[american institute of aeronautics and astronautics 45th aiaa/asme/asce/ahs/asc structures,...

1 American Institute of Aeronautics and Astronautics

BIAXIAL STRENGTH MEASUREMENTS OF IM7/977-2 CARBON/EPOXY LAMINATES USING TABBED CRUCIFORM SPECIMENS

Jason T. Ash*

South Dakota School of Mines and Technology Mechanical Engineering Department

Rapid City, SD 57701

Jeffry S. Welsh, Ph.D.ϯ Air Force Research Laboratory

Space Vehicles Directorate Kirtland Air Force Base, NM 87117

ABSTRACT

Thickness-tapered cruciform specimens have previously been used to measure the biaxial strength of various

carbon/epoxy cross-ply laminates. In the present work an alternative specimen production method was investigated that requires no machining of the gage section. A total of 27 specimens were tested to produce a complete failure envelope in the σ1-σ2 stress space. Results were compared with five specimens produced by the previous manufacturing method. In addition, finite element analysis (FEA) was conducted on both these specimens and resulting strains were to within 5% of the measured experimental results. Additional geometries were machined into the specimens in the continued effort to improve the specimen geometry to promote failure within the gage section for all stress ratios. Three separate modifications were made and seven specimens of each were tested at various stress ratios. Comparisons are made between experimental and FEA results.

INTRODUCTION

Over the past several years, many new developments involving the process for predicting ultimate failure of laminated fiber reinforced composite (FRP) materials have been realized. While many of these new approaches are a result of significantly improved computational power, the overall approach towards predicting failure in these complex materials is shifting towards more complex failure theories.1-5 In general, micro-level failure prediction is beginning to emerge as a viable alternative to macro-level theories. This trend being forced, at least in part, by frustrations of design engineers when using many of the more established failure theories to predict the failure of composite materials with only mild success.1 While the existing failure theories were a natural evolution for anisotropic materials, they simply have not proven to be accurate for predicting failure for laminated composite materials. As a result, many engineers are forced to use overly conservative designs that ultimately hinder the development of these materials to many applications.

Parallel to the revitalized interest in predicting failure for FRP materials has been an increased interest in the ability to generate accurate experimental biaxial (two-

*Student Member, ME Instructor/PhD Student ϯAIAA Member, Aerospace Engineer

dimensional) data, which can be used to validate the numerous failure prediction models being promoted. Perhaps not totally unexpected, this increased attention on experimental data has exposed the composites community to the paucity of data that currently exists.1,2,5-7

A seemingly benign complication adding to the current confusion within the composites design community is that there is no widely accepted definition of failure for composite materials.1-3 The complex nature of composite failures, which are often laminate dependent, almost guarantees that a diverse interpretation of failure will be a byproduct of any analysis or application. To an experimentalist in search of material characterization, ultimate specimen failure can easily be defined as the maximum stress/strain/deflection obtained during a particular test, with little regard to any initial damage done to the test specimen. There are, however, numerous examples in which the ultimate failure properties of the material have little bearing on the design. It is not hard to appreciate the considerable task facing the composites community if it is to develop a universal failure theory that is capable of describing the complex behavior of composite materials.

It is however, a challenge that has not gone ignored by the composites community. Considerable effort and expense has been expended developing numerous

45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference19 - 22 April 2004, Palm Springs, California

AIAA 2004-1641

This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.


techniques to predict failure in composite materials and in an effort to, at the very least, take a community-wide assessment of the current state of the practice.2,3 Although not all-inclusive, the considerable study being performed by Hinton, Kaddour, and Soden, has been successful in evaluating the current state of the practice with regards to failure prediction.3 Perhaps the greatest benefit to this type of round-robin study is that it serves as a benchmark to the industry, representing the current practices when subjected to identical conditions, and is considered by the present authors as a landmark study. However, it has also demonstrated, in spectacular fashion, the lack of agreement between numerous failure theories that are being widely used in practice. Analysis of laminate configurations and material systems that are generally considered routine and often used in service within the industry, resulted in ultimate strength differences as high as 900%, with no two predictions generating the exact same biaxial failure envelope.2

The present study involves continuing efforts to generate accurate experimental biaxial failure data for laminated fiber-reinforced composite materials. Details of thickness-tapered cruciform specimen design, testing procedures, and FEA results will be presented.

