The Following are the tasks you are given in the sheet metal forming department: a) A cylindrical part is warm upset forged in an open die. Do = 50 mm and ho = 40 mm. Final height || 20 mm. Coefficient of friction at the die -work interface = 0.20. The work material has a flow curve defined by: K 600 MPa and n = 0.12. Determine the force in the operation (a) just as the yield point is reached (yield at strain = 0.002), (b) at h = 30 mm, and (c) at h = 20 mm. (e) Draw the force as a function of part height and discuss the relationship. v, F II ho he D; (b) Given h = 30, = In(40/30) = In 1.333 = 0.287 Y = 600(0.287).12 = 516.6 MPa 3 V= 78,540 mm from part (a) above. At h = 30, A = V/h = 78,540/30 = 2618 mm? Corresponding D=57.7 mm (from A = AD?/4) Kf= 1 + 0.4(.2)(57.7)/30 = 1.154 F = 1.154(516.6)(2618) = 1,560,557 N (c) Given h = 20, = In(40/20) = In 2.0 = 0.693 Yf= 600(0.693)0.12 = 574.2 MPa V = 78,540 mm' from part (a) above. At h = 20, A = V/h = 78,540/20 = 3927 mm? Corresponding D= 70.7 mm (from A = 7D/4) K= 1+ 0.4(.2)(70.7)/20 = 1.283 F = 1.283(574.2)(3927) = 2,892,661 N