Modulus engineering

Fig. 1. Specific strength and Young s modulus of various engineering materials where CF = carbon fiber HM/UHM = high modulus/ultrahigh modulus ...

The use of elastomeric modifiers for toughening thermoset resias generally results ia lowering the glass transition temperature, modulus, and strength of the modified system. More recendy, ductile engineering thermoplastics and functional thermoplastic oligomers have been used as modifiers for epoxy matrix resias and other thermosets (12). 

Now for some real numbers. Table 3.1 is a ranked list of Young s modulus of materials - we will use it later in solving problems and in selecting materials for particular applications. Diamond is at the top, with a modulus of lOOOGPa soft rubbers and foamed polymers are at the bottom with moduli as low as 0.001 GPa. You can, of course, make special materials with lower moduli - jelly, for instance, has a modulus of about 10 GPa. Practical engineering materials lie in the range 10 to 10 GPa - a... 

Engineering Materials 1 Table 3.1 Data for Young s modulus, E... 

F(FG = normal (shear) component of force A = area u(w) = normal (shear) component of displacement o-(e ) = true tensile stress (nominal tensile strain) t(7) = true shear stress (true engineering shear strain) p(A) = external pressure (dilatation) v = Poisson s ratio = Young s modulus G = shear modulus K = bulk modulus. 

The usefulness of this formula is restricted by the difficulty of obtaining good values to substitute in it. They must apply to the alloy selected, and be derived from carefully controlled tests on it. The stress value, S, reflects an engineer s Judgment in the selection of elastic limit or some arbitrary yield strength. The modulus value must match this. The restraint coefficent, K, is seldom known with any precision. 

As indicated above, the stress-strain presentation of the data in isochronous curves is a format which is very familiar to engineers. Hence in design situations it is quite common to use these curves and obtain a secant modulus (see Section 1.4.1, Fig. 1.6) at an appropriate strain. Strictly speaking this will be different to the creep modulus or the relaxation modulus referred to above since the secant modulus relates to a situation where both stress and strain are changing. In practice the values are quite similar and as will be shown in the following sections, the values will coincide at equivalent values of strain and time. That is, a 2% secant modulus taken from a 1 year isochronous curve will be the same as a 1 year relaxation modulus taken from a 2% isometric curve. 

For isotropic materials, certain relations between the engineering constants must be satisfied. For example, the shear modulus is defined in terms of the elastic modulus, E, and Poisson s ratio, v, as... 

A simplified performance index for stiffness is readily obtained from the essentials of micromechanics theory (see, for example. Chapter 3). The fundamental engineering constants for a unidirectionally reinforced lamina, ., 2, v.,2, and G.,2, are easily analyzed with simple back-of-the-envelope calculations that reveal which engineering constants are dominated by the fiber properties, which by the matrix properties, and which are not dominated by either fiber or matrix properties. Recall that the fiber-direction modulus, is fiber-dominated. Moreover, both the modulus transverse to the fibers, 2, and the shear modulus, G12. are matrix-dominated. Finally, the Poisson s ratio, v.,2, is neither fiber-dominated nor matrix-dominated. Accordingly, if for design purposes the matrix has been selected but the value of 1 is insufficient, then another more-capable fiber system is necessary. Flowever, if 2 and/or G12 are insufficient, then selection of a different fiber system will do no practical good. The actual problem is the matrix systemi The same arguments apply to variations in the relative percentages of fiber and matrix for a fixed material system. 

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