Chapter 6- Materials Flashcards
Within Hooke’s law region
F = kx Force = force constant x extension N = Nm-1 x m
Past the elastic limit
Hooke’s law no longer applies (greater extension)
Plastically deformed as it doesn’t return to the same length when you let it go
Energy stored in spring
1/2 k x^2
Substitute Hooke’s law into the area under the curve (E = 1/2 Fx)
Springs in series
On top of each other
The inverse of the total force constant is the sum of the inverse of each
Springs in parallel
Alongside each other
The total force constant is the sum of each individual
The force applied to each is the total force divided by the number of springs
Brittle
Fails under load by cracking - little plastic deformation
Ductile
Can be drawn into wires and have a very large plastic region
Hysteresis Loop
An example is rubber
The area under the loading line is greater than the area under the unloading line
Still follows Hooke’s law
Shows energy is transferred to thermal (difference in areas under)
Work from force extension graph
Area under the loading curve
Energy stored from force extension graph
Area under unloading curve
Stress
The force per cross-section area
Stress equation
Stress = Force/Area σ = F/A
Units Pa or Nm^-2
Strain
A measure of the relative change in length, the extension per unit length
Strain equation
Strain = extension/original length ε = x/L
No units
Young’s Modulus
Stiffness = Stress/strain E = σ/ε E = F/A divided by x/L E = FL/Ax
Units Pa/Nm^-2
Stress-strain vs force-extension graphs
Both have the same shape, stress-strain preferable as they depend on the properties of a material rather than the dimensions
Stress-strain graph shape
Increase proportionally until the limit of proportionality, when strain is greater. Then it reaches the elastic limit in this section. It reaches a yield point where a large amount of plastic deformation (strain) happens without extra load. It flattens before increasing slightly to a peak (ultimate tensile strength) before decreasing as it breaks.
Metal wire
Follows Hooke’s law until a fairly high elastic limit and then starts to curve
Unloading curve identical to loading before elastic limit
After the elastic limit, the unloading curve is parallel to the the Hooke’s law region all the way up
Rubber
Loading curve starts with a high gradient before flattening and then rising again
Unloading curve broadly the same shape but lower
Does not follow Hooke’s law
When strain is the x-axis
Polythene
Does not obey Hooke’s law, no elastic region
Loading curve similar to rubber but steeper earlier on
The unloading curve is a steep straight line not passing through the origin to represent plastic deformation
Thermal energy wasted from a force extension graph
Area between the loading and unloading curves
