Elasticity Flashcards
1
Q
What are the primary bonds?
A
Ionic
Covalent
Metallic.
They are all relatively strong
2
Q
What are the secondary bonds?
A
Van der Walls
Hydrogen Bonds.
They are relatively weaker than the primary bonds.
3
Q
Explain metallic bonds
A
A sea of electrons (and they lose their highest energy electron)
Non-directional.
Strong
Allows electrical conductivity (due to the free electrons)
Shiny - free electrons reflect photons.
4
Q
Explain ionic bonds
A
Negatively and positively charged ions attracted to each other.
Allows electrostatic attraction
Non-directional
Doesn’t conduct electricity/ Is a good insulator.
5
Q
Give some examples of metallic bonds
A
Al, Cu, Au, Ni.
6
Q
Explain covalent bonds
A
Directional
Shared electrons in certain orbitals
Strong
No electrical conductivity
7
Q
Give an example of an ionic bond
A
NaCl
8
Q
Explain hydrogen bonds
A
By electrostatic attraction between 2 or more electrically neutral molecules.
Directional.
9
Q
Explain van der Walls forces
A
Non-directional bonds
Created due to the non-uniform electron density distribution in an atom in a certain space and time, that creates a polarity.
Weakest bond.
10
Q
Strength of the bonds, starting with the strongest.
A
Covalent, metallic, ionic, hydrogen, Van der Wall.
11
Q
What are ceramics usually made of?
A
Covalent bonds and are really good insulators, and very stiff and strong.
12
Q
What are polymers usually made of?
A
The chain of monomers can interact with other chains by the Van der Wall forces, but to actually form the chains, the molecules are linked of covalent bonds.
Very low stiffness and strength, low melting point and no conductivity.
13
Q
Define energy barrier
A
The energy that must be overcome to go from one stable to another stable equilibrium position.
14
Q
If you have a graph of Potential energy (U(x)) against x, then what do the stationary points show?
A
The particle is in equilibrium, because the gradient is equal to the force at that point.
15
Q
What does a minimum stationary point on a U(x) - x graph show?
A
A minimum shows stable equilibrium, and a maximum shows unstable equilibrium.
16
Q
What does the interatomic potential mean?
A
I think it’s the energy required for the atoms to stay as close as they can, without any additional forces being applied on them.
17
Q
Formula for the Electrostatic potential
A
U(r) = -A/(r^m)+ B/(r^n), where n>m.
The negative part is the attractive part, the positive part is the repulsive part.
18
Q
What is U(o)
A
The bond energy. The energy at which the distance between the 2 atoms is the equilibrium bond length. This is when there is no force applied at all
19
Q
What is the universal physical principle
A
A system will spontaneously evolve towards states that minimise the potential energy.
20
Q
∂U / ∂x =
A
Force.
U = potential energy.
21
Q
Equation for shear stress
A
shear stress = Shear molding x shear strain.
22
Q
Equation for calculating the Young’s modulus using the equilibriums stiffness
A
Young’s Modulus = Equilibrium stiffness / r0.
r0 - bond length or radius length?
23
Q
Long form of FCC
A
Face Centre Cubic
24
Q
Examples of FCC
A
Al, Cu, Au.
25
Long form of HCP
Hexagonal Closed Packed.
26
Examples of HCP
Mg, Ti at Room temperature.
27
Explain HCP
ABA.
| First layer is the same as the third
28
Explain FCC
ABC.
| The third layer is the same as the 1st, but just 1 atom disordered.
29
Define coordination number
The number of atoms in DIRECT CONTACT with a certain atom. Represented by 'Z'.
30
What is the packing density
Volume occupied by atoms in the cell/ total volume of cell.
31
Z of FCC
12.
32
Packing density of FCC
0.74
33
Atoms per unit cell for FCC
4
34
Miller indices - how to represent negative vectors
number with a dash on top.
35
How to write the planes
Just find the reciprocal of the number to get the plane. If a line isn't touching an axis at all, then it is infinity for that axis.
