Question

Describe in your own words the three strengthening mechanisms discussed in this chapter (i.e., grain size reduction, solid-solution strengthening and strain hardening). Be sure to explain how dislocations are involved in each of the strengthening techniques.

Answer 1

Step-by-step explanation:

Strengthening by grain size reduction

• It is based on the fact that dislocations will experience hindrances while trying to move from a grain into the next because of abrupt change in orientation of planes.

• Hindrances can be two types: forcible change of slip direction, and discontinuous slip plane.
• Smaller the grain size, often a dislocation encounters a hindrance. Yield strength of material will be increased.
• Yield strength is related to grain size (diameter, d ) as Hall Petch relation:

`\sigma_(y)=\sigma_(i)+k d^(-1 / 2)`

Strengthening by Grain size reduction (contd..)

• Grain size reduction improves not only strength, but also the toughness of many alloys.
• If d is average grain diameter,
  `S_(v)` is grain boundary area per unit volume,
  `N_(L)` is mean number of intercepts of grain boundaries per unit length of test line,
  `N_(A)` is number of grains per unit area on a polished surface:

`S_(v)=2 N_(L) \quad d=(3)/(S_(v))=(3)/(2 N_(L)) \quad d=\sqrt{(6)/(\pi V_(A))}`

• Grain size can also be measured by comparing the grains at a fixed magnification with standard grain size charts.

• Other method: Use of ASTM grain size number (Z). It is related to grain diameter, (in mm) as follows:

`D=(1)/(100) \sqrt{(645)/(2^(6-1))}`

Solid solution strengthening

• Impure foreign atoms in a single phase material produces lattice strains which can anchor the dislocations.

• Effectiveness of this strengthening depends on two factors size difference and volume fraction of solute. Solute atoms interact with dislocations in many ways:

- elastic interaction

- modulus interaction

- stacking-fault interaction

- electrical interaction

- short-range order interaction

- long-range order interaction