Longitudinal strength of discontinuous fiber-reinforced composite Solution

STEP 0: Pre-Calculation Summary
Formula Used
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)
σcd = σf*Vf*(1-(lc/(2*l)))+τm*(1-Vf)
This formula uses 6 Variables
Variables Used
Longitudinal strength of composite(discontinous fiber) - (Measured in Pascal) - Longitudinal strength of composite(discontinous fiber) that is discontinuous and aligned fiber matrix composite. The length of fiber is greater than the critical length.
Tensile Strength of Fiber - (Measured in Pascal) - Tensile Strength of Fiber in the fiber-reinforced composite.
Volume Fraction of Fiber - Volume Fraction of Fiber in fiber reinforced composite.
Critical Fiber Length - (Measured in Meter) - Critical fiber length that is necessary for effective strengthening and stiffening of the composite material.
Fiber length - (Measured in Meter) - Fiber length is a statistical average length of fibers present in the composite.
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
Tensile Strength of Fiber: 170 Megapascal --> 170000000 Pascal (Check conversion here)
Volume Fraction of Fiber: 0.5 --> No Conversion Required
Critical Fiber Length: 0.25 Millimeter --> 0.00025 Meter (Check conversion here)
Fiber length: 0.001 Meter --> 0.001 Meter No Conversion Required
Stress in Matrix: 70 Megapascal --> 70000000 Pascal (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σcd = σf*Vf*(1-(lc/(2*l)))+τm*(1-Vf) --> 170000000*0.5*(1-(0.00025/(2*0.001)))+70000000*(1-0.5)
Evaluating ... ...
σcd = 109375000
STEP 3: Convert Result to Output's Unit
109375000 Pascal -->109.375 Megapascal (Check conversion here)
FINAL ANSWER
109.375 Megapascal <-- Longitudinal strength of composite(discontinous fiber)
(Calculation completed in 00.004 seconds)

Credits

Created by Hariharan V S
Indian Institute of Technology (IIT), Chennai
Hariharan V S has created this Calculator and 25+ more calculators!
Verified by Team Softusvista
Softusvista Office (Pune), India
Team Softusvista has verified this Calculator and 1100+ more calculators!

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 Formula

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)
σcd = σf*Vf*(1-(lc/(2*l)))+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?

Longitudinal strength of discontinuous fiber-reinforced composite calculator uses 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) to calculate the Longitudinal strength of composite(discontinous fiber), Longitudinal strength of discontinuous fiber-reinforced composite ( the fiber is aligned). Longitudinal strength of composite(discontinous fiber) is denoted by σcd symbol.

How to calculate Longitudinal strength of discontinuous fiber-reinforced composite using this online calculator? To use this online calculator for Longitudinal strength of discontinuous fiber-reinforced composite, enter Tensile Strength of Fiber f), Volume Fraction of Fiber (Vf), Critical Fiber Length (lc), Fiber length (l) & Stress in Matrix m) and hit the calculate button. Here is how the Longitudinal strength of discontinuous fiber-reinforced composite calculation can be explained with given input values -> 0.000109 = 170000000*0.5*(1-(0.00025/(2*0.001)))+70000000*(1-0.5).

FAQ

What is Longitudinal strength of discontinuous fiber-reinforced composite?
Longitudinal strength of discontinuous fiber-reinforced composite ( the fiber is aligned) and is represented as σcd = σf*Vf*(1-(lc/(2*l)))+τm*(1-Vf) or 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). Tensile Strength of Fiber in the fiber-reinforced composite, Volume Fraction of Fiber in fiber reinforced composite, Critical fiber length that is necessary for effective strengthening and stiffening of the composite material, Fiber length is a statistical average length of fibers present in the composite & Stress in matrix is the stress at the failure of composite.
How to calculate Longitudinal strength of discontinuous fiber-reinforced composite?
Longitudinal strength of discontinuous fiber-reinforced composite ( the fiber is aligned) is calculated using 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). To calculate Longitudinal strength of discontinuous fiber-reinforced composite, you need Tensile Strength of Fiber f), Volume Fraction of Fiber (Vf), Critical Fiber Length (lc), Fiber length (l) & Stress in Matrix m). With our tool, you need to enter the respective value for Tensile Strength of Fiber, Volume Fraction of Fiber, Critical Fiber Length, Fiber length & Stress in Matrix and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!