Study of the Effect of Damage on the Electrical Impedance of Carbon Nanotube Reinforced Epoxy Nanocomposites

Within the scope of this work is the study of the effect of damage on the electrical hysteretic behaviour of carbon nanotube (CNT) reinforced epoxy nanocomposites. For that purpose CNT reinforced epoxy nanocomposites were subjected to different levels of damage and their response to an AC voltage excitation was monitored. The correlation between frequency dependent impedance properties and level of damage was extensively studied. The AC frequency response of the interrogated specimens from 10Hz up to 0.5MHz revealed a strong correlation between the level of damage and the hysteresis of the studied materials.


Introduction
Coupled property interaction in engineering structures may administer multiple functionalities.In order to exploit coupled field interaction for application such as structural health monitoring (SHM), an in depth understanding of the principles that relate structural integrity to internal properties is indispensable.Typical example is the electromechanical coupling which relates electrical properties to the mechanical response and/or the durability of the structure in the case of composites reinforced with a conductive phase such as carbon nanotubes (CNTs).
Due to their unique structure and excellent electrical and mechanical properties, CNTs have attracted wide attention as multifunctional nanofillers for polymer based nanocomposites [1][2][3][4][5][6].On the other hand, epoxy resins are well established as the matrix of advanced composites for several engineering applications, as they offer satisfactory specific stiffness and strength as well as durability.During the past decade, epoxy resin-based CNT composites were extensively studied by many researchers for their electrical properties [7][8][9][10][11].These composites could potentially, among others, be used for conductive coatings, electrostatic dissipation, electrostatic painting, and electromagnetic interference shielding applications.
As aforementioned, electrical properties act as a potential indicator for the evaluation of composite's structural integrity.Numerous researchers attempt a direct correlation between the inherent structural integrity and the variation of electrical properties.Whilst reversible changes in the electrical properties relate solely to strain, irreversible electrical resistance change relates to internal damage of the composite material [12][13][14][15][16][17].In a typical study, the structural integrity of a hybrid Carbon Fiber Reinforced Polymers (CFRPs) with MWCTs in the matrix material was evaluated concurrently with the self-sensing abilities of the composite [18].The underlying principle of self-sensing relates to a percolated electrical network within the insulating matrix which works as an inherent sensor in the composite structure.As a result, any changes in this electrical network of nanocomposites and CFRPs, when subjected to load, provide a direct measure for strain (reversible) and damage accumulation (irreversible).
More recently, the CNT dispersion in typical epoxy matrices process has been successfully related to the impedance of the system and has been modelled using an equivalent electrical circuit [19,20].However, little research effort has been devoted to the study of the impedance properties of nanoreinforcement composites and its relation to loading history and/or internal damage.Impedance spectroscopy (IS) may be employed as a method for damage characterization and could provide useful information about the internal integrity of the material.It may be argued that damage (e.g., manifested as microcracks or hydrolysis in the case of an epoxy subjected to mechanical or environmental loading, resp.) may cumulatively increase the hysteretic behaviour of the material, as it increases its capacitance.IS is a dynamic technique where a monochromatic signal, involving the single frequency V = /2, is applied through a material volume and measuring the resulting phase delay and amplitude of the resulting current.Using this method, researches achieved a correlation between IS measurements and the internal integrity of several composite materials [21,22].Fazzino et al. [23] have successfully characterised progressive damage initiation and progression in thin woven glass/epoxy composites using IS.They reported a noteworthy sensitivity, especially during the first 25% of fatigue life fraction.Kang et al. [17] developed an electric model for a SWNT/PMMA sensor, by correlating the electrical impedance properties to the nanocomposite processing including the functionalization, dispersion, and annealing of the nanotubes.In another work, Pohl et al. [24] employed the IS as a tool for structural health monitoring of smart CFRP structures.They managed to detect damage (delamination) due to low-velocity impact by monitoring changes in the magnitude of the impedance over a wide frequency range.Peairs and coworkers [25] showed that impedance-based techniques are capable of the in situ structural health monitoring of the space shuttle ground structure.They focused on the optimization of the sensor frequency range in order to ensure maximum sensitivity for correlation with the integrity of the interrogated structure.
The main purpose of this study is to enhance the resolving ability of the electrical based methodologies via the employment of AC configurations.These involve the study of the effect of damage on the hysteretic electrical behavior of carbon nanotube reinforced epoxy nanocomposites by measuring phase delays at several frequencies varying from 10 Hz up to 0.5 MHz of AC voltage for different levels of cyclic thermal shock damage.
The behaviour of the composite after cyclic thermal shock exposure is of primary importance in high performance structures, such as those encountered in the aerospace industry where advanced composites continuously gain higher market share.Typically, an aircraft structure is subjected to a thermal shock cycle for every landing and take-off procedure.Under these conditions, the aircraft is subjected to temperature extremes ranging from approximately −30 ∘ C to 30 ∘ C in a period of 15 min [26].On the other hand, new aircrafts such as the Dreamliner possess a fully composite fuselage [27].In a typical composite system, thermal shock is expected to create internal defects in the structure mainly due to the differential thermal expansion coefficient between the reinforcement and the matrix, additional to any degradation independently caused to the constituent phases [28].In a recent study, it was suggested that thermal shock induced damage in CNT reinforced epoxies is manifested as deterioration of the interface due to thermal stress concentration around the CNTs [29].In order to detect and quantify thermal shock induced damage, IS was employed using a typical frequency spectrum analysis setup in order to assess the AC frequency dependence of damage and attempt the simulation of its evolution with a simple equivalent electrical circuit.

