Effect of spatial distribution of fibers on elastic properties of unidirectional carbon/carbon composites

Carbon/Carbon composites finds its applications in several high temperature applications in the field of Space, Aviation etc. Designing of components or sub systems with carbon/carbon composites is a challenging task. It requires prediction of elastic properties with a very high accuracy. The prediction can be normally done by analytical, numerical or experimental methods. At the design stage the designers resort to numerical predictions as the experimental methods are not feasible during design stage. Analytical methods are complex and difficult to implement. The designers use numerical methods for prediction of elastic properties using Finite Element Modeling (FEM). The spatial distribution of fibers in matrix has an effect on results of prediction of elastic constants. The generation of random spatial distribution of fibers in representative volume element (RVE) challenging. The present work is aimed at study of effect of spatial distribution of fiber in numerical prediction of elastic properties of unidirectional carbon/carbon composites. MATLAB algorithm is used to generate the spatial distribution of fibers in unidirectional carbon/carbon composites. The RVE elements with various random fiber distributions are modeled using numerical Finite element Model using ABAQUS with EasyPBC plugin. The predicted elastic properties have shown significant variation to uniformly distributed fibers.


Introduction
Carbon/Carbon composites finds its applications in several high temperature applications in the field of Space, Aviation; Air craft brakes, discs etc. Designing of components or sub systems with carbon/carbon composites is a challenging task. It requires prediction of elastic properties with a very high accuracy. The prediction can be normally done by analytical, numerical or experimental methods. At the design stage the designers resort to numerical predictions as the experimental methods are not feasible. Analytical methods are complex and difficult to implement. The designers use numerical methods for prediction of elastic properties using Finite Element Modeling (FEM). The spatial distribution of fibers in matrix has an effect on elastic constants. The generation of random spatial distribution of fibers in representative volume element (RVE) is challenging. The present work is aimed at study of effect of spatial distribution of fiber on elastic properties of unidirectional carbon/carbon composites. MATLAB algorithm is used to generate the spatial distribution of fibers in unidirectional carbon/carbon composites.
Aram bahmani et al. [1] [13] presented a method to enhance strength and toughness using heat-treated interface modification for carbon/carbon composites. Lei Yang et al. [14] presented a method based on random sequential expansion for generation of random fiber distribution of fibers in fiber reinforced composites. Hai Qing et al. [15] performed two dimensional finite element simulations in metal matrix composites using silicon carbide reinforcement in aluminum alloy for evaluation of damage and deformation. WeijianGe et al. [16] the proposed a method for spatial random distribution of fibers based on iterative improvements with high volume fraction. Chao et al. [17] performed Micromechanical modeling of unidirectional composites. The authors have performed modelling with random fiber and interphase thickness distributions.Bo Cheng Jin et al. [18] has numerically created representative volume elements of unidirectional random filaments and fibers using PYTHON.The author has used modified random sequential adsorption for increasing the volume fraction of fibers.Venkata et al. [19] have compared the values of elastic constants evaluated by using analytical method and numerical methods. Some authors have studied analytical methods for evaluation of elastic properties [20].
In the present work the Effect of spatial distribution of fibers on numerical prediction of elastic properties of Unidirectional Carbon/Carbon composites is evaluated. The elastic properties are evaluated through numerical homogenization methods with uniform and random distribution of fibers. The random distribution is repeated for 10 iterations. The elastic properties evaluated using uniform distribution of fibers are compared with that of random distribution of fibers.

Objective
The objective of the current study is to study the effect of spatial distribution of fibers in unidirectional Carbon/Carbon composites on prediction of elastic properties. The steps involved are − Create the iterations with uniform distribution and random fibers distribution using MATLAB [21] code − Create Representative volume elements (RVE) for uniform and random distributions using ABAQUSCAE − Perform post processing to evaluate elastic properties of carbon/carbon composites FEM using EasyPBC plugin [22]. − Compare elastic properties of from FEM using models of uniform distribution and random distribution.

Development of iteration through MATLAB algorithm
A MATLAB algorithm was developed to generate the iteration with random distribution of fibers. The developed code required inputs such as radius of the fiber, side length of the RVE and volume fraction. The code developed performs its intended function in three steps. In first step it creates a hard model with uniform distribution of fibers. The second step includes the random removal of fibers to achieve the desired the volume fraction of the fibers. The third step is stirring of the fibers. The MATLAB algorithm output include various iteration of random fiber distributions. The present study was done with fiber radius of 0.5mm, RVE side length 5 mm and with a volume fraction of 0.5. Ten iterations obtained using MATLAB algorithm were shown in Fig.1 to Fig. 10.

Modelling and Meshing
The output of MATLAB code is used to create geometric model in ABAQUSCAE. The representative volume elements are created with uniform and random distribution of fibers. The carbon fibers are considered orthotropic and carbon matrix is considered isotropic. The properties carbon matrix and carbon fiber [11] for the material were assigned. The properties are given in table 2 and table 3. The RVEs with uniform and random distribution of fibers is given in Fig.11 and Fig.12.

FEM analysis through ABAQUS CAE
The model is then exported to ABAQUS for FEM study to evaluate of elastic properties. The representative volume element is treated a part of periodic material. The RVE homogenization needs uniform strains on for evaluation of elastic properties. Periodic boundary conditions ensure that the deformed surfaces of RVE remain periodic. The periodic boundary conditions are possible to be implemented in Abaqus with EasyPBC plugin. In the present study the elastic properties are evaluated using EasyPBC plugin. The stresses at the boundary conditions for material with uniformly distributed fibers is shown in Fig.13 to Fig. 20.

RESULTS AND DISCUSSION
The effect of spatial distribution of fibers is on elastic constants is evaluated through numerical methods. The Table 4 shows the elastic properties evaluated through various iterations of fiber distribution. Table 5 shows the variation of elastic properties between the random and uniform distributions of UD c/c composite.