The subject of mechanical property measurement is extensive, but a majority of the testing that occurs is only conventionally carried out at a fixed temperature. Here the main focus will be on how mechanical properties change during temperature ramp tests. There are many good reasons for performing such tests. A rather tragic example of the variation of material performance with temperature is the Challenger space shuttle disaster. Here the rubber O-rings used to seal the booster rocket’s individual sections had lost their normal rubbery behaviour, since the cold temperatures on the launch pad had caused the material to approach its glass transition. In this stiffened condition, the seal was impaired and this was one of the contributing factors to the tragic accident. Many materials applications in the aerospace industry have critical temperature limits and materials for biomedical applications should ideally be tested at 37◦C and in an appropriate body fluid.

There are two main types of mechanical thermal analysis instruments, namely thermomechanical analysis and dynamic mechanical analysis, TMA and DMA respectively. The first is a simple technique that has been available for many years and simply records change of sample length as a function of changing temperature. Despite this simplicity it enables the measurement of phase transitions, glass transition temperature and coefficient of thermal expansion. It has the advantage of being simple to use and perhaps more importantly the interpretation of results is quite straightforward.

The second method is DMA. What is DMA? DMA is a technique for measuring the modulus and damping factor of a sample. The modulus is a measure of how stiff or flimsy a sample is and the amount of damping a material can provide is related to the energy it can absorb. DMA is commonly used on a variety of materials, for example thermoplastics, thermosets, composites and biomaterials. The samples may be presented in a variety of forms including bars, strips, discs, fibres and films. Even powders can be tested when suitable containment is arranged.

How does it work? DMA applies a force and measures the displacement response to this force. This results in a stiffness measurement that can be converted into a modulus value if the sample dimensions and deformation geometry are known. When the temperature is changed these measured properties change quite markedly and this yields important information about the materials’ molecular structure.

The aim of this guide is to cover as many practically important aspects of TMA and DMA as possible. Many theoretical texts exist, describing detailed deformational mechanisms of specific polymer systems and the molecular relaxations that are responsible for the observed behaviour. Such studies are generally made over a long period of time and with considerable experience on the part of the research investigator. Whilst DMA is an invaluable tool for this work, its routine application is generally far more trivial. I should estimate that over 50% of measurements carried out are to determine the glass transition, or an equally identifiable feature that affects the use of the material under test. It is likely that a good deal less than 20% of all measurements are devoted to a detailed structural investigation of the material at the molecular level.

The practical choice of sample geometry, techniques for specifying the glass transition temperature and dealing with errors from geometry and heating rate will all be presented. Where possible this will be shown on representative data from real samples.

A mention of materials that are suitable candidates for dynamic mechanical analysis would be useful. The simple answer is any material where there is a need to know its modulus or damping factor under periodic and small strain loading conditions. Of course, the class of materials that would be most usefully described by these parameters is the one having viscoelastic behaviour. Materials having long molecules, such as synthetic and natural polymers, are immediate candidates, but are by no means the only ones. Any material that forms a glass will have viscoelastic behaviour. Typically these are referred to as ‘amorphous’, in that they have no regular crystalline structure. There are also large numbers of such materials that are classified as semi-crystalline (and by implication, semi-amorphous). Such structures usually contain one phase within the other. This will be further discussed under the subject of glass transition. Generally inorganics, such as metals and ceramics, will predominantly exhibit elastic behaviour, but under special circumstances such as elevated temperature, unusual processing routes, e.g. fast quenching, this may not be the case. However, standard DMA equipment may not cover a suitable temperature or force range for these materials.

Many mechanical property measurement tests do not deal with samples that change as a function of time. For example, the application of force to a steel sample at room temperature causes an instantaneous extension that does not change with time. If the load is increased the extension immediately increases to a new value, proportional to the load increase. This is Hooke’s law and describes the behaviour of materials within their linear elastic range.

The opposite end of the spectrum to elastic behaviour is viscous behaviour. This is readily evident in liquids where they flow in response to an applied force. Frequently, the action of gravity on the fluid mass is sufficient to cause significant flow (witness the phenomenon of spilt milk!). If we consider a simple fluid such as water, it follows Newtonian behaviour. The ratio of force to the rate of the applied strain defines a viscosity, which is a constant over a wide range of force and strain rates.