36
Hexagonal unit cell
[ u v t w]
where w = z plane.
and u + v + t = 0
And only for HCP.
37
What is a unit cell for an FCC crystal?
Is a cube of side length a, 8 atoms centres in the corners and 6 atoms centred on the face-centres.
Has a coordination number of 12, and a packing density of 0.74.
38
Atoms/ unit cell for simple cubic, body-centred cubic and FCC
Simple cubic: 1 (8 x 1/8)
Body centred cubic: (1/8 x 8) +1 = 2
FCC : (1/8 x8) + (1/2x6) = 4
39
What is a shear force?
It is the force required to simply dislocate the atoms.
40
Types of Dislocations
1. Edge dislocations.
| 2. Screw dislocations
41
Edge dislocations
The symbol is the same as that for perpendicular.
The block has an extra half-plane of atoms with the lower edge lying along the dislocation line, and they are moved by the distance b NORMAL to the edge dislocation line.
42
Burgers vector explanation
Displacement distance of the atoms around the dislocation. It is counted clockwise.
43
Screw dislocation
The cut has happened and the clock is almost twisted. Move the top of the cut portion relative to the bottom by a distance b PARALLEL to the cut.
The symbol is S.
44
Define a slip
Movement of the dislocation. (also called glide)
45
Define a slip plane
The crystallographic plane on which the dislocation moves.
46
What is a slip direction
The crystallographic direction in the slip plane along which the dislocation moves.
47
Define the slip system
The slip plane + the slip direction.
48
What is slip step?
The atomic displacement left in the crystal by the dislocation.
49
How to represent a direction?
Family of directions?
Planes?
Family of planes?
Direction: [ ]
Family of directions : < >
Planes: ( )
Family of planes: { }
50
Dislocation motion properties of metals
Dislocation motion is easy.
Non-directional bonding.
Close-packed directions for slip.
Metals are soft and ductile.
51
Dislocation motion properties of covalent ceramics
Dislocation motion is hard.
The bonding is directional and angular bonding.
It is hard and brittle.
52
Dislocation motion properties of ionic ceramics
Dislocation motion is hard.
Non-directional.
Generally, need to avoid oppositely charged ions.
It is hard and brittle under tension.
53
What is a close packed plane?
{1 1 1}
54
What is a closed packed directions?
< 1 1 0>
55
Why are metals so ductile?
It is because they have many slip systems, which allows them to have dislocations in many directions and planes. (for FCC, they have 12 slip systems)
56
Does BCC have any close packed planes or directions?
BCC doesn't have any close packed planes. There are no planes where the atoms are touching each other. BCC does have close packed directions though, which is the diagonals, which are touching each other.
This makes is less ductile than the FCC.
57
Do hexagonal close packed planes have close packed planes? If yes, what is it?
{0 0 0 1}
58
Order HCP, BCC, and FCC in descending order of ductility
FCC is the most ductile. then BCC , and finally HCP is the least ductile.
Ductility decreases as you decrease the number of slip systems.
59
What does the Schmidt factor show?
It shows you if a certain slip plane will be activated or not under the given conditions of the applied stress. Only used for single crystal materials.
60
What is a single crystal material?
The crystal lattice is continuous and there are no grain boundaries in it.
61
What is the same between 2 single crystals in the same polycrystal?
They have the same atomic packing (so FCC, BCC etc.), but different orientation.
62
Are polycrystal stronger than single crystals?
Polycrystals are stronger because they have many grain boundaries. The grain boundaries are barriers to dislocation.
63
Purpose of strengthening mechanisms?
To hinder the dislocation motion.
64
Name the 4 types of strengthening mechanisms.
Solid solution strengthening.
Precipitation strengthening.
Grain size strengthening.
Work hardening.
65
Define solid solution strengthening and give information on it.
You mix atoms of different elements/ species in the host, so that the dislocation motion can be hindered. The atomic mismatch between atoms leads to a stress-strain fields that interact with the dislocations and lead to reduced mobility.
There are two types: substitutional and interstitial solid solution.
