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Volume Fraction of Fiber from EM of Composite (Longitudinal Direction) Calculator

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Polymer Matrix Composites Elastic Modulus

✖Elastic Modulus Composite (Longitudinal Direction) refers to a material property when subjected to tensile or compressive forces along the longitudinal direction.ⓘ Elastic Modulus Composite (Longitudinal Direction) [E_cl]			+10% -10%
✖Elastic Modulus of Matrix typically refers to the elastic modulus or young's modulus of the material composing the matrix phase in a composite material.ⓘ Elastic Modulus of Matrix [E_m]			+10% -10%
✖Volume Fraction of Matrix is the Volume fraction of the matrix used in composite.ⓘ Volume Fraction of Matrix [V_m]			+10% -10%
✖Elastic Modulus of Fiber, also known as young's modulus, refers to the stiffness of the material, it represents the ratio of stress to strain within the elastic limit of the material.ⓘ Elastic Modulus of Fiber [E_f]			+10% -10%

✖Volume Fraction of Fiber also known as fiber volume fraction or simply fiber fraction, is a measure of the volume occupied by fibers within a composite material.ⓘ Volume Fraction of Fiber from EM of Composite (Longitudinal Direction) [V_f]

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Volume Fraction of Fiber from EM of Composite (Longitudinal Direction) Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume Fraction of Fiber = (Elastic Modulus Composite (Longitudinal Direction)-Elastic Modulus of Matrix*Volume Fraction of Matrix)/Elastic Modulus of Fiber
V_f = (E_cl-E_m*V_m)/E_f
This formula uses 5 Variables

Variables Used

Volume Fraction of Fiber - Volume Fraction of Fiber also known as fiber volume fraction or simply fiber fraction, is a measure of the volume occupied by fibers within a composite material.
Elastic Modulus Composite (Longitudinal Direction) - (Measured in Pascal) - Elastic Modulus Composite (Longitudinal Direction) refers to a material property when subjected to tensile or compressive forces along the longitudinal direction.
Elastic Modulus of Matrix - (Measured in Pascal) - Elastic Modulus of Matrix typically refers to the elastic modulus or young's modulus of the material composing the matrix phase in a composite material.
Volume Fraction of Matrix - Volume Fraction of Matrix is the Volume fraction of the matrix used in composite.
Elastic Modulus of Fiber - (Measured in Pascal) - Elastic Modulus of Fiber, also known as young's modulus, refers to the stiffness of the material, it represents the ratio of stress to strain within the elastic limit of the material.

STEP 1: Convert Input(s) to Base Unit

Elastic Modulus Composite (Longitudinal Direction): 200 Megapascal --> 200000000 Pascal (Check conversion here)
Elastic Modulus of Matrix: 200.025 Megapascal --> 200025000 Pascal (Check conversion here)
Volume Fraction of Matrix: 0.4 --> No Conversion Required
Elastic Modulus of Fiber: 200 Megapascal --> 200000000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_f = (E_cl-E_m*V_m)/E_f --> (200000000-200025000*0.4)/200000000

Evaluating ... ...

V_f = 0.59995

STEP 3: Convert Result to Output's Unit

0.59995 --> No Conversion Required

FINAL ANSWER

0.59995 <-- Volume Fraction of Fiber

(Calculation completed in 00.007 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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< Polymer Matrix Composites Calculators

Volume Fraction of Matrix from EM of Composite (Longitudinal Direction)

LaTeX Go Volume Fraction of Matrix = (Elastic Modulus Composite (Longitudinal Direction)-Elastic Modulus of Fiber*Volume Fraction of Fiber)/Elastic Modulus of Matrix

Fiber-Matrix Bonding Strength given Critical Length of Fiber

LaTeX Go Fiber Matrix Bonding Strength = (Tensile Strength of Fiber*Fiber Diameter)/(2*Critical Fiber Length)

Tensile Strength of Fiber given Critical Fiber Length

LaTeX Go Tensile Strength of Fiber = (2*Critical Fiber Length*Fiber Matrix Bonding Strength)/Fiber Diameter

Fiber Diameter given Critical Fiber Length

LaTeX Go Fiber Diameter = (Critical Fiber Length*2*Fiber Matrix Bonding Strength)/Tensile Strength of Fiber

Volume Fraction of Fiber from EM of Composite (Longitudinal Direction) Formula

LaTeX Go

Volume Fraction of Fiber = (Elastic Modulus Composite (Longitudinal Direction)-Elastic Modulus of Matrix*Volume Fraction of Matrix)/Elastic Modulus of Fiber
V_f = (E_cl-E_m*V_m)/E_f

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 Volume Fraction of Fiber from EM of Composite (Longitudinal Direction)?

