Elastic modulus of 3D carbon/carbon composite using image-based finite element simulations and experiments
Introduction
Multidirectional C/C composites are attractive for making parts of structures that need to withstand multidirectional mechanical and thermal stresses. In literature, micro-mechanics has been used to determine the properties of these composites from known constituent’s properties [1]. The 3D reinforced C/C composites are commonly used in aerospace applications, such as rocket engines, nose cones and re-entry heat shields and their properties depend on factors such as fiber architecture, fiber volume fraction, interfacial properties, and internal damage. It is generally observed [4], [5], [6], [7] that C/C composites have significant damage in the form of matrix and interfacial cracks, voids and distortion of the bundles, etc. This damage originates in C/C composites during manufacturing process due to matrix shrinkage and high thermal stresses generated due to the mismatch between coefficients of thermal expansion of bundle and matrix. These complexities of C/C composites make it difficult to determine their properties using analytical methods. The analysis of the structure made of these composites at full scale by considering the heterogeneity and defects in the composites is computationally expensive and difficult to solve. In general, the structure is considered homogenous at structural length scale and heterogeneous at the microstructure level. The equivalent energized homogeneous properties of the composite for structural analysis are derived from the unit cell analysis. The unit cell is a repeated or periodic volume element of the composite, which can reproduce the whole composite structure by translation or reflection. This is analyzed for six individual load cases to determine the equivalent material properties. A systematic implementation of unit cell analysis with asymptotic homogenization and periodic boundary conditions is done by Rao et al. [2], [3]. Rao et al. [2] included the effects of damage due to processing temperature by modeling the fiber bundle/matrix interfaces of C/C composites by cohesive elements and degrading the properties of matrix using an isotropic damage variable. The interfacial properties such as debond stress and fracture energy release rate for cohesive interaction between the bundle/matrix interfaces were taken from literature [8]. Here, we perform pull-out tests, shear lag analysis [9], [10], [11], [12] and finite element (FE) simulations to determine the interfacial properties. In the past, Hatta et al. [13], [14], [15] have conducted a series of experiments on 2D and 3D orthogonal C/C composites to study the influence of the interfacial strength for the tensile, compressive and shear loadings. Aoki et al. [16] developed the fiber bundle push-out and pull-out test setup for interfacial characterization of the 3D C/C orthogonal composite at room as well as elevated temperatures.
C/C composites also have damage in the form of imperfections like voids and distortion of bundles. These imperfections can be considered directly in the analysis by obtaining the FE mesh from X-ray tomographic images. Many applications of this approach for reconstruction of FE mesh are found in the area of biomechanics, metal matrix composite, foam, and cement paste [17], [18], [19], [20]. Ali et al. [21] simulated the tensile test on plane woven C/C composite by reconstructing an image-based unit cell, which was then analyzed to determine the homogenized modulus using finite element method. The mechanical properties used for the constituents were determined by nanoindentation test. Sharma et al. [22] studied the effect of the variation of microstructure on the mechanical properties of C/C composite by reconstructing FE mesh form X-ray tomographic images and using asymptotic homogenization with periodic boundary condition to determine the mechanical properties. The interfaces between the bundles and matrix were assumed perfectly bonded. Later, Sharma et al. [7] have performed such image-based FE simulations of the fiber bundle push-out tests to obtain the interfacial properties of bundle/matrix interface. Vorel et al. [23] reconstructed the statically equivalent unit cell for plain weave C/C composite from X-ray tomography to determine the thermal properties.
In the present study, X-ray tomography was used to explore the microstructure of C/C composite and to introduce the observed features in FE meshes. In future, we refer to the analysis based on these meshes as image-based analysis. Pull-out tests were performed for interfacial characterization of bundle/matrix interface and the interfacial parameters were obtained by fitting the experimental data to shear lag model (Kerans and Parthasarathy (K–P) [10]). The interfacial properties obtained from the shear-lag model were used as an initial guess for image-based FE simulation of pull-out tests to determine the properties of frictional cohesive interactions at bundle/matrix interface. The properties obtained for frictional cohesive interactions were used in the unit cell simulations to obtain the homogenized elastic moduli. Finally, the tensile tests were conducted to determine the elastic properties of the composite experimentally. These values were compared to that obtained from simulations.
Section snippets
Material
The 3D orthogonal hybrid architecture consisted of rectangular bundles in x and y directions and circular rods in the z-direction. The rods were made of 15,000 fibers and rectangular bundles contained 25,000 fibers approximately. C/C composite under investigation was prepared by using pitch based technique for matrix impregnation. In the fabrication process of C/C composite, the preforms of the fiber were prepared, stacked and then impregnated with matrix followed by densification cycles. A
Pull-out test
This section on pull-out test is divided into two parts; experiments and simulation. In the experiments the fiber bundle was pulled out of composite and interfacial parameters such as coefficient of friction, debond shear stress, and fracture energy release rate were determined by fitting the data of load displacement curve to the shear-lag model of K–P [10]. Later, the experiments were simulated using image-based FE meshes with frictional cohesive surfaces to represent the bundle/matrix
Homogenization
The equivalent homogeneous moduli of C/C composite were determined by simulation of the uniaxial tension test and these were validated by conducting uniaxial tension tests. The details of the simulations are discussed in next section.
Conclusions
The imperfections in the C/C composites such as cracks, voids and distortions of the bundles originate during the manufacturing process have been explored using X-ray tomography. In past, studies on the properties of C/C composites are either based on the idealized microstructure or assumption of perfect bonding at the bundle/matrix interface. These limitations have been partially overcome in the present study by reconstructing the microstructure from tomographic images and modeling of the
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