Critical Fiber Length Solution

STEP 0: Pre-Calculation Summary
Formula Used
Critical Fiber Length = Tensile Strength of Fiber*Fiber Diameter/(2*Critical Shear Stress)
lc = ฯƒf*d/(2*ฯ„c)
This formula uses 4 Variables
Variables Used
Critical Fiber Length - (Measured in Meter) - Critical fiber length that is necessary for effective strengthening and stiffening of the composite material.
Tensile Strength of Fiber - (Measured in Pascal) - Tensile Strength of Fiber in the fiber-reinforced composite.
Fiber Diameter - (Measured in Meter) - Fiber Diameter in the fiber-reinforced composites.
Critical Shear Stress - (Measured in Pascal) - Critical shear stress is either the fiber-matrix bond strength or the shear yield stress of matrix, whichever is lower.
STEP 1: Convert Input(s) to Base Unit
Tensile Strength of Fiber: 6.375 Megapascal --> 6375000 Pascal (Check conversion here)
Fiber Diameter: 10 Millimeter --> 0.01 Meter (Check conversion here)
Critical Shear Stress: 3.01 Megapascal --> 3010000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
lc = ฯƒf*d/(2*ฯ„c) --> 6375000*0.01/(2*3010000)
Evaluating ... ...
lc = 0.0105897009966777
STEP 3: Convert Result to Output's Unit
0.0105897009966777 Meter -->10.5897009966777 Millimeter (Check conversion here)
FINAL ANSWER
10.5897009966777 โ‰ˆ 10.5897 Millimeter <-- Critical Fiber Length
(Calculation completed in 00.004 seconds)

Credits

Created by Hariharan V S
Indian Institute of Technology (IIT), Chennai
Hariharan V S has created this Calculator and 25+ more calculators!
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10+ Ceramics and Composites Calculators

Young's Modulus of composite in transverse direction
Go Young's modulus in transverse direction = (Young's modulus of matrix in composite*Young's modulus of fiber in composite)/(Volume Fraction of Fiber*Young's modulus of matrix in composite+(1-Volume Fraction of Fiber)*Young's modulus of fiber in composite)
Longitudinal strength of discontinuous fiber-reinforced composite
Go Longitudinal strength of composite(discontinous fiber) = Tensile Strength of Fiber*Volume Fraction of Fiber*(1-(Critical Fiber Length/(2*Fiber length)))+Stress in Matrix*(1-Volume Fraction of Fiber)
Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length)
Go Longitudinal strength of composite(discontinous fiber less than lc) = (Volume Fraction of Fiber*Fiber length*Critical Shear Stress/Fiber Diameter)+Stress in Matrix*(1-Volume Fraction of Fiber)
Young's Modulus of composite in longitudinal direction
Go Young's modulus of composite in longitudinal direction = Young's modulus of matrix in composite*(1-Volume Fraction of Fiber)+Young's modulus of fiber in composite*Volume Fraction of Fiber
Young's Modulus of porous material
Go Young's modulus of porous material = Young's modulus of non-porous material*(1-(0.019*Volume Percent of Porosity)+(0.00009*Volume Percent of Porosity*Volume Percent of Porosity))
Schottky Defect Concentration
Go Number of Schottky Defects = Number of atomic sites*exp(-Activation energy for Schottky formation/(2*Universal Gas Constant*Temperature))
Longitudinal Strength of Composite
Go Longitudinal Strength of Composite = Stress in Matrix*(1-Volume Fraction of Fiber)+Tensile Strength of Fiber*Volume Fraction of Fiber
Percent ionic character
Go Percent Ionic Character = 100*(1-exp(-0.25*(Electronegativity of element A-Electronegativity of element B)^2))
Critical Fiber Length
Go Critical Fiber Length = Tensile Strength of Fiber*Fiber Diameter/(2*Critical Shear Stress)
Young's Modulus from shear modulus
Go Young's Modulus = 2*Shear Modulus*(1+Poisson's Ratio)

