Characterization of Interfacial Normal Tensile Strength in Composite
Materials Using Cruciform Specimens
Senior, Aerospace Engineering
Texas A&M University
ABSTRACT: An in depth finite element analysis of the cruciform specimen used in interfacial normal
strength tests was conducted. The purpose of the study was to verify the optimized cruciform geometry that
has been tested by previous researchers and to gain insight into any other types of test specimens that
could possibly outperform the cruciform. Parametric studies of the cruciform’s geometry were used to
confirm the optimized dimensions. It was found that the cruciform can probably not be optimized any
further and a different type of specimen would have to be used to increase performance.
INTRODUCTION The problems associated with a straight-
With the increased use of composite sided specimen can be overcome by using a
materials in aerospace applications, there cruciform shaped specimen as shown in
has been great interest in characterizing the Figure 1. This type of test was first
fiber-matrix interface properties of these introduced by Gundel et al.  and it’s
materials. If these properties could be effectiveness has been demonstrated on
measured accurately, more robust failure SCS-0/epoxy composites. While this type
models of composites could be developed. of test works well with this particular
This would allow future aerospace designs material system, there have been some
to take full advantage of the benefits of difficulties applying it to graphite/epoxy
composite materials. materials due to the small size and low
transverse modulus of the graphite fibers
In particular, if the interfacial normal tensile . The strong fiber-matrix interface of this
strength could be accurately measured, the system caused the specimens to fail
response of unidirectional composites to prematurely at the fillet region. Bechel et al.
transverse loading could be predicted more solved this problem by adding reinforcing
accurately. This property has also been face sheets to their specimens.
identified as playing a significant role in
debonding of the interface of ceramic-matrix
composites . A simple straight sided
specimen with a single fiber embedded in it
has often been used to estimate this
property. The specimen is loaded in the
direction transverse to the fiber, and the
fiber-matrix interface is monitored for signs
of debonding. The main disadvantage to
this type of test is the presence of large
stress singularities where the fiber meets the
free edge . These large stress
concentrations cause fiber debonding to
occur prematurely which results in an
underestimate of the true interfacial strength.
Figure 1. Cruciform Geometry and Nomenclature.
With all of its advantages, the cruciform
remains somewhat difficult to fabricate. For
this reason, there is interest in developing
other types of specimens that could possibly
outperform the cruciform and also be easier
to construct. In this study, the cruciform
specimen was modeled in order to confirm
previous results . The information
obtained from this model was then used to
develop an optimized cruciform geometry
that maximizes stress at the fiber-matrix
interface and minimizes stress at the fillet
The ABAQUS finite element code was used
to rigorously model the test specimens. To
aid in the analysis of the different
configurations, Python scripting files were
used to define each model in ABAQUS so
that parametric studies could easily be Figure 2. 2D Cruciform Mesh.
During the course of the study, the After analyzing the two dimensional
ABAQUS models were run on either an SGI cruciform, 3D models were created. Eight
supercomputer or a dual core machine node 3D brick elements were used to model
running Windows XP. The dual core the epoxy matrix and SCS-0 fiber sections,
machine was found to be sufficient to handle and the corresponding mesh is shown in
the size of the problem at hand. Figure 3. Note that symmetry planes were
In order to gain a better understanding of once again exploited so that 1/8 of the
how the cruciform shape reacts to loading, geometry was modeled. The mesh was
2D finite element models of the cruciform refined at the fiber-matrix interface and fillet
shape were first analyzed. For simplicity, radius areas while other areas were given a
the fiber was not modeled so that the epoxy coarser mesh in order to optimize
matrix was the only section analyzed. Also, computational efficiency. Script files were
symmetry planes were exploited in all three once again used to vary the loading arm
coordinate directions so that only 1/4 of the width, wing height, fillet radius, specimen
geometry was modeled. Script files were thickness, and fiber radius while holding the
used to vary the loading arm width, wing overall length and width of the specimen
height, and fillet radius while holding the constant. A 3D model of a straight sided
overall length and width of the specimen specimen with fiber was also analyzed to
constant. Figure 2 shows the mesh of one of give a baseline for how well the cruciform
the 2D configurations. performs.
stress concentrations were also present in the
fillet regions for every configuration tested.
Further, it was found that increasing loading
arm width while decreasing wing height
increases the ratio of interface stress to fillet
Figure 3. 3D Cruciform Mesh.
Figure 4. Stress Contour Plot of 2D Model with
Stress Concentration Factors at Key Locations.
The 2D Cruciform models provided a
qualitative measure of how sensitive the
cruciform specimen is to several geometric The 3D cruciform models were used to
parameters. Using stress contour plots like obtain quantitative measures of the
the one in Figure 4, it was found that the cruciform’s effectiveness. Figure 5 shows a
cruciform specimen does promote increased stress contour plot of the model which
stress concentrations at the interior of the agrees with the 2D results. The 3D plot also
specimen while decreasing stresses in the highlights the interface region which was
wings and at the fiber ends. However, large left out of the 2D models.
Figure 5. Stress Contour Plot of 3D Model.
