materials Flashcards
what does hooke’s law apply to, and when?
MATERIALS
hooke’s law applies to all materials, but only up to a point (the limit of proportionality)
what is Hooke’s law?
MATERIALS
Hooke’s law states that “the extension of a stretched wire (x) is proportional to the load or force (F)”
what happens if a weight is attached to a metal wire, where the top of the wire is supported (like tied around the clamp of a stand)?
MATERIALS
⋅ if a metal wire is supported at the top and then a weight is attached to the bottom of the wire, the wire stretches
⋅ the weight pulls down with a force F, so the wire will exert an equal force back on the support
what forces are required for a material to deform?
MATERIALS
a material will only deform (stretch, bend, twist, etc) if there is a pair of opposing forces acting on it (newton’s third law of motion)
what can hooke’s law be written as in equation form?
MATERIALS
hooke’s law can be written as: F = kx
where
k = spring constant
what does the spring constant depend on and what does it also measure?
MATERIALS
⋅ k depends on the object being stretched
⋅ k is also a measure of the stiffness of an object
what are the units for a spring constant?
MATERIALS
the units for k are: N m^-1
what does stretching a material create across the material?
MATERIALS
stretching a material creates tension across the material
where does the tension created in a stretched material act, and what is this an example of?
MATERIALS
⋅ forces of tension act along the same line as the forces stretching the material but in the opposite direction at each end of the material
⋅ they ‘pull’ on the object at either end of the material [pulling it together]
⋅ this is an example of newton’s third law of motion
does hooke’s law also apply to springs and why?
MATERIALS
⋅ YES
⋅ the extension of a spring is proportional to the force applied to it, so hooke’s law applies
what happens when you apply a pair of opposite forces to a metal spring?
MATERIALS
⋅ like any other material/object, a metal spring also changes in length when you apply a pair of opposite forces to it
what does it mean if the forces applied on a metal spring is compressive?
MATERIALS
⋅ if the forces applied on a metal spring is compressive, the spring is being squashed
⋅ and therefore the extension of the spring is negative
does hooke’s law work for compressive forces as well as tensile forces?
MATERIALS
⋅ yes, hooke’s law works just as well for compressive forces as tensile forces
⋅ for a spring, the spring constant (k) has the same value whether the forces are tensile or compressive (however this is not true for all materials)
do all materials obey hooke’s law?
MATERIALS
⋅ yes
⋅ hooke’s law doesn’t just apply to metal springs and wires, all other materials obey it up to a point (up to limit of proportionality)
when does hooke’s law stop working and what does this mean?
MATERIALS
⋅ hooke’s law stops working when the load attached to the object is great enough
⋅ this means that there is a limit to the force you can apply for hooke’s law to stay true (the limit of proportionality)
what does this graph show?
MATERIALS
⋅ the graph shows the force against the extension for [stretching] a typical wire or spring
⋅ the graph up to the point P shows that the hooke’s law is being obeyed - bc there is a linear relationship between the force and the extension (so the relationship is proportional)
⋅ when the force becomes great enough, the graph starts to curve (between points P and E)
-> metals generally obey hooke’s law up to the limit of proportionality (P)
⋅ the point marked E on the graph is called the elastic limit
-> if you exceed the elastic limit, the material will be permanently stretched (after the elastic limit, the material has plastically deformed)
-> up to the point E, the material elastically deforms - so if you remove all the forces, the material will return to its original length
⋅ beyond the elastic limit, the material will stretch further for a given force
how does rubber obey hooke’s law?
MATERIALS
some materials, like rubber, only obey hooke’s law for really small extensions
up to what point does a material show elastic deformation and what does it show after this point?
MATERIALS
a material will show elastic deformation up to its elastic limit, and plastic deformation beyond it
what types of stretches can a material undergo?
MATERIALS
materials can stretch elastically or plastically
what is elastic deformation?
MATERIALS
if a deformation is elastic, a material will return to its original shape once the forces applied are removed
what happens when a material is elastically deformed?
MATERIALS
when a material is put under tension:
1) when a material is put under tension, the atoms of the material are pulled apart from one another
2) atoms can move slightly relative to their equlibrium/resting positions, without changing their actual position in the material
3) once the load is removed, atoms return to their equilibrium distance apart
what is plastic deformation?
