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 10 Hz up to 0.5 MHz revealed a strong correlation between the level of damage and the hysteresis of the studied materials.
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 [
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 [
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 [
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 [
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.
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
Sonication process.
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 mm3 were removed from the mould and postcured at 120°C for 4 h.
Prismatic specimens of 60 × 100 × 4 mm3 were cut from the plates using a water lubricated table diamond saw (Figure
(a) Specimen geometry and (b) final specimen.
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.
For the purposes of electrical measurements, electrodes were attached at the side surfaces (left and right surface, as seen in Figure
Impedance spectroscopy was performed using a dielectric spectrometer-frequency spectrum analyser (DETA-SCOPE L1 provided by Advise Ltd.) (Figure
Experimental setup for the IS measurements.
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.
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
The Bode plots, that is, magnitude of impedance or phase delay versus frequency, can be seen in Figures
As can be seen in Figure
Bode plot-impedance magnitude versus frequency.
arg
Nyquist plot for the three specimens.
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
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 (
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:
This behavior can be attributed to the decrease in the dielectric constant of the specimen due to microcracks. In detail, capacitance is expressed by
Also the relative permittivity of the air
This can be easily distinguished in Figure
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
Equivalent RC circuit: R and C versus number of thermal shock 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.
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.
The authors declare that there is no conflict of interests regarding the publication of this paper.
The authors acknowledge the “THALES-GSRT ID I.D: 593 Mis: 379412” and “ACP3-GA-20l3-6054l2-HIPOCRATES” research programs for financial support.