MAT-44

Rule of mixtures

Isostrain composite modulus.

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GoverningRule of mixtures

Governing equation

E=E_f V_f+E_m(1-V_f)

where

Ef: Ef (GPa)
Em: Em (GPa)
Vf: Vf (—)
E: Rule of mixtures (GPa)

Lecture brief

Historical brief

Hooke (1678), Hall–Petch grain size, Arrhenius activation and Paris fatigue-crack growth are the spine of materials selection. The sheets relate stress, microstructure and life. This sheet (MAT-44 — Rule of mixtures) is the form associated with Rule of mixtures. Working symbols: $Ef$ , $Em$ , $Vf$ $\rightarrow$ $E$ . Isostrain composite modulus. Pedagogical SI sheet with a live model and a swept parameter.

Purpose

Purpose: compute

E

from

Ef

Em

Vf

in Materials via

E=E_f V_f+E_m(1-V_f)

Isostrain composite modulus. Use it when a real materials question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

Ef = 230.000\,\mathrm{GPa}

Em = 3.500\,\mathrm{GPa}

Vf = 0.500\,\mathrm{—}

, the governing relation

E=E_f V_f+E_m(1-V_f)

yields

E = 116.750\,\mathrm{GPa}

. One governing identity, SI units, a single sweep on the sheet. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Ef Ef230 GPaEm Em3.5 GPaVf Vf0.5 —

Outputs

Rule of mixtures E116.750 GPa

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Narration of this film

One governing identity, SI units, a single sweep on the sheet.

Isostrain composite modulus. Pedagogical SI sheet with a live model and a swept parameter.

Reading speed

Watch on YouTube