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.

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

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2016.

8

Y. H.

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

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