CRANFIELD UNIVERSITY
Olivier Larmande
Simulation of Composite Helicopter Subfloor Impact on Water with LSDyna
School of Engineering Aerospace Vehicle Design
MSc Academic Year: 2009 - 2010
Supervisor: Kevin Hughes September 2010
CRANFIELD UNIVERSITY
School of Engineering Aerospace Vehicle Design
MSc
Academic Year 2009 - 2010
Olivier Larmande
Simulation of Composite Helicopter Subfloor Impact on Water with LSDyna
Supervisor: Kevin Hughes
September 2010 This thesis is submitted in partial fulfilment of the requirements for the degree of Aerospace Vehicle Design
© Cranfield University 2010. All rights reserved. No part of this publication may be reproduced without the written permission of the copyright owner.
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HEALTH WARNING
"This thesis has been assessed as of satisfactory standard for the award of a Master of Science degree in Aerospace Vehicle Design. This thesis covers the part of the assessment concerned with the Group Design Project/Individual Research Project. Readers must be aware that the work contained is not necessarily 100% correct, and caution should be exercised if the thesis or the data it contains is being used for future work. If in doubt, please refer to the supervisor named in the thesis, or the Department of Aerospace Technology."
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ABSTRACT One of the ways to improve the safety of helicopters is to enhance their crashworthiness capabilities. Composite materials are particularly helpful in this field thanks to their high energy absorption characteristics, especially when compared to aluminium alloys. The research in the crashworthiness field is driven by numerical simulation methods, which has the potential to give cost-efficient results by limiting the needed number of costly drop-tests of real airframes. As composite materials have been used in the aeronautical industry and specifically in helicopters for some decades, their behaviour is now well understood. However, it is very complex and, as such, difficult to simulate accurately in computer simulations. The research has been at first mainly focused on impacts with hard surfaces; this choice is highlighted by the regulation MIL-STD-1290, which is the only official regulation on the topic and deals only with hard surfaces or soft soil impacts. The aim of this work is to evaluate the capacity of the commercial software LS-Dyna to simulate the impact of a helicopter subfloor into water, using stock material models and techniques. Real drop-tests of a helicopter subfloor concept (developed during the program CAST) are simulated, and the results given by the simulation evaluated against these tests. The vertical speed of impact during those tests was 8 m/s. A composite material model has been chosen, and validated by simulating a tube crush and reaching the right energy absorption amount. Then, this material model has been assigned to a geometrical model of a concept helicopter subfloor. The last step was to simulate a drop of the subfloor in water and on a hard surface, to confirm previous results obtained with house-made specially developed material models.
Keywords: Composite, Crashworthiness, Dyna, Water, Helicopter.
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ACKNOWLEDGMENTS
Above all, the author want to acknowledge the most needed assistance and expertise he constantly received from Dr Kevin Hughes, who supervised this work. He also would like to thank his family for their constant support through this year, and Florian Truchelut for his support. Special thanks also are addressed to Ms Sylviane Wignacourt for her hard work in giving her students opportunities to finish their studies abroad.
He also would like to give acknowledgments: To the team of the Comet Café, whose unfortunate absence during one of the final weeks of the thesis had a dramatic impact on the frequentation of Building 83; To the University, whose constant will to improve the comfort of its students and the quality of the snack machines prevented us from the use of these very machines, for our own good; To the University, again, for sponsoring my year in this course, allowing me to specialize my studies in the field of aeronautics in a quiet atmosphere (and an efficiency-enhancing weather); To all AVD students who contributed to the heating of Pegasus room; And to Ravinka Seresinhe and Victoria Otto, for the ballistic studies of the second part of the year.
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TABLE OF CONTENTS List of Tables ..................................................................................................................... 7 List of figures .................................................................................................................... 7 1.
Introduction ............................................................................................................ 11 1.1. General scope ...................................................................................................... 11 1.2. Aims and objectives ............................................................................................. 12 1.3. Previous work on the topic.................................................................................. 13 1.4. Thesis structure ................................................................................................... 14
2.
Helicopter Crashworthiness ................................................................................... 15 2.1. Context ................................................................................................................ 15 2.2. Structural elements ............................................................................................. 19 2.3. Subfloor designs .................................................................................................. 25 2.4. Optimisation of crashworthy structures ............................................................. 28 2.5. Conclusion ........................................................................................................... 31
3.
Composite materials and tube tests ...................................................................... 32 3.1. Cylindrical energy-absorbing tubes theory ......................................................... 33 3.2. Results.................................................................................................................. 36 3.3. Conclusion ........................................................................................................... 41
4.
Modelling for crashworthiness............................................................................... 42 4.1. Integration method ............................................................................................. 42 4.2. SPH ....................................................................................................................... 43 4.3. Composite modelling in LS-Dyna ......................................................................... 47 4.4. Advanced composite material models ................................................................ 50 4.5. Conclusion ........................................................................................................... 52
5.
Material Model Validation ..................................................................................... 53 5.1. Limitations ........................................................................................................... 53 5
5.2. Test data .............................................................................................................. 54 5.3. Material choice and parameters ......................................................................... 55 5.4. Peak Force and triggers ....................................................................................... 56 5.5. Average crushing loads ........................................................................................ 61 5.6. Coarser mesh ....................................................................................................... 62 5.7. Conclusion ........................................................................................................... 62 6.
Water validation ..................................................................................................... 64 6.1. Setting the experiment ........................................................................................ 64 6.2. Solid elements water: sensitivity to various parameters .................................... 69 6.3. Behaviour of SPH particles .................................................................................. 75 6.4. Final models ......................................................................................................... 79 6.5. Conclusion ........................................................................................................... 80
7.
Subfloor crash ......................................................................................................... 81 7.1. Solid model .......................................................................................................... 81 7.2. Hybrid model ....................................................................................................... 83
8.
Conclusions ............................................................................................................. 85 8.1. Discussion ............................................................................................................ 85 8.2. Conclusion ........................................................................................................... 86 8.3. Further work ........................................................................................................ 86
References ...................................................................................................................... 88 APPENDIX A
Unit system ............................................................................................. 1
APPENDIX B
Material data (2) ..................................................................................... 2
APPENDIX C
Part data (2) ............................................................................................ 3
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LIST OF TABLES Table 1: Efficiency of the CWFS (CrashWorthy Fuel System) 1979-1976....................... 19 Table 2: Composite material models available in LS-Dyna ............................................ 49 Table 3: Element deletion parameters for Mat. 054-055 .............................................. 50 Table 4: Physical data of the composite material .......................................................... 54 Table 5: Experimental test data, quoted in (2) – rigid wall 66.8kg, initial velocity 7m/s55 Table 6: Peak forces obtained with various triggers (11328 elements model) ............. 59 Table 7: Peak forces obtained with various triggers (4182 elements model) ............... 60 Table 8: Average crushing load results for 11328 elements model ............................... 61 Table 9: Average crushing load results for 4182 elements model ................................. 62 Table 10: Water model parameters (2) .......................................................................... 65
LIST OF FIGURES Figure 1: Influence of the various RIFs on the global safety (5) ..................................... 17 Figure 2: Geometrical shape of a double-sine-wave beam (7) ...................................... 20 Figure 3: Cross-section of a tensor skin panel (Ref (9)).................................................. 21 Figure 4: Impact force in a 3-layer PE/epoxy panel, (transverse shear loading) (9) ...... 22 Figure 5: Results of dynamic impact of a spherical tip on various panels(10) ............... 23 Figure 6: DEA deployment methods: linear (left) or radial (right) (11).......................... 24 Figure 7: Modes of failure of a linear DEA. Honeycomb (Kevlar fabric, 45° from the load direction) crushed by a steel block at 22.2 feet/s (11)................................................... 25 Figure 8: Partial subfloor view with interconnecting beams (13) .................................. 26 Figure 9: Overview of the CAST subfloor (14) ................................................................ 27 Figure 10: Energy absorption mechanism for water impact (14) .................................. 28 7
