Longitudinal Strength of Composite Calculator

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✖Stress in matrix is the stress at the failure of composite.ⓘ Stress in Matrix [τ_m]			+10% -10%
✖Volume Fraction of Fiber in fiber reinforced composite.ⓘ Volume Fraction of Fiber [V_f]			+10% -10%
✖Tensile Strength of Fiber in the fiber-reinforced composite.ⓘ Tensile Strength of Fiber [σ_f]			+10% -10%

✖Longitudinal Strength of Composite, that is aligned and continuous fiber reinforced composite.ⓘ Longitudinal Strength of Composite [σ_cl]

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Longitudinal Strength of Composite

Formula

`"σ"_{"cl"} = "τ"_{"m"}*(1-"V"_{"f"})+"σ"_{"f"}*"V"_{"f"}`

Example

`"31.865MPa"="70.1MPa"*(1-"0.6")+"6.375MPa"*"0.6"`

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Longitudinal Strength of Composite Solution

STEP 0: Pre-Calculation Summary

Formula Used

Longitudinal Strength of Composite = Stress in Matrix*(1-Volume Fraction of Fiber)+Tensile Strength of Fiber*Volume Fraction of Fiber
σ_cl = τ_m*(1-V_f)+σ_f*V_f
This formula uses 4 Variables

Variables Used

Longitudinal Strength of Composite - (Measured in Pascal) - Longitudinal Strength of Composite, that is aligned and continuous fiber reinforced composite.
Stress in Matrix - (Measured in Pascal) - Stress in matrix is the stress at the failure of composite.
Volume Fraction of Fiber - Volume Fraction of Fiber in fiber reinforced composite.
Tensile Strength of Fiber - (Measured in Pascal) - Tensile Strength of Fiber in the fiber-reinforced composite.

STEP 1: Convert Input(s) to Base Unit

Stress in Matrix: 70.1 Megapascal --> 70100000 Pascal (Check conversion here)
Volume Fraction of Fiber: 0.6 --> No Conversion Required
Tensile Strength of Fiber: 6.375 Megapascal --> 6375000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_cl = τ_m*(1-V_f)+σ_f*V_f --> 70100000*(1-0.6)+6375000*0.6

Evaluating ... ...

σ_cl = 31865000

STEP 3: Convert Result to Output's Unit

31865000 Pascal -->31.865 Megapascal (Check conversion here)

FINAL ANSWER

31.865 Megapascal <-- Longitudinal Strength of Composite

(Calculation completed in 00.004 seconds)

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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 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)

Longitudinal Strength of Composite Formula

Longitudinal Strength of Composite = Stress in Matrix*(1-Volume Fraction of Fiber)+Tensile Strength of Fiber*Volume Fraction of Fiber
σ_cl = τ_m*(1-V_f)+σ_f*V_f

Assumptions used

If it is assumed that strain on fiber is more than strain on matrix, then fibers
will fail before the matrix. Once the fibers have fractured, the majority of the load that was borne by the fibers is now transferred to the matrix.

How to Calculate Longitudinal Strength of Composite?

Longitudinal Strength of Composite calculator uses Longitudinal Strength of Composite = Stress in Matrix*(1-Volume Fraction of Fiber)+Tensile Strength of Fiber*Volume Fraction of Fiber to calculate the Longitudinal Strength of Composite, Longitudinal strength of composite, that is aligned and continuous fiber reinforced composite. Longitudinal Strength of Composite is denoted by σ_cl symbol.

How to calculate Longitudinal Strength of Composite using this online calculator? To use this online calculator for Longitudinal Strength of Composite, enter Stress in Matrix (τ_m), Volume Fraction of Fiber (V_f) & Tensile Strength of Fiber (σ_f) and hit the calculate button. Here is how the Longitudinal Strength of Composite calculation can be explained with given input values -> 3.2E-5 = 70100000*(1-0.6)+6375000*0.6.

FAQ

What is Longitudinal Strength of Composite?

Longitudinal strength of composite, that is aligned and continuous fiber reinforced composite and is represented as σ_cl = τ_m*(1-V_f)+σ_f*V_f or Longitudinal Strength of Composite = Stress in Matrix*(1-Volume Fraction of Fiber)+Tensile Strength of Fiber*Volume Fraction of Fiber. Stress in matrix is the stress at the failure of composite, Volume Fraction of Fiber in fiber reinforced composite & Tensile Strength of Fiber in the fiber-reinforced composite.

How to calculate Longitudinal Strength of Composite?

Longitudinal strength of composite, that is aligned and continuous fiber reinforced composite is calculated using Longitudinal Strength of Composite = Stress in Matrix*(1-Volume Fraction of Fiber)+Tensile Strength of Fiber*Volume Fraction of Fiber. To calculate Longitudinal Strength of Composite, you need Stress in Matrix (τ_m), Volume Fraction of Fiber (V_f) & Tensile Strength of Fiber (σ_f). With our tool, you need to enter the respective value for Stress in Matrix, Volume Fraction of Fiber & Tensile Strength of Fiber 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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