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))
σc = sqrt(2*E*γs/(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
σc = sqrt(2*E*γs/(pi*a)) --> sqrt(2*15*0.3/(pi*1E-05))
Evaluating ... ...
σc = 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 00.004 seconds)

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Failure Testing in Materials Calculators

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-Original Length)*100/Original Length

Critical stress for crack propagation Formula

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