Figure 11: Representation of an evaluation function with two parameters (15) .......... 29 Figure 12: Helicopter skid landing gear modelled for optimisation (15) ....................... 30 Figure 13: Typical load-displacement curves of crush tubes with different materials and configurations (17) ......................................................................................................... 35 Figure 14: Plug initiator and chamfer (left); chamfer alone (right) (thin-walled tube) (17) .................................................................................................................................. 37 Figure 15: Contribution of the debris wedge in the energy absorption (17) ................. 38 Figure 16: Various modes of failure for statically crushed thin-walled tubes (18) ........ 39 Figure 17: Set of neighbouring particles and h(23) ........................................................ 45 Figure 18: Micro-mechanical composite material model (25) ....................................... 51 Figure 19: Effect of rigid wall contact breaking on the crushing simulation.................. 56 Figure 20: Load-Time curve of the trigger collapse of a composite tube ...................... 57 Figure 21: Trigger behaviour (2 rows bent inwards, 2.21°)............................................ 58 Figure 22: Location of the acceleration sensors on the impactor.................................. 66 Figure 23: Experimental data (CAST program - cylinder drop test in water) ................. 67 Figure 24: Variation of load factor history with initial impactor height ........................ 68 Figure 25: Influence of SLSFAC on the acceleration peaks............................................. 69 Figure 26: Influence of water element size on the acceleration peak of a cylindrical impactor ......................................................................................................................... 70 Figure 27: Quality of mesh and surface draping ............................................................ 71 Figure 28: Influence of water depth (4cm and 5cm element-depth) on the acceleration peak of the two sensors ................................................................................................. 72 Figure 29: Pressure history with varying boundary conditions...................................... 73 Figure 30: Acceleration for various boundary conditions .............................................. 74 Figure 31: Elements monitored ...................................................................................... 75 Figure 32: Pressure recordings for solid and hybrid models .......................................... 76 8
Figure 33: Comparison of acceleration curves for solid and hybrid models.................. 77 Figure 34: Acceleration curves for a 40x40x40 SPH water block (SLSFAC=10) .............. 78 Figure 35: Acceleration curves for a 60x60x60 SPH water block (SLSFAC=0.55) ........... 78 Figure 36: Water model results - solid model ................................................................ 79 Figure 37: Water model results - hybrid model ............................................................. 80 Figure 38: Acceleration plot, subfloor drop test – 3x3x3 solid elements water – initial impact speed 8m/s ......................................................................................................... 81 Figure 39: Location of the sensors ................................................................................. 82 Figure 40: Acceleration plot, subfloor drop test – hybrid (solid + SPH) water – initial impact speed 8m/s ......................................................................................................... 83 Figure 41: 3D plot, subfloor, hybrid water, t=0, 0.6, 1.2, 1.8, 2.4, 3.0 cs ....................... 84
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NOMENCLATURE
Force
S SCL
Area (section) Sustained Crushing Load
SEA r
Specific Energy Absorption Point in space
F
Density
Dirac function
m A
Mass Function
W
Kernel Function
Pressure
P
Speed vector Stress Longitudinal tensile strength Longitudinal compressive strength Transverse tensile strength Transverse compressive strength Shear strength
E G
Young’s modulus Shear modulus
ν C
Poisson’s ratio Speed of sound
γ0 E0
Gruneisen gamma Internal energy
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1. INTRODUCTION
1.1. General scope Since the introduction of helicopters at the beginning of the 1940s, their safety has been greatly increased, with little modifications to the general configuration of the airframe. Further improvement of safety in helicopters will be allowed by working in two distinct fields: reducing the number of helicopter accidents by flying hour; and reducing the lethality of each accident (improving the helicopter crashworthiness). An important parameter for the crashworthiness of an airframe is its capacity to absorb the energy of the crash. This can be improved by skilful design of the structure, and with the help of new materials. The composite materials are particularly suited for design of crashworthy airframes, because they have a better energy absorption potential than metals in general. This is one of the reasons why helicopter manufacturers are more and more relying on composite materials to produce their machines, another reasons being the lightweight of such materials, and their good vibration characteristics. One of the last examples of this trend is the NH-90, of which the structure is mostly made of composite materials(1). However, the crash of a helicopter is such a complex physical problem that it is very difficult to predict the capacity of a given design to absorb efficiently the crash energy. Therefore, the research on crashworthiness is conducted using drop tests to evaluate the value of existing or new structural designs or materials. But a drop test is a very expensive and lengthy operation, for which one needs to buy or built a fuselage subfloor, or even a whole airframe, prepare high-speed cameras, rent a dedicated facility, and spend hours installing more sensors and cables than in a conference room. The dramatic progress of computer performance has allowed the increased use of simulation tools based on finite element calculations, with very good reproducibility capacities, but still rather poor predictive performances. These tools are indeed using parameters in order to compensate for the distance between the models used and the reality, and these parameters need to be tuned differently for each different situation, depending on the speed of the crash, the average size of the mesh, or the material used.
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It is then necessary, in order to model a given crash with such tools, to validate the model built in the software against real tests data. Once the model is validated for a given set of parameters (geometry, impact speed, etc.), it is possible to slightly modify the test conditions in the software in order to test the result of a structural design change, or the behaviour of the same structure in a crash on a different surface. All this work can be performed using the data provided by few crash tests, which is cheaper and quicker. The difficulty of this process partly depends on the material modelled. Composite materials are now used in the aeronautic industry since a few decades, and their behaviour is reasonably well understood; but it is not easy to model in finite element software. Their energy absorption mechanisms are very different from the metal ones, because they tend to be brittle materials, which absorb energy by fractures or delamination, whereas the metals absorb energy by plastic deformation. Therefore, a lot of work has been done during the last decades to implement improved composite material models in simulation tools. Currently, in its version 971, LS-Dyna includes 11 different material models created to simulate the behaviour of composites.
1.2. Aims and objectives The crashworthiness of a given helicopter airframe depends on the type of impact, and more precisely the surface of impact: hard surface, soft soil or water. The absorption mechanisms are different and it is therefore difficult to design an airframe having good capacities for all these surfaces. In this context, the use of simulation tools allows to increase the number of tests while reducing the cost of the test campaign. However, these tools do not always give right answers, and it is still necessary to validate them against real-life drop tests. The final aim of this study is to evaluate the capacity of the commercial simulation tool LS-Dyna to simulate correctly, with stock material models, the crash of a helicopter subfloor on various surfaces. The material model used will be Material 54 from LSDyna. More specifically, the results given by the simulations will be compared to the work of Germán Pérez Garijo (2). A simulation of the crushing of a composite tube is run in order to compare the results with equivalent real tests and validate the material model used. Then, a study on the
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water model is done, with solid elements, SPH elements, and with a hybrid water model. At last, a simulation of the drop test in water is to be done and the results compared to the existing simulation results. Therefore, the objectives are the following: •
Choice and validation of a composite material model against test data, by simulation of a composite tube crushing;
•
Validation of a water model against test data, investigating SPH elements, solid elements, as well as a combination of both, by performing simulations of a drop test;
•
Drop test of a provided helicopter subfloor model, and comparison of the results with test data;
•
Comparison of all the results with the work of German Pérez Garijo (2).
1.3. Previous work on the topic Most of the work presented here follows the work of German Pérez Garijo, a thesis published in 2004 in Cranfield University (2). The main objective of this work was to “simulate a composite subfloor structure when impacting on water using the Explicite Finite Element Code DYNA3D”. This simulation was then compared with a real droptest conducted as a part of the CAST (Crashworthiness of Helicopter on Water: Design of Structures using Advanced Simulation Tools) project. In order to avoid numerical problems, Pérez Garijo had to modify an existing composite material model, basically giving to the material a damage model. Material model 41 in DYNA3D was used. In this model, when fibre or matrix fails, the corresponding stress components are zeroed linearly over the following 100 timesteps. A breakage of the fibre in one direction does not prevent the material from reacting loads perpendicular to this direction (this material models a fabric ply). This stock model was improved by adding a damage parameter for each in-plane loading direction (longitudinal, transverse and in shear); moreover, the damage can be different in tension and compression. The degradation of the material is based on a max strain criterion. When degraded, the material loses a part of its elastic properties; when the maximal strain is reached, the element is deleted. This model was validated against a tube-crushing type experiment, comparing the stock material with the improved model, and both of them with the experiment. A 13
mesh sensitivity study was performed, as well as a study on the best way to trigger the tube collapse. These studies gave, with the best trigger configuration and the improved material model, a peak force 16% too high and an average force reasonably similar to the recorded force (within 7%). A water model was then validated, based on the Gruneisen equation. The water is modelled by solid elements, with an automatic contact algorithm for the contact with the impactor, a cylinder. A study on the influence of the mesh size, the total water volume, the contact stiffness, the boundary conditions and the material model was conducted. All this work is again modelling a real drop test. Finally, the subfloor model using the improved material model was dropped in the validated water, at 8m/s, with good results.
1.4. Thesis structure This work is divided in three main parts. The first one, in Chapter 2, tries to give an overview of the main “tricks” which are used, or could be used, to enhance the crashworthiness of helicopters. These are mainly the Sine-Wave beam, the Tensor-Skin concept and the Deployable Energy Absorbers. Two different subfloor designs are also reviewed. Then, a second part is dedicated to a description of the composite materials behaviour under crash loads, and the various options available to model these behaviours in computer-based simulations, and more specifically in LS-DYNA. Finally, the last part describes the simulations done: first, the validation of the composite material model and the water model; and then, more briefly, the drop-test of the helicopter subfloor itself. In this last part, all the simulations are modelling the same experiments as Pérez-Garijo modelled (2).
