Materials (UNFINISHED) Flashcards
Density =
Mass / volume
Density
Mass per unit volume
Volume of a sphere
4/3 pi x r^3
Volume of a cylinder
pi x r^2 x l
Hooke’s Law
The extension of the material is directly proportional to the applied force(load) up to the limit of proportionality
Hooke’s Law equation
Force = Spring constant x Extension
Spring constant
Measures the stiffness of a material. The larger the spring constant, the stiffer the material
What does a material obeying Hooke’s Law look like on a force-extension graph
Straight line through the origin
Limit of proportionality
The point beyond which Hooke’s law is no longer true when stretching a material. The extension is no longer proportional to the applied force
What does the limit of proportionality look like on a graph
Where the line starts to curve (flatten out)
Elastic limit
The maximum amount a material can be stretched and still return to its original length (above which the material will no longer be elastic)
Where on the force-extension graph is the elastic limit found
After the limit of proportionality
What is the gradient of a force-extension graph, with force on the y-axis and extension on the x-axis
The spring constant
Tensile forces
Forces which stretch the object
Tensile stress
The force exerted per unit cross-sectional area of a material
Tensile stress (sigma) =
Force applied / cross-sectional area
Ultimate tensile stress
Maximum force per original cross-sectional area a wire is able to support until it breaks
Units for tensile stress
Pa
Tensile strain
Extension per unit length
Tensile strain =
Change in length / Original length
Why does strain have no units
Because it is a ratio of lengths
What do stress-strain curves describe
The properties of materials, e.g. whether they are brittle, ductile, have elastic and or plastic behaviour
Yield stress
Force per unit area at which the material extend plastically for no/ a small increase in stress
What does the area under the Hooke’s Law (straight line) region of the graph represent
The elastic strain energy stored per unit volume (only for Hooke’s Law) / work done (for both Hooke’s law and not)
Breaking point
The stress at this point is the breaking stress. The maximum stress a material can stand before it fractures
Elastic region
The region of the graph until the elastic limit. In this region, the material will return to its original shape when the applied force is removed
Plastic region
The region of the graph after the elastic limit. In this region, the material has deformed permanently and will not return to its original shape when the applied force is removed.
Equation for the energy stored under a force-extension graph (obeying Hooke’s Law)
1/2 x Force x Change in Length
What does the area under a force-extension graph which does not obey Hooke’s law represent
Work done
What happens to the work done before a material reaches its elastic limit
It is ALL stored as elastic strain energy
What is the second equation for elastic strain energy
E = 1/2 x k x (change in length)^2
What happens to stress as the force applied to the material increases
Stress increases
Breaking stress
Maximum stress a material can stand before it fractures(breaks)
When is a material considered ductile
Materials with a high breaking stress are considered ductile, this means it can extend more before breaking because of plastic deformation
Examples of a ductile material
Copper
What is spring energy transformed to when a vertical spring is extended and contracted
Kinetic energy and Gravitation potential energy
What is elastic potential energy / spring energy transformed to for a horizontal spring
Only KE
Elastic deformation
When the load is removed, the object will return to its original shape
Plastic deformation
The material is permanently deformed. When the load is removed, the object won’t return to its original shape or length
Where on a stress-strain graph does the plastic region start and end
Start - At the elastic limit
End - At the point of fracture
Brittle materials
Very little to no plastic region e.g. glass and concrete
Ductile materials
Larger plastic region e.g. rubber and copper
How to identify a brittle material on any graph up to their breaking point
A straight line through the origins with no or negligible curved region
How to identify a DUCTILE material on any graph up to their breaking point
Straight line through the origin then curving towards the X-axis
What does the area between loading and unloading line represent
Work done to permanently deform the wire
When a metal wire is loaded and stretched beyond its limit of proportionality what does it undergo
Plastic deformation
After the wire is plastically deformed and the force is removed, what happens
The extension decreases and the unloading line is parallel to the loading line (since k is the same) but it does not go through the origin
How is energy conserved when a car goes over a bump
The energy is absorbed by shock absorbers.
KE is converted to thermal energy which is then dissipated
What is the Young Modulus
The measure of the ability of a material to withstand changes in length with an added load
Why is the Young Modulus useful
It gives info about the stiffness of a material
Useful for engineer to make sure the materials used can withstand sufficient forces
Definition of Young Modulus
Ratio of tensile stress and tensile strain
Young modulus =
Tensile stress / Tensile strain = Force x original length / cross sectional area x extension
Gradient of a linear stress-strain graph
young’s modulus
Area under linear stress-strain graph
Energy stored per unit volume
