Composite elastic moduli

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

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. 

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) ... 

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

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 ... 

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. 

The importance of polymer composites arises largely from the fact that such low density materials can have unusually high elastic modulus and tensile strength. Polymers have extensive applications in various fields of industry and agriculture. They are used as constructional materials or protective coatings. Exploitation of polymers is of special importance for products that may be exposed to the radiation or temperature, since the use of polymers make it possible to decrease the consumption of expensive (and, sometimes, deficient) metals and alloys, and to extent the lifetime of the whole product. 

Nylon-6. Nylon-6—clay nanometer composites using montmorillonite clay intercalated with 12-aminolauric acid have been produced (37,38). When mixed with S-caprolactam and polymerized at 100°C for 30 min, a nylon clay—hybrid (NCH) was produced. Transmission electron microscopy (tern) and x-ray diffraction of the NCH confirm both the intercalation and molecular level of mixing between the two phases. The benefits of such materials over ordinary nylon-6 or nonmolecularly mixed, clay-reinforced nylon-6 include increased heat distortion temperature, elastic modulus, tensile strength, and dynamic elastic modulus throughout the —150 to 250°C temperature range. 

Metal-Matrix Composites. A metal-matrix composite (MMC) is comprised of a metal ahoy, less than 50% by volume that is reinforced by one or more constituents with a significantly higher elastic modulus. Reinforcement materials include carbides, oxides, graphite, borides, intermetahics or even polymeric products. These materials can be used in the form of whiskers, continuous or discontinuous fibers, or particles. Matrices can be made from metal ahoys of Mg, Al, Ti, Cu, Ni or Fe. In addition, intermetahic compounds such as titanium and nickel aluminides, Ti Al and Ni Al, respectively, are also used as a matrix material (58,59). P/M MMC can be formed by a variety of full-density hot consolidation processes, including hot pressing, hot isostatic pressing, extmsion, or forging. 

Beryllium and aluminum are virtually insoluble in one another in the soHd state. The potential therefore exists for an aluminum—beryllium metal matrix composite with lower density and higher elastic modulus, ie, improved specific modulus, than conventional aluminum alloys produced by ingot or powder metal processing. At least one wrought composite system with nominally 62 wt % Be and 38 wt % A1 has seen limited use in aerospace appheations (see Composites). 

Armor. Sihcon carbide is used as a candidate in composite armor protection systems. Its high hardness, compressive strength, and elastic modulus provide superior baUistic capabihty to defeat high velocity projectile threats. In addition, its low specific density makes it suitable for apphcations where weight requirements are critical (11). 

Indentation has been used for over 100 years to determine hardness of materials [8J. For a given indenter geometry (e.g. spherical or pyramidal), hardness is determined by the ratio of the applied load to the projected area of contact, which was determined optically after indentation. For low loads and contacts with small dimensionality (e.g. when indenting thin films or composites), a new way to determine the contact size was needed. Depth-sensing nanoindentation [2] was developed to eliminate the need to visualize the indents, and resulted in the added capability of measuring properties like elastic modulus and creep. 

In a uniaxial tension test to determine the elastic modulus of the composite material, E, the stress and strain states will be assumed to be macroscopically uniform in consonance with the basic presumption that the composite material is macroscopically Isotropic and homogene-ous. However, on a microscopic scSeTBotFTfhe sfre and strain states will be nonuniform. In the uniaxial tension test,... 

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