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. INTRODUCTIONA fiber reinforced composite laminate is made up ofseveral layers of orientated plies.

Failure of one ply affects the stiffnessand remaining strength of the composite laminate but does not result in totalfailure. The failure modes of composite material include compressive, tensileor shear fracture of the matrix 1. Most of the time inpractice composite fail due to impact damage 1. The problem is thatthe human eye cannot identify the internal damage in composite materials. Thismakes it difficult to determine the structural integrity of the compositematerials after impact damage. Investigating damage in composite materials canbe in form of mechanical failures as internal delamination or cracks 1. It isimportant to be able to identify the internal damage in a composite, forexample, for cost reduction by minimizing the inspection time and effort tocheck for failures.

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There is a methodology to identify damage in compositematerial by using electrical impedance testing. Grafen 2 has made a linkbetween electrical impedance testing and the sound absorption theory of Wijnant3to identify damage in composite materials. From the sound absorption theory ofWijnant 3,the power absorption coefficient can be determined. The power absorptioncoefficient ? can have a relationwith electrical impedance testing to identify damage in composites.ObjectiveThis research is an addition to the study of Grafen 2. Grafen conducted aresearch 2by testing two similar composite plates (PEKK/AS4D) with different internalfailures. When comparing the test results with the theory of Wijnant 3, the results werenot as expected. According to the test results of Grafen 2, the powerabsorption coefficient was not between 0 and 1.

Physically it would imply thatthe power absorption coefficient should be between 0 and 1 3. The amount ofenergy can be fully reflected and not more. The other way around no less thanno energy can be reflected. Therefore, the power absorption coefficient shouldbe between 0 and 1.

The objective is to identify the main reason why the testresults of Graven 2deviate from the theory of Wijnant 3,hence to answer the question:  “What is the main reason that the power coefficient (?) is notbetween 0 and 1 in the research of Grafen?”HypothesisThe expectation is that there is a relation betweenthe power absorption coefficient and electrical impedance. If there is arelation, then the absorption coefficient must be between 0 and 1.THEORETICALBACKGROUND Oomen 4 showed that the power absorption coefficient can be used as anindicator to identify damage in composite materials. Oomen 4 also showed that thepower absorption coefficient can be used to detect damage as an experimentalvalidation. For the experiments 4,a composite plate (Carbon/PPS) was used. The experiments were based on measuringthe electrical impedance of a composite structure. Originally, the soundabsorption theory of Wijnant 3is based on acoustic impedance experiments. It isimportant to state that in the acoustic impedance experiments, waves were propagated into a non-solid material.

This willresult into longitudinal waves. It this situation, which is based on electricalimpedance experiments, waves were propagated into asolid material. This will result into a combination of longitudinal wavesand shear waves. This research will focus on the relation between the powerabsorption coefficient and electrical impedance testing. Powerabsorption coefficientWijnant 3defined an absorption coefficient, which is based on a new definition ofincident power.

In this method, the incident intensity is defined as the timeaverage value of the positive values of the instantaneous power 3. If the soundpressure and particle velocity in a certain direction are known, then the totalintensity can be determined. For plane waves, this quantity is the sum of theincident- and reflected sound intensity in that direction 3.

The incident- andreflected intensity can be determined with active intensity. In theresearch of Oomen 4a novel absorption coefficient is defined that used a point force exerted onthe system and the velocity of the system at the excitation point. This iscalled the power absorption coefficient. Thedefinition of the power absorption coefficient ? is defined as:                              (1)where  denotes theincident (input) power and  denotes the nettactive power. The nett activepower is the time-averaged power, defined as the product of the force and thevelocity.

In the same manner, voltage and current can be used in the electricaldomain to determine the electrical impedance 4.In the mechanical domain the force and the velocity can be measured at anexcitation point to obtain the instantaneous power. Determining the fraction ofnett active and input power will result in how much power is absorbed. ElectricalimpedanceImpedance is a property used in many methods for Non-DestructiveTesting 5.

Non-Destructive Testing is a research area in which methods aredeveloped and used to detect damage before failure occurs. Impedance shows thefrequency dependent resistance and is the ratio of voltage over current 5. This is called theelectrical impedance. To measure the electrical impedance of the compositeplate, an input signal with a certain value must be sent through the materialby piezoelectric transducers (PZTs), which is attached to the structure. Theelectrical impedance responses of the piezo-electric materials make it possibleto obtain the mechanical properties of the structure, and therefore damages canbe detected 6.

