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

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:

                $S_{v}=2 N_{L} \quad d=\frac{3}{S_{v}}=\frac{3}{2 N_{L}} \quad d=\sqrt{\frac{6}{\pi V_{A}}}$

• 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:

                 $D=\frac{1}{100} \sqrt{\frac{645}{2^{6-1}}}$

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