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Notes: Abstract A theoretical model was introduced for the evaluation of the boundary layer developed between the main phases during the preparation of unidirectional fiber composites. It has been shown that this thin layer influences considerably the physical properties of the composite. It was assumed that the physical properties of themesophase unfold from those of the hard-core fibers to those of the softer matrix. Thus, a multicylinder model was assumed improving the classical two-cylinder model introduced by Hashin and Rosen for the representative volume element of the composite. Based on thermodynamic phenomena appearing at the glass transition temperatures of the composite and concerning the positions and the sizes of the heat-capacity jumps there, as well as on the experimental values of the longitudinal elastic modulus of the composite, the extent of the mesophase and the mechanical properties of the composite may be accurately evaluated. This version of the model is based on a previous one concerning a multilayer model, but it is considerably improved in order to take into consideration, in a realistic manner, the physical phenomena developed in fiber reinforced composites.

Notes: Abstract The degree of adhesion developed between matrix and inclusions in composites is among the main factors characterizing their mechanical and physical behavior. The quality of adhesion depends mainly on the boundary layer created between inclusions and matrix because of chemisorption, physisorption and mechanical constraint phenomena developed between the main phases in the RVE of a composite. The extent of this boundary layer, which is called mesophase or interphase, may be a potential means for defining the quality of adhesion. While almost all previous models describing the mechanical and physical properties of composites are based on the concept of mathematical and smooth interfaces constituting the boundaries of the phases, a series of recent models developed by the author and his collaborators consider a more pragmatic situation at the interfaces between phases assuming the existence of boundary layers between phases ensuring a continuous transition of the properties of adjacent phases, which should be accepted as being in conformity with the physical and chemical procedures happening at these boundaries. The unfolding type of models introduced by the author aims to fill the gap by trying to accommodate the properties of neighbouring phases by transition boundary layers with varying properties between the bounds of the limiting phases. Thus, the unfolding models constitute a powerful means, where the notion of mesophase was introduced for defininig the RVE of a composite. The RVE was considered as consisting of the two main phases (the reinforcement and the matrix), coupled together by the intermediate phase, whose variable mechanical properties unfold from those of the reinforcement to those of the matrix. The extent of mesophase was evaluated by the three different and alternate methods, that is: i) by considering the variations in the heat capacity jumps,ΔC p , of the matrix material and the respective composite, appearing at the respective glass-transition temperatures of both substances. Based on thermodynamic measurements with differential scanning calorimetry, the extents of these jumps were accurately measured and these defined the thickness of the mesophase. It was further assumed that the steep variations of the mechanical properties in the mesophase follows negative-power laws, whose exponents were derived by measuring the moduli of the matrix, inclusions and the composite and assuming the validity of an improved law of mixtures. § ii) by evaluating the extent of mesophase along the whole range of temperature by using exclusively the mechanical properties of the storage and loss compliances and moduli of the composite and the matrix, without making recourse to thermal or other types of measurements and without limitations at the glass transition temperatures, and § iii) by defining the extent of the mesophase by the same method, but evaluating the properties of the mesophase or mesophases by methods based on diffusion laws of mutually soluble phases or impregnations. This method is convenient for studying polymer-polymer composites and composites with encapsulated or sized phases. By applying all three variations of the unfolding model it was shown that all three possibilities of defining the extent and the variable properties of mesophases are equivalent and, furthermore, they yield reasonable results. Moreover, experimental evidence with either particulates, or fiber composites indicated clearly that the introduction of the mesophase yields a better and more flexible model for interpreting in a realistic manner the complicated phenomena appearing in all composites used in engineering applications.

Notes: Abstract In this paper the mesophase developed between main phases in fibrous composites was studied assuming that it constitutes a diffuse boundary. This type of mesophase is normally developed in polymer-polymer adjacent phases and it it useful for the study of modern composites disposing a coupling agent between main phases. At the high temperature of reaction of phases during the casting process both neighboring phases are partly liquified, allowing a two-way movement of elements of either phase whose intensity and extent depends on the particular diffusion characteristics of either phase and the affinities between them. The characteristics of this diffusion reaction were studied and their influence on the development and the properties of the adhesion between phases were established, especially for fiber composites. Interesting results were derived concerning the extent of the diffusive mesophase and its mechanical properties, as well as its contribution on the global mechanical behavior of the composite. Finally, the results were found to be in agreement with previously established models.

