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)
σcd' = (Vf*l*τc/d)+τm*(1-Vf)
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
σcd' = (Vf*l*τc/d)+τm*(1-Vf) --> (0.5*0.001*80000000/1E-05)+70000000*(1-0.5)
Evaluating ... ...
σcd' = 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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Longitudinal strength of discontinuous fiber-reinforced composite ( less than critical length) Formula

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)
σcd' = (Vf*l*τc/d)+τm*(1-Vf)

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 σcd' 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 (Vf), Fiber length (l), Critical Shear Stress c), Fiber Diameter (d) & Stress in Matrix 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 σcd' = (Vf*l*τc/d)+τm*(1-Vf) 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 (Vf), Fiber length (l), Critical Shear Stress c), Fiber Diameter (d) & Stress in Matrix 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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