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Materials Equations > Plasticity Equations > Flashcards

Plasticity Equations Flashcards

1
Q

What is the true stress defined as?

A
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2
Q

What is the true strain of a material ?

A
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3
Q

How do you derive the plastic energy ?

A
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4
Q

What is the vickers hardness ?

A
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5
Q

What is the relationship between hardness and yield strength ?

A
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6
Q

What is the flexural strength of concrete ?

A
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7
Q

What is the yield strength in tension ?

A
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8
Q

What is the yield strength in shear ?

A
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9
Q

What are the principal stresses ?

A
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10
Q

What is the rankine yield criterion?

A
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11
Q

What is the Tresca Yield criterion ?

A
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12
Q

How do you derive von Mises 2d plane strength conditions ?

A
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13
Q

What is the stress related to moments ? What is ymax?

A
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14
Q

What is the elastic section modulus?

A
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15
Q

What is the plastic section modulus ?

A
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16
Q

What is the failure moment ?

A
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17
Q

What is plastic deformation?

A

When load is removed, material is permanently deformed.

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18
Q

When is plasticity favourable?

A

Can absorb large amounts of energy before it breaks, e.g. a car crash.

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19
Q

What is an extensionometer?

A

Records how much a specimen extends before it necks

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20
Q

What is proof stress?

A

If elastic limit is not clear, draw stress-strain line at 0.1% or 0.2%.

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21
Q

How do you calculate the elongation at failure?

A

Draw stress-strain curve backwards from fracture point.

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22
Q

What is the elastic limit?

A

The highest stress at which strains are fully recoverable

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23
Q

What happens beyond the elastic limit?

A

Plastic deformation, then brittle fracture

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24
Q

What is brittle fracture ?

A

Propagation of a crack with no/very little plastic deformation.

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25
Q

What is ductility?

A

A measurement of a material’s ability to undergo significant plastic deformation before failure.

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26
Q

What is brittleness?

A

A material’s characteristic when subjected to stress, it breaks without significant plastic deformation.

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27
Q

Are metals and polymers ductile?

A

Yes

28
Q

What is strain hardening>

A

Strengthening the metal by plastic deformation

29
Q

When does necking occur?

A

At max tensile stress

30
Q

When are polymers ductile?

A

When tested at high temperatures

31
Q

When are polymers brittle?

A

When tested at low temperatures

32
Q

What are the 3 main properties of ceramics?

A

Brittle, high Young’s Modulus, high compressive strength.

33
Q

What do tensile and compressive test require?

A

A large sample, and they are destrucitve

34
Q

What do hardness tests require?

A

A small volume and are non-destructive.

35
Q

What happens in a hardness test?

A

A diamond or ball shape is pressed into the surface of a material.
Hardness is determined by its resistance to indentation.
Large hardness means high resistance to plastic deformation

36
Q

What would be the difference between playdough and concrete in a hardness test?

A

Playdough would not resist, whereas concrete would.

37
Q

What is the Vickers hardness test?

A

Where a diamond shaped inductor is press under a static load

38
Q

What is the resulting hardness Hv from a Vickers test?

A

Hv = k x (F/d^2)

39
Q

What is the compressive strength of a material?

A

The max stress that a material can carry in a compressive test.

40
Q

What is the flexural strength?

A

The stress in a material just before it yields

41
Q

In compression, what happens to the area of the specimen?

A

Increases

42
Q

To calculate the true stress of a material, what do we need to do?

A

Divide the force by the new area due to compression etc.W

43
Q

When are true stresses and true strains calculated?

A

When there is a significant change in the area (deformation)

44
Q

What is the equation of the true strain?

A

ln(1+ strain)

45
Q

What is the plastic strain?

A

Total strain - elastic strain

46
Q

What does the total work equal?

A

The plastic work + elastic work = the integral of plastic strain x stress

47
Q
A
48
Q

What is the maximum principal stress theory?

A
49
Q

If the maximum principal stress = max yield stress, what happens?

A

The material yields

50
Q

What is the tresca criteriojn?

A
51
Q

Strength limitedd design:

A

I

52
Q

What are vacancies ?

A
53
Q

What are solute atoms ?

A
54
Q

What are dislocations?

A
55
Q

Do vacancies effect yield strength?

A

NO

56
Q

Do dislocations effect yield strength?

A

Lower the yield strength

57
Q

Do solute atoms and grain bourdaries effect yield strength?

A

Yes, they increase yield strength

58
Q

What is yield?

A

The movement of dislocations within the structure, permanent/plastic deformation.

59
Q

When do dislocations find it easiest to move?

A

In perfect cyrstals with no imperfections.

60
Q

Without dislocations, what would a metal not be?

A

Malleable

61
Q

What does the strength of a material depend on (in terms of dislocations)?

A

The force required to move the dislocation, not the bonding energy between the atoms.

62
Q

How can we reduce dislocation movement?

A

Add obstacles, e.g. solute atoms, which increases hardness

63
Q

What is solid strength strengthening?

A

What alloys are made of, solute atoms added to a pure atom to produce additional stress fields, increasing strength.

64
Q

What is precipitation and dispersion strengthening?

A

A way of alloying, where the impurity may precipitate as a small particle. The smaller the particle the greater the strength.

65
Q

What is work hardening?

A

When moving dislocation planes intersect and obstruct each other , increasing the yield stress.

66
Q

What are grain boundaries?

A

Boundaries that allow for dislocation movement .

67
Q

How can you alter grain size?

A

Heat treatment after plastic deformation.

Materials Equations (11 decks)

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