As noted in Section 3.15, for single crystals of some substances, the physical properties...

As noted in Section 3.15, for single crystals of some substances, the physical properties are anisotropic—that is, they depend on crystallographic direction. One such property is the modulus of elasticity. For cubic single crystals, the modulus of elasticity in a general [uvw] direction, Euvw, is described by the relationship

where E(100) and E(111) are the moduli of elasticity in the [100] and [111] directions, respectively; a, b, and g are the cosines of the angles between [uvw] and the respective [100], [010], and [001] directions. Verify that the E(110) values for aluminum, copper, and iron in Table 3.4 are correct.

Table 3.4 Modulus of Elasticity Values for Several Metals at Various Crystallographic Orientations

Source: R. W. Hertzberg, Deformation and Fracture Mechanics of Engineering Materials, 3rd edition. Copyright © 1989 by John Wiley&Sons, New York. Reprinted by permission of John Wiley&Sons, Inc.