Elastic Moduli of materials chap 2

Question 1

What is stress?

Answer 1

The effect of the force applied

sigma= force/ cross sectional area (base)

Question 2

Benefits of using stress?

Answer 2

Same stress regardless of change in material in comparison with force

Question 3

What is strain?

Answer 3

Deformation in response to applied force

- final length - original/ original length

Question 4

Benefits of using strain?

Answer 4

Preferred to elongation as you can use regardless of material size or length

Question 5

Young modulus curves

Answer 5

• relationship between stress and strain

Metals
- low strain levels = linear relationships

Ceramics
- linear relationship between stress and strain until sudden fracture

Shape memory alloy
NiTi
- has memory of original shape
- initially linear then deforms but deformation is reversible

Question 6

Hooke’s law

Answer 6

• Relationship between stress and strain is linear when strain is small
• when the relationship is linear is when we are in the materials’ elastic regime and the form is recoverable
  stress= materials property (E) times strain

Question 7

Basic stress and strain states?

• definition
• Equation

Answer 7

1. Tension(+) and Compression(-) stress and strain
   - uniaxial tension = going out
   - uniaxial compression = going in
   - Equations
   same as OG stress and strain resulting in Hooke’s law
2. Shear stress and strain
   - stress - force over cross sectional area
   - strain = tan theta
   - Hooke’s law= shear stress = shear modulus x shear strain
3. Hydrostatic pressure (stress)
   - signs are opposite to uniaxial
   compression (+) (under the sea) and tension
   (-) (on mountain)

• (dilation) = change in volume/ original volume
• Hooke’s law = hydrostatic pressure= negative bulk modulus x dilation

Question 8

What are the complex stress and strain states?

Answer 8

1. Biaxial tension and compression ( equilibrium force on all sides)
2. Bending (tension on one side compression on next and middle strain neutral)- s-s are non uniform
3. Torsion (rotating shaft)- pure shear
   Equation :
   shear strain = theta/ original length x r
   shear stress = Gtheta/ original length x r
   max will be times original radius

Question 9

Poisson’s ratio?

Answer 9

relationship between lateral (diameter) strain and axial (length) strain

v cylinder = - lateral strain ( final diameter over original diameter for cylinder)/ axial strain ( final
length/ original length for cylinder)

v rectangle ba
strain x and strain y = lateral
strain z axial
strain x = strain y = negative Poisson’s ratio x strain z

Question 10

What does Poisson’s ratio mean?

Answer 10

v= 0.5 little change in volume- iso-volume

v< 0.5 variation in volume

Question 11

Isotropic/ ani-tropic

Answer 11

• isotropic = same behaviour in all directions of rotation

- ani-tropic = metals, plastics, wood

Question 12

homogenous / heterogenous

Answer 12

= same behaviour when elongated or translated

= heterogenous = rocks

Question 13

Effect of Elastic moduli ?

Answer 13

The higher the elastic moduli the less the material deforms
Low E 
- vaulting poles
- springs
-cushions

High E
- bridge

Question 14

What are the three primary types of interatomic bonding?

Answer 14

• Strong bonds (1000-4000K)
• Ionic
• covalent
• Metallic

Question 15

What is ionic bonding?

Answer 15

• Non metal and metal
• non directional bonding = efficient packaging
• metallic easily give up their valence electrons to the non metallic
• in the process all atoms acquire a stable or inert gas configuration and an electrical configuration as they become ions
• High electron negativity

Question 16

What is covalent bonding?

Answer 16

• non metals
• directional (specific packing)
• establish stable electron configurations by the sharing of electron
• similar EN
• ceramics: pottery, rocks, glass
• high melting point metals : W,Mo, Ta
• Polymers!!!- back bone of polymer chains

Question 17

What is metallic bonding?

Answer 17

• in metals and their alloys
• bond between sea of delocalized electrons and positive metal ions
• non directional (packed tightly)
• freedom of movement

Question 18

What is secondary interatomic bonding?

Answer 18

• weak bonds (100-500K)
• Van der Walls
• Hydrogen bonding

Question 19

What is a dipole?

Answer 19

A moment where there is a separation between the positive and negative parts of an atom = electric dipole

Question 20

Types of a dipole

Answer 20

• electrically symmetrical
• fluctuating
• induced
• permanent

Question 21

What is Young’s modulus?

Answer 21

Measures how easily a material deforms or stretches

Small no= very elastic

Question 22

Bonding force

Answer 22

Bonding force is the coulombic attraction or repulsion between two oppositely charged species.
When they’re a certain (r-separation) they begin to be attracted but they can’t get too close especially atoms as they negative electron clouds will start to repulse as they overlap.

Pulling apart atoms will be resisted by attractive force and compressing atoms will be resisted by repulsive/restrictive force

Question 23

Behavior of force with relation to distance?

