Hall - Petch Relation Calculator

✖Constant in Hall Petch relation which has the dimensions that of stress.ⓘ Constant in Hall Petch relation [𝛔₀]			+10% -10%
✖Coefficient in Hall Petch relation that is multiplie with the grain size. The units correspond to MPa/sqrt(mm).ⓘ Coefficient in Hall Petch relation [K]			+10% -10%
✖Grain size (in mm)is the average size of grains in metal/alloy.ⓘ Grain size (in mm) [d]			+10% -10%

✖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.ⓘ Hall - Petch Relation [σ_y]

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Formula

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Hall - Petch Relation

Formula

`"σ"_{"y"} = "𝛔"_{"0"}+("K"/sqrt("d"))`

Example

`"53.95285N/mm²"="50MPa"+("2.5MPa*sqrt(mm)"/sqrt("0.4mm"))`

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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)))
σ_y = 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

σ_y = 𝛔₀+(K/sqrt(d)) --> 50000000+(79056.9415042095/sqrt(0.0004))

Evaluating ... ...

σ_y = 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 00.004 seconds)

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< 2 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)))
σ_y = 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 σ_y 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 σ_y = 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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