Experimental Section
2.1.Materials.The matrix material consisted of a two-part epoxy resin, that is, Araldite LY 564 and Aradur 2954 by Huntsman Advanced Materials, Switzerland.The mix ratio was 100 : 35 by weight.As reinforcement, Multiwalled Carbon Nanotubes (MWCNTs) supplied by ARKEMA, France, were used.They were synthesized by Catalyzed Chemical Vapor Deposition (CCVD); the tube diameter ranged from 10 to 15 nm and the tube length was more than 500 nm.

Processing of the Nanocomposites: Sonication.
Efficient dispersion quality of the CNTs in the epoxy matrix was achieved via sonication using an ultrasonic mixer (UP400S, Hielscher).CNTs and Araldite LY 564 resin were carefully weighed and mixed together in a beaker.An ice bath was also used so as to avoid overheating of the polymer resin and introduction of defects on the CNTs surface (Figure 1).CNTs were dispersed in the matrix using sonication for 4 h at 100% of the full amplitude of the probe, that is, 400 W.
At the end of the sonication process, the hardener was added to the modified resin and the mixture was mechanically stirred for approximately 10 min.Prior to casting, the mixture was degassed for another 10 min in a vacuum oven at 25 ∘ C for another 10 min.Finally, the mixture was cast to silicon rubber moulds and cured at 60 ∘ C for 2 h.The square plates of approximately 150 × 150 × 4 mm 3 were removed from the mould and postcured at 120 ∘ C for 4 h.
Prismatic specimens of 60 × 100 × 4 mm 3 were cut from the plates using a water lubricated table diamond saw (Figure 2).Finally, the specimens were lightly sanded in order to (i) remove defects from the manufacturing process and (ii) prepare the side surface for the application of the measuring electrodes.

Testing Procedure
2.3.1.Cyclic Thermal Shock.All specimens were subjected to several cycles of cyclic thermal shock in order to simulate temperature changes which occur to aircraft structures.The interrogated specimens were divided into three groups.The first group consisted of undamaged specimens and was employed as reference.The second and third groups of specimens were subjected to a series of 30 and 70 thermal shock cycles, respectively.Each cycle consisted of the following two steps, executed in sequence: (a) residence for 2 h at a bath containing a mixture of water and ethylene glycol at −30 ∘ C and (b) residence for 2 h at a bath containing plain water as heating medium +30 ∘ C. Transport between the two baths was performed manually in less than 5 s.During the thermal shock cycles, all specimens were sealed in PE bags so as to prevent diffusion of the heating/cooling medium in the polymer matrix.

