Journal Publication

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 10, Number 15 (2015) pp 35825-35831
© Research India Publications. http://www.ripublication.com
35825
Strength Prediction of Composite T-Joints With and Without Cut-outs
Veerandra Chakkaravarthy Aa
, Nikhil krishnana
, M.Nivethaa
, Vinu Ra
, V.Sivakumara,
a
Department of Aerospace Engineering, Amrita Vishwa Vidyapeetham, Amritanagar P.O, Coimbatore 641112, India.
v_sivakumar@cb.amrita.edu
Abstract- Composite materials are widely used in the aircraft
industry. The spars and ribs in aircraft wings attached to the skin
form a T-joint. The objective of this project is to analyse the
differences in the structural properties of composite T-joints with
and without cut-outs, and thus optimize a cut-out configuration
that gives the best structural properties. A composite T-joint was
modelled with standard dimensions using T-300/Carbon epoxy
Prepreg as the material. The model was subjected to pulling, shear
and bending loads. Finite element analysis and Tsai-Hill failure
analysis were done on the model. Maintaining a constant area,
different cut-out configurations were modelled on the T-joint and
analysed just as the model without cut-out. The results obtained
for all the models were tabulated, and the structural integrity of
the models was compared using the Tsai-Hill failure criteria. The
best cut-out configuration was identified based on the results
obtained.
Keywords: T-Joint, cut-out shape, Finite element analysis,
composite, Tsai-Hill failure criteria.
List of symbols
X (Xt or Normal strength (tensile or compressive
Xc ) respectively) of lamina in fiber direction-1
Y (Yt or Normal strength (tensile or compressive
Yc ) respectively) of lamina in transverse to the
fiber direction-1
Z (Zt or Normal strength (tensile or compressive
Zc ) respectively) of lamina in principal
material direction-3, i.e., perpendicular to
plane of lamina
R,S and Shear strengths of lamina in planes 2-3,
T 1-3 and 1-2 respectively
σ1, σ2 and Normal stress components in principal
σ3 material directions 1, 2 and 3, respectively
(the subscript 1 referring to the fiber
direction)
τ1, τ2 and Shear stress components in principal
τ3 material directions 1, 2 and 3, respectively
(the subscript 1 referring to the fiber
direction)
Introduction
Composites materials are made by the combination of chemically
distinct materials. Composites possess superior properties over
the individual constituent materials. A unique advantage of using
composites over other materials is the ability to use multiple
combinations of resins and reinforcements in different
orientations which enables custom tailoring of physical and
chemical properties of a structure. Another major advantage of
using composites is due to its low density, it possesses a
higher specific strength compared to conventional materials.
The flexibility during designing and manufacturing processes
and the structural superiority over conventional materials
have caused a huge rise in the amount of composite materials
used in many engineering industries.
T-joints play an important role in structural applications in
multiple branches of the engineering industry. Numerous
methods have been developed to improve the strength of T-
joints. One such method is to add additional stiffeners to the
weaker regions of T-joints. Such method has been
extensively studied by Vijayaraju et al. [1]. Spars and Ribs
that are attached to the skins of aircraft wings forms T-joints.
In most of the aircrafts, fuel is stored in their wings. Hence
cut-outs have to be made on the ribs to facilitate for fuel tank.
Extensive studies have been done on the effect of cut-outs on
the structure by Sivakumar et al. [2] and Morishima et al. [4].
The former have optimized a cut-out configuration that gave
the best performance by comparing different configurations
using failure criteria. The T-joints in aircrafts are subjected to
complex loading system. Stickler et al. [3] performed FEA on
composite T-joints with transverse stitching, subjected to
transverse, shear and bending loads. Modelling of T-joint is
essential and due consideration has to be given to the various
parameters of the T-joint. The effects of these parameters on
the T-joint have been studied by Li et al. [5] and Silvaa et al.
[6].
