IMPROVEMENT IN ENERGY ABSORPTION THROUGH USE OF BISTABLE STRUCTURES

Z. Whitman, V. La Saponara, D. O. Adams,

Department of Mechanical Engineering S. Leelavanichkul, A. Cherkaev, E. Cherkaev, V. Vinogradov,

Department of Mathematics, University of Utah, Salt Lake City, UT 84112

ABSTRACT

Many avenues have been explored while searching for energy absorption measures to incorporate into our modern designs. From a simple Strength of Materials standpoint, it is most effective to use a uniaxial tensile member since all the material is stressed equally. The disadvantage of a single member consists of the fact that once instabilities develop, only a small part of its length can absorb energy. The concepts of “main link” and “waiting link” are discussed in this paper: they allow a structure to exhibit numerous controlled instabilities with a resulting increase of energy absorption. The other advantage of this structural concept is a fail safe condition of the length still being intact by the unbroken waiting links. This is accomplished through the appropriate designation of waiting link variables. Composites which exhibit linearly elastic behavior are also excellent candidates for these structures. KEYWORDS: Bistable, Energy absorption, Composite

1. INTRODUCTION Automotive structures have evolved from the need to meet the basic needs for transportation to structures where safety considerations, crumple zones and energy absorption are critical. Most safety devices implemented in automobiles require a given activation energy and then use progressive deformation and damage to absorb the impact. The problem with this approach is that the car in its ‘crumpled’ form is weaker than the structure before impact, which may compromise the safety of its occupants. Bistable structures are characterized by a damaged phase which is stronger than the undamaged phase, and are advocated for their energy absorption capabilities and fail safe mechanisms for automotive and aerospace applications, ship constructions, armors, etc. The concept of bistable structures was introduced by Cherkaev and Slepyan [1-3] in 1995. Their work showed that a considerable increase in energy could be absorbed for the same volume of material while remaining cohesive after impact. This was due to the waiting links. A similar concept using high deformation viscoelastic solids was introduced by Dancila, [4], in 1998. The stress/strain energy curve of a bistable structure has two or more parts in which the structure is stable, separated by unstable regions. A novel design of a bistable structure is made of a chain-like structure composed of a “main link” and “a waiting link”, [1-3]: the main link is designed in order to fracture first, but is connected to the waiting link, which provides a redundant load path.

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As the main link fractures, the connected waiting link begins resisting the external load and will deform accordingly. Some design concepts for metallic and composite bistable structures are discussed in this paper. The first proof-of-concepts of the mathematical model of Cherkaev and Slepyan [1-3] has been provided by metallic bistable chain-like structures, which were designed, manufactured, tested and modeled in order to exhibit the desired response. Bistable structures made of stitched sandwich composites are investigated because of their proven high stiffness-to-weight ratio, high damage tolerance and energy absorption, [5, 7-18], and the possibility to tailor their properties to the load requirements.

2. INVESTIGATION OF BISTABLE LINKAGES: TYPES OF ELEMENTS

Three main types of tensile bistable elements are proposed, which exhibit the desired response and energy absorption properties. The first two types utilize a main link made of a ductile material. The unstable necking of this ductile element allows an increase in energy absorption through many necking regions occurring along the length of the link instead of a single location. The first element type, called Tensile Element 1 (TE1), has a waiting link designed in order to allow the main link to fracture. This allows reaching the maximum amount of energy that the main link can absorb. Also, any slack between the fractured main link and the waiting link elastically relaxes the rest of the chain, leading to a rather minimal amount of extra energy absorption since the load must re-stress the relaxed links. Consequently, the fracture of the main link results in an explosive release of energy, possibly damaging other elements thus the TE1 is most effective in relatively slow strain situations. The second element considered, called Tensile Element 2 (TE2), has the same main link used for Tensile Element 1, but this time the connected waiting link straightens and carries load after the main link necks but before its fracture. This configuration allows for a more stable uniform response with no sudden drops in load. Since the main link provides much of the load carrying capacity for the element, a lighter and smaller waiting element can be utilized, with further gain in weight with respect to Tensile Element 1. Finally, the third element, called Tensile Element 3 (TE3), employees a main link material which exhibits a relatively brittle response with little or no plastic deformation before fracture. In this configuration, any slack in the waiting link translates into the elastic reduction in strain of the other unbroken links. The benefit with this linkage is that variations of the length of the waiting element allow recovering as much strain as it is desired, because of the lack of plastic deformation. Once a main link has broken, a brittle waiting link can perform the same function as the main link by absorbing energy and then relaxing after the following fracture, essentially “recharging” the element. For this study, carbon fiber reinforced composites are considered since they can be easily tailored by varying materials and fiber direction. This third type of bistable element has the potential to absorb much more energy than the other two types. Once these elements’ response has been quantified through Finite Element Analysis (FEA) or by testing, any combination of main links and waiting links may be designed, with a resulting chain where the elements are in series or in a net-type structure, with a rectangular lay-out (Figure 1), hexagonal or linear lay-outs.

