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1/8 pages total
P.M. Anderson
•
(614) 2920176
•
(614) 2921537•
email:
[email protected]
Practice Final
Materials Science and Engineering 765
Introduction to Mechanical Behavior of Materials
Spring Quarter, 2005
SOLUTIONS
Instructions:
Please Read Before Beginning!
You have1 hour and 48 minutes to answer all 6 problems on this exam.
You may use a
calculator and an 8.5" by 11" doublesided sheet of notes in your own handwriting.
Write all
answers on the question sheet in the space provided.
Continue on the reverse side of the sheet if
more space is needed.
Good Luck!
1.
Interaction Between Dislocations
Determine the glide and climb forces exerted on an edge dislocation that lies along the z
direction, and is located at a position (x, y) from a parallel screw dislocation.
(Note:
if you
did not write down the stress state produced by dislocations, then you may borrow a textbook
from me).
We use the diagram below and note that the glide and climb forces on the edge dislocation
are given by:
F
glide
edge
L
=
F
x
edge
L
=
σ
xy
screw
(x,y)b
edge
F
climb
edge
L
=
F
y
edge
L
=
−σ
xx
screw
edge
Since the screw dislocation does not produce components
σ
xy
and
σ
xx
, the glide and climb
forces on the edge dislocation are both zero.
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2.
Crystal Slip Systems
(a)
List three slip systems that are in the family of <110> slip directions and {111} slip
planes.
We can take several possibilities here.
For the sake of an example, we take:
n
(1)
as {1 1 1}/sqrt(3), s
(1)
as {1 0 1}/sqrt(2)
n
(2)
as {1 1 1}/sqrt(3), s
(2)
as {1 1 0}/sqrt(2)
n
(3)
as {1 1 1}/sqrt(3), s
(3)
as {1 1 0}/sqrt(2)
(b)
What direct plastic strain in the 1direction would be produced if a single crystal of
volume 1mm
3
deformed by having each of the systems you mention above slip together, so
that the slipped area for each of the systems is 1mm
2
.
Assume that the Burgers vector
magnitude is b = 2.5
⋅
10
10
m
We realize that:
ε
ij
P
=
ε
ij
P(1)
+
ε
ij
P(2)
+
ε
ij
P(3)
where
ε
ij
P(
α
)
=
A
s
(
α
)
b
(
α
)
2V
n
i
s
j
+
n
j
s
i
( )
(
α
)
If we insert the values mentioned above and set i = 1 and j = 1, then:
ε
ij
P
=
2.5
×
10
−
7
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 Spring '05
 Anderson
 Materials Science And Engineering, Yield surface, Von Mises yield criterion

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