ME 303 MANUFACTURING ENGINEERING PROBLEM SETS(Questions with Answers,100% SCORE)

ME 303 MANUFACTURING ENGINEERING PROBLEM SETS Prepared by: Kamil Özden Ural Uluer Salih Alan Mehmet Bilal AtarPROBLEM SET FOR CHAPTER 2 Q2.1 A copper bar is to be cold rolled into a section which must have a min ...

ME 303 MANUFACTURING ENGINEERING PROBLEM SETS Prepared by: Kamil Özden Ural Uluer Salih Alan Mehmet Bilal AtarPROBLEM SET FOR CHAPTER 2 Q2.1 A copper 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. Solution a) from volume constancy b)Q2.3 A tensile bar was machined with a stepped gage section consisting of two regions of different diameters. The initial diameters of the two regions were 2.0 cm and 1.9 cm. After a certain amount of stretching in tension, the diameters of the two regions were measured as 1.893 cm and 1.698 cm, respectively. Assuming the tensile strain hardening is described by , find n for the material. Solution Strains at larger and smaller diameter sections are respectively: ( ) ( ) The load carrying capacities at two sections must be the same: ⁄ 2.0 cm ccm cm 1.9 cm cm 1.893 cm 1.698 cm Before: After: rrrrrQ2.4 A steel test specimen (modulus of elasticiy = 205 GPa) in a compression test has a starting height of 50mm and diameter of 38 mm. The metal yields (0.2% offset) at a load 600kN. At a load of 1100kN, the height has been reduced to 40mm. Assuming that the cross-sectional area increases uniformly during the test, determine the followings: a) Yield strength in MPa b) Total strain at the offset yield point c) Flow stress in Mpa and the plastic strain under the load of 1100kN d) Strength coefficient K in MPa if strain hardening exponent is 0.25 Solution a) ( ) b) ( ) c) ( ) ( ) d)Q2.5 A test specimen in a tensile test has a gage length of 50 mm and a cross-sectional area of 316 mm2. During the test the specimen yields (0.2% offset) under a load of 140kN. The corresponding gage length is 50.2 mm. The maximum load of 200 kN is reached at a gage length of 58 mm. Determine the followings: a) Yield strength in MPa b) Modulus of elasticity in GPa c) Tensile strength in MPa d) Percentage elongation if fracture occurs at a gage length of 66 mm e) Percentage area reduction (ductility) if the specimen necked to an area of 156 mm2 f) Strain hardening exponent n and strength coefficient K in MPa. g) New yield strength and tensile strength in MPa and the ductility for the specimen with a 20% cold work. Solution a) b