Notes: Abstract The size of the mesophase, which constitutes a boundary layer between fillers and matrix in composites, has been efficiently evaluated by the modified two-term unfolding model, which was based on delicate DSC measurements of the heat capacity jumps at the glass transitions of the composite and its constituent phases [1,2]. This model is now used to evaluate the mesophase along the whole viscoelastic spectrum of the composite, by making measurements of the storage and loss compliances or moduli of the composite and matrix and without making recourse to any other type of special measurement at the glass transition temperature of the substances. By applying this model the following important results were derived: i) Lipatov's empirical formula for defining the mesophase atT g was shown to yield reasonable results and ii) the evaluation of the size of mesophase over the entire viscoelastic spectrum was shown to remain almost constant and in conformity with the values defined by the other versions of the model. Extensive application of the experimental results of the literature indicated the mutual proof of the validity of these affine models.

Notes: Abstract Expressions for the evaluation of the transverse and longitudinal elastic moduli and the major Poisson ratio of unidirectional fiber composites are derived. The model described is based on the correct version of Kerner's model, which in our case is conveniently modified by introducing a mesophase layer between the fiber and the matrix in the representative volume element surrounding the typical fiber. The expression for the longitudinal elastic modulus derived in this paper, and the law of mixtures already presented in previous papers, give concordant results. Therefore, the law of mixtures, taking the mesophase also into account, and the two-term unfolding model for the mesophase are used for the evaluation of its extent and its properties. The model was applied to a glass filament-epoxy resin composite and its predictions were found to be in good agreement with the experimental data.

Notes: Abstract An accurate relationship for the shear modulus of particulates is derived based on the Kerner model, but not using its approximate relations. Furthermore, the model takes into account the existence of the mesophase layer between the inclusions and the matrix, which acts as a smooth transition boundary layer between constituent materials. By applying Christensen's field to the Kerner model, modified by introducing the mesophase, the new model is liberated from any inconsistencies. Experimental evidence and application to a glass particle-epoxy resin-matrix composite indicated the superiority of the model over previous ones.

Notes: Abstract A theoretical model, consisting of a series of infinite concentric cylinders surrounding a fiber in a composite material, was introduced in this paper to give a quantitative account of interface phenomena, already experimentally observed. A series of specimens, conveniently designed to represent the theoretical model, were subjected to dynamic modes of loading to measure the amount of adhesion between fibers and matrices by means of an adhesion coefficient developed in the theory. It was found that theoretical results for the adhesion between matrix and filler were compatible with the structural characteristics of the specimens tested.

Notes: Abstract A new and accurate relationship for the shear modulus in the fiber direction of unidirectional fiber composites is derived, based on the Kerner model concepts but not using its approximate relationships. Furthermore, this model is extended by taking into account the mesophase between the fiber and the matrix accomodating smoothly the mechanical properties between neighbouring phases. The introduction of the mesophase results in an improvement of the theoretical predictions, which now approach close to experimental values for the moduli of different fibrous composites.

Notes: Abstract A theoretical model for the evaluation of the elastic modulus in particulate composites has been developed. The method takes into account the existence of a mesophase between main phases, which constitutes an important parameter influencing the behaviour of a composite material. This layer between the matrix and filler develops different physico-chemical properties from those of the constituent phases and variable ones along its thickness. The effect of the progressive variation of the elastic modulus of the mesophase on the modulus of the composite was estimated by applying various simple laws of variation. Convenient laws of variation were introduced, varying from a simple one, assuming a linear law, to a more refined one using a parabolic law. Experimental results with particulates, based on iron-filled epoxy composites, compared satisfactorily with other models. However, the model based on a parabolic law was superior to all others on physical grounds.

Notes: Abstract A new relation for the prediction of the transverse shear modulus in unidirectional fiber composites has been derived. The theoretical results of this relationship are in better agreement with the experiments than those of other relations, existing in the literature. The discrepancies, which are observed among the theoretical predictions and the experimental values, are explained by the consideration of the boundary layers existing between the matrix and the fibers of the composite. A new model, which includes the intermediate phase between the matrix and the fiber, called the mesophase, is considered in order to take into account the above-mentioned layers.