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Critical Fiber Length Calculator

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✖Tensile Strength of Fiber refers to the maximum stress a material can withstand while being stretched or pulled before breaking.ⓘ Tensile Strength of Fiber [σ_f]			+10% -10%
✖Fiber Diameter refers to the width or diameter of the individual fibers within a material, such as in composite materials or textiles.ⓘ Fiber Diameter [d]			+10% -10%
✖Critical Shear Stress is either the fiber matrix bond strength or the shear yield stress of matrix , whichever is lower.ⓘ Critical Shear Stress [τ_c]			+10% -10%

✖Critical Fiber Length that is necessary for effective strengthening and stiffening of the composite material.ⓘ Critical Fiber Length [l_c]

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Critical Fiber Length Solution

STEP 0: Pre-Calculation Summary

Formula Used

Critical Fiber Length = Tensile Strength of Fiber*Fiber Diameter/(2*Critical Shear Stress)
l_c = σ_f*d/(2*τ_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 refers to the maximum stress a material can withstand while being stretched or pulled before breaking.
Fiber Diameter - (Measured in Meter) - Fiber Diameter refers to the width or diameter of the individual fibers within a material, such as in composite materials or textiles.
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

l_c = σ_f*d/(2*τ_c) --> 6375000*0.01/(2*3010000)

Evaluating ... ...

l_c = 0.0105897009966777

STEP 3: Convert Result to Output's Unit

0.0105897009966777 Meter -->10.5897009966777 Millimeter (Check conversion here)

FINAL ANSWER

10.5897009966777 ≈ 10.5897 Millimeter <-- Critical Fiber Length

(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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LaTeX Go Number of Schottky Defects = Number of atomic sites*exp(-Activation energy for Schottky formation/(2*Universal Gas Constant*Temperature))

Critical Fiber Length

LaTeX Go Critical Fiber Length = Tensile Strength of Fiber*Fiber Diameter/(2*Critical Shear Stress)

Young's Modulus from shear modulus

LaTeX Go Young's Modulus = 2*Shear Modulus*(1+Poisson's Ratio)

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Volume Fraction of Matrix from EM of Composite (Longitudinal Direction)

LaTeX Go Volume Fraction of Matrix = (Elastic Modulus Composite (Longitudinal Direction)-Elastic Modulus of Fiber*Volume Fraction of Fiber)/Elastic Modulus of Matrix

Fiber-Matrix Bonding Strength given Critical Length of Fiber

LaTeX Go Fiber Matrix Bonding Strength = (Tensile Strength of Fiber*Fiber Diameter)/(2*Critical Fiber Length)

Tensile Strength of Fiber given Critical Fiber Length

LaTeX Go Tensile Strength of Fiber = (2*Critical Fiber Length*Fiber Matrix Bonding Strength)/Fiber Diameter

Fiber Diameter given Critical Fiber Length

LaTeX Go Fiber Diameter = (Critical Fiber Length*2*Fiber Matrix Bonding Strength)/Tensile Strength of Fiber

Critical Fiber Length Formula

LaTeX Go

Critical Fiber Length = Tensile Strength of Fiber*Fiber Diameter/(2*Critical Shear Stress)
l_c = σ_f*d/(2*τ_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 a parameter used in the study of composite materials, particularly in the context of fiber-reinforced composites. It refers to the minimum length of a fiber required within a composite material to effectively transfer load and improve mechanical properties such as strength and stiffness of the composite material. Critical Fiber Length is denoted by l_c 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 (σ_f), Fiber Diameter (d) & Critical Shear Stress (τ_c) and hit the calculate button. Here is how the Critical Fiber Length calculation can be explained with given input values -> 10589.7 = 6375000*0.01/(2*3010000).

FAQ

What is Critical Fiber Length?

Critical Fiber Length is a parameter used in the study of composite materials, particularly in the context of fiber-reinforced composites. It refers to the minimum length of a fiber required within a composite material to effectively transfer load and improve mechanical properties such as strength and stiffness of the composite material and is represented as l_c = σ_f*d/(2*τ_c) or Critical Fiber Length = Tensile Strength of Fiber*Fiber Diameter/(2*Critical Shear Stress). Tensile Strength of Fiber refers to the maximum stress a material can withstand while being stretched or pulled before breaking, Fiber Diameter refers to the width or diameter of the individual fibers within a material, such as in composite materials or textiles & 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 a parameter used in the study of composite materials, particularly in the context of fiber-reinforced composites. It refers to the minimum length of a fiber required within a composite material to effectively transfer load and improve mechanical properties such as strength and stiffness 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 (σ_f), Fiber Diameter (d) & Critical Shear Stress (τ_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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