A Large Aperture Ultrasonic Receiver for Through-
Transmission Determination of Elastic Constants of
Composite Materials
Julio C. Adamowski , Marco A. B. Andrade, Nicolas Perez, Flávio Buiochi
Department of Mechatronics Engineering
Escola Politécnica da Universidade de São Paulo
São Paulo, Brazil
jcadamow@usp.br
Abstract—This paper describes the use of a large aperture PVDF
receiver in angle beam through-transmission method of velocity
measurement in fiber reinforced composites. This technique
avoids the beam diffraction effect that occurs when using limited
size ultrasonic transducers. This effect increases as the frequency
decreases for the same size of transducer. On the other hand, the
velocity dispersion effect, present in composite materials,
increases with frequency. Analyzing the diffraction effect, it was
observed that the longitudinal velocity in an aluminum plate
increases more than 1 % when using a pair of 1 MHz
transducers. That effect disappears when using the large
aperture receiver and it is negligible when using a pair of 10 MHz
transducers. On the other hand, it was observed that in the
acrylic plate the longitudinal velocity increases 0.7 %, and
increases more than 0.8 % in a 2.115 mm thick CFRP (carbon
fiber reinforced plastic) plate, from 1 to 10 MHz. As a
compromise between axial resolution and velocity dispersion, the
elastic constants of the unidirectional CFRP plate were
determined in the frequency of 2.25 MHz, showing good
agreement with tensile test results.
Keywords: composite materials, elastic constants, PVDF
receiver, diffraction
I. INTRODUCTION
The determination of elastic constants of anisotropic
materials by measurement of the density and ultrasonic
velocities has been studied by several researchers in the last
four decades [1], [2].
An anisotropic material is described by 21 independent
elastic constants. The number of elastic constants is reduced to
nine when the material has orthotropic symmetry. This number
may be further reduced when there is more symmetry in the
material. A unidirectional carbon-fiber/epoxy laminate can be
considered as transversely isotropic and the number of
independent elastic constants is reduced to five [2].
The determination of elastic constants from a set of bulk
ultrasonic wave phase velocities in an arbitrary direction of a
measured sample of composite material is based on the
Christoffel’s equation [3].
The accuracy of elastic constants is highly dependent on the
precision of the velocity measurement. The immersion
through-transmission method is based on the measurement of a
time delay between the time spent by the wave traveling in the
absence of the sample material and the time with the sample
material. This time delay is used to calculate the phase velocity
and the refraction angle in the sample [4].
There are several factors which introduce errors when
measuring velocities, such as: parallelism of the sample
surfaces, temperature gradients, velocity dispersion, acoustic
diffraction, mechanical precision of the measurement device,
etc [5]. It can be shown that an infinite-plane receiver with
uniform sensitivity yields a plane wave-only measurement [6].
In practice this receiver is obtained by using a piezoelectric
PVDF (Polyvinylidene Fluoride) thin-film receiver, sufficiently
large to intercept the entire propagating wave and electroded
throughout its entire extent [7]. This technique avoids the beam
diffraction effect that occurs when using limited size ultrasonic
transducers. This effect increases as the frequency decreases
for the same size of transducer. On the other hand, the velocity
dispersion effect, present in composite materials, increases with
frequency.
In this work a large aperture PVDF receiver is used
together with a piezoelectric ceramic emitter in through-
transmission method of ultrasonic velocity measurement in
solid material plates immersed in water. It is analyzed the
diffraction effect in longitudinal velocity measurement when
using conventional non-destructive testing (NDT) ultrasonic
transducers in the range of 1 to 10 MHz and the velocity
dispersion in acrylic and CFRP plates. The elastic constants of
a unidirectional CFRP plate are determined using phase
velocities measured with an angle beam through-transmission
assembly using the diffraction-free PVDF receiver.
II. DIFFRACTION AND DISPERSION EFFECTS ON VELOCITY
MEASUREMENT
The experiments have been made in a goniometer device
immersed in distilled water. The water inside the goniometer
was kept at 21.50 ± 0.05
o
C with the aid of a thermostatic bath.
The goniometer device allows changing the emitter and the
We would like to thank the following Brazilian sponsor agencies:
CAPES, CNPq and ANP; and PETROBRAS for financial support.
1524 978-1-4244-2480-1/08/$25.00 ©2008 IEEE 2008 IEEE International Ultrasonics Symposium Proceedings
Digital Object Identifier: 10.1109/ULTSYM.2008.0371