Materials Flashcards
What is the density of a material?
Its mass per unit volume
What is the equation for density?
Density = mass / volume
What 1 g cm^-3 equal to?
1000 kg m^-3
Why does oil float on water?
It has a lower density than water
Why will a solid object float on a fluid?
If its density is less than the density of the fluid
What is Hooke’s Law?
The extension of a stretched wire is directly proportional to the force applied
What happens, in terms of forces, when a light metal wire is supported at the top and then has a weight attached at the bottom?
The weight pulls down with a force, stretching the wire. Once the wire stops stretching, the forces will be in equilibrium and there will be an equal and opposite reaction force at the support
What is an objects stiffness constant?
The force needed to extend it by 1m
What is the equation for Hooke’s Law?
Force = stiffness constant x extension
What does a tensile force do?
Stretches something
What does a compressive force do?
Squashes something
What are 2 features of a force-extension graph that shows the material obeys Hooke’s Law?
It’s a straight line through the origin
What is the gradient of a force-extension graph equal to?
Stiffness constant
At what point on a force-extension graph does an object reach its elastic limit?
When the graph starts to curve
What happens if you increase the force past the elastic limit?
The material will be permanently stretched (and won’t go back to original shape when force is removed)
What is the elastic limit of an object?
The force beyond which a material will be permanently stretched
What is the limit of proportionality?
The point beyond which the force is no longer proportional to the extension (so the gradient of a force-extension graph is no longer linear)
On a force-extension graph, where do you mark the limit of proportionality?
When the line of the graph is no longer straight
What are 5 the steps for the experiment to investigate the extension?
- Set up a clamp stand and clamp with a spring attached
- Take a measurement of the original length of the spring
- One at a time, add weights to the bottom of the spring, and measure the new length
- Calculate extension by doing extension = new length - original length
- Plot a graph of force against extension
When investigating the extension of a spring in a lab, why do you trial investigation first?
So you can work out the size and range of weights to get lots of measurements before the objects break
What does loading mean?
Increasing the force on the material
What does unloading mean?
Reducing the force on the material
What is elastic deformation?
Where the material returns to it’s original shape once the forces are removed - there’s no permanent extension
How can you tell a material is elastic from a force-extension curve showing loading and unloading?
If both lines start and end in the same position
What happens when a material is put under tension?
The atoms of the material are pulled apart from one another, as atoms can move small distances from their equilibrium position without changing position in the material
What happens to the atoms in a material once a force is removed?
The atoms return to their equilibrium distance apart
For a metal, elastic deformation happens as long as…?
Hooke’s Law is obeyed
What is plastic deformation?
Where the material is permanently stretched after the force is removed
What happens to the atoms in a material when plastic deformation occurs?
Some atoms in the material move position relative to one another. When the load is removed, the atoms don’t return to their original positions.
When does plastic deformation happen with metals?
When the metal is stretched past its elastic limit
What is tensile stress?
The force applied divided by the cross-sectional area
What is a tensile force?
A force that stretches something
What is tensile strain?
The change in length divided by the original length of the material
What is the equation for tensile stress?
Stress = force / cross-sectional area
What are the units for stress?
Pa or Nm^-2
What does stress cause?
Strain
What are compressive forces?
Forces that squash a material
What is the equation for tensile strain?
Strain = extension / original Length
What are the units for strain?
There are no units because it’s a ratio
What happens when a greater tensile force is applied to a material?
The stress increases
What does the effect of stress on a material do to the atoms of the material?
Pulls the atoms apart from one another until eventually the stress becomes so great they separate completely, so the material breaks
What is the breaking stress?
The stress at which the atoms in a material separate, so the material breaks
What is the ultimate tensile stress?
The maximum stress that the material can withstand
What is the area under a force-extension graph equal to?
The elastic strain energy stored in it
What is elastic strain energy?
The energy stored in a stretched material
What is the energy stored in the stretched material equal to?
Work done on the material in stretching it
What is the equation for elastic strain energy?
Energy = 0.5 x stiffness constant x extension^2
How can you derive the equation E=0.5FΔL?
From a force-extension graph, the energy is the area under the graph. As the area is a triangle (when obeying Hooke’s Law), 0.5 base x height = 0.5FΔL
Energy is always…. when stretching?
