Materials Flashcards
Define density
Density is the mass per unit volume
What is density a measure of?
Density is the measure of the compactness of a substance. It relates the mass of a substance to how much space it takes up
What is the formula for density?
Density = Mass/Volume
What Greek symbol is often used to represent density?
‘Rho’ (Looks like the letter p)
What are the units of density?
The units of density are grams per centimetre cubed or kilograms per metre cubed
What does the density of an object depend on?
The density of an object depends on what it is made of. Density does not vary with size or shape
What does the average density of an object determine?
The average density of an object determines whether it floats or sinks. A solid object will float on a fluid if it has a lower density than the fluid.
What is the density of water and what does this mean?
Water has a density of 1g per cm cubed. This means that 1cm cubed of water has a mass of 1g
What happens when a metal wire is supported at the top and then a weight is attached to the bottom?
If a metal wire is supported at the top and then a weight is attached to the bottom the wire stretches. The weight pulls down with a force of F producing an equal and opposite force at the support.
Define Hooke’s Law
Hooke’s law states that the extension of a stretched object is directly proportional to the load or force applied provided the limit of proportionality has not been exceeded.
How can Hooke’s Law be written as a formula?
Force = Spring Constant*Extension
What does ‘k’ mean in the formula for Hooke’s law?
K is a constant called the stiffness of an object that depends on the object being stretched
What is the relationship between springs and Hooke’s law?
Springs obey Hooke’s law, when you apply a pair of opposite forces the extension or compression of a spring is proportional to the force applied.
What is ‘k’ usually called for springs?
The spring constant
What is the relationship between Hooke’s law and compressive and tensile forces?
Hooke’s law works just as well for compressive forces as well as tensile forces. For a spring k has the same value whether the forces are tensile or compressive. This is not true for all materials.
What is the relationship between Hooke’s law and all other materials?
Hooke’s law doesn’t just apply to metal springs and wires. Most other materials obey it up to a point.
What happens to a spring when tensile forces are applied to it?
The spring is stretched
What happens to a spring when compressive forces are applied to it?
The spring is squashed
When does Hooke’s law stop working?
When force is great enough
What part of a graph shows that Hooke’s law is being obeyed?
When the graph is a straight line showing a straight line relationship between force and extension
Up to which point do metals generally obey Hooke’s law to?
The limit of proportionality
How can the limit of proportionality on a force extension graph be identified?
The limit of proportionality occurs when the graph starts to curve
What is the elastic limit of an material?
If you increase the load past the elastic limit the material will be permanently stretched. When all the force is removed the material will be longer than at the start.
What are the two different types of stretch?
Elastic and Plastic
What does it mean if a deformation is elastic?
If a deformation is elastic the material returns to its original shape and size once the forces are removed.
Explain the process of an elastic stretch
- When the material is put under tension the atoms of the material are pulled apart from one another
- Atoms can move small distances relative to their equilibrium positions without actually changing position in the material
- Once the load is removed the atoms return to their equilibrium distance apart
When does elastic deformation happen?
Elastic deformation happens as long as the elastic limit of an object is not reached
What does it mean if a deformation is plastic?
If a deformation is plastic the material is permanently stretched
Explain the process of a plastic stretch
- When the material is put under tension 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?
When an object has been stretched past its elastic limit
What is the relationship between energy and stretching?
Energy is always conserved when stretching
When a material is stretched what has to be done in stretching the material?
When a material is stretched, work has to be done in stretching the material
What is the relationship between elastic deformation and the energy stored?
If a deformation is elastic all the work done is stored as elastic strain energy in the material. When the stretching force is removed this stored energy is transferred to other forms
What is the relationship between plastic deformation and the energy stored?
If a deformation is plastic work is done to separate atoms and energy is not stored as strain energy (it’s mostly dissipated as heat).
This fact is used in transport design - crumple zones are designed to deform plastically in a crash. Some energy goes into changing the shape of the vehicle’s metal body and so less is transferred to the people inside
Define tensile stress
Tensile stress is the force applied per unit cross-sectional area
What are the units of stress?
Newtons per metre squared or Pascals
Define tensile strain
Tensile strain is the extension per unit original length
What are the units of strain?
Strain has no units, its just a ratio and is usually written as a number. It can also be written as a percentage
What is the formula for calculating stress?
Stress = Force/Area
What is the formula for calculating strain?
Strain = Change in length/Original length
What effect does the forces producing the stress and strain have on the equations for stress and strain?
It doesn’t matter whether the forces producing the stress and strain are tensile or compressive, the same equations apply. The only difference is that you tend to think of tensile forces as positive and compressive forces as negative
What is a stress big enough to break a material called?
The breaking stress
What happens to a material when a greater tensile force is applied to it and what is the effect of this?
The stress on the material increases. The effect of the stress is to start to pull the atoms apart from one another. Eventually the stress becomes so great that atoms separate completely and the material breaks. The stress at which this occurs is called the breaking stress
What is the point marked UTS on a stress strain graph mean?
The point marked UTS is called the ultimate tensile stress. This is the maximum stress that the material can withstand
What do UTS and breaking stress have in common?
