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

✖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 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 [V_f]			+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 from EM of Composite (Longitudinal Direction) [V_m]

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Formula

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

Formula

`"V"_{"m"} = ("E"_{"CL"}-"E"_{"f"}*"V"_{"f"})/"E"_{"m"}`

Example

`"0.39995"=("200.0MPa"-"200MPa"*"0.6")/"200.025MPa"`

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

STEP 0: Pre-Calculation Summary

Formula Used

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

Variables Used

Volume Fraction of Matrix - Volume Fraction of Matrix is the Volume fraction of the matrix used in composite.
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 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.
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 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.

STEP 1: Convert Input(s) to Base Unit

Elastic Modulus Composite (Longitudinal Direction): 200 Megapascal --> 200000000 Pascal (Check conversion here)
Elastic Modulus of Fiber: 200 Megapascal --> 200000000 Pascal (Check conversion here)
Volume Fraction of Fiber: 0.6 --> No Conversion Required
Elastic Modulus of Matrix: 200.025 Megapascal --> 200025000 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_m = (E_CL-E_f*V_f)/E_m --> (200000000-200000000*0.6)/200025000

Evaluating ... ...

V_m = 0.399950006249219

STEP 3: Convert Result to Output's Unit

0.399950006249219 --> No Conversion Required

FINAL ANSWER

0.399950006249219 ≈ 0.39995 <-- Volume Fraction of Matrix

(Calculation completed in 00.004 seconds)

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Created by Rajat Vishwakarma

University Institute of Technology RGPV (UIT - RGPV), Bhopal

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< 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 EM 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)

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

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

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 Matrix from EM of Composite (Longitudinal Direction)?

Volume Fraction of Matrix from EM of Composite (Longitudinal Direction) calculator uses Volume Fraction of Matrix = (Elastic Modulus Composite (Longitudinal Direction)-Elastic Modulus of Fiber*Volume Fraction of Fiber)/Elastic Modulus of Matrix to calculate the Volume Fraction of Matrix, Volume Fraction of Matrix from EM of Composite (Longitudinal Direction) essentially represents the relationship between the composite's longitudinal elastic modulus and the elastic moduli of its constituents, along with their respective volume fractions. It allows you to calculate the volume fraction of the matrix when the elastic properties of the composite, fiber, and matrix are known. Volume Fraction of Matrix is denoted by V_m symbol.

How to calculate Volume Fraction of Matrix from EM of Composite (Longitudinal Direction) using this online calculator? To use this online calculator for Volume Fraction of Matrix from EM of Composite (Longitudinal Direction), enter Elastic Modulus Composite (Longitudinal Direction) (E_CL), Elastic Modulus of Fiber (E_f), Volume Fraction of Fiber (V_f) & Elastic Modulus of Matrix (E_m) and hit the calculate button. Here is how the Volume Fraction of Matrix from EM of Composite (Longitudinal Direction) calculation can be explained with given input values -> 0.39995 = (200000000-200000000*0.6)/200025000.

FAQ

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

Volume Fraction of Matrix from EM of Composite (Longitudinal Direction) essentially represents the relationship between the composite's longitudinal elastic modulus and the elastic moduli of its constituents, along with their respective volume fractions. It allows you to calculate the volume fraction of the matrix when the elastic properties of the composite, fiber, and matrix are known and is represented as V_m = (E_CL-E_f*V_f)/E_m or Volume Fraction of Matrix = (Elastic Modulus Composite (Longitudinal Direction)-Elastic Modulus of Fiber*Volume Fraction of Fiber)/Elastic Modulus of Matrix. Elastic Modulus Composite (Longitudinal Direction) refers to a material property when subjected to tensile or compressive forces along the longitudinal direction, 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, 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 of Matrix typically refers to the elastic modulus or young's modulus of the material composing the matrix phase in a composite material.

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

Volume Fraction of Matrix from EM of Composite (Longitudinal Direction) essentially represents the relationship between the composite's longitudinal elastic modulus and the elastic moduli of its constituents, along with their respective volume fractions. It allows you to calculate the volume fraction of the matrix when the elastic properties of the composite, fiber, and matrix are known is calculated using Volume Fraction of Matrix = (Elastic Modulus Composite (Longitudinal Direction)-Elastic Modulus of Fiber*Volume Fraction of Fiber)/Elastic Modulus of Matrix. To calculate Volume Fraction of Matrix from EM of Composite (Longitudinal Direction), you need Elastic Modulus Composite (Longitudinal Direction) (E_CL), Elastic Modulus of Fiber (E_f), Volume Fraction of Fiber (V_f) & Elastic Modulus of Matrix (E_m). With our tool, you need to enter the respective value for Elastic Modulus Composite (Longitudinal Direction), Elastic Modulus of Fiber, Volume Fraction of Fiber & Elastic Modulus of Matrix 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 Matrix?

In this formula, Volume Fraction of Matrix uses Elastic Modulus Composite (Longitudinal Direction), Elastic Modulus of Fiber, Volume Fraction of Fiber & Elastic Modulus of Matrix. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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