Describe each section of the graph below.
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Spring follows Hooke’s law; it has elastic behaviour.
Elastic limit is reached, it is permanently deformed.
Spring shows plastic behaviour; little force causes big
extension.
Spring has reached its ultimate tensile stress (UTS).
Spring has reached its breaking point and snaps.
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2.5 Graphs - Materials
Topic 2
Materials
Describing Materials
Young modulus of a material describes its stiffness.
Spring constant of a material describes its elasticity.
Stress describes the strength of a material through its
ability to withstand applied pressure.
UTS describes the maximum stress a material can take
before snapping.
Strain describes the materials ability to withstand
deformation.
Behaviour of Materials
Brittle behaviour means the material will snap after
reaching its elastic limit.
Ductile behaviour means the material is durable and has a
high plastic region.
Plastic behaviour means the material has exceeded its
elastic limit and it is now permanently deformed. Small
stress will result in large strain.
Elastic behaviour means the material obeys Hooke’s law
and will return to its original length once the load is
released, assuming the elastic limit hasn't been exceeded.
Material Graphs
Stress - strain graph is used to show
the deformation of a material.
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Gradient of a stress – strain graphs
gives you the Young modulus.
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The area gives you the elastic
energy stored per unit volume (½σε).
Force – extension graph is used to
show elastic behaviour.
Gradient gives you the spring or force
constant.
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The area of the graph gives you the
stored elastic potential energy (½Fe) .
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Properties of Material - Brittle
Brittle materials, such as a brick, can
sustain a lot of stress.
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It has a high spring constant.
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After it has reached its elastic limit,
it snaps.
Brittle material stores very little
elastic potential energy.
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Loading and unloading is
proportional to extension.
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It does not have a plastic region.
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Properties of Material - Ductile
Ductile materials, like copper, can be
drawn into a wire.
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These materials have a large plastic
region
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Ductile materials are durable.
Extension for a ductile material is the
same for loading and unloading.
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It will go back to its original length
when all load is removed.
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If elastic limit is exceeded, unloading
will be parallel to loading but it will be
permanently deformed.
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Properties of Material - Polythene
Polythene material, such as rubber,
has a high strain percentage.
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It reaches it’s elastic limit quite
easily.
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It has a high UTS, which means after
a while, it is difficult to stretch.
Extension isn't proportional due to
the atomic arrangement of particles.
Its extension when unloading is
greater than loading.
If its elastic limit is exceeded, the
extension while unloading will be
proportional.
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Question 1
To describe deformation of a material, we use a stress –
strain graph instead of force – extension graph. Explain
why.
Question 2
After exceeding the elastic limit, less energy is retrieved
when unloading from a ductile material. Explain why.
Question 3
Explain why the loading and unloading graph for polythene
is peculiar.
Question 4
Force – extension graph for polythene can be broken into
three segments. Explain each segment of this graph.