Transcript Young`s Modulus - an extension to Hooke`s Law

Young’s Modulus - an extension
to Hooke’s Law
Main Questions:
–
–
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Why are mechanical properties important for
engineers?
How is Young’s modulus related to Hooke’s Law?
How do scientists test materials to calculate the
Young’s modulus?
What is the difference between materials with high
Young’s modulus vs. materials with a low value?
Duration: 3-5 days
Amazing footage on of it here.
The main causes of engineering disasters are:
• human factors (including both 'ethical' failures
and accidents)
• design flaws
• materials failures
• extreme conditions or environments
and, of course, any combination of any of
these
Mechanical Properties
• numerical value used to compare benefits of
one material vs. another
• specific units
• serves to aid in material selection
Hooke’s Law
• The amount of force applied
is proportional to the
amount of displacement
(length of stretch or
compression).
– The stronger the force applied,
the greater the displacement is.
10 N
20 N
30 N
– Less force applied, the smaller
the displacement of the spring.
 k = 60 N/m
60 N will produce a displacement
of 1 m
 F - applied force
 k – spring constant
 x - amount of displacement
Hooke's Law applies to all solids:
wood, bones, foam, metals, plastics,
etc...
 What force will make the spring
stretch a distance of 5 m?
 Which spring will have a greater
spring constant, aluminium
spring, or steel spring? Why?
Young’s
modulus
Young’s
Modulus
(x109 Pa)
cotton
leather
brass
copper
5
0.22
110
130
• Related to atomic bonding
lead
nylon
Brick
14
1.8
28
• Stiff - high Young's modulus
Concrete
24
Diamond
11,000
Pine
13, 1.2
natural
rubber
0.0019
• Measures resistance of
material to change its shape
when a force is applied to it
• Flexible - low Young's modulus
• Same as Hooke’s Law – the stretching of a
spring is proportional to the applied force
F = -k x
σ=Εε
stress 
F
A
strain 
L
L
Young’s Modulus
(modulus of elasticity)
stress
E
strain
F
stress
A
E 

L
strain
L
( Lf  Li ) A
E
Li
F
Stress vs. strain graphs
The Young modulus 2
large strain for little stress _
material is flexible, easy to
stretch
0
little strain for large stress
_ material is stiff, hard to
stretch
0
0
strain 
0
strain 
e.g. polymer
diamond,
steel
• Young
modulus is large for ae.g.stiff
material
– slope
of
graph is steep
The Young modulus is large for a stiff material (large stress, small strain). Graph is steep.
• Is a property of the material, independent of weight
and
shape
The Young
modulus is a property of the material not the specimen. Units of the Young modulus
–
2
MN m or MPa; for stiff materials GN m–2 or GPa. Same as units of stress, because strain is
• Units
usually
(x109 Pa)
a ratio of twoare
lengths,
e.g. extension GPa
is 1% of length
How do scientists calculate
Young’s Modulus???
•http://www.msm.cam.ac.uk/doitpoms/tlplib/thermal-expansion/simulation.php