Unit 1.5 - Solids Under Stress Flashcards
What happens when an object is subject to tensile force (tension)?
It stretches
When does an object stretch?
When it’s subject to tensile force
Tensile force
Tension
What type of force is tension?
A tensile force
What does Hooke’s Law state?
For most objects, the degree it stretches is directly proportional to the tension (provided the force is not too large)
“For most objects, the degree it stretches is directly proportional to the tension” - which law is this?
Hooke’s law
What type of behaviour does an object exhibit under Hooke’s law?
Elastic behaviour, meaning that if it’s subject to too great a stress, the object fractures
Under which law does an object exhibit elastic behaviour?
Hooke’s law
What type of graph stops being linear before an object fractures?
Tension-extension graph
What does a tension-extension graph show before an object that follow’s Hooke’s law fractures?
It stops being linear
What type of materials enter a plastic region and what does this occur to happen?
Ductile materials, meaning they’re permanently deformed by the tension
In which region are objects permanently deformed under tension?
The plastic region
What do ductile materials do to be permanently deformed by tension?
Enter the plastic region
What would show a more stiff object on a force-extension graph?
A steeper line
What would a steeper line on a force-extension graph show?
A more stiff object
How is the force-extension graph set out? Why?
Extension on the x-axis, force on the y-axis
Tensile testing machines are usually designed to apply a specific extension and measure the tension produced
What are tensile testing machines usually designed to do?
Apply a specific extension and measure the tension produced
What type of machines measure the tension of an object?
Tensile testing machines
What does the gradient on a force-extension graph show?
The stiffness of the object (spring constant for the spring)
On what type of graph is the gradient the stiffness of the object (spring constant for the spring) ?
Force-extension
What shows the stiffness of an object (spring constant for a spring) on a force extension graph?
The gradient
Spring constant
The force per unit extension
The force per unit extension
The spring constant
Hooke’s law equation
F = kx
What is the spring constant in Hooke’s Law’s equation?
K
(F = kx)
Spring constant unit
Nm-1
How do we work out the gradient?
Change in y
——————
Change in x
What does the area underneath show on a force-extension graph?
The work done stretching the object
(For elastic materials - the elastic potential energy stored)
What shows the work done stretching the object and For elastic materials - the elastic potential energy stored) on a force-extension graph?
The area underneath the graph
The area underneath which type of graph show the work done in stretching an object (or the elastic potential energy stored in elastic materials)?
Force-extension
For what type of objects does the area underneath a force-extension graph show elastic potential energy stored?
Elastic materials
Elastic potential energy
The energy possessed by an object when it has been deformed due to forces acting on it
The energy possessed by an object when it has been deformed due to forces acting on it
Elastic potential energy
Elastic strain
Strain that disappears when the stress is removed - the specimen returns to its original size and shape
Strain that disappears when the stress is removed - the specimen returns to its original size and shape
Elastic strain
Plastic strain
When a material is permanently deformed
Atoms have been re-arranged
Mainly in ductile materials
“When a material is permanently deformed due to atoms being re-arranged” - what type of strain is this?
Plastic strain
What type of materials experience plastic strain?
Ductile materials
How does a material become deformed during plastic strain?
Atoms become re-arranged
Brittle
A material that does not deform plastically (snaps before reaching this)
What type of material does not not deform plastically and what does it do instead?
Brittle materials
Snap before reaching this
Fracture
When the material breaks
Fracture can be ductile or brittle
When a material breaks
Fracture
What are the two forms of fracture?
Ductile or brittle fractures
Ductile
The ability of a material to deform plastically
A ductile material can be drawn into wires
What type of material can be drawn into wires?
Ductile materials
The ability of a material to deform plastically
Ductility
Deform
Change in shape due to a stress
Change in shape due to a stress
Deform
Stiffness
A measure of the materials resistance to deformation
Is related to Young’s Modulus
(Higher = stiffer)
A measure of a material’s resistance to deformation
Stiffness
What does a higher Young’s modulus mean?