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Figure 1

Net of bistable elements. Main links are represented in blue, waiting links in green. 2.1 Tensile Bistable Element Type 1 (TE1) For this linkage, several designs were examined using common engineering materials such as aluminum, mild steel, and copper. Aluminum was selected because of its light weight and availability. Mild A36 steel was also a candidate for this study because of its ductility. Finally, 11000 copper was included because its stress/strain curves exhibit a large necking region with respect to the total plastic region. Chains of bistable elements made of these materials were designed, manufactured and tested. For sake of simplicity, a main link was developed and sized based on the ASTM standard E6-2000b and is shown in Figure 2.

38.1 9.525

31.75

6.35

6.35

19.05

Figure 2 To the left a 5052 H32 Aluminum alloy bistable structure with one main link and one waiting link. To the right, sketch of links with dimensions in mm (not to scale). Note that the waiting link was curved to the shape in Figure 10a. The waiting link is 20% longer than the main link.

38.1

9.525

6.35

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5052-H32 Aluminum was used. Other alloys, which can be heat treated, might be better options for the project, and will be considered for future work. Many different designs were assessed and tested, but the most effective was a dog bone-shaped linkage which could be easily assembled by bolting different sections together. To quantify the responses of each component (main link, waiting link and main + waiting links), three tests were carried out. The first one was a static tensile test of the main link by itself. The second test evaluated the waiting link, which is initially curved. It was imperative to keep constant the initial node-to-node distance for main link and waiting link. To give the correct pre-load to the waiting link, a full element (main link + waiting link) was inserted in the MTI testing machine and preloaded. Once the load train straightened at the value of 44.5 N (10 lbs), the machine stopped the preload sequence and waits for the user to run the actual test. At this point, the main link was cut through so it did not carry any load for the remainder of the test. This ensured that the waiting link responded exactly as it would in a full element. Finally, the last test was performed on a full element (one main link + one waiting link). Figures 3, 4 and 5 show pictures of these tests as well as the appropriate element’s responses.

Figure 3 a) test for the main link, b) test for the waiting link (the main link has been cut), c) test for full element. 5052-H32 aluminum has been used in the elements.

31.75 mm

a) b) c)

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Figure 4 a) response of a typical main link made of 5052-H32 aluminum; b) typical response of a

waiting link of the same material.

a) b)

Main Link: Force vs. Displacement

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Figure 5 Response of a typical full bistable link made of 5052-H32 aluminum

Full Bistable Linkage: Force vs. Displacement

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As can be observed in Figure 4b, the response of the waiting link is quite hard to predict, and any future finite element model would need to capture the non-linear straightening of the waiting link and the work hardening that occurs. Figure 5 shows that the overall response of this linkage exhibits a second phase which is stronger than the first. Moreover, each of the three materials examined in this study has been found to have quite different responses when used to manufacture the linkages. The response of the main link (Figure 6) is easily predicted since it is obtained by just the traditional ASTM E6-2000b tensile test. The main link is straight, hence its response will mimic the stress/strain diagrams for the material and can be determined by knowing its length and cross-sectional area.

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Figure 6 Behavior of main links for different materials

(aluminum, steel and copper)

Multiple Main Links of Different Materials: Force vs. Displacement

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AluminumSteelCopper

The waiting links’ response, however, can vary noticeably because it is a function of the work hardening coefficient, radius of curvature, width, thickness and length of the link. Figure 7 shows the response of waiting links manufactured with the three materials examined. It was expected that each waiting link would almost reach its maximum load carrying capacity at nominally the same displacement for all waiting links, based on the fact that the geometry is the same. However, this was not the case. The steel waiting link reached 15% of its full capacity before becoming fully straight. The aluminum exhibited a 50% reduction in full load plastic zone while the steel reduced only 10% less than the copper. As the steel link started to plastically deform, it was expected that its plastic sectional area would be less than the area of a straight and non-plastically deformed element. The quantification of this area change was difficult to predict.

