MSE 230 Fall 2012 EXAM I Closed book 1 sheet of notes 8 5 x11 writing on both sides allowed 1 a 05 b 05 c 10 Name total 20 total 15 2 Recitation day and time Kara Luitjohan R3 Thur 10 30 R6 Thur 4 30 Andrew Kustas R10 Thur 9 30 R5 Fri 10 30 3 20 4 05 5 Abhishek Bawiskar R4 Thur 1 30 R12 Fri 11 30 Yuefeng Wang R8 Thur 2 30 R11 Thur 3 30 a 05 b 10 total 15 Total 75 Good Luck 1 20 1 Short answer questions 5 a Make a qualitative sketch of the molecular weight distributions for two batches of polyethylene that were polymerized under different conditions Batch 1 was polymerized such that Mw Mn and Batch 2 was polymerized such that Mw Mn Batch 1 Batch 2 Polymer Amount Polymer Amount Molecular Weight Molecular Weight 5 b Match the values of Young s modulus and coefficient of thermal expansion with the appropriate material Values of Young s modulus GPa Coefficient of Thermal Expansion Values C 1 Material 10 c E GPa 2 7 115 304 3 0 10 6 17 10 6 120 10 6 C 1 Copper x10 6 Polystyrene x10 6 Silicon Nitride x10 6 Circle either TRUE or FALSE i In general volume is not conserved during elastic deformation TRUE FALSE ii Given the same molecular weight and chemical composition a polymer composed of linear chains will crystallize more readily than a polymer composed of branched chains TRUE FALSE iii Heating a crystalline metal will cause its x ray diffraction peaks to shift slightly to the right TRUE FALSE iv The slope at r r0 of the potential energy vs separation distance curve is proportional to Young s modulus TRUE FALSE v In a BCC crystal structure the atoms touch along the 111 TRUE FALSE 2 15 2 Crystals Structures Planes and Directions 6 a Draw the following inside the cubes provided z z z y y x 101 012 x 212 y x 121 4 b Please fill in the blanks The drawing below shows the arrangement of atoms on the of a metal 5 c Which of the following are possible slip systems for a FCC metal Circle your answer s i 1 1 1 10 1 ii 1 1 0 110 iii 11 1 1 01 iv 1 1 1 0 1 1 v 10 1 1 1 1 3 20 3 Relatively Short Calculations circle one answer for each problem no partial credit The next page is left blank for your use but no partial will be given for anything written there 5 a The potential energy between the two atoms ions is given by E A B r rn where E is the potential energy r the separation distance between atoms and A B and n are constants Given that A 7 25 10 18 J m B 1 44 10 95 J m9 and n 9 the equilibrium separation distance r0 in units of nm is i 0 210 nm ii 0 255 nm iv 0 194 nm v 0 168 nm iii 0 283 nm 5 b Beginning with the peak having the lowest 2 angle and moving to increasing 2 theta angles the first three x ray diffraction peaks for a FCC crystal structure are i 110 200 211 ii 100 010 001 iv 111 200 220 v 111 200 311 iii 100 110 111 5 c The lattice parameter of silver is 0 407 nm at room temperature X ray diffraction is performed at room temperature on silver using Cu K x rays 0 154 nm The 2 peak position corresponding to the interplanar spacing of the 222 in silver is i 27 6 ii 81 8 iv 40 9 v 64 7 iii 55 2 5 d Given a ductile metal with a Young s modulus of 150 GPa and a yield stress of 500 MPa the maximum possible elastic strain before the onset of plastic deformation is i 0 0020 ii 0 30 iv 0 033 v 0 0033 iii 3 33 4 THIS PAGE LEFT INTENTIONALLY BLANK TO PROVIDE WORK SPACE FOR PROBLEM 3 THIS IS FOR YOUR USE ONLY NO PARTIAL CREDIT WILL BE GIVEN FOR ANYTHING WRITTEN ON THIS PAGE 5 5 4 A polycrystalline bar of a metallic alloy is subjected to triaxial loading at room temperature The alloy has a yield stress yield 270 MPa and a Poisson ratio 0 35 z y x Given that a tensile stress of 175 MPa is applied in the y direction and a tensile stress of 50 MPa is applied in the z direction calculate the applied stress in the x direction such that the strain in the z direction z is 0 6 15 5 You are provided with two cylinders each containing the same volume of copper Initially Cylinder 2 is shorter and has a larger diameter than Cylinder 1 Cylinder 2 is stretched in uniaxial tension past its yield stress and after deformation is complete Cylinder 2 has the same length and diameter as Cylinder 1 the deformation is uniform along the cylinder there is no observed necking Properties of Undeformed Copper y 69 MPa UTS 200 MPa Strain at fracture 0 45 Strain Hardening Constants for Copper K 530 MPa n 0 44 Cylinder 1 Cylinder 2 Before Deformation Length mm Diameter mm 120 10 100 10 95 After Deformation Length mm Diameter mm not deformed not deformed 120 10 5 a Calculate the true stress being applied to applied to Cylinder 2 at the completion of uniaxial stretching e g when it has reached the same length as Cylinder 1 10 b Using the property data for undeformed copper provided above draw a quantitatively correct engineering stress strain curve for Cylinder 1 subjected to a uniaxial tensile stress and tested to fracture On the same plot add a qualitatively correct engineering stress curve curve for Cylinder 2 tested to fracture paying attention to how you expect the properties of Cylinder 2 to compare with Cylinder 1 Clearly label each curve as belonging to either Cylinder 1 or Cylinder 2
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