# Mid-term exam 02 by keralaguest

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MATERIALS SELECTION                                                          FALL SEMESTER
530.352                                                                    PROF. K.J. HEMKER

MID-TERM EXAMINATION (Closed book - closed notes - open mind)
October 28th, 2002
1.    We have covered a number of different topics in class. Briefly answer 5 out of the 6
questions listed here. Be sure to cross out the one that you do not want me to grade.
(5 points each; 25 points total)

i)     Describe the atomic structure of polymers like polystyrine; what is the basic
structure and how big is it? Explain the difference between thermoset and
thermoplastic, between branched and cross-linked, and between Tglass and Tmelting

ii)    Draw and label the (121) plane. Is there a <110>-type direction [uvw] on this
plane? If so, what is it? What is the <111>-type direction on this plane?

530.352 Materials Selection              Mid-term Exam 2002                             Page 1 of 9
1.    cont. (answer 5 out of 6)

iii)   You work for Ferrari and your boss would like you to design a new piston rod
such that it is both light-weight and does not buckle when loaded in compression.
You may assume that piston rod is cylindrical with a diameter of 6 mm and a
length of 25 cm and that the following relations hold:
m   r 2l 

 2E I        3E r 4
Pbuc kling             
l2           4l 2
Derive the [F][G][M] equation and give the materials index (M1) to minimize the
weight of the sticks.

iv)    One way to slow down dislocations and make a metal stronger is to add a second
element and make a solid solution alloy. About how much solute is there in a
solid solution alloy? Give the empirical relation for the solid solution
strengthening. How does solid solution strengthening work?

530.352 Materials Selection          Mid-term Exam 2002                                Page 2 of 9
1.    cont. (answer 5 out of 6)
v)     Briefly describe three ways to measure or predict the elastic constants of a
material. Which one is the most accurate?

vi)    Circle the following choices that make these statements true. This question is
properties and from where they come. Hint: there is only one correct option (circle) per
question.

a) The Young’s moduli of most engineering ceramics are on the order of 100’s of
[ Pa, / kPa / MPa / GPa / TPa ].

b) In a compression test, the true stress is [ higher / lower ] than the engineering
stress.

c) Decreasing the grain size a metallic alloy by a factor of 100 will result in a
[ 0.01 / 0.1 / 10 / 100 / 1000 ] fold increase in tensile strength of the alloy.

d) As a general rule, the strength of a polymer [ increases / decreases / is not
affected ] with an increase in the molecular weight of the chains.

e) The asymmetry of the potential well describing the interaction between
neighboring atoms is related to the [ elastic modulus / lattice parameter /
melting temperature / coefficient of thermal expansion ] of the material.

530.352 Materials Selection             Mid-term Exam 2002                                     Page 3 of 9
2.    The interactions between neighboring atoms in metals and ceramics often described in
terms of a “potential well”. Label the axes of the drawings given below (4 points) and use
these curves to describe:

i)     The Young’s modulus (E). (5 points)

ii)    The coefficient of thermal expansion. (3 points)
.

530.352 Materials Selection           Mid-term Exam 2002                               Page 4 of 9
2.    continued:
iii)   What is the basic isotropic equation for 3D Hooke’s Law? (5 points)

iv)    If a thin film of Al is deposited onto a Si
substrate at 525C and then cooled to room                            Al
temperature (25C). The in-plane strain is              Si
given by th = T = 0.01.
Assume that zz = 0 and
calculate xx and yy. (8 points)
EAl = 70 GPa and =1/3

530.352 Materials Selection           Mid-term Exam 2002                               Page 5 of 9
3.    Aluminum has a face centered cubic (fcc) crystal structure and dislocations are known to
glide on close packed planes with Burgers vectors along the close packed directions.
i)     Draw the unit cell for the fcc crystal structure and identify the family of close
packed directions (draw a line for and label one of these directions) and close
packed family of planes (shade and label one of these planes on your drawing).
(8 points)

Closely packed directions

< , , >

Closely packed planes

{ , , }

ii)    Many aluminum alloys are precipitation strengthened. What is precipitation
hardening and what three steps to you have to take to make a precipitation
strengthen alloy? (5 points)

530.352 Materials Selection           Mid-term Exam 2002                                  Page 6 of 9
#3 Continued …
iii)   Explain what happens microstructurally to give the curve shown below. Why
does the strength increase with ageing? Why does it reach a peak and then
decrease if the alloy is aged for a long time? (8 points)

50

y (ksi)        40

30

Heat Treating Time

iv)    If an Al alloy is over-aged and the distance between precipitates increases from
2.5 microns (10-6 m) to 10 microns. What would be the corresponding change in
strength? (4 points) Note: G = 70 GPa and |b| = 2.5 x 10-8 cm.

530.352 Materials Selection          Mid-term Exam 2002                                Page 7 of 9
4.    Dislocations play an important role in determining the mechanical properties of metals and

i)     A bar containing two edge dislocations is attached to a rigid wall as shown below.
What would the stress state in the bar be if you were to pull down on the outer
edge of the bar? Show this by indicating the sense of the tensile and shear stress
on the unit elements drawn below. Remember to balance the moments.
If the dislocations can glide, but not climb, where are their final positions?
(6 points)

ii)    Draw a left-handed screw dislocation. What is the relationship between the
Burger’s vector and the line direction of this LHS dislocation? Does the LHS
move perpendicular or parallel to the Burger’s vector? (4 points)

530.352 Materials Selection            Mid-term Exam 2002                                  Page 8 of 9
#4 Continued …
iii)   For the dislocation loop drawn below, indicate the character (+E,-E,RHS,LHS)
of the dislocation segments in each of the four dashed boxes. Given the applied
shear stress, show the direction of motion of each of these four segments.
Would this loop expand or shrink? (15 points)
Recall: t  b = extra half plane.

530.352 Materials Selection               Mid-term Exam 2002                           Page 9 of 9

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