Dynamic Mechanical Analysis (DMA) measures the mechanical properties of materials while they are subjected to a periodic stress, usually applied sinusoidally.
If a material is subjected to a mechanical force it may behave in a variety of ways, illustrated above. A brittle material will deform reversibly to a small amount and then fracture. A ductile material will also deform reversibly up to a certain amount and then yield and flow under the applied force until it begins to harden under load and then fail. Up to the elastic limit, the material will return to its former shape and size when the force is removed. Beyond this point deformation is irreversible i.e. creep has occurred.
Stress (s ) is defined as the force applied per unit area ie.
s = F/A
Stress has units of N/m2 or Pa.
The applied stress will cause a deformation measured by the strain (e) which is the deformation per unit dimension. For a simple tensile experiment:
e = D l/l
where Dl is the change in length and l is the original length. Strain has no units and is often given in % for convenience.
For a perfectly elastic material the sample will obey Hooke’s law:
E = s /e
Where E is the tensile modulus (i.e. stress/strain). Other types of mechanical moduli may be defined depending on how the specimen is deformed - eg. Shear modulus (G) = shear stress/shear strain. Distortion of the sample will occurs as the cross-sectional area of the specimen deceases as its length increases. This is called Poisson’s ratio (v) and relates the tensile modulus to the shear modulus so:
G = E/(2(1+v))
For most materials v is between 0 and 0.5.
For DMA a low stress is applied in a sinusoidal fashion so that the sample is always within the elastic region of its stress-strain curve. For a perfectly elastic material the stress and strain are perfectly in phase ie.
Instead of deforming reversibly under load, a material may flow. The velocity of the flow (ds /dt) is related to the stress by Newton’s law:
e = h .ds /dt
Where h is the viscosity. Under dynamic loading, the stress-strain curves are now 90° out of phase since the strain is proportional to the rate of change of the stress:
Most polymeric materials show a combination of both types of behaviour - i.e. they react elastically, and flow to some extent at the same time, and are termed "viscoelastic". The Stress and Strain curves are therefore out of phase, as above, but by an amount less than 90°.
DMA measures the amplitudes of the stress and strain as well as the phase angle (d) between them. This is used to resolve the modulus into an in-phase component - the storage modulus (E’) - and an out-of-phase component - the loss modulus (E"). The relationship between these quantities and the dynamic (or complex) modulus (E*) may be represented by an Argand diagram:
A useful quantity is the damping factor or loss tangent (tan d) which is the ratio E"/E’ and is the amount of mechanical energy dissipated as heat during the loading/unloading cycle. From the above discussion, it is apparent that for a perfectly elastic material tan d is zero whereas a perfectly viscous material tan δ is infinite.
A typical instrument for performing DMA can deform the sample in a number of different ways as illustrated below.
The sample is deformed by the application of the stress, which is applied by a force motor, while the resulting strain is measured by a position transducer. All the sample mounting arrangements are interchangeable, and fit into a space around 10cm across within the furnace. The cantilever bending mounts are used for solid samples of low to moderate stiffness. Compression and shear mounts can be used for soft materials, or even liquids of high viscosity. The tension mount is particularly useful for fibres or films and elastomers. Gelation and cure of liquids can be studied by soaking a glass-fibre braid, and mounting this in a cantilever system. Thin films (e.g. paints or lacquers) may also be studied supported on a thin metal shim.