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In essence, the phase angle between the stress and strain tells us a great deal about the viscoelasticity of the material. For one, a small phase angle indicates that the material is highly elastic; a large phase angle indicates the material is highly viscous. Furthermore, separating the properties of modulus, viscosity, compliance, or strain into two separate terms allows the analysis of the elasticity or the viscosity of a material. The elastic response of the material is analogous to storage of energy in a spring, while the viscosity of material can be thought of as the source of energy loss.
A few key viscoelastic terms can be calculated from dynamic analysis; their equations and significance are detailed in Table 1 .
| Term | Equation | Significance |
|---|---|---|
| Complex modulus ( E *) | E* = E’ + iE” | Overall modulus representing stiffness of material; combined elastic and viscous components |
| Elastic modulus ( E’ ) | E’ = ( σ o /γ o ) cosδ | Storage modulus; measures stored energy and represents elastic portion |
| Viscous modulus ( E” ) | E” = ( σ o /γ o ) sinδ | Loss modulus; contribution of viscous component on polymer that flows under stress |
| Loss tangent ( tan δ) | Tan δ = E”/E’ | Damping or index of viscoelasticity; compares viscous and elastic moduli |
A temperature sweep is the most common DMA test used on solid materials. In this experiment, the frequency and amplitude of oscillating stress is held constant while the temperature is increased. The temperature can be raised in a stepwise fashion, where the sample temperature is increased by larger intervals (e.g., 5 o C) and allowed to equilibrate before measurements are taken. Continuous heating routines can also be used (1-2 o C/minute). Typically, the results of temperature sweeps are displayed as storage and loss moduli as well as tan delta as a function of temperature. For polymers, these results are highly indicative of polymer structure. An example of a thermal sweep of a polymer is detailed later in this module.
In time scans, the temperature of the sample is held constant, and properties are measured as functions of time, gas changes, or other parameters. This experiment is commonly used when studying curing of thermosets, materials that change chemically upon heating. Data is presented graphically using modulus as a function of time; curing profiles can be derived from this information.
Frequency scans test a range of frequencies at a constant temperature to analyze the effect of change in frequency on temperature-driven changes in material. This type of experiment is typically run on fluids or polymer melts. The results of frequency scans are displayed as modulus and viscosity as functions of log frequency.
The most common instrument for DMA is the forced resonance analyzer, which is ideal for measuring material response to temperature sweeps. The analyzer controls deformation, temperature, sample geometry, and sample environment.
Figure 3 displays the important components of the DMA, including the motor and driveshaft used to apply torsional stress as well as the linear variable differential transformer (LVDT) used to measure linear displacement. The carriage contains the sample and is typically enveloped by a furnace and heat sink.
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