Choosing a sample to suit the stiffness range of your DMA (Dynamic Mechanical Analysis) is the single most important factor in obtaining good results. You will need to know the stiffness range of the dynamic mechanical analyzer being used together with your sample’s highest and lowest expected value of modulus, or an approximation if the material has not been measured before. From this information the ideal sample size can be calculated.

Different geometric arrangements have inherently different stiffnesses. If they are ranked from the highest to the lowest, the following results:

Simple shear > tension > clamped bending > three-point bending

All commercially available DMAs support these geometries.

The stiffness of the different geometries is quite intuitive. Consider deforming a 150-mm steel rule between your fingers. It bends with only a small applied force but requires considerably more force to achieve the same displacement in tension and finally it is very hard to shear (from one surface to the other) as it is very stiff. This is exactly how the DMA (Dynamic Mechanical Analysis) sees any sample presented to it. Therefore, a wide range of moduli can be covered by the appropriate choice of geometry. Clamped bending is a good general choice as it covers the working range of most DMAs for convenient sized sample bars and it is the easiest to use. Three-point (or simply supported) bending is a good choice for high-modulus materials that exhibit a high rubbery modulus, for example fibre reinforced composite samples. Tension is suitable for film samples, where the natural high stiffness of this form compensates for the low sample thickness, in order to properly exploit the stiffness range of the DMA instrument being used. Simple shear is a good choice for rubbers and gels, as it is a stiff geometry and suits their low moduli. Rubbers and gels can also be tested in compression and whilst samples are easy to mount in this mode of geometry, modulus accuracy is generally poor.

Most dynamic mechanical analyzers display the valid range of modulus for a particular sample geometry. Ensure that the results obtained are well within these limits or adjust the sample size accordingly to better fit the range of the DMA being used. The lower stiffness limit of the instrument will dictate when the measurement has to stop.

Table 1 gives an indication of the choice of sample geometry and dimensions as appropriate to the modulus range being measured. The best choice indications are the experiments that will generate the best data with the least adjustment of instrument parameters. These data will suit most DMAs having a 10–20N load range. Instruments with a larger load capacity may be able to accommodate larger samples, but thermal equilibrium will be poor, unless very slow heating rates are used. Therefore, the indicated sizes are preferred. Aim to keep the dynamic strain amplitude between 0.1 and 0.2%. Figure 1 shows a schematic of available sample geometries.

Table 1. Typical geometry, sample dimensions and heating rates for samples of given modulus

The combination of modulus and sample size must be chosen to suit. Tension mode, see Figure c, is the best mode for thin films (<20 um) having a modulus between 10⁹ and 10⁶ Pa. The stiff nature of tension geometry compensates for the low sample stiffness and best suits the stiffness range of the DMA. If there is a need to measure the rubbery modulus of films, then thicker films (>100 um) will enable the use of longer free lengths, which will yield more accurate moduli. A dynamic displacement amplitude of 10 um will result in a 0.1% peak strain for a 10 mm long sample.

Bar samples are easily tested using single cantilever mode, see Figure 1a. A sample 2 mm thick, 5–10 mm wide and 50 mm long is easy to mould and handle. Such a bar can produce two samples for single cantilever geometry, having a free length of 10 mm, or one sample for dual cantilever mode; see Figure 1b. For a sample of free length 10 mm, thickness 2 mm and width 5 mm, both single and dual cantilever modes with a dynamic displacement amplitude of 25 um will result in a 0.15% peak strain for a 10 mm long sample. Single cantilever bending is preferred over dual, since the latter can result in large residual stress build-up. Note also that a dual cantilever sample is effectively two single cantilever samples. Heating or cooling rates of 1 or 2◦C/min will produce reasonably accurate transition temperatures. Rates of 5–10◦C/min will be in error, but provide rapid results for comparative testing. Samples with thickness greater than 2mm are not optimum. Ideally the sample should be machined to reduce the thickness to 2 mm, unless the sample is inhomogeneous, where reduction of thickness would alter its properties. The reason for keeping the thickness to a minimum is to avoid excessive thermal lag errors. Another advantage of using clamped bending modes, such as single or dual cantilever, is that no static force control is necessary. This enormously simplifies the experiment.

Figure 1. Schematic of available sample geometries. (a) Top left – single cantilever bending; (b) top right – dual cantilever bending; (c) middle left – tension; (d) middle right – compression; (e) bottom left – three-point bending; (f) bottom right – shear. Note that for these definitions the sample length, l, is always taken as the distance between the fixed clamp and the driveshaft clamp.

