W14 - Mechanical Properties of Materials II

Question 1

What are the positive directions in a stress element?

Answer 1

Normal stress
• tensile (+ve)
• compressive stress (-ve)

Shear stress
• +ve if arrows are in top right corner
• -ve arrows in top left corner

Rotations
• +ve CCW
• -ve CW

Question 2

What did the principle stresses indicate? What else is special about them?

Answer 2

Maximum axial stresses

Shear stresses are zero

Maximum shear stresses occur at 45* to the principle stress plane

Question 3

Write important features of Mohrs circle

Answer 3

+ve axial stress go towards the right
+ve shear stress point downwards

Angle in circle = 2*real angle

Question 4

What is the ‘Burgers Vector’?

Answer 4

“The amount of distortion introduced into the lattice by a dislocation”

Burgers vector is the difference between the circuit in the perfect crystal and the dislocated crystal.

Edge dislocation - BV is perpendicular to the dislocation

Screw - BV is parallel to the dislocation

Question 5

What are strain fields around a dislocation?

Answer 5

Dislocations distort the crystal lattice around them, causing strain fields

• where there are additional atoms (behind edge dislocations) compressive stresses are formed
• missing atoms (in front of dislocation) tensile stresses are formed

These decrease radially

Question 6

Movement of dislocations in reference to the shear stress direction

Answer 6

Edge - movement is parallel to the applied shear stress

Screw - movement perpendicular to the applied shear stress

Question 7

Define slip, slip plane, slip direction

Answer 7

Slip - process by which plastic deformation is produced by dislocation movement

Slip plane - Crystallographic plane along which the dislocation line traverses
• greatest planar density

Slip direction - specific directions, in the plane, along which dislocation motion occurs
• greatest linear density

Question 8

What is a slip system?

Answer 8

A crystal structure may have multiple slip planes and slip directions within them, hence

“ a combination of the slip plane and slip direction”
• will operate such that atomic distortion that accompanies the motion of a dislocation is a minimum

Question 9

What are resolved shear stresses?

Answer 9

Even though an applied stress may be purely tensile or compressive, shear components at all BUT parallel and perpendicular alignments to the stress direction - these are termed RST

RST = sigma•cos(phi)•cos(lambda)

Question 10

What is lambda and phi when calculating RST?

Answer 10

Lambda = dot product of SLIP DIRECTION & STRESS DIRECTION

Phi = dot product of PLANE NORMAL & STRESS DIRECTION

note: slip plane (abc) = plane normal direction [abc]

Question 11

What are the 4 main ways to strengthen a metal?

Answer 11

1. Grain size (reduce)
2. Solid solution
3. Precipitation
4. Strain Hardening

Question 12

How does grain size affect dislocation movement?

Answer 12

1. Grain boundaries act as barriers to slip
2. More misorientation at GB, bigger the barrier
3. Smaller grain size means there more GBs and so more barriers to slip

Sigma_y = sigma_0 + k_y*d^-1/2

Question 13

How does solid solutions increase strength?

Answer 13

1. Impurity atoms distort the lattice and generate stress
2. Impurity atoms attracted to dislocation cores because of the increased vacancies
3. This internal stress can be a barrier to dislocation movement
4. Impurities will diffuse into strain regions around dislocations which can partially cancel the strains caused by the dislocations

Question 14

How does Precipitates work to increase strength?

Answer 14

1. Add precipitates of a different phase to the material
2. If precipitates are harder (and thus more brittle) than the matrix phase, then they act as obstacles for the dislocation movement
3. When a dislocation meets a precipitate, it can ‘cut through’ or ‘extrude’ between precipitates. Both processes require energy and thus slow dislocations down
   • more loops, less space for dislocations to move through, the material becomes more resistant to slip

Question 15

How does strain hardening make a material stronger?

Answer 15

1. Slip is easy at first as it only occurs on a single plane
2. More dislocations means slips occur on other planes, when these interact they inhibit each others movement
3. Hence more stress is required to give an equivalent strain (SH)
   • a material that is stressed to a certain plastic strain will have increased its yield strength (if it is loaded again).

Question 16

What is cold working?

Answer 16

It is a type of strain hardening
1. When a material is deformed at room temp, a reduction in cross-sectional area leads to an increase in dislocation density and results in SH.

eg. Forging, rolling, drawing, extrusion etc

Yield strength increases however the ductility decreases substantially