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Critical Fiber Length Formula

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Critical Fiber Length that is necessary for effective strengthening and stiffening of the composite material. Check FAQs

l c = σ f \cdot \frac{d}{2 \cdot τ c}

l_c - Critical Fiber Length?σ_f - Tensile Strength of Fiber?d - Fiber Diameter?τ_c - Critical Shear Stress?

Critical Fiber Length Example

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Here is how the Critical Fiber Length equation looks like with Values.

Here is how the Critical Fiber Length equation looks like with Units.

Here is how the Critical Fiber Length equation looks like.

10.5897 = 6.375 \cdot \frac{10}{2 \cdot 3.01}

10.5897mm = 6.375MPa \cdot \frac{10mm}{2 \cdot 3.01MPa}

10.5897 = 6.375 \cdot \frac{10}{2 \cdot 3.01}

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Critical Fiber Length Solution

Follow our step by step solution on how to calculate Critical Fiber Length?

FIRST Step Consider the formula

l c = σ f \cdot \frac{d}{2 \cdot τ c}

Next Step Substitute values of Variables

∴

l c = 6.375MPa \cdot \frac{10mm}{2 \cdot 3.01MPa}

Next Step Convert Units

∴

l c = 6.4E+6Pa \cdot \frac{0.01m}{2 \cdot 3E+6Pa}

Next Step Prepare to Evaluate

∴

l c = 6.4E+6 \cdot \frac{0.01}{2 \cdot 3E+6}

Next Step Evaluate

∴

l c = 0.0105897009966777m

Next Step Convert to Output's Unit

∴

l c = 10.5897009966777mm

LAST Step Rounding Answer

∴

l c = 10.5897mm

Critical Fiber Length Formula Elements

Variables

Critical Fiber Length

Critical Fiber Length that is necessary for effective strengthening and stiffening of the composite material.

Symbol: l_c

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Critical Fiber Length

Tensile Strength of Fiber

Tensile Strength of Fiber refers to the maximum stress a material can withstand while being stretched or pulled before breaking.

Symbol: σ_f

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Tensile Strength of Fiber

Fiber Diameter

Fiber Diameter refers to the width or diameter of the individual fibers within a material, such as in composite materials or textiles.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Fiber Diameter

Critical Shear Stress

Critical Shear Stress is either the fiber matrix bond strength or the shear yield stress of matrix , whichever is lower.

Symbol: τ_c

Measurement: PressureUnit: MPa

Note: Value should be greater than 0.

Formulas to find Critical Shear Stress

Other formulas in Ceramics and Composites category

Go Tensile Strength of Fiber given Critical Fiber Length

σ f = \frac{2 \cdot l c \cdot τ}{d}

Go Fiber Diameter given Critical Fiber Length

d = \frac{l c \cdot 2 \cdot τ}{σ f}

Go Fiber-Matrix Bonding Strength given Critical Length of Fiber

τ = \frac{σ f \cdot d}{2 \cdot l c}

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

V m = \frac{E cl - E f \cdot V f}{E m}

How to Evaluate Critical Fiber Length?

Critical Fiber Length evaluator uses Critical Fiber Length = Tensile Strength of Fiber*Fiber Diameter/(2*Critical Shear Stress) to evaluate 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 evaluate Critical Fiber Length using this online evaluator? To use this online evaluator for Critical Fiber Length, enter Tensile Strength of Fiber (σ_f), Fiber Diameter (d) & Critical Shear Stress (τ_c) and hit the calculate button.

FAQs on Critical Fiber Length

What is the formula to find Critical Fiber Length?

The formula of Critical Fiber Length is expressed as Critical Fiber Length = Tensile Strength of Fiber*Fiber Diameter/(2*Critical Shear Stress). Here is an example- 10589.7 = 6375000*0.01/(2*3010000).

How to calculate Critical Fiber Length?

With Tensile Strength of Fiber (σ_f), Fiber Diameter (d) & Critical Shear Stress (τ_c) we can find Critical Fiber Length using the formula - Critical Fiber Length = Tensile Strength of Fiber*Fiber Diameter/(2*Critical Shear Stress).

Can the Critical Fiber Length be negative?

No, the Critical Fiber Length, measured in Length cannot be negative.

Which unit is used to measure Critical Fiber Length?

Critical Fiber Length is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Critical Fiber Length can be measured.

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Critical Fiber Length Formula

Critical Fiber Length Example

Critical Fiber Length Solution

Critical Fiber Length Formula Elements

Other formulas in Ceramics and Composites category

How to Evaluate Critical Fiber Length?

FAQs on Critical Fiber Length

Variable Name