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Slide 1

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Deformation of Solids
You be able to:
(a) appreciate that deformation is caused by a pair of forces
and that, in one dimension, the deformation can be tensile or
(b) describe the behaviour of springs and wires in terms of
load, extension, Hooke's law and the spring constant.
(c) define and use the terms elastic limit, stress, strain and
the Young modulus.
(d) describe an experiment to determine the Young modulus of
a metal in the form of a wire.
(e) distinguish between elastic and plastic deformation of a
(f) deduce the strain energy in a deformed material from the
area under the force-extension graph.
(g) demonstrate knowledge of the force-extension graphs for
typical ductile, brittle and polymeric materials, including an
understanding of ultimate tensile stress.…read more

Slide 2

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· The gradient of a stress/strain curve
will give you the Young Modulus
· The graphs look a bit odd at first
because the x and y axes have
swapped over from how they were
lower down the school…read more

Slide 3

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Stress-Strain Curves
Stress-strain graphs are really a development of force-
extension graphs, simply taking into account the factors
needed to ensure a fair test. A typical stress-strain graph
looks like this:…read more

Slide 4

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We can describe the details of the
graph as:
P is the limit of proportionality,
where the linear relationship
between stress and strain
E is the elastic limit. Below the
elastic limit, the wire will return
to its original shape.
·Y is the yield point, where plastic deformation begins. A large
increase in strain is seen for a small increase in stress.
·UTS is the ultimate tensile stress, the maximum stress that is
applied to a wire without its snapping. It is sometimes called the
breaking stress. Notice that beyond the UTS, the force required
to snap the wire is less.
·S is the point where the wire snaps.…read more

Slide 5

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We can draw stress-strain graphs of
materials that show other properties.
Curve A shows a brittle material. This
material is also strong because there is
little strain for a high stress. The
fracture of a brittle material is sudden
and catastrophic, with little or no plastic
deformation. Brittle materials crack
under tension and the stress increases
around the cracks. Cracks propagate less
under compression.
·Curve B is a strong material which is not ductile. Steel wires
stretch very little, and break suddenly. There can be a lot of elastic
strain energy in a steel wire under tension and it will "whiplash" if it
breaks. The ends are razor sharp and such a failure is very
dangerous indeed.
·Curve C is a ductile material
·Curve D is a plastic material. Notice a very large strain for a small
stress. The material will not go back to its original length.…read more

Slide 6

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Brittle material breaks here.
Ductile material stretches
Stress / permanently beyond its elastic
Pa limit.
Release of stress.
If a material is stiff,
it produces little
strain so will have a
(0,0) steeper gradient.
Permanent Deformation.…read more

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