(10) 1. True and False Circle either TRUE or FALSE i: The equilibrium separation distance, r 0, is the distance at which TRUE FALSE the potential energ between atoms (or ions) is ero. r 0 is the distance at which the potential energ is at a minimum. ii: A Young s modulus of 1 GPa is a reasonable value for a bulk TRUE FALSE polmeric material. iii: Polethlene polmeried such that the polethlene chains TRUE FALSE have branches is epected to have a higher degree of crstallinit than polethlene polmeried such that the polethlene chains are linear. iv: Polmers for which M w >> M n have a narrow molecular weight TRUE FALSE distribution. v: In a BCC crstal structure the atoms touch along the <111>. TRUE FALSE
(15) 2. Planes, Directions and slip sstems. (6) a) Draw the following inside the cubes provided. 1 [121] (210)& [121] (112)& (4) b) The drawing below shows the arrangement of atoms in the {100} of either the FCC or BCC crstal structure. First, circle whether this is the FCC or BCC structure. Second, use arrows to label the <100> and the <110> (one arrow for each famil of directions is sufficient). [011]& [121] The structure is FCC <100>% <110>% (5) c) In the space provided to the right, state whether the pairs of planes and directions below are possible slip sstems for: a FCC metal (write FCC ), for a BCC metal (write BCC ), or are not possible slip sstems for either FCC or BCC (write N ). 110 i) 111 111 ii) 101 iii) 111 $ FCC 011 iv) 110 110 v) 011 111 $ N $ FCC $ N $ BCC
(10) 3. Relativel Short Calculations, circle one answer for each problem, no partial credit. 2 The net page is left blank for our use, but no partial will be given for anthing written there. (5) a) A bar of a metal with a square cross section is subjected to a tensile stress of 75 MPa in the -direction and a tensile stress 350 MPa in the - direction. Given that the ield stress is 400 MPa, E=120 GPa and ν=0.30, the applied stress in the -direction required to produce a strain of ero in the -direction (ε =0) is: i) a 100 MPa compressive stress ii) a 100 MPa tensile stress iii) a stress of 0 MPa iv) can t perform the calculation due to plastic deformation. v) a 350 MPa tensile stress (5) b) A clindrical rod of 1020 steel 100 mm in length and having a diameter of 10 mm is subjected an applied tensile load of 35,000 N. Given that the Young s modulus of 1020 steel is 200 GPa and the ield stress is 240 MPa, the strain along the ais of the clinder resulting from the applied load is: i) 0.00056 ii) 0.0022 iii) 0.0012 iv) 0.00086 v) can t perform the calculation due to plastic deformation. The applied stress is 445.6 MPa. Since the applied stress is greater than the ield stress Hooke s law does not appl due to plastic deformation. If ou went ahead and used Hooke s law anwa ou would get a strain of 0.0022.
3
4 (15) 4. The plot below represents the -ra diffraction data (collected at room temperature using - ras with a wavelength of λ=0.154 nm) for an unknown metal that has either a FCC or BCC structure. Intensit( (2) a) Calculate the interplanar spacing associated with the peak at 52 two theta. d = λ 2sinθ d = 0.154nm 2( sin26 ) = 0.176nm 20( 30( 40( 50( 60( 70( 80( 36.2 ( 2Θ 52.0 ( 65.0 ( 76.7 ( (2) b) Calculate the lattice parameter of the unknown metal. The peak at 52 two theta will be the (200) regardless of whether the crstal structure is FCC or BCC. See document a = d h 2 + k 2 + l 2 = d 2 2 + 0 2 + 0 2 = 0.352nm (7) c) Determine if the metal has a FCC or BCC structure. Show our work and use calculations to justif our choice. You need to recognie that the lattice parameter does not change from -ra peak to -ra peak, so regardless of the interplanar spacing and Miller s inde, a should be the same. If the unknown metal has a FCC structure the Miller s indicies for the first two peaks are (111) and (200). If the structure is BCC the Miller s indicies of the first two peaks are (110) and (200). Knowing the Miller s inde and d- spacing one ma calculate the lattice parameter (a). For FCC, a(36.2 ) = 0.248 1 2 +1 2 +1 2 = 0.43 nm, and a(52 ) = 0.352 2 2 + 0 2 + 0 2 = 0.35 nm For BCC, a(36.2 ) = 0.248 1 2 +1 2 + 0 2 = 0.35 nm, and a(52 ) = 0.352 2 2 + 0 2 + 0 2 = 0.35 nm Since the BCC lattice parameter values are independent of peak position the crstal structure is BCC. (4) d) Given our answer in part c), write out the Miller s inde for each peak net to the listed two theta angle below. Following the selection rules for BCC, h+k+l=even, one gets 36.2 : (110) 52.0 : (200) 65.0 : (211) 76.7 : (220)
(10) 5. Yield stress of undeformed cartridge brass: σ ield =120 MPa, σ UTS =225 MPa. Strain hardening constants for cartridge brass: K=900 MPa, n=0.49 An undeformed rectangular plate of cartridge brass is reduced in thickness b room temperature plastic deformation using a rolling mill. A mechanical test specimen cut from the strain hardened plate is tested in uniaial tension, resulting in the engineering stress-strain curve shown below. The stress data in the curve is quantitativel correct while the strain data is qualitativel correct. 5 (5) a) Calculate the amount of true strain in the deformed plate that resulted in the stress-strain curve above. The ke to this problem is to recognie that the ield stress of the deformed sample is equal to the true stress of the undeformed sample when it has reached the true strain that ou need to calculate. From the stress-strain curve, the ield stress of the deformed sample is approimatel 250 MPa. σ T = Kε T n lnσ T = ln K + n lnε T $ ε T = ep lnσ ln K ' T % & n ( ) = 0.073 $ ε T = ep lnσ T ln K' % & n ( ) (5) b) On the plot above, draw an engineering stress-strain curve reflecting the epected mechanical behavior of undeformed cartridge brass when subjected to testing in uniaial tension. Your plot should be quantitativel correct where possible, e.g., using the data provided above. The main elements are that the slope representing Young s modulus should be the same for the undeformed sample, the ield stress should be at approimatel 120 MPa, and the stress-strain curve should be at a maimum at the ultimate tensile strength of 225 MPa.