The composites D. Sarkissian*, W.N. Sewnath University of

The relation between the power
absorption coefficient and electrical impedance testing to identify damage in
composites

 
D. Sarkissian*, W.N. Sewnath
 
University of Twente, Faculty of
Mechanical Engineering, Drienerlolaan 5, 7500AE Enschede, The Netherlands
*corresponding author [email protected]
 

ABSTRACT: Composite materials consist out of a
combination of fibers and matrix, which makes the materials structurally
strong and stiff. Failure of one ply affects the stiffness and remaining
strength of the composite laminate but does not result in total failure. The problem is that the human eye cannot
identify the internal damage in composite materials. Therefore, there is a
methodology to identify the damage in composite materials by using electrical
impedance testing. This methodology can be linked with the power absorption
coefficient ? of the sound
absorption theory. Theoretical research on the equations used to calculate
the power absorption coefficient ? has
been conducted. By analyzing and implementing the equations of ? in combination with the measurement
data in Matlab, ? resulted in 1. This
means the amount of energy that goes into the composite structures is fully
absorbed. So, there is a relation between the power absorption coefficient
and electrical impedance. The goal is to identify damage in composite
materials by electrical impedance testing with the power absorption
coefficient. With this research it can be concluded, that it is possible to
identify damage in composites using the power absorption coefficient.

Key words: Power
absorption coefficient, electrical impedance, composite damage detection.

INTRODUCTION

A fiber reinforced composite laminate is made up of
several layers of orientated plies. Failure of one ply affects the stiffness
and remaining strength of the composite laminate but does not result in total
failure. The failure modes of composite material include compressive, tensile
or shear fracture of the matrix 1. Most of the time in
practice composite fail due to impact damage 1. The problem is that
the human eye cannot identify the internal damage in composite materials. This
makes it difficult to determine the structural integrity of the composite
materials after impact damage. Investigating damage in composite materials can
be in form of mechanical failures as internal delamination or cracks 1. It is
important to be able to identify the internal damage in a composite, for
example, for cost reduction by minimizing the inspection time and effort to
check for failures.

There is a methodology to identify damage in composite
material by using electrical impedance testing. Grafen 2 has made a link
between electrical impedance testing and the sound absorption theory of Wijnant
3
to identify damage in composite materials. From the sound absorption theory of
Wijnant 3,
the power absorption coefficient can be determined. The power absorption
coefficient ? can have a relation
with electrical impedance testing to identify damage in composites.

Objective

This research is an addition to the study of Grafen 2. Grafen conducted a
research 2
by testing two similar composite plates (PEKK/AS4D) with different internal
failures. When comparing the test results with the theory of Wijnant 3, the results were
not as expected. According to the test results of Grafen 2, the power
absorption coefficient was not between 0 and 1. Physically it would imply that
the power absorption coefficient should be between 0 and 1 3. The amount of
energy can be fully reflected and not more. The other way around no less than
no energy can be reflected. Therefore, the power absorption coefficient should
be between 0 and 1. The objective is to identify the main reason why the test
results of Graven 2
deviate from the theory of Wijnant 3,
hence to answer the question:  

“What is the main reason that the power coefficient (?) is not
between 0 and 1 in the research of Grafen?”

Hypothesis

The expectation is that there is a relation between
the power absorption coefficient and electrical impedance. If there is a
relation, then the absorption coefficient must be between 0 and 1.

THEORETICAL
BACKGROUND

Oomen 4 showed that the power absorption coefficient can be used as an
indicator to identify damage in composite materials. Oomen 4 also showed that the
power absorption coefficient can be used to detect damage as an experimental
validation. For the experiments 4,
a composite plate (Carbon/PPS) was used. The experiments were based on measuring
the electrical impedance of a composite structure.

Originally, the sound
absorption theory of Wijnant 3
is based on acoustic impedance experiments. It is
important to state that in the acoustic impedance experiments, waves were propagated into a non-solid material. This will
result into longitudinal waves. It this situation, which is based on electrical
impedance experiments, waves were propagated into a
solid material. This will result into a combination of longitudinal waves
and shear waves. This research will focus on the relation between the power
absorption coefficient and electrical impedance testing.

