Enter the materials constant for starting stress dislocation movement (MPa), the strengthening coefficient (MPa-m^1/2), and the average grain diameter (m) into the Hall-Petch Calculator. The calculator will evaluate the yield stress. 

Hall-Petch Formula

The following formula is used to calculate the Hall-Petch. 

YS = MC + K / SQRT(d)

Variables:

  • YS is the yield stress (MPa)
  • MC is the materials constant for starting stress dislocation movement (MPa) 
  • K is the strengthening coefficient (MPa-m^1/2) 
  • d is the average grain diameter (m) 

How to Calculate Yield Stress From Hall-Petch Equation?

The following steps outline how to calculate the yield stress using the Hall-Petch equation.


  1. First, determine the materials constant for starting stress dislocation movement (MPa).
  2. Next, determine the strengthening coefficient (MPa-m^1/2). 
  3. Next, determine the average grain diameter (m). 
  4. Next, gather the formula from above = YS = MC + K / SQRT(d).
  5. Finally, calculate the yield stress.
  6. After inserting the variables and calculating the result, check your answer with the calculator above. 

Example Problem:

Use the following variables as an example problem to test your knowledge.

materials constant for starting stress dislocation movement (MPa) = 25

strengthening coefficient (MPa-m^1/2) = .40

average grain diameter (m) = .75

YS = MC + K / SQRT(d) =  ?