A stiffer material
What figure would mean a stiffer material if it was higher?
Young’s modulus
Hooke’s law
The tension in a spring or wire is proportional to its extension from its natural length, provided the extension is not too great
The tension in a spring or wire is proportional to its extension from its natural length, provided the extension is not too great
Hooke’s law
What prevents the atoms of an object being pulled apart or pushed together?
The forces between the atoms
How much does an object extend by when a force is applied?
Δl
If a bar has its cross-sectional area increased to 2A, how much is the total F that needs to be applied for the same Δl?
2F
Which ratio must be kept the same if two bars of the same composition and length will be stretched by the same amount?
F/A ratio
What is “two bars of the same composition with the same length will be stretched by the same amount if the ratio F/A is the same” the definition for?
Tensile stress
What’s the symbol for tensile stress?
σ
What’s σ the symbol for?
Tensile stress
Tensile stress definition
The force per unit area applied when equal forces act on a body
The force per unit area applied
Tensile stress
Stress equation
Stress (σ) = force
———
Cross sectional area (m^2)
What’s F/A the equation for?
Stress
Unit of stress
Pa
What’s the total extension if two bars are welded end to end and why?
2Δl, as tension has the same value (F) in each half, so each half extends by Δl
Which ratio is the same for two bars of the same composition, same cross-sectional area and same tension?
Δl
—
l
Under which conditions is the Δl/l ratio the same?
With two bars of the same composition, the same cross-sectional area and the same tension
What is the Δl/l quantity known as?
Tensile strain
Tensile strain symbol
ε
ε meaning
Tensile strain
Strain equation
Strain (ε) = extension (Δl)
———————
Original length (l)
What’s extension (Δl). the equation for?
———————
Original length (l)
Strain
Units of strain
No units (remember to make this clear)
What’s proportional in the elastic region?
Force is proportional to extension
(Stress is proportional to strain)
In which region is force proportional to extension (stress proportional to strain)?
The elastic region
Young’s modulus in simple terms
How stiff a material is
Young’s modulus symbol
E
E symbol meaning
Young’s modulus
What does a higher Young’s modulus value mean for a material?
More stiff = less elastic deformation
What would show that a material is more stiff and what would this lead to?
A higher Young’s modulus value
Less elastic deformation
What type of material experiences less elastic deformation?
A stiff material
Young’s modulus equation (in data book)?
E = σ
—
ε
What’s E = σ the equation for calculating?
—
ε
Young’s modulus
How do we actually work out Young’s modulus?
E = Fl
—
AΔl
Units of Young’s modulus
Nm-2 or Pa
Which type of material has the highest Young’s modulus value?
Ceramics
Which material has a medium Young’s modulus?
Metals
Which type of material has the lowest Young’s modulus?
Polymers
Which two types of materials have the highest Young’s modulus values and why?
Ceramics and metals
Interatomic bonds (strong)
Which type of material has the lowest Young’s modulus value and why?
Polymers
Intermolecular bonds = weak
Which are the strongest - interatomic bonds or intermolecular bonds?
Interatomic bonds
How do we calculate elastic potential energy? Why?
Tensile force x extension
As work = force applied x distance in that direction
What’s the area underneath a force-extension graph?
Energy stored in the material
What shows the energy stored in the material in an extension-force graph?
Area underneath
The area underneath which type of graph shows the energy stored in the material?
Extension-force
What’s the equation for calculating the energy stored in a material/work done by it?
1/2fx OR 1/2kx^2
What are 1/2fx and 1/2kx^2 used for calculating?
The energy stored in a material
Which elements go across each axis on an extension-force graph?
Extension - x-axis
Force - y-axis
What do we do if the extension and force are along the wrong axes on an extension-force graph?
The spring constant is calculated as 1/gradient
When is spring constant calculated as 1/gradient
When the extension and force are along the wrong axis on an extension-force graph
What type of samples do we use for stress-strain curves?
