Unit 1.5 Solids under stress Flashcards
(105 cards)
1
Q
What happens to opposite ends of objects when equal and opposite forces are applied to them?
A
Its particles (molecules/ atoms/ ions) will be forced into new equilibrium positions with respect to one another.
2
Q
State 3 forces which can be applied on opposite ends of an object?
A
- Compressive
- Tensile
- Shear
3
Q
What term is used for objects that are applied under forces?
A
Stress
4
Q
Define tension.
A
The force which an object exerts on external objects because it is being stretched.
5
Q
Define Hooke’s law.
A
The tension is directly proportional to the extension, provided that the extension is not too great.
6
Q
Describe an elastic material.
A
It is able to return to its original form when stress is removed.
7
Q
Define extension.
A
Increase in length.
8
Q
Give the symbol used for extension.
A
Δl
9
Q
State the gradient in a force - extension graph.
A
Spring constant, k
10
Q
Describe spring constant.
A
Stiffness of the object.
11
Q
State the area under a force - extension graph.
A
Work done in stretching.
12
Q
What is the compressive stress and strain?
A
They are defined in exactly the same way as tensile stress and strain.
13
Q
Define compression modulus.
A
Ratio of compressive stress to strain.
14
Q
What has the same value as small compressions?
A
The Young modulus.
15
Q
Define tensile stress, σ.
A
The tension per unit cross section.
16
Q
State the formula for tensile stress, σ.
A
σ = F / A
17
Q
What is “F” in the formula for tensile stress?
A
Tension
18
Q
What is “A” in the formula for tensile stress?
A
Cross - sectional area
19
Q
Define tensile strain, ε.
A
The extension per unit length due to an applied stress.
20
Q
State the formula for tensile strain, ε.
A
ε = Δl / l
21
Q
What is “Δl” in the formula for tensile stress?
A
Extension (the increase in length).
22
Q
What is “l” in the formula for tensile stress?
A
Original length
23
Q
Define Young modulus.
A
For a material that obeys Hooke’s law, the Young modulus is:
E = tensile stress / tensile strain
24
Q
What tends to be the Young moduli for a “Hookean material”?
A
100 GPa range
25
State the units for Young modulus.
Pa
26
State the units for stress.
Pa
27
State the units for strain.
None
28
What tends to be the stress of a "Hookean material"?
They are very large (in the 100 MPa range)
29
What tends to be the strain of a "Hookean material"?
Very small: a strain of 0.001 or less.
30
Define elastic strain.
The strain that disappears when the stress is removed, that is the specimen returns to its original size and shape.
31
Define plastic strain.
The strain that decreases only slightly when the stress is removed.
32
Define elastic limit.
The point at which deformation ceases to be elastic.
33
Describe the behaviour of an elastic material.
For small values of strain, materials return to their original size and shape if the stress is removed.
34
State the term used for the elastic limit of an object (e.g. spring).
Load
35
State the term used for the elastic limit of a material (e.g. copper).
Stress
36
State the 1st formula for energy (relating to springs).
W = 1/2 Fx or W = 1/2 FΔl
37
State the 2nd formula for energy (relating to springs).
W = 1/2 kx²
38
State the formula for force (relating to springs).
F = kx
39
State 4 other work done formulas (relating to springs).
1. W = 1/2 kx² or W = 1/2 k(Δl)²
2. W = 1/2 (F²/k)
3. W = 1/2 (F²/Δl)
40
Describe what this formula is referring to W = 1/2 FΔl.
It gives the energy stored in a body by virtue of its deformation. This energy is variously referred to as strain energy or elastic potential energy.
41
What does the area of a force-extension graph give?
The work done in stretching a Hookean object is given (W = 1/2 FΔl).
42
Describe how the work done formula (W = 1/2 FΔl) is derived using the force-extension graph.
Releasing the tension and allowing the object to contract allows it to do work in its turn and, because the graph for relaxation is the same as for tensioning (for Hookean materials), the work done by the object in relaxing is the same as the work done on the object during deformation.
43
Give an example on how hysteresis is formed in a force-extension graph.
If the extension of a rubber band is measured when it is loaded (e.g. by hanging 100g masses) and then unloaded, a load-extension curve is obtained. The unloading curve is below the loading curve. This phenomenon is called hysteresis.
44
Give a use for hysteresis.
It is responsible for rolling resistance in car tryes.
45
What does the area under the loading curve for a hysteresis graph represent?
Work done on the rubber in extension.
46
What does the area under the unloading curve for a hysteresis graph represent?
Work done by the rubber in contracting
47
What does the area between the loading and unloading curve represent?
The mechanical energy loss in the cycle: it is transferred to internal energy in the rubber and then lost as heat.
48
What does the formula 1/2 σε for Hookean materials represent?
The strain energy per unit volume
49
State how to derive W = 1/2 σε.
1. W = 1/2 FΔl
2. W / V = 1/2 (FΔl / Al) - Rearrange to get W as the subject
3. W = 1/2 (F / A * Δl / l)
4. W = 1/2 σε
50
Define ductile.
It is able to be drawn into a wire.
51
Define malleable.
It is able to be hammered into shape.
52
Give 3 examples of ductile materials.
Many metals, such as steel, aluminium and copper.
53
Describe ductile materials.
They are malleable, especially when hot.
54
What type of metal is a ductile material?
They are crystalline.
55
What do crystalline metals have?
A periodic structure called a lattice.
56
Describe the lattice particles in metals.
They are positive ions - atoms that have lost one or more electrons. They are held together by a 'sea' of negatively charged delocalised electrons which are free to move between the ions.
57
Describe metal ions.
