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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 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 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: The influence of the hard or soft inclusions and the mesophase layers in either a soft-hard-soft or hard-soft-hard combination of biphase plates submitted to dynamic tensile loads on the fracture mode and bifurcation process in both phases was investigated in this paper. It was assumed that the soft or hard matrix is infolding the hard or soft inclusion of the plate, so that the plate constitutes a meridional section of the representative volume element of a unidirectional fiber composite, or a principal section of a particulate. The influence of the mechanical properties of either phase on the crack propagation velocity and the initiation of crack bifurcation was studied by using high-speed photography and dynamic caustics. The results showed that the propagating crack tended to bifurcate either in the brittle or in the mesophase layer under certain conditions of propagation velocity. It was shown that bifurcation of a propagating crack depends on the elastic moduli and Poisson's ratios of the phases, as well as on the extent of the mesophase layer, which depended on the adhesion quality of phases.

Notes: High-impact polystyrene (HIPS) constitutes a mechanically attractive composite, consisting of a glassy matrix and a rubberlike particle phase (gel phase). Dynamic mechanical spectroscopy was performed for the polystyrene matrix for three different types of HIPS as well as for the concentrated gel-phase material, at the vicinity of the respective glass-transition temperatures (Tg). An approximate estimation of the gel-phase modulus was attempted by using known mechanical models. A comparison with experiments was also made. The modulus of the composite was found to be lower than the theoretical lower bound for particulate composites. This was attributed to a separate phase between gel particles and the matrix. A diffusion-type variation of the modulus of this mesophase layer was estimated, and a correlation between calculated fitting parametric exponents and impact behavior of HIPS was found. Moreover, the Tgs of the materials under investigation were also measured with two independent methods. It was found that all types of HIPS presented higher Tgs than the pure matrix by 5 to 10°C with the highest Tg found being that of the gel-enriched material. The shift of Tgs to higher temperatures was attributed to an eventual increase of the effective cross-link density of the matrix because of grafting.

Notes: The dynamic mechanical properties of composite materials, consisting of an epoxy matrix filled with iron particles, were determined over a temperature range. The storage- and loss moduli were evaluated in a Dynastat apparatus, with the parameters being the volume fraction of filler and the test frequency. A theoretical model was developed for comparing the experimental results with the theoretical predictions. A satisfactory correlation was obtained for the glassy region of the composite.