Samples of uniform cross-sectional area
What do stress-strain curves analyse?
Te strength of solids under tension
What does the precise shape of the stress-strain curve vary with?
-type of material
-history of the material (e.g - heat or working treatment)
Draw and label a typical stress-strain curve
(Check notes)
What comes first on a stress-strain curve - the elastic limit or the limit of proportionality?
The limit of proportionality
Where on a stress-strain curve would the gradient be the Young’s modulus of the material?
On the limit of proportionality
What does the limit of proportionality show for a material and how on a stress-strain curve?
The gradient is the Young’s modulus of the material
How do we find out the Young’s modulus of a material on a stress-strain curve?
At the limit of proportionality
The gradient of which part of a stress-strain curve shows the Young’s modulus of the material?
The limit of proportionality
In which region on a stress-strain curve is the strain directly proportional to the stress and can deformation be reversed?
Elastic region
What is the relationship between stress and strain in the elastic region?
Directly proportional
What can occur to a material in the elastic region alone?
Deformation can be reversed
What occurs beyond the elastic region?
Plastic deformation
Beyond which point does plastic deformation occur?
Beyond the elastic region
What happens if the stress is removed at the elastic limit of a material?
The material returns to its normal size
Beyond which point is he deformation of a material permanent?
Beyond the yield point
What does a material show at its yield point?
A large increase in strain for little or no increase in stress
At which point is a large increase in strain shown for a material for little or no increase in stress?
The yield point
Which part on a stress-strain curve shows when an object is experiencing necking?
Where the curve bends downwards
What the curve of the stress-strain bending downwards show?
Where the material experiences necking
Necking
A narrowing of the region where the sample will eventually break
A narrowing of the region where the sample will eventually break
Necking
What does what type of materials does necking occur to?
Ductile materials deforming plastically
Which type of materials don’t experience necking?
Brittle materials that don’t deform plastically
What does necking increase on the object?
The stress
What is necking caused by?
An increased number of edge dislocations, causing the wire to lengthen
How does necking actually occur?
The volume is constant, but the cross-sectional area is decreasing so the stress point increases until the material breaks
Which materials are the only ones to experience plastic deformation?
Ductile materials
What does plastic deformation derive from?
Crystalline structure
What does the crystalline structure derive?
Plastic deformation
What happens when a metal crystal forms (to help explain plastic deformation)?
Edge dislocations will frequently appear where a plane of atoms will not be complete before the next plane
When do edge dislocations frequently appear in a material?
When a metal crystal forms
How is a dislocation represented on an atomic diagram?
A gap
What does a gap in an atomic diagram represent?
A dislocation in the regular array of atoms
What happens in terms of a dislocation of a material when the force is large enough?
The bond next to the dislocation is stretched further and will snap, causing the dislocation to move, then bonding to the next atom
What happens to the bonds between atoms when a force is applied? Why?
The bonds between atoms will stretch as extra stress is caused to the bonds
When will the bonds between atoms stretch? Why?
When a force is applied, as extra stress is cause to the bonds
Give a molecular description of plastic deformation
-if the force applied is large enough, the bond next to the dislocation is stretched further, and will snap, causing the dislocation to move
-the free atom bonds with the next
-the process continues until the last bond is formed and the dislocation has moved to the edge of the crystal or grain as each plane has slides over the nearest one
What can we see following plastic deformation?
When the tensile stress is removed, the changed shape remains, giving us a longer material
What do metals contain which results in a large increase in strain with little stress?
Edge dislocations
Which type of materials contain many edge dislocations an what does this result in?
Metals, resulting in a large increase in strain with little stress
What does a material containing many edge dislocations cause?
A large increase in strain with little stress
What would make an object permanently longer?
Plastic deformation
How are metals strengthened?
Impurities are introduced
What does introducing impurities to a material do?