One of the major differences between elastic and viscous behaviour is that in the former case a sample will always return to its original size upon removal of the load; i.e. the deformation is fully recoverable. Clearly this does not occur in the case of a liquid. The flow in a Newtonian liquid is permanent and the fluid will retain its new shape, even if the load is removed. Some materials behave between the elastic and viscous regime. Such materials are described as viscoelastic and many glass forming or amorphous materials fall into this category. For example, the continuous increase in length with time under the influence of a constant applied force defines a phenomenon called ‘creep’. This occurs since the materials’ molecules do not have a simple instantaneous response to the applied force. Frequently these materials can be modelled as having three response mechanisms. One is elastic (just like a spring), the other is viscous (just like a dashpot, or hydraulic damper such as a shock absorber) and the other is a combination of these elements in parallel (e.g. a Voigt element). A material can be modelled as a summation of many of these elements, in order to arrive at a mathematical expression for the observed relaxation time of the material.

The spring part represents force or energy that is put into the sample that will be fully and instantaneously recoverable upon removal of the load. This can be identified as elastic behaviour. The dashpot part represents the force that is put into the sample that results in permanent deformation and is lost. Neither the sample deformation nor this energy can be recovered. This can be identified as viscous behaviour. The parallel spring and dashpot element can be identified with viscoelastic behaviour. Here the deformation is more complex. This element successfully describes the phenomenon of creep and recovery observed in many materials. As the force is applied little happens at first. The spring cannot respond as it is limited by the dashpot, which only has a slow response to any applied force. As time increases, the dashpot starts to extend and therefore the sample extends as well. This process continues until the extension of the spring element gradually accounts for a greater proportion of the applied force. During this process the sample continues to lengthen, but at a slowing rate. This is creep. Eventually, the spring accounts for the total applied force. At this point there is no driving force to extend the dashpot, so the creep process stops. In practice this may take many years, or even hundreds of years of creep, since the sample is required to reach equilibrium behaviour for this to occur.

It is interesting if we now consider the removal of the force from the parallel spring and dashpot element. The spring is now fully extended and as the load is removed the stretched spring will start to press back on the dashpot. We now see the process occurring in reverse. Again the dashpot is slow to respond, but as it starts to move the sample will gradually return to the unloaded position. The spring and dashpot element will eventually reach its original position. This is creep recovery. In practice, the question of whether a sample fully recovers will depend on the model that describes how the molecular structure responds to force. If there is a large contribution from a purely dashpot element, then much of the deformation will be permanent. This is the situation in linear polymers with no cross-linking, LDPE for example. In the absence of a purely dashpot element, much of the deformation will be recoverable. This is the situation in highly cross-linked polymers, epoxy resins for example.

Therefore, a mathematical model to fit the time-dependent response to an applied force can be derived for a material. If the chemical structure is known, from FTIR or NMR studies for example, then it may be possible to relate real chemical elements, or specific moieties to the elements of the mathematical model. Since DMA is routed in periodic loading it affords excellent opportunities for studying time-dependent behaviour.

Regarding the glass transition (Tg), first, it is useful to know which materials exhibit a glass transition. Those that form glasses have common characteristics, namely those that hinder the formation of crystalline phases, usually due to having high molecular weight molecules, whose unwieldy nature precludes their easy alignment to form crystalline phases. Most polymers can exist in an amorphous condition (amorphous – having no crystalline structure).

When a solid undergoes the transition between its glassy and rubbery state, the key parameter that changes is the molecular relaxation time. The amount of molecular motion that can occur at any instant is determined by the mobility of the structure, which in turn depends upon the energy available to move the molecules.

