Civil Engineering Reference
In-Depth Information
Therefore, the slope of the curve of length versus temperature
yields
α
l
L
1
and the coefficient of linear thermal expansion is obtained by
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.
Dynamic Mechanical Analysis (DMA)
[52]-[59]
3.2
The following equations describe the stress-strain relationship
(Fig. 8) as measured by DMA:
Eq. (17)
σ
=
σ
o
sin (
ω
t
) cos
δ
+
σ
o
cos (
ω
t
) sin
δ
Eq. (18)
ε
=
ε
o
sin (
ω
t
)
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.
, occurs when stress is in-phase with
strain. The
imaginary
component is 90° out-of-phase with strain and
corresponds to
The
real
component,
σ
o
cos
δ
. The stress-strain components can be resolved and
real and imaginary components of modulus are obtained:
σ
o
sin
δ
Eq. (19)
σ
=
ε
o
E
´ sin (
ω
t
) +
ε
o
E
´´ cos (
ω
t
)
where
E´
= (
is a measure of recoverable strain energy in a
deformed body and is known as the
storage
modulus.
E
´´ = (
σ
o
/
ε
o
) cos
δ
σ
o
/
ε
o
) sin
δ
,
