ME 303 MANUFACTURING ENGINEERING

r bar is to be cold rolled into a section which must have a min. tensile strength of 390 MPa. If the final cross-sectional area is 20.13 mm2 and assuming the flow properties of the workpiece material are given as K = 450 MPa, n = 0.33. Calculate the followings: a) The tensile strength of the annealed material. b) The initial diameter of the copper bar. Solution It is important to understand the question well. In this question, the copper bar is annealed first then a cold rolling operation is done on it. Initial diameter of the copper bar is same before and after the annealing operation. a) Flow stress of the plastically deformed bar could be shown as . As shown in Course Slides at UTS Then UTS of the original bar (no annealing, no cold working) is found as below: u = 450 (0.33)0.33 u = 312.12 MPa Since before necking occurs ( n) area stays constant at the whole bar, the formula below could be used: By putting the area ratio into the formula (i) UTS of the annealed material is found as:b) For this question d0 can be found by using the ratio: if n (which means necking is not started yet) with the UTScw value given in the question as UTScw = 390 MPa, to check the value So n which means that necking started, then UTScw becomes equal to flow stress of the deformed material,Q2.2 A steel tensile specimen with an initial diameter of 20mm and gage length of 120mm is subjected to a load of 125 kN and a gage length of 135mm is observed. Assuming uniform deformation at this point, calculate the followings: a) calculate the true stress, strain and the instantaneous diameter b) supposing the plastic behavior of the specimen material is expressed as (MPa) estimate the yield strength of the deformed specimen