensive review of the thermal expansion coefficients for numerous plastics is provided in [5].

Siehe auch

• Thermomechanical analysis
• Thermal stress analysis
• Thermoelastic effect
• Glass transition temperature
• Shrinkage test
• Viscoelastic material behaviour
• Anisotropy

References

[1]	Grellmann, W., Seidler, S. (Eds.): Kunststoffprüfung. Carl Hanser, Munich (2025) 4th Edition, pp. 307–310 (ISBN 978-3-446-44718-9; E-Book: ISBN 978-3-446-48105-3; see AMK-Library under A 23)
[2]	Sirch, C., Bierögel, C., Grellmann, W.: Wirkung von Eigenspannungen auf die lokale Dehnung von Kunststoffen. In: Langer, B., Rödel, T. (Eds.): Polymerwerkstoffe. Tagungsband PolyMerTec 2014, CD-ROM, Merseburg (2014) 556–561
[3]	Sirch, C., Bierögel, C., Grellmann, W.: Wirkung von Eigenspannungen auf die lokale Dehnung von Kunststoffen. In: Christ, H.-J. (Eds.): Fortschritte in der Werkstoffprüfung für Forschung und Praxis. Proceedings Werkstoffprüfung 2013, Publishing House Stahleisen GmbH, Düsseldorf (2013) 181–186 (ISBN 978-3-514-60806-9; see AMK-Library under M 26)
[4]	Grellmann, W., Bierögel, C., Sirch, C., Oluschinski, A.: Thermische Spannungs- und Dehnungsanalyse an Kunststoffen. In: Pohl, M. (Eds.): Konstruktion, Werkstoffentwicklung und Schadensanalyse. Proceedings Werkstoffprüfung 2010, Publishing House Stahleisen GmbH, Düsseldorf (2010) 365–370 (ISBN 978-3-514-00778-9, see AMK-Library under M 18)
[5]	Archodoulaki, V.-M., Seidler, S.: Thermomechanical properties. In: Grellmann, W., Seidler, S.: Mechanical and Thermomechanical Properties of Polymers. Landolt-Börnstein. Volume VIII/6A3, Springer, Berlin (2014) 34–44, (ISBN 978-3-642-55165-9; see AMK-Library under A 16)