Strengthens it
How do impurities strengthen a material?
Create a barrier for dislocation movement
What create a barrier for dislocation movement and what does this do to a material?
Impurities
Makes them stronger
What are the 3 main classifications of solids?
Crystalline, amorphous, polymeric
What are crystalline, amorphous and polymeric?
3 main classifications of solids
What do the classifications of solids depen on?
The order and structure of he atoms and molecule in the material
Crystal
A solid in which atoms are arranged in a regular array, with a long-range order
A solid in which atoms are arranged in a regular array, with a long-range order
Crystal
Polycrystalline
Consists of many crystals known as grain, arranged randomly
What classification of a solid consists of many crystals known as grain, arranged randomly?
Polycrystalline
What are the many crystals in a polycrystalline structure known as?
Grain
What type of materials have polycrystalline structures?
Metals
Many ionic minerals (e.g - salt)
What type of structures do metals and ionic minerals such as salt have?
Polycrystalline
What’s the name for the space between grains in a polycrystalline structure?
Grain boundary
Grain boundary
Space between grains in a polycrystalline structure
Amorphous solid
Atoms are arranged randomly, with no regular order
In what type of solid are atoms arranged randomly with no regular order?
Amorphous solid
What type of solids do we use to describe amorphous ones?
Brick and glass
What type of solids a are back and glass?
Amorphous solids
Why are brick and glass not perfect examples of amorphous solids?
Although there’s no long-range order in the way atoms are arranged, there may be ordered clusters of atoms
Polymeric solid
Long, chain-like molecules
Long, chain-like molecules solid classification
Polymeric solid
Examples of which type of solid classification are rare?
Amorphous solids
Examples of polymeric solids
Rubber, wood, synthetic polymers (e.g - nylon and polythene)
What are rubber, wood and synthetic polymers such as nylon and polythene examples of?
Polymeric solids
Example of a brittle material
Glass
What type of material is glass?
Brittle
What are proportional for brittle materials?
Stress and strain
Do brittle material’s obey Hooke’s law?
Yes
Which region on the stress-strain graph to brittle materials remain in?
Elastic region
Compare the breaking stress of ductile and brittle materials
Much smaller for brittle materials
What type of material has the smallest breaking stress?
Brittle materials
What type of material tend to have higher Young’s modulus? What does this mean for it?
Brittle material - they’re stiffer
Compare the Young’s modulus of brittle and ductile materials
Higher for brittle materials
Can brittle materials be deformed plastically? Why?
No, since they do not have a crystalline structure (amorphous)
What structure do brittle materials have?
Amorphous
What type of materials are amorphous?
Brittle ones
What type of material cannot be deformed plastically? Why?
Brittle materials, as they don’t have a crystalline structure
What happens to a brittle material when the elastic limit is reached?
They break
What type of material breaks when the elastic limit is reached?
Brittle
At which point does a brittle material break?
At the elastic limit
Describe how brittle materials break and give a reason why
“Cleanly” due to small imperfections (scratches) on the surface that cause stresses to be concentrated on particular bonds
What type of materials break “cleanly” and why?
Brittle materials due to small scratches/imperfections on the surface that cause stresses to be concentrated in on area
What do scratches on the surface of a brittle material do?
Cause a material to break “cleanly” as stresses are concentrated on particular bonds
Where do the bonds break in a brittle material why?
By the tip of the crack due to the stress being high here
How does a crack elongate in a brittle material?
As the bonds break at the tip of the crack (stress here is high), the stress is transferred to place more tension in the next bond along (the crack elongates, resulting in even higher stress at the tip) and the material breaks in the same direction (but not along a plane)
What happens when a crack elongates in a brittle material?
There’s an even higher stress at the tip and the material breaks in the same direction
When is there even higher stress at the tip of a crack in brittle materials?
When it elongates
What increases at the tip of a crack as it elongates in a brittle material?
Stress
How does a material break during a brittle fracture?
