The project included aspects of both theory and experimentation.  Finite element analysis (FEA) (a numerical/graphical structural analysis computer tool) and various fatigue theories were compared and supported by coupon, panel and full-size testing.  The "test case" was the J/24 class sailboat, a design that has enjoyed a long production run and has a reputation for durability. This six-year study on the durability of marine composites was conducted at the University of California, Berkeley and the U.S. Naval Academy and supported by the American Bureau of Shipping, TPI (builder of the J Boats), OCSC (a sailing school located in Berkeley, California) and Maricomp (a small structural analysis company in Costa Mesa, California).

First, here are some pictures of a J/24 finite element model showing the effects of hydrostatic pressure and backstay tension.  The first picture is what the boat would be like if no loads (such as gravity, wind or water) were imposed; essentially the vessel would be "floating in space."  The second picture simulates (and exaggerates!) the deformations caused by loads occurring when the vessel is statically floating alongside the dock and the backstay is pulled tight.  The plot shows displacements in inches with the maximum deflection a little under 0.16 inches. To determine the accuracy of the FEA, tests of three boats were performed, and the analytical results were within 3% of the measurements for each vessel.

The FEA model was constructed using the COSMOS/M finite element software for PC's.  Models such as these can be used to dramatically reduce the weight in a vessel's structure making the boat faster and easier (and less expensive!) to build.  Routinely used in commercial and naval vessel design, finite element analysis is also used in the design of America's Cup yachts and some other recreational craft.  In this case the analysis was used to predict stress and strain ranges and compare the strain gage results from the sailing experiments. The final model included 8500 elements and 47,000 degrees-of-freedom.

To accurately model the vessel, information about the boat's shape, construction and building materials were required. The geometry and construction details were provided by TPI. The material properties were derived from testing coupons also provided by TPI. The following picture shows a coupon subjected to tensile testing. The coupon is the J/24 hull laminate without the core or gelcoat. (Core provides little, if any, strength in tension and complicates the tensile testing procedure.) The wires are connected to strain gauges (the orange rectangles) which accurately measure the amount that the material stretches.

Where failure occurs is shown by the white areas characterized by fiber fracture.  Some damage was evident along the entire coupon length.  Extensive damage is often seen in E-glass/polyester resin laminates like these where the resin often fails before the fibers.

The next picture shows a specimen which failed in compression.  In this case the core is important in preventing buckling.  The failure mode for this specimen included the outer hull skin peeling away from the core and then fracturing.  Interestingly, all seven of the cored compressive specimens failed in different modes, but the range of failure stresses was small.

Additional tests were run to determine: uncored compressive, shear, flex and long-term moisture effects. The next four pictures show the 3-point and 4-point test fixtures and their corresponding finite element models. The FEA accurately predicted deflections, but underpredicted the strength. This last result was due to stress concentrations occurring where the grips held the tensile specimens. These stress concentrations caused the specimens to fail at values lower than those likely to be seen in the field. These lower values were used in the FEA, however, resulting in underpredicted strength as the flexural specimens grips did not cause as large stress concentrations.
 

To compare the results from the mostly "1-Dimensional" coupon tests, which may have been influenced by edge effects or stress concentrations at the support or load points, tests were also performed on the same materials in a panel configuration. Two panels were cut 24" square and had moisture conditions representing boats that were either wet or dry sailed. In other words the outer laminate was either submerged or dry and the inner laminate was dry. The following two pictures show the jig and the FEA predicted deflections (at 8.4 psi). The following plot shows the predicted and measured results. Results showed excellent correlation between the FEA model that included the frame and the material data derived from ASTM tests (for wet conditions). The vertical trend of the FEA model indicated failure was predicted before it occurred. This was due to the conservative material properties derived from the tensile tests. Using tensile properties from the 4-point flex tests gave significantly better results, although still conservative.

To determine the moisture absorption rates for the laminates, the coupons and panels were soaked in water for periods up to three years and periodically weighed and measured. To prevent artificially high moisture absorption through the edges and core, the edges and inner face was coated with multiple layers of acrylic sealer and varnish. An advantage to this sealing method is that it does not significantly increase the material's stiffness or strength. A common way to predict moisture absorption is by the Fickian diffusion model. The following plot shows measured and best-fit theoretical prediction.

To determine what the actual weight gained for a boat is, the weight of laminate submerged in water can be multiplied by the graphed values. For the J/24, this works out to less than two pounds. As some owners reported gains of "50-100 pounds", other sources of moisture absorption must be present. These could include fairing compounds, sails and cushions.