Substitutional solid solution is when an atom is added in to replace an original atom of the lattice. The added atom should be of the same size as the host atoms.
Interstitial solid solution is when the added atom is much smaller than the host atoms and fits itself into a gap between the host atoms.
When these new atoms are added into the lattice, it creates a stress-strain field around the added atoms (aka impurity)
66
How does solid solution strengthening hinder the dislocation motion?
The interaction of the stress/strain field of the dislocation interacts with the distortions caused by the impurities. For example, the impurity may generate a local shear at a place that opposes the dislocation motion.
67
What is the precipitation strengthening and how do the 2 choices work?
If the microstructure of the materials contains a second phase precipitate, then the dislocations will also interact with the second material.
The precipitates act as obstacles as the dislocations have to either cut through them or bow around them, creating a strengthening effect.
68
How to decide when the precipitate strengthening will cut or bow around?
Numerous, closely-packed small particles must be cut by dislocations and the bigger particles are more difficult to cut.
Fewer, wider-spaced large particles can be bowed-around by dislocations. More widely-spaced particles are easier to bow around.
69
What is so special about grain refinement strengthening?
When the strength increases, then the ductility also increases.
70
Explain grain refinement strengthening
Grain boundaries are barriers to slip. Essentially, dislocations have to change direction at a grain boundary and the because the grain boundary region is disordered. the discontinuity in the slip planes increases. Barrier strength increases with misorientation. So by decreasing the grain size, there are more barriers to slip.
71
What is equi-axed grains?
The grains look the same from every direction.
72
Define isotropic grain size distribution
Since grains are approx. spherical and randomly oriented.
73
Define the anisotropic grain size distribution.
The rolling affects the grain orientation and shape.
74
Why does the ductility increase with strength in grain refinement?
There are more grains, so there is an increased strength. However, more grains also means that there are more slip systems, therefore increasing the ductility.
75
Types of work hardening
- Forging
- Rolling
- Drawing
- Extrusion
76
Explain work hardening
Plastic deformation is applied to the material, leading to multiple dislocations, increasing the dislocation density in the material. As the dislocations interact with each other, they get tangled up and can act as obstacles, hindering motion, leading to a strengthening of the material.
77
How to calculate the dislocation density
Total dislocation length/ unit volume.
78
Why is ice less dense than water
The lattice arrangement allows water molecules to be more spread out in ice than in water.
79
If a material is in compression, then what is the strain?
Strain should be negative.
80
Why are covalent bonds - which are directional - less dense than ionically or metallically bonded ones?
Because if they are directional, they cannot pack together in a dense manner, and so they have a less dense material.
81
What is the difference between atomic structure and crystal structure?
Atomic refers to the protons, neutrons and electrons in an atom, but the crystal structure is the arrangement of atoms in a crystalline solid.
82
Be careful for measurements of fracture toughness?
Units can be a bit messy - so be careful.
83
Different modes of fracture
Mode I - Tension opening mode
Mode II - In plane shear mode
Mode III - Out-of-plane shear mode
84
List all the mechanisms of crack initiation.
- Microvoids coalescence
- Mechanical actions and machining
- Fatigue
- Thermal fatigue
- Chemical corrosion
85
Explain Mechanisms of Crack initiation - microvoids coalescence
- In ductile materials, where there are regions of high plastic strains, voids can be created.
- They usually start at inclusions such as precipitates.
- The voids expands and elongate, until they form cracks.
- Eventually, the cracks propagate until they finally turn into a fracture.
86
Explain Mechanisms of Crack initiation - Mechanical actions and machining
- Cuts or scratches on the surface
| - Surface roughness left from machining induces surface microcracks.
87
Explain Mechanisms of Crack initiation - fatigue
- Repeatedly straining a materials in the elastic part
| - At high number of cycles, the micro-cracks appear and eventually propagate to form cracks.
88
Explain Mechanisms of Crack initiation - thermal fatigue
- Fatigue caused by periodic variation of temperatures
89
Explain Mechanisms of Crack initiation - chemical corrosion
- Materials can have corrosion or oxidation at the surface and may propagate inside and create deep cracks.
