Page 353 - Book Hosokawa Nanoparticle Technology Handbook

6.2 MECHANICAL PROPERTIES FUNDAMENTALS
With the measurement of surface sound velocity, it
can be applied to the measurement of elastic constants
σ on thin films. It is reported that laser is used for gen-
erating and measuring the surface wave, and the
sound velocity on thin films can be measured [7].
In nanomaterials, the elastic constants on the mate-
x rials with two phases can be discussed. For the Young’s
modulus of two phase materials, two models are
reported for giving upper and lower limit of the value.
The two phase with Young’s modulus of E and E ,
1
2
with the volume fraction of V and V , the upper limit
2
1
of the Young’s modulus of the mixed material, E is
U
E V E V E (6.2.3)
L U 11 2 2
and the lower limit, E becomes
L
EE
E 12 (6.2.4)
L
VE V E
12
2 1
y
For discussing the mechanical vibration, dumping of
the vibration is another point of interest in the materi-
s: tensile stress
L: original length als. Internal friction is a material parameter relating to
1
x: strain parallel to stress elastic constants [8, 9]. Internal friction, Q ,
y: strain perpendicular to stress expresses the energy loss on the vibration, or the delay
of the vibration, and it is called loss tangent (tan ),
too. Internal friction can be determined with the
E (Young’s modulus) = s / (x / L)
n (Poisson’s ratio) = y / x applied vibration energy, W, and the lost energy W
with one cycle of vibration.
Figure 6.2.8
Schematic figure on Young’s modulus, E, and Poisson’s Q 1 W (6.2.5)
ratio, . 2 W
High frequency Ultrasonic sound Echo
pulse generator Amplifier

Transducer

Trigger
Buffer rod Signal

Specimen

Trigger generator Oscilloscope
Synchronize

Figure 6.2.9
Example of the measurement system for ultrasonic sound velocity.

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