In this paper, a composite T-joint was modelled with
dimensions obtained from K.Vijayaraju, P.D.Mangalgiri,
B.Dattaguru’s work [1]. The material used as composite plies
was carbon T-300. The material used as adhesive was an
epoxy resin. The properties of these materials were obtained
from V.Sivakumar’s work [2]. Fixed boundary constraint was
applied on the skin on both sides of the T-joint. Pulling loads,
shear loads and bending loads were applied on the webs of
the T-joints. In order to find the strength parameters of the
model, structural analysis and failure analysis were done on
the model. Tsai-Hill failure criterion was used to study the
structural integrity of the model. The stress distribution over
the model was analysed. Different cut-out profiles were
incorporated on the web of the base model. Failure analysis
and structural analysis were done on each model. The stress
distribution was analysed for all models and the Tsai-Hill
failure index values obtained from the failure analysis were
used to compare the strengths of all the models, under all
loading conditions. For each loading condition, the cut-out
which gave the best result were identified. Considering the
performance of all the models under all three loading
conditions, a model was chosen which had the best cut-out
profile.

35826
The results obtained would help in deciding the quantity of
material that can be saved during the manufacturing of spars for
aircraft wings. As the results obtained were for composite T-
joints, they would help in choosing the right material for making
composite T-joints in aircraft wings. Perhaps additional work that
could have been done for the project was to understand the
performance of the composite T-joint models subjected to all the
loading conditions simultaneously. These results would be useful
since aircraft wings are subjected to all the applied loading
conditions during flight. In the present work a numerical analysis
for various shapes of the cut-out on the web of the T-joint model
was carried out to study the structural behaviour of the model.
Geometric Modelling
The composite T-joint was modelled with dimensions obtained
from the progressive failure of T-Stiffened Skins [1]. This
configuration consists of a T-stiffener bonded with a skin of 2.7
mm thickness. The web of the model was a symmetric composite
layup with adhesive layer in middle and 8 plies on its either side.
It was 2.5 mm thick. The thickness of the flanges was reduced in
successive steps of 2 plies four times. The ends of each pair
flange plies were separated by 3mm. Two adhesive layers connect
the stiffener plies with the skin on both sides of the T-joint and
also both stiffener sets of the web as shown in Fig. 1. The depth
of the T-joint which was a dimension perpendicular to the plane
of the paper was 100 mm as shown in Fig. 2.
Fig.1 Schematic illustration of the cross section of the T-joint
specimens.
FE Formulation
The finite element analysis software package Abaqus_v6.10 was
used for processing and analyzing these models. The analysis was
done using solid 8-node isoparametric elements (C3D8R)[8]. All
the six stress components were obtained for all the elements. As
the in-plane and inter-laminar stresses are bound to peak near the
periphery of the cut-out and the stiffener curve, the meshing done
for these regions should be very fine. Five models having
different cut-out shapes were modelled.
Fig.2 Isometric view of Base T-joint model
Failure Model
As these finite element models were three dimensional
composite structures, the Tsai-Hill failure criterion was
applied to analyze their structural behaviour under the
application of load [2].
σ1
2
+ σ2
2
+ σ3
2
+ τ23
2
+ τ13
2
+ τ12
2
– + – ] σ1σ2 – + – ] σ1σ3
– + – ] σ2σ3 1 (1)
After the analysis, six stress components were extracted for
all elements in the model. Substituting these stress values in
the Eq.1 the Tsai-Hill failure indices value were obtained for
all the elements. These Tsai-Hill failure index values were
used to compare the strength of different models.