Three-point (or simply supported) bending (see Figure 1e) is a good choice for high modulus materials that exhibit only a small change in modulus throughout the test, for example measurements in the sub-Tg region only. A typical analysis to measure Tg of an amorphous polymer would give a poor result in this mode as the sample would collapse under its own weight after passing through the glass transition. This mode of deformation will yield the most accurate modulus values, especially for high-stiffness samples, as the clamping errors associated with this geometry are the lowest. This geometry also applies a small strain amplitude for a given dynamic displacement amplitude and is therefore suitable for brittle samples, such as inorganic glass and ceramics. For a sample with a free length of 15 mm, 5 wide and 2mm thick, an 80um dynamic displacement amplitude results in a 0.1% dynamic strain.

Simple shear, see Figure 1f, is a good choice for rubbers and gels, as it is a stiff geometry. Accurate modulus values for samples with moduli about 10³–10⁷ Pa can be obtained. For stiffer samples, results are generally better if the sample is bonded to the shear holder. This avoids the sample slipping. Cyanoacrylate adhesives form a rapid setting and rigid glue layer that is suitable for room temperature testing of rubbers (the Tg of superglue is approximately 140◦C). As with clamped bending, there is no need for imposition of a static preload. For a sample with a thickness of 1 mm and a diameter of 10 mm, a 10 um dynamic displacement amplitude results in a 1% dynamic shear strain. Generally, this mode of geometry will be used for lower modulus, where a higher strain amplitude may be beneficial.

Finally, there is compression mode; see Figure 1d. Generally, it is better to use the other modes discussed above, but compression mode does find application in giving an easy determination of the transition temperature of irregularly shaped, small samples and materials such as powders. The reason for this is that this mode invariably suffers the most errors. In a compression test the sample should freely grow in area as it is squashed, just as a tension sample freely contracts in its width and thickness (due to Poisson’s ratio). In practice, this condition is rarely satisfied and a geometric error result, leading to inaccurate modulus values. Secondly, only relatively low modulus materials (rubbers) can be accommodated by the instrument’s stiffness range (just as with shear mode). However, this does lead to one favourable application area for compression, namely the testing of foams. Here we have low-modulus materials that can be tested with varying degrees of ‘crush’, which affects the measured modulus. Therefore, foams are a special class of materials ideally suited to testing in compression mode.

Single and dual cantilever clamped bending modes will give the best results for measurements through the glass transition for samples having a thickness of at least 2 mm. Good data can be obtained with minimum preparation or precautions. Single cantilever is always preferred, since with dual cantilever mode as the sample is held firmly at either end it is impossible for there to be any movement to relax thermal stresses. This causes a build-up of either tension or compression along the sample length, which may yield a false modulus result. Similarly, DMA (Dynamic Mechanical Analysis) instruments whose driveshaft has a degree of lateral compliance are preferred as this automatically compensates for the change in sample length due to thermal expansion or contraction when using single cantilever mode. The only time when dual cantilever mode has an advantage is when a sample has significant molecular orientation. This would cause a large amount of retraction (or extension) as it passes through the glass transition, which in turn would cause excessive movement of the driveshaft. The fixed clamps at either end of the dual cantilever geometry prevent any movement of the sample or driveshaft and preserve the orientation.

Shear mode is also an easy mode to use, with minimal sample precautions required. Only samples having a modulus 10⁷ Pa or less can be tested in this mode, since higher modulus materials would be too stiff in this geometry.

Tensionmodegenerally gives good results, but it is complicated by the need to superimpose a static force on the dynamic, in order to establish correct measurement conditions. The same is true for compression mode.

Three-point bending is the best choice of geometry for accurate modulus determination. In fact, testing an accurately machined steel sample (ordinary steel, not stainless) is certainly the best way of verifying a DMAs’ modulus measuring accuracy. Despite this, a poor choice of sample dimensions or displacement amplitude can yield results which are wrong. First, it is best that no sample is over 5mmin width. It is very hard to clamp or uniformly load wide samples, unless they are very flat. Keeping the width to about 5mm avoids the problem and only has a small effect on sample stiffness. Second, the strain developed in three-point (or simply supported) bending is four times lower than that for an equivalent length in clamped bending. Also, the fact that stiff samples are more likely to be tested means that the length will probably be longer and these factors reduce the strain for a given dynamic displacement amplitude. Aim for a strain of at least 0.1%. For a sample length 15 mm, 5 mm wide and 2mm thick, an 80 um dynamic displacement amplitude results in a 0.1% dynamic strain. If very small displacements (<10 um) are used, there is a distinct possibility that the sample simply ‘settles’ on the clamps and we are not testing it in bending mode at all, but a complex bending/torsional mode that yields an incorrect value of modulus. Note that friction can occur in three-point bending, so the measured tan δ value is sometimes higher. The effect on E’’ is generally small and as tan δ increases around Tg the frictional contribution is insignificant

In tension, compression and three-point bending modes, it is necessary to superimpose a static force larger than the applied dynamic force, to ensure that the sample remains under a net tensile or compressive force. Failure to satisfy this condition will either cause the sample to buckle (in tension) or to lose contact with the sample clamps in compression or three-point bending. In either case an erroneous modulus results. All instruments provide various methods of dealing with this problem, ranging from manual control to a number of automatic loading regimes. However, successful measurements are difficult to obtain on materials that creep excessively. This will be especially true close to the glass transition for amorphous polymers and close to the melting point for semi-crystalline polymers. For this reason, materials such as low-density polyethylene (LDPE) may be difficult to measure in these modes. If creep is excessive, little can be done and it is much simpler to obtain results in clamped bending mode for example.

