report term project

7/31/2019 Report Term Project

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WING SPAR IN CARBON/EPOXY

Subject: Mechanics of Composite

Submitted to: DR. S. KAMRAN AFAQ

Submitted by: IMRAN SAJID SHAHID

ROLL NO: 12SP-MS-ME-002

Deaprtment of Mechanical Engineering

HITECH University Taxila



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Problem Statement:

Consider an airplane with the internal structure (excluding facings) shown

schematically in the following figure. It consists of a spar and several ribs. The spar is a

lmaniate of carbon/epoxy fabric with Vf=45% fiber volume fraction, the composition of

which varies with longitudinal coordinate x-axis in the flange and in the web. Apreliminary calculation of the flap in isostatic equilibrium reveals the maximum stress

resultant in the zones of the spar indicated in the figure. One proposes for each of these

zones of the composition indicated in the figure below.

1. Evaluate the elastic properties of the laminate in these two zones.

2. Verify the two corresponding laminates at rupture strength.

Thickness of layer of fabric is 0.24mm and Properties of carbon/epoxy fabric are;

EL [MPa] 54000

ET [MPa] 54000

GLT [MPa] 4000

LT 0.045

+Xt [MPa] 420

-Xt [MPa] 360

+Yt [MPa] 420

-Yt [MPa] 360

S [MPa] 55

[kg/m3] 1450



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GLOBAL STRAINS AND PLY STRESSES:

Global Strain can be calculated as:

{0} xy = [Sbar]avg

}xy

Since,

0

x= Nx / (N.L.* 0.24mm)

{0}xy Matrix becomes:

[-202 ; 0.0 ; 0.0 ]

Calculate {s}xy in each ply 00

and 450

plies:

{}xy = [Qbar] {0} xy

Transformed {s}xy in orthotropic axes of ply, by using:

{}LT = [T] {0}xy

Where,

[T] = Transformation Matrix



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MATLAB Results are:

RUPTURE STRENGTH:

Using Hill-Tasi Failure criterion for both layers

Factor of Safety for both plies can be calculated by :

Ply with lowest Safety Factor will FAIL first.



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MATLAB Results are:

2 ZONE-2:

ELASTIC MODULII CALCUALTION:



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GLOBAL STRAINS AND PLY STRESSES:

RUPTURE STRENGTH:

MATLAB PROGRAMM FOR ELASTIC MODULII & RUPTURE STRENGTH:

First part will do calculations for flanges:

!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>



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clc

clear all

% Term Project Carbon/Epoxy Flap Spar design

% --------------------INPUT DECK-------------------------------

Nx = -435; % Applied Force in x-dir

Nxy = -30 % Applied Force in xy-dir

deg0_ply=67; % Layers percentage in 0degree


degpplus45_ply=33; % Layers percentage in 45degree

degminus45_ply=0; % Layers percentage in -45degree

% Material Properties and Strengths

E_L = 54000; E_T=54000; G_LT=4000; v_LT=0.045; V_f=45/100;

X_t = 420;

Y_t = 420;

X_c = 360;

Y_c = 360;

S_tc = 55;

e = 0.24; % Thickness of single bidirectional Carbon/Epoxy ply

NL_F = 9; % Number of Layers in Flange

NL_W = 5; % Number of Layers in Web

%--------------------------------------------------------------------------------------------------------------------------------------

S = C_M( E_L,E_T,G_LT,v_LT ); % Compliance Matrix

Q = inv(S); % Rigidity Matrix

Q_avg=(Qbar(Q,0)*deg0_ply/100)+(Qbar(Q,90)*deg90_ply/100)+ ...

(Qbar(Q,45)*degpplus45_ply/100)+(Qbar(Q,-45)*degminus45_ply/100);

S_avg = inv(Q_avg);

Ex=1/S_avg(1,1); % Global Modulii Properties

Ey=1/S_avg(2,2);

Gxy=1/S_avg(3,3);



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vxy=-1*(S_avg(1,2)/S_avg(1,1));

vyx=-1*(S_avg(1,2)/S_avg(2,2));

disp('[Qbar]avg Matrix =')

disp(Q_avg)

disp('[Sbar]avg Matrix =')

disp(S_avg)

disp('Longitudinal Young Modulus of Laminate =')

disp(Ex)

disp('Transverse Young Modulus of Laminate =')

disp(Ey)

disp('Shear Modulus of Laminate =')

disp(Gxy)

disp('Major Poissons ratio =')

disp(vxy)

disp('Minor Poissons ratio =')

disp(vyx)