Material Property
The properties of T300/carbon epoxy Prepreg [2] were used
for analysis. The mechanical and strength limits are provided
in the Tables 1 and 2
Table1 Mechanical Properties of T300/Carbon epoxy
Mechanical properties Values
Young’s Modulus, E1 132.58GPa
Young’s Modulus, E1=E2 10.8GPa
Shear Modulus, G12=G13 5.7GPa
Shear Modulus, G23 3.4GPa
Poisson’s Ratio, ʋ12 = ʋ13 0.24
Poisson’s Ratio, ʋ23 0.49

35827
Table 2 Strength Properties of T300/Carbon epoxy
Strength properties Values, MPa
X 1520
Y=Z 43.8
R 67.6
S=T 89.9
Stiffener Layup
The thickness of each lamina is 0.15mm. A total of 8 layers were
stacked to obtain the stiffener thickness of 1.2mm. The stacking
sequence used in the analysis was same as that used in the
composite manufacturing industry. The stacking sequence used
was as follows: [45/-45/0/45/0/-45/0/90].
Skin Layup
The thickness of each lamina is 0.3mm. A total of 9 layers were
stacked to obtain the stiffener thickness of 2.7mm. The stacking
sequence used in the analysis was same as that used in the
composite manufacturing industry. The stacking sequence used
was as follows: [45/-45/0/45/0/-45/0/90/0]. Keeping the cut-out
area constant at 314 mm2
, five T-joints were modelled with
different cut-out shapes on their web as shown in Fig.3. Of those,
three shapes were basic geometrical shape such as circle,
horizontal ellipse, and vertical ellipse. The square and diamond
shapes were filleted on their vertices. The dimensions of the cut-
outs are given in the Table 3.
(a) (b) (c)
(d) (e)
Fig. 3 Illustration of different cut-out shapes (a) Circle - Type I
(b) Horizontal ellipse - Type II (c) Vertical ellipse - Type III (d)
Square - Type IV (e) Diamond – Type V
Boundary and Loading Conditions
The skin was constrained for deflection in x, y and z directions at
the bottom surface of the T-joint for 7.25mm from the edge of the
skin on either side. Fig.3 shows the constraints applied on the
skin. Three types of load were applied on the T-joint.
Table 3 Dimensions of the cut-outs
Type
Cut-out
shapes
Parameter
Values,
mm
I Circle Radius 10
II Horizontal Semi-major axis 12.9
ellipse Semi-minor axis 7.75
III Vertical Semi-major axis 12.9
ellipse Semi-minor axis 7.75
IV Square Side 17.82
Fillet radius 2
V Diamond Diagonal 1 32.53
Diagonal 2 19.52
Fillet radius 2
Fig.3. Location of boundary constraints
i Transverse Pulling Load
A uniform transverse pulling load of 15.2 MPa was applied
on the loading surface (as shown in Fig.2) of the web in the
positive Y-direction.
ii Shear Load
A uniform shear load of 15.2 MPa was applied on the loading
surface (as shown in Fig.2) of the web in the negative Z-
direction.
iii Bending Load
A Bending load of 38N was applied on the loading surface of
the web in the negative X-direction as shown in Fig.4
Fig.4. Bending load applied for the base 'T' configuration

35828
Validation study
A composite T-joint of carbon T-300 as composite ply and epoxy
resin as the adhesive in Progressive Failure of T Stiffened Skins
[1] was modelled with a change in depth (as shown in Fig. 2) of
the model from 150mm [1] to 100mm. Transverse pulling load
was applied on the loading surface of the web. From the test data
of the study [1] it has been found that the failure load of the
structure was 4.561 kN and corresponding maximum deflection
of the T-joint was 4.5 mm in the positive Y-direction as shown in
Fig. 2. Since a force of 4.561kN was applied for the 150mm deep
structure, a proportional load of 3.041kN was applied for the
100mm deep finite element structure and numerical study was
carried out. From the results obtained it was found that the
maximum deflection of the T-joint was 4.615 mm as shown in
Fig. 5.
Fig.5 Finite element analysis of Base model for pulling load
The maximum deflection showed a variation of 2.56 %, which
made our results very similar to the results obtained in
Progressive Failure of T Stiffened Skins [1].
Stress discussion
The six stress values of all the elements were fed into Tsai-Hill
failure equation (Eq1) to find Tsai-Hill failure index value. These
values were generally high near the cut-out and the stiffener curve
locations as shown in Fig. 6 and 7.