In addition to stress contour plots, the stress
values for every tested configuration were 1.6
probed to find the stresses at key locations in
Stress Concentration Factor
the model. The stresses at the interface and
fillet regions were of particular interest
because they can be used to predict if the 1
cruciform will fail at the fillets before fiber 0.8
debonding occurs. Plots of these two 0.6
stresses as a function of several different 0.4
geometric parameters were obtained. 0.2
Figure 6 is a plot of interface and fillet stress 0 5 10 15 20
as a function of loading arm width. Notice Loading Arm Width (mm)
that the stresses are normalized with respect
to the far field applied stress to give the Figure 6. SCF versus Loading Arm Width.
stress concentration factor (SCF). The stress
component used to calculate the SCF was
the component in the loading direction. It is As can be seen in Figure 7, a decrease in
obvious from the figure that a favorable wing height causes an increase in interface
interface to fillet stress ratio can be attained stress and a decrease in fillet stress. A
by increasing the loading arm width. desirable interface to fillet stress ratio can be
obtained for any wing height less than about
6 mm. However, the cruciform becomes Specimen thickness and fiber radius are
increasingly difficult to fabricate with wings essentially the same parameter since
that are less than about 2 mm tall . increasing the thickness should have the
same effect as decreasing the fiber radius.
Both parameters were still studied in order
1.6 to verify the validity of the model. Figure 9
shows that a thicker specimen results in a
Stress Concentration Factor
1.2 more favorable interface to fillet stress ratio.
1 However, it appears that there is a limit to
0.8 this behavior so that any thickness greater
than about 1.5 mm would not give any
significant gain to the stress ratio. As
Fillet SCF expected, Figure 10 shows that increasing
the fiber radius has the same negative effect
0 5 10 15 20 on the interface to fillet stress ratio that
Wing Height (mm)
decreasing the specimen thickness does.
Figure 7. SCF versus Wing Height.
Stress Concentration Factor
The effect of fillet radius on the interface
and fillet SCFs is shown in Figure 8. It can
be seen that as the fillet radius is increased, 1
the stresses at the interface and fillet are 0.8
both reduced. This means that the interface 0.6
to fillet stress ratio is relatively insensitive to 0.4
the fillet radius. However, the figure also 0.2
suggests that because the fillet and 0
0 0.5 1 1.5 2
interfacial stresses have almost the same Thickness (mm)
value for small and large fillet radii, the
optimum fillet radius is about 4 mm. Figure 9. SCF versus Specimen Thickness.
Stress Concentration Factor
Stress Concentration Factor
Fillet SCF Fillet SCF
Interface SCF Interface SCF
0 2 4 6 8 10 0 20 40 60 80 100 120 140
Fillet Radius (mm) Fiber Radius (microns)
Figure 8. SCF versus Fillet Radius. Figure 10. SCF versus Fiber Radius
Using the results from the parametric studies type of specimen will most likely need to be
given above, an optimized cruciform developed. This new specimen could be
geometry was developed. This geometry is either a cruciform with some novel
given in Table 1 along with the optimized modification or a specimen with an entirely
geometry that Bechel et al. developed. different shape altogether.
These results were used to create another
Future research into other types of
model with the optimized dimensions in
geometries will be conducted as a result of
order to verify the effectiveness of the
this study. Several novel designs could
modifications. This optimized model
include a straight sided specimen with either
exhibited the best interface to fillet stress
holes or reinforcing tabs at the free edge of
ratio of all the configurations tested.
the fiber. These holes or tabs could possibly
reduce or eliminate the stress singularity at
SUMMARY AND DISCUSSION the fiber ends. Another possible design
would be to eliminate the fillets of the
Table 1 indicates that the results obtained cruciform by making an elongated octagonal
from this analysis agree quite well with specimen with reinforcing face sheets. An
work previously done. The only significant in depth analysis of these possible designs
difference between the results is the would have to be performed to see whether
optimized fillet radius. As mentioned they could match or outperform the
previously, the results indicated that varying cruciform.
the fillet radius does not significantly affect
the interface to fillet stress ratio. However,
Bechel et al. did find that the fillet radius
can affect this ratio. The main reason for
this discrepancy is probably a mesh
refinement issue with the models.
While the cruciform geometry has been
optimized in this and previous studies, this
type of specimen has probably reached a
limit to its optimization. In order to
characterize a fiber-matrix interface that is
much stronger than the SCS-0/epoxy system
(such as the graphite/epoxy system), a new
Table 1: Optimized Cruciform Geometry
Loading Arm Wing Fillet
Width Height Radius Thickness
Optimized Geometry 15 mm 4 mm 4 mm 1.0 mm
Geometry Obtained by Bechel
et al. 14.8 mm 3.4 mm 6.4 mm 0.6-1.0 mm
ACKNOWLEDGEMENTS corner singularities on interfacial normal
I’d like to thank Dr. John Whitcomb for strength: application in model unidirectional
mentoring me and showing me how to composites. Composites, Part B:
perform a nontrivial analysis. Engineering, 1999; 30:115-34.
I’d also like to thank the rest of the Alpha  Gundel DB, Majumdar BS, Miracle DB.
team for their help and support. Evaluation of the transverse response of
fiber-reinforced composites using a cross-
This Research Experience for shaped sample geometry. Scripta Metall
Undergraduates Site is sponsored by the 1995; 33:2057-65.
National Science Foundation Grant No.
0453578, the Air Force Office of Scientific  G. P. Tandon, R. Y. Kim, and V. T.
Research, U.S. Air Force, Department of Bechel, Evaluation of Interfacial Normal
Defense and NASA Cooperative Agreement Strength in a SCS-0/epoxy Composite with
No. NCC1-02038. Cruciform Specimens, Composites Sci.
Technol., vol. 60, no. 12–13, pp. 2281–
 Bechel, V.T. and Tandon, G.P. Modified
Cruciform Test for Application to
 Pagano NJ. On the micromechanical Graphite/Epoxy Composites, Mechanics of
failure modes in a class of ideal brittle Advanced Materials and Structures, 9: 1–17.
matrix composites. Part 1. Coated-fiber (2002).
composites. Composites Part B 1998;
 Tandon GP, Kim RY, Warrier SG,
Majumdar BS. Influence of free edge and