Respuesta :
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:
[tex]\sigma_{y}=\sigma_{i}+k d^{-1 / 2}[/tex]
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, [tex]S_{v}[/tex] is grain boundary area per unit volume, [tex]N_{L}[/tex] is mean number of intercepts of grain boundaries per unit length of test line, [tex]N_{A}[/tex] is number of grains per unit area on a polished surface:
[tex]S_{v}=2 N_{L} \quad d=\frac{3}{S_{v}}=\frac{3}{2 N_{L}} \quad d=\sqrt{\frac{6}{\pi V_{A}}}[/tex]
- 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:
[tex]D=\frac{1}{100} \sqrt{\frac{645}{2^{6-1}}}[/tex]
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