Fig.6. Stress concentration observed at the cut-out proximity
Fig.7 Locations of stress concentration observed near
stiffener curve
Results and Discussions
Stress concentration and failure behaviour of all the five
models were studied for all the three loading conditions. The
strength of the models with different cut-out configurations
were compared using the Tsai-Hill failure criterion. The
observations made for each loading condition are given
below.
i. Transverse Pulling Load
A uniform transverse pulling load of 15.2 MPa was applied
on the loading surface of the web. The Tsai-Hill failure index
values of all five models were shown in Fig. 8 and 9. From
the Fig. 8 it has been seen that the Type-I cut-out model has
the Tsai-Hill failure index value of 1.2580 and thus failing
for the applied load. Type-II cut-out model has the Tsai-Hill
failure index value of 2.2514 which is the highest among the
Fig.8. Tsai-Hill failure index value at cut-out proximity for
transverse pulling load
0
0.5
1
1.5
2
2.5
Tail-Hillfailureindex
Cut-outshapes
Tsai-Hillfailure index value at cut-out
proximity forTransvere Pulling load
stress concentration
stress concentration

35829
five models and thus it is the least desirable cut-out shape for a
transverse pulling load. Similarly Type-IV and Type-V cut-out
models have the Tsai-Hill failure index value of 1.0752 and 2.291
respectively and fails for the applied Transverse pulling load.
Among the five cut-out shapes only Type-III (vertical ellipse) cut-
out model doesn’t fail for the applied pulling load and hence it is
the desirable cut-out shape for the Transverse pulling load.
From Fig. 9 it can be seen that the Tsai-Hill failure index value
near the stiffener curve for all the cut-out models were in the
range of 0.2795 to 0.2831 and were less prone to failure than the
regions near the cut-outs. Here also the Type-III cut-out model
was the desirable cut-out shape as it had the lowest Tsai-Hill
failure index value of 0.2795 among all other cut-outs.
Fig.9. Tsai-Hill failure index value near the stiffener curve for
Transverse Pulling load
ii Shear Load
A uniform shear load of 15.2 MPa was applied on the top surface
of the web. The Tsai-Hill failure index values of all 12 models
were shown in Fig. 10 and 11
From the Fig. 10 it has been seen that the Type-I cut-out model
has the Tsai-Hill failure index value of 0.03255 which is lesser
than Type-II cut-out model but greater than the Type-III cut-out
model. Type-IV and Type-V cut-out models have the Tsai-Hill
failure index values of 0.06256 and 0.059 respectively for the
applied Shear load. Among the five cut-out models Type-IV cut-
out model has the highest Tsai-Hill failure index value of 0.06256
and is the least desirable cut-out shape for a Shear load. Type-III
cut-out model has lowest Tsai-Hill failure index value of 0.02798
for the applied load which is three times lesser than Type-IV
model and hence it is the desirable cut-out shape for the shear
load.
Fig.10. Tsai-Hill failure index value at cut-out proximity for
Shear load
From Fig. 11 it can be seen that the Tsai-Hill failure index
value near the stiffener curve for all the cut-out models were
in the range of 0.00473 to 0.00490 and were less prone to
failure than the regions near the cut-outs.
Fig.11 Tsai-Hill failure index value near the stiffener curve
for Shear load
0.25
0.255
0.26
0.265
0.27
0.275
0.28
0.285
0.29
Cut-outshapes
Tsai-Hillfailure index value near the
stiffnercurve for Transvere Pullingload
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Cut-outshapes
Tsai-Hillfailure index value at Cut-out
proximity forShear load
0.0045
0.00455
0.0046
0.00465
0.0047
0.00475
0.0048
0.00485
0.0049
Cut-outshapes
Tsai-Hillfailure index value near the
stiffener curve for Shear load

35830
Here also the Type-III cut-out model was the desirable cut-out
shape as it has the lowest Tsai-Hill failure index value of 0.00473
among all other cut-outs.
iii Bending Load
A Bending load of 38N was applied on the top surface of the web.