They are spheres, they usually pack with the least potential energy into planes with the hexagonal arrangement, with ions in the plane above nestling in the gaps.
58
Describe gas-turbine blades.
They have been developed consisting of single crystals of a 'superalloy' of nickel.
59
What are most metal samples?
Polycrystalline
60
What happens to Polycrystalline when it solidifies from the molten state?
Crystallisation occurs at many points independently.
61
Describe what happens during the crystallisation process?
This results in a large number of very small interlocking crystals (grains).
62
Describe the orientation of crystal planes during crystallisation.
It is random from one grain to the next. A typical grain will have ~10⁵ lattice planes.
63
Describe the grain boundaries during crystallisation.
They have a large component of impurity atoms which are forced out of the grains during crystallisation.
64
Describe another point about the structure of ductile metals.
It is the presence of irregularities within the lattice.
65
State 2 irregularities in ductile metals.
1. Edge dislocation
2. Point defect
66
Define edge dislocation.
It is where an additional 1/2,-plane of ions is present.
67
Define point defect.
It is where a lattice ion is missing or a 'foreign' atoms or just an additional ion is present.
68
What makes up the mechanical properties of polycrystalline metals?
The combination of regular lattice, grain boundaries and dislocations.
69
State the gradient in a stress-strain graph.
Young modulus of the material
70
Describe the shape of the graph from O to P in a stress-strain graph.
It is a linear portion OP.
71
What is point "P" at the stress-strain graph?
Limit of proportionality
72
What comes after point "P" in a stress-strain graph?
Point E
73
Describe point "E" in a stress-strain graph.
It is the elastic limit. Only strains up to E are elastic; beyond E they are plastic.
74
What comes after point "E" in a stress-strain graph?
Point "Y"
75
Describe point "Y" in a stress-strain graph.
The yield point, Y, at which the material shows a large increase in strain for little or no increase in stress. The stress here is called yield stress, σᵧ.
76
State the name given between point "Y" and point "X" in a stress-strain graph.
An extensive plastic region
77
Describe what happens in between point "Y" and point "X" in a stress-strain graph.
The maximum stress is called the breaking stress or ultimate tensile strength, σₓ. X on the graph marks the breaking point.
78
Describe the largest strain region of the stress-strain curve.
It It typically bends downwards. In this region, the sample exhibits necking.
79
Define necking.
It is a narrowing of the region where it will eventually break.
80
State the 2 factors affecting the shape of a stress-strain graph.
1. It varies with material
2. The history of the material (e.g. heat or working treatment)
81
When calculating stress what value is used?
The unstrained cross sectional area of the material, i.e. the value before a stress is applied.
82
Describe what happens when a material is put under low tension, i.e. σ < σₑ.
The separation between the lattice particles (ions) is increased. This is elastic deformation because the forces between the particles pull them back to their initial position when the tension is removed.
83
What is plastic deformation caused by?
An irreversible rearrangement of particles. This is made possible by the presence of edge dislocations.
84
Describe the dislocation movement which produces plastic strain.
The dislocation moves to the right under the influence of the applied forces.
85
Describe what happens during yield stress.
The individual ions only move slightly; the ions above a certain point drops into a lower potential energy position in the next plane, so that the extra 1/2- plane moves to the right until it reaches the grain boundary; the crystal becomes more elongated. The stress at which this happens is the yield stress.
86
What happens when the yield stress is removed?
The dislocation does not move back, so this elongation is plastic.
87
State factor 1 after yield stress is removed.
Edge dislocations can get entangled limiting their movement.
88
State factor 2 after yield stress is removed.
The size of the grains- the smaller the grains, the less the freedom of movement of the dislocations.
89
State factor 3 after yield stress is removed.
The presence of point dislocations: foreign atoms can inhibit the movement of edge dislocations; a void in the lattice spawns more edge dislocations.
90
State 2 factors which can affect the factors of when the yield stress is removed.
1. For different metals, e.g. alloys (i.e. steel) changing the composition.
2. Heating and quenching regimes
91
Describe the metal properties for certain metals when under heating or quenching regimes.
It can make the metal more or less ductile and cold working generally makes a metal stiffer and less ductile because it causes dislocation entanglement.
92
State 3 brittle materials.
1. Cast iron
2. Ceramics
3. Masonry
93
Describe brittle materials.
They are totally elastic and generally Hookean, up to the breaking stress.
94
State 3 structures metals can have.
1. Amorphous (non-crystalline)
2. Crystalline (quartz)
3. Amorphous (glass)
95
Explain why amorphous materials are brittle.
Due to the absence of a crystal structure which means that there can be no dislocations to move and produce plastic deformation.
96
Describe the structure of a crystalline.
The crystals are very small and the presence of a large fraction if impurity atoms means that dislocations are pinned down.
97
Describe brittle materials under tension.
They are weak under tension, i.e. their breaking stress is low.
98
Describe what happens to ductile materials when it is under ductile fracture.
When broken, the pieces can be fitted back together. This is because of the absence of plastic deformation.
99
Define crack propagation.
Failure under tension
100
Describe the forces within the atoms when under crack propagation.
The interatomic forces cannot cross the gap because the atoms are apart, so the forces must be transmitted around the tip of the crack, leading to a greatly magnified stress.
101
What are stress lines?
These show how the tension links the atoms in the material (they can be shown in red).
102
102
What happens to brittle materials when it is lead to magnified stress?
The brittle material starts to break at the crack tip: the crack extends which increases the stress at the tip and so the crack propagates (at the speed of sound in the material) resulting in catastrophic failure.
103
State 1 of the 2 factors in where brittle materials can be used in load-bearing structures if the brittle member is.
Compressively pre-stressed in manufacture
104
