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Fracture toughness Formula

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Fracture Toughness is the critical stress intensity factor of a sharp crack where propagation of the crack suddenly becomes rapid and unlimited. Check FAQs

K I = Y \cdot σ \cdot \sqrt{π \cdot a}

K_I - Fracture Toughness?Y - Dimensionless Parameter in Fracture Toughness?σ - Applied stress?a - Crack Length?π - Archimedes' constant?

Fracture toughness Example

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Here is how the Fracture toughness equation looks like with Values.

Here is how the Fracture toughness equation looks like with Units.

Here is how the Fracture toughness equation looks like.

5.8E-7 = 1.1 \cdot 93.3 \cdot \sqrt{3.1416 \cdot 10}

5.8E-7MPa*sqrt(m) = 1.1 \cdot 93.3Pa \cdot \sqrt{3.1416 \cdot 10μm}

5.8E-7 = 1.1 \cdot 93.3 \cdot \sqrt{3.1416 \cdot 10}

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Fracture toughness Solution

Follow our step by step solution on how to calculate Fracture toughness?

FIRST Step Consider the formula

K I = Y \cdot σ \cdot \sqrt{π \cdot a}

Next Step Substitute values of Variables

∴

K I = 1.1 \cdot 93.3Pa \cdot \sqrt{π \cdot 10μm}

Next Step Substitute values of Constants

∴

K I = 1.1 \cdot 93.3Pa \cdot \sqrt{3.1416 \cdot 10μm}

Next Step Convert Units

∴

K I = 1.1 \cdot 93.3Pa \cdot \sqrt{3.1416 \cdot 1E-5m}

Next Step Prepare to Evaluate

∴

K I = 1.1 \cdot 93.3 \cdot \sqrt{3.1416 \cdot 1E-5}

Next Step Evaluate

∴

K I = 0.57524024853892Pa*sqrt(m)

Next Step Convert to Output's Unit

∴

K I = 5.7524024853892E-07MPa*sqrt(m)

LAST Step Rounding Answer

∴

K I = 5.8E-7MPa*sqrt(m)

Fracture toughness Formula Elements

Variables

Constants

Functions

Fracture Toughness

Fracture Toughness is the critical stress intensity factor of a sharp crack where propagation of the crack suddenly becomes rapid and unlimited.

Symbol: K_I

Measurement: Fracture ToughnessUnit: MPa*sqrt(m)

Note: Value should be greater than 0.

Formulas to find Fracture Toughness

Dimensionless Parameter in Fracture Toughness

Dimensionless parameter in fracture toughness expression depends on both crack and specimen sizes and geometries, as well as the manner of load application.

Symbol: Y

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Dimensionless Parameter in Fracture Toughness

Applied stress

Applied stress is denoted by the symbol σ.

Symbol: σ

Measurement: PressureUnit: Pa

Note: Value should be greater than 0.

Formulas to find Applied stress

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 Fracture toughness?

Fracture toughness evaluator uses Fracture Toughness = Dimensionless Parameter in Fracture Toughness*Applied stress*sqrt(pi*Crack Length) to evaluate the Fracture Toughness, Fracture toughness is a property that is a measure of a material’s resistance to brittle fracture when a crack is present. Fracture Toughness is denoted by K_I symbol.

How to evaluate Fracture toughness using this online evaluator? To use this online evaluator for Fracture toughness, enter Dimensionless Parameter in Fracture Toughness (Y), Applied stress (σ) & Crack Length (a) and hit the calculate button.

FAQs on Fracture toughness

What is the formula to find Fracture toughness?

The formula of Fracture toughness is expressed as Fracture Toughness = Dimensionless Parameter in Fracture Toughness*Applied stress*sqrt(pi*Crack Length). Here is an example- 5.8E-13 = 1.1*93.3*sqrt(pi*1E-05).

How to calculate Fracture toughness?

With Dimensionless Parameter in Fracture Toughness (Y), Applied stress (σ) & Crack Length (a) we can find Fracture toughness using the formula - Fracture Toughness = Dimensionless Parameter in Fracture Toughness*Applied stress*sqrt(pi*Crack Length). This formula also uses Archimedes' constant and Square Root Function function(s).

Can the Fracture toughness be negative?

No, the Fracture toughness, measured in Fracture Toughness cannot be negative.

Which unit is used to measure Fracture toughness?

Fracture toughness is usually measured using the Megapascal sqrt(meter)[MPa*sqrt(m)] for Fracture Toughness. Pascal sqrt(meter)[MPa*sqrt(m)] are the few other units in which Fracture toughness can be measured.

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Fracture toughness Formula

Fracture toughness Example

Fracture toughness Solution

Fracture toughness Formula Elements

Other formulas in Failure Testing in Materials category

How to Evaluate Fracture toughness?

FAQs on Fracture toughness

Variable Name