Thermomechanical Analysis for the Detection of Change of Material Characteristics due to Aging

Vincent Leube, Sommersemester 2021

1. Introduction

The Thermomechanical Analysis measures the linear thermal expansion of a solid test piece depending on the temperature. This can be performed either under a small, constant load (Thermomechanical Analysis, short TMA) or a dynamic load (Dynamic Thermomechanical Analysis, short DTMA). This method is often employed to describe the thermal and aging properties of plastics.

The linear thermal expansion coefficient can be specified either as a mean value α(ΔT) or as a differential value α(T). The differential value  is used more commonly. These values are calculated according to ISO 11359-2 [1]:

Mean coefficient of linear thermal expansion:                  $//<![CDATA[ \begin{array}{l}α (ΔT)= ΔL/ΔT∙1/L_0\end{array} //]]>$

Differential coefficient of linear thermal expansion:        $//<![CDATA[ \begin{array}{l}α(T)=\frac{(dL)_p}{(dT)_p} ∙1/L_0 =\frac{(dL/dt)_p}{(dT/dt)_p} ∙1/L_0\end{array} //]]>$

2. TMA

2.1 Test Set-Up

The test specimen is placed inside a temperature programmable furnace. A floating measurement probe is placed on the test specimen and applies a small downward force. The test specimen is slowly heated by the temperature programmable furnace. Any change in linear dimension is translated to the measurement probe and measured by the displacement transducer [2].

Test specimens can be either cylinders, cubes, rods, foils or fibers. Cylinders and cubes are usually tested under compression (measurement probes 1-3), while rods, foils and fibers are tested in tension (measurement probe 4).

A measurement probe with a large contact area is beneficial for an accurate quantification of the linear thermal expansion. Therefore, depending on the size of the test specimen, either a normal probe (1) with a contact area of 5 mm² or a macro probe (2) with a contact area of 28 mm² is used.

Penetration probes are used to measure a materials softening temperature. The extended tip probe of 0.8 mm² will start penetrating the test specimen at the softening temperature if applied with a larger load, thus resulting in a clear signal. [1]

2.2 Observable Variables

TMA can be used to quantify the linear thermal expansion and the glass transition temperature. Especially the glass transition temperature is relevant for the aging properties of polymers, since it shifts to higher temperatures over time. [3]

All experiments must account for the anisotropy of tested materials.

2.3 Calibration

TMA has two crucial variables, which must be calibrated: The measured temperature and the linear expansion.

To calibrate the temperature a test specimen made of a pure low melting point metal like Indium or Zinc is placed between two disks and slowly heated. Once the melting point is reached the measurement log of expansion over temperature will show a sharp bend, where the metal melts and is forced out of the two disks. The point where two tangents before and after the sharp bend meet corresponds to the melting point of the metal. [4]

To calibrate multiple temperatures in one experiment several different low melting metals can be stacked between disks. [4]

To calibrate the linear expansion a metallic test specimen with a known, reversible thermal expansion coefficient is employed and the difference between the measurement log and the known value adjusted. [2]

3. DMA Test Set-Up

In contrast to TMA tests DTMA tests apply a variable, most commonly sinusoidal force to the test specimen. This can be done in compression, shearing, torsion or bending.

DTMA Machines can measure the applied force and the resulting amplitude, or vice versa, as a result of the test specimen’s temperature. This can be expressed as a complex elasticity or shear modulus over temperature. Complex modules contain both the storage modulus and the loss modulus, thus providing information about the materials elasticity versus its dampening characteristics [5]. The complex elasticity modulus, storage modulus and loss modulus are defined by DIN EN ISO 6721-1. [6] as:

$//<![CDATA[ \begin{array}{l}|E^* |=σ_A/ε_A\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}|E^* |=\sqrt{[E'(ω)]^2+[E''(ω)]^2 }\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}E^{'} (ω)=|E^* |∙\cos⁡δ\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}E'' (ω)=|E^* |∙\sin⁡δ\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}\tan⁡δ=\frac{E'' (ω)}{E^{'} (ω) }\end{array} //]]>$

4. Use for describing aging

There are four major mechanisms of aging in polymers:

• Chemical Breakdown: The chemical structure of a polymer can be changed by heat, light and/or the presence of other substances e.g. water. This change in the chemical structure often releases small molecules such as water or acids. These can migrate through the polymers structure and lead to further chemical changes. [7]
• Chain Scission: The polymers chains can be cut by heat and/or ionizing radiation. The physical properties of a polymer depend on the chain length, therefore this form of aging leads to inferior mechanical properties. [7]
• Cross-Linking: The absorption of ionizing radiation can also lead to the cross-linking of polymer chains. This leads to the embrittlement of the polymer. [7]
• Physical Degradation: The Additives employed to change the polymers physical properties can migrate to the surface of the object, therefore depriving the material of those changes. [7]

These and other mechanisms all lead to a change of the physical properties. These include, but are not limited to: Elasticity module, shear module, storage module, loss module, tensile strength and glass transition temperature.[2, 5, 8]

The TMA analysis can quantify the change in glass transition temperature, while the DTMA analysis can quantify elasticity module, shear module, storage module and loss module. [2] These two analysis methods provide a very comprehensive method of describing the mechanical property changes during aging.

5. Sources

[1]      ISO. ISO 11359-2 (ISO 11359-2); 1999 (01.10.1999)

[2]      Ehrenstein GW, Riedel G, Trawiel P. Praxis der Thermischen Analyse von Kunststoffen. 2., völlig überarbeitete Auflage. München: Carl Hanser Verlag; 2003 // 2004

[3]      Minguez R, Barrenetxea L, Solaberrieta E, et al. A simple approach to understand the physical aging in polymers. Eur. J. Phys. 2019; 40: 15502. doi:10.1088/1361-6404/aaf244

[4]      ISO. ISO 11359-1. 2. Aufl. (11359-1); 2014 (15.01.2014)

[5]      Boubakri A, Haddar N, Elleuch K, et al. Influence of thermal aging on tensile and creep behavior of thermoplastic polyurethane. Comptes Rendus Mécanique 2011; 339: 666–673. doi:10.1016/j.crme.2011.07.003

[6]      DIN EN ISO 6721-1. 09. Aufl.; 83.080.01; 2019 (09.2019)

[7]      Quya A, Williamson C. Plastics. Collecting and Conserving. Edinburgh: NMS Publishing Limited; 1999

[8]      Giachet M.T., M. Schilling, J. Mazurek, et al. Characterization of Chemical and Physical Properties of Animation Cels from the Walt Disney Animation Research Library. ICOM-CC 17th Triennial Conference 2014 Melbourne 2014