1
Assignment #2 Solutions
ME264 Materials Science for Mechanical Engineering
Spring 2009
Due Date: 25 February 2009
(3 pts)
1. (1.5pt)
(a)
Define
Poisson’s ratio
,
ν
, and
dilatation
,
∆
, in the straining of an elastic solid.
(b)
Calculate the dilatation
∆
in the uniaxial elastic extension of a bar of material,
assuming strains are small, in terms of
ν
and the tensile strain,
ε
. Hence find the
value of
ν
for which the volume change during elastic deformation is zero.
(c)
Poisson’s ratio for most metals is about 0.3. For cork it is close to zero; for
rubber it is close to 0.5. What are the approximate volume changes in each of
these materials during an elastic tensile strain of
ε
?
Solution:
(b)
The following figure shows the uniaxial elastic extension of a bar of material.
The change in axial length :
0
l
l
l
δ
ε
=
The length of the bar under uniaxial elastic extension:
(
)
0
0
0
0
1
l
l
l
l
l
l
l
l
l
l
δ
ε
ε
=
+
=
+
=
+
The cross sectional area of the bar under uniaxial elastic extension:
(
)
2
0
1
l
A
v
A
ε
=

Proof:
2
0
0
A
r
π
=
:cross sectional area before elastic extension.
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 Spring '09
 Asst.Prof.A.FethiOkyar
 Mechanical Engineering, Strain, Tensile strength, uniaxial elastic extension, Chromium Niobium Molybdenum Tantalum Tungsten, εr δl

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