SPECIMEN CONFIGURATIONS Thickness-tapered cruciform specimens have

previously been used to measure the biaxial strength of various carbon/epoxy cross-ply laminates.8,9 The main method of producing the specimens was to lay-up a flat laminate [0/90]10s from which the desired cruciform specimen shape, including gage section, could be machined out using a computer numeric controlled (CNC) mill and high-speed router. Although various cruciform configurations have been studied, all the methods required machining out the gage section where failure is desired.9 The primary concern with this process is the possibility of fiber damage occurring during the machining of the gage section. The present work focuses on an alternative method for specimen production, which will be referred to as a ‘built-up’ specimen. This involves preparing a thinner IM7/977-2 carbon/epoxy laminate [0/90]4s and sandwiching it between two G10 glass/epoxy tabs with the same cruciform geometry. The G10 tabs are adhesively bonded to the carbon/epoxy laminate using Hysol 9309 epoxy adhesive and were machined to the desired thickness-tapering geometry prior to bonding thereby requiring no machining of the gage section. Several of the former ‘standard’ specimens were made for comparison with the built-up specimens. Photographs of a standard and built-up thickness-tapered specimen

after final machining are shown in Figures 1 and 2, respectively.

Figure 1. Standard cruciform specimen.

Figure 2. Built-up cruciform specimen.

There were a few subtle differences in geometry between the two types of cruciform specimens. A schematic drawing of the built-up specimen with all the major dimensions used in the present study is shown in Figure 3. For the built-up specimen there was variability in the arm thickness between 5.59-6.10 mm (0.22-0.24 in). The nominal dimension is shown for the arm thickness in Figure 3. The authors were not concerned a great deal about this variability, since the main area of interest is the gage section of the cruciform, which had much less dimensional variability. As for the standard specimen, the main differences from Figure 3 is that the arm thickness measured 5.08 mm (0.20 in) thick, the width of the gage section was 25.4 mm (1.0 in) instead of 30.5 mm (1.2 in), and there was a smooth transition from the gage section to the thickness-taper area. The thickness-taper on the G10 material of the built-up specimen did not extend all the way down to the gage section and a nominal ridge of 0.737 mm (0.029 in) remained.


Ø4.78

28.4

2.03

.7371.173.18

5.84

161

15.2

19.7

30.5

64.8

R12.7

7.32

R6.35

R7.62

15.2

Figure 3. Schematic drawing of the built-up specimen (mm)

EXPERIMENTAL RESULTS For this study, a total of twenty-seven built-up

cruciform specimens were tested at nine different biaxial stress ratios, with three repetitions each, to determine the strengths in each of the quadrants of the σ1-σ2 stress space. Five standard cruciform specimens were produced and tested at similar stress ratios. An undesirable failure mode was observed for the built-up specimens where failure would occur in the narrow section of the arm by the curvature. The curvature by the narrow portion of the arm is necessary to prevent the load from bypassing the gage section and being reacted by the transverse arms. Although it is desired for failure to occur within the gage section, the data obtained represents a minimum strength value for this material. Table 1 presents the average ultimate strengths for each of the stress ratios, where the number of specimen tested for each stress ratio is indicated by the footnotes.

When testing the specimens, the arms of the cruciform are loaded in tension or compression at a constant displacement rate in the x-direction. The y-direction is controlled so that the desired load ratio is

maintained throughout the test. As with any cruciform-shaped specimen, the resulting load in the gage section is not equivalent to the load applied to the arms due to a portion of the load being reacted by the transverse arms. To account for this load distribution, strain gages were attached to a portion of the specimens and the actual strain through the gage section measured. Multiplying the measured strain by the modulus of the laminate, determined by classical lamination theory, allowed the actual stress to be determined. An area correction factor can then be used to accurately determine the stress in the biaxially-loaded gage section. The standard specimen had an area correction factor ranging from 0.75-0.81 (stress dependent) whereas the built-up specimen had a constant area correction factor of 0.97. The experimental data presented in Table 1 were corrected by multiplying the experimentally determined ultimate strength data by this area correction factor. It is possible that the differences in the area correction factor can be attributed to the different gage section geometry for the two specimens. To visualize the failure data in σ1-σ2 stress space, the data presented in Table 1 are presented graphically in Figure 4.


