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Materials Equations > Elasticity Equations > Flashcards

Elasticity Equations Flashcards

1
Q

What is engineering stress ?

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2
Q

What is engineering strain ?

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3
Q

What is Poisson’s ratio?

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4
Q

What is shear strain?

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5
Q

What is dilitation due to hydrostatic pressure ?

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6
Q

What is Hooke’s law for axial stress?

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7
Q

What is Hookes law for shear stress ?

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8
Q

What is Hookes law for hydrostatic pressure ?

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9
Q

What is the relationship between the shear modulus (G) and poisssons ratio? ( hint Young’s modulus)

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10
Q

What is the relationship between the bulk modulus (K) and poussins ratio ?

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11
Q

How can it be derived that K roughly equals E?

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12
Q

How can it be derived that G roughly equals 3/8 E?

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13
Q

What is the elastic energy per unit volume?

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14
Q

In a composite, what is the volume fibre fraction?

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15
Q

What is the density of a composite ?

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16
Q

How do you derive the tensile stress of a composite ?

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17
Q

How do you derive the Young’s modulus of a composite with its fibres parallel to the strain?

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18
Q

How do you derive the Young’s modulus of a composite with its fibres perpendicular to the strain?

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19
Q

What are the two phenomona at the atomic level that affect the value of the Young’s Modulus?

A

The interatomic bonds and the atom packing

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20
Q

What are the 2 types of bonding between atoms?

A

Primary bonds and secondary bonds

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21
Q

What are the 3 types of primary bonds?

A

Ionic, covalent and metallic

22
Q

What are the 2 types of secondary bonds?

A

Van der waals and hydrogen bonds

23
Q

What are ceramics held together by?

A

Ionic and covalent bonds

24
Q

What are metals held together by?

A

Metallic bonding

25
Q

What is ionic bonding?

A

When 2 oppositely charged ions are attracted to each other due to interactions between anions and cations

26
Q

What are the properties of ionic bonds?

A

Strong, brittle, high metlting/boiling points

27
Q

What is covalent bonding?

A

A chemical bond between atoms who share electrons

28
Q

What are the properties of covalent bonds?

A

Stiff, brittle, high melting point, low electrical conductivity

29
Q

What is metallic bonding?

A

Where there is elcectrostatic attraction between positive metal ion and negative electrons ‘electron cloud’

30
Q

What are the properties of metallic bonding?

A

Stiff, ductile and condictive

31
Q

What are all metals and ceramics made up of?

A

Small crystals or grains, in a regular, repeated or 3d pattern.

32
Q

What do ‘sphered’ refer to?

A

Atoms or ions

33
Q

What does a close packing of spheres mean?

A

Little gaps, largest possible volume occupied by volumes within the spheres

34
Q

In most metals, what are the 2 ways spheres are packed together?

A

Closed packed hexagonol or face-centred cubic

35
Q

What are polymers?

A

Engineered materials, which are characterised by more complex structures than metals

36
Q

How are separate polymer chains linked together?

A

By weak hdyrogen bonds, which are easily broken

37
Q

Why are polymers thermoplastic and easily melt?

A

Due to the weak hydrogen bonds between the chains

38
Q

As glasses do not exhibit a long range of ordering, how are they packed?

A

In a non-crystalline (amorphous) way

39
Q

What is the cohesive energy?

A

The additonal energy due to the arranegment of atoms in a crystalline state compared to the gap state

40
Q

What does a higher cohesive energy mean?

A

More energy is required to break the atom bonds in a solid completely, so a higher young’s modulus

41
Q

What does S0, the stiffness in a bond in terms of covesive energy equal?

A

radius x Young’s modulus

42
Q

How do you measure the Young’s Modulus of a material?

A

Apply compressive force to the sample, measure the virbational frequency, the velocity depends on the Young’s Modulus and material density

V = root ( E / density )

43
Q

Why do we use engineered composites?

A

To get the ideal properties we need

44
Q

What does reinforcement + matrix give us?

A

A composite

45
Q

What is an MMC, CMC and PMC?

A

Metal Matrix Composite, Ceramic Matrix Composite, Polymer Matrix Composite

46
Q

What is MFRC, GFRC, PFRC?

A

Metal Fibre reinforced concrete, glass-fibred reinforced concrete and polymer fibre reinforced concrete

47
Q

What are the benefits of fibre-reinforced polymers?

A

High-stiffness to weight ratio, high strength to weight ratio, corrosion resistance, fatigue resistance

48
Q

What are the negatives of fibre-reinforced polymers?

A

High cost, not recyclable and difficult to predict behaviour.

49
Q

What are chopped fibres?

A

Firbres that are randomly distributed

50
Q

What does the volume of a composite equal?

A

Volume of matrix + Volume of fibres

51
Q

Give 2 examples of fibre-reinforced composites:

A

-Concrete fibre reinforced polymer, reinforced concrete

Materials Equations (11 decks)

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