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
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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.
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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
• 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