Coupon fatigue testing took about a year and a half and was performed using 1" wide coupons in a 4-point bending configuration. Although wave loading occurs at a rate close to 1 Hz, the specimens were tested at rates ranging from 0.1 to 5 Hz, depending on the magnitude of the stress range. The higher the stress range, the lower the rate. From these tests a series of stiffness-based S-N curves were developed, showing the influence of fatigue on stiffness. The following plot shows the preliminary curves. On the plot, a curve labeled "12.5% wet" indicates that the specimens had their outer skin submerged until saturated, and that the stress cycled to a value of 12.5% of the static failure strain. Two important findings were evident. One was that no appreciable fatigue occurred below 25% of the static failure strain. The other was that for this laminate a 20% drop in stiffness generally predicted fatigue failure.

During the summer of 1999 some on-the-water testing was performed in San Francisco Bay using two J/24's supplied by OCSC. One was a 1981-vintage boat that saw very few hours of use (about 50 hours/year) prior to the testing.  The other was a 1984 boat that averaged over 800 hours/year of sailing, for a total of more than 11,000 total sailing hours at the time of testing! The goal of the comparison testing was to see if a difference in stiffness could be measured, indicating the amount of fatigue.  The methods used to check these included static measurements at the dock (discussed above) and underway dynamic strain readings.

The following picture shows the location of the two strain gages  located on the outside of the hull. Two others were located at the same spots on the inside.  Other gages were located on the forestay and chainplates to measure rig loads. Additionally, an accelerometer was mounted above the strain gages giving an indication of the boat's response in waves.

The next picture shows the boat sailing in the test area. A laptop recorded the gage and accelerometer readings. Note the Golden Gate Bridge on the left and the light air!  Atypical for San Francisco in July!

The waves were about 1' high and the windspeed was 10-12 knots.  The graph shows the predicted significant wave height and wave period for this area. These were generated using the Corps of Engineers' modified JONSWOP spectrum, which was originally developed to predict wave conditions in the North Sea. The wind information was supplied by WindCall, a company specializing in weather information for boardsailors. Their station locations in Berkeley and Albany were just downwind of the test area. Typical winter breezes range from 0-12 knots. During the spring and summer however the afternoon breezes often reach 25 knots. The table summarizes the wind speed for the Berkeley Circle over a typical year.

The greatest source of fatigue for most vessels is wave loads. To determine the number of waves encountered by a sailing vessel the wave speed and angle and the boat speed and angle must be known, as well as the number of hours sailed. This is somewhat complicated in a sailing vessel as the boat's speed is derived from the wind and the sailors' skill. As the tested boats were mostly sailed by students this was quite a variable!

To solve this problem a probabilistic analysis was performed using results from testing and a velocity prediction program. The end result was the prediction that the heavily-used boat had seen roughly 10.2 million waves, versus roughly 600,000 for the less used (but older) boat.

The next picture (the deck is removed for clarity) shows the quasi-static FEA prediction of the hull deflecting when hitting a 1' high wave in the bow (slamming).  The boat is heeled over on port tack and the scale is highly exaggerated! Note the localized "bump" from the wave impact. Other analysis performed on 6" through 3' waves gave the predicted strains across the wind range experienced by the vessel's used in the Berkeley Circle.

The dockside "string tests" indicated the 1981 boat was about 15% less stiff in global longitudinal bending than a brand-new boat, and the heavily used 1984 boat was 52% less stiff than a new boat.  Although performance prediction is not part of this project, lower longitudinal stiffness can also be linked to a performance loss in sailboats through increased headstay sag and loss of waterline length.

The panel flexural stiffness measured during sailing indicated the lightly-used boat was 4% less stiff than a new boat and the heavily-used boat was 18% less stiff than when new. Predictions were based on a linear damage accumulation model, combined with probabilistic analysis. The simplest version of the equation looked like:

Using the FEA predicted strains gave a stiffness reduction of 3% and 14% respectively, which was good considering the lack of information on "high-stress, low-cycle" (HSLC) fatigue. HSLC is any event that includes a high load, and is usually infrequent. These include collisions!

The difference in measurements between the two tests is significant, both in value and in importance. The string test measures both the hull structure and the rig components, and the strain gages measure just the material they are attached to, in this case the hull laminate. From the testing it appeared the rigging components, and their attachment to the hull were subject to much more fatigue softening than the hull laminate. Interestingly, the crew that sailed both boats were asked to immediately comment on the two boats' conditions. Universally they felt the newer (more used) boat felt "softer".

