Elastic Properties of Cold-Rolled and Annealed Sheets of Phosphorus Steel Having High Normal Plastic anisotropy

The elastic properties of as-cold-rolled and of the subsequently annealed sheets of a phosphorus steel having high normal plastic anisotropy and low planar plastic anisotropy have been calculated according to the averaging procedures of Voigt, Reuss, and Hill incorporated with texture-weighting functions. The calculated values of Young's modulus in the various directtions lying in the plane of the sheet were compared with those determined experimentally by ultrasonic measurements. Results indicate that the Hill averages are very close to reality, whereas the Voigt and Reuss averages are somewhat too high and too low, respectively, in comparison with experimentally measured values. This paper has been prepared to help familiarize metallurgists, engineers, and students with the mathematical treatments that can be used for such studies. The procedures used for the calculations are described in detail, and examples of calculations are provided in the Appendix.