The Tsai-Hill failure index values of all 12 models were shown in
Fig. 12 and 13.
From Fig. 12 and 13 it has been found that the Tsai-Hill failure
index value near stiffener curve was greater than Tsai-Hill failure
index value at cut-out proximity for bending load and hence the
region near the stiffener curve were more prone to failure than the
regions near the cut-out. From Fig.12 it can be seen that the Tsai-
Hill failure index value near the cut-out region for all the cut-out
models were in the range of 0.05912 to 0.06858. Here also the
Type-III cut-out model was the desirable cut-out shape as it has
the lowest Tsai-Hill failure index value of 0.06071 among all
other cut-outs. From the Fig. 13 shows that the Type-I cut-out
model has the Tsai-Hill failure index value of 0.1066 which is
lesser than Type-II cut-out model but greater than the Type-III
cut-out model. Type-IV and Type-V cut-out models have the
Tsai-Hill failure index value of 0.10107 and 0.13125 respectively
for the applied Shear load. Among the five cut-out models Type-
V cut-out model has the highest Tsai-Hill failure index value of
0.13125 and is the least desirable cut-out shape for a Shear load.
Type-III cut-out model has lowest Tsai-Hill failure index value of
0.10247 for the applied load and hence it is the desirable cut-out
shape for the bending load.
Fig.12 Tsai-Hill failure index value at cut-out proximity for
shear load
Fig.13 Tsai-Hill failure index value near the stiffener
curve for Shear load
Conclusion
The composite T-joint with five different cut-out
configurations at the web of the T-joint were analysed for the
three basic (transverse, shear and bending) loading
configurations. The Tsai-Hill failure criteria was chosen for
the failure indices. By scrutinizing the results the Type-III
(Vertical-ellipse) configuration found to be less failure
indices both at the hole proximity and near the stiffener cure
regions, hence the vertical-ellipse model would be the best
cut-out to be incorporated in the composite T-joints. At the
same time Type-II (Horizontal-ellipse) model was found to
be critical in most of the load cases.
References
[1] K. Vijayaraju, P.D. Mangalgiri , B. Dattaguru,
"Experimental study of failure and failure
progression in T-stiffened skins", Journal of
Composite Structures 64 pp. 227-234, 2004.
[2] V.Sivakumar et al, "Optimisation of cut-out shape on
composite plate under in-plane shear loading",
Journal of failure analysis and prevention, Vol 12,
Issue 2, pp. 204-213, 2012.
[3] P.B. Stickler, M. Ramulu, P.S. Johnson,
"Experimental and numerical analysis of transverse
stitched T-joints in bending", Journal of Composite
Structures 50 pp. 17-27, 2000.
[4] S.Guo and R.Morishima, "Design, Analysis and
Testing of Sandwich T-joint Structures", Composite
Structures 94 pp. 229-238, 2011.
0.04
0.045
0.05
0.055
0.06
0.065
0.07
0.075
Cut-outshapes
Tsai-Hillfailure index value at hole
proximity forBending load
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Cut-outshapes
Tsai-Hill failure index value near the
stiffnercurve for Bending load

35831
[5] W. Li, L. Blunt, K.J. Stout, "Stiffness analysis of
adhesive bonded Tee joints", International Journal of
Adhesion & Adhesives 19, pp. 315-320, 1999.
[6] Lucas F.M. da Silva, R.D. Adams "The strength of
adhesively bonded T-joints", International Journal of
Adhesion & Adhesives 22, pp. 311-315, 2002.
[7] C. Liu et al, "Measurement of the fracture toughness of a
fiber reinforced composite using the Brazilian disk
geometry", International Journal of Fracture 87, pp. 241-
263, 1997.
[8] ABAQUS V.6.10, "ABAQUS/Standard User’s Manual",
Simulia, Dasault systems, 2010.

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