12 Volume Fraction of Fiber Calculators

Volume Fraction of Matrix from EM of Composite (Transverse direction)
Go Volume Fraction of Matrix = Elastic Modulus of Matrix/Elastic Modulus Composite (Transverse Direction)-(Elastic Modulus of Matrix*Volume Fraction of Fiber)/Elastic Modulus of Fiber
Volume Fraction of Fiber from EM of Composite (Transverse Direction)
Go Volume Fraction of Fiber = Elastic Modulus of Fiber/Elastic Modulus Composite (Transverse Direction)-(Volume Fraction of Matrix*Elastic Modulus of Fiber)/Elastic Modulus of Matrix
Volume Fraction of Matrix from E of Composite (Longitudinal Direction)
Go Volume Fraction of Matrix = (Elastic Modulus Composite (Longitudinal Direction)-Elastic Modulus of Fiber*Volume Fraction of Fiber)/Elastic Modulus of Matrix
Volume Fraction of Fiber from EM of Composite (Longitudinal Direction)
Go Volume Fraction of Fiber = (Elastic Modulus Composite (Longitudinal Direction)-Elastic Modulus of Matrix*Volume Fraction of Matrix)/Elastic Modulus of Fiber
Tensile Strength of Matrix given Longitudinal Tensile Strength of Composite
Go Tensile Strength of Matrix = (Longitudinal Strength of Composite-Tensile Strength of Fiber*Volume Fraction of Fiber)/(1-Volume Fraction of Fiber)
Tensile Strength of Fiber from Longitudinal Tensile Strength of Composite
Go Tensile Strength of Fiber = (Longitudinal Strength of Composite-Tensile Strength of Matrix*(1-Volume Fraction of Fiber))/Volume Fraction of Fiber
Volume Fraction of Fiber from Longitudinal Tensile Strength of Composite
Go Volume Fraction of Fiber = (Tensile Strength of Matrix-Longitudinal Strength of Composite)/(Tensile Strength of Matrix-Tensile Strength of Fiber)
Longitudinal Strength of Composite
Go Longitudinal Strength of Composite = Stress in Matrix*(1-Volume Fraction of Fiber)+Tensile Strength of Fiber*Volume Fraction of Fiber
Fiber-Matrix Bonding Strength given Critical Length of Fiber
Go Fiber-Matrix Bonding Strength = (Tensile Strength of Fiber*Fiber Diameter)/(2*Critical Fiber Length)
Tensile Strength of Fiber given Critical Fiber Length
Go Tensile Strength of Fiber = (2*Critical Fiber Length*Fiber-Matrix Bonding Strength)/Fiber Diameter
Fiber Diameter given Critical Fiber Length
Go Fiber Diameter = (Critical Fiber Length*2*Fiber-Matrix Bonding Strength)/Tensile Strength of Fiber
Critical Fiber Length
Go Critical Fiber Length = Tensile Strength of Fiber*Fiber Diameter/(2*Critical Shear Stress)

Critical Fiber Length Formula

Critical Fiber Length = Tensile Strength of Fiber*Fiber Diameter/(2*Critical Shear Stress)
lc = ฯƒf*d/(2*ฯ„c)

Continuous and discontinuous fibers

Fibers that have length greater than 15 times the critical fiber length are called continuous fibers and fibers with smaller length are called discontinuous fibers.

How to Calculate Critical Fiber Length?

Critical Fiber Length calculator uses Critical Fiber Length = Tensile Strength of Fiber*Fiber Diameter/(2*Critical Shear Stress) to calculate the Critical Fiber Length, Critical fiber length is necessary for effective strengthening and stiffening of the composite material. Critical Fiber Length is denoted by lc symbol.

How to calculate Critical Fiber Length using this online calculator? To use this online calculator for Critical Fiber Length, enter Tensile Strength of Fiber (ฯƒf), Fiber Diameter (d) & Critical Shear Stress (ฯ„c) and hit the calculate button. Here is how the Critical Fiber Length calculation can be explained with given input values -> 10625 = 6375000*0.01/(2*3010000).

FAQ

What is Critical Fiber Length?
Critical fiber length is necessary for effective strengthening and stiffening of the composite material and is represented as lc = ฯƒf*d/(2*ฯ„c) or Critical Fiber Length = Tensile Strength of Fiber*Fiber Diameter/(2*Critical Shear Stress). Tensile Strength of Fiber in the fiber-reinforced composite, Fiber Diameter in the fiber-reinforced composites & Critical shear stress is either the fiber-matrix bond strength or the shear yield stress of matrix, whichever is lower.
How to calculate Critical Fiber Length?
Critical fiber length is necessary for effective strengthening and stiffening of the composite material is calculated using Critical Fiber Length = Tensile Strength of Fiber*Fiber Diameter/(2*Critical Shear Stress). To calculate Critical Fiber Length, you need Tensile Strength of Fiber (ฯƒf), Fiber Diameter (d) & Critical Shear Stress (ฯ„c). With our tool, you need to enter the respective value for Tensile Strength of Fiber, Fiber Diameter & Critical Shear Stress 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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