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2. HELICOPTER CRASHWORTHINESS The crashworthiness of a vehicle can be defined as its ability to withstand a crash (against the ground, any vertical obstacle, another vehicle…), while allowing its occupants to survive without serious injuries. The crashworthiness is different from the safety, which does not only take in account the survivability rate in accidents, but also the accident rate. In order to increase the survivability of a crash in a given vehicle, several aims need to be reached (3): •
Minimise the deformation of the structure around the occupants, to avoid crushing them;
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Keep the accelerations experienced by the occupants under tolerable limits;
•
Limit the possibility of collision between the occupants and their surroundings, by restraining them;
•
Give the occupants a sufficient time to evacuate the wreck, for example before a fire, or before the sinking of the vehicle into the water.
2.1. Context
2.1.1. Helicopter crashworthiness The usual crash conditions of helicopters are different from the typical plane crash conditions. The easiest way for a pilot to manage a survivable impact with the ground is to get his plane on a reasonable rate of descent, for which he needs forward speed; and the plane crashes with an important forward speed. On the other hand, helicopters have arguably poor gliding capabilities and tend to impact with a lot of vertical downward speed, and a less important forward velocity component. This is why most of the work on helicopter crashworthiness is focused on the low structure: landing gear, subfloor, and of course seats. The design of these structural components for crashworthiness is challenging, because of the little space available to absorb energy. Indeed, the goal of a crashworthy structure is basically to fail in a controlled manner, maximising the average crushing load and if possible the time to failure, in order to absorb a great amount of energy before being totally destroyed. All of this must be 15
done while minimising the deceleration of the occupants. The less space is available between the occupants and the crash surface, the easiest it is to slow them down progressively. In helicopters, this space is very limited. Another challenge is to design these components for impact on different surfaces, namely hard surfaces, soft soils or water. Some structural elements which can be essential for crashes into one type of surface may be totally negligible for crashes on another surface. This is for example the case of the landing gear, which is vital for hard surfaces crashes but hardly absorbs any energy during water crashes. The vertical accelerations sustainable for a human occupant are described in (4).
2.1.2. Impact of Crashworthiness on general safety The crashworthiness of a helicopter has an important impact on the global risk for its passengers. A report from the Norwegian SINTEF (The Foundation for Scientific and Industrial Research) about the Helicopter Safety, especially for off-shore liaisons (5), places the Crashworthiness of a helicopter represents 40% of its safety. This report tries to classify the Risk Influencing Factors (RIF), which are defined as limited groups of factors or conditions that can influence the risk associated with the use of a helicopter for transportation offshore. Four main RIF are defined: •
Crashworthiness;
•
Search & Rescue Operations;
•
Pilots/passengers preparedness;
•
Aerodrome
Their definition of crashworthiness adds various aspects to the classic impact absorption: stability on sea, cabin safety, survival equipment, emergency location equipment. The RIF “impact absorption”, which is a part of the crashworthiness RIF, represents a contribution of 8% to the global safety. It should be noticed that this study is dedicated to the “helicopter transport of personnel to, and from, fixed and floating oil- and gas installations on the Norwegian Continental Shelf (NCS)”. Therefore, it is sensible that the impact on water takes such an importance on the global safety, most of the flights being over sea.
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Figure 1: Influence of the various RIFs on the global safety (5)
2.1.3. Regulations on Impact Absorption The main available crashworthiness regulation is MIL-STD-1290 (6), introduced in 1974 and revised in 1988. This document, issued by the American Department of Defence, gives guidelines and requirements for the crash resistance of rotary wing and light fixed-wing aircraft. The impact types considered are: •
Longitudinal impact on a vertical rigid barrier at speeds under 40 ft/s;
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Vertical impact on a hard surface at speeds under 42 ft/s (with landing gear extended), or 26 ft/s if the landing gear is retracted;
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Lateral impact on a vertical rigid barrier at speeds under 30 ft/s;
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Combined vertical and longitudinal cases, in hard surface or plowed soil.
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Rolling of the cabin on the ground (up to 180 degrees attitude: complete rollover).
Generally, the main requirement is to avoid a reduction of more than 15 % of the living space in the cabin, and, for vertical impacts, the absence of injurious accelerations. In the case of vertical impacts, some design guidelines are given: 17
•
“Locate high mass components in a manner so that they will not intrude into occupied areas during the crash impact.
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Provide sufficient cockpit and cabin vertical strength to prevent the structure from crushing occupants.
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Provide crash-force attenuating structure beneath cockpit/cabin flooring and other locations as deemed appropriate.
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Provide energy absorbing landing gear.
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Provide energy absorbing crew/troop/passenger seats.”
The document also includes precise requirements for the systems, seats, cargo restraints, occupants’ retention, etc. The main shortcoming of this document is the absence of any mention to crash into the water: only crashes on hard surfaces and plowed soil are considered. Another drawback is the lack of discrimination based on the size or weight of the helicopters: the energy to be absorbed in the case of a vertical crash depends greatly on the mass of the helicopter.
2.1.4. Main breakthroughs One of the first essential breakthroughs in the field of helicopter crashworthiness was the installation of a Crashworthy Fuel System (CWFS) in all the US Army helicopters, at the beginning of the 70’s. Indeed, in the 60’s, one of the primary causes of death in helicopter crashes was the post-crash fire. The first crashworthy fuel system was installed in a UH-1H “Huey” in 1970. A study was then conduced on the efficiency of this new system, taking into consideration all the army helicopter crashes between 1970 and 1976. The results of this study are gathered in Table 1. Then, a Crash Survival Design Guide was issued, gathering all the state-of-the-art ideas in one handbook, which was updated regularly. This handbook gave the basis to the MIL-STD-1290A we described earlier; this last regulation was used in the design of the last US military helicopters, such as the UH-60 Black Hawk or the UH-64 Apache.
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Survivable – No CWFS Survivable – CWFS
Number of accidents
Post crash fires
1160 1258
43 16
Thermal-related fatalities 159 0
Table 1: Efficiency of the CWFS (CrashWorthy Fuel System) 1979-1976
2.2. Structural elements The typical shape and materials of the beams and other structural used in the subfloor structure of helicopters were chosen to be highly effective in their primary role, which is to transfer the flight loads. However, the crash requirements do not have much in common with this primary role, and therefore it makes sense that some specially designed parts could improve the compliance to crash requirements, while not hindering too much the load-bearing requirements. Two of these concepts are presented here, with a third one a little different from the two first because it is only designed to alleviate the crash, and does not transfer any load in normal flight. The decision to use or not these concepts is always the result off a trade-off study between the probably increased cost and the better crash-absorption capacities.
2.2.1. Sine wave beams Sine-wave beams have basically the same behaviour as crush cones. The goal is to get, from a longitudinal or transverse subfloor beam, good vertical crushing characteristics (i.e. continuous crushing, with a low peak force). The beam is constituted by a web and a flange. In order to avoid catastrophic failure the web is corrugated, thus being stabilized against buckling; and triggers are used to lower the peak force and reduce the chances of a catastrophic buckling of the beam. Sine-wave beams can be manufactured in composite materials or metals, as crush cones; their crushing behaviour will be different. According to Jiang (7), the typical metallic sine-wave beams are not as efficient as they could: due to the shape of the beam, initial local buckling is very difficult to reach. Triggers have been implemented, but “some experiment showed that the trigger 19
mechanism implemented on the sine-wave beam to control the start of crushing did not function”. Moreover, when failing, the beam rarely exhibits the more efficient mode of failure possible. A solution to correct these shortcomings proposed in (7) is to use a double-sine-wave beam, with a surface corrugated in both longitudinal and vertical directions. This second corrugation reduces the load necessary to trigger a local buckling failure, and allows a more regular failure, with less variation in the crushing load and an enhanced efficiency. Figure 2, taken from (7), shows the geometrical shape of the web of such a beam: it is obtained by sliding CURVE 2 along CURVE 1, thus giving a double-curvature surface.
Figure 2: Geometrical shape of a double-sine-wave beam (7)
This shape is of little interest for composite beams, because the privileged mode of failure is brittle fracturing rather than local buckling. For composite sine-wave beams, the triggers are more efficient. A patent describes two triggers designed to tune very precisely the behaviour in crushing. The web of the beam consists in a “sandwich” of UD plies taken between fabrics; “the bottom edge of each layer of single-directional carbon fibres is setback from the corresponding edges
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of the fabric and saw-tooth cut-outs are formed in this bottom edge” (8). The pitch of the cut-outs is chosen carefully with respect to the period of the “waving” of the web.
