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Composite materials, by nature, are universally dielectric. The distribution of the phases, including voids and cracks, has a major influence on the dielectric properties of the composite materials. The dielectric relaxation behavior measured by Broadband Dielectric Spectroscopy (BbDS) is often caused by interfacial polarization, which is known as Maxwell-Wagner-Sillars polarization that develops because of the heterogeneity of the composite materials. A prominent mechanism in the low frequency range is driven by charge accumulation at the interphases between different constituent phases. In our previous work, we observed
*in-situ* changes in dielectric behavior during static tensile testing, and also studied the effects of applied mechanical and ambient environments on composite material damage states based on the evaluation of dielectric spectral analysis parameters. In the present work, a two dimensional conformal computational model was developed using a COMSOL
™ multi-physics module to interpret the effective dielectric behavior of the resulting composite as a function of applied frequency spectra, especially the effects of volume fraction, the distribution of the defects inside of the material volume, and the influence of the permittivity and Ohmic conductivity of the host materials and defects.

The applications of composite materials are now widespread because of their various advantages over conventional isotropic materials. These heterogeneous material system’s properties can be tailored based on the needs of the application and design. Aerospace and automotive industries are using composite materials to reduce weight to increase fuel efficiency, and also for energy storage and structural stability. The automobile Company Volvo has developed structural composite materials which can store and discharge electrical energy while also being used as a car body structure, fabricated from carbon fibers and a polymer resin [

It is necessary to understand the material state changes caused by applied mechanical, thermal, and electrical fields to design and synthesize an effective material system. These complex material systems degrade progressively under combined applied field conditions. To evaluate such material state changes there are many computational tools and methods but most of them do not give a direct and quantitative assessment of the damage state. Numerous experimental techniques and methods have also been developed to measure such material state changes but most of them do not give a direct and quantitative assessment of the damage state.

During the service life of composite materials many degradation processes occur and generally this degradation initiates and evolves by microdamage development, especially matrix microcracking and crack growth, delamination, fiber fracture, fiber-matrix debonding, and microbuckling [

Broadband Dielectric Spectroscopy (BbDS) measures the interaction of EMF with a material system over a wide range of frequencies which is shown in

Various researchers have used finite element methods (FEM) to model the effective dielectric properties of periodic and random composites containing inclusions of various shapes [

COMSOL Multiphysics^{TM} for conformal modeling, and to reduce the complicacy of the model we only considered the interfacial polarization which is caused by the permittivity and conductivity difference between two constituents. We assumed that the composite materials were homogeneous, and represented defects/cracks as inclusions as shown in

In classical dielectrics the relation between the applied electric field E and the dielectric displacement D is linear and can be expressed as [

where,

If ρ is the charge density, from Maxwell’s equations we know that the dielectric displacement follows the following relationship

For current density J we can state the following from the continuity equation

From also Ohm’s law we know

Here

So from equations (2) and (3) we obtain

Now using 1, 4 and 5 we can write the following

In case of a sinusoidal applied electric field E of angular frequency

We know

From equation (7) and (8) we get

From equation (9), we can tell that in a heterogeneous material the product of the physical properties (some form of the conductivity and permittivity) and the slope of the potential must be a constant as we cross material boundaries. For the quasi-static case with harmonic input fields, the gradient of that product vanishes. The interacting field is a result of the charge difference at the interface, and unless the conductivity and permittivity of adjacent material phases are identical, there is a disruption of charge transfer at the material boundary which results in internal polarization.

To solve equation (9), we set the potential on the top electrode to be,

And on the bottom electrode,

Boundary conditions on the interfaces are,

where

here

For this model, an undamaged composite material is considered to be a homogeneous material and the cracks (here as circular inclusions) are considered to be the second phase inside of that homogeneous material system. Permittivity and ohmic conductivity of the host material were taken to be

Computer simulations were performed for different volume fractions of the inclusions.

For different volume fractions of inclusion, the real part of the permittivity was calculated from the computer simulation for a frequency of 10 Hz.