Impedance Spectroscopy (IS).
For the purposes of electrical measurements, electrodes were attached at the side surfaces (left and right surface, as seen in Figure 2(b)) of the prismatic specimens using silver conductive paste so as to minimise contact resistance and achieve good electrical coupling.
The spectrometer applied a sinusoidal electric excitation waveform of varying frequency and the induced current waveform was recorded.The excitation frequency ranged from 10 Hz to 0.5 MHz.

Results and Discussion
Within the scope of this work is to relate the internal degradation (microcracks) of the material with changes in the impedance spectra using IS.
When the material is subjected to an alternating electric field, the electric dipoles in the material are trying to orient to the direction of the field.As excitation frequency increases, inertia effects prevent the dipoles from following these changes and hysteretic effects are induced manifesting a phase delay between excitation and response signals.As a result, we expect a typical dielectric system to exhibit increasing phase delay with increasing frequency.
Thermal shock, on the other hand, induces cracks in the material due to the mismatch in the thermal expansion coefficient between the epoxy matrix and the graphitic nanoreinforcement; these cracks, which are of the order of the reinforcement, accumulate with increasing number of cycles and affect the impedance of the studied material in a dual fashion: (i) the real part of the impedance or the resistance is increasing as microcracks act as discontinuities in the conductive network created by the dispersed conductive nanophase in the composite and (ii) the imaginary part of the total impedance of the system is altered as microcracks which develop may be regarded as nanocapacitors which cumulatively contribute to the change of the imaginary part of the impedance or the reactance of the system.
Overall, impedance spectroscopy is expected to increase the dimensionality of the electrical methodology by introducing both the real and the imaginary part of the resistance, providing thus more information on the accumulating damage.This is critical for the accurate solution of the inverse problem, where the formulation of governing equations based on observation and/or experiment about any physical problem or system is required.
The sinusoidal electric potential that was applied to the material can be expressed by where the () is the external potential at time ,  0 is the amplitude of the waveform, and  is the radial frequency.The outbound signal is governed by where () is the current at time ,  0 is the amplitude of the outbound signal, and  is the phase delay.The total impedance of the system can be calculated using Ohm's law: where  is the total impedance of the system.Using Euler's relationship, the impedance is represented as a complex number with a real and an imaginary part: with ))) , where   and   are the real and the imaginary parts of the complex impedance, respectively.The Bode plots, that is, magnitude of impedance or phase delay versus frequency, can be seen in Figures 5 and 6, respectively.
As can be seen in Figure 4, the magnitude of the impedance at low frequency increases with increasing number of thermal shock cycles.In all cases, the magnitude of the impedance is constant until approximately 250 Hz, which denotes the transition from Ohmic (linear) to non-Ohmic (nonlinear).This behaviour is consistent with DC resistance measurements, where the resistance is monotonically increasing as the microcracks which are created due to thermal shock destroy the conductive CNT network in the nanocomposite [18].As should be pointed out at this stage, the magnitude of the impedance is highly affected by the presence of internal damage, exhibiting an increase of half an order of magnitude or doubling its initial value, at only 30 cycles of thermal shock, indicating that the impedance magnitude is a highly sensitive damage index.
The Bode plot of the phase delay (Figure 5) indicates an almost identical behaviour in all three cases.All systems exhibit a capacitive pattern where current leads the voltage.There is an initial part where phase oscillates around zero, indicative of an initial DC behaviour, followed by a decrease before reaching a first plateau.This plateau may be regarded as indicative of a dominant time constant at low frequencies, that is, up to approximately 0.5 MHz.
