Let us consider standards relating to Dynamic Mechanical Analysis (DMA). ISO 6721 is a multi-part standard covering principles of measurement, geometry definition and measurement of Tg for composites (ISO CD 6721 part 11).

There are several ASTM specifications that relate to DMA. The most useful are ATSM D4065-95 ‘Standard Practice for Determining and Reporting Dynamic Mechanical Properties of Plastics’ and D4092-96 ‘Standard Terminology Relating to Dynamic Mechanical Measurements on Plastics’. ASTM E1867 and E2254 deal with the calibration of temperature and storage modulus respectively. Whilst not concerning the topic of calibration, ASTM E1640-04 ‘Standard Test Method for Assignment of the Glass Transition Temperature by Dynamic Mechanical Analysis’ is also highly relevant.

The calibration of the main variables, force, displacement and temperature will be covered below. First though some discussion on the components of TMAs and DMAs would be useful.

Both the TMA (Thermomechanical Analysis) and DMA (Dynamic Mechanical Analysis) apply force and measure the displacement that results from this stimulus. Most TMAs and DMAs currently in production use linear variable displacement transducers (LVDTs) to measure displacement. Older TMAs are not fitted with motors, but rely upon a top-loading scale pan for the application of force. In TMA the force is constant for all classic experiments, therefore the manual arrangement is quite satisfactory for this work. In DMAs and more modern TMAs a voice coil type motor is employed. This comprises a light coil and former, connected via fine wires, often made from Litz wire. This assembly is either supported by springs or the drive arrangement is supported by an air bearing. Conceptually it is similar to the design of a loudspeaker.

In the case of DMAs the lighter the moving mass of the drive arrangement is, the lower the inertia correction will be. The inertia correction is given by mω², where m is the drive mass in kg and ω is the angular frequency (2πf). This factor becomes particularly significant with measurements of low stiffness materials at high frequencies.

Whilst all DMAs utilise a voice coil type motor, some are fitted with a force transducer to measure the force transmitted through the sample. This requires a different design of instrument. It is frequently and incorrectly thought that the omission of a force transducer leads to poor modulus accuracy. Provided that the voice coil motor is correctly calibrated and its own contribution to the total stiffness measurement is removed, it does not make any difference, since the force measured by the transducer and the one taken from the motor calibration are both accurate to within better than ±1%, which is adequate. Far larger errors occur from the poor choice of sample size and geometry, which leads to making measurements at the extreme ranges of the instrument. The instruments fitted with a force transducer may sometimes do better at measuring very low stiffness samples, as the contribution from the motor does not have to be subtracted. However, the force transducer is also a source of instrument compliance, which will lead to errors at high stiffnesses. Corrections can be made for compliance and in one particular DMA there is a unique design that automatically removes this contribution from the measurement.

• Force and displacement calibration

 The top-loading scalepan TMAs require no calibration. Instruments fitted with the voice coil type motors will require calibration. Most instruments achieve this by applying one or more known masses (which can be accurately measured on a balance calibrated by traceable standards) and nulling the displacement that occurs. This way the force required to rebalance the applied mass is obtained independently from the displacement measurement. The instrument measuring system will adjust the voltage or current applied to the coil, and when the displacement has been successfully nulled this value is equivalent to the force due to the applied mass. The value of force to current should be linear over the range of operation of the instrument.

Displacement calibration is usually made by inserting known thickness samples, such as slip gauges, into a suitable fixture and noting the resultant displacement. A calibration can be created from these measurements. The displacement applied should be traceable to primary or secondary standards. LVDTs are usually linear over their range of operation and typically cover ±1– to ±5 mm with resolution to ≈0.1 um or better, which is usually sufficient for most experiments.