90
Explain Mechanisms of Crack Propagation - ductile fracture
Ductile fracture - to all ductile materials - metals and polymers
- It delays the point at which the materials breaks at
- High plastic strains in the plastic zone initiates void nucleation at impurities/ inclusions.
- Crack proceeds microvoid growth and coalescence.
91
Explain Mechanisms of Crack Propagation - brittle fracture
Ceramics
- There is no plastic zone
- The atomic bonds are progressively broken and they extend the crack
- Creation of new cracked surface creates energy spending and surface tension.
92
How to calculate the strain energy
Volume x area under the stress-strain graph.
93
What are the monomers joined up using?
Covalent bonds
94
Define DP
Degree of polymerisation.
| It is the number of times that a monomer can be repeated.
95
Define Tg
It is the glass transition temperature.
| Temperature at which the secondary bonds between chains of a polymer are overcome.
96
Define amorphous
Without a clear shape.
97
What is a crystalline region?
A part of the material that is regularly packed.
98
What are the different types of classification of polymers of engineering interest?
Thermoplastic polymers or thermoplastics
Thermosetting polymers or thermosets
Elastomers
Natural polymers
99
Explain thermoplastic polymers
- Made by LINEAR POLYMERIC CHAINS with no cross-linking and occasional branching.
- When heated (just above or at Tg), the secondary bonds are melted and form a viscous liquid
100
Explain thermosetting polymers
- Made by highly cross-linked chains and networked polymers.
- Have a high level of cross linking below Tg.
- Made by mixing a resin and a hardener either at RT or upon heating.
- They will bur when they are over-heated and decompose, but do not lose their shape due to the cross-links.
101
Explain elastomers (rubbers for example)
- Made by almost linear polymers with occasional cross-links above Tg.
- At R.T, the secondary bonds have already melted.
- The cross-links that give shape memory and material is elastic to large strains.
102
Define crystallisation
Upon cooling, the molecular chains can arrange themselves in a regular pattern. However, this is hard for branches and cross-linked polymers, is more common in thermoplastics.
Some polymers can form spherulites instead.
103
Mechanical Response of polymers
- Low modulus (few GPa at max)
- Good strength (max 100MPa)
- High elastic limit
- Quite limit (as mostly empty space)
- Good toughness
- Good ductility
- Mostly aren't too good for high temperatures/
- Response can depends on multiple things.
- Difficult to design.
- Mechanical properties improve considerably when mixing with strong fibres to obtain FRP.
104
Behaviour of plastics with temperature?
Plastics tend to get more brittle as the temperature decreases, but more ductile as you increase the temperature.
105
Describe the Stress-strain graph for when the Temperature is much greater than the Tg.
Roughly a low E, until it starts to increase by a lot because of the strain stiffening of the material. Due to the molecular chains being realigned as you increase the strain. As the strain is increased, the stiffness in increased.
If unloaded at any point, it will return to the original shape, but not follow the same path.
106
How does the Youngs' modulus change for polymers when they T = Tg?
The E changes drastically, it suddenly decreases.
107
Why do polymers dissipate energy?
When a force is applied on the polymer, some parts of it acts as a spring in its elastic region. However, other parts of the polymer can have certain chains sliding out of place that have no return mechanism at all to return to their original length, and so this energy given is dissipated as kinetic energy.
108
Define viscous effects in polymers
Time dependent.
109
What is strain rate sensitivity?
Change in strain/ change in time.
The stiffness and strength increases with increasing strain rate.
Ductility decreases with an increasing strain rate.
This is because the polymers act as a force damper, which means that
F = c x v.
Therefore, if v increases, then F increases, Then, the stress increases, so the Youngs modulus increases the faster the force is applied.
110
Define creep for a polymer
The process by which a material shows a varying deformation.
Ex: A constant stress is applied, so strain increases with time.
111
Explain viscous effects: Stress Relaxation
- A strain is imposed and then held constant. Stress first increases, and then decays to a constant value.