Figure 7 Behavior of waiting links for different materials

(aluminum, steel and copper)

Multiple Waiting Links of Different Materials: Force vs. Displacement

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Using these tests as guidelines, a set of specimens was designed to take advantage of the unique energy absorption capability offered by bistable structures. An improvement in energy absorption is assessed when the bistable structure can absorb more energy than a non-bistable structure with the same amount of gauge material. For sake of simplicity, the nodes themselves (where the main and waiting links are connected) are not included in the calculations. Their size and material volume will vary based on the final design and construction, and their influence will be calculated at a later stage of this research work. Chains with one, two and three bistable linkages were manufactured with aluminum 5052-H32 and tested. The absorbed energy was calculated as the area under the load/displacement curve, and compared to the energy absorbed in the baseline specimens. Baseline specimens had the same cross-section as each full bistable link. It should be recalled that the main link and waiting link were made of 1.59 mm (0.0625 in.) thick sheet, and were respectively 6.35 mm (¼ in.) and 9.525 mm (3/8 in.) wide (Figure 2) . The baseline specimens had the same thickness and a width equal to 15.9 mm (5/8 in.), and also overall length equal to one, two and three times the length of a single element plus an additional 12%. This 12% takes into account the increased length of the waiting element based on its width with respect to the total width of the baseline specimen (20% · 9.525/15.9 = 12%). The resulting overall lengths for the three baseline specimens were 35.6 mm (1.4 in.), 71.1 mm (2.8 in.) and 107 mm (4.2 in.).

Figure 8 Comparison of displacement/force curves for three different

chains of aluminum 5052-H32

Comparison of Three Different Chains: Force vs. Displacement

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Three Elements

Two Elements

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From Figure 8, it can be observed that the deformation length of the final ‘hump’ increases with the number of bistable elements, due to the increased length of material to be plastically deformed before the waiting links start to neck and fracture.

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Figure 9 Load vs. displacement curve of the baseline specimens for

1, 2 and 3 elements

Base Line for TE1 Evaluation: Force vs. Displacement

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Figure 9 shows how the necking singularity in the baseline specimens affects in a different way the overall deformation of the specimens. The advantage of bistable structures consists in their ability to utilize multiple singularities to have a controlled failure with larger deformation energy. This aspect can be clearly seen from Figure 10.

Figure 10 Energy absorbed vs. number of elements for baseline and TE1 elements

Number of Elements vs. Energy Absorbed

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Figure 10 shows the divergent trend between the TE1 bistable elements and their equivalent baseline tensile specimens. The energy absorbed is proportional to the number of elements used in TE1 elements. On the other hand, the single necking region in the baseline elements leads to a nonlinear increase in energy absorbed, which may be significantly less than the energy absorbed in bistable elements. 2.2 Tensile Bistable Element Type 2 (TE2) TE2 type elements, where waiting links participate more in sharing the load with main links, are currently being developed. Tests are underway to evaluate similar TE1 and TE2 elements and to determine any other net benefits of using one with respect to the other. 2.3 Tensile Bistable Element Type 3 (TE3) This type of elements exhibits brittle fracture, and its absorbed elastic energy can be reused multiple times through slack in the system created by fracturing elements. For the initial evaluation, the waiting and main links have been manufactured out of plies of T-300 woven carbon fabric, which have been infiltrated with Epon 862 resin mixed with EpiKure 9553 hardener, in a Vacuum Assisted Resin Transfer Molding (VARTM) process. Several obstacles were encountered in the process. First, delamination was observed among the plies forming the waiting links and the main links. To prevent delamination, all specimens were stitched through the thickness with four rows of 5 mm (0.19 in.) spaced stitches each 5 mm apart with respect to the junction of waiting and main links. Tests will be carried out at a later stage to minimize the amount of stitching needed. An additional problem to be overcome was the creation of a curved waiting link similar to the successful metal design. Small shapes of Last-a-Foam polyurethane core with a density of 64.1 kg/m3 (4 lbs/ft3) were utilized for this purpose. Eight designs were carried out, and each iteration consisted of two specimens: in one specimen, the waiting link was formed of core and infiltrated facesheets, in the other specimen the core was removed after infiltration (with a blunt tool, to prevent damage to the fibers), so that it would not transfer shear between the main and waiting links. Results are given in Tables 1 and 2.

