# Non-destructive Methods For Composite Materials by ygw10815

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```									DGZfP-Berichtsband 94-CD                                                                DGZfP-Jahrestagung 2005
Plakat 18                                                                                      2.-4. Mai, Rostock

Non-destructive Methods For Composite Materials
Anisotropy Evaluation
D. Styra, S.V. Augutis, A. Dumcius, S. Jacenas
Department of Electronics and Measurement Systems
Kaunas University of Technology, Kaunas (Lithuania)

Q
Introduction                                             2.           C=     ;                             (2)
U
here: U – voltage between electrodes; Q
The control of sheet materials (paper,            – difference of charge between electrodes.
fiberboard and other) anisotropy is actual
Q = ε 0ε r∫∫∫
E (r )dA           (3)
materials anisotropy Lamb waves are
used. Materials can have mechanical as                                        W
well as electric anisotropy, which is
3.           C=2            ;                     (4)
U2
characteristic only to dielectric materials.          here:   W – potential electric energy
Electric anisotropy can be evaluated by               between electrodes.
measuring      permittivity    in   various
directions. The objective of this work is to                  Q=
1
2
(        )
ε 0 ∫ ∫ ∫ ε r (r ) E (r ) dV
2
(5)
create methods and equipment for
measuring permittivity anisotropy and to
check assumptions of existing connections                 It can be seen that in all expressions
between electric and mechanical sheet                 capacitance depends on permittivity.
materials anisotropy.                                     If permittivity is different in different
directions and we want the chose one,
Theory                                                according to formula (5) the biggest
dependence of energy (and capacitance as
Composite materials consist of fiber             well) on permittivity in a chosen direction
(coal, wood, glass and other fiber) and               will be the biggest when the direction of
filling. Usually fiber and filling have               electric field will coincide with a chosen
different permittivity. In some materials             permittivity direction.
fiber arrangement is chaotic, in other ones               Electric field near electrode surface
fiber has prevalent direction.          If the        places itself perpendicular to the surface
material permittivity of fiber and filling are        of the electrode.       Receding from the
different,    and    fiber  has    prevalent          surface of the electrode the direction of
direction, such materials have dielectric             the electric field depends on the
anisotropy.                                           electrodes nearby and the permittivity of
Electric capacitance forming between             the surrounding.
two electrodes can be expressed in                        The best way to evaluate electric
different ways:                                       anisotropy is to use two parallel electrodes
S                        and place a sample of tested material
1.           C = ε 0ε r     ;              (1)     between      them.       Then    the    main
d                        components of electric field will locate in
here:     ε0=8.854187817 10-21 F/m –                  straight direction between electrodes and
electric   constant;    εr   –   relative             thus the maximum of electric capacitance
permittivity;    S – overlapping areas                dependence on permittivity in a measured
between electrodes; d- distance between               direction. But this method is destructive –
electrodes.                                           in order to place electrodes in the tested
material, material must be broken.
DGZfP-Berichtsband 94-CD                                                   DGZfP-Jahrestagung 2005
Plakat 18                                                                         2.-4. Mai, Rostock

Electrodes can be put to the tested          method of finite elements. We use Ansys
material in several ways for non-                program for finite element modeling, and
destructive testing.   We have just one          capacitance      between      electrodes    we
suitable method. Electrodes have to be           calculate using “Capacitance Matrix”
placed on the surface of the tested              function.
material.                                           In our case the thickness, the width of
After   choosing    the   form  and          electrodes and the distance between them
arrangement of electrodes the maximum            can be changed.         We change relative
proportion of ∆C/C can be obtained               permittivity of tested material also.
∆C C x − C y                      Dielectric material covered with copper
=             .      (6)     was used for practical production of
C   Cx + Cy
electrodes. In order to receive modeling
here: Cx – is the capacitance when           results as close to the field experiment as
electrodes are placed in the direction x; Cy     possible a dielectric material model was
– is capacitance when electrodes are put         used in the modeling too.
in the direction y.                                 The modeling was performed with the
Then permittivity anisotropy is              0,5 mm wide electrodes having distance
∆ε       εx −εy        ∆C                between them 4,5 mm, thickness of
=            =K      ,       (7)
ε       εx +εy        C                 electrodes was 0,1 mm and relative
permittivity of test material was 50. The
here εx is permittivity in the direction x; εy
electric field potential is shown in figure 2.
is permittivity in the direction Y; K is a
coefficient,   which     depends     on   the
parameters of electrodes.
If electrodes were placed parallel and
the tested material was put between
them, then the coefficient K would be
close to 1. Electrodes are on the surface
and K will be significantly smaller than the
1. Our task is to find the optimal placing
of electrodes to have the maximum
coefficient K.

