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72 8000 7000 Drag Force Vertical Force 6000 5000 Force (lbf) 4000 3000 2000 1000 Figure 9-15. Glass foam specimen after environmental 0 freeze­thaw testing. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Time (s) (Standardized testing generally uses 300 freeze­thaw cycles. Figure 9-14. Loading history for glass foam Due to the test duration required, this was abbreviated to a pendulum test. planned 50 cycles for this effort. An unplanned cycling overrun at the test facility resulted in a total of 78 cycles.) rigid wheel used in the strut assembly, which prevented natural Following the environmental tests, the specimens were sub- smoothing that might result with a pneumatic tire. jected to a low-speed platen compression test (Figure 9-16) In arrestor applications, the severity of the loading pulses to determine the performance degradation. When compared depends on several variables: with the fresh material, the samples exhibited a 60% decrease in energy absorption capacity and compression strength. · Relative compressive strength of the material, Mechanically, the closed cell foam limits water absorption, · Flexibility of the pneumatic aircraft tire, such that water penetrates only the outer-most open pores of · Relative penetration depth of the tire, and the foam. Upon freezing, the expanding water cracks the cells, · Glued or non-glued approach to joints in the material. permitting progressively deeper penetration into the specimen as the cyclical testing proceeds. The degradation observed is, In applications involving a flexible tire, or where the blocks therefore, not surprising. are glued at all joints, the loading pulses are expected to smooth These environmental tests represent the most severe of substantially. However, the appearance of these pulses gener- circumstances, where the specimens are fully immersed in ated questions regarding the feasibility of using separate blocks water, without normal countermeasures of drainage, protective of the material in an analogous manner to the current approach packaging, or sealants. Information provided by the manu- for EMAS. Whether or not these pulses would occur during facturer indicates that cyclical temperature and humidity do overruns into the existing EMAS beds is unclear. The nature not degrade the material over time, and a number of sealants of the pulses suggests that an arrestor design using a foam are available to prevent water absorption, if required. block material should explicitly include this seam effect; it Overall, these tests indicate that the glass foam material is not sufficient to make a general assumption that separate should be protected from immersion conditions caused by blocks essentially give the same loading as a continuous bed standing water, as is done for the current cellular cement of the material. material. Additional testing could be conducted to characterize durability in non-immersion scenarios, or in immersion con- ditions where a sealant has been applied to the material. 9.3.5. Environmental Tests A basic set of environmental tests was conducted to 9.4. Modeling Effort determine the necessity for weatherproofing the glass foam material. Two 3.65 × 2.5-in. cylinders were subjected to fully The modeling effort involved several stages, as shown pre- immersed freeze­thaw testing, per ATSM C 666/C 666M-03. viously in the flowchart of Figure 9-3. A high-fidelity model The specimens were subjected to 78 freeze­thaw cycles, during for the glass foam material was calibrated to match the test data which they absorbed water and partially eroded (Figure 9-15). (Figure 9-3, block 1). Using this material model, an arrestor

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73 Figure 9-16. Platen testing of glass foam environmental test specimen. bed model was constructed and coupled with tire models for has parameters as given by Table 9-2. The calibration process the different aircraft (Figure 9-3, block 4). Finally, large batches required defining these material parameters such that the model of simulations were conducted using these paired models, which performance matched that of the physical material tests. generated volumes of data for use by the APC (also block 4). This section will discuss the arrestor model development 9.4.2.2. Multi-Tester Model and batch simulation process. Performance predictions for the glass foam arrestor concept are reserved for the following A multi-tester model was constructed to simultaneously section (9.5). replicate the four laboratory material tests (Figure 9-17). The material parameters of the multi-tester model were optimized 9.4.1. Smoothed Particle Hydrodynamics using LS-OPT, an optimization software package. LS-OPT (SPH) Formulation ran the simulations in batches iteratively; after each iteration, it narrowed the region of interest, effectively zooming in closer The glass foam arrestor models were developed in LS-DYNA, to the predicted optimum calibration point. After 8 iterations a general-purpose finite element modeling code. Within of 12 simulations each, the design was optimized for a best-fit LS-DYNA, a number of formulations exist for representing set of material parameters. solids and fluids. Due to the high compressibility of the glass Table 9-3 gives a summary of the calibration process, includ- foam material, an SPH mesh-free formulation was employed. ing the final accuracy of the calibrated model. Test metrics SPH offered the ability to represent high-dislocation solids marked with an asterisk were optimization criteria, which with accuracy while maintaining time-efficient simulations. LS-OPT attempted to minimize. The remaining metrics were Because SPH uses particles instead of the more typical finite measured, but did not act as optimization criteria. elements, the illustrations in this section depict the material Of the various metrics given, the energy absorption values as a collection of small spheres. These particles are not dis- were the most critical to match accurately. As shown, all energy jointed pieces of aggregate, but are instead mathematically inter- connected to represent a continuous solid material (Lagrangian formulation). Table 9-2. Parameters for *MAT_063 or *MAT_CRUSHABLE_FOAM. 9.4.2. Calibration to Physical Tests Parameter Symbol Description MID Material ID number 9.4.2.1. Constitutive Model RO Density LS-DYNA currently offers about 200 constitutive models; E E Young's modulus of these, about 18 are applicable to various foams. Based on PR Poisson's ratio prior experience and on a review of the LS-DYNA keyword LCID Load curve ID for nominal stress versus strain manual, several candidates were singled out for evaluation. TSC Tensile stress cutoff After some experimentation, *MAT_CRUSHABLE_FOAM DAMP Rate sensitivity via damping coefficient was selected as the best overall choice. This material model