Power
absorption coefficient

Wijnant 3
defined an absorption coefficient, which is based on a new definition of
incident power. In this method, the incident intensity is defined as the time
average value of the positive values of the instantaneous power 3. If the sound
pressure and particle velocity in a certain direction are known, then the total
intensity can be determined. For plane waves, this quantity is the sum of the
incident- and reflected sound intensity in that direction 3. The incident- and
reflected intensity can be determined with active intensity.

In the
research of Oomen 4
a novel absorption coefficient is defined that used a point force exerted on
the system and the velocity of the system at the excitation point. This is
called the power absorption coefficient. The
definition of the power absorption coefficient ? is defined as:

                              (1)

where  denotes the
incident (input) power and  denotes the nett
active power. The nett active
power is the time-averaged power, defined as the product of the force and the
velocity. In the same manner, voltage and current can be used in the electrical
domain to determine the electrical impedance 4.
In the mechanical domain the force and the velocity can be measured at an
excitation point to obtain the instantaneous power. Determining the fraction of
nett active and input power will result in how much power is absorbed.

Electrical
impedance

Impedance is a property used in many methods for Non-Destructive
Testing 5. Non-Destructive Testing is a research area in which methods are
developed and used to detect damage before failure occurs. Impedance shows the
frequency dependent resistance and is the ratio of voltage over current 5. This is called the
electrical impedance. To measure the electrical impedance of the composite
plate, an input signal with a certain value must be sent through the material
by piezoelectric transducers (PZTs), which is attached to the structure. The
electrical impedance responses of the piezo-electric materials make it possible
to obtain the mechanical properties of the structure, and therefore damages can
be detected 6.
PZT is capable of converting electrical energy into mechanical energy and vice
versa 7.

METHODOLOGY

To be able to answer the main research question a theoretical
research must be conducted on the deviant ?.
And the necessary equations to determine the power absorption coefficient must
be researched, analyzed and implemented correctly in the Matlab code to achieve
a ? between 0 and 1.

 

 

From the instantaneous power, the active power  and reactive
power  and a power
ratio PR can be determined 4, 8:

                            (2)

                            (3)

                           (4)

Where F
denotes the force, denotes the complex conjugate of V,  denotes the real part and  denotes the imaginary part. PR is the power ratio between the active
power and the amplitude of the instantaneous power. PR is a ratio and should be between 0 and 1 and therefore is always
a positive value. This means that  should also be a positive value.

The nett active
power  is defined as 4, 8:

                             (5)

where  denotes the incident input power and  denotes the reflected power.  and  can be defined as 4 8:

    (6)

        (7)

The part in the brackets of  will always result into a positive value,
which means  should be a positive value.  will always result into a negative value.

If  and  are both postive values, this will result into
that ? will
be a positive value. This is correct because the expectation is that the ? is between 0 and 1.

Equations 1 till 7 have been analyzed and implemented with
the measurement data in Matlab to determine the power absorption coefficient. The
input measurement data are signals in the time domain for force and velocity. To
plot  in the
frequency domain, the measurement data are processed in Matlab with a Fast
Fourier Transformation (FFT).

 

RESULTS
& DISCUSSION

The signals of the measurements are analyzed in the
frequency domain to determine the power absorption coefficient of the structure
in a frequency range. The equations 1 till 7 are implemented in Matlab with the
measurement data, which resulted in plots for ,   and . In figure 1
these plots are shown.

Fig. 1: 
Matlab results of ,   and .

The expected result was that the power absorption
coefficient must be between 0 and 1. The power absorption coefficient ? for the two frequencies is approximately
equal to 1, because the nett active power  and the
incident (input) power   are in phase and therefore the power is always
positive. This means that  and  are equal,
which results that ? is 1. This means
the amount of energy that goes into the test plates is completely absorbed. In
figure 1 can also be seen that and  have an equal
amplitude at any frequency value. These two waves oscillate together and their
function reach a 0 value for the same frequency value and these are both in the
positive side of the graph. This results in a resonance betweenand .

