This model uses continuum methods to predict the upper and lower bounds in performance expected from a composite. The unidirectional (UD) model represents the upper bound; the particulate model, the lower bound; and the quasi-isotropic (QI) model, the performance mid-way between the upper and lower bound. As a result, this model should be considered as a scoping tool to identify potential composite compositions, which could exhibit unique combinations of properties. It is not intended to be used as a detailed laminate analysis tool.
The anisotropic structure of continuous fiber reinforced composites can lead to significant differences in properties in the in-plane and through-thickness directions. In all cases the values quoted on the datasheet for the synthesized record represent the performance parallel to the principal reinforcement direction. For example, the properties quoted for a unidirectional fiber reinforced composite reflect the performance that is expected when the applied load is parallel to the fiber direction.
In determining the calculations for the composites (simple bounds) model, the following assumptions have been made:
The composite material is fully dense (i.e. contains no porosity).
The orientation and distribution of reinforcement within the matrix is perfect (i.e. no misalignment of fibers and uniform distribution of fibers and particulates).
Good fiber-matrix interfacial bonding is achieved (i.e. no tendency for delamination).
The scale of the reinforcement is large compared to that of the atom, molecule size, and the dislocation spacing (this allows the use of continuum methods).
The fibers have a high degree of alignment for the unidirectional model
There is perfect orientation of fibers in the Aligned model and completely random orientation of fibers in the Random model.
The random model represents a 2-D short fiber mat.
The shear strength of the interface can be approximated by that of the matrix, which in turn can be approximated as such:
The calculations that are used for the properties in the other composites models that do not depend on reinforcement geometry are also applicable to short fiber composites.
Properties are quoted in the fiber direction for the aligned fiber composite.
All the fibers present have the same aspect ratio.
Price and eco properties are simple rule of mixtures, they only take into account the constituent materials (no processing).
The equations used by the unidirectional fiber reinforced composite model are summarized below. For more information on the derivation of these equations see derivation of calculations.
For a definition of the symbols used, see symbols.
Density
Price
Young's modulus (parallel to fibers)
Flexural modulus (bending with axis normal to fibers)
Shear modulus (shear parallel to fibers)
Bulk modulus
Poisson's ratio
Yield strength (parallel to fibers)
Compression strength (parallel to fibers)
Flexural strength
Tensile strength
Thermal conductivity (parallel to fibers)
Thermal expansion (transverse to fibers)
Specific heat capacity
Electrical resistivity (parallel to fibers)
Dielectric constant
Dielectric loss tangent
Embodied energy (primary production)
CO2 footprint (primary production)
The equations used by the quasi-isotropic fiber reinforced composite model are summarized below. For more information on the derivation of these equations see derivation of calculations.
For a definition of the symbols used, see symbols.
Density
Price
Young's modulus
Flexural modulus
Shear modulus
Bulk modulus
Poisson's ratio
Yield strength
Compression strength
Flexural strength
Tensile strength
Thermal conductivity
Thermal expansion
Specific heat capacity
Electrical resistivity
Dielectric constant
Dielectric loss tangent
Embodied energy (primary production)
CO2 footprint (primary production)
The equations used by the particulate reinforced composite model are summarized below. For more information on the derivation of these equations see derivation of calculations.
For a definition of the symbols used, see symbols.
Density
Price
Young's modulus
Flexural modulus
Shear modulus
Bulk modulus
Poisson's ratio
Yield strength
Compressive strength
Flexural strength
Tensile strength
Thermal conductivity
Thermal expansion
Specific heat capacity
Electrical resistivity
Dielectric constant
Dielectric loss tangent
Embodied energy (primary production)
CO2 footprint (primary production)
The equations used by the short fiber reinforced composite model are summarized below.
For a definition of the symbols used in Composites (simple bounds) models, see symbols.
Density
Price
Young's modulus
where
Flexural modulus
Yield strength
Thermal conductivity
where
Thermal expansion
Specific heat capacity
Electrical resistivity
where
Dielectric constant
Dissipation factor
Embodied energy (primary production)
CO2 footprint (primary production)
Density
Price
Young's modulus
where
and
Flexural modulus
Yield strength
Thermal conductivity
where
and
Thermal expansion
Specific heat capacity
Electrical resistivity
where
Dielectric constant
Dissipation factor
Embodied energy (primary production)
CO2 footprint (primary production)
(* = Particulate model only, ** = Unidirectional and quasi-isotropic models only)
Calculated Property | Reinforcement properties required by calculation | Matrix properties required by calculation |
---|---|---|
Density | Density | Density |
Young's modulus | Young's modulus | Young's modulus |
Flexural modulus | Young's modulus | Young's modulus |
Shear modulus | Shear modulus | Shear modulus |
Bulk modulus | Bulk modulus | Bulk modulus |
Poisson's ratio | Poisson's ratio | Poisson's ratio |
Yield strength | Yield strength Young's modulus* |
Yield strength Young's modulus* |
Tensile strength | Tensile strength Young's modulus* |
Tensile strength Young's modulus* |
Compressive strength | Compressive
strength Young's modulus* |
Compressive
strength Yield strength Young's modulus* |
Flexural strength | Yield strength** Compressive strength** Flexural strength* Young's modulus* |
Yield strength** Compressive strength** Flexural strength* Young's modulus* |
Specific heat capacity | Specific heat
capacity Density |
Specific heat
capacity Density |
Thermal expansion coefficient | Thermal expansion
coefficient Young's modulus |
Thermal expansion
coefficient Young's modulus |
Thermal conductivity | Thermal conductivity | Thermal conductivity |
Electrical resistivity | Electrical resistivity | Electrical resistivity |
Dielectric constant | Dielectric constant | Dielectric constant |
Dielectric loss tangent | Dielectric loss tangent | Dielectric loss tangent |
Embodied energy | Embodied energy Density |
Embodied energy Density |
CO2 footprint | CO2 footprint Density |
CO2 footprint Density |
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