A summary of conclusions from the project includes:
 

1. “Traditional” single-value reduction factors on composite material properties for fatigue effects are not appropriate in most situations. These can lead to unconservative designs. Four-point bend tests yield acceptable results if the laminate is designed for tensile face failure and the span is large enough that core shear failure is unlikely.
2. Tensile modulus can be determined from tensile tests, but tensile strength is more accurate if derived from flexural tests.
3. Effects of long-term moisture exposure can not be reliably predicted through boil tests. In this case the boil test led to significant conservativeness. For laminates with low fiber volumes tensile properties as well as shear and compressive properties are effected. Significant differences were seen in the number of flexural cycles to failure, even though the inside surface, which failed first, was dry in both cases.
4. Panel testing can be replicated by finite element analysis and coupon tests. In cases where FEA is planned due to the complexity of structure, panel tests are not needed. In other cases, either FEA or panel tests can be used, although FEA offers significantly greater flexibility.
5. Relatively dense meshes are required to accurately model stresses and panel deflections when using linear shell elements. For high-cycle fatigue applications this is acceptable as in-plane deflections remain in the linear range of composites. Low-cycle applications should use a non-linear modulus profile to accurately model deflections and stresses.
6. COSMOS linear solid composite elements provided marginally accurate out-of-plane deflections and stresses, while linear shell elements can provide accurate results. Linear shell analysis can be improved by applying a single-step, in-plane, added-stiffness approximation. In cases where large deformation is combined with multi-axis loading, such as boundary constraints, geometric non-linear analysis is required.
7. Four-point flex tests return more consistent results than 3-point tests.
8. To match core shear vs. skin failure modes in an application, coupon spans must be sized large enough to eliminate premature shear failure.
9. Contrary to common opinion, edge-sealing does not influence moisture absorption rates of uncored polyester laminates. Varnishing the edges of balsa-cored laminates prevents moisture absorption while not significantly effecting stiffness.
10. The common marine practice of having thicker outer skin laminates can be justified for more than just abrasion resistance. The thicker outer skin is in compression when exposed to hydrostatic and dynamic loads. With reduced strength due to compression and moisture effects, and for practical reasons of water integrity, the common practice leads to first failure occurring with tensile failure of the inner skin.
11. Moisture absorption by the outer hull-skin did not significantly effect panel bending or strength, although it did effect the number of fatigue cycles to failure.
12. A simple, visual clue as to the onset of rapidly increasing fatigue failure is the onset of “whitening” of the resin. The size of the initial failure spots corresponds to the weave crimp dimensions. This could be used by surveyors to identify fatigue failure onset.
13. Stiffness reduction due to fatigue can be significant on small craft made of composites. In the case of some racing sailboats this verifies a commonly held opinion of boats going “soft.” Design load reduction factors of 4-8 are needed with polyester/E-glass (mat/cloth) laminates to avoid service-life stiffness reduction.
14. A proposed fatigue criteria of 40% of neat resin values appears unconservative in this application, where a value of 25% seems more appropriate. This may be due to the significantly higher cycles experienced in marine applications, the detrimental effects of moisture and most likely, the lower quality resins and fabrication methods than those used in other (such as aerospace) applications.
15. Polyester resins, which have failure strains of approximately 1% are not well matched to E-glass, which has a failure strain of nearly 5%. This leads to microcracking at a small portion of the fibers’ ultimate strength and large moisture absorption. Better combinations would include epoxy and vinyl ester resins which have failure strains of 4-7%.
16. Standard methods used for fatigue analysis of metal vessels can be applied to composite vessels, but unique S-N curves must be developed for each laminate.
17. A “Miner’s-type” damage accumulation approach can also be applied to stiffness reduction. Like the strength reduction, stiffness reduction in marine composites is dominated by low-cycle events. A few “significant events”, such as collisions, can cause the same amount of stiffness reduction as millions of cycles of wave slap.
18. A relatively simple “string” test can be used to check a vessel’s static stiffness. This also gives a good indication of the dynamic global bending stiffness. The string test may over-predict the loss of stiffness however, as it also includes the mast and pulpits and their connections to the hull and localized stress risers such as the laminate below the mast step and the stem fitting.
19. The “service-life” of recreational craft is difficult to predict. Designers should realize that some vessels may experience 10⁸ significant wave loading cycles. As most composite fatigue data only carries to 10⁶ cycles this requires a higher safety margin.

Professors Bob Bea, Alaa Mansour and Hari Dharan of UC Berkeley
Professors Dave Kreibel, Greg White and Bruce Nehrling of the US Naval Academy
Steve Burke of TPI, Steve Slaughter of Maricomp
Carl Schumacher and Gary Mull
Rich Jepsen and Anthony Sandberg of OCSC
Erich Chase, Susan and Steve Chamberlin, Nancy Pettengill, Tracy Powell, Dominique Roddier, Thom Henneberger and Brent Vaughn
Steve Crutchley, Frank Bucalo, Gary Gibson, Charlie Hoyt, Tom Sitzmann, Rusty Foard, and Jim Watts of the USNA
ENS Tullio Cellano and ENS Katy Westover, USN
David St. James of WindCall
And especially, my wife Dawn!

"Fatigue Prediction Verification of Fiberglass Hulls" in the October 2001 issue of Marine Technology

and,

The Final Report! (It is a 3.3MB pdf)
 

Back to Prof. Miller's Bio Page
Back to USNA NAOE Home Page