Comparison of Analytical and Experimental Strains in the Vicinity of an Open Hole in a Composite Laminate

Project Constructed by David H. Mollenhauer

Project Introduction

The following is a condensed version of the project constructed for the class "Scientific Visual Analysis and Multimedia" taught by the Department of Engineering Science and Mechanics at Virginia Polytechnic Institute and State University. The fully interactive project can be downloaded from the Laboratory for Scientific Visualization server located at ftp.sv.vt.edu.

Problem Description

Within the engineering and design communities, there exists a need for highly accurate analytical models for predicting stresses and strains within a laminated composite body. Many methods exist that are adequate for simple loadings, geometries, and lay-ups. For a practical laminate (one with many layers) with a hole, there has been a great deal of difficulty predicting the three-dimensional stress state in the regions near the hole edge. The stress state is extremely complex in this region and will likely be the area of failure initiation.

A relatively new three-dimensional stress/strain analysis method that appears promising is known as the Spline Variational Elastic Laminate Technology (SVELT). This technique is under development for the United States Air Force Materials Directorate by AdTech Systems Research in Beavercreek, Ohio. It has several advantages over competing techniques that will be discussed later.

One problem with a new analysis technique is that it requires validation. This validation can take the form of comparisons with other, proven analytical techniques, or comparisons with experiment. Both validation methods have been employed by the researchers working on this problem. This project discusses one method of experimental validation, moire interferometry, and the comparison of these experimental results with SVELT data. Several 28-ply laminates with holes were manufactured. Detailed three-dimensional strain and stress variations were obtained using the SVELT analysis program. Phase-shifting moire interferometry was used to measure surface strains over the region near the hole on two specimens.

Project Objectives

The objectives of this project were three-fold. First, to establish the "proper" level of experimental data smoothing to effectively display and compare the moire data with SVELT data. Second, to develop a tool that can be used to evaluate the quality of the comparison between analytical and experimental results. Finally, to produce an interactive, visual way of educating colleagues about the data reduction process and the experimental and analytical comparison.

Techniques

SVELT

A detailed description of the Spline Variational Elastic Laminate Technology (SVELT) is beyond the scope of this project. Therefore only a brief introduction will be given here.

SVELT is a stress analysis technique. The stress analysis problem is formulated by approximating the displacements with spline functions (with unknown approximation coefficients). There can be many or only a few overlapping spline functions in a given region depending on the complexity of the expected stress distribution. Strains and stresses can then be expressed in terms of these unknown spline functions. The total potential energy of the system (including loads and boundary conditions) can now be expressed and the Principle of Minimum Potential Energy can be employed to solve for the unknown spline coefficients (Bogdanovich and Iarve 1992) (Iarve and Soni 1993) (Iarve 1995).

Moire interferometry

Moire interferometry allows for the detailed measurement of in-plane displacements on a surface (Post et. al. 1994) (Dai et. al. 1990). It does this by interrogating an extremely fine diffraction grating (1200 lines/mm) attached to a specimen surface with two beams of coherent laser light. The resulting interference pattern is proportional to in-plane displacements. Until recently, these patterns were photographically recorded and analyzed by hand. This typically resulted in information at a few points along lines of interest. Within the last few years, sophisticated digital techniques have been employed that allow for digital analysis of the whole field of recorded data. Techniques using phase-shifting and 2-D Fourier transforms have resulted in enhanced sensitivity as well as full field digital information (Creath 1988) (Lassahn et. al. 1994) (Perry and McKelvie 1993).

