Rosen-Hashin model

A better approach for the Rosen-Hashin models is to adopt models, whose representative volume element consists of three phases, which are either concentric spheres for the particulates, or co-axial cylinders for the fiber-composites, with each phase maintaining its constant volume fraction 4). 

Figure 6.3 shows the longitudinal and the transverse coefficients of thermal expansion (the CTEs) predicted using the Rosen-Hashin model. The component properties of the composite used are ... 

Fig. 6.3 Numerical results based on the Rosen-Hashin model for the coefficients of thermal expansion as a function of volume fraction of fibers...

A variation on the exact soiutions is the so-caiied seif-consistent modei that is explained in simpiest engineering terms by Whitney and Riiey [3-12]. Their modei has a singie hollow fiber embedded in a concentric cylinder of matrix material as in Figure 3-26. That is, only one inclusion is considered. The volume fraction of the inclusion in the composite cylinder is the same as that of the entire body of fibers in the composite material. Such an assumption is not entirely valid because the matrix material might tend to coat the fibers imperfectiy and hence ieave voids. Note that there is no association of this model with any particular array of fibers. Also recognize the similarity between this model and the concentric-cylinder model of Hashin and Rosen [3-8]. Other more complex self-consistent models include those by Hill [3-13] and Hermans [3-14] which are discussed by Chamis and Sendeckyj [3-5]. Whitney extended his model to transversely isotropic fibers [3-15] and to twisted fibers [3-16]. 

A study of the effect of the mesophase layer on the thermomechanical behaviour and the transfer mechanism of loads between phases of composites will be presented in this study. Suitable theoretical models shall be presented, where the mesophase is taken into consideration as an additional intermediate phase. To a first approximation the mesophase material is considered as a homogeneous isotropic one, while, in further approximations, more sophisticated models have been developed, in which the mesophase material is considered as an inhomogeneous material with progressively varying properties between inclusions and matrix. Thus, improvements of the basic Hashin-Rosen models have been incorporated, making the new models more flexible and suitable to describe the real behaviour of composites. 

The novel element in these models is the introduction of a third phase in the Hashin-Rosen model, which lies between the two main phases (inclusions and matrix) and contributes to the progressive unfolding of the properties of the inclusions to those of the matrix, without discontinuities. Then, these models incoporate all transition properties of a thin boundary-layer of the matrix near the inclusions. Thus, this pseudo-phase characterizes the effectiveness of the bonding between phases and defines a adhesion factor of the composite. 

Following on Katz s [1976,1980] adaptation of the Hashin-Rosen hoUowfiber composite model [ 1964], Gottesman and Hashin [1979] presented a viscoelastic calculation using the same major assumptions. 

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