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74 Punch Specimen Hydrostatic High Rate Low Rate Platen Triaxial Platen Specimen Specimen Specimen (1/4 Symmetry) Shell membrane with 10 psi confinement Specimens After Compression Figure 9-17. Multi-tester model for glass foam material calibration. Table 9-3. Multi-tester specifications for glass foam material calibration. Test to Replicate Description Accuracy of Calibration Low-Speed Platen · 3.65 x 8-in. cylinder Test · Match stress­strain load curve with root-mean-squared error 7.0% (RMSE) to 85% compression* · Match energy absorption at 85% compression* 5.0% High-Speed Platen · 5.625 x 4-in. cylinder Test · Match stress­strain load curve with RMSE to 50% 17.7% compression* · Match energy absorption at 50% compression* 2.9% Hydrostatic · 3.65 x 8-in. cylinder Triaxial Test · 10 psi hydrostatic pressure · Match stress at 5% compression 19% Punch Test · Large block · Match stress­strain load curve with RMSE to 70% 8.4% compression · Match energy absorption at 70% compression 1.2%

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75 metrics were within 5% of the actual test values. The matching of the stress­strain load curves proved less consistent, which was expected since those curves tended to vary among the test specimens as well. The hydrostatic triaxial specimens proved somewhat dif- ficult to calibrate due to a nuance of the SPH formulation, which proved challenging to fit with a hydrostatic membrane load. Since the glass foam material exhibited little pressure dependence in testing, this was deemed a low-priority calibra- tion point. 9.4.2.3. Pendulum Model Using LS-DYNA, a model was constructed to replicate the pendulum tests (Figure 9-18). Because the material had been well-calibrated via the multi-tester, the pendulum model was used for validation of the material model, rather than for calibration. The pendulum strut was omitted because the penetrate depth of the actual test only allowed the wheel to contact the glass foam material. The foam bed was constructed with half-symmetry, such that it measured 9 ft in length, 1 ft Figure 9-19. Action sequence from glass foam in width, and 10 in. in depth. The bottom and outer sides pendulum model. of the bed were constrained to simulate the presence of the confining box. Overall, the pendulum model validated that the glass foam The wheel followed an arced path approximating that of material was well calibrated. the actual strut, with the same 1/3-diameter penetration depth into the arrestor bed. The wheel began with no rotation and was allowed to freely spin upon contact with the arrestor bed, 9.4.3. Tire and Arrestor Simulations just as in the actual test (Figure 9-19). Using the calibrated glass foam material model previously The SPH particles were sized to 0.75 in., which was based on described (Section 9.4.2), a large-scale arrestor model was particle size scaling relationships developed in other simulation created in LS-DYNA to simulate overruns by aircraft tires. No sets to maintain reasonable accuracy. This provided four par- ticles across the half-width of the wheel, which was the smallest 8000 characteristic length of the interface. A separate particle size Test Drag Force convergence study was not undertaken for this model. Test Vertical Force Model Drag Force The resulting loads matched the test data well, though no Model Vertical Force pulses were observed due to the lack of material seams in the 6000 model (Figure 9-20). The average drag and vertical loads were within 6% and 1% of the average test results, respectively. Force (lbf) Since the test data showed a 6 to 10% variation for these two 4000 metrics, the model is within the experimental data scatter. 2000 0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 Time (s) Figure 9-20. Comparison of test and model load Figure 9-18. Overview of glass foam pendulum model. histories for glass foam pendulum test.