Theoretical investigation – modeling
Fig. 2.     Electric potential between two
In    order    to    evaluate      electric   electrodes, when 1 – test material; 2 –
anisotropy, anisotropic electric field has to    dielectric material, with εr=2; 3 - electrodes;
be created. For this reason, electrodes of
comb type will be used, when the length              The dependence coefficient K on
of electrodes is much bigger than other          permittivity of tested material was
parameters (fig.1).                              investigated.       The    modeling     was
performed with the 2,5 mm wide
electrodes having distance between them
2,5 mm and 0,1 mm thickness of
electrodes. The dependence coefficient K
on permittivity of tested material is shown
in figure 3.
Fig.1     Electrodes:      a – the width of
electrodes; b – the distance between
electrodes; h – the thickness of electrodes.

In order to optimize electrodes and find
the maximum parameter K we will use the
DGZfP-Berichtsband 94-CD                                                                                     DGZfP-Jahrestagung 2005
Plakat 18                                                                                                           2.-4. Mai, Rostock

0,19                                                        0,035
K
0,17                                                           K                                                                  3

0,15                                                                                                                                          2
0,03
0,13                                                                                                                                          1

0,11

0,09                                                        0,025

0,07

0,05
0,02
0,03

0,01
Permittivity
0   20    40       60   80   100              120
0,015
Fig.3   The dependence of K on tested
material relative permittivity εr
0,01
a/b
0       1       2       3       4   5     6       7       8           9             10

It can be seen from figure 3, that the
coefficient K is bigger when relative                       Fig.5 The dependence of K on a/b, when:
1 – test material; 2 – dielectric material, with
permittivity of testing material is bigger.
εr=2; 3 - electrodes;
This happens because electric flux density
in tested material increases, when relative
permittivity of testing material is bigger.                      0,09                                                              2

Electric flux density is shown in figure 4.
K
0,08                                                                          3

0,07                                                                          1

0,06

0,05

0,04

0,03

0,02
0       1       2       3   4   5     6   7       8           9            10
a/b

Fig.6 The dependence of K on a/b, when:
1 – test material; 2 – dielectric material, with
εr=2; 3 - electrodes;

It can be seen from figures 5 and 6
that the proportion ∆C/C and the
Fig. 4 Electric flux density, when: 1 – test
coefficient K are bigger when electrodes
material; 2 – dielectric material, with εr=2; 3
- electrodes;
are placed directly to the tested object.
As it is shown in figure 5, when the
Two     cases    of     modeling    were                proportion a/b decreases, the proportion
performed. In the first case electrodes                     a/b is increasing to the limit a/b = 0,667.
were placed to the tested material through                  When proportion a/b is smaller than
1 mm thick dielectric material, which                       0,667, the proportion ∆C/C and coefficient
relative permittivity is εr=2. In the second                K decreases.        This happens because
case electrodes were put to the tested                      electric field lines close in dielectric
material directly.      In both cases the                   material no.2 and only a small part of
results showed the dependence of                            them reaches the tested material.
coefficient K on the proportion a/b, when                       When electrodes are placed directly to
the thickness of electrodes is h = 0,1 mm.                  the tested material the proportion ∆C/C as
Both dependences are shown in figures 5                     well as the coefficient K increase and the
and 6.                                                      proportion a/b is decreasing.          This
modeling clearly shows that:
1. It is necessary to place electrodes
directly to the tested object;
2. The smaller is the proportion
between the width of electrodes and the
DGZfP-Berichtsband 94-CD                                                      DGZfP-Jahrestagung 2005
Plakat 18                                                                            2.-4. Mai, Rostock