? is 1, this means the amount of power that is put in
at the excitation point is equal to the amount of power dissipated. So the PZT
is placed on a location where the amount of power is fully absorbed. When the
composite structure is excited in a resonance frequency, the power is absorbed
efficiently and the power absorption coefficient will be 1. This is also the case
here and this proves the hypothesis is correct. This concludes that there is a
relation between the power absorption coefficient and electrical impedance
testing to identify damage in composites.

According to Grafen 2,
the study of van Dijk & van Dijk 5 was based on the
expectation that a delamination in a composite would absorb all the energy and
not reflect any energy. In figure 1, it can be seen that this is the case and
the expectation is met in this research.

CONCLUSION

This research aimed to answer the question on what the
main reason is that the power coefficient ?
is not between 0 and 1 in the research of Grafen 2. The main reason was
an error in the implementation of the equations to determine the power
absorption coefficient in the Matlab code. By analyzing and implementing the
equations of the power absorption coefficient correctly in the Matlab, results that
? is 1 over the frequency range. This
means the amount of energy that goes into the test plates is completely
absorbed. 

The hypothesis was that there is a relation between the
power absorption coefficient and electrical impedance. If there is a relation,
then the absorption coefficient must be between 0 and 1. The power absorption
coefficient is 1 over the frequency range. This concludes that the hypothesis
is correct and there is a relation between the power absorption coefficient and
electrical impedance testing to identify damage in composites.

The goal is to eventually to identify damage in
composite materials by electrical impedance testing with the power absorption
coefficient to identify damage in composite materials. With this research it
can be concluded, that it is possible to identify damage in composites with
this method.

RECOMMENDATIONS

To be able to identify damage in composites, it is recommended to perform
the experiments differently. The test method and the number of tests are not
sufficient enough in the research of Grafen 2
to identify damage in composites. The following changes are recommended:

Grafen 2 had performed
experiments with two damaged test plates with different delamination. To see if
there is damage present in the composite structure, it is recommended to
perform experiments on the composite structure in undamaged and damaged state. Then
the power absorption coefficient can be analyzed to see the difference of a damage
and un-damaged composite structure. The
force and the velocity have been measured at one excitation point in the experiments
of Grafen 2. It is recommended to measure the force and the
velocity and different excitations points on the test plate. This means that
the PZTs must be attached on different points on the test plate. Every
excitation point has a different influence in the outcome of the efficiency to
determine the power absorption coefficient.  It is recommended to repeat the tests multiple times
and to determine the average values of the measurement results. This is an
important factor because it gives a degree of certainty about the measurement
results and it provides more reliable results.

ACKNOWLEDGEMENTS

This research was supported by R. Loendersloot. We
would like to show our gratitude to R. Loendersloot for sharing his pearls of
wisdom with us during the course of this research and not to forget also his
guidance and feedback.

We would also like to thank L. Grafen for her time and
explanation of her work. And at the end, we would like to thank Y.H. Wijnant
for explaining his theory on the sound absorption coefficient.

REFERENCES

1

M. Niu,
Composite airframe structures, Hong Kong: Hong Kong Conmilt Press Limited,
2010.

2

L. N.
Grafen, “The use of electrical impedance in the identifying of
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2017, 227-233, Enschede, 2017.

3

Y. H.
Wijnant, E. R. Kuipers and A. De Boer, “Development and application of a
new method for the insitu,” in Proceedings of 24th International Conference
on Noise and Vibration Engineering, ISMA 2010, 1-14, Leuven, Belgium, 2010.

4

M. Oomen,
Master Thesis: Non destructive testing using power absorption, Enschede:
University of Twente, 2013.

5

A. van
Dijk and B. van Dijk, “Determine the severity of the delamination inside a
composite by analysing impedance,” in Proceedings of the Academic 2017,
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6

G. Park
and D. Inman, “Structural Health Monitoring using Piezoelectric Impedance
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7

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and L. Y. Y. , “Fatiuge damage diagnosis and prognosis using
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(SHM) in Aerospace Structures, Elsevier Woodhead Publishing, Philadelphia,
2016.

8

Y. H.
Wijnant, E. R. Kuipers and A. De Boer, “An alternative coefficient for
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