2.2.2. Tensor skin concept The tensor skin concept is trying to alleviate the extremely brittle behaviour of composite panels, when compared to metal panels. It is mostly useful for crashes in water. In such a situation, as we said before, the landing gear will not absorb any energy, and a great pressure will be applied on the bottom skin of the helicopter. Where metal panels will “rack along the rivets lines with large plastic deformations” (9), absorbing a lot of energy in the process, composite panels will experience a brittle failure, let the water pass without absorbing a lot of energy. They won’t be able to transfer a lot of loads to the beams or crushing cones located beneath the floor, and most of the energy will have to be absorbed by the seats. Tensor skin panels, on the opposite, are behaving quite like metal panels, and are able to sustain great deformations before failing. Therefore, they don’t let the water load directly the floor and can transfer loads to the structure of the subfloor. The idea is derived from a classical honeycomb sandwich panel, the main difference being the core, which consists in a corrugated polyethylene/epoxy laminate. The core is then sandwiched by two standard carbon/epoxy or aramid/epoxy laminates.
Figure 3: Cross-section of a tensor skin panel (Ref (9))
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2.2.2.1.
Modes of failure
When the panel is submitted to high loads, the outer laminates will fail in a brittle mode, and the core will be unfolded and deformed plastically, allowing a great strain at failure. The load/deflection curve of the panel, in transverse loading (loaded by a spherical tip), shows two peak loads. The first one appears quickly, and corresponds to the failure of the brittle faces. The load then decreases quickly, and slowly builds as the core if unfolding. The second peak load, higher than the first one, corresponds to the failure of the core. Please report to the following section, 2.2.2.2, to have more details about the various configurations tested.
Figure 4: Impact force in a 3-layer PE/epoxy panel, (transverse shear loading) (9)
2.2.2.2.
Experimental results
Several tests were carried during the European BRITTLE EURAM project (9), in order to assess the efficiency of various laminate designs. At first, two laminates were tested for transverse loads: either 3 layers of ±45 degrees fabric, or 3 layers of 0/90 degrees 22
fabric. The tests showed that only the first design enabled the skin skin panel to transfer enough load to the subfloor before failing, mainly because of the higher shear deformation capacity. A further test with only 2 layers of ±45 fabric was conducted, but the results showed that the core was too thin to be able to transfer transfer proper loads. When tested in shear, the tensor skin panel had slightly worse characteristics when compared to a standard honeycomb panel: it was heavier and had inferior shear modulus and load carrying capacity. According to (9),, the tensor panel was not optimised for this loading case, and a change in the direction of the faces plies pl could improve the situation;; however, it might be necessary to add additional layers in order to have equivalent characteristics compared to a honeycomb sandwich in shear. The point of the design being to absorb efficiently energy, tests were done to evaluate its behaviour in case of impact (by a 150 mm hemispherical aluminium head). The results here are clear, the honeycomb panel being penetrated, penetra , while the 2 and 3 layers ±45 fabric stopped the head, the core being unfolded but not destroyed. The deformation and the 1st peak load of the tensor panels are lower than the ones of the honeycomb panel, while the energy absorption is higher.
Figure 5:: Results of dynamic impact of a spherical tip on various panels(10) panels
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2.2.3. Deployable Energy Absorbers NASA is currently in the process of developing Deployable Energy Absorbers, in order to increase the crashworthiness over all types of surfaces (11). These DEA are honeycomb structures, which are stored in a folded state to reduce the volume occupied and can be unfolded at will, to prepare for the crash. Two modes of deployment can be used, the linear and the radial deployments. They are illustrated in Figure 6. The linear deployment has greater specific energy absorption, due to the perfect geometry, but the radial deployment allows a good reaction to loads coming from various directions.
Figure 6: DEA deployment methods: linear (left) or radial (right) (11)
Tests with a DEA made from Kevlar fabrics, orientated at ±45° relatively to the crushing direction, with a thickness of 0.01 in (0.254 mm) and a cell width of 1.0 in (2.54 cm), demonstrated the concept. “The primary mechanisms for energy absorption are local buckling, tearing, and delamination”. (11) The local buckling and tearing modes of failure can clearly be seen on Figure 7.
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Figure 7: Modes of failure of a linear DEA. Honeycomb (Kevlar fabric, 45° from the load direction) crushed by a steel block at 22.2 feet/s (11)
2.3. Subfloor designs It has been shown by Campbell (12) that an excellent way to reduce the peak acceleration at the impact in water is to change the external shape of the subfloor with a V (or a reversed V) shape, even with a very slight angle (nearly flat). However, this would force the designers to change totally their way of working and to date, there is no publicly known design of a helicopter using this bottom skin shape. The major changes are done in the internal structure of the subfloor. Two designs with a very different philosophy will be quickly reviewed.
2.3.1. Subfloor with trapezoidal-shaped beams One of the problems of classical composite (or metal) crush tubes is the fact that they are sensitive to the direction of loading. This can be partially made good using conical tubes, which are still absorbing energy with non-perpendicular loads, although they are generally less efficient for purely vertical loads. A patent (13) describes a solution in the form of a set of longitudinal and lateral trapezoidal beams, which are all interconnected. All these beams are filling the space between the floor of the helicopter and the outer bottom skin. 25
Figure 8: Partial subfloor view with interconnecting beams (13)
This design, although interesting because it tries to increase the crashworthiness of the helicopter for lateral and longitudinal loads instead of focusing exclusively on vertical impacts, does not give any consideration to crash into water. The load might be too low to collapse properly the structure, which may result in too high accelerations for the passengers.
2.3.2. CAST program concept subfloor The European Project CAST (Crashworthiness of Helicopter on Water: Design of Structures using Advanced Simulation Tools) has resulted in the proposition and test of a concept of helicopter subfloor. The main feature of this subfloor is its polyvalence, as it is efficient in case of impact on hard surfaces as well as impact on water. Two different energy absorption mechanisms are used for this. In the case of an impact on a hard surface, the energy absorption will mainly be due to the six conical crush cones disposed in two longitudinal rows. The tubes are connected to the structure (longitudinal beams, and ribs). 26
Rib Longeron
Bottom Shell
Frame Crush Cone
Skin Panel
Figure 9: Overview of the CAST subfloor (14)
However, when the subfloor impacts the water, the force applied on the cones will not be sufficient to cause their failure. “During water impact two energy absorption mechanisms are active: structural deformation and water movement. The main concern during the impact on water is the integrity of the subfloor skin to ensure the transfer of the water pressure to the main beams. The current design is based on an aramid/rohacell sandwich skin with open edge, which will deform to a cylindrical shape enhancing the force transfer. This asymmetric sandwich panel is stiff enough to withstand regular flight loads, such as shear and bending forces”. (2)
27
Figure 10:: Energy absorption mechanism for water impact (14)
“During During the water Impact the connection between the skin and core is supposed to fail under the bending loads which occur caused by the water pressure (cf. Figure 10). Due to the acting peeling stresses the separation of the core proceeds and leads to reduced bending stiffness and subsequently higher membrane forces in the skin. The membrane forces, which develop in the skin, are transferred to stiff longitudinal beams through the longitudinal aluminium angle and doubler.” (2) The deformation of the bottom skin is facilitated by its link with the longitudinal beams, an aluminium m hinge which can bend easily. For all other technical details, please refer to (2).
2.4. Optimisation of crashworthy structures The design of crashworthy structures in composite materials lets a lot of place to the “trial and error” process: as it is difficult to predict by analysis the behaviour of a component under crash loads, automatic optimisation of crashworthy structures is highly complex. The main problems existing are the long time needed to get simulation results, and the difficulty to interpret these results, due partly to their noisy character.
28
And all the process of course depends on the quality of the simulations, which are by themselves challenging as this work should prove. Therefore, the research in this field in quite active currently and some algorithms are developed for structure optimisation (for crashworthiness). The goal of these algorithms is to reduce the number of finite element simulations needed to converge towards an optimised structure, which is defined as a structure which minimises the acceleration peaks while maximizing the energy absorption capacity, with a low weight, and while respecting design constraints. An example of such an algorithm is given in the Journal of the American Helicopter Society (15), based on mathematical methods of which the detailed description would be largely out of the scope of this work. However, it seems interesting to give a very basic description of the process. Optimisation is based on a “search space”. The structure to optimise is defined by parameters (geometrical parameters as well as material parameters); all the combinations of these parameters define the search space, or design space. This space is limited by the constraints (for example the total length of the structure). To optimise the structure is to find the combination of the parameters, inside the design space, which gives the better structure. The need of a definition of a “better” structure arises. This evaluation is done by a function, which “marks” each structure according to its properties: acceleration peak, energy absorption, etc.
Figure 11: Representation of an evaluation function with two parameters (15) 29
Once the design space and the evaluation function are defined, the idea is to test several structures, mark them, and (thanks to an algorithm) converge towards the structure with the better mark. This last step is entirely based on mathematic theories. For the crashworthiness field, the costlier step is probably the evaluation of a given structure: each evaluation corresponds to a finite elements simulation of a structure. Therefore, to be able to reduce the number of evaluations is of great importance.
