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Critical stress for crack propagation Calculator

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✖Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.ⓘ Young's Modulus [E]			+10% -10%
✖Specific surface energy is the surface energy needed for creation of new surface during crack propagation in a brittle material.ⓘ Specific surface energy [γ_s]			+10% -10%
✖Crack length represents the length of a surface crack, or half of the length of an internal crack.ⓘ Crack Length [a]			+10% -10%

✖Critical stress required for crack propagation in a brittle material.ⓘ Critical stress for crack propagation [σ_c]

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Critical stress for crack propagation Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical stress = sqrt(2*Young's Modulus*Specific surface energy/(pi*Crack Length))
σ_c = sqrt(2*E*γ_s/(pi*a))
This formula uses 1 Constants, 1 Functions, 4 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

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

Critical stress - (Measured in Pascal) - Critical stress required for crack propagation in a brittle material.
Young's Modulus - (Measured in Newton per Meter) - Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.
Specific surface energy - (Measured in Newton per Meter) - Specific surface energy is the surface energy needed for creation of new surface during crack propagation in a brittle material.
Crack Length - (Measured in Meter) - Crack length represents the length of a surface crack, or half of the length of an internal crack.

STEP 1: Convert Input(s) to Base Unit

Young's Modulus: 15 Newton per Meter --> 15 Newton per Meter No Conversion Required
Specific surface energy: 0.3 Newton per Meter --> 0.3 Newton per Meter No Conversion Required
Crack Length: 10 Micrometer --> 1E-05 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_c = sqrt(2*E*γ_s/(pi*a)) --> sqrt(2*15*0.3/(pi*1E-05))

Evaluating ... ...

σ_c = 535.237234845831

STEP 3: Convert Result to Output's Unit

535.237234845831 Pascal -->0.000535237234845831 Megapascal (Check conversion here)

FINAL ANSWER

0.000535237234845831 ≈ 0.000535 Megapascal <-- Critical stress

(Calculation completed in 00.020 seconds)

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< Failure Testing in Materials Calculators

Critical stress for crack propagation

LaTeX Go Critical stress = sqrt(2*Young's Modulus*Specific surface energy/(pi*Crack Length))

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Percent reduction in area

LaTeX Go Percent reduction in area = (Cross-sectional Area-Fracture area)*100/Cross-sectional Area

Percent elongation

LaTeX Go Percent elongation = (Fracture Length-Original Length)*100/Original Length

Critical stress for crack propagation Formula

LaTeX Go

Critical stress = sqrt(2*Young's Modulus*Specific surface energy/(pi*Crack Length))
σ_c = sqrt(2*E*γ_s/(pi*a))

Cracks in brittle materials

All brittle materials contain a population of small cracks that have a range of sizes, geometries, and orientations. When the magnitude of a tensile stress at the tip of one of these flaws exceeds the value of this critical stress, a crack forms and then propagates, which results in fracture.

How to Calculate Critical stress for crack propagation?

Critical stress for crack propagation calculator uses Critical stress = sqrt(2*Young's Modulus*Specific surface energy/(pi*Crack Length)) to calculate the Critical stress, Critical stress for crack propagation is the minimum stress required for propagation of crack in a brittle material. Critical stress is denoted by σ_c symbol.

How to calculate Critical stress for crack propagation using this online calculator? To use this online calculator for Critical stress for crack propagation, enter Young's Modulus (E), Specific surface energy (γ_s) & Crack Length (a) and hit the calculate button. Here is how the Critical stress for crack propagation calculation can be explained with given input values -> 5.4E-10 = sqrt(2*15*0.3/(pi*1E-05)).

FAQ

What is Critical stress for crack propagation?

Critical stress for crack propagation is the minimum stress required for propagation of crack in a brittle material and is represented as σ_c = sqrt(2*E*γ_s/(pi*a)) or Critical stress = sqrt(2*Young's Modulus*Specific surface energy/(pi*Crack Length)). Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain, Specific surface energy is the surface energy needed for creation of new surface during crack propagation in a brittle material & Crack length represents the length of a surface crack, or half of the length of an internal crack.

How to calculate Critical stress for crack propagation?

Critical stress for crack propagation is the minimum stress required for propagation of crack in a brittle material is calculated using Critical stress = sqrt(2*Young's Modulus*Specific surface energy/(pi*Crack Length)). To calculate Critical stress for crack propagation, you need Young's Modulus (E), Specific surface energy (γ_s) & Crack Length (a). With our tool, you need to enter the respective value for Young's Modulus, Specific surface energy & Crack Length 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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