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Young’s Modulus - an extension to Hooke’s Law
Main Questions:– 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
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
10 N
20 N
30 N
• 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.
– Less force applied, the smaller the displacement of the spring.
F - applied force k – spring constant x - amount of displacement
k = 60 N/m 60 N will produce a displacement of 1 m
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?
Hooke's Law applies to all solids: wood, bones, foam, metals, plastics, etc...
Young’s modulus
• Measures resistance of material to change its shape when a force is applied to it
• Related to atomic bonding
• Stiff - high Young's modulus
• Flexible - low Young's modulus
Young’s Modulus (x109 Pa)
cotton 5
leather 0.22
brass 110
copper 130
lead 14
nylon 1.8
Brick 28
Concrete 24
Diamond 11,000
Pine 13, 1.2
natural rubber
0.0019
• Same as Hooke’s Law – the stretching of a spring is proportional to the applied force
F = -k x
σ = Ε ε
Young’s Modulus (modulus of elasticity)
A
F stress
L
Lstrain
strain
stressE
F
A
L
LLE
i
if )(
LLA
F
strain
stressE
• Young modulus is large for a stiff material – slope of graph is steep
• Is a property of the material, independent of weight and shape
• Units are usually GPa (x109 Pa)
The Young modulus 2
The Young modulus is a property of the material not the specimen. Units of the Young modulusMN m–2 or MPa; for stiff materials GN m–2 or GPa. Same as units of stress, because strain isa ratio of two lengths, e.g. extension is 1% of length
The Young modulus is large for a stiff material (large stress, small strain). Graph is steep.
large strain for little stress _
material is flexible, easy tostretch
little strain for large stress_ material is stiff, hard tostretch
strain strain
0
0
0
0
e.g. polymer e.g. diamond, steel
Stress vs. strain graphs
How do scientists calculate Young’s Modulus???
•http://www.msm.cam.ac.uk/doitpoms/tlplib/thermal-expansion/simulation.php