Figure 12: Helicopter skid landing gear modelled for optimisation (15)
The optimisation algorithm defined in (15) is tested on a simple crashworthy structure: a helicopter skid landing gear. The optimisation is done on the two crossbeams, divided in 8 sections each. These beams use a tapered hollow circular cross-section. The two parameters which are optimised are the inner and the outer radius of the section. Using left/right symmetry, only 8 sections are optimised, with 2 parameters each, which gives 16 parameters to optimise. Here, the evaluation function is simply the specific energy absorbed. 30
With “only” 21. 16 1 4 441 simulations, the result is a reduction of 40% of the acceleration peak, an energy absorption increase of 6 %, a specific energy absorption increase of 13.1 %, and a reduction of the weight by 7.2 kg (about 6 %), when compared to a “baseline” design.
2.5. Conclusion Improving helicopter crashworthiness has been one major goal in the industry since the 70’s. Most of the work done yet has been focused on two fields: reduce the impact lethality for crashes on hard surfaces; and increase the after-crash survivability rate, for example with the CrashWorthy Fuel System. More recently, the water-impact lethality has been considered. Some structural innovations can help the designers to produce crashworthy structures, while keeping a low weight. The sine-waved beams, already used in airplanes, are efficient energy-absorption parts. The tests done on the tensor-skin concept seem also to show a great potential. The Deployable Energy Absorbers could allow the designers to retrofit old helicopters with much improved crashworthiness capabilities on hard surfaces. On the assembly side (as opposed to the structural parts side), two subfloor concepts are reviewed, included the CAST subfloor, which tries to get good water-impact behaviour, while keeping an excellent hard surface-impact one.
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3. COMPOSITE MATERIALS AND TUBE TESTS Composite materials can be defined as hybrid materials, made from two or more materials, at a macroscopic level. The typical composite material in the aeronautic industry is now the carbon/epoxy. Very thin carbon fibres are gathered in packs, which are then put in an epoxy matrix. The carbon fibres have excellent properties in the axis of the fibres: strength and Young modulus. However, they are very poor in the other axes, and it is the matrix which can give them some cohesion, and some interesting transverse properties. A carbon fibre / epoxy matrix assembly constitutes a ply, with a thickness usually under 0.2 mm; several plies are added to form a laminate. The properties of each ply are somewhere between the properties of the fibre and the properties of the matrix; the fibre direction has the highest Young modulus. The properties of a layer therefore depend on the relative volume of fibre or the matrix. If all the fibres in the ply are orientated in the same direction, the ply is Unidirectional (UD). In this case, in order to keep reasonably good properties in all the loading directions, it is required to stack plies with various fibre directions. Alternatively, it is possible to use woven fabrics, which merges, in one ply, two fibre directions. The carbon fibres do not show a plastic behaviour, they are elastic and have a very low strain failure, in the order of 1.5%. The matrix on the other hand can have a plastic deformation, even if is it is quite limited, the usual strain to failure being around 4%. Kevlar fibres can also exhibit plastic behaviour. Having a low density, usually around 1.6 kg/cm3, and strength comparable or better than usual metals, composite materials have an excellent strength to weight ratio. However, this is true in the direction of the fibre, and we have seen that it is not possible, in most cases, to use only plies whose fibres are in the direction of the load. Therefore, the actual gain in weight for a given composite structure over a classical metallic structure is never given, and is an objective only reached by optimisation of the structure.
Energy absorption mechanisms The energy absorption mechanisms are one of the major differences between composites and metals. The main way for a metallic structure to absorb energy is plastic deformation. This leads to design methods relying on plastic hinges: the 32
structure bends at some chosen points, in a quite predictable way. The energy absorbed by a plastic hinge is directly related to the angle of rotation of the parts around this hinge. These characteristics allow the designers to do the first calculations by hand, or using simple software. As composite materials are usually rather brittle, even if some of them, less brittle than others, are sometimes defined as “ductile”, they hardly can absorb any energy by plastic deformation. The energy absorption relies on these main mechanisms: •
Fibre failure;
•
Matrix failure;
•
Delamination or debonding;
•
Friction between delaminated plies or material elements (debris).
Usually, a composite structure failure involves several or even all these energyabsorption mechanisms. Depending on the situation, one or the other of these modes can represent most of the energy absorbed.
3.1. Cylindrical energy-absorbing tubes theory A classical test of the energy absorbing behaviour of composite materials is to crush a composite tube; it is possible to find many articles in literature describing this type of tests. This is probably partly motivated by the fact that composite tubes are actually used to absorb energy in several types of structures: some of these tests are sometimes readily usable in actual structures. The difference between composite and metal behaviour is shown in section 3.1.2. The more efficient and easy to control energy-absorbing behaviour, for a tube, is to collapse progressively. The important parameters in such a collapse are: •
The initial force required to initialize the failure. This force can be controlled by triggers, little imperfections designed purposely in order to get a tube failure at a given force. The other advantage of the triggers is that they are designed to fail first: this allows the designer to choose to a certain extent the failure process of the tube. Such triggers can for example consist in a chamfered end.
•
The average force throughout the test.
33
•
The specific energy absorbed, i.e. the energy absorbed divided by the mass of the tube. This parameter is especially pertinent for aircrafts and specifically helicopters, where the designers try to keep their structure as light as possible.
3.1.1. Crushing behaviours All composites tubes won’t necessary crush progressively and nicely, although this is usually the goal of the design. The crushing behaviour of a tube (for given test conditions) depends on the material used as well as on the geometry. Catastrophic failure will occur according to the size of the inter-laminar cracks which are formed when the force is applied (16): •
If they are really small, and their length stays inferior to the ply thickness, then the force necessary to crush the tube will be too high: once this force attained the tube will fail catastrophically.
•
If, on the other hand, they propagate easily, they can propagate through the whole tube, thus not allowing the tube to resist anymore to the force applied, and causing a catastrophic failure.
If the tube crushes progressively, several modes are possible. The first mode of failure is the Transverse Shearing mode. This mode of failure is “characterised by a wedgeshaped laminar cross-section with one or multiple short inter-laminar and longitudinal cracks which form partial lamina bundles” (16). The failure mechanisms are here the inter-laminar crack growth and the lamina bundle fracture; the second is the principal energy absorption mechanism. This mode is usually associated with very brittle fibre reinforcements. The second possible mode is the Lamina Bending mode. Here, the inter-laminar cracks are more important, and the lamina bundles do not fracture, and are only bent by the force applied. The main failure, and energy absorption mechanism, is the crack growth. Another energy absorption mechanism is friction: friction of the fibres against the crushing surface, and friction between the different lamina bundles. Some materials show exclusively, or not, this mode of failure. These two first modes of failure are usually referred as brittle failure modes in the literature. The third and last mode is comparable to the failure mode of metallic crushing tubes: the Local Bucking crushing mode. It can be occasionally shown by brittle composite materials, if the following conditions are respected (16): 34
•
Inter-laminar stresses low compared to the matrix strength. This prevents the formation of inter-laminar cracks, which brings either a catastrophic failure (as seen before), or a local buckling crushing mode.
•
Matrix with a higher failure strain than the fibre
•
Matrix deforming plastically at high stresses.
3.1.2. Typical load curves The goal of a crash tube is to absorb a maximum of energy. Generally, the goal is to manage to reach the sustained crushing load as fast as possible, and to have a crushing load as regular as possible. Metal tubes, which tend to fail by local buckling, exhibit quasi-periodic curves: the force increases until the local buckling critical force is reached; the load necessary to continue the folding of the material is lower. When the folding is complete, the load increases again, and the cycle goes on and on. For composites which exhibit brittle fracture modes, the load-deflection curve is usually nearly perfect, with an initial peak way above the sustained crushing load, followed by a quite constant load. The peak force, which could cause unsustainable accelerations to the occupants of the vehicle in case of crash, can be eliminated or reduced by the use of a trigger.
Figure 13: Typical load-displacement curves of crush tubes with different materials and configurations (17) 35
3.1.3. Conventions In order to compare the performances of the tubes, it is necessary to measure the same quantities. Different authors tend to use different quantities, choosing the ones they think are the most suited to their particular test. •
After the initial crushing of the tube, the load needed to continuously crush the tube is usually relatively constant. This load is defined as the sustained crushing load (18), SCL.
•
One of the most used criterion is then the Specific Crushing Stress, which takes in account the density of the material :
.
Where F is the instantaneous crushing load; is the density of the material; and S is the cross-section area of the tube.
•
(1)
It is also possible to use the sustained crushing load, to get the Specific Energy Absorption (also designed in the literature Sustained Specific Crushing Stress) :
.
Where SCL is the Sustained Crushing Load; is the density of the material; and S is the cross-section area of the tube.
