Page 38 - Handbook of Thermal Analysis of Construction Materials

22 Chapter 1 - Thermoanalytical Techniques

Therefore, the slope of the curve of length versus temperature
yields α L and the coefficient of linear thermal expansion is obtained by
l 1
dividing by L .
1
There are some drawbacks with thermomechanical analysis. Proper
calibration is required to obtain reliable and reproducible data. Other
sources of errors include slippage of the probe on the specimen and
specimens undergoing creep in addition to length changes.

3.2 Dynamic Mechanical Analysis (DMA) [52]–[59]

The following equations describe the stress-strain relationship
(Fig. 8) as measured by DMA:

Eq. (17) σ = σ sin (ωt) cos δ + σ cos (ωt) sin δ
o
o
Eq. (18) ε = ε sin (ωt)
o
where σ is the stress, ω the angular frequency, t is the time, δ is the phase
angle, and ε is the strain.

Figure 8. Stress-strain relationship measured by DMA.

The real component, σ cos δ, occurs when stress is in-phase with
o
strain. The imaginary component is 90° out-of-phase with strain and
corresponds to σ sin δ. The stress-strain components can be resolved and
o
real and imaginary components of modulus are obtained:

Eq. (19) σ = ε E´ sin (ωt) + ε E´´ cos (ωt)
o
o
where E´ = (σ /ε ) cos δ is a measure of recoverable strain energy in a
o
o
deformed body and is known as the storage modulus. E´´ = (σ /ε ) sin δ ,
o
o