Chapter 17, Problem 17.32P

Interpretation Introduction

Interpretation:

The value of stress acting on each given fiber should be calculated.

Concept introduction:

Stress is defined as the ratio of force per unit area given by relation:

  $\text{Stress = }\frac{\text{Force}}{\text{Area}}$

The relationship of modulus of elasticity with fractions of composites if the materials have strong bonding the relationship is given as:

  $\begin{array}{l}\left(\frac{{\text{σ}}_m}{{\text{σ}}_{\text{f}}}\right)=\left(\frac{E_m}{E_{\text{f}}}\right)\\ \text{f}\text{=}\frac{{\text{A}}_{\text{f}}}{{\text{A}}_{\text{f}}\text{+}\left(\frac{E_m}{E_{\text{f}}}\right){\text{A}}_m}\end{array}$

f is the fraction of component

A_fis the area of fiber.

A_m is the area of matrix.

E_m is the modulus of elasticity for matrix.

E_f is the modulus of elasticity of fiber.