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Critical stress for crack propagation Formula

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Critical stress required for crack propagation in a brittle material. Check FAQs

σ c = \sqrt{2 \cdot E \cdot \frac{γ s}{π \cdot a}}

σ_c - Critical stress?E - Young's Modulus?γ_s - Specific surface energy?a - Crack Length?π - Archimedes' constant?

Critical stress for crack propagation Example

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Here is how the Critical stress for crack propagation equation looks like with Values.

Here is how the Critical stress for crack propagation equation looks like with Units.

Here is how the Critical stress for crack propagation equation looks like.

0.0005 = \sqrt{2 \cdot 15 \cdot \frac{0.3}{3.1416 \cdot 10}}

0.0005MPa = \sqrt{2 \cdot 15N/m \cdot \frac{0.3N/m}{3.1416 \cdot 10μm}}

0.0005 = \sqrt{2 \cdot 15 \cdot \frac{0.3}{3.1416 \cdot 10}}

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Critical stress for crack propagation Solution

Follow our step by step solution on how to calculate Critical stress for crack propagation?

FIRST Step Consider the formula

σ c = \sqrt{2 \cdot E \cdot \frac{γ s}{π \cdot a}}

Next Step Substitute values of Variables

∴

σ c = \sqrt{2 \cdot 15N/m \cdot \frac{0.3N/m}{π \cdot 10μm}}

Next Step Substitute values of Constants

∴

σ c = \sqrt{2 \cdot 15N/m \cdot \frac{0.3N/m}{3.1416 \cdot 10μm}}

Next Step Convert Units

∴

σ c = \sqrt{2 \cdot 15N/m \cdot \frac{0.3N/m}{3.1416 \cdot 1E-5m}}

Next Step Prepare to Evaluate

∴

σ c = \sqrt{2 \cdot 15 \cdot \frac{0.3}{3.1416 \cdot 1E-5}}

Next Step Evaluate

∴

σ c = 535.237234845831Pa

Next Step Convert to Output's Unit

∴

σ c = 0.000535237234845831MPa

LAST Step Rounding Answer

∴

σ c = 0.0005MPa

Critical stress for crack propagation Formula Elements

Variables

Constants

Functions

Critical stress

Critical stress required for crack propagation in a brittle material.

Symbol: σ_c

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Critical stress

Young's Modulus

Young's Modulus is a mechanical property of linear elastic solid substances. It describes the relationship between longitudinal stress and longitudinal strain.

Symbol: E

Measurement: Stiffness ConstantUnit: N/m

Note: Value should be greater than 0.

Formulas to find Young's Modulus

Specific surface energy

Specific surface energy is the surface energy needed for creation of new surface during crack propagation in a brittle material.

Symbol: γ_s

Measurement: Surface TensionUnit: N/m

Note: Value should be greater than 0.

Formulas to find Specific surface energy

Crack Length

Crack length represents the length of a surface crack, or half of the length of an internal crack.

Symbol: a

Measurement: LengthUnit: μm

Note: Value should be greater than 0.

Formulas to find Crack Length

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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)

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How to Evaluate Critical stress for crack propagation?

Critical stress for crack propagation evaluator uses Critical stress = sqrt(2*Young's Modulus*Specific surface energy/(pi*Crack Length)) to evaluate 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 evaluate Critical stress for crack propagation using this online evaluator? To use this online evaluator for Critical stress for crack propagation, enter Young's Modulus (E), Specific surface energy (γ_s) & Crack Length (a) and hit the calculate button.

FAQs on Critical stress for crack propagation

What is the formula to find Critical stress for crack propagation?

The formula of Critical stress for crack propagation is expressed as Critical stress = sqrt(2*Young's Modulus*Specific surface energy/(pi*Crack Length)). Here is an example- 5.4E-10 = sqrt(2*15*0.3/(pi*1E-05)).

How to calculate Critical stress for crack propagation?

With Young's Modulus (E), Specific surface energy (γ_s) & Crack Length (a) we can find Critical stress for crack propagation using the formula - Critical stress = sqrt(2*Young's Modulus*Specific surface energy/(pi*Crack Length)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

Can the Critical stress for crack propagation be negative?

No, the Critical stress for crack propagation, measured in Pressure cannot be negative.

Which unit is used to measure Critical stress for crack propagation?

Critical stress for crack propagation is usually measured using the Megapascal[MPa] for Pressure. Pascal[MPa], Kilopascal[MPa], Bar[MPa] are the few other units in which Critical stress for crack propagation can be measured.

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Critical stress for crack propagation Formula

Critical stress for crack propagation Example

Critical stress for crack propagation Solution

Critical stress for crack propagation Formula Elements

Other formulas in Failure Testing in Materials category

How to Evaluate Critical stress for crack propagation?

FAQs on Critical stress for crack propagation

Variable Name