Tritec 2000 DMA Manual

2 Principles of DMA – forced non-resonance technique

2.1 Introduction

The forced non-resonance technique is one of the simpler dynamic mechanical methods to understand. In most commercially available instruments a force is applied to a sample and the amplitude and phase of the resultant displacement are measured. All of these instruments employ a linear actuator where the force applied is calculated from a knowledge of the input signal to the electro-magnet coils in the driver.

An alternative to the above is where a force transducer is used to measure the applied load, with the sample between this transducer and the magnetic driver. These are the two types of arrangement that are found with the forced non-resonance technique. In each case the sample is driven at a frequency below that of the test arrangement. The typical frequency range of such instruments is 0.001 to 1000 Hz. Any measurements below 0.01 Hz take too long for most analytical experiments, especially if data are required as a function of temperature and resonance often occurs at frequencies >100 Hz, depending upon the sample stiffness.

2.2 Terms and definitions

In a dynamic mechanical test it is the sample stiffness and loss that are being measured. The sample stiffness will depend upon its Modulus of Elasticity and its geometry or shape. The modulus measured will depend upon the choice of geometry, Young’s (E*) for tension, compression and bending, Shear (G*) for torsion. The modulus is defined as the stress per unit area divided by the strain resulting from the applied force. Therefore it is a measure of the material’s resistance to deformation, the higher the modulus the more rigid the material is.
The definition given above for modulus does not take time into account. For materials that exhibit time-invariant deformation, for example metals and ceramics at room temperature, any measurement of strain will lead to a constant value of modulus. However for materials that exhibit time-dependent deformation, such as polymers, the quoted modulus must include a time to be valid. This is where dynamic mechanical testing offers a powerful advantage. Dynamic mechanical testers apply a periodic stress or strain to a sample and measure the resulting strain or stress response. Due to the time-dependent properties of polymers the resultant response is out-of-phase with the applied stimulus. The Complex Modulus M* is defined as the instantaneous ratio of the stress/ strain. To understand the deformational mechanisms occurring in the material this is resolved into an in-phase and out-of-phase response. This is equivalent to a complex number (see below), where M’ is the in-phase or elastic response this being the recoverable or stored energy.

M'' is the imaginary or viscous response, this being proportional to the irrecoverable or dissipated energy. Thus for a completely elastic material M*=M', whilst for a totally viscous material M*=M''. d is the measured phase lag between the applied stimulus and the response. Tan d is given by the ratio M''/ M' and is proportional to the ratio of energy dissipated/ energy stored. This is called the loss tangent or damping factor. This is one of the key parameters in dynamic mechanical testing, since it is seen to increase during transitions between different deformational mechanisms.

In-phase or Storage (real) properties	Out-of-Phase or loss (imaginary) properties
Youngs’ (Pa) E' = \|s/e \| cos d	E'' = \|s /e \| sin d
Shear (Pa) G' = \|t /g \| cos d	G'' = \|t /g \| sin d
Compliance D' = \|e /s \| cos d	D'' = \|e /s\| sin d
(m²N^-1) D' = E' / (E'²+E''²)	D'' = E'' / (E'²+E''²)
Viscosity (PaS) h ' = G''/w	h ''= G'/w
where w = 2pf	where w = 2pf

Often the choice of geometry will be dictated by the sample being investigated. For example thin films can only be measured accurately in tension. Fortunately all good dynamic mechanical testers perform well in tension and should deal with the necessary pretension forces fully automatically, including those associated with large modulus changes that may occur at the glass transition. Pretension is necessary in order to maintain the sample under a net tension to prevent buckling that would otherwise occur. Tension should be the first choice for any sample less than 1mm thick. Samples with thicker then 1mm will probably be too stiff for the instrument in tension and bending mode would be preferable in this case. Materials that creep excessively, such as polyethylene, may be difficult to test in tension, due to creep under the pretension force.
Bending mode is probably the most accommodating geometry, in that common-sized bars (50x10x2mm) of material are readily tested. Such sizes are within the ranges of most commercial dynamic mechanical testers. Clamped modes will yield better results over the whole temperature range, but suffer from clamping effects (see below), whilst simply supported modes (3-point bending) yield the most accurate moduli.
Torsion is a good choice of geometry, but since this has a low inherent stiffness it necessitates reasonably large samples. Also few dynamic mechanical testers have a torsional capability.
Simple shear is an excellent means of measuring low modulus materials, such as rubbers, gels and pastes. Glassy materials will be too stiff for most dynamic mechanical testers in this mode.
Compression is the worst choice for any sample. It is the mode with the most geometrical errors (assumption of perfect lubrication at surface), but is often the only way to measure irregularly shaped samples. Under these circumstances an accurate modulus cannot be obtained, but transition information should not be compromised. Again due to instrument range it is only suitable for rubbers, gels and pastes.