Hall - Petch Relation Solution

STEP 0: Pre-Calculation Summary
Formula Used
Yield Strength = Constant in Hall Petch relation+(Coefficient in Hall Petch relation/sqrt(Grain size (in mm)))
σy = 𝛔0+(K/sqrt(d))
This formula uses 1 Functions, 4 Variables
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Yield Strength - (Measured in Pascal) - Yield strength can be defined as follows, a straight line is constructed parallel to elastic portion of stress–strain curve at strain offset of 0.002.
Constant in Hall Petch relation - (Measured in Pascal) - Constant in Hall Petch relation which has the dimensions that of stress.
Coefficient in Hall Petch relation - (Measured in Pascal Sqrt(meter)) - Coefficient in Hall Petch relation that is multiplie with the grain size. The units correspond to MPa/sqrt(mm).
Grain size (in mm) - (Measured in Meter) - Grain size (in mm)is the average size of grains in metal/alloy.
STEP 1: Convert Input(s) to Base Unit
Constant in Hall Petch relation: 50 Megapascal --> 50000000 Pascal (Check conversion ​here)
Coefficient in Hall Petch relation: 2.5 Megapascal Sqrt(millimeter) --> 79056.9415042095 Pascal Sqrt(meter) (Check conversion ​here)
Grain size (in mm): 0.4 Millimeter --> 0.0004 Meter (Check conversion ​here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σy = 𝛔0+(K/sqrt(d)) --> 50000000+(79056.9415042095/sqrt(0.0004))
Evaluating ... ...
σy = 53952847.0752105
STEP 3: Convert Result to Output's Unit
53952847.0752105 Pascal -->53.9528470752105 Newton per Square Millimeter (Check conversion ​here)
FINAL ANSWER
53.9528470752105 53.95285 Newton per Square Millimeter <-- Yield Strength
(Calculation completed in 00.020 seconds)

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Grain Size Calculators

Hall - Petch Relation
​ Go Yield Strength = Constant in Hall Petch relation+(Coefficient in Hall Petch relation/sqrt(Grain size (in mm)))
ASTM grain size number to Number of grains
​ Go Number of grains at M X = (2^(ASTM grain size number-1))*(100/Magnification)^2

Hall - Petch Relation Formula

Yield Strength = Constant in Hall Petch relation+(Coefficient in Hall Petch relation/sqrt(Grain size (in mm)))
σy = 𝛔0+(K/sqrt(d))

What is Hall - Petch relation?

The Hall–Petch relationship tells us that we could achieve strength in materials that is as high as their own theoretical strength by reducing grain size. Indeed, their strength continues to increase with decreasing grain size to approximately 20–30 nm where the strength peaks. Finer grain sizes also increase toughness, which is an uncommon coincidence since strength and toughness are normally inversely related as mentioned earlier.

How to Calculate Hall - Petch Relation?

Hall - Petch Relation calculator uses Yield Strength = Constant in Hall Petch relation+(Coefficient in Hall Petch relation/sqrt(Grain size (in mm))) to calculate the Yield Strength, The Hall - Petch relation tells us that we could achieve strength in materials that is as high as their own theoretical strength by reducing grain size. Yield Strength is denoted by σy symbol.

How to calculate Hall - Petch Relation using this online calculator? To use this online calculator for Hall - Petch Relation, enter Constant in Hall Petch relation (𝛔0), Coefficient in Hall Petch relation (K) & Grain size (in mm) (d) and hit the calculate button. Here is how the Hall - Petch Relation calculation can be explained with given input values -> 5.4E-5 = 50000000+(79056.9415042095/sqrt(0.0004)).

FAQ

What is Hall - Petch Relation?
The Hall - Petch relation tells us that we could achieve strength in materials that is as high as their own theoretical strength by reducing grain size and is represented as σy = 𝛔0+(K/sqrt(d)) or Yield Strength = Constant in Hall Petch relation+(Coefficient in Hall Petch relation/sqrt(Grain size (in mm))). Constant in Hall Petch relation which has the dimensions that of stress, Coefficient in Hall Petch relation that is multiplie with the grain size. The units correspond to MPa/sqrt(mm) & Grain size (in mm)is the average size of grains in metal/alloy.
How to calculate Hall - Petch Relation?
The Hall - Petch relation tells us that we could achieve strength in materials that is as high as their own theoretical strength by reducing grain size is calculated using Yield Strength = Constant in Hall Petch relation+(Coefficient in Hall Petch relation/sqrt(Grain size (in mm))). To calculate Hall - Petch Relation, you need Constant in Hall Petch relation (𝛔0), Coefficient in Hall Petch relation (K) & Grain size (in mm) (d). With our tool, you need to enter the respective value for Constant in Hall Petch relation, Coefficient in Hall Petch relation & Grain size (in mm) and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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