In the same direction, but not along a plane
What prevents crack propagation in a brittle material?
Increasing the breaking stress
What prevents crack propagation in a brittle material?
Increasing its breaking stress
In which way does a compression force move on a concrete block?
Inwards
In which direction does the tension force move on a concrete block?
Ouwards
How does tension affect normal concrete?
Cracks
Fails at a lower force
Which force is responsible for making concrete crack and in which direction does this act?
Tension, outwards
What happens when pouring concrete over steel rods under tension?
No cracks (at lower forces)
Fails at approx. 2x the load
When does concrete fail when poured over steel rods under tension in comparison to normal concrete?
At approx. 2x the load
What enables concrete to be able to last approx. 2x the original load?
Pouring it over steel rods under tension
Draw the forces acting on normal concrete v.s concrete poured over a steel rod under tension
(Check notes)
Name 2 ways of increasing the breaking stress of a brittle material
- Reduce the number of surface cracks
- Form the material under compression
Example of reducing the number of surface cracks on a material to increase its breaking stress
Thinner glass fibres have less cracks per unit area as thy have cooled more quickly - do not propagate as readily
What type of glass do not propagate as readily and why?
Thinner glass fibres, have cooled more quickly and therefore have fewer cracks per unit area
How do thin glass fibres have few cracks per unit area? What does this lead to?
Have been cooled more quickly - do not propagate as readily
Examples of materials formed under compression
Toughened glass and prestressed concrete
What does forming a material under compression do?
Stops cracks opening up and propagating
How is concrete pre-stressed?
Poured around steel rods under tension and when the tension is released, the concrete will be under compression
What does compression do to a crack?
Stress acts to close the crack
What does a crack do under …
Compression
Tension
Stress acts to close crack
Concentrated stress - the crack propagates
Why does the crack propagate on a brittle material under tension?
The stress is concentrated
Rubber
A polymer, formed of long chains of bonded carbon atoms
Name a polymer formed of long chains of bonded carbon atoms
Rubber
Which atoms bonded is rubber made of?
Bonded carbon atoms
What structure does rubber have?
Polymeric
Which bond can rotate in rubber and what does this allow it to do?
C-C bond, so the polymer molecule can assume a huge number of random shapes
What can the C-C bond in rubber do and what does this lead to?
Rotate so the polymer molecule can assume a huge number of random shapes
How can a rubber molecule assume a large number of shapes?
The C-C bond can rotate
What IS polymer?
Polymerised isoprene
Polymerised - what? Is rubber?
Isoprene
Draw isoprene’s molecular structure
(Check notes)
What happens during the polymerisation of isoprene?
The two double bonds are opened up, enabling repeating units to link together to produce poly-isoprene, where the 2 central carbons are double bonded
Draw poly-isoprenes molecular structure
(Check notes)
What are double bonded in poly-isoprene?
The 2 central carbons
What’s significant about the 2 central carbons in poly-isoprene?
Double bonded
What is poly-isoprene?
Rubber
What’s the difference between C=C and C-C bonds?
C=C —> not free to rotate
C-C —> free to rotate
Which type of bond is free to rotate C-C or C=C bonds?
C-C bonds
Describe the structure of a rubber molecule
“Tangled up”
Why is the structure of rubber all tangled up?
When the molecule is close to other parts of the chain, weak cross linkages are formed
What forms cross linkages in rubber?
The molecule with other parts of the chain
What happens when a stress is initially applied to rubber?
The bonds are being stretched and are rotated so that the molecules become straighter
Describe the force needed to extend rubber compared to crystalline and amorphous solids
Much lower
Crystalline material example
Metal
Amorphous solid example
Glass
When does rubber become slightly more difficult to stretch?
When the molecules are under such stress that they’re more or less straight
Draw rubber’s stress-strain curve
(Check notes)
Describe the first section of the loading curve of rubber
Steeper due to weak cross molecular bonds being overcome
What makes rubber hard to stretch initially?
