Ultrasonic Prediction of r-value in Deep Drawing Steels

The textures of five types of deep drawing steels were measured and analyzed using the series expansion method. Electromagnetic acoustic (EMAT) techniques were employed to determine the elastic anisotropy in terms of the angular variation of the ultrasonic velocities. The series expansion formalism was employed for predicting the elastic and plastic anisotropies from texture data. Comparison with the experimental measurements of Young's modulus indicates that the elastic energy method can accurately reproduce the elastic anisotropy if the single crystal elastic constants are appropriately chosen. The angular variation of ther-value in the rolling plane was calculated from the ODF coefficients by means of the pancake relaxed constraint model using an appropriate CRSS ratio for glide on the {112} 〈111〉 and {110} 〈111〉 slip systems. The fourth order and first sixth order ODF coefficients were calculatednondestructively from the anisotropy of the ultrasonic velocities. The calculated pole figures based on the ODF coefficients obtained in this way are similar to those derived from complete X-ray data. It is shown that the plastic properties of commercial deep drawing steels are predicted more accurately when the 4th-and 6th-order ODF coefficients are employed than when only the 4th-order ones are used.