Relationship between contractile strain ratioR and texture in zirconium alloy tubing

The crystallographic textures of zirconium alloy tubing used as cladding in nuclear reactor fuel are commonly characterized by the quantitative texture numbersF (Källström) and f_r (Kearns) which are derived from the direct and inverse pole figures. The texture numbers of zircaloy 2 and 4 tubes have been correlated experimentally with the value of the contractile strain ratioR which is a measure of the plastic anisotropy of the tube. The correlations were based on the results of 20 different tubing lots. Thef _r-R correlation shows much less data scatter than theF-R correlation. By assuming a simple plastic deformation model for zirconium alloys the following relations between texture and anisotropy are obtained:F=R- 1/R+1 and f_r = R/R+1 The theoretically derived relations are in good agreement with the experimental data. The procedure of correlating texture with plastic anisotropy is not limited to zirconium alloy tubing, but should be equally applicable to textured sheet and plate materials and other alloys with a limited number of slip systems.