%

h_F = e * NL_F; % height of a laminate

sigma_oxy_F = [Nx/h_F; 0; 0]; % Global Stresses in xy

epsilon_oxy_F = S_avg * sigma_oxy_F; % Global Strains in xy

sigma_xy_090_F = Qbar(Q,0) * epsilon_oxy_F; % Ply stresses in 0/90 deg layers in xy dir

sigma_LT_090_F = TransformationMatrix(0) * sigma_xy_090_F; % Ply stresses in 0/90 deg layers in LT(material) dir

sigma_xy_45_F = Qbar(Q,45) * epsilon_oxy_F; % Ply stresses in 45 deg layers in xy dir

sigma_LT_45_F = TransformationMatrix(45) * sigma_xy_45_F; % Ply stresses in 45 deg layers in LT(material) dir

% Hill-Tasi Failure Criterion for 0/90 plies

HT_090_F = (sigma_LT_090_F(1,1)/X_c)^2+(sigma_LT_090_F(2,1)/Y_t)^2- ...

(sigma_LT_090_F(1,1)*sigma_LT_090_F(2,1)/X_c^2)+ ...

(sigma_LT_090_F(3,1)/S_tc)^2;

FOS_090_F = (( 1/(HT_090_F)) - 1) *100;



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!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

Second part will do calculations for Web:

!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

clc

clear all

% Term Project Carbon/Epoxy Flap Spar design

% --------------------INPUT DECK-------------------------------

Nx = -435; % Applied Force in x-dir

Nxy = -30 % Applied Force in xy-dir



degpplus45_ply=60; % Layers percentage in 45degree

degminus45_ply=0; % Layers percentage in -45degree

% Material Properties and Strengths

E_L = 54000; E_T=54000; G_LT=4000; v_LT=0.045; V_f=45/100;

X_t = 420;

Y_t = 420;

X_c = 360;

Y_c = 360;

S_tc = 55;

e = 0.24; % Thickness of single bidirectional Carbon/Epoxy ply

NL_F = 9; % Number of Layers in Flange

NL_W = 5; % Number of Layers in Web

%--------------------------------------------------------------

S = C_M( E_L,E_T,G_LT,v_LT ); % Compliance Matrix

Q = inv(S); % Rigidity Matrix



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Q_avg=(Qbar(Q,0)*deg0_ply/100)+(Qbar(Q,90)*deg90_ply/100)+ ...

(Qbar(Q,45)*degpplus45_ply/100)+(Qbar(Q,-45)*degminus45_ply/100);

S_avg = inv(Q_avg);

Ex=1/S_avg(1,1); % Global Modulii Properties

Ey=1/S_avg(2,2);

Gxy=1/S_avg(3,3);

vxy=-1*(S_avg(1,2)/S_avg(1,1));

vyx=-1*(S_avg(1,2)/S_avg(2,2));

disp('[Qbar]avg Matrix =')

disp(Q_avg)

disp('[Sbar]avg Matrix =')

disp(S_avg)

disp('Longitudinal Young Modulus of Laminate =')

disp(Ex)

disp('Transverse Young Modulus of Laminate =')

disp(Ey)

disp('Shear Modulus of Laminate =')

disp(Gxy)

disp('Major Poissons ratio =')

disp(vxy)

disp('Minor Poissons ratio =')

disp(vyx)

%

h_W = e * NL_W; % height of a laminate

sigma_oxy_W = [0; 0; Nxy/h_W]; % Global Stresses in xy

epsilon_oxy_W = S_avg * sigma_oxy_W; % Global Strains in xy



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sigma_xy_090_W = Qbar(Q,0) * epsilon_oxy_W; % Ply stresses in 0/90 deg layers in xy dir

sigma_LT_090_W = TransformationMatrix(0) * sigma_xy_090_W; % Ply stresses in 0/90 deg layers in

LT(material) dir

sigma_xy_45_W = Qbar(Q,45) * epsilon_oxy_W; % Ply stresses in 45 deg layers in xy dir

sigma_LT_45_W = TransformationMatrix(45) * sigma_xy_45_W; % Ply stresses in 45 deg layers in

LT(material) dir

% Hill-Tasi Failure Criterion for 0/90 plies

HT_090_W = (sigma_LT_090_W(1,1)/X_c)^2+(sigma_LT_090_W(2,1)/Y_t)^2- ...

(sigma_LT_090_W(1,1)*sigma_LT_090_W(2,1)/X_c^2)+ ...

(sigma_LT_090_W(3,1)/S_tc)^2;

FOS_090_W = (( 1/(HT_090_W)) - 1)*100;

!>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>

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