They both depend on conditions such as temperature
Why do engineers have to consider the UTS and breaking stress of materials when designing a structure?
Engineers have to consider the UTS and breaking stress of materials when designing a structure as they need to make sure the stress on a material won’t reach the UTS when the conditions change
How can the elastic strain energy be calculated from a force-extension graph?
Elastic strain energy is equal to the area under a force-extension graph
Why can elastic strain energy be calculated by calculating the area under a force extension graph?
Work has to be done to stretch a material. Before the elastic limit is reached all this work done in stretching is stored as elastic strain energy in the material. On a graph of force against extension the elastic strain energy is given by the area under the graph
What happens to the spring constant if there are two springs in series?
It halves
What happens to the spring constant if there are two springs in parallel?
It doubles
Which is easier to stretch, two springs in series or two springs in parallel?
two springs in series
What does a tensile stress cause?
A tensile strain
What is the formula for calculating the elastic strain energy or energy stored in a material provided it obeys Hooke’s law?
E = 0.5ForceExtension
What is the Young Modulus?
When you apply a load to stretch a material it experiences a tensile stress and a tensile strain.
Up to the limit of proportionality the stress and strain of a material are proportional to each other.
So below this limit for a particular material stress divided by strain is a constant.
This constant is called the young modulus
What letter/symbol is used to represent the Young Modulus?
E
What is the formula for calculating the Young Modulus?
- Stress/Strain
- (ForceInitial Length) / (Change in lengthCross-sectional area)
What are the units of the Young Modulus?
Newtons per metre squared or pascals since strain has no units
What is the Young Modulus a measure of?
The Young Modulus is the measure of the stiffness of a material. It is used by engineers to make sure the materials they are using can withstand sufficient forces.
Explain the practical for calculating the Young Modulus of a wire
1- The test wire should be thin and as long as possible. The longer and thinner the wire the more it extends for the same force, this reduces the uncertainty in your measurements.
2- First you need to find the cross-sectional area of the wire. Use a micrometer to measure the diameter of the wire in several places and take an average of your measurements. By assuming that the cross-section is circular you can use the formula PIr^2
3- Clamp the wire to a bench so you can hang weights off one end of it. Start with the smallest weight necessary to straighten the wire. Don’t include this weight in the final calculations.
4- Measure the distance between the fixed end of the wire and the marker on the wire, this is the unstretched length
5- If you increase the weight the wire stretches and the marker moves
6- Increase the weight in steps recording the marker reading each time, the extension is the difference between this reading and the unstretched length. If the markings on the measuring equipment are quite far apart you can interpolate between them.
7- You can use the results to calculate the stress and strain of the wire and plot a stress and strain graph
8- The gradient of the graph gives the Young Modulus
How can you avoid random errors in the Young Modulus of a wire practical?
To avoid random errors you should use a thin marker on the wire and always look directly at the marker and ruler when measuring extension
How can you calculate the Young Modulus from a stress-strain graph?
By calculating the gradient of the graph
What is the area under a stress-strain graph equal to?
The strain energy or energy stored per unit volume
Provided that a stress-strain graph is a straight line how can the energy per unit volume be calculated using a formula?
Energy per unit volume = 0.5stressstrain
What are the three key points on a stress-strain graph?
- Limit of proportionality
- Elastic Limit
- Yield Point
What is the limit of proportionality on a stress-strain graph?
After the limit of proportionality the graph is no longer a straight line but it starts to bend. At this point the material stops obeying Hooke’s law but would still return to its original shape if the stress was removed
What is the elastic limit on a stress-strain graph?
At the elastic limit a material starts to behave plastically. From the elastic limit onwards the material would no longer return to its original shape if the stress was removed
What is the yield point on a stress-strain graph?
At the yield point a material suddenly starts to stretch without any extra load. The yield point or yield stress is the stress at which a large amount of plastic deformation takes place with a constant or reduced load
For which materials do the stress-strain graphs not curve?
Brittle Materials
Explain the reasons for the shape of a stress-strain graph of a brittle material
The graph starts as a straight line through the origin so brittle materials obey Hooke’s law.
However when the stress reaches a certain point the material suddenly fractures (breaks) it doesn’t deform plastically
What are some examples of brittle materials?
Chocolate bars
Ceramics
Glass
Pottery
What is the difference between force-extension graphs and stress-strain graphs?
Force-extension graphs are specific for the tested object and depend on its dimensions.
Stress-strain graphs describe the general behaviour of a material because stress and strain are independent of the dimensions
Why is the unloading line parallel to the loading line on a force-extension graph?
The unloading line is parallel to the loading line because the stiffness is still the same since the forces between the atoms are the same as they were during the loading
Why doesn’t the unloading line go through the origin on a force-extension graph?
As a wire has been stretched past its elastic limit and deformed plastically so it has been permanently stretched. Therefore the unloading line doesn’t go through the origin
What is the area between the loading and unloading line on a force-extension graph for a wire equal to?
The work done to permanently deform the wire
What formula can be used to find the Young Modulus from a force extension graph?
Gradient * (Length/Area)
What does a large plastic region on a stress-strain graph mean?
The material is ductile