(2)
3.2. Results The literature describes extensively the parameters which can change the energy absorption characteristics of a tube. Some interesting results of the tests done are reported here.
3.2.1. Triggers Some early papers ((18) or (19)) seem to suggest that the trigger can only have an impact on the peak force, but generally could not modify noticeably the average crush load, and therefore the SEA. In this context, the aim of the trigger is mainly to avoid 36
any catastrophic failure of the tube, and to limit the maximal acceleration experienced by the occupants of the vehicle. More recently, however, some studies have tried to investigate the effect of various triggers on the SEA for Carbon/Epoxy tubes in quasi-static tests. In (17), for example, two triggers were studied: •
a 45° chamfer, machined at the low end of the tube ;
•
a 2.5 mm plug initiator, combined with the same 45° chamfer.
Figure 14: Plug initiator and chamfer (left); chamfer alone (right) (thin-walled tube) (17)
The plug initiator is “a machined die, inserted into the end of the tube that becomes the crushing surface. Altering the radius of this plug produces varying results; as the radius approaches the wall thickness of the specimen the specific energy absorption (SEA) values increase”(17). It appears that the two different triggers can produce different failure mechanisms. In the case of the plug, all the material is forced out of the tube diameter, while when the only trigger is a chamfer, approximately half of the material stays inside while the tube crushes. Apart from the material failure, the two main friction phenomena are between the adjacent plies, and between the material and the crushing surface. A debris wedge of formed, which causes an inter-laminar failure at mid-thickness, and
37
the friction between this wedge and the adjacent plies absorbs energy and is added to the two previous types of friction.
Figure 15: Contribution of the debris wedge in the energy absorption (17)
This slight modification of the failure mechanisms is enough to change significantly the energy absorbed, and the chamfer alone has a higher SEA than the plug added to the chamfer.
3.2.2. Ply orientation Farley, in (18), shows that the ply orientation can have a great impact on the energy absorbed. However, the impact can vary according to the material used. For example, the SEA globally increases with the angle of the plies in the case of Kevlar/Epoxy (K/E) 38
and Glass/Epoxy (Gl/E) tubes, but decreases with the angle of the plies for Graphite/Epoxy (Gr/E) tubes. For energy absorption needs, the Gr/E tubes seem to be more efficient, as they absorb more energy than the Gl/E and K/E tubes for ply angles inferior to 45°, and have an equivalent behaviour for ply angles superior to 60°.
3.2.3. Failure modes The failure mode can change with the material used, even for composite tubes. Generally, according to (18), the Gr/E and Gl/E tubes fail in a brittle mode (lamina bending or transverse shearing), while the K/E tubes fail in a local buckling mode (also called accordian mode in (18)). This difference of behaviour only comes here from the fibre properties, as the matrix is the same for all tubes: the graphite and glass fibres show brittle failures, while the Kevlar fibre has “an elastic-plastic response with some splitting”. It is shown in the following figure.
Figure 16: Various modes of failure for statically crushed thin-walled tubes (18)
According to (19), it seems that the tubes failing in the transverse shearing mode (named here fracturing mode) tend to absorb more energy than the tubes showing the lamina bending mode (here the bending mode).
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3.2.4. Strain rates The study done in (18) tends to show that the strain rate have no impact on the behaviour of the tubes under 7.6 m/s, and showed that “failure modes, energy absorption mechanism and post-crushing integrity observed in the dynamic tests and the static tests were similar”. The dynamic tests were done with a 45 kg mass having an initial velocity of 7.6 m/s. This value is still quite low compared to the maximal vertical speed quoted by MIL-STD-1290, which is 42 ft/s (12.80 m/s). However, multiple tests described in (17) with crushing speeds going from 0.25 to 4 m/s showed that the SEA tends to be reduced as the crushing speed increases, for carbon/epoxy tubes. This dependence is not the same according to the type of trigger used, and the maximal drop in SEA recorded was 22 % (for a 2.5 mm plug). However, the dispersion in the results for the same speed is too important to give a lot of importance to this value. A more thorough study, in (20), taking in account speeds from 0.01 m/s to 12 m/s, shows that the carbon tubes response to the strain rate can vary according to the configuration of the laminate (ply angles). For carbon/epoxy UD tubes, the fibre properties are not strain-rate dependant, but the matrix properties are. When such tubes have 0 degrees plies, the fibre failure in these plies represents an important part of the energy absorption; therefore these tubes are nearly not strain-rate dependant. However, when they are constituted only of plies at an angle, the dependence to the strain rate varies with the angle of the plies. For Kevlar/epoxy UD tubes, as the matrix and the fibre properties are rate-dependant, all the tubes show dependence to the strain rate which varies according to the laminate used.
3.2.5. Fibre and Matrix maximum strain In (19), tests are described which focus on “the effects fibre and matrix maximum strain at failure have on the energy absorption of fibre reinforced composites”. According to the tests, with equivalent matrices the better energy absorption characteristics are with the fibres which have the higher failure strain. The same idea is applicable to matrices: the higher the matrix failure strain, the more energy is absorbed.
40
The differences between two different matrix/fibre combinations can vary according to the ply angles, as they can change the failure mode, but the general trend is that a high strain at failure enhances energy absorption characteristics.
3.3. Conclusion Composite materials have, generally speaking, more complex modes of failure and energy absorption mechanisms when compared to metals. These mechanisms vary greatly with the choice of the materials (matrix and fibre), with its orientation or with the geometrical characteristics of the part tested. Generally speaking, the composites have potentially better energy-absorption capabilities than metals.
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4. MODELLING FOR CRASHWORTHINESS The tools available to model crashes are now rather efficient and can help a lot during the design process. The main method uses finite elements, but it is also possible to model fluids or materials behaving nearly like fluids using SPH: Smooth Particles Hydrodynamics. It is possible to use both methods in the same simulation, in order for example to model a bird strike: the bird can be modelled using SPH, while the impacted structured is modelled with finite elements. A very important part in the process of simulating a crash is the choice of the materials and the material properties. In LS-Dyna, a little less than 200 different material models are implemented (21). Composite models are usually especially detailed, and include a good quantity of parameters to tune the elastic properties of the material as well as the damage model or the failure conditions. If some of these parameters are directly linked to real-life properties, for example the Young Modulus or the Poisson’s ratio of a material, others can be present to make good the lack of precision of the modelling. The latter are usually harder to choose and need to be tested in simple simulations, to test that they allow a good consistence between real tests and simulations. Pieces of software like LS-Dyna usually allow one to implement his own material model, specifically designed for a particular simulation or test, or simply to improve the existing models. The research in this field is particularly alive for composite materials, and a lot of improved models are created and presented in literature.
4.1. Integration method LS-Dyna allows the user to choose his preferred integration method. Basically, two methods are available, both being direct integration methods: the explicit integration method, and the implicit integration method. The difference lays in the calculation of the node displacements. (4) In the explicit method, the displacements of the nodes at a time t+1 depend on the previous displacements, speeds and accelerations of the nodes. The equation expressing this dependence is only stable conditionally: the time-step must be inferior to a number proportional to the minimal time of travel of a pressure wave in an element. This means that the time-step is more or less dictated by the size of the smaller element.
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In the implicit method, the displacements of the nodes at t+1 also require the acceleration and the speed at t+1. This allows having a non-conditional stability of the process, whatever is the time-step. However, of course the time-step still influences the accuracy of the calculations. Although the non-conditional stability is great on the paper, the implicit integration method is less used than the explicit method for crash simulation codes, because they are not performing as well when the time-step must be decreased for precision reasons. In LS-Dyna, the default method is the explicit method. However, it is possible to use the implicit method, although it is not compatible with all the material models or element types. It is also possible to begin a simulation with the explicit method, to stop it at a given time and to switch to implicit method. For the purposes of this work, only explicit methods were used.
4.2. SPH SPH stands for “Smoothed Particle Hydrodynamics”, the first intent being to provide an efficient means of calculation for astrophysics problems, dealing with huge masses of gas or particles, moving in open and empty spaces. More precisely, it “was invented to simulate non-axisymmetric phenomena in astrophysics” (22). Its great force compared to standard finite element methods is that this method does not rely at all on a spatial grid. When modelling fluids, finite elements are not always adequate, as they cannot always capture the fluidness of the water, for example. SPH solves this issue with a system of particles which can interact with each other, and are considered as material points, not deformable like solid elements. This evacuates all the issue linked with highly deformed Lagrangian mesh. This characteristic is particularly useful in the case of crashworthiness in water, because it allows the simulation to model the possible rupture of the skin, and the water surge in the subfloor structure. This phenomenon is difficult to model with water solid elements, which will be too distorted to allow a proper running of the calculations and will crash the simulation.
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4.2.1. Interpolation: the core of the SPH method SPH is based on an interpolation method, which allows approximating functions in space (22). If, for example, we consider the function , we can approximate it with the function , defined below: . , . !
