# Fiber Volume Fraction and Rule of Mixtures Calculator

> Source: https://netray.co/tools/composite-fiber-volume-fraction-rule-of-mixtures-calculator
> Publisher: Netray (netray.co), AI and integration engineering for ERP and manufacturing systems.
> Section: Free Tools

## Short answer

Convert resin or fiber weight fraction into fiber volume fraction, then estimate laminate density and first-pass modulus with the rule of mixtures and the inverse rule.

## Category

engineering-plm

## Industry

Composites Manufacturing

## Audience

- Composites engineer
- Process engineer
- Quality engineer
- Estimator

## Tool

**Kind:** calculator

**Inputs:**

#### Fiber weight fraction

**Key:** wf

**Type:** slider

**Default:** 65

**Min:** 30

**Max:** 90

**Step:** 1

**Unit:** % by weight

**Help:** Equals 100 minus resin content by weight. A prepreg at 35% resin content is 65% fiber by weight.

#### Fiber density

**Key:** rf

**Type:** number

**Default:** 1.78

**Min:** 0.9

**Max:** 3

**Step:** 0.01

**Unit:** g/cm3

**Help:** Carbon about 1.76 to 1.80, E-glass about 2.54 to 2.60, aramid about 1.44.

#### Matrix density

**Key:** rm

**Type:** number

**Default:** 1.25

**Min:** 0.9

**Max:** 1.6

**Step:** 0.01

**Unit:** g/cm3

**Help:** Cured epoxy is typically 1.1 to 1.3.

#### Fiber modulus

**Key:** ef

**Type:** number

**Default:** 230

**Min:** 10

**Max:** 600

**Step:** 1

**Unit:** GPa

**Help:** Fiber tensile modulus from the fiber datasheet (T300 class about 230).

#### Matrix modulus

**Key:** em

**Type:** number

**Default:** 3.5

**Min:** 0.5

**Max:** 10

**Step:** 0.1

**Unit:** GPa

**Help:** Cured neat resin modulus, typically 2.7 to 4.1 GPa for epoxy.

#### Void content

**Key:** voids

**Type:** slider

**Default:** 1

**Min:** 0

**Max:** 8

**Step:** 0.1

**Unit:** % by volume

**Help:** From acid digestion, burn-off or ultrasonic correlation. Aerospace parts usually target under 2%.

**Outputs:**

#### Fiber weight fraction

**Key:** wfr

**Expr:** wf / 100

**Format:** decimal

#### Fiber volume fraction before voids

**Key:** vfi

**Expr:** (wfr / rf) / (wfr / rf + (1 - wfr) / rm)

**Format:** decimal

**Description:** Vf = (Wf/rho_f) / (Wf/rho_f + Wm/rho_m)

#### Fiber volume fraction (void adjusted)

**Key:** vf

**Expr:** vfi * (1 - voids / 100) * 100

**Format:** percent

**Primary:** true

**Description:** Voids displace both fiber and matrix, so Vf is scaled by one minus the void fraction.

#### Matrix volume fraction

**Key:** vm

**Expr:** (1 - vfi) * (1 - voids / 100) * 100

**Format:** percent

#### Composite density

**Key:** rhoc

**Expr:** (vf / 100) * rf + (vm / 100) * rm

**Format:** decimal

**Description:** g/cm3, voids contribute zero mass.

#### Longitudinal modulus E1 (rule of mixtures)

**Key:** e1

**Expr:** (vf / 100) * ef + (vm / 100) * em

**Format:** decimal

**Primary:** true

**Description:** GPa, upper bound for aligned continuous fiber loaded along the fiber.

#### Transverse modulus E2 (inverse rule)

**Key:** e2

**Expr:** ((vf + vm) / 100) / ((vf / 100) / ef + (vm / 100) / em)

**Format:** decimal

**Description:** GPa, a lower-bound estimate. Halpin-Tsai gives a more realistic value.

#### Specific longitudinal stiffness

**Key:** spec

**Expr:** e1 / rhoc

**Format:** decimal

**Description:** GPa per g/cm3, useful for comparing material systems by weight.

**Chart:**

#### E1 and E2 (GPa) versus fiber weight fraction

**Type:** line

**X:** wf

**From:** 35

**To:** 85

**Steps:** 26

**Series:**

- e1
- e2

**Disclaimer:** First-pass engineering estimate for continuous unidirectional fiber. It is not a design allowable. Use tested laminate properties for structural sign-off.

