1.1 Research motivation
Fiber composites, because of their superior mechanical performances and light weight properties, have been extensively employed in various applications. This study aims to investigate the mechanical behaviors of fiber composites with three different fiber arrays, i.e., square edge packing, square diagonal packing, and hexagonal packing. The thermal-mechanical properties as well as the damping behaviors of composites are the focus in the paper. It is well known that the micro architecture of the fiber may influence the mechanical performance of the fiber composites. However, the extent of the fiber effect on the behavior of composites which are very crucial to composites design and application has not been studied systematically. In this paper, the micromechanical analytical scheme was employed to model the micromechanical structures of the fiber composites and the overall properties based on different microstructures were discussed.
1.2 Paper review
In the manufacturing process, the fiber composites were usually cured at high temperatures followed by the cooling stage to room temperature. During the cooling, because of the mismatch in the coefficients of thermal expansion of the fiber and matrix together with the mutual constraint effect, the thermal residual stress was induced in the constituents. The magnitude of the residual stress relies on the properties of the fiber and matrix as well as the associated microstructures of the fiber composites, including the fiber shape and fiber packing arrangements. In addition, the formation of residual stress may have influences on the constitutive behaviors of
the fiber composites, especially in the nonlinear range because the nonlinear behavior is highly dependent on the stress states of the composites.
The constitutive behaviors of the composites with different fiber architectures have been characterized by many researchers using either finite element analysis or analytical micromechanical approach [2–7]. Sun and Vaidya [2] use the finite element method to predict the elastic modulus for boron/aluminum by utilizing the periodic boundary conditions which was the salient of the representative volume element (RVE). Furthermore, Zhu and Sun [3] investigated the nonlinear behaviors of AS4/PEEK composites with three different fiber arrays under off-axis loading using finite element approach. It was found that the nonlinear behaviors of the composites were quite sensitive to the fiber packing arrangement. The similar conclusions were also addressed by Hsu et al. [4], who proposed an analytical micromechanical model for simulating the nonlinearity of AS4/PEEK composites subjected to combined transverse compression and shear loading. Orozco and Pindera [5] conducted a micromechanical analysis using the GMC model on the two-phase composites with randomly distributed fibers, indicating that as the number of the refined sub-cells in the unit cell is increased, the behaviors of the composites tend to be that of a transversely isotropic solid. The influences of fiber shape and fiber distribution on the elastic/plastic behavior of metal matrix composites were examined by Pindera and Bednarcyk [6] using the GMC micromechanical model. It was shown that the fiber packing exhibits a substantially greater effect on the responses of the composite materials than does the fiber shape. Pindera et al. [7] investigated the nonlinear behaviors of the boron/aluminum composites subjected to tensile, compressive and off-axis loadings. The thermal residual stress was considered in their analysis in order to explain the differences of initial yielding in tension and compression. The effect of residual stresses on yielding of SiC/Ti plates was also reported by Zhou et al.
[8]. Aghdam et al. [9] accounts for residual stresses, off-axis orientation and the interface condition between fiber and matrix on the constitutive behaviors of SiC/Ti metal matrix composites. However, their analysis is limited to single fiber array (square). A comprehensive review regarding the effect of fiber arrangement on the elastic and inelastic responses of fiber composites was provided by Arnold et al. [10].
In light of the aforementioned investigations, it was suggested that the behaviors of the fiber composites were mainly dominated by the fiber packing arrangements.
However, few studies concerning the influence of the residual stress arising from curing associated with different fiber arrays on the performances of fiber composites have been reported.
Regarding to the damping behaviors of fiber composites, Saravanos and Chamis [11] used the unified micromechanical model to evaluate the damping property of unidirectional fiber composites with off-axis loading. Hwang and Gibson [12]
utilized the finite element approach and the micromechanical strain energy to predict the damping property of the fiber-matrix interphase effects. It was also indicated that for the longitudinal, transverse and out of plane shear loading, material damping does not change much even though the interphase size was increased. In the previous review, most of the efforts were made to understand the basic damping properties of composites from the constitutive behavior of the ingredient in conjunction with the microstructure. However, the vibration damping responses of composite structures built based on the unidirectional composites with different fiber arrays has not been examined comprehensively so far. Although Kaliske and Rothert [13] utilized the GMC model to find the longitudinal damping property of fiber composites and then applied those damping properties to derive the structure modal damping capacity with the different fiber orientation, the microstructure effect on the damping responses was not discussed in their study.
1.3 Research approach
The outline of the thesis and the primary tasks of each chapter are addressed as follows. For the unidirectional composites, the fibers in general are displayed randomly within the matrix. To investigate the fiber array effect, three typical fiber arrangements, i.e., square edge packing, square diagonal packing, and hexagonal packing were assumed in our fiber composites. An appropriate RVE corresponding to each fiber array was selected in the micromechanical analysis where the fiber was considered to be linear elastic with low damping capacity, and the matrix was assumed to be a nonlinear with high damping capacity. By using Aboudi’s GMC micromechanical model [1], the incremental form of the constitutive relations of the composites was established in terms of the constituent properties as well as the geometry parameters of the RVE, from which the thermal residual stress within the ingredients was calculated. After a numerical iteration, the corresponding stress and strain relations of the composites in the presence of thermal residual stress subjected to off-axis loading were generated. The results were compared to those calculated from the composites without taking into account the thermal stress effect, which were presented in Chapter 2.
In addition, the fundamental assumptions in the GMC micromechanical model were examined and compared to the other micromechanical model. The stress and strain curves calculated based on the different micromechanical models were also discussed in Chapter 3.
Moreover, from the GMC micromechanical analysis, the stress-states within each ingredient can be evaluated properly. Based on the results, the damping capacity of the unidirectional composites with simple loading can be obtained using energy dissipation concept. With the damping capacity of the unidirectional
composites with different fiber arrays, the vibration damping properties of the composite structures can be calculated from the FEM analysis together with the energy dissipation concept. All detail procedures and results were illustrated in Chapter 4.
Finally, the conclusions of the thesis were summarized in the Chapter 5.
Chapter 2 Effect of fiber array on thermal-mechanical behaviors of fiber