Elasticity composite

Fiber/composite Elastic modulus (GPa) Tensile strength (GPa) Density (g/cm ) Specific stiffness (MJ/kg) Specific strength (MJ/kg)... 

Ki = a y/a is the stress intensity factor, and F, the material constant, both of which depend on the degree of anisotropy of the composite controlled by the composite elastic moduli in the longitudinal and transverse directions, El and Ej, in-plane Poisson ratio, vlt, and Glj. For a perfectly isotropic material, jr/8(l + Vlt) 0.3. Also, the material parameters, i and < 2 are given by ... 

Figure 9. Composite elastic modulus (orientation considerations)...

On the basis of what has been discussed, we are in the position to provide a unified understanding and approach to the composite elastic modulus, yield stress, and stress-strain curve of polymers dispersed with particles in uniaxial compression. The interaction between filler particles is treated by a mean field analysis, and the system as a whole is macroscopically homogeneous. Effective Young s modulus (JE0) of the composite is given by [44]... 

In this study the effect of texture on fracture toughness was studied by varying the template s aspect ratio. SEM analyses were done for microstmeture characterization. Rocking curve was done to quantify the orientation distribution of mullite grains in the mullite/zirconia composite. Elastic modulus, strength, hardness and toughness of the composites were measured and correlated to the textured microstructure. 

Most composite geometries differ from the two simple cases considered. For many microscopic composites, the phase geometry may be unknown. However, it is still possible to predict bounds (limits) for the composite elastic moduli. 

Berryman JG. Role of porosity in estimates of composite elastic constants. Trans ASME J Energy Resour Tech 1994 116 87-96. 

A polymeric matrix is strengthened or stiffened by a particulate second phase in a very complex manner. The particles appear to restrict the mobility and deformability of the matrix by introducing a mechanical restraint, the degree of restraint depending on the particulate spacing and on the properties of the particle and matrix. In the simplest possible case, two bounds have been predicted for the composite elastic modulus (Broutman and Krock, 1967, Chapters 1 and 16 Lange, 1974 see also Section 2.6.4 of this book) ... 

Varies by included regressors and sample composition Elasticities ran ... 

For the transverse shear modulus, the approach designated self-consistent was based on the formula obtained by the self-consistent method for the plane-strain bulk modulus (11.61), on the transverse modulus calculated using the Chamis approach (11.49b) and the in-plane Poisson s ratio given by the rule of mixtures. Except when used to predict the axial modulus and the major Poisson s ratio, the rule of mixtures underestimates the remaining composite elastic properties. The Bridging Model proved to be a very effective theory to account for all five elastic properties for unidirectional composites that are transversely isotropic. 

Favis [7] has summarized in a well-structured chapter the effect of the viscosity ratio, blend composition, elasticity, shear stress, and interfacial modification in immiscible blends on the final phase morphology. 

Fiber/Composite Elastic Modulus, GPa Tensile Strength, GPa Density, g/cm Specific Stiffness, MJ/kg Specific Strength, MJ/kg... 

Velasco et al. [83] performed indentation reboimd tests on PO foams of different densities and chemical compositions. Elastic moduh were calculated and found to increase when foam density and polymer crystallinity increased. 

The autiiors [19] proposed to use for nanocomposites elasticity modulus E determination a modified mixtures rule, which in original variant gives upper limiting value of composites elasticity modulus [10] ... 

The complete absence of interaction and ideal slippage between filler and polymer matrix, when the composite elasticity modulus is defined practically by the polymer cross-section (compare with the plot of Figure 9.21) and is connected with the filling degree by the equation ... 

The micromechanics analysis which follows will use the mechanics of materials approach to obtain equations relating these composite elastic properties to the engineering elastic moduli of the fibers and matrix (Fp, Gf, J,f, and E, G, The key featnre of the mechanics of materials approach is the simplifying assnmption that planes perpendicular to the axis of the fibers remain plain during elastic deformation. 

This is the normal Hook s Law (1975) where, IQ is the spring constant or the cantilever stiffness. The Ah is the indentation depth, depends on the applied load F(Ah) on the materials. The Hertz model [10] and Sneddon s formula [11] give the relationship between [F(Ah) /Ah)] and composite elastic modulus of axisymmetric indenting tip and sample. 

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