Each molecular deformation process that occurs within a material will have a characteristic relaxation time, and depending upon the temperature and frequency of test the sample will respond in a relaxed or unrelaxed manner. Put more simply, the molecular deformation process either occurs or it does not. The glass transition temperature Tg is the region where the transition from glassy (unrelaxed) to rubbery (relaxed) deformation occurs. In a dynamic mechanical modulus determination carried out at a certain frequency, if the test temperature is above the Tg for the frequency being used, then the measured polymer modulus will be low and commensurate with that of a rubber. Rubbers are characterized as easily extensible materials due to their fully mobile molecular bonds; i.e. their relaxation time is very short compared to the applied loading timescale. These flexible bonds and an availability of ‘free volume’ allow co-operative motion of the material’s main backbone. This means that the structure is able to respond to the applied stress and the molecules immediately (well very fast anyway) take up a new equilibrium position, resulting in little resistance to the applied force, which is the reason that the rubbery modulus is low, typically 1–10 MPa. Compare this to a sample tested below its glass transition. Now the relaxation time will be very long and it will be impossible for the molecules to take up new equilibrium positions. Consequently, a different molecular deformation mechanism occurs. Instead of free rotation around the main backbone of the polymer, occurring with little resistance, there is a regime of bond stretching and opening and displacement against Van de Waals forces. The resultant modulus is much higher (typically 1–5 GPa) since only a small deformation results for the level of force, meaning that the material is much stiffer than when it is above Tg. This partly explains why so many glassy polymers have the same modulus, since their glassy deformational mechanisms are very similar, at least for the low strains used in DMA.

Many factors must be considered when attempting to define the glass transition process. The importance of relaxation time has been mentioned. Free volume also plays an important part in polymer behaviour and in the Tg process. The concept of free volume is the existence of so much space between neighbouring molecular chains that facilitates their cooperative motion. Flory and Fox have postulated a definition of Tg based upon the temperature where this quantity becomes constant. Below Tg, glassy behaviour is observed since the free volume has a constant value that is too small to allow the conformational arrangements associated with rubbery behaviour. Above Tg the free volume increases with increasing temperature and facilitates the large-scale conformational rearrangements that define rubber elasticity. In this argument, the attainment of a critical free volume is the definition of the glass transition temperature.

The glass transition can also be considered on an energetic basis. Glassy behaviour results when the thermal energy available is insufficient to overcome the potential barriers for segmental motion to occur. In this condition we have a ‘frozen’ liquid, where we are in the regime of bond opening and stretching as discussed above. As the temperature increases the vibrational amplitude increases and when it becomes comparable to the energy barriers, we are in the Tg region. Here marked frequency dependence is observable in parameters such as the storage and loss modulus (E’ and E’’). Low frequencies yield values expected from a rubbery material, whereas high frequencies yield values typical of glassy material. This is due to the response of the molecular motion of the material having a specific relaxation time, which is sympathetic to the applied frequency. When the material’s relaxation time is fast, it will respond as a rubber and when it is very slow, compared to the timescale of the experiment, it will exhibit glassy behaviour. Once through the Tg region, all relaxation times become short, with respect to the applied loading frequency and therefore all frequencies produce a rubbery response. This explains why we see frequency dispersion of the complex modulus properties as a result of molecular relaxations.

This explains two key features of the glass transition, or Tg. It must be regarded as a range of behaviour rather than a single point and secondly it is sensitive to the measurement technique employed to evaluate it. Therefore, there is no such thing as a single Tg value for any material, unlike a melting point, which can be uniquely defined. Therefore, it is always important to state all measurement conditions, such as method of determination, heating rate and frequency of test, as these will all affect the result. Finally, the parameter (E’’) chosen to represent the Tg can also change significantly from material to material.

The collective motion of regions of the material observed at the Tg is not the only deformational mechanism that can occur in amorphous materials. With long molecule materials, such as polymers, sugars and proteins, limited sections of the polymer backbone, side groups, or parts of side groups, can also move. These are referred to as secondary relaxations. The normal convention for naming these is to assign the highest temperature process, which is always the glass transition as the α process, the first one below Tg as the β process, the next lowest as the γ, and so on. These sub-Tg processes are due to limited motion, for example the rotation of a pendant side group, or some other process, such as deformation at an interface. The latter is a macroscopic structural feature, whilst the former is a molecular or microscopic structural feature.