Dynamic mechanical analysis is an investigative tool. It is a probing technique to determine the material’s structure. Normally the loads and strains applied are small (0.1–1%) and at the lower levels they do not influence the materials’ structure at all; this is desirable. The behaviour of most materials studied by DMA can be described as viscoelastic. Normally we strive to keep the deformation within the linear viscoelastic region. Here the modulus has a constant value, independent of the applied strain. As the strain is increased the modulus will fall if we move into the non-linear behaviour region. Also, a large third harmonic distortion can be observed in the strain signal. Strictly speaking, tan δ is no longer defined under these conditions, since the harmonic distortion means that we effectively have more than one frequency. However, measurements are made in this region and tan δ values are quoted. As long as the strain remains below≈0.2%, most materials will be within the linear viscoelastic region (except carbon-filled rubbers; see below). Typical force ranges and samples sizes for DMA (Dynamic Mechanical Analysis) usually ensure that these conditions can be met. One range of materials that do exhibit strong non-linear behaviour at smaller strains is carbon-filled rubber. With this class of materials the modulus can change by a factor of 10 when the strain changes from 0.01 to 0.1%. This is due to an interaction of the carbon black with the rubber. It is normal practice to condition or ‘scrag’ such samples by exposing them to a high strain, often at a higher frequency before measurements start. At high strain amplitudes the temporary structure attained between the carbon filler particles and the rubber breaks down, thereby removing some of the strain dependence seen in the modulus. After several days the temporary structure it regained. This conditioning of the rubber leads to more reproducible measurements.

It is desirable to check whether a material is within its linear viscoelastic range before commencing a series of measurements. This can be done by performing a strain scan on the glassy material for about 0.01–5% (or the maximum possible strain). If a constant modulus is obtained over the whole range, then we are within the linear range. If the modulus starts to drop at a certain level then this is the onset of non-linear behaviour, and unless there is a specific reason to study this effect strains should be kept below this level. Most rubbers will be within the linear viscoelastic range up to at least 10% strain. The important exception is carbon-filled rubbers, as mentioned above. If your DMA has the potential to give the magnitude of the third harmonic component to the displacement, then this should also follow the strain-dependent modulus and increase as non-linear behaviour is encountered, as described above. For normal testing the magnitude of the third harmonic should be below 2%.

There are some theoretical reasons why certain modes of geometry are preferable, in addition to the practical ones discussed so far. The first consideration is that some modes have affine deformation (each unit of structure experiences the same strain), whilst others are inhomogeneous (a gradient of strain exists throughout the sample, with a neutral axis in the central plane). Tension, compression and shear cause affine deformation, whilst bending (all types) and torsion result in inhomogeneous strain. This usually has very little practical significance, especially if the sample strain is small (<0.1%). However, for highly filled (carbon black) rubber materials that exhibit significant strain dependence, a difference may be observed in changing from one mode of deformation to the other as the strain magnitude will be different.

If dealing with highly strain-dependent materials the strain equivalence must be taken into account. A strain of 0.1% in simple shear, for example, would be equivalent to a strain = 0.1/√3% in tension.

Generally, experiments work better if the sample is heated from the lowest to the highest temperature. This is due to the fact that the sample will shrink as it cools and becomes loose in the clamps, worsening the modulus accuracy. Therefore, the clamps are preferably tightened at the lowest temperature and always below the glass transition temperature, if this is possible. Most DMA (Dynamic Mechanical Analysis) manufacturers provide a torque driver to ensure the correct clamping pressure on glassy samples. This ensures that the highest value of the glassy modulus is obtained and that reproducibility is improved, especially with different operators. If the sample becomes excessively loose, strong spring washers can be used under the sample clamps in order to apply a constant pressure. This can be quite successful, although such measures are unnecessary for most samples.

If sample testing is to be carried out only in the rubbery region then clamps should be tightened only finger tight. Use of the torque driver will cause excessive deformation of the sample. Also, since these materials have a lower modulus, it is unnecessary to clamp them so tightly. Another technique for testing rubbers is to prepare them with metal ends that can be securely clamped or alternatively glue them directly to the instrument clamps. The latter method is frequently used for shear samples.