# Behaviour of materials, (stress and strain)

Everything you need to know about extension, stress, strain, etc. Enjoy!

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• Created on: 07-01-11 22:02

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Behaviour of Springs and Materials
If a metal wire is supported at the top then a weight attached to the bottom, it
stretches. The weight pulls down with force F, producing an equal and opposite
force at the support. Deformation only happens when a pair of opposite forces act.
Tensile forces: Compressive forces:
F=ke This is Hooke's Law: force and extension are proportional, (this only applies
to some materials and for the rest only until the elastic limit). K, (the gradient of
the graph), is the spring constant.
Elastic deformation: returns to original length when force is released as the
energy is used to pull atoms apart but their bonds are maintained.
shape when the force is released as energy is used to break the atom's bonds, so they move into
new positions.
Level of deformation: the increase in the spring's length after the force is removed past the elastic
limit.
The spring past its elastic limit when the force is removed, note the gradient, (k), is the
same.
The area under a force against extension/ compression graph is the work done by the force. Until the
elastic limit it is stored as elastic (strain) potential energy, so E=0.5Fx
or E=0.5kx²
e.g. For the graph on the right the work done is the area under the
graph: 0.2x50x0.5= 5J
The energy stored is the area under the elastic deformation:
0.2x50x0.5= 5J
e.g. For the graph on the left the work done is the area under the
graph:
5J+20J= 25J
The energy stored is the area under the elastic deformation:
5J
The area under plastic deformation is released as heat; here 20J is
lost as heat.
Stress= F/A, force per unit cross-sectional area, measured in pascals, (Pa).
Strain= x/l, extension per original length
Young's modulus: the ration between stress and strain, measured in pascals, (Pa): stress/strain
Ultimate tensile strength, (breaking stress): the maximum stress a material can stand without
breaking
An experiment to stretch a wire:

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### Page 2

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Wear safety goggles, ping!
Use as long and thin a wire as possible, as it will extend more for the same force, (reduces
error).
1. Find the smallest weight necessary to straighten the wire, (found by placing masses on a
balance and multiplying by g to find the force).
2. Measure the distance between the fixed end of the wire and the marker with a ruler, this is

### Page 3

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The material does not deform plastically, deforms elastically very little
When stress is applied to a brittle material any tiny cracks in the material's surface get bigger
until the material breaks, this is called brittle fracture.…read more