Metals- Strengthening

Question 1

How does dislocation density affect the strength of a material?

Answer 1

The more dislocations that are present in a material the higher the probability that these dislocations will interact with each other, inhibiting each other’s motion and hence strengthening the material. This is known as forest hardening

Question 2

Formula for dislocation density

Answer 2

ρ=1/L^2
Where ρ is dislocation density
L is average spacing between two dislocations
For a simple cubic array of L^2 only one dislocation will be present

Question 3

Formula for effect of dislocation density on material strength

Answer 3

σY proportional to Gbρ^1/2

Question 4

How do grain boundaries increase the material’s strength in relation to forming dislocations?

Answer 4

They are sources of dislocations so increase the dislocation density resulting in an increase in strength

Question 5

Grain boundaries as obstacles to dislocation motion

Answer 5

Orientation differences across boundaries means dislocations can’t easily move from one grain to the next. Means dislocations pile up at grain boundaries increasing the strength of the material. As they pile up they also experience repellent forces which further increases the strength (stress required to move the dislocation further).

Question 6

How the effect of grain size works

Answer 6

One grain is favourably oriented for yield (dislocation glide) to initiate. As dislocations pile up at boundary they exert a stress on the next grain. When this stress is sufficient the next grain will yield. So for smaller grains only short dislocation pile ups are possible meaning less stress exerted on next grain so need an even higher macroscopic stress to initiate yield in the next grain if first one is small

Question 7

Hall-Petch equation

Answer 7

σY=σ0+ksuby/d^x
Where σ0 is intrinsic strength of the crystal
k sub y is a constant
d is the grain diameter
x is the exponent which is constant for a given material (often 2)
Means smaller grain give higher strength

Question 8

What can elemental additions do in relation to the main element’s crystal structure?

Answer 8

Dissolve within its crystal structure (solid solution)

Precipitate out as a separate crystal (solid solution of the main element and another phase)

Question 9

Why do elemental additions lead to strengthening effects?

Answer 9

Depending on relative size difference between different atoms found in solid solution distortions will be observed in the crystal lattice. These distortions give rise to stress fields in the crystal. These lead to strengthening effects as the distorted lattice will affect/inhibit dislocation motion

Question 10

Two types of solutes

Answer 10

Substitutional or interstitial

Question 11

Relative sizes of substitutional and interstitial solutes

Answer 11

Substitutional substitute onto an existing lattice point and the atoms are usually a similar size to the base element.
Interstitial often significantly smaller than substitutional and instead occupy gaps between lattice points

Question 12

How does strength vary concentration of element in the alloy?

Answer 12

σY proportional to KC^1/2
Where K is constant
C is concentration of the element in the alloy

Question 13

Effect of size of substitutional solute atoms

Answer 13

If solute atom smaller than atoms of crystal it resides in it produces spherically symmetric tensile stress field. If larger it introduces a spherically symmetric compressive stress field. Larger atoms position themselves in tensile field of dislocation. Smaller atoms found in the compressive field of dislocation. In practice dislocations faster than solute atoms so dislocation moves relative to solute atoms and spends more time in these energetically favourable configurations, further strengthening

Question 14

Why do interstitial solute atoms have a greater effect compared to substitutional?

Answer 14

Larger strains being generated (atoms still much larger than spaces they occupy). Strains may be asymmetrical (can generate shear stresses as well). Usually interstitials very small so high diffusivities and can diffuse to tensile field of dislocations

Question 15

Cottrell atmosphere

Answer 15

The accumulation of interstitial atoms at dislocations. Very common in steels with C atoms

Question 16

Stress vs strain graph for carbon steels

Answer 16

Linear up to upper yield stress. Then comes down a bit to horizontal with bumps. Then, at lower yield stress, curve up with decreasing gradient.

Question 17

Explain stress vs strain graph for carbon steels

Answer 17

When material reaches upper yield stress, dislocations escape Cottrell atmospheres. Sharp drop in stress as stress required to move the dislocations lower since they are unlocked. Stress concentration at ends of sample initiate yielding in these sections. As localised yielding occurs, samples work harden leading to wavy morphology observed as local yield strength increases. When sample fully covered by Luders bands (lower yield stress) bulk deformation can continue

Question 18

Effect of temperature on stress vs strain graph for materials with large fraction of interstitial solutes

Answer 18

Graph moves down and right

Question 19

How does temperature affect the solute atoms? (Portevin-Le Chatelier)

Answer 19

At high enough T the C atoms sufficiently mobile to move with dislocations so don’t inhibit their motion. At intermediate T interstitial atoms and dislocations move with similar speeds. Dislocations repeatedly escape Cottrell atmospheres (reducing strength) but interstitials quickly diffuse and catch up to reform Cottrell atmospheres (increase strength) which is serrated yielding