HallPetch Equation Calculator

Introduction

The Hall-Petch equation is used to describe the relationship between the yield strength of a material and its grain size. It states that the yield strength increases as the grain size decreases, due to the increased number of grain boundaries which act as obstacles to dislocation movement.

How to Use the Calculator

1. Enter the yield strength at infinite grain size (σ₀) in MPa.
2. Enter the grain size (d) in micrometers (µm).
3. Enter the yield strength constant (k) in MPa·µm^1/2.
4. Click the "Calculate" button to compute the yield strength at the given grain size.
5. Click the "Reset" button to clear all input fields and start over.

Formula Explanation

The Hall-Petch equation is given by:

σ = σ₀ + k * d^-1/2

Where:

• σ = Yield Strength at given grain size (MPa)
• σ₀ = Yield Strength at infinite grain size (MPa)
• k = Yield Strength Constant (MPa·µm^1/2)
• d = Grain Size (µm)

Applications

This calculator is useful for materials scientists and engineers who need to predict the yield strength of materials based on their grain size. It can help in optimizing material properties for various applications.