Weak cross molecular bonds being overcome
Describe the second part of the loading section on rubber’s stress-strain curve
Gradient decreases since the stress is simply rotating the single C-C bonds as the molecules straighten
When does it take little force to extend rubber?
When rotating C-C bonds as the molecules straighten
Describe the last part of the loading section of rubber’s stress-strain curve
Molecules are now straight so more stress is required per unit strain to extend the stronger covalent bonds in the straight chain
What is required to extend rubber after the molecules have been straightened and why?
More stress per unit strain due to the stronger covalent bonds
Does rubber obey Hooke’s law?
Only when the force/stress is small
What does rubber obey when the stress is small?
Hooke’s law
Describe the first part of the unloading of rubber on its stress-strain curve
Less energy is released than was taken in during loading (heat lost to surroundings)
Why is less energy released when unloading rubber than loading it?
Heat is lost to surroundings
Describe the second part of the unloading part of rubber’s stress-strain curve
Similar curve for loading, just lower (less energy)
Why is the curve lower for unloading rubber compared to loading it?
Energy loss
Describe the last part of the stress-strain graph of rubber when its unloaded
Curve returns to the origin as the cross-linking weak bonds reform randomly within the polymer chains
What happens at the end of stretching rubber?
Cross-linking weak bonds reform
What is the area under the curve equal to on a stress-strain curve?
Work done
Is more work done loading or unloading rubber? What evidence backs this up?
Loading - work is the area under the graph and this line is higher
Elastic hysteresis
The extra energy used to stretch a material that’s transferred to vibrational energy
The extra energy used to stretch a material that’s transferred to vibrational energy
Elastic hysteresis
How do we work out hysteresis?
The loop inside the curve is the difference between loading and offloading the rubber and is the energy converted into heat during the whole loading/offloading cycle
What represents hysteresis on the stress-strain graph?
The loop inside the curve
What does the loop inside the curve represent on a stress-strain curve?
Hysteresis
What are the intermolecular bonds that are initially broken upon stretching rubber known as?
Van der Waal forces
Why is the area under the loading curve greater than the area under the unloading curve on a hysteresis graph?
When energy is put into the band when extending it, it also heats up the rubber.
This energy isn’t available as we de-stress the rubber = lower curve
When does a rubber band heat up?
Only when being stretched
Does a higher Young’s modulus mean a stiffer material?
So long as the materials are the same size, yes
What rule has to apply for a material to be stiffer with a higher Young’s modulus value?
The materials have to be the same size
What is concrete weak in?
Tension
What is a steel rod strong in?
Tension
Name something that’s weak in tension
Concrete
Name something that’s strong in tension
Steel rod
Permanent set
Where a material is stretched/compressed and doesn’t return to its original length
Where a material is stretched/compressed and doesn’t return to its original length
Permanent set
How is accuracy preserved when drawing a gradient?
Drawing a larger triangle
Example of a crystalline structure
Diamond
Diamond structure
Crystalline
Glass structure
Amorphous
Material with an amorphous structure
Glass
What does an increased temperature do to the value of Young’s modulus and why?
Increases
Molecules become entangled as vibrations increase, making the material stiffer
What causes the value of Young’s modulus to increase?
Increase in temperature
Explain and show where on a stress-strain curve a sample exhibits necking
The largest strain on a stress-strain curve that typically bends downwards
(The end of the stress-strain curve)
Why is it useful that the concrete is under compression when pre-stressed?
Inhibits crack propagation and they’re forced to close
Describe the process by which a brittle material fractures
Small imperfections (scratches) on the surface
Causes stresses to be concentrated on particular bonds when under tension
Does adding carbon atoms make a material more or less ductile? Why?
Less ductile
Create barriers for dislocation movement
Does the value for Young’s modulus depend on the size of the material?
No
Relationship between spring constant and extension
Inversely proportional