distance between them, the bigger is the             Experimental research/investigation
proportion ∆C/C, as well as the coefficient
K.                                                       A special capacitance comb shown in
Also theoretical dependence of the K             figure 8 was made for experimental
on the thickness of electrodes was                   materials testing.
investigated.       The    modeling    was
performed with the 2,5 mm wide
electrodes having the distance between
them 2,5 mm. The dependence of the K
on the thickness of electrodes is shown in
figure 7.
0,07
K
0,06                                                Fig.8   A special capacitance comb for
0,05
permittivity anisotropy estimation with
MS3110 [6]
0,04

0,03                                                    This     transducer     evaluates     two
0,02                                                capacitances at once: one capacitance
reflects the permittivity εx in the direction
0,01
0      0,5    1      1,5       2   h   2,5   x, another capacitance reflects permittivity
εy in the direction y.
Fig.7       The dependence of K on h
The microchip MS3110 was used for
As it can be seen in figure 7, it is             capacitance measurement (This microchip
thinner are the electrodes, the bigger is            measurement resolution 4aF/rtHz) [6].
the proportion ∆C/C and the coefficient K.           RLC measurement instrument “Instec LRC
After several modeling procedures the            – 819” was used for calibration.
following conclusions were drawn:                        The experiments were carried out with
1. Electrodes have to be placed to the           paper and fiberboard.            In order to
tested material directly;                            minimize the influence of surrounding
2. The width of electrodes a and the             factors, all the system was not moved
thickness of electrodes h have to be as              during the experiment and only the tested
small as possible;                                   material – paper and fiberboard was
3. The distance between electrodes               rotated.        The     material   with    low
has to be as big as possible.                        permittivity was used to ensure paper
4. Common permittivity of tested                 pressing. To reduce the influence of the
material has to be estimated.                        pressing material it was in a fixed position
The capacitance of about 0,6pF forms             – its position towards the position of the
between two electrodes with the length of            capacitance comb did not change.
45 mm, the thickness h = 0,1 mm, the                     In order to compare electric and
width a = 0,5 mm, and the distance                   mechanical         anisotropy,      ultrasonic
between the electrodes is b = 4,5 mm. In             anisotropy      testing    was     performed.
order to increase the capacitance more               Measurement of Lamb waves propagation
electrodes were placed together. In this             velocity was measured with “Hardboard
way an electrode comb, called a                      Strength Meter” [4].
capacitance comb, was made. Increasing                   The results of paper anisotropy
a number of electrodes, the electric                 measurement using electric and Lamb
capacitance C as well as the difference              wave methods [5,6] are shown in fig 9(a).
between      capacitances   ∆C   increase.           The results of fiberboard anisotropy
Therefore the proportion ∆C/C and the                measurement using electric and Lamb
coefficient K stay unchanged.                        wave methods are shown in fig 9(b).
Measurement were performed every 10
degrees of circle perimeter.
DGZfP-Berichtsband 94-CD                                                                                                DGZfP-Jahrestagung 2005
Plakat 18                                                                                                                      2.-4. Mai, Rostock

In paper, fiber arrangement has strong
0                                             prevalent direction – it is proven by both
electric and ultrasonic methods.
350     4         10
340                           20
330               3,5                     30
320
3
40                         In fiberboard fiber arrangement is
310                        2,5                                50
more chaotic – it is confirmed by the
results of both electric and ultrasonic
300                               2                                     60
1,5
methods.
290                                                                           70
1
The results of experiments show that
280                                                                               80
0,5
270                                     0                                           90
the both paper and fiberboard properties
260                                                                               100
can be evaluated ultrasonic as well as
250                                                                           110
electrical method.
240                                                                     120
Common permittivity of tested material
has to be estimated. In order to estimate
230                                                           130
220                                                   140
210                                       150                          common permittivity and permittivity
200                           160
190
180
170
anisotropy, special capacitance transducer
was created. Schematic of this transducer
is shown in figure 10.
Fig.9 a)     The dependence of paper
properties on direction:      - Lamb waves
velocity in kilometers per second;       -
change of electric capacitance in 0,1 Pico

