Question

The equation which describes the relationship between grain size and the yield of polycrystalline metals is called as?

• A. Burgers’ equation
• B. Hall – Petch equation
• C. Boltzmann equation
• D. Braags’ equation

Hint:

The Hall-Petch equation explains that reducing grain size increases the yield strength of materials by increasing the number of grain boundaries that hinder dislocation movement.

Answer 1

The Correct Option is B

The Hall-Petch equation is widely used in materials science to describe the relationship between grain size and the yield strength of polycrystalline materials. It suggests that the yield strength of a metal increases as the grain size decreases. This is because smaller grains create more grain boundaries, which act as barriers to dislocation movement, thus enhancing the material's strength. The equation can be expressed as: \[ \sigma_y = \sigma_0 + k_y d^{-1/2} \] where:
- \( \sigma_y \) is the yield strength,
- \( \sigma_0 \) is a constant (intercept),
- \( k_y \) is a material constant,
- \( d \) is the average grain diameter.
The Hall-Petch equation is a key concept in understanding how the microstructure of materials influences their mechanical properties. It highlights the importance of grain refinement in improving the strength of polycrystalline metals.
Hence, the correct answer is: Hall – Petch equation.