Table 1. Average biaxial ultimate strengths for IM7/977-2 carbon/epoxy laminates Stress ratio Lay-up

CV CV(MPa) (ksi) (%) (MPa) (ksi) (%)

1/1 Sa 730 106 10.2 730 106 9.00/1 Sb NA NA NA 930 135 NA

-1/-1 Sa -553 -80.3 0.4 -555 -80.6 2.11/1 Buc 780 113 3.1 775 112 3.02/1 Buc 786 114 5.9 395 57.3 5.00/1 Buc NA NA NA 839 122 0.82/-1 Buc 775 112 6.0 -393 -57.0 6.41/-1 Buc 462 67.0 16.4 -463 -67.2 15.91/-2 Buc 255 36.9 2.4 -491 -71.3 3.7-1/0 Buc -458 -66.5 2.6 NA NA NA-1/-2 Buc -254 -36.8 3.4 -499 -72.4 3.0-1/-1 Buc -451 -65.4 2.4 -465 -67.5 3.4

Average y-directionAverage x-direction

Ultimate Strength Ultimate Strength

a2 standard specimen b1 standard specimen c3 built-up specimen

Figure 4. Biaxial failure data for standard and built-up specimens.


FINITE ELEMENT COMPARISON

Because the arbitrary nature of defining the gage section dimensions merely for convenient stress analysis, validation of the procedures used to correct for this nuance must be performed, as was done in the present study. Finite element analysis was conducted using ABAQUS v6.3 to determine the ability to predict the stress/strain distribution within the gage section of the cruciform specimen. The analysis results were compared directly with experimental data collected from the experimental study. To begin, verification modeling was conducted to show that composite shell elements could be used in place of 8-node solid continuum elements to model the cruciform geometry. It was found that the composite shell elements predicted very similar stresses to that of the 3-D solid continuum elements at ABAQUS analysis times of two minutes compared to twenty-two minutes. Similar time savings were found in model development and analysis of ABAQUS results when using the composite shell elements.

All results presented in the paper were obtained using the composite shell elements (S4 and S3R). Meshing of the cruciform geometry was conducted using FEMAP and element sizes typically 0.635 mm (0.025 in) square were used in the gage section. Pictures of the standard and built-up meshes and average normal stress contours (SSAVG) are shown in Figures 5 and 6. All of the meshing was conducted manually using the ‘generate between’ commands in addition to adding and deleting triangular elements to fit the geometric contours imported from SolidWorks models.

To enable accurate modeling of the thickness-tapered geometry, various element properties were assigned to the composite shell elements. The property of the element defines the number of composite layers, the layer orientation, and the material of each layer. The gage section and tabs were each given their own property and then the thickness-taper was defined by stepping up the thickness in rows extending from the gage section to the tab material. This forms a discontinuous leading edge through the thickness-taper, but this is a standard practice in finite element modeling when considering for example the modeling of a thickness-tapered beam.

Presented in Table 2 are the definition of the layer thickness and laminate thickness for each property and the resulting lay-up configuration. For the standard specimen, the only material used was the IM7/977-2 carbon/epoxy material. Balanced cross-ply layers within the core of the composite are all 127 µm (0.005 in) thick and the top and bottom layer thickness are the values presented in Table 2. Likewise, the core of the built-up specimen [0/90]4s is made of 127 µm (0.005 in) thick cross-ply layers of IM7/977-2 carbon/epoxy and the additional thickness for the rows and tabs is a result of the thickness-tapered G10 glass/epoxy material. Again, the layer thickness defined in Table 2 is only for the top and bottom layers. Laminate thickness for each row were determined by fitting a 12.7 mm (0.5 in) radius circle through the endpoints of the curvature, which corresponds to the radius of the high-speed router used to machine the thickness-taper profile. The equation for the circle was then used to determine the laminate thickness at the center of each element. In all

Figure 5. Standard specimen (MPa).

Figure 6. Built-up specimen (MPa).