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76 protective cover layer for the bed was included in the model; material. The smallest bed, used for the 18-in. nose tire of the it was assumed that a well-designed cover layer (likely made CRJ-200, was 120 in. long and 9 in. wide. The largest bed, used of thin plastic or a spray-on polymer) should have minimal for the 49-in. main tire of the B747-400, was 225 in. long and impact on the mechanical response. The model further assumed 36 in. wide. a continuous material, and material seams were not included. All beds were constructed with a 36-in. depth. However, the Figure 9-21 illustrates the model with a 36-in. depth and a effective depth of the bed was adjusted by use of a movable B737-800 main-gear tire (Goodyear H44.5 × 16.5) at 50% rigid plane (Figure 9-22). Only the upper part of the material, penetration depth. above the rigid plane, was involved in the overrun compression. This approach enabled various depths to be rapidly configured within a single arrestor bed model. 9.4.3.1. Arrestor Bed Models SPH particle sizes were chosen based on the tire size. An The arrestor bed models were constructed using half- error estimation process was undertaken to determine the symmetry to reduce computation time. They varied in size required particle size to maintain an acceptably low discretiza- depending on the aircraft tire being used. The bed length was tion error. For the larger tires, a 2 in. particle size was found determined by the distance required for the tire to make a to have less than a 4% error for the predicted drag and verti- certain number of rotations such that the loading settled to a cal loads. For smaller tires, the particle size was reduced to 1 in. steady-state condition. The bed width was determined by the to maintain similar size proportionality. Based on the parti- tire width such that artificial boundary effects were minimal cle and bed size variations, a typical bed model had nominally and the response approximated that of a wide bed of the 45K particles. Small Pieces of Glass Foam Fragment Off of Bed Deformable Finite Element Aircraft Tire Model Arrestor and Tire Model Uses Half- Symmetry SPH Arrestor Bed Tire Penetrates Vertically to a Prescribed Depth Material Compressed by Tire Figure 9-21. Model of combined tire and glass foam arrestor system.

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77 Rigid Plane at 18- inch Depth Only Upper Part of Material 36-inch Involved in Compression Deep Bed Figure 9-22. Adjustable height of glass foam arrestor bed. 9.4.3.2. Tire Models material underwent compression. The interplay of the tire and arrestor compression created oscillations in the measured The tire models were fully deformable finite element models loads. This oscillating behavior was further amplified by the (FEM), as discussed in Appendix F. Table 9-4 summarizes the free-spinning nature of the tire. Eventually the tire would tire models developed. Each tire model was calibrated to match settle to a constant rate of rotation, which proved to be a the actual tire's load-deflection performance up to 80% of the function of the forward speed, depth, and interface friction. maximum bottoming load. This 80% load became a limit It was found that a minimum forward travel distance was criterion during the batch simulations. required for the loads and rotation to reach steady-state con- The deformable nature of the tires produced an accurate ditions before load measurements could be made. representation of the interface between the tire and the arrestor Sequencing options included several factors: material. As the load on the tire increased due to deeper bed penetration, the contact area became flatter with an increased · Prescribed vertical penetrations versus prescribed vertical surface area. This shape change created a corresponding loads, increase in the load on the tire. · Applying the vertical penetration/load before or after begin- ning the forward motion, and 9.4.3.3. Sequencing of Simulations · Applying the forward motion before or after making contact with the bed. Because the tires in the LS-DYNA simulations were deformable and were allowed to spin freely, a sequencing Depending on the sequencing method used to accelerate the method was required to create stable, fast-running simula- tions. These two factors were additional complications that tire and set the penetration depth, the initial oscillations could were not present in the EDEM software package aggregate be more or less severe. This in turn could require longer or simulations. However, the inclusion of these factors led to shorter simulation times and longer or shorter arrestor beds. higher-fidelity results. Because the arrestor­tire models were to be run repeatedly in From a mechanical standpoint, as the axle of the wheel large batches, it was important to develop a sequencing method- penetrated the bed vertically, both the tire and the arrestor ology that would produce efficient simulation run times. Multiple methods were attempted through experimentation before settling on the approach illustrated by Figure 9-23. The tire was first pressed downward into the material to a prescribed Table 9-4. FEM tire library for glass depth. Then the tire was accelerated to the desired forward foam arrestor models. speed and spun-up to an initial rotation speed (typically about Aircraft Landing Gear Tire Designation one-third of the ideal rotation rate expected on hard pavement). CRJ-200 Main Gear H29x9.0-15 The prescribed spin rate was then released, allowing the tire Nose Gear R18x4.4 to settle to a natural rotation rate, while the forward motion continued at a constant speed. After the oscillations settled B737-800 Main Gear H44.5x16.5-21 out of the system, the steady-state vertical and drag loads were Nose Gear H27x7.7-15 measured. B747-400 Main Gear H49x19-22 The final result was an accurate prediction of the loads on Nose Gear H49x19-22 the tire under free-spinning un-braked conditions.