Along with the impedance measure, results show changes in both real and imaginary parts of the impedance with damage.The Nyquist plot, that is, the real versus the imaginary part of the impedance as calculated from (5), can be seen in Figure 6.The experimental Nyquist plot is different from that of a typical RC circuit in parallel, which is a semicircle and possesses a single time constant, but is indicative of a strong capacitance element which is scaled according to the level of damage, as was also suggested by Figure 5.As was also noticed in Figure 5, scanning at frequencies higher than 1 MHz is required for more time constants that may be involved in the behaviour of the material.
More analytically, the frequency dependent part of the impedance or its imaginary part relates to capacitance and inductance properties of the interrogated element when seen as a typical electrical circuit and is expressed by the total reactance of the system:  where  is the total reactance,   is  the inductive reactance,   is the capacitive reactance,  is the radial frequency,  is the inductance, and  is the capacitance.The negative values of the imaginary part of the impedance, or that current leads the voltage, that have been obtained for all cases indicate the presence of capacitance that can be expressed by This behavior can be attributed to the decrease in the dielectric constant of the specimen due to microcracks.In detail, capacitance is expressed by where  0 is  the permittivity of free space and has a value of 8.85×10 −12 C 2 /Nm 2 ,   is the relative permittivity of the material,  is the area, and  is the thickness.The introduction of defects (microcracks) lowers the conductivity of the system; therefore the relative permittivity of the material is changing.The total capacitance of the nanocomposite is then represented by where  is the concentration of the air (voids) inside the material and   is the relative permittivity of the air.Also the relative permittivity of the air (  ) has lower values than the relative permittivity of composite (  ).Thus, capacitance of the system is decreasing.On the other hand according to (7) the imaginary part of the impedance is increasing upon damage.
This can be easily distinguished in Figure 6 where the Nyquist plot of imaginary part versus the real part of the impedance is depicted.As it can be seen there is dramatic increase at approximately one order of magnitude in the imaginary part (-ImZ) of the impedance for the specimen that was subjected to 70 cycles of thermal shock compared with the undamaged one.
Assuming a simple and a typical RC circuit in parallel to simulate the behaviour of the system, we may simulate the induced damage as a function of the capacitance.
In Figure 7 we may see the equivalent resistance and capacitance of the system as a function of the thermal shock cycles.The interpolation was performed using the LEVMW Complex Nonlinear Least Squares software (Copyright: James Ross Macdonald).As can be seen, the resistance of the material is monotonically increasing whereas the capacitance of the system is decreasing significantly with increasing number of cycles.
Overall, it can be seen that IS is potentially a powerful tool for assessing damage induced in nanoreinforced composite materials.Of particular interest are (i) the extreme sensitivity of the system, (ii) the increase in the dimensionality of the problem (i.e., damage may be correlated with both the measure and the phase of the impedance), and (iii) the ability to model primary damage phenomena using simple equivalent circuits.

Conclusions
In this work, the electrical AC response of specimens that were subjected to increasing cycles of thermal shock was monitored.Phase and magnitude of the impedance of the specimen were recorded using a frequency scan from 10 Hz up to 0.5 MHz.
Impedance spectroscopy provided useful information about the internal state of the material.
Results indicate a direct correlation between the degradation of the material and the measure of the impedance, which proved extremely sensitive to the changes invoked in the material microstructure due to thermal shock.
All specimens exhibited an initial DC behaviour until approximately 250 Hz, as well as a capacitance behaviour with a dominant capacitance element at approximately 1 KHz, which scaled with increasing damage.
As was shown, the electrical behaviour of the system may be adequately modelled by simulating it as a simple RC circuit in parallel.Under this assumption, the resistance of the equivalent circuit is monotonically increasing due to the disruption of the conductive CNT network in the material.At the same time, the total capacitance of the material is decreasing as the developed cracks at the nanoscale cumulatively affect the macroscopic capacitance of the material.

Figure 3 :
Figure 3: Experimental setup for the IS measurements.

Figure 6 :
Figure 6: Nyquist plot for the three specimens.

Figure 7 :
Figure 7: Equivalent RC circuit: R and C versus number of thermal shock cycles.