Materials
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Forces
Stress
Strain
Stress / strain graphs
Young’s modulus
Strength
Strain energy & toughness
Materials - 1
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Forces on materials
• Forces can act in different directions to change the shape or size of an
object.
Materials - 2
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Forces on materials - tension
• Tension forces at to stretch an object.
Materials - 3
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Forces on materials - compression
• Compression forces act to squash an object.
Materials - 4
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Forces on materials - shear
• Shear forces act sideways on an object.
Materials - 5
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Stress
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Stress is the force applied per area.
Stress can be compression or tension.
Measured in Pascal: 1Pa = 1N / m2.
Material stresses are usually measured in MPa or
GPa as areas are small.
• 1kg sitting on a 10 cm square.....
F
σ=
A
Stress = 10N / 0.01m2 = 1000 Pa
Materials - 6
0.1 m x 0.1 m = 0.01 m2
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Strain
• Strain is the % increase in length of an object (as a response to
stress).
• Strain = change in length / original length
• Strain has no unit as it is a ratio.
L
ΔL
ε=
L
∆L
ε = 5 cm / 20 cm = 25%
Materials - 7
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Stress / strain graphs
Stiffest
(least strain
for stress)
Brile behaviour
Strongest
(highest stress
before breaking)
Plastic (ductile) behaviour
Materials - 8
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Stiffness - Young’s Modulus
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Young’s Modulus / Modulus of stiffness
Young’s Modulus = stress / strain
It is the gradient of the stress / strain graph.
Measured in Pa (usually GPa).
σ
E=
ε
6
300×10 Pa
E=
0.0025
11
E =1.2×10 Pa
E =120×GPa
Materials - 9
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Young’s Modulus
Materials - 10
Material
Young’s modulus (GPa)
Carbon fibre
410
Steel
200
Kevlar
140
Glass
70
Bone
14
Pine
10
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Strength
• Strength is normally defined as the stress that causes a material to
break.
• Strength is measured in Pa (usually MPa).
• Some examples of every-day materials:
Material
Tensile strength (MPa)
Compressive strength (MPa)
Cast iron
170
550
Carbon fibre
2000
0
Granite
0
240
Pine
40
35
Bone
130
170
• Strongest materials under tension include carbon fibre, steel.
• Strongest materials under compression include steel, stone.
Materials - 11
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Strain energy & toughness
• Strain energy is the energy stored when work is done to change the
length of an object.
• The area under a stress strain graph:
F ΔL
F ×ΔL
σ ×ε = ×
=
A L
A×L
Work
=
Volume
• Toughness is description of the amount of energy required to break a
material.
• Tough materials tend to exhibit plastic deformations before breaking.
• This is found by the area under the stress / strain graph.
• Tough materials include many metals, tendons ( joining bone to muscle),
rubber, kevlar
Materials - 12
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Toughness - energy calculations
Work
Stress × strain =
Volume
Work 1
= (3×10 8 N /m 2 )×(2.5×10−3 )
Volume 2
5
= 3.8×10 J /m
Materials - 13
3
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