• Temperature calibration

 Temperature calibration is arguably one of the most contentious and important issues when dealing with thermal analysis instrumentation. DMAs in particular have very good sensitivity for the measurement of glass transition temperatures and the tan δ peak, for example, would provide an excellent parameter to calibrate the instrument. Unfortunately, any other technique that would produce a tan δ value would give a different result. Therefore, users frequently resort to a melting point measurement, which can be verified by other instruments, for example DSC. Unfortunately, large samples are required for DMA, which can be difficult to obtain or expensive and the large weakness of these tests is that they do not accurately simulate typical samples measured. Many samples will be poor thermal conductors, whereas the melting point standards are usually metals that have high thermal conductivities. Since the DMA measurement will stop when the metal melts, this occurs even if a large gradient exists across the sample.

Frequently, ‘standard’ polymers are used to check the accuracy of a DMA. Such materials include polymethylmethacrylate (PMMA), polyetherimide (PEI) and polyethersulphone (PES). The tan δ or E’’ loss peaks can be used to compare the temperature measured with other users. Unfortunately, these temperatures cannot be determined on any instrument other than a DMA, so they cannot be used as calibrations, but they are useful checks on reproducibility. Details of how to quote the Tg value can be found in ISO6721 part 11 – in preparation.

• Effect of heating rate

For samples approximately 2mm thick, most DMAs return thermal lag errors of about 1◦C for each 1◦C/min of heating rate. This was established in a round robin survey carried out by the NPL. This is easy to check. Three Tg determinations should be made at heating rates of say 1◦, 3◦ and 5◦C/min. A new sample should be used each time. The measured Tg temperature is recorded against heating rate and a plot extrapolating back to 0◦C/min should be constructed. The value at 0◦C/min is the true Tg and the slope of the line is the thermal lag error as a function of heating rate.

Therefore a 1 or 2◦C/min test will provide more accurate temperature information, but will of course take longer. If tests are only made for comparative purposes the temperature error is largely insignificant. Thicker samples are not preferred as they will cause larger thermal lag errors.

• Modulus determination

The main purpose of DMA (Dynamic Mechanical Analysis) is to make measurements as a function of temperature. This invariably results in a compromise between optimum modulus determination and the best use of the DMA stiffness range. Three-point bending and tension geometry are the best modes for accurate modulus determination. Modulus errors occur for all clamped geometries. They are greatest for clamped bending samples having a short length and will be least significant for tension measurements on thin films. This is due to the relative stiffness of the sample. The error is due to movement of the sample within the clamps, which is not factored in the geometry constant. This is a consequence of the clamps’ stiffness being inadequate for the stiffness of the sample under test and consequently the clamping arrangement deforms in the test. Both the measured E’ and E’’ values will be in error by a similar amount (this is true where the phase angle δ is small), therefore the tan δ value will be accurate (see below).

Three-point (or simply supported) bending is free of such clamping errors and therefore the measured moduli are correct. In fact, testing an accurately machined steel sample (ordinary steel, not stainless) is certainly the best way of verifying a DMA’s modulus measuring accuracy. The clamping error is difficult to correct since this error depends upon the sample stiffness, its modulus and its aspect ratio. By the time the sample reaches the rubbery condition this error is insignificant, due to the low sample stiffness.

Since the error is a constant value which adds to the length, it can be mitigated by ensuring that stiff samples are run with long free lengths, at least 10 mm. Fortunately, such samples tend to show the least drop in modulus at Tg, especially fibre reinforced composites, and therefore measurement of the minimum modulus value is not an issue with such samples. Alternatively thinner samples can be produced, which therefore have a lower sample stiffness. Remember that doubling the length decreases the sample stiffness by 8 times, as does halving the sample thickness. Doing both reduces the stiffness by 16 times.

This error can be quantified in a series of experiments that are quick to perform. The sample should be measured over at least three lengths and a plot of l/E ^1/3 versus l is constructed. The slope of this line (1/E ^1/3) then yields the true modulus whilst the intercept with the x-axis yields the effective sample length deforming within the clamps. This length can be quite significant, >1 mm for stiff, thick samples. This is a very significant error on, say, a 5 mm length, considering the cubic dependence of the geometry constant on length. The modulus value obtained from the slope should agree very well with a determination made with three-point (or simply supported) bending mode.