Kemer theory

Many theories have been advanced for predicting the modulus of filled composites. The Kemer theory is often used for the G modulus in the case of filled systems containing spheres Halpin--Tsai modified the Kemer equation in a more general form Lewis and Nielsen suggested a further modification by taking into consideration the packing factor and obtained, in the case of E modulus, the following equation ... 

The analysis of DMA results shows that theoretical models of a composite with a hard filler dispersed in a soft matrix do not account for the observed increase in the modulus. The experimental moduli in Fig. 9 are much higher compared with the theory of the Kemer-Nielsen (11) model (curve 1) (eq.l). 

The interlayer model represents an extension of van der Pool s theory derived from works by Frohlich and Sack devoted to viscosity of suspension by a shell-model. Van der Poel obtained expressions for G and K (bulk modulus). In his model, the filler sphere of a radius, a, is supposed to be sturounded by the sphere of the matrix material with radius 1. The sphere in sphere obtained in this way is sturotmded by the great sphere of radius, R, consisting of material with macroscopic properties of heterogeneous composition. The residts of calculations according to the equations proposed by van der Poel are very close to those obtained using the Kemer equation. Detailed description of this approach can be found elsewhere. ... 

The interlayer model was developed by Maurer et al. The model of the particulate-filled system is taken in which a representative volume element is assumed which contains a single particle with the interlayer surrounded by a shell of matrix material, which is itself surrounded by material with composite properties (almost the same as Kemer s model). The radii of the shell are chosen in accordance with the volume fraction of the fQler, interlayer, and matrix. Depending on the external field applied to the representative volmne element, the physical properties can be calculated on the basis of different boundary conditions. The equations for displacements and stresses in the system are derived for filler, interlayer, matrix, and composite, assuming the specific elastic constants for every phase. This theory enables one to calculate the elastic modulus of composite, depending on the properties of the matrix, interlayer, and filler. In... 

The theory of viscoelastic properties of geterogeneous composites of the polymer-polymer type was developed on the basis of the well-know equation of Kemer 117). This equation is represented for the shear modulus G in this form... 

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