Specimen Configuration

The specimen configuration considered in this research consisted of a 28-ply IM-7/5250-4 laminate with a symmetric stacking sequence of [45/0/-45/0/0/45/90/45/0/0/45/0/-45/0]s. The coupon dimensions were essentially the same for the analytical and experimental sections of this research. Coupons were nominally 12 inches long and 1.25 inches wide as shown in Figure 1 (20 KiloByte gif file). A 0.25 inch hole was drilled through the center of each laminate. The thickness, however, differed slightly from analysis to experiment. The analytical coupon thickness was based on the quoted lamina thickness of 0.00527 inches which produce a laminate thickness of 0.148 inches. The experimental coupon examined with moire interferometry had an average laminate thickness of 0.155 inches with and average ply thickness of 0.00554 inches. Both the analytical model and experimental test were conducted at approximately 1000 pounds applied tensile loading resulting in a discrepancy in far field applied stress. To match the far field applied stress, the experimental results were multiplied by 1.04.

Procedure

Moire Interferometry Testing

Two specimens were examined with moire interferometry. A preliminary experiment was conducted on a specimen with a relatively significant amount of drilling damage present around the hole. The hole for the second specimen was drilled using a new drill and face plates clamped on both faces. The resulting hole was better than the first but still exhibited a slight bit of damage ( Figure 2 -- 72 KiloByte gif file). The procedure and results described in this project pertain to the second specimen.

Testing was conducted on a manually-operated, screw-driven tensile testing machine located on an vibration isolation table. The specimen did not have tabs and was gripped on the last 1.5 inches of each end. A moire interferometer of the type detailed in Mollenhauer et. al. (1994) was use in conjunction with a photographic camera and a charge-couple-device (ccd) camera for gathering and recording the interference patterns associated with the in-plane displacements on the surface of the specimen ( Figure 3 -- 42 KiloByte gif file). The digital images and resulting data sets were made up of matrices of 512 by 480 data points. Data was gathered at a load of 1011 pounds.

Data Reduction

The interference patterns were reduced to displacements using software developed at the Idaho National Engineering Laboratory (INEL) and detailed in Lassahn et. al. (1994). Displacement data was manipulated using the computer program Spyglass Transform. Strains were then obtained by using numerical differentiation in conjunction with the standard small strain/displacement equations.

Due to the noise amplifying nature of numerical differentiation, the displacement data required smoothing before obtaining strains. This was accomplished within Spyglass Transform using a central weighted averaging routine. Unfortunately, this routine cannot recognize the difference between good data points (those representing the specimen) and bad data points (those representing the hole). The result of many smoothing operations would be a gross contamination of the data point areas. A method of overcoming this shortcoming proved to be robust and relatively simple to implement. By fixing certain good data points in a boundary region around the hole at their original unsmoothed values, a smoothing operation can be accomplished without contaminating the good data with influences from the bad data. The result after many smoothing passes was a border region of variably smoothed displacement data with no contamination from the bad data within the hole. The following animation shows the sequence of smoothing with and without edge data replacement. It is recommended that this animation be viewed one frame at a time (smoothing animation -- 202 KiloByte QuickTime file). For those who do not have QuickTime access, the following 6 gif files contain the same information. These are smooth #1, smooth #2, smooth #3, smooth #4, smooth #5, and smooth #6 all of which are 40K gif files.

Results and Discussion

Two methods were used to determine appropriate levels of smoothing for the three components of in-plane strain. The first method involved visually comparing the analytical strains to the various levels of smoothed moire data and then making an intuitive choice of the appropriate level of smoothing (known as the "intuitive" choice). The second method involved calculating the difference between the SVELT and moire data for each smoothing pass. This information was then evaluated over different regions surrounding the hole and the smoothing level corresponding to the minimum of the absolute value of the average difference was the level chosen (known as the "mean difference" choice).

Animations of the intuitive smoothing comparison for axial strain, transverse strain, and shear strain (all approximately 1.2 MegaByte QuickTime files) show smoothing levels from 0 to 200 smoothes (but not all frames are shown). For those who do not have access to QuickTime, the following are representative frames of the intuitive comparison movies for axial and transverse strains: axial strain and transverse strain (both 46 KiloByte gif files).