Table 1 Investigation of composite bistable links. The process involved eight iterations, with changes in

the core shape, use of teflon, change of ply configuration. Numbers in grey indicate that a bistable type of response was observed in the tests. The ply configuration denotes the number of

plies given to the waiting link, a, and main links, b, in format a+b.

Iteration Number First Second Third Fourth Energy Absorbed With Core (J) 12.9 8.2 12.3 5.8

Energy Absorbed With Core Removed (J) 7.6 7.3 11.5 4.5

Core Shape TrapezoidSmall

Circular Segment

Large circular

segment

Large Circular Segment

% Wait Produced 8.8% 3.9% 10.6% 10.6% Teflon Wraped Core Shape No No No No

Ply configuration 4+2 4+2 4+2 2+1

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Table 2

Iteration Number Fifth Sixth Seventh Eighth

Energy Absorbed With Core (J) 4.3 5.0 4.6 5.8 Energy Absorbed With Core Removed (J) 4.5 5.6 6.5 5.4

Core Shape Broken Edge

Trapezoid

Broken Edge

Trapezoid

Large Circular Segment

Round Gumdrop

% Wait Produced 6.7% 6.7% 10.6% 23.4% Teflon Wraped Core Shape No Yes Yes Yes

Ply configuration 2+1 2+1 2+1 2+1 A bistable response was assessed by the fact that the failure of the main link was followed by the failure of the waiting link in two separate instances. In all of the cases examined, no waiting link proved to be stronger than the main link. Figure 11 shows the iterations in the core shape.

a) b)

c) d)

e)Figure 11

Bistable links with a) trapezoid shape, iteration 1; b) small circular segment, iteration 2; c) broken edge trapezoid, iteration 5,6; d) large circular segment,

iteration 3, 4, 7; d) gumdrop shape, iteration 8.

5 mm

The first iteration gave mixed results. While the configuration with the core proved to be bistable, the one with the removed core did not. The initial fracture of the main link of these first iteration specimens seemed to create the propagation of a strong damage wave along the chain. This damage wave caused rupture of the waiting like at nearly the same moment of main link’s

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rupture. This same failure mode was seen in the tests on the second iteration specimens, which had a shallow arc shape meant to reduce the local curvature of the trapezoid shape. In the third and fourth iterations, similar specimens were manufactured and tested, with the only difference consisting of the different number of plies in main and waiting links. The fourth iteration had half the number of plies with respect to the third iteration, thus effectively reducing the thickness of the waiting link and thereby the bending stress. The third iteration specimens broke at the junction of the main and waiting links with the foam core. This failure may be due in part due to a combined effect of resin excess at the junction as well as a smaller radius of curvature for this core shape. The fourth iteration specimens showed a bistable behavior, possibly because of a less thick waiting link. However, the matrix excess at the junction caused their failure. To reduce this problem, Teflon cloth was placed between the T-300 cloth and the foam core in iterations six through eight. A comparison between iterations five and six shows that Teflon’s insertion was quite effective. The specimens with the Teflon behaved in a bistable manner and thus dissipated much more energy than the specimens without. Responses from the bistable configurations are shown in Figures 12-15 below.

Fourth Iteration

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Figure 12 Response of fourth type of bistable specimens

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Sixth Iteration

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Figure 13 Response of sixth type of bistable specimens

In the seventh iteration, an excess of resin at the junction caused the curved shape of the waiting link to be maintained until a value of 896 N (200 lbs) was reached in the second branch of load/displacement curve. At that point, the curved specimen snapped. The analogous specimen without core exhibited an unusual response, which could be justified by considering the shock wave from one of the three main links’ breakage to cause the further main link to crack most of the way through the width. This resulted in the final fracture being obtained at a much smaller load (1344 N) than the value needed for the first fracture.

Seventh Iteration

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Figure 14 Response of seventh type of bistable specimens

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The last specimen examined in this preliminary study was iteration eight, which turned out to have too much curvature, with resulting excess resin at the crease between waiting link, main link and core.

Figure 15 Response of eighth type of bistable specimens

Eight Iteration

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Both specimens in Figure 15 exhibited a load drop when the excess matrix was debonded from the fibers at the indicated location, which caused the waiting links in the two specimens to break at that section (Figure 16).

