Chapter 4, Problem 4.50P

Interpretation Introduction

(a)

Interpretation:

The constants in the Hall-Petch equation should be determined.

Concept Introduction:

Hall-petch equation is:

  ${\sigma }_y={\sigma }_0+K{d}^{-1/2}\mathrm{............}\left(1\right)$

The expression of Hall-Pitch equation relating yield strength $\left({\sigma }_y\right)$ is:

  ${\sigma }_y={\sigma }_0+K{d}^{-1/2}\mathrm{............}\left(1\right)$

Here, $d$ is average diameter of grains and ${\sigma }_0$ and $K$ are constants for the metal.

Interpretation Introduction

(b)

Interpretation:

The strength of the titanium should be determined.

Concept Introduction:

Hall-petch equation is:

  ${\sigma }_y={\sigma }_0+K{d}^{-1/2}\mathrm{............}\left(1\right)$

The expression of Hall-Pitch equation relating yield strength $\left({\sigma }_y\right)$ is:

  ${\sigma }_y={\sigma }_0+K{d}^{-1/2}\mathrm{............}\left(1\right)$

Here, $d$ is average diameter of grains and ${\sigma }_0$ and $K$ are constants for the metal.