A can with a hemispherical bottom is made by a hybrid process combining stretch-forming followed by deep drawing in the same punch stroke, starting with a 1.0 mm thick Ti alloy blank. In the first stage (left), the hemispherical bottom is stretch-formed over the end of the punch by clamping the sheet tightly in the hold- down. In the second stage (right), the hold- down pressure is reduced to allow drawing of the wall. (a) Calculate the thickness of the hemispherical end assuming it is uniform. The surface area of a sphere is 4tr. (b) If the limiting draw ratio (LDR) of the Ti alloy is 4.2, calculate the maximum blank diameter and length of the drawn part of the can (i.e., not including the hemispherical end) assuming no wall thinning in drawing. LDR = ratio of the maximum blank to drawn can diameter. (c) Mark and clearly label on the yield surface below the state of stress during forming (assuming no work-hardening) in each of the areas i.-iii. (9) i. ii. iii. bottom of the hemispherical end during stretch-forming flange during drawing. wall during drawing. 02 &