How to Calculate Thermal Expansion Coefficient Without Overall Density?

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SUMMARY

To calculate the thermal expansion coefficient (α) of a composite material without knowing its overall density, one must first determine the volume fractions of the individual components, which are the fibers and the matrix. If the mass fractions of the materials are known, they can be used to derive the composite density, allowing for the calculation of volume fractions. Turner’s Formula can then be applied to find the thermal expansion coefficient using the established volume fractions and the individual thermal expansion coefficients of the materials.

PREREQUISITES
  • Understanding of composite materials and their properties
  • Knowledge of Young's modulus and its significance in material science
  • Familiarity with thermal expansion coefficients and their calculation
  • Ability to work with mass fractions and volume fractions in composites
NEXT STEPS
  • Research how to calculate composite density from mass fractions
  • Study Turner’s Formula for thermal expansion coefficient calculations
  • Explore methods for determining volume fractions in composite materials
  • Learn about the relationship between Young's modulus and thermal expansion in composites
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Material scientists, engineers working with composite materials, and researchers focused on thermal properties of materials will benefit from this discussion.

ravenscroft
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I need a question answered. If given the density of 2 materials in a composite, the fibres & the matrix, but not the over all density of the composite, how can one go about finding the thermal expansion coefficient, alpha of the composite? I have Youngs modulus, density of each individual material, & α's of each material. I can use Turners Formula when i have have the volume fraction, but can I get those (the volume fractions) without the overall density of the composite?
Thanks for any help or insight.
 
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ravenscroft said:
I need a question answered. If given the density of 2 materials in a composite, the fibres & the matrix, but not the over all density of the composite, how can one go about finding the thermal expansion coefficient, alpha of the composite? I have Youngs modulus, density of each individual material, & α's of each material. I can use Turners Formula when i have have the volume fraction, but can I get those (the volume fractions) without the overall density of the composite?
Thanks for any help or insight.
You obviously can't do it if you don't know the volume fraction, and, as you said, you can't get that unless you know the density of the composite. By any chance, do you have some idea of the layout of the materials in the cross section, or the proportions of the materials that were combined to make the composite (i.e., the mass fractions of the materials)? If you know the mass fractions, then you know the composite density and the volume fractions.

Chet
 

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