Optimum Choice of Method and Evaluation in DMA Measurements of Composites

Introduction

Besides being used to measure mechanical quantities of materials, dynamic mechanical analysis (DMA) is also an excellent method for determining characteristic values such as the glass transition temperature. This often yields information that relates to the composition of materials. The evaluation and interpretation of data is relatively easy for isotropic materials because the properties and hence the measured values do not vary with the direction of measurement. Furthermore, with isotropic materials, the data obtained from different measuring modes such as shear, tension and bending can be directly compared.

In the case of anisotropic composites, the mechanical properties and hence quantities depend on the spatial direction, the structure of the material and the measuring mode. The influence of these factors is discussed using laminates as an example.

Representation of the Mechanical Data

The modulus

In a DMA measurement, the sample is subjected to the action of a dynamic force, F, at a selected frequency. The sample responds to the applied stress with a dynamic deformation, x. The deformation has the same frequency as the force but is somewhat delayed. The delay is observed as a phase shift, j. The complex modulus can be derived from the amplitude of the force, Fa, the deformation, xa, and the phase shift, taking into account the geometry factor. Depending on the type of applied stress, one obtains the shear modulus, G* , or the elastic modulus (Young’s modulus, tensile modulus), E* . Both G* and E* consist of a storage component (G′ or E′) and a loss component (G″ or E″). The components of the modulus are functions of temperature, T, and frequency, f (ω= 2π f)

G* (T,ω) = G*(T,ω) + iG" (T,ω)    (1a)

E*(T,ω) = E' (T,ω) + iE" (T,ω)       (1b)

The storage modulus characterizes the elastic behavior of the material. It corresponds to that part of the deformation which occurs in phase with the applied periodic force. In the viscous component, force and deformation are phase-shifted by p/2 relative to one another. This component corresponds to the loss modulus and is a measure of the mechanical energy that is dissipated (i.e. converted to heat). In eqs (1a) and (1b), the difference in the phase shift is expressed by the imaginary unit i = √-1 

The compliance

While the modulus describes the “stiffness” of a material, the compliance characterizes its “softness”. In general, the compliance is the reciprocal value of the complex modulus. One distinguishes between shear compliance, J* , and tensile compliance, D* :

J*(T,ω) = 1/G*(T,ω)      (2a)

D*(T,ω) = 1/E* (T,ω)    (2b)

The complex shear compliance is then 

J*(T,ω) =G'/G'² + G^"2     (3)

where the storage compliance  

J'= G'/G'² + G^""2             (4)

and the loss compliance  

J"=G"/G'² + G"²             (5)

Similar relationships can be derived for the tensile compliance.

The loss Factor

The determination of modulus and compliance depend on the sample geometry. In particular, when E* and D* are determined in bending, tension or compression measurements, the result is significantly influenced by changes in the geometry of the sample that occur during the measurement.

Conclusions

With isotropic materials, the modulus and compliance are equivalent to one another. In contrast, since the mechanical properties of anisotropic composites are direction dependent, the measurement results depend not only on the direction of measurement but also on the measuring mode used. This has to be taken into account when planning measurements in order to obtain the maximum amount of information. If possible, simple geometry factors should be used because they allow interrelationships to be more easily identified. This means that shear, tension and compression measurements are preferable to bending measurements such as three-point-bending or single cantilever.

Due to the versatility of the METTLER TOLEDO DMA/SDTA861e , there are almost no restrictions regarding the measurement modes that can be used. The main factors that contribute to this are the high stiffness of the clamping assemblies, the large force range, the external preparation of samples, and the precise force and displacement measurement. Depending on the particular analytical problem, attention should also be given to the optimum presentation of measurement data. It is quite possible that compliance curves show the required information more clearly than the widely used modulus curves [1]. 

^{Optimum Choice of Method and Evaluation in DMA Measurements of Composites | Thermal Analysis Application No. UC 261 | Application published in METTLER TOLEDO Thermal Analysis UserCom 26}