Composite materials modulus

Galculate the upper and lower values for the modulus of the composite material, and plot them, together with the data, as a function of Vf. Which set of values most nearly describes the results Why How does the modulus of a random chopped-fibre composite differ from those of an aligned continuous-fibre composite ... 

A composite material consists of flat, thin metal plates of uniform thickness glued one to another with a thin, epoxy-resin layer (also of uniform thickness) to form a multi-decker-sandwich structure. Young s modulus of the metal is Ej, that of the epoxy resin is E2 (where E2 < Ej) and the volume fraction of metal is Vj. Find the ratio of the maximum composite modulus to the minimum composite modulus in terms of Ej, E2 and V. Which value of gives the largest ratio ... 

Today, carbon fibers are still mainly of interest as reinforcement in composite materials [7] where high strength and stiffness, combined with low weight, are required. For example, the world-wide consumption of carbon fibers in 1993 was 7,300 t (compared with a production capacity of 13,000 t) of which 36 % was used in aerospace applications, 43 % in sports materials, with the remaining 21 % being used in other industries. This consumption appears to have increased rapidly (at 15 % per year since the early 1980s), at about the same rate as production, accompanied by a marked decrease in fiber cost (especially for high modulus fibers). 

Two observations are useful to rationalize why in Figures 2-11 and 2-12 (1) Gyy exceeds l (2) E45. is less than for composite materials that have a fiber modulus much greater than the matrix modulus ... 

Another test used to determine the shear modulus and shear strength of a composite material is the sandwich cross-beam test due to Shockey and described by Waddoups [2-17]. The composite lamina... 

The first modulus to be determined is that of the composite material in the 1-direction, that is, in the fiber direction. From Figure 3-5,... 

The apparent Young s modulus, E2, of the composite material in the direction transverse to the fibers is considered next. In the mechanics of materials approach, the same transverse stress, 02, is assumed to be applied to both the fiber and the matrix as in Figure 3-9. That is, equilibrium of adjacent elements in the composite material (fibers and matrix) must occur (certainly plausible). However, we cannot make any plausible approximation or assumption about the strains in the fiber and in the matrix in the 2-direction. 

Predicted results for E2 are plotted in Figure 3-10 for three values of the fiber-to-matrix-modulus ratio. Note that if Vj = 1, the modulus predicted is that of the fibers. However, recognize that a perfect bond between fibers is then implied if a tensile <32 is applied. No such bond is implied if a compressive 02 is applied. Observe also that more than 50% by volume of fibers is required to raise the transverse modulus E2 to twice the matrix modulus even if E, = 10 x E ,l That is, the fibers do not contribute much to the transverse modulus unless the percentage of fibers is impractically high. Thus, the composite material property E2 is matrix-dominated. 

Which is plotted in Figure 3-16 for several values of Gf/G. Only for a fiber volume of greater than 50% of the total volume does G.,2 rise above twice G even when Gf/Gn, = 101 As with E2, the composite material shear modulus G. 2 is matrix-dominated. Measured values of G.,2 have a relation to the predicted values similar to those for E2 in Figure 3-12 (see Section 3.4.2). 

Use a mechanics of materials approach to determine the apparent Young s modulus for a composite material with an inclusion of arbitrary shape in a cubic element of equal unit-length sides as In the representative volume element (RVE) of Figure 3-17. Fill in the details to show that the modulus is... 

Determine the expression for the modulus of a composite material stiffened by particles of any cross section but prismatic along the direction in which the modulus is desired as in Figure 3-18. 

Paul [3-4] was apparently the first to use the bounding (variational) techniques of linear elasticity to examine the bounds on the moduli of multiphase materials. His work was directed toward-analvsis of the elastic moduli of alloyed metals rath, tha tow5 rdJ ber-reW composite materials. Accordiriglyrthe treatment is for an js 6pjc composite material made of different isotropic constituents. The omposifeTnaterial is isotropic because the alloyed constituents are uniformly dispersed and have no preferred orientation. The modulus of the matrix material is... 

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,... 

Consider a dispersion-stiffened composite material. Determine the Influence on the upper bound for the apparent Young s modulus of different Poisson s ratios in the matrix and In the dispersed material. Consider the following three combinations of material properties of the constituent materials ... 

Use the bounding techniques of elasticity to determine upper and lower bounds on the shear modulus, G, of a dispersion-stiffened composite materietl. Express the results In terms of the shear moduli of the constituents (G for the matrix and G for the dispersed particles) and their respective volume fractions (V and V,j). The representative volume element of the composite material should be subjected to a macroscopically uniform shear stress t which results in a macroscopically uniform shear strain y. 

The mechanics of materials approach to the estimation of stiffness of a composite material has been shown to be an upper bound on the actual stiffness. Paul [3-4] compared the upper and lower bound stiffness predictions with experimental data [3-24 and 3-25] for an alloy of tungsten carbide in cobalt. Tungsten carbide (WC) has a Young s modulus of 102 X 10 psi (703 GPa) and a Poisson s ratio of. 22. Cobalt (Co) has a Young s modulus of 30x 10 psi (207 GPa) and a Poisson s ratio of. 3. 

Tsai conducted experiments to measure the various moduli of glass-fiber-epoxy-resin composite materials [3-1]. The glass fibers and epoxy resin had a Young s modulus and Poisson s ratio of 10.6 x 10 psi (73 GPa) and. 22 and. 5 x 10 psi (3.5 GPa) and. 35, respectively. 

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