Acoustoelastic determination of the higher order orientation distribution function coefficients up tol = 12 and their use for the on-line prediction ofr-value

The higher order orientation distribution function (ODF) coefficients up tol = 12 in cold-rolled and annealed sheet steels were evaluated and calculatednondestructively from the anisotropy of the ultrasonic velocities of the lowest order symmetrical Lamb (S0) and shear horizontal (SH 0) waves propagating in the rolling plane. The elastic energy method was employed, together with a decomposition of the texture into the principal preferred orientations, following a procedure originally developed for Young’s modulus data obtained destructively. Plastic strain ratios are estimated using the series expansion method, in conjunction with a relaxed constraint (pancake) grain interaction model. Ther- value predictions based on the ODF coefficients obtained in this study are compared with tensile data and with empirical predictions made using the Modul-r approach.