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Mind Map by Kieran Lancaster, updated more than 1 year ago
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Created by Kieran Lancaster
almost 7 years ago
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Chapter 6 - Materials
- Springs and Hooke's Law
- A helical spring undergoes tensile deformation when tensile forces
are exerted, and compressive deformation when compressive forces
are exerted
- Here is a force extension graph for a spring. The line is straight up until the elastic
limit, where there is elastic deformation. The spring returns to it's original length
- Above the elastic limit, the spring undergoes plastic deformation. where there are
permanent structural changes. The spring stays at permanent extension once the force is
removed.
- Above the elastic limit, the spring undergoes plastic deformation. where there are
permanent structural changes. The spring stays at permanent extension once the force is
removed.
- Hookes law = The extension of the spring is directly
proportional to the force applied, below the elastic limit
- The force constant k
(Units Nm^-1) is a
measure of stiffness of
the spring, and is given by
the gradient of the graph
- The force constant k
(Units Nm^-1) is a
measure of stiffness of
the spring, and is given by
the gradient of the graph
- A helical spring undergoes tensile deformation when tensile forces
are exerted, and compressive deformation when compressive forces
are exerted
- Elastic potential energy
- If work is done below the elastic limit, the work
done on the material can be fully recovered,
- However, above the elastic llimit, atoms have been moved into new
permanent positions, meaning the work done is not recoverable
- However, above the elastic llimit, atoms have been moved into new
permanent positions, meaning the work done is not recoverable
- The area underneath a force-extension graph = Work done
- Since the area under the graph is the area of a triangle, E=0.5Fx
- By using hookes law, of F=kx, another equation can also be created.
E=0.5(kx)x, therefore E=0.5kx^2
- By using hookes law, of F=kx, another equation can also be created.
E=0.5(kx)x, therefore E=0.5kx^2
- Since the area under the graph is the area of a triangle, E=0.5Fx
- If work is done below the elastic limit, the work
done on the material can be fully recovered,
- Deforming
materials
- Different materials respond differently to tensile forces, meaning the
loading and unloading curves will not be the same
- METAL
- For metal, hookes law is followed until the elastic limit,
meaning that the unloading curve is identical below this limit.
Beyond however, there is plastic deformation and the
unloading curve is parallel, with permanent extension x.
- For metal, hookes law is followed until the elastic limit,
meaning that the unloading curve is identical below this limit.
Beyond however, there is plastic deformation and the
unloading curve is parallel, with permanent extension x.
- RUBBER
- They do not obey hookes law, there is elastic deformation.
The Hysterisis loop is due to differences of work done.
More work is done stretching the band than unloading it.
The area inside the loop is the energy released when the
material is loaded then unloaded, meaning it's hotter
- They do not obey hookes law, there is elastic deformation.
The Hysterisis loop is due to differences of work done.
More work is done stretching the band than unloading it.
The area inside the loop is the energy released when the
material is loaded then unloaded, meaning it's hotter
- POLYTHENE
- Used in plastic bags, polythene does not obey
hookes law. Very easy to stretch with little force,
resulting in plastic deformation
- Used in plastic bags, polythene does not obey
hookes law. Very easy to stretch with little force,
resulting in plastic deformation
- METAL
- Different materials respond differently to tensile forces, meaning the
loading and unloading curves will not be the same
- Stress, Strain, and the Young
Modulus
- Tensile stress (Pa) = Force applied per unit
cross-sectional area
- Tensile strain (No unit's as it's a ratio) = The fractional
change in the original length of the wire
- The following is a stress-strain graph for a
ductile (steel)material, i.e which can be
hammered or drawn in into a wire
- Stress is directly proportional to strain until point P
- Hookes law is followed until the elastic limit E, with
elastic deformation
- At the Yield points, the material extends rapidly.
Non-steel materials may not have this
- Point U is the maximum stress a material withstands before it
breaks. Beyond this point, necking occurs, where the steel
becomes thinner and weaker
- The Rupture strength, or breaking point is when the material breaks
- The Rupture strength, or breaking point is when the material breaks
- Point U is the maximum stress a material withstands before it
breaks. Beyond this point, necking occurs, where the steel
becomes thinner and weaker
- At the Yield points, the material extends rapidly.
Non-steel materials may not have this
- Hookes law is followed until the elastic limit E, with
elastic deformation
- Stress is directly proportional to strain until point P
- The ratio of stress to strain is the Young modulus (Units Nm^-2), and
is found by the gradient of the linear region of a stress strain graph
- Brittle materials experience elastic deformation until their breaking point, but polymeric
(Rubber or polythene) behave differently based on temperature and structure
- Determining the Young modulus of a wire
- Measure Diameter d of the wire with a micrometer, to then work
out C.S.A. Average measurements can improve accuracy
- The tensile force is worked out using F=mg,
where m is the mass hanger and g=9.81
- After applying each mass, work out the extension change
from the original length, again repeating readings
- For each load, the stress and strain values are plotted on a stress strain
graph. The gradient of the linear section gives the Young modulus
- For each load, the stress and strain values are plotted on a stress strain
graph. The gradient of the linear section gives the Young modulus
- After applying each mass, work out the extension change
from the original length, again repeating readings
- The tensile force is worked out using F=mg,
where m is the mass hanger and g=9.81
- Measure Diameter d of the wire with a micrometer, to then work
out C.S.A. Average measurements can improve accuracy
- Tensile stress (Pa) = Force applied per unit
cross-sectional area
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