Fracture toughness Calculator

✖Dimensionless parameter in fracture toughness expression depends on both crack and specimen sizes and geometries, as well as the manner of load application.ⓘ Dimensionless Parameter in Fracture Toughness [Y]			+10% -10%
✖Applied stress is denoted by the symbol σ.ⓘ Applied stress [σ]			+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%

✖Fracture Toughness is the critical stress intensity factor of a sharp crack where propagation of the crack suddenly becomes rapid and unlimited.ⓘ Fracture toughness [K_I]

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Formula

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Fracture toughness

Formula

`"K"_{"I"} = "Y"*"σ"*sqrt(pi*"a")`

Example

`"5.8E^-7MPa*sqrt(m)"="1.1"*"93.3Pa"*sqrt(pi*"10μm")`

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Fracture toughness Solution

STEP 0: Pre-Calculation Summary

Formula Used

Fracture Toughness = Dimensionless Parameter in Fracture Toughness*Applied stress*sqrt(pi*Crack Length)
K_I = Y*σ*sqrt(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

Fracture Toughness - (Measured in Pascal sqrt(meter)) - Fracture Toughness is the critical stress intensity factor of a sharp crack where propagation of the crack suddenly becomes rapid and unlimited.
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.
Applied stress - (Measured in Pascal) - Applied stress is denoted by the symbol σ.
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

Dimensionless Parameter in Fracture Toughness: 1.1 --> No Conversion Required
Applied stress: 93.3 Pascal --> 93.3 Pascal No Conversion Required
Crack Length: 10 Micrometer --> 1E-05 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

K_I = Y*σ*sqrt(pi*a) --> 1.1*93.3*sqrt(pi*1E-05)

Evaluating ... ...

K_I = 0.57524024853892

STEP 3: Convert Result to Output's Unit

0.57524024853892 Pascal sqrt(meter) -->5.7524024853892E-07 Megapascal sqrt(meter) (Check conversion here)

FINAL ANSWER

5.7524024853892E-07 ≈ 5.8E-7 Megapascal sqrt(meter) <-- Fracture Toughness

(Calculation completed in 00.004 seconds)

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Created by Hariharan V S

Indian Institute of Technology (IIT), Chennai

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< 12 Failure Testing in Materials Calculators

Fracture toughness

Go Fracture Toughness = Dimensionless Parameter in Fracture Toughness*Applied stress*sqrt(pi*Crack Length)

Critical stress for crack propagation

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

Percent cold work

Go Percent cold work = 100*(Cross-sectional Area-Area after deformation)/Cross-sectional Area

Percent reduction in area

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

Percent elongation

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

Stress concentration factor

Go Stress Concentration Factor = 2*sqrt(Crack Length/Radius of curvature)

Mean stress of stress cycle (fatigue)

Go Mean Stress of Stress Cycle = (Maximum Tensile Stress+Minimum compressive stress)/2

Maximum stress at crack tip

Go Maximum Stress at Crack Tip = Stress Concentration Factor*Applied stress

Range of stress (fatigue)

Go Range of stress = Maximum Tensile Stress-Minimum compressive stress

Stress ratio (fatigue)

Go Stress ratio = Minimum compressive stress/Maximum Tensile Stress

Modulus of resilience

Go Modulus of Resilience = Yield Strength^2/(2*Young's Modulus)

Stress amplitude (fatigue)

Go Stress Amplitude = Range of stress/2

Fracture toughness Formula

Fracture Toughness = Dimensionless Parameter in Fracture Toughness*Applied stress*sqrt(pi*Crack Length)
K_I = Y*σ*sqrt(pi*a)

Fracture toughness for brittle and ductile materials

Brittle materials, for which appreciable plastic deformation is not possible in front of an advancing crack, have low values and are vulnerable to catastrophic failure. On the other hand, values are relatively large for ductile materials and can undergo deformation before failure.

How to Calculate Fracture toughness?

Fracture toughness calculator uses Fracture Toughness = Dimensionless Parameter in Fracture Toughness*Applied stress*sqrt(pi*Crack Length) to calculate 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 calculate Fracture toughness using this online calculator? To use this online calculator for Fracture toughness, enter Dimensionless Parameter in Fracture Toughness (Y), Applied stress (σ) & Crack Length (a) and hit the calculate button. Here is how the Fracture toughness calculation can be explained with given input values -> 5.8E-13 = 1.1*93.3*sqrt(pi*1E-05).

FAQ

What is Fracture toughness?

Fracture toughness is a property that is a measure of a material’s resistance to brittle fracture when a crack is present and is represented as K_I = Y*σ*sqrt(pi*a) or Fracture Toughness = Dimensionless Parameter in Fracture Toughness*Applied stress*sqrt(pi*Crack Length). Dimensionless parameter in fracture toughness expression depends on both crack and specimen sizes and geometries, as well as the manner of load application, Applied stress is denoted by the symbol σ & Crack length represents the length of a surface crack, or half of the length of an internal crack.

How to calculate Fracture toughness?

Fracture toughness is a property that is a measure of a material’s resistance to brittle fracture when a crack is present is calculated using Fracture Toughness = Dimensionless Parameter in Fracture Toughness*Applied stress*sqrt(pi*Crack Length). To calculate Fracture toughness, you need Dimensionless Parameter in Fracture Toughness (Y), Applied stress (σ) & Crack Length (a). With our tool, you need to enter the respective value for Dimensionless Parameter in Fracture Toughness, Applied stress & 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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