(1)
This expression is used to calculate a weighted mean of the function over the space; this mean value is used to approximate the value of at point . The weight given to each value of the function is the value of the function at this point. The function is called an interpolating Kernel. In order to get an exact result, one would need to put all the weight on point , which would be done with the following expression: . . !
(2)
Where is the Dirac delta function
This is why the properties of the function are:
lim ,
(3)
, . ! 1
(4)
%&'
In this context, we can see as a measure of the precision wanted: when it tends to zero, the error tends to zero as well. It accounts for the “area” around the point taken in account for the calculation of W. A figure explaining for the discretized equations is shown at the end of this section. These expressions are discretized for numerical calculations. The space is divided between particles, and equation (1) becomes:
44
) * + . +
,+ . + , +
(5)
“where the summation index b denotes a particle label and the summation is all over the particles” (22); + is the value of the function at point + ; And ,+ and + are the mass and the density of the particle b.
Here,
-. /.
corresponds to the “volume” of space which represents the particle, which
was previously embodied by the ! in the integral equations. If we want to get the gradient of such a function: 1 * + . 0 +
,+ 1 + , .0 +
(6)
Figure 17: Set of neighbouring particles and h(23)
4.2.2. Kernels The choice of the kernel can have a noticeable impact on the precision of the result (22). Since the beginning of the SPH theory, a lot of kernels have been studied. One very famous kernel is the Gaussian kernel (the formulation below is for 3D problems, other exist for 1D, 2D or ND problems):
45
234)) ,
1
6 5 87 .
6
. 9 :;
< ⁄%
? @ 5. 6
(8)
Where M is a spline function defined by equation (11): 3 E1 3. A 7 . A 6 4 C >A 1 6 D . 2 A C 4 B 0
if 0 I A I 1;
if 1 I x I 2 otherwise
S
(9)
With this kernel, all the elements which are at a longer distance than 2×h from a particle will not contribute to the calculation of the properties of this particle. For this kernel, “the dominant error term in the integral interpolant is T 7 ” (22). In order to decrease the error, it is possible to normalize standard kernels. For example, in 3D the Super Gaussian kernel: U4VW; 234)) ,
1
6 5 87 .
5 < < . X 7 Z . 9 :; ⁄% 6 2
With this kernel, the error is decreased to T
[ .
(10)
However, it is obvious that in some
part of the space, the kernel takes negative values (when \ ]5⁄2), and to calculate an average with some negative weights, as small as they can be, can be dangerous. According to (22), “this can have serious consequences when there is a sharp change in density. An undershoot occurs, and the density may become negative” (22).
46
4.2.3. Equations of motion Now, the method can be applied to the equations of fluids dynamics. The first one is the Euler equation of motion (for incompressible and inviscid fluids): .
! 1_ 0 !^
(11)
1_ using the following identity: accuracy reasons to expand 0
We could directly use equation (6) to calculate the gradient, but it is better for
_ 1 _ 1 X Z . `1_ . `1 0 7
(12)
1_ !a 0 _ _ 1 X Z . `1Z X0 !^ 7
(13)
!a _a _b * ,b . c 7 7 d . `1a b a , !^ a b
(14)
b
With the same ideas, it is then possible to include the equations of fluid dynamics into the method.
4.3. Composite modelling in LS-Dyna Various material models are present in LS-Dyna, and enable the modelling of various composite characteristics. Some of these material models can be used with, or are designed for, solid elements.
4.3.1. *Part_Composite and delamination LS-Dyna has a new way of modelling composite materials, using a *Part_Composite entity with shell elements. A *Part_Composite card gathers all the information about the part: the number of plies, the type of shell, and for each ply: the orientation, the material model used (each different ply can use a different material model), and the 47
thickness. All the information previously stored in a Section card is now in the *Part_Composite card. The first choice to make is about the delamination. If one wants to model the delamination which will occur during the crash, then he needs to model several layers of material; the elements of the various layers are then linked by force-limited liaisons, which will absorb energy before failing. This approach increases the amount of data needed before beginning the simulation, but allows for more details. This approach is not compatible with the use of the *Part_Composite card, because a *Part_Composite part will be represented by only one layer of shell elements, with several integration points. The goal of the thesis being to evaluate the capacity of stock LS-Dyna to reproduce results obtained with specialized models coded for Dyna, the original helicopter subfloor model was re-used. The implementation of the delamination aspect would have meant further work on the subfloor model, which given its complexity would have been time-consuming; furthermore, it would have increased several times the number of elements, thus extending the calculation time. Therefore, the author decided not to chose this approach.
4.3.2. Material models in LS-Dyna Then, a material model has to be chosen. To model composite materials, quite a wide choice is available. In the scope of this thesis, only the following models were taken into consideration: Materials 22, 54-55, 58, 59, and 116 (cf. Table 2). The material 5455 has been chosen for the various simulations performed for this thesis. As the choice was not made before having run some simulations with various materials, it will be discussed in section 5.3; but as this material has been the only one to be used, its behaviour will be presented here. This material is applicable to shell elements and solid elements. The material models 54 and 55 are actually basically the same model, but with two different criteria for the matrix failure (24): material model 54 uses the Chang matrix failure criterion, while material model 55 uses the Tsai-Wu failure criterion. Both use the Chang failure criterion for the fibre failure.
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MAT_022 MAT_054-055
*MAT_COMPOSITE_DAMAGE *MAT_ENHANCED_COMPOSITE_DAMAGE
MAT_058 MAT_059
*MAT_LAMINATED_COMPOSITE_FABRIC *MAT_COMPOSITE_FAILURE_OPTION_MODEL
MAT_116
*MAT_COMPOSITE_LAYUP
Table 2: Composite material models available in LS-Dyna
The equations of the Chang failure criterion are quoted in the LS-Dyna Theory Manual (24). The criterion for the fibre is in tension is: 33 7 3+ 7 9e7 X Z f. X Z
9e7 I 1 elastic behaviour S g 7 9e \ 1 failure
(15)
Where 33 is the stress in the first main fibre direction, 3+ is the stress in shear, is the longitudinal tensile strength, the shear strength, and f a model parameter.
For the fibre in compression, the criterion is the same, but with the compressive parameters and without any interaction from the shear. For the matrix in tension: 7 9-
++ 7 3+ 7 X Z f. X Z
9e7 I 1 elastic behaviour S g 7 9e \ 1 failure
(16)
Where ++ is the stress in the second main fibre direction, 3+ is the stress in shear, and is the transverse tensile strength
Actually, this criterion is only a way to get an element failure. By using the parameters TFAIL, DFAILT, DFAILC and EFS, it is possible instead to trigger the failure according to a time step criterion, or to a strain or effective strain criterion. For example, using TFAIL allows one to delete all the elements which time-steps are inferior to a value (defined by TFAIL). The value is either expressed in fraction of the initial time-step for TFAIL between 0.1 and 1, or in absolute value for TFAIL between 0 and 0.1.
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For the purposes of the study, the author used a combination of the TFAIL parameter and the Cheng failure criterion. The use of the DFAILC and DFAILT parameters (which give a limit strain) was experimented, but not kept. Following is a table summarising the various parameters discussed here.
Parameter TFAIL
Characteristics It is a time-step criteria to trigger the deletion of elements. When TFAIL is between 0 and 0.1, the element is deleted when its time-step is smaller than TFAIL. When TFAIL is bigger than 0.1, the element is deleted when “the quotient of the actual time step and the original time step drops below the given value”. (21)
DFAILT
“Maximum strain for fiber tension (MAT_054 only). (Maximum 1 = 100% strain). The layer in the element is completely removed after the maximum tensile strain in the fiber direction is reached. If a nonzero value is given for DFAILT, a nonzero, negative value must also be provided for DFAILC.” (21) “Maximum strain for fiber compression (MAT_054 only). (Maximum -1 = 100% compression). The layer in the element is completely removed after the maximum compressive strain in the fiber direction is reached. The input value should be negative and is required if DFAILT > 0.” (21)
DFAILC
EFS
“Effective failure strain (MAT_054 only).” (21)
Table 3: Element deletion parameters for Mat. 054-055
4.4. Advanced composite material models Some other composite materials have been developed externally, by researchers, for LS-Dyna. One example will be taken with a strain-dependant, non linear, micromechanics material model, described in (25). The basic idea is to get a macro-mechanical behaviour from the modelling of micromechanical phenomena. This allows, for example, to model separately the matrix and the fibres as two different materials interacting, something rather impossible for most stock models in LS-Dyna (which generally consider each composite layer as a whole, excepted for failure criteria).
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This separation between the matrix properties and the fibre properties allows one to model accurately the strain rate sensitivity of the material. As we have seen in section 3.1, the matrix is usually strain rate sensitive, which is not the case for all the fibres (and specifically not the case for carbon fibres).