Composite materials are filled with various additive materials to achieve the desired mechanical, thermal and electrical properties. Typical filler materials used for the present modeling are carbon or glass fibers. The use of these fibers as filler materials introduces a water sensitive component into the polymer composites. Glass fibers are well known for their water affinity on their surfaces. Currently, epoxies are widely used matrix materials in

composite industries, which also have the potential of being sensitive to moist conditions or humid environments. Soles and Yee [

There are many theories about the state of water molecules in polymers. Adamson [

Water has a higher dielectric permittivity and conductivity than the glass fiber and matrix, so it has strong effects on the dielectric properties, i.e. relative permittivity and dielectric loss, of the material system. In the literature it is well established that water absorption increases the dielectric constant of the dielectric material [

When composite materials go through degradation processes, microcracks typically form and these micro- cracks can also be filled with moist air, and condensed or adsorbed water layers can form on the surface of those defects. In our two phase model we saw an interfacial polarization (Maxwell-Wagner-Sillars polarization) that is present in the low frequency region of the frequency spectra. If a water layer is present on the surface of the defect it will become electrically conductive. Since the host material and defect have low electrical conductivity and permittivity is not significantly high, this will give rise to interfacial polarization.

For the tri-layer model, the total volume fraction is the sum of the volume fraction of the defect and the volume fraction of the conductive layer. For all of the cases of tri-layer modelling, the conductive layer thickness was specified as 0.5 micro meter. We observed that for two phase models, the real part of the permittivity was almost linear but in

It is also clear from

As shown in

Dielectric loss (the imaginary part of the permittivity) also varies with volume fraction and it is illustrated in

The corresponding Cole-Cole plot,

A distributed damage model was created to see the effect of the distribution of the damage. A dielectric study was performed for a certain volume fraction of inclusion, and then that inclusion was divided into 10 inclusions while keeping the total volume fraction the same.

Figures 23-26 show the change of dielectric properties of a single damage volume and distributed damage volumes with the same amount of volume fraction without any conductive layer around the defects. The dielectric loss increased for the distributed damage because of the presence of more interfacial polarization.

Figures 27-29 show the change of dielectric properties of a single damage phase and distributed damage with the same amount of volume fraction with a conductive layer around the defect. The dielectric loss increased for the distributed damage because of more interfacial polarization and it is more evident than the prior case because the conductive layer around the defect leads to increased interfacial polarization.

The difference between the static permittivity and the limiting high frequency dielectric permittivity is called the Dielectric relaxation strength (DRS),

where,

In this paper, we have demonstrated a computational model to predict global dielectric property changes caused by increasing defects inside of a materials system. We show that the dielectric character of the defects, their volume, and the morphology of the defect surfaces play an important role in the overall dielectric properties of the materials system during degradation. The data presented here also demonstrate the possibility of using dielectric properties to model and interpret the progressive damage of heterogonous materials systems.

In general, we have shown that the dielectric properties of heterogeneous systems are influenced by various physical factors: electrical and structural interactions between particles, heterogeneity of morphological and electrical properties of the constituent phases, frequency dependence of electrical phase parameters, intra-parti- cle structure, particle shape, size, orientation and, volume and surface fraction of the constituent phases. This dependence complicates the determination of the electrical parameters of heterogeneous materials from the observed global dielectric relaxation spectra, but also presents us with an opportunity to recover important information not only about the electrical and structural properties of constituents but also about the interactions between constituents, including the parent materials and damage phases. Further theoretical and experimental investigation is required to fully understand the changes in dielectric spectra associated with many of the specific damage accumulation events and local details in heterogeneous material systems.

From the results presented in this paper, it can be concluded that analysis of the dielectric data gives us information about the type of material state changes throughout the mechanical life of a composite material. It should be emphasized that these changes in the dielectric properties are distinct and measurable changes in material state, and that they are caused by a non-conservative, non-equilibrium material response to the applied fields. Opportunities for further understanding include the identification of the material and physical limitations of this method of characterization, e.g., specimen size, material property ranges, and specimen shapes that are most and least suited to the approach. A robust study of the interpretation of dielectric data associated with specific damage modes and details is also needed.

RasselRaihan,FazleRabbi,VamseeVadlamudi,KennethReifsnider, (2015) Composite Materials Damage Modeling Based on Dielectric Properties. Materials Sciences and Applications,06,1033-1053. doi: 10.4236/msa.2015.611103