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EN222: Mechanics of Solids
Homework 2: Dislocations
Due Thursday February 16, 2006
Division of Engineering
Brown University
1. Using the method of images, calculate the stress fields induced by a screw dislocation near the
interface between an elastic solid and a very stiff (rigid) solid.
Assume that the two solids are
perfectly bonded.
Calculate the configurational force acting on the dislocation, and state whether
the dislocation is attracted to or repelled from the interface.
2. The complex potentials generating the solution to an edge dislocation at the origin of an infinite
solid were given in class as
()
12
00
22
( )
log( )
( )
log( )
8(
1
)
1
)
Eb i
b
Eb
ib
zi
z
z
i
z
ω
πν
+
−
Ω=
−
=
−−
where
are the burgers vector components. Using whatever symbolic manipulation program you
like, check the formulas given below for the displacement and stress state.
If you find an error,
please give the correct solution!
i
b
1
12 2
2
21 1
1
log( )
cos2
sin 2
2
4
(1
)
8
)
1
log( )
sin 2
2
4
)
8
)
b
ub
r
b
b
b
r
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 Spring '09
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 Stress

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