Elastic constants engineering

As with other anisotropic materials, Hooke s Law for cubic crystals may be expressed in terms of the engineering elastic constants. Equation (2.57) can be written as... 

Many polycrystalline ceramics consist of a random array of single crystals and, in these cases, the materials are elastically isotropic. As shown in Table 2.3, only two elastic constants are needed to describe a linear elastic deformation, c, and Cl2- For convenience, the engineering elastic constants can be used, and one obtains Eqs. (2.65)-(2-70). There is, however, an additional relationship between c,... 

These relationships are known as Newton s Law of viscous flow a is termed the fluidity and -q the dynamical shear viscosity. Newton s Law is analogous to Hooke s Law, except shear strain has been replaced by shear strain rate and the shear modulus by shear viscosity. As shown later, this analogy is often very important in solving viscoelastic problems. In uniaxial tension, the viscous equivalent to Hooke s Law would be a=7] ds/dt), where q is the uniaxial viscosity. As v=0.5 for many fluids, this equation can be re-written as <7-=3Tj(de/dO using t7=t /[2(1+v)], the latter equation being the equivalent of the interrelationship between three engineering elastic constants, (fi=E/[2il + v)]). 

Name the four engineering elastic constants for isotropic materials. 

The engineering elastic constants of isotropic materials can be measured from static loading. Name two other general measurement techniques. 

As only two elastic constants are needed to describe the linear elastic behavior of isotropic materials, there are various relationships between the four engineering elastic constants. Some of these are given below. 

In practical applications of oriented polymers we are concerned with films or fibres, which reduces the number of independent elastic constants to nine or six, respectively. It is also convenient at this stage to limit the discussion to the compliance constants because these can be related directly to the readily measured engineering elastic constants, such as Young s moduli, shear moduli and Poisson s ratios. 

Hence one can choose any two of the four elastic parameters K, G, E, and v to specify uniquely the other two engineering elastic constants. Because K and G are bounded as shown before, E is also bounded, Ey E> r, by expressions obtained from Eqs. (12)-(15) and (21). There is no analogous bound to v. 

Summarizing the results obtained above, the compliance matrix for an orthotropic lamina can be expressed in terms of engineering elastic constants as... 

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