MATERIALS
if a material plastically deforms, the material is permanently stretched and won’t return to its original shape when the forces are removed
what happens to atoms during plastic deformation? (simple)
MATERIALS
1) some atoms in the material move position relative to one another
2) when the load is removed, the atoms don’t return to their original positions
what is an elastic material and what is a plastic material?
MATERIALS
⋅ an ‘elastic material’ is a material that deforms elastically
⋅ a ‘plastic material’ is a material that deforms plastically
how do you investigate the extensions of an object by stretching an object?(practical)
MATERIALS
method:
1) set up experiment as shown in diagram - support object being tested at top (eg. by clamp) and measure its original length with ruler
2) add masses on at time to bottom of object
3) after each weight is added, measure new length of object, then CALCULATE EXTENSION: extension = new length - original length
4) plot graph of FORCE (weight, which = mass x g) against EXTENSION for results
analysing the data:
⋅ where line of best fit is STRAIGHT, object obeys hooke’s law + gradient = k (as F = kx, like y = mx)
⋅ if you’ve loaded object beyond its limit of proportionality, graph will start to curve
how much a material stretches for an applied force depends on what? and what does this mean?
MATERIALS
⋅ how much a material stretches for a particular applied force depends on its dimensions
⋅ so the spring constant (k) won’t be constant for all samples of a particular material
if spring constant changes from one sample of material to another, what should you use to compare materials instead?
MATERIALS
if you want to compare one material to another, you need to compare their stresses and strains instead
what is strain caused by, in the simplest of terms?
MATERIALS
stress causes strain
what does it mean if forces stretch a material and if other forces squash a material?
MATERIALS
⋅ as said before, a material subjected to a pair of opposite forces might deform, i.e. change shape
⋅ if forces stretch a material, they are tensile forces
⋅ if forces squash materials, they are compressive forces
what is stress defined as and what are its units?
MATERIALS
⋅ stress is defined as the tension (force applied) divided by the cross-sectional area of the material
⋅ the units for stress are: N m^-2 or Pascals, Pa
what equation defines stress?
MATERIALS
⋅ stress = force applied / cross-sectional area
⋅ σ = F/A
what is strain defined as and does it have units?
MATERIALS
⋅ strain is defined as extension (i.e. change in length) divided by the original length of material
⋅ no, strain has no units as it is a ratio (of lengths)
what equation defines strain?
MATERIALS
⋅ strain = extension / original length
⋅ ε = x/L
when using the equations for stress and strain, does it matter if the forces are tensile or compressive?
MATERIALS
⋅ it doesn’t matter whether the forces producing the stress and strain are tensile or compressive, the same equations still apply
⋅ the only difference is that you tend to think of the tensile forces as positive and the compressive forces as negative (so compressive forces would cause negative extension)
what do you call the stress at which a material breaks?
MATERIALS
the stress that is big enough to cause a material to break is called the fracture stress
what happens to the stress on a material as the tensile force applied to the material increases?
MATERIALS
as the tensile force applied to a material increases, the stress on the material increases
describe what happens at points UTS and B on this stress-strain graph for a hypothetical material
MATERIALS
⋅ UTS on the graph shows the ultimate tensile strength of the material
⋅ point B shows the fracture stress (stress at which a material fractures):
1) as the stress increases, the atoms start to be pulled apart from one another, causing atomic planes to slip over one another
2) eventually the stress becomes so great that atomic planes can no longer slip over each other and you’re pulling on the actual bonds between atoms, causing the atoms to separate completely
3) when the atoms separate completely, the material fractures (breaks)
what is given by the area under a force-extension graph up to the elastic limit?
MATERIALS
1) on a graph of force against extension, the work done [/energy transferred to a material when it is stretched or compressed] is given by the area under the graph
2) before the elastic limit, all work done in stretching or compressing the material is stored as energy in the material
3) this stored energy is called elastic strain energy
how do you find the young modulus of a material/wire? (method)
MATERIALS
1) set up apparatus as shown below:
2) find cross-sectional area of wire using micrometer
⋅ do this by measuring diameter of wire at three different points along wire + find average diameter
⋅ then use area of circle = πr^2
3) clamp wire to bench (as shown in diagram) so you can hang weights off one end of it
⋅ start with smallest weight necessary to straighten wire (DON’T include this weight in your final calculations)
4) measure distance between fixed end of wire + marker - this is your unstretched length
then if you increase weight, wire stretches + marker moves
5) increase weight in steps (eg, in 1 N intervals), measuring extension each time
⋅ extension = marker’s position - unstretched length
⋅ use balance to accurately find weight you add at each step
6) use your results from this experiment to calculate stress + strain on wire, + plot stress-strain graph
7) gradient of stress-strain graph gives young modulus, E
what should you consider about the wire when setting up the equipment for investigating the E of a wire? (for practical)
MATERIALS
⋅ when setting up the equipment, the test wire used should be thin, and as long as possible
⋅ bc the longer and the thinner the wire, the more it extends for the same force, reducing the uncertainty in your measurements [for the extension, x]
what two things does a stress-strain graph give?
