Chapter 17, Problem 17.55P

Interpretation Introduction

Interpretation:

Modulus of elasticity of composite for parallel and perpendicular condition should be determined.

Concept introduction:

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

Relation for modulus of elasticity is given as:

  $E_C=f_{glass}{E}_{glass}+f_{polymer}{E}_{polymer}$

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

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

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

Relation for modulus of elasticity perpendicular to fiber is given as:

  $\frac{1}{E_C}=\frac{f_{glass}}{E_{glass}}+\frac{f_{polymer}}{E_{polymer}}$

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

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

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