## Treatise on materials science and technology, Volume 3 |

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Page 57

They calculated the variation of Young's modulus in the

function of angle to the rolling direction and found agreement with the

experimental values obtained from measurements on a rolled sheet of aus-

formed steel.

They calculated the variation of Young's modulus in the

**rolling plane**as afunction of angle to the rolling direction and found agreement with the

experimental values obtained from measurements on a rolled sheet of aus-

formed steel.

Page 69

The symmetry about the direction at 45° to the

similar to (001) [110]. The decrease in the anisotropy for annealing at 750°C is

significant [after Papadakis (123).] the

The symmetry about the direction at 45° to the

**rolling**direction indicates a texturesimilar to (001) [110]. The decrease in the anisotropy for annealing at 750°C is

significant [after Papadakis (123).] the

**plane**wave shear and longitudinal ...Page 70

0' 30° 60° 90° ANGLE BETWEEN PROPAGATION AND ROLLING DIRECTIONS

Fig. 34. ... The symmetry about 45° in the

in the 45° direction would tend to indicate a (100) [011] texture or possibly a ...

0' 30° 60° 90° ANGLE BETWEEN PROPAGATION AND ROLLING DIRECTIONS

Fig. 34. ... The symmetry about 45° in the

**rolling plane**with the maximum velocityin the 45° direction would tend to indicate a (100) [011] texture or possibly a ...

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### Common terms and phrases

Alers aluminum Andreatch anisotropic Appl axis calculated compressive stress copper crystallographic orientation cubic crystals determine direction cosines displacement gradients displacements along 001 elastic moduli elastic wave propagation energy-flux vector equation of motion experimental germanium given by Eq hydrostatic pressure hydrostatic pressure longitudinal hydrostatic pressure transverse ideal orientation interaction isotropic solid linear elastic wave longitudinal wave longitudinal wave propagating materials mode transverse wave nonlinear elastic wave obtain Papadakis particle displacements phonons Phys plane wave pressure longitudinal wave pressure transverse wave pure mode longitudinal pure mode transverse quasitransverse waves rolling direction rolling plane second harmonic second-order elastic constants shear wave single crystals six third-order elastic stress along 001 stress along 110 Substituting Eqs symmetry test specimen texture third-order elastic constants Thurston and Brugger transducer transverse wave ultrasonic beam ultrasonic pulse uniaxial stress values wave along 100 wave normal wave speeds wave velocity Young's modulus