Week 2

Question 1

How many components of stress are there for a 3D system?

Answer 1

9

Question 2

What is the stress element?

Answer 2

A way of representing the stresses acting at a point on the body of a system by isolating a small element of the material to show the stresses on all its faces. In 2d we draw 3 components:
- The horizontal normal stress
- The vertical normal stress
- The shear stress

Question 3

What is the sign convention when a normal stress acts in the same direction as the face of the element?

Answer 3

Positive

Question 4

In what direction do tensile and compressive stresses point respectively?

Answer 4

Tensile: Outwards
Compressive: Inwards

Question 5

In what direction do positive and negative shear point respectively?

Answer 5

Positive: Right
Negative: Left

Question 6

What are principal stresses?

Answer 6

The maximum and minimum stresses

Question 7

What are principal planes?

Answer 7

The planes on which the principle stresses act. Shear stresses are 0 on the principle planes

Question 8

How do we determine the maximum shear stress?

Answer 8

Differentiate the transformation equation for shear

Question 9

What is Mohr’s circle?

Answer 9

A way of visualizing stresses in a 2D system by plotting a circle on axes of shear and normal stress. This forms a circle that tells you what is going on in a stress element

Question 10

What are the six special cases of stress and what do their Mohr’s circles look like?

Answer 10

• General Tension (Mohr’s circle on right and not touching y-axis)
• Uniaxial Tension (Mohr’s circle on right and touching y-axis)
• General tension and expression (Mohr’s circle in slightly off-center)
• General Compression (Mohr’s circle on left and not touching y-axis)
• Uniaxial compression (Mohr’s circle on right and touching y-axis)
• Pure Shear (Mohr’s circle at the origin)

Question 11

What is a cantilever?

Answer 11

A rigid structural element that extends horizontally and is supported at only one end

Question 12

What is a girder?

Answer 12

Girders are the main supports of a large structure and will support the smaller beams

Question 13

In a simply supported beam, where is the stress the greatest?

Answer 13

In the middle due to the shear forces across the beam building up to the weakest point

Question 14

How does the stress in a simply supported beam change?

Answer 14

It changes from compressive stress at the top to tensile stress at the bottom
- If the material is elastic and follows Hooke’s law, at some point there exists a zero-stress neutral axis which is at the center of gravity of the beam

Question 15

Why are beams with I-shed cross sections often used in metal structures?

Answer 15

Material near the neutral axis carries little stress so it just adds weight for little structural purpose. Most of our material needs to be at the edge so that we can use structures that concentrate the material where most of the load is

Question 16

What are edge dislocations?

Answer 16

Terminations of planes of atoms in the middle of the crystal and can be interpreted as an additional half plane of atoms between two planes

Question 17

What are screw dislocations?

Answer 17

Dislocations that are shifted out of the plane of the material so occur in 3D

Question 18

What do Burgers vectors measure?

Answer 18

The amount of distortion introduced into the lattice by a dislocation

Question 19

What is the direction of the Burgers vector in edge dislocations relative to the dislocation?

Answer 19

Perpendicular

Question 20

What is the direction of the Burgers vector in screw dislocations relative to the dislocation?

Answer 20

Parallel

Question 21

What is slip?

Answer 21

The movement of dislocations through a material, typically in the direction of he densest crystal plane

Question 22

How do dislocations move during slip?

Answer 22

Dislocations break a few bonds at a time moving along like a caterpillar:
- Dangling bond at dislocation
- New bond forms, old bond breaks
- New dangling bond formed
- Repeat

Question 23

Do dislocations interact with eachother?

Answer 23

They do due to their strain fields

Question 24

What happens when dislocations with the same sign are on the same plane?

Answer 24

They repel each other

Question 25

What happens when dislocations with the different signs are on the same plane?

Answer 25

They attract each other

Question 26

In what kind of planes does slip usually occur?

Answer 26

Close-packed planes

Question 27

Where does slip occur first (angle)?

Answer 27

On slip planes closest to 45 degrees.

Question 28

In polycrystalline systems, where do dislocations occur first?

Answer 28

In grains angled towards the highest resolved shear stress

Question 29

Why are polycrystalline materials generally stronger than single crystals? Answer in terms of dislocations.

Answer 29

Grain boundaries impede the motion of dislocations due to the change in direction at the boundary

Question 30

What factors can affect the strength of metals?

Answer 30

- Grain size - Solid solution - Precipitation - Strain hardening

Question 31

What is a stacking fault?

Answer 31

When two lattice planes deviate from the normal stacking arrangement.

Question 32

What is a twin boundary?

Answer 32

When a stacking fault extends over many layers, the crystal switches to a mirror symmetrical layer

Question 33

What is a grain boundary?

Answer 33

The interface between two regions of different crystalline order or orientation.

Question 34

What are low angle grain boundaries?

Answer 34

Grain boundaries with a misorientation angle less than 15 degrees and are considered to be a collection of isolated and distinct dislocations.

Question 35

What are high angle grain boundaries?

Answer 35

Grain boundaries with higher misorientation angles and have a poorer fit with each other, resulting in a disordered region at the interface.

Question 36

Where do impurities often segregate to?

Answer 36

The disordered region where grains meet and both corrosion and cracking can occur at a grain boundary.

Question 37

How can solid solutions be used to strengthen materials?

Answer 37

Impurity atoms distort the atoms and generate stress but are attracted to the dislocation cores due to increased vacancies. This internal stress can be a barrier to dislocation movement.

Question 38

What are substantial impurities?

Answer 38

Impurities that are larger or smaller than the lattice atoms diffuse to the strained regions around dislocations. The distortion of the lattice due to the impurity atoms can partially cancel the strains caused by the dislocation.

Question 39

What happens when a dislocation meets a precipitate?

Answer 39

It can: - Cut through the precipitate - Extrude between precipitates Both require energy and so slow dislocation movement. As more loops appear, the space left for dislocations to move through becomes smaller making the material more resistant to slip.

Question 40

What is cold working?

Answer 40

When a material is deformed at room temperature, a reduction in cross-sectional area leads to an increase in dislocation density and resulting strain hardening.