Hall - Petch Relation Formula

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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. Check FAQs
σy=𝛔0+(Kd)
σy - Yield Strength?𝛔0 - Constant in Hall Petch relation?K - Coefficient in Hall Petch relation?d - Grain size (in mm)?

Hall - Petch Relation Example

With values
With units
Only example

Here is how the Hall - Petch Relation equation looks like with Values.

Here is how the Hall - Petch Relation equation looks like with Units.

Here is how the Hall - Petch Relation equation looks like.

53.9528Edit=50Edit+(2.5Edit0.4Edit)
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Hall - Petch Relation Solution

Follow our step by step solution on how to calculate Hall - Petch Relation?

FIRST Step Consider the formula
σy=𝛔0+(Kd)
Next Step Substitute values of Variables
σy=50MPa+(2.5MPa*sqrt(mm)0.4mm)
Next Step Convert Units
σy=5E+7Pa+(79056.9415Pa*sqrt(m)0.0004m)
Next Step Prepare to Evaluate
σy=5E+7+(79056.94150.0004)
Next Step Evaluate
σy=53952847.0752105Pa
Next Step Convert to Output's Unit
σy=53.9528470752105N/mm²
LAST Step Rounding Answer
σy=53.9528N/mm²

Hall - Petch Relation Formula Elements

Variables
Functions
Yield Strength
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.
Symbol: σy
Measurement: PressureUnit: N/mm²
Note: Value should be greater than 0.
Constant in Hall Petch relation
Constant in Hall Petch relation which has the dimensions that of stress.
Symbol: 𝛔0
Measurement: PressureUnit: MPa
Note: Value can be positive or negative.
Coefficient in Hall Petch relation
Coefficient in Hall Petch relation that is multiplie with the grain size. The units correspond to MPa/sqrt(mm).
Symbol: K
Measurement: Hall-Petch CoefficientUnit: MPa*sqrt(mm)
Note: Value can be positive or negative.
Grain size (in mm)
Grain size (in mm)is the average size of grains in metal/alloy.
Symbol: d
Measurement: LengthUnit: mm
Note: Value should be greater than 0.
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.
Syntax: sqrt(Number)

Other formulas in Grain Size category

​Go ASTM grain size number to Number of grains
NM=(2n-1)(100m)2

How to Evaluate Hall - Petch Relation?

Hall - Petch Relation evaluator uses Yield Strength = Constant in Hall Petch relation+(Coefficient in Hall Petch relation/sqrt(Grain size (in mm))) to evaluate 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 evaluate Hall - Petch Relation using this online evaluator? To use this online evaluator 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.

FAQs on Hall - Petch Relation

What is the formula to find Hall - Petch Relation?
The formula of Hall - Petch Relation is expressed as Yield Strength = Constant in Hall Petch relation+(Coefficient in Hall Petch relation/sqrt(Grain size (in mm))). Here is an example- 5.4E-5 = 50000000+(79056.9415042095/sqrt(0.0004)).
How to calculate Hall - Petch Relation?
With Constant in Hall Petch relation (𝛔0), Coefficient in Hall Petch relation (K) & Grain size (in mm) (d) we can find Hall - Petch Relation using the formula - Yield Strength = Constant in Hall Petch relation+(Coefficient in Hall Petch relation/sqrt(Grain size (in mm))). This formula also uses Square Root (sqrt) function(s).
Can the Hall - Petch Relation be negative?
No, the Hall - Petch Relation, measured in Pressure cannot be negative.
Which unit is used to measure Hall - Petch Relation?
Hall - Petch Relation is usually measured using the Newton per Square Millimeter[N/mm²] for Pressure. Pascal[N/mm²], Kilopascal[N/mm²], Bar[N/mm²] are the few other units in which Hall - Petch Relation can be measured.
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