Characterization of Interfacial Normal Tensile Strength

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					     Characterization of Interfacial Normal Tensile Strength in Composite
                    Materials Using Cruciform Specimens

                                         Kevin Maxwell
                                 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. [3] and it’s
materials. If these properties could be                     effectiveness has been demonstrated on
measured accurately, more robust failure                    SCS-0/epoxy composites[4]. 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            [5]. 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 [1]. 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 [2].            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 [4].      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
                                                                                                                      Fillet SCF
geometric parameters were obtained.                                                       0.2
                                                                                                                      Interface SCF
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 [4].                                                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
                                                                  Interface SCF
                                                                                       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
                                                                                                                                                                 Fillet SCF
the fillet radius. However, the figure also                                                                           0.2
                                                                                                                                                                 Interface SCF
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.

                               1.6                                                                                    1.6
 Stress Concentration Factor

                                                                                        Stress Concentration Factor

                               1.4                                                                                    1.4

                               1.2                                                                                    1.2

                                1                                                                                       1

                               0.8                                                                                    0.8

                               0.6                                                                                    0.6

                               0.4                                                                                    0.4
                                                                  Fillet SCF                                                                                     Fillet SCF
                               0.2                                                                                    0.2
                                                                  Interface SCF                                                                                  Interface SCF
                                0                                                                                       0
                                     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   [3] 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    [4] 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–
                                               2296, (2000).
                                               [5] Bechel, V.T. and Tandon, G.P. Modified
                                               Cruciform Test for Application to
[1] 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;
[2] Tandon GP, Kim RY, Warrier SG,
Majumdar BS. Influence of free edge and