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78 Tire begins above arrestor Tire presses down into arrestor Tire accelerates f orward and is given an initial spin rate Tire continues f orward and is allowed to f reely spin Steady-state vertical and drag loads are measured Figure 9-23. Sequencing method for glass foam arrestor model. 9.4.4. Batch Simulations a tire to travel the required minimum distance. Loading at speeds below 10 knots was based on the extrapolated Using the arrestor bed model, large batches of simulations metamodel data fit.); were conducted to generate substantial bodies of data for a wide · Bed depth, in incremental depths from 3 to 36 in. (Fig- range of overrun conditions. This data was then assembled ure 9-24); and into "metamodels" for uploading and use by the APC. · Penetration into the bed, from 10% to 100% of maximum penetration depth. 9.4.4.1. Methodology Batch simulations were conducted for each tire with three Due to the two sources of compression (arrestor material and open variables: tire), the definition for penetration depth was more complex than for the rigid tire approach used for the aggregate arrestor · Speed, from 10 to 70 knots (Speeds below 10 knots were models. Two conditions defined the maximum penetration impractical due to the long simulation times required for depth: Penetration Tire Rut Depth Depth Deflection Bottoming Depth Bed Depth Figure 9-24. Depth definitions for glass foam bed models.

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79 1. The maximum penetration depth was considered to be As the table shows, the points used in the metamodels were 85% of the bed depth (fully compressed material) plus the often less than the total number of simulations conducted. deflection of the tire at 80% of the bottoming load. Beyond This discrepancy was caused by simulations that failed prior this degree of penetration, the tire models were no longer to termination due to tire overloading, or simulations that had accurate. not adequately settled to steady-state conditions for accurate 2. For small tires in deep beds, the maximum penetration load measurement. The smaller tires experienced a greater was further limited to be no greater than the tire diameter. percentage of omitted runs than the larger tires due to the At depths beyond this, the simulations often did not settle to relative loading severity and greater proportional penetra- steady-state conditions. (This depth issue ultimately proved tion depths. irrelevant, since most functional arrestor bed designs generated with the APC did not use bed depths that were 9.4.4.3. Parameter Sensitivities greater than the tire diameter.) Using the metamodels, it is possible to review how sensitive The large batch simulations were conducted using LS-OPT. the landing gear loads are to the different variables of speed, Based on the initial model files, LS-OPT generated permuta- bed depth, and penetration percentage. Figure 9-25 shows a tions with various speeds, bed depths, and penetration levels. surface plot for the 44.5-in. main-gear tire of the B737 in an It sequentially executed the simulations and extracted the load 18-in. deep glass foam arrestor bed. data from them. Generally, the batches were conducted in Stronger drag loads (shown as the lower, more negative multiple iterations of 10 simulations each. Additional itera- values) occur when the penetration ratio increases, up to the tions were added to improve accuracy as needed. maximum of 1.0 (or 100%). The loading is, therefore, strongly dependent on the depth of penetration into the bed, as would 9.4.4.2. Summary Tables of Metamodels be expected. By contrast, the variation with speed shows very little The output from the batch simulations was extracted and change between 10 and 70 knots. The loading is fairly insen- assembled automatically by LS-OPT, where metamodels were sitive to speed, reflecting the low rate-sensitivity that was constructed for the drag and vertical load forces. Metamodeling exhibited during the small-scale lab testing. Practically speak- is analogous to fitting a curve through experimental data, except ing, this means that the glass foam system will exert nearly it is applied to multi-dimensional data sets. These data sets the same deceleration load on an aircraft travelling at high were four-dimensional, including speed, depth, penetration, or low speed. This behavior is desirable for an arrestor and and load (either vertical or drag). The metamodels were radial is consistent with the general behavior of the current EMAS basis function (RBF) networks, which can effectively capture material. non-linear behaviors including multiple concavity changes across the data set. 9.4.4.4. Data Transformation Table 9-5 summarizes the fit quality for the metamodels. The root-mean-squared (RMS) error was typically below 5%, The final metamodel data for each tire was converted for use and the R-squared value was typically above 0.98, indicating by the APC. LS-OPT was used to extract nominally 9,000 data good fit quality with minimal noise. points from each metamodel and export it into tabular form. Table 9-5. Metamodel accuracy summary for glass foam arrestor bed. Simulations Points Tire Response RMS Error R2 Conducted Used Drag 2.35% 0.999 H49 49 49 Vertical 5.25% 0.988 Drag 2.78% 0.999 H44 70 67 Vertical 1.08% 0.999 Drag 2.78% 0.998 H29 60 60 Vertical 4.88% 0.986 Drag 3.21% 0.998 R27 60 47 Vertical 5.06% 0.982 Drag 3.74% 0.995 H18 100 86 Vertical 5.83% 0.969