A stainless steel is being considered to make valves for an internal combustion engine. The following mechanical properties were obtained on an annealed specimen at room temperature: Ar = 60 %; the 2.00 in. gage length is 2.006 in. long when yielding occurs and 2.500 in. long when the maximum load is applied; Tensile strength is 58,558 psi. (a) How many annealing cycles would be required to cold form (upset) a 1 in. diameter head on the end of a 14 in. diameter annealed bar? The piece need not be annealed after the last forming step. (b) What is the yield strength of the material in the head of the valve after the last forming step? What will be the average flow stress and the work done per unit volume in this step?