Fiber-Matrix Bonding Strength given Critical Length of Fiber Calculator

✖Tensile Strength of Fiber in the fiber-reinforced composite.ⓘ Tensile Strength of Fiber [σ_f]			+10% -10%
✖Fiber Diameter in the fiber-reinforced composites.ⓘ Fiber Diameter [d]			+10% -10%
✖Critical fiber length that is necessary for effective strengthening and stiffening of the composite material.ⓘ Critical Fiber Length [l_c]			+10% -10%

✖Fiber-Matrix Bonding Strength can also be taken as shear yield strength of the matrix.ⓘ Fiber-Matrix Bonding Strength given Critical Length of Fiber [τ]

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Fiber-Matrix Bonding Strength given Critical Length of Fiber

Formula

`"τ" = ("σ"_{"f"}*"d")/(2*"l"_{"c"})`

Example

`"3MPa"=("6.375MPa"*"10mm")/(2*"10.625mm")`

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Fiber-Matrix Bonding Strength given Critical Length of Fiber Solution

STEP 0: Pre-Calculation Summary

Formula Used

Fiber-Matrix Bonding Strength = (Tensile Strength of Fiber*Fiber Diameter)/(2*Critical Fiber Length)
τ = (σ_f*d)/(2*l_c)
This formula uses 4 Variables

Variables Used

Fiber-Matrix Bonding Strength - (Measured in Pascal) - Fiber-Matrix Bonding Strength can also be taken as shear yield strength of the matrix.
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 Fiber Length - (Measured in Meter) - Critical fiber length that is necessary for effective strengthening and stiffening of the composite material.

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 Fiber Length: 10.625 Millimeter --> 0.010625 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

τ = (σ_f*d)/(2*l_c) --> (6375000*0.01)/(2*0.010625)

Evaluating ... ...

τ = 3000000

STEP 3: Convert Result to Output's Unit

3000000 Pascal -->3 Megapascal (Check conversion here)

FINAL ANSWER

3 Megapascal <-- Fiber-Matrix Bonding Strength

(Calculation completed in 00.004 seconds)

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Created by Rajat Vishwakarma

University Institute of Technology RGPV (UIT - RGPV), Bhopal

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Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi

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< 12 Polymer Matrix Composites 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)

Fiber-Matrix Bonding Strength given Critical Length of Fiber Formula

Fiber-Matrix Bonding Strength = (Tensile Strength of Fiber*Fiber Diameter)/(2*Critical Fiber Length)
τ = (σ_f*d)/(2*l_c)

What are polymer matrix composites (PMC)?

Polymer matrix composites have organic polymer matrix with strengthening fibers in the matrix. Matrix holds and protects the fibers in place while transmitting the load to them. Advanced composites are a class of Polymer matrix composites that have high mechanical properties (strength and stiffness) compared to the normal reinforced plastics and are used in aerospace applications. Reinforced plastics are relatively inexpensive and are widely used.

How to Calculate Fiber-Matrix Bonding Strength given Critical Length of Fiber?

Fiber-Matrix Bonding Strength given Critical Length of Fiber calculator uses Fiber-Matrix Bonding Strength = (Tensile Strength of Fiber*Fiber Diameter)/(2*Critical Fiber Length) to calculate the Fiber-Matrix Bonding Strength, Fiber-Matrix Bonding Strength given Critical Length of Fiber formula is defined as shear yield strength of the matrix. Fiber-Matrix Bonding Strength is denoted by τ symbol.

How to calculate Fiber-Matrix Bonding Strength given Critical Length of Fiber using this online calculator? To use this online calculator for Fiber-Matrix Bonding Strength given Critical Length of Fiber, enter Tensile Strength of Fiber (σ_f), Fiber Diameter (d) & Critical Fiber Length (l_c) and hit the calculate button. Here is how the Fiber-Matrix Bonding Strength given Critical Length of Fiber calculation can be explained with given input values -> 8E-5 = (6375000*0.01)/(2*0.010625).

FAQ

What is Fiber-Matrix Bonding Strength given Critical Length of Fiber?

Fiber-Matrix Bonding Strength given Critical Length of Fiber formula is defined as shear yield strength of the matrix and is represented as τ = (σ_f*d)/(2*l_c) or Fiber-Matrix Bonding Strength = (Tensile Strength of Fiber*Fiber Diameter)/(2*Critical Fiber Length). Tensile Strength of Fiber in the fiber-reinforced composite, Fiber Diameter in the fiber-reinforced composites & Critical fiber length that is necessary for effective strengthening and stiffening of the composite material.

How to calculate Fiber-Matrix Bonding Strength given Critical Length of Fiber?

Fiber-Matrix Bonding Strength given Critical Length of Fiber formula is defined as shear yield strength of the matrix is calculated using Fiber-Matrix Bonding Strength = (Tensile Strength of Fiber*Fiber Diameter)/(2*Critical Fiber Length). To calculate Fiber-Matrix Bonding Strength given Critical Length of Fiber, you need Tensile Strength of Fiber (σ_f), Fiber Diameter (d) & Critical Fiber Length (l_c). With our tool, you need to enter the respective value for Tensile Strength of Fiber, Fiber Diameter & Critical Fiber 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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