112
Define viscoelasticity
Recoverable strains, elastic and viscous deformation mechanisms are active.
113
Define viscoplasticity
Permanent strains. Elastic, plastic and viscous deformation mechanisms are active.
114
Classification of ceramics
- Glasses (held together by covalent bonds)
- Vitreous ceramics (clay)
- Engineering ceramics (man-made crystalline ceramics made by heating non-metals C or oxides)
- Cement and concrete
- Natural ceramics (natural diamonds, rocks and stone)
- Ionic ceramics (hard, brittle, refractory solids)
115
Ceramic alloys
- Ceramic alloys: different compounds mixed at high temperatures
- Composites are often required because ceramics by themselves are quite brittle.
116
Mechanical response of ceramics
- Very high modulus (10^2 GPa)
- Low elastic limit
- High compressive strength
- Lower tensile strength
- Very high hardness
- Plastic deformation normally absent
- Retain mechanical properties at high temperatures
117
Why are ceramics brittle?
They are full of defects, which causes it to propagate under mechanical loading.
Such as:
- Grain boundaries.
- Inclusions of different materials/ phases
- Voids left by manufacturing process
- Micro-cracks due to high residual thermal stresses
- Presidence of glassy phases between crystalline phases.
118
How do cracks behave if they are normal to the direction of the uniaxial stress (in ceramics)?
In tension: the cracks open and may propagate. The cracks open perpendicular to the direction of the stress applied
Compression: Cracks stay closed.
119
How do cracks behave if they are at an incline to the direction of the uniaxial stress (in ceramics)?
Tension: The cracks propagate in a direction still perpendicular to the direction of the stress applied.
Compression: The cracks actually want to slip over each other and propagate that way, but there is friction at the interface that delays any movement at all. Instead, the crack propagates parallel to the direction of the stress applied.
120
Why don't ceramics show plasticity?
Plasticity required dislocations, which happens as a certain stress. However, because ceramics have defects which causes it to be brittle, the stress can never reach that required to allow dislocations to occur. The material breaks before the material can show plasticity.
121
How to make ceramics show plasticity?
- Remove defects from ceramics.
- Perform a confined compression test, so a high hydrostatic stress is applied, crack propagation is suppressed and the ceramic is forced to deform by dislocation motion, leading to plasticity.
122
Define a composite material?
A mixture of 2 or more constituent materials to combine and enhance properties of constituents, to create a continuous matrix materials and reinforcing filler material.
123
In a composite material - the strain the fibre greater than that in the matrix?
The strain is greater in the fibre than the matrix, because the fibres are stronger than the matrix for a given F.
124
What happens to the stress-strain curve for the foam as it is compressed?
During the elastic region, the parent material deforms elastically.
During the plateau region, there is plastic buckling and bending of the cell walls at approximately constant stress.
125
Explain densification to foams when they are compressed?
When the foam walls are crushed to the point where the walls are actually fully in contact with each other, causing the material to stiffen up.
126
Define viscoelasticity for polymers
Made up of recoverable strains, elastic and viscous deformation mechanisms are active. Dissipation associated with sliding action between chain, elasticity associated with stretching and folding of polymer network.
127
Define viscoplasticity for polymers
Permanent strains, elastic, plastic and viscous deformation mechanisms are active.
128
Defects in crystalline ceramics
- Grain boundaries
- Inclusions
- Voids due to manufacturing process
- Micro-cracks
- Presence of glassy phases between crystalline phases.
129
How to calculate the change in density in a material when it changes its structureT
Calculate how many atoms are in each structure, then calculate the volume per atom in each structure. The change in volume is the change in density.
130
What happens to ceramics in uniaxial tension?
Unstable propagation of micro-cracks leads to the final fracture.
131
What happens to ceramics in uniaxial compression?
First, there is stable propagation of microcracks.
| Then, coalescence of micro-cracks and unstable propagation of macro-cracks.
132
What happens to ceramics in confined compression?
- Dislocation plasticity and stable propagation of micro-cracks.
