Prediction of elastic and plastic anisotropy in deep drawing steels

Yield stresses and r-values were measured as a function of inclination with respect to the rolling direction on thirty-one steels selected from high strength low alloy (HSLA), Al-killed (AKDQ), interstitial free (IF1 and IF2) and rimmed (RIM) types. Modul-r and electromagnetic acoustic (EMAT) techniques were employed to determine the elastic anisotropy in terms of the angular variation of Young's modulus and the ultrasonic velocities, respectively. Orientation distribution functions (ODF's) were also measured for these steels in their as-received states and after deformation in tension and in drawing. The various initial textures and their evolutions along the latter strain path are analyzed in terms of the 4- and 6-ear behaviours commonly observed during the forming of cylindrical cups.The series expansion method was employed for predicting the elastic and plastic anisotropies from the initial texture data. Comparison with the experimental measurements of Young's modulus indicates that the so-called elastic energy method can accurately reproduce the elastic anisotropy if the single crystal elastic constants are appropriately chosen within their ranges of uncertainty. The systematic evaluation of various grain interaction models for predicting the polycrystal plastic anisotropy reveals that the "pancake" relaxed constraint model is a more accurate predictor of the behaviour than the Taylor, Sachs-Kochendorfer, or other relaxed constraint models. The best quantitative agreement is obtained when the critical resolved shear stress (CRSS) ratio for glide on the $ {112 } langle 111 rangle$ and $ {110 } langle 111 rangle$ systems is 0.95 (except for the AKDQ and IF2 grades, for which values of 0.90 and 1.0, respectively, are preferred).The ODF coefficients of order greater than 4 were evaluated and calculated non-destructively from the anisotropy of the ultrasonic velocities of the lowest order symmetrical Lamb (S$ sb{ rm o}$) and shear horizontal (SH$ sb{ rm o}$) waves propagating in the rolling plane. The elastic energy method was employed, together with a decomposition of the texture into the principal preferred orientations. 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