Answer 23

At big r, force is positive (attractive) and at small r force is negative (restrictive)

Question 24

Bond Stiffness

Answer 24

The gradient of f-r curve is a measure of the bond stiffness at a certain point
Also directly correlates to Young’s modulus, as S increases, Young’s modulus increases

Question 25

What is the order of strongest to weakest bonds?

Answer 25

ionic> covalent>metallic>hydrogen>Van der Walls

Question 26

Draw out the shear schematic diagram

Question 27

Draw the young modulus curve for metals, ceramic and polymers

Question 28

Bond energy

Answer 28

Potential energy of the bond between two atoms | The trough in the UR curve indicates the strength of the interatomic bonds

Question 29

Draw F-r curves for weak and strong materials

Answer 29

- assymetrical | gradient - bond stiffness- Young's modulus

Question 30

Draw U-r curves for strong and weak materials

Answer 30

- integral of FR - assymertrical - end of smiling face starting vertical

Question 31

How does bonding force dictate a material’s properties?

Answer 31

- For polymers- strongs bonds within atoms (covalent bonds) but have weak bonds between chains (van der walls)- due to this weak bonds- a lot of free space, and not tight packing of atoms, and weak bonds in polymer materials allows for the greater ductility which they display - For metals- metallic bonds- force of attraction between positive metal ion cores and sea of delocalised electrons, sea of delocalised electrons sheilds ion cores from repelling allowing for tighter packing and more dense materials leading to higher strength, stiffness and density but the electrons allow the layers of atoms to slide past each other which also makes metals ductile - For ceramics bonding forces are ionic to covalent - because of the ionic bonding ( cations sharing electrons with anions), atoms cannot slide past each other, if tensile forces applied, ceramics immediately break at yeild point because the cations and anions are brought into contact and repel each other causing fracture

Question 32

Coefficient of Thermal expansion (a1)

Answer 32

Solid expands when heated and contracts when cooled coefficient of thermal expansion= rate of contraction and expansion - a1 = change in strain T over change in T strain T = change in length over og. length when temperature increases, mean position of UR curves increases and shifts to left path of mean position --> describes thermal expansion slope of the mean distance curve defines a1

Question 33

Melting

Answer 33

The collapse of a crystalline structure of atoms when atomic vibration due to increased temperature is strong enough determined also by bond energy as well as the crystal structure

Question 34

What is the effect of a materials' Young modulus what does it tell us about the material?

Question 35

What is the range of Young's modulus for each class of material?

Question 36

How do you work out the percent ionic character for ceramic materials? - work it out for CaF2 , MgO, Sio2, SiC, Si3N4 and NaCl, Al203

Question 37

Hydrogen bonding?

Answer 37

FON and H Coloumbic forces between polar molecules such as HF,H20,NH3, due to the H at the end of atoms being attracted strongly to the negative ends of the molecule - reason why some polar molecules have such high melting points

Question 38

Draw the tetrahedron of bonding to understand the bonding present in the three classes of materials?

Question 39

What are bonding forces?

Answer 39

The attractive or repulses forces between atoms, molecules or ions

Question 40

How does bonding forces contribute to Young's modulus?

Answer 40

- The slope of F-r curves = stiffness of the material = change in force over change in separation, - young's modulus is a measure of the stiffness of a material as it measures how easily a material deforms - young's modulus is also reflection of all the bonds that are actioned when stress is applied

Question 41

Where are attractive and repulsive force at a majority

Answer 41

- Fa when r is large when there is pulling of atoms apart with r greater than equilibrium separation- above the x-axis - Fr when there is r smaller than the equilibrium separation when atoms are being pulled together - below the x-axis

Question 42

Stiffness and seperation

Question 43

What is the equation for coloumbic force of attraction?

Question 44

What is fmax

Answer 44

The highest point on the f-r curve the theoretical maximum force a bond can endure the theoretical strength of a material the stronger the bonding the higher the fmax

Question 45

What is the equation for bond energy

Answer 45

Aq1Q2/r

Question 46

Relationship between thermal expansion, bond energy, melting temp

Answer 46

Higher the bond energy, smaller the thermal expansion co-efficient the higher the bond energy, the stronger the bond, the lower the thermal expansion coefficient and the higher the melting temperature and the closer atoms are to each other- think of physical attraction- farther apart less strong attraction

Question 47

What happens to a material under uniaxial tensile loading

Answer 47

- elongate in axial directions( length) and contract in lateral direction

Question 48

What are the 4 elastic properties of a maerial? EGKv

Answer 48

E- Young's modulus G shear modulus K Bulk's modulus v Poisson's ratio

Question 49

bonding type dictates

Answer 49

- electrical conductivity - thermal conductivity - chemical reactivity

Question 50

bonding strength dictates

Answer 50

- - elastic modulus - - melting temp - - theoretical strength - - thermal expansion coefficent