MSE 250 HW 3 Due 09/13/2015
Reading: Callister Chapter 5 and 6
Academic Integrity: Students are encouraged to study with a partner or small group, but each student should complete their homework by themselves (no copying allowed). Please write clearly, show all work in an organized fashion, and circle answers.
1) a) Explain why metals are ductile and ceramics are brittle, in terms of their dislocation motion.
b) Draw 2 pictures to sequentially show an edge dislocation gliding through a crystal, using dots to represent the atoms.
c) Draw 2 pictures to show how a dislocation can climb by capturing a vacancy.
d) What factors limit dislocation mobility?
e) What positive and negative effects does limiting dislocation mobility have on mechanical properties?
2) a) Draw what would happen to the grain structure if a metal with small grains were heated to a high temperature (before and after picture).
b) How will this affect its mechanical properties (strength, ductility)? Hint: think about how the motion of dislocations is blocked by grain boundaries.
3) Determine the rate of diffusivity of Cu in Al at 450K, using D = Do exp (-ED/RT), where Do = 0.15 cm2/sec, and ED = 125 kJ/mole. Note that 1 kJ = 1000 J.
Determine the temperature at which the diffusivity D of Cu in Al is twice the diffusivity at 400K.
5) Using your result for D of Cu in Al at 400K, estimate the distance that a Cu impurity would diffuse in Al at 400 K after 1.5 hours. Use the simple estimate x = (Dt)1/2 – Be careful with your units.
6) The following stress-strain points are generated for a titanium alloy for aerospace applications:
s (in MPa) e (unitless)
Calculate Young’s modulus for this alloy. (Hint: think about whether you should use only some of the points or all of the points).
7) An steel wire (0.5 inch diameter, 100 m long) is used to pull an elevator car between floors in a building. The spool is located at the top of the elevator shaft (100m above the car on the ground floor). If the weight of the unloaded elevator car is 0.5 ton, and if there are 4 people in the elevator, and each weighs an average of 150 pounds:
a) calculate the stress (in pounds per sq. inch) and strain in the cable when the elevator car is resting on the ground,
b) calculate the strain of the wire when it begins its ascent (all weight is on the cable),
c) calculate the change in length of the cable between the states in a) and b) above.
d) determine the change in the diameter of the wire between the states in a) and b) above (Poisson’s ratio is 0.30 for steel) – be sure to indicate the proper sign (positive for increase, negative for decrease)
State your assumptions. EFe = 30 x 106 psi (pounds per square inch). [hint: be careful with the units]
8) An Aluminum rod of radius 0.03 m and length 2.0 M is pulled on with a tensile force of 300,000 N, and the bar stretches to a length of 2.003 m. The radius of the bar is reduced to 0.029985 m.
Determine the stress, strain, Young’ modulus (E), and Poisson’s ratio (n) from this test. Use the Young’s modulus and Poisson’s ratio to determine the Bulk Modulus and Shear Modulus, using the equations given in class.
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MSE 250 HW 3 Due 09/13/2015