Page 80 - Riem-Vol6_nº2

251 IBRACON Structures and Materials Journal • 2013 • vol. 6 • nº 2
L. P. PERLIN | R. C. A. PINTO
For each reading performed, there is a specific spatial position
of the emitting and of the receiving transducers. Initially, it was
considered that the pulse travels in a linear path between both
transducers, and thus, the mathematical line equation between
transducers is defined, according to Figure 7. The real path of the
pulse, however, may contour objects or regions with low velocities,
as shown in Jackson et al. [19]. In this case, a more complex ap-
proach needs to be used when programming. This complexity is
not yet included in TUCon in its actual phase.
Some aspects should be taken into account when defining the grid
to be used in ultrasonic tomography. From a pure mathematical
point of view, the Radon Transform does not define limits to the
lowest element size to be used, and thus the lowest grid spac-
ing. A great number of elements would allow a more precise result
since the domain would be discretized in yet smaller elements.
The number of reading points and the total number of readings
would also be greater which would contribute to a better result.
The possibility of infinitesimal grid spacing would yield theoretically
a perfect result.
However, according to results presented by Schechter et al [20],
the wave front is not perfectly circular, depending mainly on the
size of the transducer used to generate it. Therefore, small varia-
tions in the transducer position would not influence significantly on
the ultrasound readings. Other limiting factors are the wave length
and the total time required to perform all readings. If an internal
flaw is smaller than the wave length it will not be detectable, and
thus there is no need to define grid spacing smaller than the gener-
ated wave length. Moreover, the smaller the grid spacing the great-
er the number of readings leading to a much greater execution
time for all readings. As a consequence, the decision of the grid
spacing should take into account all of this aforementioned factors.
The elemnts of matrix Dm,n are calculated following a simple pro-
cedure. With the grid spacing and ray-path equation defined, it
is possible to determine the interception points, numbering them
in an ascending order according to Figure 8. With the points
numbered, the distance between successive points can be easily
calculated.
With the matrix Dm,n and the vector Tm determined, the iterative
process of Optimized Cimmino solves the system. The result is
then exported for further graphical treatment. The flowchart of the
program can be found in Figure 9. The TUCon main window is
displayed in Figure 10.
4. Experimental program
4.1 Description of experimental program
Four 20 cm cubic specimens were produced in the laboratory. In-
side each specimen, a small EPS block was inserted prior to con-
creting. Figure 11 shows the geometry of the produced cubes with
the position and dimension of the EPS blocks. Metallic molds were
used in order to obtain surfaces without irregularities, improving
the ultrasound readings. The process of concreting and prepara-
tion of specimens is shown in Figure 12.
Once demolded, the specimens were wrapped with plastic film for
10 days. A 5 cm grid spacing mesh (Figure 12-d) was chosen as
reference for transducer position. Each specimen was tested using
200 kHz ultrasound transducers.
4.2 Ultrasound readings
The experiments were performed in a two-dimensional palne, us-
ing a 2.5 cm spacing grid at the horizontal median plane of the
specimens. This allowed performing an ultrasonic tomography at
mid-height of the cube exactly at the middle of the internal flaw
produced by the EPS. This configuration is similar to a possible
Figure 7 – Pulse travels through
different discretized elements
Figure 8 – Pulse travels through
different discretized
elements with numbering
of the intersection points Figure 9 – Flowchart of use and processing
of TUCon