FEA Property Layer Laminate Layer LaminateLocation Number Standard Specimen µm (in) mm (in) Built-Up Specimen µm (in) mm (in)Gage Section 1 [0/90]4s 127 (0.005) 2.03 (0.080) [0/90]4s 127 (0.005) 2.03 (0.080)Row 1 3 90,[0/90]4s,90 76.2 (0.003) 2.18 (0.086) 0,[0/90]4s,0 813 (0.032) 3.66 (0.144)Row 2 4 [0/90]5s 127 (0.005) 2.54 (0.100) 0,[0/90]4s,0 991 (0.039) 4.01 (0.158)Row 3 5 0,90,[0/90]5s,90,0 76.2 (0.003) 2.95 (0.116) 0,[0/90]4s,0 1194 (0.047) 4.42 (0.174)Row 4 6 0,90,[0/90]6s,90,0 76.2 (0.003) 3.45 (0.136) 0,[0/90]4s,0 1448 (0.057) 2.03 (0.194)Row 5 7 [0/90]8s 127 (0.005) 4.06 (0.160) 0,[0/90]4s,0 1753 (0.069) 5.54 (0.218)Row 6 8 90,[0/90]9s,90 76.2 (0.003) 4.72 (0.186) NA NA NATabs 2 [0/90]10s 127 (0.005) 5.08 (0.200) 0,[0/90]4s,0 1905 (0.075) 5.84 (0.230)

Thickness ThicknessTable 2. Laminate definitions for the standard and built-up specimens

six rows were used to define the thickness-taper for the standard specimen and five rows were used for the built-up specimen due to a narrower thickness-taper. The property definitions are labeled on both Figures 5 and 6 showing the narrower gage section for the standard specimen.

Material properties for the IM7/977-2 material system were obtained through previous in-house testing in accordance with applicable ASTM Standards. The 2-D orthotropic material properties used were as follows: E1 = 173 GPa (25.1 Msi), E2 = 9.17 GPa (1.33 Msi), G12 = G13 = 5.65 GPa (0.82 Msi), G23 = 3.03 GPa (0.44 Msi), and ν12 = 0.34. The material orientation in the property definition correctly orientates the layer stiffness definition. In addition, the 2-D orthotropic assumption was verified by the equation given in the ABAQUS manual.10 The isotropic G10 glass/epoxy material properties were obtained from the manufacturer as follows: E = 17.6 GPa (2.55 Msi) and ν = 0.4. The orientation of zero degrees was given for these layers as shown in Table 2, but the orientation does not matter, as the material behavior is nearly isotropic.

The final model was a 1/4 symmetry model of the cruciform specimen and as such symmetry boundary conditions were placed along the x and y axis of the specimen. In addition, loading was applied to the specimen that corresponded to the failure load measured during experimentation for each of the 0/1 specimens with the strain gages. Since the 0/1 configuration was used the loading was placed on the y-axis arm and only half the failure load was applied due to symmetry conditions. For the standard specimen the failure load was 59.8 kN (13.45 kip), so a 854 N (192 lb) load was applied to the center node on the symmetry line and a 1708 N (384 lb) load was applied to the remaining 17 nodes along the top. Likewise, the built-up specimen failed at around 53.4 kN (12 kip) and the

loads were distributed accordingly with the symmetry node only half the load of the other 17 nodes.

During the experimentation, the standard specimen in the 0/1 stress ratio had 10 strain gages applied across the width. Unfortunately, only six strain gages could be monitored at a time, so the specimen was initially loaded up to 331 MPa (48 ksi). The readings of the strain gages to failure on the next run were considered inaccurate due to residual strain that was left over after the first loading. But comparisons are made between the FEA and first run of experimental strains at 331 MPa (48 ksi) as shown in Figure 7. Three strain gages were used on the built-up specimens, so there was adequate instrumentation to measure these simultaneously up to failure. The experimental strains were fairly symmetric about the center of the gage, so the x-axis displays only the position from the center to the outer edge of the gage section.

