The mechanical properties of cobalt may be improved by...

The mechanical properties of cobalt may be improved by incorporating fine particles of tungsten carbide (WC). Given that the moduli of elasticity of these materials are, respectively, $200 \mathrm{GPa}\left(30 \times 10^{6} \mathrm{psi}\right)$ and $700 \mathrm{GPa}$. $\left(102 \times 10^{6} \mathrm{psi}\right),$ plot modulus of elasticity versus the volume percent of WC in Co from 0 to 100 vol\%, using both upper- and lowerbound expressions.

The mechanical properties of cobalt may be improved by incorporating fine particles of tungsten carbide (WC). Given that the moduli of elasticity of these materials are, respectively, $200 \mathrm{GPa}\left(30 \times 10^{6} \mathrm{psi}\right)$ and $700 \mathrm{GPa}$.
$\left(102 \times 10^{6} \mathrm{psi}\right),$ plot modulus of elasticity versus the volume percent of WC in Co from 0 to 100 vol\%, using both upper- and lowerbound expressions.

Key Concepts

Modulus of Elasticity

The modulus of elasticity is a measure of a material’s resistance to elastic deformation under load. It is a critical mechanical property used to assess and compare the stiffness of different materials, reflecting how a material will deform under applied stress.

Composite Materials

Composite materials are engineered by combining two or more constituent materials to achieve properties that are superior to or different from those of the individual components. The behavior of the composite depends on the properties of the constituents as well as their distribution and interaction within the material.

Volume Fraction

The volume fraction represents the proportion of one constituent's volume relative to the total volume in a composite. It is a key parameter in determining the overall properties of a composite material, as it dictates how much each component contributes to the composite’s performance.

Rule of Mixtures (Voigt Upper Bound)

The rule of mixtures, often referred to as the Voigt model for the upper bound, assumes that the strain is uniform throughout the composite. This model gives an upper limit estimate for the composite modulus by taking a linear combination of the moduli of the individual constituents according to their volume fractions.

Inverse Rule of Mixtures (Reuss Lower Bound)

The inverse rule of mixtures, associated with the Reuss model for the lower bound, assumes that the stress is uniformly distributed across the composite. This approach estimates a lower bound for the composite’s modulus by taking the reciprocal of the volume-fraction-weighted sum of the reciprocals of the individual moduli.

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