Figure 16 Failure in 8th iteration specimen due to

excess resin

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The presence of the core increased the stiffness of the elements with respect to the case of no core, as could be expected. In all but two iterations (fifth and seventh), the specimens with the core absorbed more energy. Removing the core is an additional step which may be costly (especially in 2-D configurations where other links could potentially block its removal). Future studies will consider the use of fiberglass which has a higher strain at failure, and design an optimal composite bistable structure.

3. SUMMARY AND CONCLUSIONS

Experimental investigations of bistable structures were presented in this paper. Bistable structures exhibit a large increase of energy absorption with respect to traditional structures due to the synergistic interactions of main links and waiting links, which are designed to break in a controlled way. Bistable structures have the potential to be a breakthrough in all fail safe applications. Metallic and composite bistable elements were designed. In metallic bistable elements, results are available for three types of materials and chain-like configurations with different numbers of bistable links. Multiple necking sites allowed the structures to behave as bistable and absorb more energy than in the case of the baseline specimens. Bistable elements made of steel and copper are likely to be excellent candidates because of the large amount of necking in comparison to their overall yielding. In composite bistable elements, sandwich stitched composites were designed, manufactured and tested. The effect of the core shape, its absence, and length of waiting link was assessed. The main challenge seems to prevent excess resin from being the weakest link in the structures. Further studies will identify an optimal composite bistable structure with the largest energy absorption capability per unit weight.

ACKNOWLEDGEMENTS

The support of the Army Research Office grant ARO No. 41363-MA is greatly appreciated.

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6. G. Demelio, K. Genovese, C. Pappalettere, An experimental investigation of static and fatigue behaviour of sandwich composite panels joined by fasteners, Composites: Part B, 32, pp. 299-308 (2001) 7. K. S. Raju, and J. S. Tomblin, Energy Absorption Characteristics of Stitched Composite Sandwich Panels, Journal of Composite Materials, 33, pp. 712-728 (1999) 8. L. E. Stanley, D. O. Adams, Development and Evaluation of Stitched Sandwich Panels, NASA/CR-2001-211025, June 2001 9. L. E. Stanley, S. S. Gharpure, D. O. Adams, Mechanical Property Evaluation of Stitched Composite Sandwich Panels, Proceedings of the 45th International SAMPE Symposium and Exhibition, Long Beach, CA, May 2000 10. L. E. Stanley, D. O. Adams, Evaluation of Stitched Composite Sandwich Panels Under Interlaminar Loading, Proceedings of the American Society for Composites Technical Conference, Blacksburg, VA, September 2001 11. L. E. Stanley, D. O. Adams, Damage Tolerance of Stitched Composite Sandwich Structures, Proceedings of the 46th International SAMPE Symposium and Exhibition, Long Beach, CA, May 2001 12. J. M. Butterfield, D. O. Adams, Effects of Stitching on the Compression After Impact Strength of Sandwich Composites, Proceedings of the 49th International SAMPE Symposium and Exhibition, Long Beach, CA, May 2004 13. A. L. Van Otten, N. S. Ellerbeck, D. O. Adams, C. Nailadi, K. Shahwan, Evaluation of Sandwich Composites for Automotive Applications, Proceedings of the 49th International SAMPE Symposium and Exhibition, Long Beach, CA, May 2004 14. V. Ghate, V. La Saponara, P. Singh, Z. Whitman, Buckling and Face Wrinkling Behavior of Stitched Sandwich Plates, accepted for publication by the International Journal of Solids and Structures, January 2005 15. J. H. Kim, Y. S. Lee, B. J. Park, D. H. Kim, Evaluation of Durability and Strength of Stitched Foam-Cored Sandwich Structures, Composite Structures, pp. 543-550 (1999) 16. P. Singh, V. La Saponara, Experimental Investigation on Performance of angle-Stitched Sandwich Structures, AIAA 2004-1705, Proceedings of tjhe 45th AIAA Structures, Structural Dynamics and Materials Conference (SDM 2004), Palm Springs, CA, April 2004 17. Z. Whitman, M. Worley, V. Ghate, V. La Saponara, Experimental and Numerical Analysis of Notched Stitched Sandwich Structures, submitted to the SAMPE (Society for the Advancement of Material and Process Engineering) 2005 International Sjymposium and Exhibition, to be held on May 2005 in Long Beach, CA 18. V. La Saponara, S. Kamaya, Evaluation of Static Compression Properties of Notched Stitched Sandwich Structures, AIAA 2004-1704, Proceedings of the 45th AIAA Structures, Structural Dynamics and Material Conference, (SDM 2004), Palm Springs, CA, April 2004

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