Figures 7 and 8 show a remarkable comparison between the experimental measurements and the FEA results. There is roughly a 3-5% variation between the measured and predicted strains. Looking at the thickness, the experimental standard specimen was about this percentage thicker than the FEA model, which would make it more stiff and deform less; whereas the built-up specimen was about this percentage thinner than the FEA model, which would make it less stiff and deform more. This was observed in both Figures 7 and 8, so even this small variation may be attributed to similar variations in the gage section thickness. But these variations are negligible for the purposes presented in the paper. The stress distributions shown in Figures 5 and 6 are the average normal y-stress (SSAVG) for the laminate and correspond directly to the ultimate failure strength data presented in Table 1, which is a bulk average stress for the laminate.


0.0E+00

5.0E-04

1.0E-03

1.5E-03

2.0E-03

2.5E-03

3.0E-03

3.5E-03

4.0E-03

0 3 6 9 12 15

Position from the center of gage, mm

Stra

in

Exp.

FEA

Figure 7. Standard specimen strain comparison (loaded to 331 MPa (48 ksi)).

0.0E+00

2.0E-03

4.0E-03

6.0E-03

8.0E-03

1.0E-02

1.2E-02

0 5 10 15 20

Position from the center of gage, mm

Stra

in

Exp.

FEA

Figure 8. Built-up specimen strain comparison (loaded to failure 839 MPa (122 ksi)).

The area correction factors were also calculated from the FEA results by adding up the reaction forces within the gage section and dividing by the load applied to the arms. Results were again with close agreement where the predicted area correction factor for the standard specimen was 0.77 and experimentally this was determined to be between 0.75 – 0.81 dependent upon the magnitude of stress. For the built-up specimen the FEA results predict an area correction factor of 0.90 where experimentally this was determined to be 0.97 on average. However, as seen in Figure 8, only three gages were used to determine this correction factor and if the corresponding strain locations were used from the FEA, the predicted area correction factor would be 0.94.

SPECIMEN MODIFICATIONS

In addition to the standard and built-up configurations, modifications were made to remaining built-up specimens in an attempt to produce an area correction factor near unity. For these specimens, slots running through the center of the arms up to the curvature of the gage section were machined out using a 3.2 mm (0.125 in) router bit. Using the same router bit, another set of specimens were modified by machining out the corners of the gage section with a diagonal slot through the G10 material only. Another set of specimens were modified not to obtain strength data for the material, but to obtain failure data for a composite with a stress concentration produced by drilling a 4.8 mm (0.188 in) diameter hole centrally

located in the gage section. Seven specimens were modified for each of the three configurations and schematic diagrams of each are shown in Figures 9-11.

Figure 9. Arm slot modification (mm).

Figure 10. Corner slot modification (mm).


Figure 11. Center hole modification (mm)

Experimental Results for Modified Specimens

One specimen of each modification was tested at the 0/1 stress ratio with three strain gages for both the modifications with the arm and corner slot. Two strain gages were applied to the specimen with the central hole. Failure strength data were collected for these as well as two repeated specimens at the 1/1, 1/-1, and -1/-1 stress ratios. Due to the changes in specimen geometry, new area correction factors needed to be calculated based on the 0/1 experiments that had strain gages attached. Unfortunately, the results of the strain gages suggested that an area correction factor of around 1.5 was required for all three cases. This suggests that if a 44.5 kN (10 kip) load is applied to the loading arms, then a 66.7 kN (15 kip) load travels through the gage

section, obviously indicating an instrumentation failure and voiding all meaningful strain data results. However, it was shown previously, that there was very good agreement between the experimental strains and FEA results for the standard and built-up specimens. For the current work, the FEA results for the modified specimens could then be used to determine a predicted area correction factor that could be used to adjust the data as explained in the following section. Finite Element Analysis of Modified Specimens

To model the modified specimens only required minor changes to the previous built-up model. The arm slot model only required the deletion of elements around the arm slot and then remeshing in that area to connect all the elements. The corner slot model only required changing the property definitions through the corner slot area to the gage section property. The width of the slot was intentionally placed into the built-up model, so that this could be converted over to the corner slot model easily. Elements were deleted again for the center hole model and the surrounding area remeshed. The property and material definitions remained the same for all the models. Again the failure loading for each of the 0/1 stress ratio cases was placed into their respective finite element models. Figures of the average normal y-stress contours for these three specimens are shown in Figures 12-14.