Animations of the difference method for determining the appropriate smoothing level for axial strain, transverse strain, and shear strain (all approximately 1.4 MegaByte QuickTime files) also show smoothing levels from 0 to 200 smoothes (but not all frames are shown). For those who do not have access to QuickTime, the following are representative frames of the difference comparison movies for axial and transverse strains: axial strain and transverse strain (both 46 KiloByte gif files).

The levels of smoothing chosen by the intuitive method were 40 smoothing passes for each component of strain. The mean difference method suggested 50, 80, and 40 passes for the axial, transverse, and shear strain components, respectively. It is believed that the 80 smoothing passes suggested by the mean difference method represents too much smoothing. The more the experimental data is manipulated, the more likely real behavior is potentially lost or obscured. The final results for axial strain, transverse strain, and shear strain (all approximately 100 KiloByte QuickTime files) show SVELT data compared with the final intuitive choice and the mean difference choice (there are three frames in each of the movies that are probably best viewed frame-by-frame). For those who do not have access to QuickTime, the following are representative frames of the final choices of smoothing levels for axial and transverse strains: SVELT axial strain, moire axial strain, SVELT transverse strain, and moire transverse strain (all 39 KiloByte gif files).

Conclusions

1) The method of smoothing while replacing the edge data avoids contamination of the good data.

2) The smoothing levels chosen with the mean difference method appear to be mostly within the bounds of what would be the intuitive choice of smoothing levels. The mean difference method is somewhat dependent on the choice of the region to be considered. It therefore is not a preferred method over intuition.

3) The comparison of experimental and analytical results show astonishingly good agreement. This is especially the case when it is noted that the SVELT model was developed and run before the experimental results were available. In addition to this, the initial moire experimentation was conducted without prior knowledge of the SVELT results. Discrepancies near the hole edge may be due to the damage present in the experimental specimen, due to the data reduction techniques, and/or due to errors in the SVELT analysis method. Further effort is necessary to identify the cause of the small discrepancies observed.

4) The results obtained through phase-shifting moire interferometry are a good beginning for validating the SVELT analysis method.

Additional Information

Production Details: contains a brief list of the computer systems and software used to construct this project.

Credits: Thanks the many people who have helped in the construction of this project.

Author Information: Contains information on the author of the project.

References

Bogdanovich, A. and Iarve, E., "Numerical Analysis of Impact Deformation and Failure in Composite Plates," Journal of Composite Materials , Vol. 26, No. 4, pp. 520-545 (1992).

Creath, K., "Phase-Measurement Interferometry Techniques," Progress in Optics , Vol. 26, pp. 350-393 (1988).

Dai, F., McKelvie, J., and Post, D., "an Interpretation of Moire Interferometry from Wavefront Interference Theory," Optics and Lasers in Engineering , Vol. 12, No. 2, pp. 101-118 (1990).

Iarve, E. and Soni, S., "Three-Dimensional Stress Analysis in Compression Loaded Laminates Containing an Open Hole," Composite Materials and Structures, Proceedings of the Winter Annual Meeting of the ASME , AD-Vol. 37, pp. 117-132 (1993).

Iarve, E., "Spline Variational Three Dimensional Stress Analysis of Laminated Composite Plates With Open Holes," (submitted to The International Journal of Solids and Structures 1995). Lassahn, G., Taylor, P., Deason, V., and Lassahn, J., "Multiphase Fringe Analysis with Unknown Phase Shifts," Optical Engineering , Vol. 33, No. 6, pp. 2039-44 (1994).

Mollenhauer, D., Ifju, P., and Han, B., "A Compact, Robust, and Versatile Moire Interferometer," Optics and Lasers in Engineering, Vol. 22 (1994).

Perry, K., and McKelvie, J., "A Comparison of Phase Shifting and Fourier Methods in the Analysis of Discontinuous Fringe Patterns," Optics and Lasers in Engineering , Vol. 19, pp. 269-284 (1993).

Post, D., Han, B., and Ifju, P., High Sensitivity Moire: Experimental Analysis for Mechanics and Materials , Springer-Verlag Inc., New York (1994).