Modulus of composites

Russel, W.B. (1973), On the effective moduli of composite materials effect of fiber length and geometry at dilute concentrations. J. Appl. Math. Phys. (ZAMP) 24, 581-599. 

Figure 8. Dependence of yield stress on silicone content of BPF carbonate-silicone block polymers. Line is calculated from Halpin-Tsai equations for moduli of composite of rigid matrix containing soft spherical inclusions.

Young s modulus in general. With subscripts C, M, PB, PS, P moduli of composite, matrix phase, polybutadiene, polystyrene, and particle, respectively Activation energy... 

The numerical simulation method of Termonia [67-72] was reviewed in Section 20.C.1 since it can be used in calculating the elastic moduli of composites. As described in that discussion, this method actually allows the calculation of complete stress-strain curves for fiber-reinforced composites. It must be emphasized that the ability of this method to simulate the mechanical properties of composites under large deformation by using a reasonable physical model is of far greater importance and uniqueness than its ability to model the elastic behavior. 

L.E. Nielsen, Generalized equation for the elastic moduli of composite materials, J. Appl. Phys., 41(11), 4626-4627 (1970). 

Dynamic mechanical characteristics, mostly in the form of the temperature response of shear or Young s modulus and mechanical loss, have been used with considerable success for the analysis of multiphase polymer systems. In many cases, however, the results were evaluated rather qualitatively. One purpose of this report is to demonstrate that it is possible to get quantitative information on phase volumes and phase structure by using existing theories of elastic moduli of composite materials. Furthermore, some special anomalies of the dynamic mechanical behavior of two-phase systems having a rubbery phase dispersed within a rigid matrix are discussed these anomalies arise from the energy distribution and from mechanical interactions between the phases. 

E and E correspond to the elastic moduli of composite and matrix, respectively represents the shape factor, which is dependent on filler geometry and loading direction q)f is the inorganic volume fraction 11 is given by the expression... 

An interpolation procedure applied by Halpin and Tsai [17,18] has led to general expressions for the moduli of composites, as given by Eqs. (2.18) and (2.19). Note that for = 0, Eq. (2.18) reduces to that for the lower hmit, Eq. (2.8), and for = infinity, it becomes equal to the upper limit for continuous composites, Eq. (2.7). By empirical curve fitting, the value of = 2(l/d) has been shown to predict the tensile modulus of aligned short-fiber composites in the direction of the fibers, and the value of = 0.5 can be used for the transverse modulus. Other mathematical relationships for modulus calculations of composites with discontinuous fillers include the Takaya-nagi and the Mori-Tanaka equations [20]. 

The theories suggest that the elastic moduli of composites containing particulates with an aspect ratio of unity should be independent of the dimensions of the filler and dependent only on the relative moduli of filler and matrix, their volume fractions, and... 

Tsai C. L. and Daniel I. M. (1990) Determination of in-plane and out-of-plane shear moduli of composite materials. Experimental Mechanics, 30(3), 295-299. 

The A values of different systems are listed in Table 2.6 the relationships between different specific moduli of composite material and fiber content are shown in Figure 2.10. 

In Eq. (6.26), G. and G j are the longitudinal and transverse elastic moduli of composite with uni directionally aligned anisotropic inclusions, respectively. 

Walpole [10] for the overall moduli of composite materials reinforced by disc-like particles, i.e. transversely isotropic spheroids with zero aspect ratio. Note that the developments drawn in this paper give a general formulation, function of an arbitrary aspect ratio, which lead to the Walpole solution [10] if the aspect ratio is zero. 

Figure 4. Soft segment crystallinity of CNF composite Table 1. Tensile moduli of composites at 60°C (MPa)...

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