## Content

**Intro:** Fiber volume fraction (Vf) is the single most important process number in a composite part because stiffness, strength, density and cost per unit of performance all follow from it. This calculator converts the weight fraction you know from the prepreg datasheet or a burn-off test into volume fraction and then estimates density and ply-level modulus.

**Sections:**

#### How to use the calculator

**Body:** Start with the fiber weight fraction. For prepreg this is 100 minus the resin content on the datasheet, for example 65% for a 35% resin content material. Enter the fiber and matrix densities from the supplier datasheets, the fiber and neat resin moduli, and the void content measured by digestion or ultrasonic correlation. The primary results are the void-adjusted Vf and the longitudinal modulus E1. The sweep chart shows how E1 and E2 move as the fiber weight fraction changes, which is useful when judging how much resin bleed or squeeze-out a cure cycle can tolerate.

**Bullets:**

- Use measured density, not nominal, when you have it from a lot certificate.
- Enter void content as a volume percent, not weight percent.
- Change the matrix density to see why high-resin laminates are heavier per unit stiffness.

#### The formulas behind it

**Body:** Volume fraction from weight fraction is Vf = (Wf/rho_f) / (Wf/rho_f + Wm/rho_m), which is the same conversion described in ASTM D3171 for constituent content. The void-adjusted value multiplies by (1 - Vv). Composite density is the volume-weighted sum of fiber and matrix density. The rule of mixtures E1 = Vf*Ef + Vm*Em predicts stiffness along the fibers and is accurate to a few percent for aligned continuous fiber. The inverse rule E2 = 1 / (Vf/Ef + Vm/Em) treats fiber and matrix in series and under-predicts real transverse stiffness, so treat it as a lower bound.

#### Worked example

**Body:** A carbon/epoxy prepreg at 35% resin by weight, fiber density 1.78, resin density 1.25 and 1% voids gives about 56% Vf, a composite density near 1.54 g/cm3 and E1 near 130 GPa for a 230 GPa fiber. If the cure cycle bleeds off an extra 3 points of resin, the weight fraction rises to 68% and E1 rises roughly 6%, but the part also becomes drier and more void-prone at the surface. The chart makes that trade visible: stiffness grows almost linearly with Wf while transverse stiffness barely moves.

#### Common mistakes

**Body:** The most frequent error is mixing resin content on a prepreg basis with fiber areal weight on a cured-laminate basis. Another is using dry fiber density for a sized or coated fiber without checking the datasheet. Voids are often ignored, yet a 3% void content cuts Vf by 3% of itself and can reduce interlaminar shear strength far more than this stiffness model shows. Finally, E2 and shear are matrix dominated, so never use this calculator for matrix-driven failure modes or for woven fabrics without a fabric architecture correction.

**Cta:** If constituent test results and lot certificates live in your ERP or quality system, Netray can pull them into a lot-level Vf and density report automatically, on-premises if you need it.

**Faq:**

#### What is a good fiber volume fraction for carbon fiber prepreg?

**Answer:** Autoclave-cured aerospace carbon/epoxy laminates typically land between 55% and 62% Vf. Out-of-autoclave prepreg is often 52% to 58%, and wet layup or infusion parts are usually 40% to 55%. Your material specification and qualification data set the actual acceptance window.

#### Does the rule of mixtures work for woven fabric?

**Answer:** Only as a rough guide. Fabric has crimp and fibers in two directions, so you must apply the fraction of fiber in the loaded direction and a knockdown for crimp. For woven laminates use supplier data or classical laminate theory with tested ply properties.

#### How is fiber volume fraction measured in practice?

**Answer:** Common methods are matrix digestion in acid (ASTM D3171 procedure B), matrix burn-off for glass (procedure G), and image analysis of polished sections. Digestion or burn-off gives weight fractions, which you convert to volume fraction with this calculator.

#### Why does adding voids lower the fiber volume fraction?

**Answer:** Voids occupy space but contain no fiber or matrix, so for a fixed volume the share taken by fiber falls by the void fraction. Mechanical properties drop faster than this because voids also act as stress concentrators and weaken the matrix-dominated properties.

## Search terms

fiber volume fraction calculator, rule of mixtures calculator composites, fiber weight fraction to volume fraction, composite density calculator, carbon epoxy modulus estimate, void content fiber volume fraction, composite E1 E2 rule of mixtures, resin content to fiber volume

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