Volume Fraction of Fiber from EM of Composite (Longitudinal Direction) calculator uses Volume Fraction of Fiber = (Elastic Modulus Composite (Longitudinal Direction)-Elastic Modulus of Matrix*Volume Fraction of Matrix)/Elastic Modulus of Fiber to calculate the Volume Fraction of Fiber, Volume Fraction of Fiber from EM of Composite (Longitudinal Direction) can be defined from the effective modulus (EM) of the composite in the longitudinal direction. This relationship is often expressed using various micromechanical models such as the rule of mixtures, Halpin-Tsai model, or Mori-Tanaka model. Volume Fraction of Fiber is denoted by V_f symbol.

How to calculate Volume Fraction of Fiber from EM of Composite (Longitudinal Direction) using this online calculator? To use this online calculator for Volume Fraction of Fiber from EM of Composite (Longitudinal Direction), enter Elastic Modulus Composite (Longitudinal Direction) (E_cl), Elastic Modulus of Matrix (E_m), Volume Fraction of Matrix (V_m) & Elastic Modulus of Fiber (E_f) and hit the calculate button. Here is how the Volume Fraction of Fiber from EM of Composite (Longitudinal Direction) calculation can be explained with given input values -> 0.59995 = (200000000-200025000*0.4)/200000000.

FAQ

What is Volume Fraction of Fiber from EM of Composite (Longitudinal Direction)?

Volume Fraction of Fiber from EM of Composite (Longitudinal Direction) can be defined from the effective modulus (EM) of the composite in the longitudinal direction. This relationship is often expressed using various micromechanical models such as the rule of mixtures, Halpin-Tsai model, or Mori-Tanaka model and is represented as V_f = (E_cl-E_m*V_m)/E_f or Volume Fraction of Fiber = (Elastic Modulus Composite (Longitudinal Direction)-Elastic Modulus of Matrix*Volume Fraction of Matrix)/Elastic Modulus of Fiber. Elastic Modulus Composite (Longitudinal Direction) refers to a material property when subjected to tensile or compressive forces along the longitudinal direction, Elastic Modulus of Matrix typically refers to the elastic modulus or young's modulus of the material composing the matrix phase in a composite material, Volume Fraction of Matrix is the Volume fraction of the matrix used in composite & Elastic Modulus of Fiber, also known as young's modulus, refers to the stiffness of the material, it represents the ratio of stress to strain within the elastic limit of the material.

How to calculate Volume Fraction of Fiber from EM of Composite (Longitudinal Direction)?

Volume Fraction of Fiber from EM of Composite (Longitudinal Direction) can be defined from the effective modulus (EM) of the composite in the longitudinal direction. This relationship is often expressed using various micromechanical models such as the rule of mixtures, Halpin-Tsai model, or Mori-Tanaka model is calculated using Volume Fraction of Fiber = (Elastic Modulus Composite (Longitudinal Direction)-Elastic Modulus of Matrix*Volume Fraction of Matrix)/Elastic Modulus of Fiber. To calculate Volume Fraction of Fiber from EM of Composite (Longitudinal Direction), you need Elastic Modulus Composite (Longitudinal Direction) (E_cl), Elastic Modulus of Matrix (E_m), Volume Fraction of Matrix (V_m) & Elastic Modulus of Fiber (E_f). With our tool, you need to enter the respective value for Elastic Modulus Composite (Longitudinal Direction), Elastic Modulus of Matrix, Volume Fraction of Matrix & Elastic Modulus of Fiber and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Volume Fraction of Fiber?

In this formula, Volume Fraction of Fiber uses Elastic Modulus Composite (Longitudinal Direction), Elastic Modulus of Matrix, Volume Fraction of Matrix & Elastic Modulus of Fiber. We can use 2 other way(s) to calculate the same, which is/are as follows -

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 Fiber = (Tensile Strength of Matrix-Longitudinal Strength of Composite)/(Tensile Strength of Matrix-Tensile Strength of Fiber)

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