Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length) Calculator

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✖Volume Fraction of Fiber in fiber reinforced composite.ⓘ Volume Fraction of Fiber [V_f]			+10% -10%
✖Fiber length is a statistical average length of fibers present in the composite.ⓘ Fiber length [l]			+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%
✖Fiber Diameter in the fiber-reinforced composites.ⓘ Fiber Diameter [d]			+10% -10%
✖Stress in matrix is the stress at the failure of composite.ⓘ Stress in Matrix [τ_m]			+10% -10%

✖Longitudinal strength of composite(discontinous fiber less than lc) that is the length of fiber is smaller than the critical length in discontinuous aligned fiber reinforced composite.ⓘ Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length) [σ_cd']

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Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length)

Formula

`"σ"_{"cd'"} = ("V"_{"f"}*"l"*"τ"_{"c"}/"d")+"τ"_{"m"}*(1-"V"_{"f"})`

Example

`"4035MPa"=("0.5"*"0.001m"*"80MPa"/"0.01mm")+"70MPa"*(1-"0.5")`

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Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length) Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)
σ_cd' = (V_f*l*τ_c/d)+τ_m*(1-V_f)
This formula uses 6 Variables

Variables Used

Longitudinal strength of composite(discontinous fiber less than lc) - (Measured in Pascal) - Longitudinal strength of composite(discontinous fiber less than lc) that is the length of fiber is smaller than the critical length in discontinuous aligned fiber reinforced composite.
Volume Fraction of Fiber - Volume Fraction of Fiber in fiber reinforced composite.
Fiber length - (Measured in Meter) - Fiber length is a statistical average length of fibers present in the composite.
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.
Fiber Diameter - (Measured in Meter) - Fiber Diameter in the fiber-reinforced composites.
Stress in Matrix - (Measured in Pascal) - Stress in matrix is the stress at the failure of composite.

STEP 1: Convert Input(s) to Base Unit

Volume Fraction of Fiber: 0.5 --> No Conversion Required
Fiber length: 0.001 Meter --> 0.001 Meter No Conversion Required
Critical Shear Stress: 80 Megapascal --> 80000000 Pascal (Check conversion here)
Fiber Diameter: 0.01 Millimeter --> 1E-05 Meter (Check conversion here)
Stress in Matrix: 70 Megapascal --> 70000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ_cd' = (V_f*l*τ_c/d)+τ_m*(1-V_f) --> (0.5*0.001*80000000/1E-05)+70000000*(1-0.5)

Evaluating ... ...

σ_cd' = 4035000000

STEP 3: Convert Result to Output's Unit

4035000000 Pascal -->4035 Megapascal (Check conversion here)

FINAL ANSWER

4035 Megapascal <-- Longitudinal strength of composite(discontinous fiber less than lc)

(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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< 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)

Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length) Formula

Discontinuous and Aligned Fiber reinforced composites

Even though reinforcement efficiency is lower for discontinuous than for continuous fibers, discontinuous and aligned fiber composites are becoming increasingly more important in the commercial market. Chopped glass fibers are used most extensively; however, carbon and aramid discontinuous fibers are also employed.These short fiber composites can be produced having moduli of elasticity and tensile strengths that approach 90% and 50%, respectively, of their continuous fiber counterparts.

How to Calculate Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length)?

Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length) calculator uses 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) to calculate the Longitudinal strength of composite(discontinous fiber less than lc), Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length) that is length of fiber is less than critical length. Longitudinal strength of composite(discontinous fiber less than lc) is denoted by σ_cd' symbol.

How to calculate Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length) using this online calculator? To use this online calculator for Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length), enter Volume Fraction of Fiber (V_f), Fiber length (l), Critical Shear Stress (τ_c), Fiber Diameter (d) & Stress in Matrix (τ_m) and hit the calculate button. Here is how the Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length) calculation can be explained with given input values -> 0.004035 = (0.5*0.001*80000000/1E-05)+70000000*(1-0.5).

FAQ

What is Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length)?

Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length) that is length of fiber is less than critical length and is represented as σ_cd' = (V_f*l*τ_c/d)+τ_m*(1-V_f) or 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). Volume Fraction of Fiber in fiber reinforced composite, Fiber length is a statistical average length of fibers present in the composite, Critical shear stress is either the fiber-matrix bond strength or the shear yield stress of matrix, whichever is lower, Fiber Diameter in the fiber-reinforced composites & Stress in matrix is the stress at the failure of composite.

How to calculate Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length)?

Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length) that is length of fiber is less than critical length is calculated using 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). To calculate Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length), you need Volume Fraction of Fiber (V_f), Fiber length (l), Critical Shear Stress (τ_c), Fiber Diameter (d) & Stress in Matrix (τ_m). With our tool, you need to enter the respective value for Volume Fraction of Fiber, Fiber length, Critical Shear Stress, Fiber Diameter & Stress in Matrix 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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