Energy is always conserved when stretching
Explain how the conservation of energy works for elastic deformation
All the work done is stored as elastic strain energy. When the force is removed, this stored energy is transferred to other forms
Explain how the conservation of energy works for plastic deformation
Work is done to separate the atoms. The energy is not stored as strain energy, so is mostly dissipated as heat
Explain the conservation of energy in springs
When a vertical spring with a mass hanging directly below it is stretched, elastic strain energy is stored in the spring. When the end of the spring with the mass is released, energy is transferred to kinetic energy (spring contracts) and gravitational potential energy. The spring then compresses and the kinetic energy is transferred back to elastic strain energy
What can the energy changes in an oscillating spring be summed up as?
Change in kinetic energy = Change in potential energy
Why are modern cars required to have crumple zones that plastically deform?
So that the car’s kinetic energy goes into changing the shape of the bumper, so less is transferred to the people inside
Up to the limit of proportionality, the stress and strain of a material are…?
Up to the limit of proportionality, the stress and strain of a material are proportional to each other
What is the Young Modulus?
The stress divided by the strain of a material up to the limit of proportionality
What is the equation for Young Modulus?
E = tensile stress / tensile strain
What are the units of Young Modulus?
Pa or Nm^-2 (units of stress because strain has no units)
What are the 6 steps for the Young Modulus experiment?
- Find cross-sectional area of wire using a micrometer to measure the diameter
- Clamp the wire to a bench so you can hang weights off the end
- Start with the smallest weight to straighten the wire (don’t use this in calculations)
- Measure the distance between the fixed end of the wire and a marker on the wire (this is unstretched length)
- Add weights to the end in 100g intervals and measure the distance to the marker as above, then calculate the extension
- Use results to calculate stress and strain then plot a stress-strain graph
How do you work out the Young Modulus from a stress-strain graph?
Work out the gradient
What is the area under a stress-strain graph equal to?
The strain energy per unit volume (energy per 1 m^3 o wire)
What should the stress-strain graph look like if it is obeying Hooke’s Law?
A straight line
What is the equation for energy per unit volume?
E = 0.5 x stress x strain
Describe a stress-strain graph before the limit of proportionality
A straight line through the origin, as it is obeying Hooke’s Law. Gradient is constant as it’s the Young Modulus
Describe a stress-strain graph after the limit of proportionality
The graph starts to bend, as the material is no longer obeying Hooke’s Law, but would return to its original size and shape when stress is removed
Describe a stress-strain graph after the elastic limit
The graph curves more, as the material starts to behave plastically, so the material would no longer return to its original shape and size
Describe a stress-strain graph after the yield point
The graph suddenly drops a bit
What happens at the yield point?
The material suddenly starts to stretch without any extra load.
What is the yield point?
The stress at which a large amount of plastic deformation takes place with a constant or reduced load
When is an example that plastic deformation is useful?
If you want to draw copper into long, thin wires
What is the difference between a force-extension graph and a stress-strain graph?
Force-extension graphs are specific for the tested object, whereas stress-strain graphs describe the general behaviour of the material
Why are force-extension graphs specific to the tested object?
Because the shape of the graph is affected by the dimensions of the object
On a force-extension graph for a wire, how do you draw the unloading?
A dotted line which starts at the point the force was removed and is parallel to the loading line
What does it mean, on a force-extension graph, if the unloading line doesn’t go through the origin?
The object has been deformed plastically so is permanently stretched
What is the area between loading and unloading force on a force-extension graph equal to?
The work done to permanently deform the wire
What does the gradient of a force-extension graph equal?
The stiffness constant
Describe what the stress-strain graph looks like for a brittle material
A straight line with no curves until it stops
What happens when the stress-strain graph stops for a brittle material?
The material fractures
Do brittle materials obey Hooke’s Law?
Yes, as the stress-strain graph is a straight line through the origin
Describe the force-extension graph for a brittle material
A straight line until the material reaches a point where it fractures
What happens if you apply a force to a brittle material?
Brittle materials don’t plastically deform so they fracture when the force gets too great
Why are brittle materials brittle?
They have a rigid structure
What is a brittle fracture?
When a stress applied to a brittle material causes tiny cracks at the material’s surface to get bigger until the material breaks completely
What 2 types of atom arrangements are in ceramics?
Crystalline and Polycrystalline
What is a polycrystalline structure?
Where there are many regions of crystalline structure
What makes ceramics brittle?
The atoms in a ceramic are bonded in a rigid structure
What happens in non-brittle materials when a crack appears?
The atoms within the material can move to prevent the crack getting larger
