Fig. $2$ Cross$-$section view

Use Equations $1$ to $9$ in the paper to calculate the elastic modulus in three directions $(E_x,E_y,E_z)$ of the

sample in Fig. $2.$

All the elastic constants that will be used are summarized in the table below.

Hints:

According to the lecture notes, the volume fractions of solid, infill and carbon fibers in Equation

$9$ can be simplified as the area fractions of each part in Fig. $2.$

Since the directions of carbon fibers are all $0($longitudinal direction$),$ Equation $9$ can be

simplified as $[K_{\text{a}\text{v}\text{e}}]=V_{\text{i}\text{n}\text{f}\text{i}\text{l}\text{l}}[K_{\text{i}\text{n}\text{f}\text{i}\text{l}\text{l}}]+V_{\text{s}\text{o}\text{l}\text{i}\text{d}}[K_{\text{s}\text{o}\text{l}\text{i}\text{d}}]+V_{CF}[K_{CF}]$Download the paper entitled "Tensile and Flexural Behaviors of Additively Manufactured

Continuous Carbon Fiber$-$Reinforced Polymer Composites" from webcourses under

Files$->$Homework$->$HW$2$

Read the paper and learn how to estimate the elastic modulus of fiber$-$reinforced polymer composites

using the stiffness averaging method.

Implement the stiffness averaging method using a programming language such as MATLAB or

MATHCAD.

Submit a report in word or PDF format on webcourses. In this report, please document how the elastic

modulus is estimated. The report should include:

a$.$ Code

b$.$ Stiffness and compliance matrices of

i$.$ Solid section

ii$.$ Infill section

iii. Carbon fiber section

iv$.$ Total composite structure based on the stiffness averaging method

c$.$ Volume fractions

i$.$ Solid section

ii$.$ Infill section

iii. Carbon fiber section

d$.$ Elastic moduli in $x,y,z$ directions

Problem description:

The dimension of the specimen is shown in Fig. $1.$ The cross$-$section view of the specimen is shown in Fig.

It is simplified from Fig. $2($b$)$ in the original paper. The solid layers are represented with dark grey and

consist of Onyx with $10\%$ porosity density. The infill layers are represented with light grey and consist of

Onyx with $50\%$ porosity density. There are $10$ layers of solid on top and bottom and $8$ layers of infill in the

middle so that a sandwich structure is formed. Layer height is $0\mathrm{.}125$ mm for both solid and infill. Carbon

fibers are embedded in the solid layers in the form of concentric rings. The diameter of carbon fibers is $0\mathrm{.}35$

mm $.$ Fig. $2$ shows the cross$-$section view of two concentric fiber rings on both top and bottom.