0
350    3          10
340                           20
330                                       30
2,5
320                                                   40
310                            2                                  50               Fig.10   Capacitance comb for Common
300                              1,5                                      60          permittivity and permittivity anisotropy
290                                   1                                           70      estimation
280                                   0,5                                            80

270                                     0                                             90
This type of capacitance transducer has
two valuable signals – output frequency
260                                                                                  100
and output voltage.          Frequency is
proportional to common capacitance and
250                                                                               110

voltage is proportional to change of
240                                                                       120
230                                                               130
220                                                   140
capacitance.    Common permittivity and
320
340                           160
150                          permittivity anisotropy can be estimated
350
180
170
using this equipment.

Fig.9 b) The dependence of fiberboard                                                           Conclusion
properties on direction:         - Lamb waves
velocity in kilometers per second;           -                                                    •    The experiments show that paper
change of electric capacitance in 0,1 pF minus                                                  and     fiberboard   properties   can     be
7 pF.                                                                                           evaluated by using both ultrasonic and
electrical methods;
Two lines are shown in fig.9.     One                                                         •    Electrodes have to be placed as
marked with triangles (      ), shows the                                                       close to the tested materials as possible.
dependence of Lamb waves velocity on                                                              •    Electrodes have to be as thin and
direction in kilometers per second. The                                                         narrow as possible.
other one marked with squares (          )                                                        •    Common permittivity of tested
shows the change of electric capacitance                                                        material has to be estimated
dependence on direction in 0,1 Pico farads
minus 7 pF.
DGZfP-Berichtsband 94-CD                                             DGZfP-Jahrestagung 2005
Plakat 18                                                                   2.-4. Mai, Rostock

References
D. Styra, V. Augutis, A. Dumciu, S.
1. И.Г.Матис.      Электроемкостные      Jacenas
преобразователи для неразрушющего            Nondestructive      methods      for
контроля. Рига: Зинатне, 1982. –304с.        composite    materials   anisotropy
2. American Society for Testing and      testing
Materials (1996) D 1037-96a. Standard
test methods for evaluating properties of    Summary
wood-base fiber and particle panel              Composite materials are widely used
materials. ASTM Anal Book of standards.      nowadays. These materials usually have
Vol     4.10.    Wood.     ASTM,      West   various anisotropical properties because of
Conshohocken. PA, Pp. 136-165.               fiber in them.
Hardboard      Strength       Measurement    anisotropy evaluation methods: electrical
Methods.          ISSN          1392-1223.   and ultrasonic. Ultrasonic method is based
Measurements, No 1 (29). Kaunas,             on     precision   Lamb     wave    velocity
Kaunas University of Technology.             measurement. Electric method is based on
4. V.   Augutis,   A.   Dumcius,    V.   permittivity measurement, using special
Dzenkauskas, V. Dzimidavicius, D. Styra.     capacitance transducers.
(2004). Hardboard Strength Meter. ISSN          It was found, that experimental results
1392-1223. Measurements, No 1 (29).          of both methods strongly correlated with
Kaunas, Kaunas University of Technology.     results of known strength determination
5. V. Augutis, A. Dumcius, D. Gailius,   methods.
D. Styra, S. Jacenas.         (2004). The       These methods can be used for
Ultrasonic Method of Hardboard Testing.      anisotropy evaluation of fiberboard, paper
ISSN 1392-2114. Ultrasound, No 4 (53).       and other composite materials. In
Kaunas, Ultrasound Institute.                addition,     both    methods     can    be
6. http://www.microsensors.com/          implemented in production line

Studentu g. 50, 443 k., 51368 Kaunas
tel./fax.: +37037 451617, e-mail:
Darius.Styra@ktu.lt

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