MATERIALS
⋅ the gradient of a stress-strain graph gives the young modulus (E) of a material
⋅ the area under the graph gives the elastic strain energy (or elastic strain energy stored) per unit volume of material (i.e. energy stored per 1 m^3 of wire)
what does the stress-strain graph look like for a ductile material?
MATERIALS
⋅ the stress-strain graphs for ductile materials curve
do the stress-strain graphs for different materials change and why?
MATERIALS
⋅ yes, they do change
⋅ bc different solids have different properties, their stress-strain graphs look different too
what do the different points on this stress-strain graph for ductile material mean?
MATERIALS
Y - point Y is the yield stress
⋅ here the material suddenly starts to stretch without any extra load or with a reduced load
E - point E is the elastic limit
⋅ at this point, the material starts to behave plastically
⋅ from point E onwards, the material would no longer return to its original shape once the stress is removed
P - point P is the limit of proportionality
⋅ after point P, the graph is no longer a straight line but instead 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 (so behaves elastically up to point P)
⋅ before point P, the graph is a straight line through the origin
⋅ this shows that, before point P, the material is obeying hooke’s law
what happens when you apply a force to a metal? (atomic spacing)
MATERIALS
1) when a force is applied to a metal, the interatomic spacing between ions increases
2) this increase in interatomic spacing is uniform during elastic deformation
3) once the stress is high enough to cause plastic deformation, planes of atoms within the metal slip over each other (+ form new bonds [holding planes in place])
4) if there is a dislocation in the metal, the stress needed to cause slipping is lower than the stress needed to cause slipping in a perfect metal
what are the properties of ceramics?
MATERIALS
1) ceramics like pottery, brick and glass are made by melting certain materials and then letting them cool
2) arrangements of the atoms in a ceramic can be crystalline or polycrystalline (as shown below)
⋅ the atoms in each grain of crystalline structure line up in the same direction
3) some ceramics like glass are amorphous
⋅ amorphous: there’s no overall pattern; atoms are arranged at random
⋅ the quicker a molten ceramic is cooled, the more likely it is to be amorphous
4) ceramics rarely deform plastically before they fracture bc:
⋅ the random atomic bonding in [amorphous] ceramics means there are no slip planes in ceramic lattices
⋅ bc of random atomic bonding, ceramics also don’t have mobile dislocations (dislocations that can move) - meaning that ceramics rarely deform plastically before they fracture
5) ceramics are stiff and brittle bc:
⋅ the atoms in ceramics are ionically or covalently bonded in a giant rigid structure
⋅ the strong [covalent] bonds between atoms make ceramics very stiff
⋅ while the rigid structure means that ceramics are very brittle
6) ceramics break via crack propagation bc:
⋅ ceramics being brittle means that cracks spread through them when they fracture
⋅cracks spread bc the applied force acts on a small area (the tip of the crack) so the stress is high
what are the properties of polymers?
MATERIALS
1) polymers are very strong bc:
⋅ the monomers in a polymer chain are covalently bonded together, and so are very hard to separate
⋅ this makes even the thinnest polymer materials very strong
2) polymers are very flexible bc:
⋅ polymer chains are often entangled, and can be unravelled by rotating about their bonds when you pull them
⋅ unravelling polymers by rotating about their bonds is what makes polymer materials flexible
⋅ the more easily the monomers can rotate, the more the chains will untangle and the more flexible the polymer will be
3) polymers can be very rigid bc:
⋅ the strength and the number of bonds between the polymer chains also affect the polymer’s flexibility
⋅ the stronger the cross-linking bonds and/or the more cross-linking bonds in the polymer material, the more rigid the material
