1 Purdue University School of Materials Engineering MSE 230 Fall 2007 Exam I Solutions September 27 2007 Show All Work and Put Units on Answers Name Recitation Day and Time Recitation Instructor s Name 1 17 2 18 3 15 4 15 5 10 6 15 7 10 Total 100 2 Short Answer 17 pts 1a On the set of axis below schematically draw the force versus atomic distance curve for Fe and Al with regards to the area near ro Label each graph 555 1b Six dog bone samples of lead Pb are heavily coldworked at room temperature One of the samples is immediately tested in tension the remaining five samples are tested over the next hour one every ten minutes As a function of time how would the yield stress vary or if it wouldn t why not Indicate on the plot below Pb recrystallizes at room temperature therefore reducing the dislocation density which will decrease the yield strength We would expect that the strength would diminish with time 5 3 1c Using the image of a methane molecule CH4 and the periodic chart below answer the following questions A periodic chart is provided i On the image indicate with an x the location and number of electron s that do not participate in bonding if any ii Indicate with an C the location and number of electron s from carbon that participate in bonding if any iii Indicate with a H the location and number of electron s from hydrogen that participate in bonding if any iv What is type of bonding indicated in the figure 7 H P 1 17 4 Slip Directions and Planes 18 pts 2a Draw a 2 dimensional representation of an edge dislocation using atoms or lines to represent columns and rows of atoms 2 b Draw a 2 d view of the edge dislocation above after it has emerged at the surface Label the slip plane and show the direction of shear responsible for the dislocation s emergence on the surface 4 c Draw the 1 1 0 slip plane for a BCC unit cell 4 d Draw a 2 dimensional representation of this plane using a hard sphere model to indicate how atoms touch or don t touch in this plane Label the edge lengths of your plane in terms of a e On the 2 d view of the plane drawn in part d label the slip direction s and provide their indice s 4 4 P 2 18 5 X ray Diffraction 15 pts 3 An x ray diffractometer output for an element that has either the BCC or FCC crystal structure showed diffraction peaks at the following 2 angles 38 60o 55 71o 69 70o and 82 55o The wavelength of the incoming radiation was equal to 0 15405 nm a Is this diffraction pattern from an FCC or BCC metal Show all work and reasoning for full credit answer will require math The calculated a or lattice parameter should be the same independent of diffraction peak Therefore our approach is too analyze two peaks as if it is BCC and FCC If BCC then peak 1 is 110 2 d sin If FCC then peak 1 is 111 38 6 15405nm 2d110 sin 2 d110 0 233nm 2d sin d110 a 38 6 15405nm 2d111 sin 2 d111 0 233 12 12 0 2 a 0 3295 nm a d111 3 0 4036 Peak 2 for BCC is 200 2 55 71D d 200 0 1649nm Peak 2 for FCC is 200 FCC 2 55 71D d 0 3298 not equal to 200 d111 a 0 3295nm The lattice parameter based on the assumption of BCC are the same it is BCC 12 b What are the indices of the four diffraction peaks beginning at 38 6o 110 200 211 220 are the first indices that have all h k l even numbers 3 P 3 15 6 Fracture Toughness 15 pts 4 An aircraft component is fabricated from an aluminum alloy that has a plane strain fracture toughness of 40 MPa m For an applied stress of 300 MPa what size of sharp crack will cause brittle fracture Assume the crack is located on the edge of a large specimen K Ic Y a 2 2 KI c 40 Y 1 1 300 4 6 x10 5 m ac 5 or 4 6mm b Knowing that the yield stress is 300 MPa make a numerically correct sketch of the stress versus crack length graph indicating the yield stress and critical stress c as a function of crack length Put an S in the safe area s Yield stress not affected by crack size drawn as horizontal line The critical stress fracture mechanics to cause stress is a function of crack length The two design criteria intersect at 4 6 mm 5 c Assume that the specimen is loaded in plane stress what effect would that have on the schematic drawn in part b Sketch the effect on the graph above clearly labeling the effect as plane stress In plane stress Kc is higher than in plane strain therefore the crack length can be longer before failure occurs 5 P 4 15 7 Strengthening Mechanisms 10 pts 5 A cylindrical rod of annealed brass originally 11 mm in diameter is to be cold worked Assume that the circular cross section is maintained during the drawing process The final diameter should be 8 mm for the application USE A STRAIGHT EDGE TO INTERPRET GRAPHS Using math and text show the processing steps to get a 8 mm diameter wire with a yield strength of at least 350 MPa and a ductility of at least 15 elongation A lathe is not available Area of circle d2 4 r2 Note it is possible to get these properties from Brass 1st Step Consult the Graphs Data Below y 350MPa need cw 20 EL 15 need cw 26 so CW 23 is good If I go from 11 mm to 8 mm directly CW 112 8 2 100 47 which is 112 too much to get the desired properties So you need an intermediate value of di d i2 8 2 0 23 d i 9 1mm d i2 So start at 11 mm CW to 9 1 mm Anneal then perform final CW to 8 mm P 5 10 8 Stress Strain Mechanical Properties 15 pts 6 A cylindrical metal specimen 15 mm in diameter and 150 mm long is to be subjected to a tensile stress of 50 MPa at this stress level the resulting deformation will be totally elastic a If the elongation must be less than 0 072 mm which of the metals in the table below are suitable E L L 50 x 10 6 Pa L 072 x10 3 m E 104GPa L 150 x10 3 m The modulus must be equal to or greater than 104 GPa 9 Circle correct answers Al Brass Copper Mg Nickel Steel Titanium Tungsten b Without regard to your answers in part a if the maximum permissible diameter increase is 2 3 x 10 3 mm when the tensile …
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