Chapter 17, Problem 17.28P

Interpretation Introduction

Interpretation:

The modulus of elasticity and tensile strength parallel to fibers should be calculated.

Concept introduction:

Rules of mixtures for particulate composites is:

  $\begin{array}{l}{\rho }_c={\displaystyle \sum \left(f_i{\rho }_i\right)}\text{for}\left\{\text{i}\text{=}\text{1}\mathrm{..........}\text{n}\right\}\\ {\rho }_c=f_1{\rho }_1+f_2{\rho }_2\mathrm{...................}{f}_n{\rho }_n\end{array}$

Where

  ${\rho }_c=$ density of composite

  $f_i=$ volume fraction of i component

  ${\rho }_i=$ density of i component

Volume fraction is defined as

  $\begin{array}{l}f=\frac{V_1}{V_1+V_2}\\ f=\text{volume}\text{fraction}\\ V_1=\text{volume}\text{of}\text{first}\text{component}\\ V_2=\text{volume}\text{of}\text{second}\text{component}\end{array}$

Modulus of elasticity is defined as the ratio of shear stress to shear strain.

Relation for modulus of elasticity is given as:

  $E_C=f_f{E}_f+f_{Al}{E}_{Al}$

  $f_f{E}_f$ are the volume fraction and modulus of elasticity for borsic fiber.

  $f_{Al}{E}_{Al}$ are the volume fraction and modulus of elasticity for aluminum.

Tensile strength is defined as the ratio of force per unit area.

Relation for tensile strength parallel to fiber is given as,

  $T{S}_f=f_{f}T{S}_f+f_{Al}T{S}_{fAl}$

  $f_{f}T{S}_f$ are the volume fraction and tensile strength of fiber.

  $f_{Al}T{S}_{fAl}$ are the volume fraction and tensile strength of aluminum fiber.