Figure 12. Arm slot model (MPa).

Figure 13. Corner slot model (MPa).


One thing to note from the figures of the stress contours, is that the failure load for each specimen was applied to the FEA model. The stress contour scales of all the pictures were adjusted to the contours of the standard specimen, so that a direct comparison could be made between the contours. For all specimens, the failure load produces roughly the same average stress as designated by the green area in the each of the gage sections. The area correction factor for the specimen with arm slots, corner slots, and a center hole was determined to be 0.90, 0.91, and 0.90, respectively. Using these area correction factors determined by FEA, the failure strengths obtained experimentally were adjusted to give the average failure strength as shown in Table 3. The modification (Mod.) column presents the three modifications: arm slots (AS), corners slots (CS), and center hole (CH).

Figure 14. Center hole model (MPa). Table 3. Average biaxial ultimate strengths for modified built-up specimens

Stress ratio Mod.CV CV

(MPa) (ksi) (%) (MPa) (ksi) (%)1/1 ASa 701 102 6.3 701 102 6.30/1 ASb NA NA NA 606 87.9 NA1/-1 ASa 459 66.6 1.9 -454 -65.9 2.7-1/-1 ASa -423 -61.4 2.3 -422 -61.2 3.21/1 CSa 700 101 9.5 700 101 7.00/1 CSb NA NA NA 728 106 NA1/-1 CSa 421 61.1 4.4 -423 -61.3 6.6-1/-1 CSa -400 -58.1 0.9 -402 -58.3 1.21/1 CHa 704 102 0.6 711 103 0.60/1 CHb NA NA NA 738 107 NA1/-1 CHa 291 42.2 2.7 -287 -41.7 3.4-1/-1 CHa -379 -54.9 0.1 -382 -55.4 3.0

Average x-direction Average y-directionUltimate Strength Ultimate Strength

a2 specimen b1 specimen

DISCUSSION OF RESULTS

From the experimental data presented, it can be seen that the built-up specimens had low coefficients of variation with an average of around 5%. The single outlier being one of the 1/-1 stress ratio specimens where one specimen broke at a higher stress than the previous two leading to a coefficient of variation of 16.4%. This trend in data scatter was similar with the standard specimen and modified specimens. For both the 0/1 and -1/-1 stress ratios, the standard specimen measured ultimate strengths 10% and 18% higher, respectively, than the built-up specimens. For the 1/1

stress ratio, the standard specimen measured an ultimate strength that was 6.4% lower than the built-up specimen. There are several factors that could account for this discrepancy. The first is that the measurement of the gage section geometry is difficult for any thickness-tapered cruciform specimen. The reason for this is that the thickness-taper fillets toward the gage section and there is no well-defined boundary. In terms of failure location, the (T/T) cases all failed in the narrow section of the arm right next to the gage section. The ultimate strengths then only indicate the stress in the gage section at the time of arm failure and not the true ultimate strength of the material (i.e., a


conservative measurement of the ultimate strength). Another frequent concern is the possibility of buckling occurring in the compression/compression stress cases. To determine that this was not a factor in the present study, the -1/-1 and -1/0 stress ratios were completed again with additional built-up specimens while placing a slight compressive force through the thickness of the gage section to eliminate buckling. Results of this experimentation showed the strength values only slightly increased, which indicated global specimen buckling was not present during the tests. When plotting the failure envelope for all the different specimen geometries excluding the case with a central hole, the trend in a wider data scatter between different specimen geometries is apparent as shown in Figure 15.

Ideally, in addition to having low data scatter among different repetitions of the same specimen geometry, there would be relatively low scatter between different specimen geometries since the same material property is being measured. It is believed that the main reason there is such a scatter between the different geometries is again due to failure occurring at the narrow section of

the arm rather than the gage section. It can be seen from Figure 15, that the small tick on the x-axis before 690 MPa (100 ksi) represents the failure strength for the specimen with the arm slot. This is roughly 20% lower than other specimens at the same stress ratio, clearly indicating the propensity for arm failure to occur at the narrow section was exasperated by the removal of material in that region.