PZT is capable of converting electrical energy into mechanical energy and viceversa 7.METHODOLOGYTo be able to answer the main research question a theoreticalresearch must be conducted on the deviant ?.And the necessary equations to determine the power absorption coefficient mustbe researched, analyzed and implemented correctly in the Matlab code to achievea ? between 0 and 1.   From the instantaneous power, the active power  and reactivepower  and a powerratio PR can be determined 4, 8:                            (2)                            (3)                           (4)Where Fdenotes the force, denotes the complex conjugate of V,  denotes the real part and  denotes the imaginary part. PR is the power ratio between the activepower and the amplitude of the instantaneous power.

PR is a ratio and should be between 0 and 1 and therefore is alwaysa positive value. This means that  should also be a positive value. The nett activepower  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 intothat ? willbe 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 withthe measurement data in Matlab to determine the power absorption coefficient. Theinput measurement data are signals in the time domain for force and velocity. Toplot  in thefrequency domain, the measurement data are processed in Matlab with a FastFourier Transformation (FFT).

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

Fig. 1: Matlab results of ,   and .The expected result was that the power absorptioncoefficient must be between 0 and 1. The power absorption coefficient ? for the two frequencies is approximatelyequal to 1, because the nett active power  and theincident (input) power   are in phase and therefore the power is alwayspositive. This means that  and  are equal,which results that ? is 1. This meansthe amount of energy that goes into the test plates is completely absorbed.

Infigure 1 can also be seen that and  have an equalamplitude at any frequency value. These two waves oscillate together and theirfunction reach a 0 value for the same frequency value and these are both in thepositive side of the graph. This results in a resonance betweenand . ? is 1, this means the amount of power that is put inat the excitation point is equal to the amount of power dissipated.

So the PZTis placed on a location where the amount of power is fully absorbed. When thecomposite structure is excited in a resonance frequency, the power is absorbedefficiently and the power absorption coefficient will be 1. This is also the casehere and this proves the hypothesis is correct. This concludes that there is arelation between the power absorption coefficient and electrical impedancetesting to identify damage in composites.According to Grafen 2,the study of van Dijk & van Dijk 5 was based on theexpectation that a delamination in a composite would absorb all the energy andnot reflect any energy.

In figure 1, it can be seen that this is the case andthe expectation is met in this research.CONCLUSIONThis research aimed to answer the question on what themain reason is that the power coefficient ?is not between 0 and 1 in the research of Grafen 2. The main reason wasan error in the implementation of the equations to determine the powerabsorption coefficient in the Matlab code. By analyzing and implementing theequations of the power absorption coefficient correctly in the Matlab, results that? is 1 over the frequency range. Thismeans the amount of energy that goes into the test plates is completelyabsorbed.  The hypothesis was that there is a relation between thepower absorption coefficient and electrical impedance.

If there is a relation,then the absorption coefficient must be between 0 and 1. The power absorptioncoefficient is 1 over the frequency range. This concludes that the hypothesisis correct and there is a relation between the power absorption coefficient andelectrical impedance testing to identify damage in composites.The goal is to eventually to identify damage incomposite materials by electrical impedance testing with the power absorptioncoefficient to identify damage in composite materials. With this research itcan be concluded, that it is possible to identify damage in composites withthis method.RECOMMENDATIONSTo be able to identify damage in composites, it is recommended to performthe experiments differently. The test method and the number of tests are notsufficient enough in the research of Grafen 2to identify damage in composites. The following changes are recommended: Grafen 2 had performedexperiments with two damaged test plates with different delamination.

To see ifthere is damage present in the composite structure, it is recommended toperform experiments on the composite structure in undamaged and damaged state. Thenthe power absorption coefficient can be analyzed to see the difference of a damageand un-damaged composite structure. Theforce and the velocity have been measured at one excitation point in the experimentsof Grafen 2. It is recommended to measure the force and thevelocity and different excitations points on the test plate. This means thatthe PZTs must be attached on different points on the test plate. Everyexcitation point has a different influence in the outcome of the efficiency todetermine the power absorption coefficient.  It is recommended to repeat the tests multiple timesand to determine the average values of the measurement results.

This is animportant factor because it gives a degree of certainty about the measurementresults and it provides more reliable results.ACKNOWLEDGEMENTSThis research was supported by R. Loendersloot. Wewould like to show our gratitude to R. Loendersloot for sharing his pearls ofwisdom with us during the course of this research and not to forget also hisguidance and feedback. We would also like to thank L. Grafen for her time andexplanation of her work. And at the end, we would like to thank Y.

H. Wijnantfor 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 delaminations inside composite materials,” in Proceedings of the Academic 2017, 227-233, Enschede, 2017. 3 Y.

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