CONCLUSIONS

The authors feel that a substantial amount of

information has been learned from the present study. Low data scatter obtained for like specimens indicates the specimen fabrication technique is very consistent and produces very similar specimens, which is a feat among itself when testing composite materials. Failure strengths of the built-up specimen were both higher and lower than the standard specimen indicating that fiber damage is not very significant in the standard specimen and either method works well for specimen fabrication.

Figure 15. Biaxial failure data for four specimen geometries.


In addition, modeling the specimen geometry using composite shell elements proved to be a powerful technique. The thickness-taper was easily incorporated into the model through the property definition in FEMAP. Analysis of the FEA data to determine strain fields and area correction factor was considerably easier as well when compared with the 3-D continuum counterpart. Remarkable comparisons were made between the experimental and FEA strains for the standard and built-up cases. Although future work will inevitably continue experimentation of cruciform specimens, the current plan is to conduct a more rigorous FEA study to improve the specimen geometry to obtain repeated failures in the gage section.

ACKNOWLEDGEMENTS

The authors are grateful for the support of the Air Force Research Laboratory and the Space Scholars Program. We would also like to thank the following personnel in the space vehicles directorate for their assistance on this work including Dr. Aaron Adler, Wayne Kellingsworth, Gregory Sanford, and Marty Wyse. Cruciform specimens tested in this study were prepared by James Green, University of Wyoming, and insight about specimen modification was provided by Richard McLaughlin, Alfred University. Finally, the lead author would like to express his thanks toward his mentor, Dr. Jeffry Welsh, for his guidance through this project.

REFERENCES 1 Hinton, M.J., and Soden, P.D., “Predicting Failure in

Composite Laminates: The Background to the Exercise,” Composites Science and Technology, Vol. 7, No. 58, 1998, pp. 1001-1010.

2 Soden, P.D., Hinton, M.J., and Kaddour, A.S., “A Comparison of the Predictive Capabilities of Current Failure Theories for Composite Laminates,” Composites Science and Technology, Vol. 7, No. 58, 1998, pp. 1225-1254.

3 Hinton, M.J., Kaddour, A.S., and Soden, P.D., “A Comparison of the Predictive Capabilities of Current Failure Theories for Composite Laminates, Judged Against Experimental Evidence,” Composites Science and Technology, Vol. 62, Nos. 12-13, 2002, pp. 1725-1797.

4 Gosse, J., and Wollschlager, J., “Implicit Physical Modeling of Composite Materials and Bonded Structure,” Proceedings of the 4th Annual Composite Durability Workshop, August 26-27, 2001, Albuquerque, NM, pp. 14-23.

5 Chen, A.S., and Matthews, F.L., “A Review of Multiaxial/Biaxial Loading Tests for Composite Materials,” Composites, Vol. 24, No. 5, 1993, pp. 395-405.

6 Hinton, M.J., Kaddour, A.S., and Soden, P.D., “Evaluation of Failure Prediction in Composite Laminates: Background to ‘Part B’ of the Exercise,” Composites Science and Technology, Vol. 62, Nos. 12-13, 2002, pp. 1481-1488.

7 Soden, Hinton, M.J., and P.D.,Kaddour, “Biaxial Test Results for Strength and Deformation of a Range of E-Glass and Carbon Fibre Reinforced Composite Laminates: Failure Exercise Benchmark Data,” Composites Science and Technology, Vol. 62, Nos. 12-13, 2002, pp. 1489-1514.

8 Welsh, J. S. and Adams, D. F., “Biaxial and triaxial failure strengths of 6061-T6 aluminum and AS4/3501-6 carbon/epoxy laminates obtained by testing thickness-tapered cruciform specimens.” Journal of Composites Technology Research, Vol. 23, No. 2, 2001, pp.111-121.

9 Welsh, J. S. and Adams, D. F., “An experimental investigation of the biaxial strength of IM6/3501-6 carbon/epoxy cross-ply laminates using cruciform specimens.” Composites: Part A, Vol. 33, 2002, pp.829-839.

10 Hibbit, Karlsson, & Sorensen, Inc. “Linear elasticity using Type=Engineering Constants.” ABAQUS/Standard User’s Manual Vol. II, Ver. 6.3, Section 10.2.1, 2002.

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