Figure 18: Micro-mechanical composite material model (25)
The idea shown in Figure 2 is to divide each part of the composite laminate in layers; each layer is constituted by small elements, which are themselves divided in a fibre part and a matrix part. The proportion of fibre and matrix in the laminate can be tailored to match the real material.
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4.5. Conclusion A quick review of the methods needed to model helicopter crashes in LS-Dyna has been done. The ideas behind the SPH method, useful to model water crashes (as well as birdstrikes) have been described, as well as one useful LS-Dyna composite material model and the ways to model laminates in LS-Dyna.
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5. MATERIAL MODEL VALIDATION In order to validate a material model before using it in the subfloor model, tests were done on a cylindrical tube. Several models were compared, the test not only allowing to validate the material model, but also to choose one among the various stock models available in LS-Dyna. The tests were therefore basically divided in two main sequences: the first one trying to get crushing characteristics comparable to the real tests by evaluating various material models and tuning their parameters; the second one to test thoroughly the chosen material, and the influence of the various parameters available on the crushing response. The goal was to match the experimental data given in Section 5.2 with the simulation, playing in two main fields: •
A trigger system, designed to reduce the peak force;
•
The parameters of the material, to match the average crushing force
The two are not entirely independent, as the trigger has also a slight impact on the average crushing force. However, the material parameters have only a negligible influence on the peak force. Therefore, the idea was to: •
Choose a mesh size;
•
Tune the trigger in order to get the good peak force; if impossible, refine the mesh;
•
Once the good trigger has been found, vary the material model parameters to get an accurate crushing force.
5.1. Limitations The validation of the material model is however very limited: it is very mesh-sensitive. The various triggers tested are all mesh-sensitive, as all the material parameters. This is partly due to the rather coarse modelling of the energy absorption mechanisms. As we have seen, the energy absorption mechanisms for crushed carbon/epoxy tubes are the delamination, the friction between the various plies and the debris wedges or the crushing surfaces, and the fibre or matrix failure. (cf. Figure 15, Figure 16).
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This modelling only takes in account the fibre and matrix failures, and the friction or the delamination are completely neglected, even if they actually represent a great part of the absorbed energy, if not the majority. This shortcoming can be corrected thanks to the parameters described in section 5.3, TSIZE, TFAIL or ERODS (even if ERODS is supposed to actually have a physical meaning), but as these parameters are not physical and mesh-dependant, it is necessary to tune them to match real test data. Therefore, the simulation cannot hope to give any predictive results: we can only try to reproduce more or less accurately real tests results, and not try to predict them.
5.2. Test data All the geometrical and physical material data used for the tests was taken from (2). The tube has an external diameter of 52.10 mm, and is constituted of 6 carbon/epoxy fabric layers. Each fabric layer has a thickness of 0.28 mm, and its two mean directions are along the axis of the tube and along its circumference. The physical data used, and common to all the material models, is given in Table 4 (2) (some data has been corrected): Density (Kg/m3)
1600
G1 (MPa)
6000
E1 (GPa) E2 (GPa)
72.2 72.2
G2 (MPa) G3 (MPa)
6000 6000
E3 (GPa) ν12 ν23
11.12 0.04 0.062
Sc (MPa) Xt (MPa) Xc (MPa)
66 833 698.3
ν13
0.062
Yt (MPa) Yc (MPa)
833 698.3
Table 4: Physical data of the composite material
The tube is crushed by a rigid wall with a mass of 66.8 kg, moving at an initial velocity of 7 m/s. The experimental data from the test is gathered in Table 5:
54
Average Force (N) Maximum Force (N)
29746 100938
Specific Energy Absorbed (J/g)
22.9
Table 5: Experimental test data, quoted in (2) – rigid wall 66.8kg, initial velocity 7m/s
Three distinct models of tube were used to simulate the test data. The tube was modelled by a unique layer of elements in all cases. The models included a 11328elements model, a 4182-elements model and a 322-elements elements model. According to Garijo (2), who made similar tests with models of 12000, 6000 and 3000 elements, the results were comparable between the 12000 and the 6000-elements models, and he therefore chose to stick with its medium-sized model.
5.3. Material choice and parameters As we described earlier, the first sequence was to choose a suitable material model. Material 58 (*MAT_LAMINATED_COMPOSITE_FABRIC) was the first material selected, because it was referenced in the literature ((26) and (27)), and had a good set of parameters apparently allowing one to tune it rather precisely. The parameters include: •
an ERODS parameter, allowing the user to delete an element with a strain criterion;
•
a TSIZE parameter, allowing to delete elements which are decreasing too much the time step;
•
SLIMT parameters (one for each tension, compression in both main directions, and shear), which can give some plastic properties to the material.
However, the author encountered a lot of issues with this material model, and was not able to get a good match between the simulation results and the experiments: the average force always stayed under 20 kN, giving an unacceptable error. Another annoying problem was the fact that after a while (the exact time depending on the parameters of the simulation), the contact between the tube and the rigid walls tended to disappear, letting the tube fly through the open space. 55
Figure 19: Effect of rigid wall contact breaking on the crushing simulation
This last problem was partially solved using the mass scaling option of LS-Dyna, but the first problem stayed. After some time spent in vain trials, this material was rejected, despite its qualities. Material model MAT_029 (*MAT_FORCE_LIMITED) and Material model MAT_059 (*MAT_COMPOSITE_FAILURE_OPTION_MODEL) were also tested with material 54-55. This last material was finally chosen as the one giving the better crushing load.
5.4. Peak Force and triggers Three main types of triggers were tested: •
Reduced thickness at the top end of the tube;
•
Top-end element rows bent inwards (or outwards);
•
Deletion of some elements in the top rows.
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5.4.1. Triggers and TFAIL In order to check that the TFAIL parameter was not influencing the trigger (at least when in a reasonable range), some tests were done with the same model, only varying the TFAIL parameter, and stopping the simulation after the collapse of the trigger. The test was done for a TFAIL going from 5.10-8 to a TFAIL of 0.101. For this model, the time step at the beginning was 2.25.10-5 s; a TFAIL of 0.101 means that the minimal time step authorized is approximately 2.25.10-6 s. The trigger consisted in bending the upper end of the tube inwards, on the first two rows, on an angle of 2.21 degrees (using the scaling tool). It appeared that for the whole range tested, TFAIL did not have any visible impact: even the raw (non-filtered) load curves were identical. Given the totally absent influence of TFAIL on the peak loads for this trigger, it was assumed that for all triggers the peak load would be independent of the TFAIL parameter.
5.4.2. Typical trigger behaviour 160 140 120
Crushing force (kN)
100 80 60 40 20 0
0
0,5 TFAIL 5e-7
1
1,5
Time (ms)
Figure 20: Load-Time curve of the trigger collapse of a composite tube
The above curve shows a side effect of all the triggers implemented during the tests: they create actually two peak forces. The first one occurs when the crushing surface 57
first meets the end of the tube; and the second when the trigger collapse is finished and when the crushing surface meets the tube. Smoother transitions were sought, but all of them featured this multiple-peak phenomenon.
Figure 21: Trigger behaviour (2 rows bent inwards, 2.21°) 58
In quite a lot of cases, the triggers tested actually increased the maximal peak force, when compared to the peak force for a tube without any trigger. In Figure 21, we can see the typical behaviour of the triggers, which can explain the two load peaks. The pictures are taken at 0, 0.2, 0.4, 0.6, 0.8, 1.0 ms. Between the two first pictures, the tube is loaded by the crushing surface and is compressed. In the second picture, the trigger is working: the upper end is bending towards the inside of the tube. But the two first rows are folded rather than being crushed, which nearly zeroes the crushing load, and the wall is quickly meeting the first non-weakened part of the tube (picture 3 and 4). There, as the trigger has been easily folded, it does not really weaken the upper part of the tube, and the only use of the trigger has been to absorb a fraction of the kinetic energy of the wall; in other words, the trigger did not play its role. This is why in some cases the trigger actually increases the peak load: after the trigger failure, the rest of the tube is still “intact”, and may be even reinforced by the trigger elements which have not been deleted.
5.4.3. Trigger results
Trigger type Experiment (no trigger) Outwards, 1 row, 2.21° Outwards, 2 rows, 2.21°
Peak force (kN) 100.938 158.5 175.5
Error (%) 0 57.03 73.87
Outwards, 3 rows, 2.21°
175.5
Inwards, 1 row, 2.21° Inwards, 1 row, 0.9°
186.7 166.6
73.87 84.97 65.05
Inwards, 2 rows, 2.21° Inwards, 3 rows, 2.21°
138.9 171.4
37.61 69.81
Thickness, 3 plies on 3 last rows
105.3
4.32
Table 6: Peak forces obtained with various triggers (11328 elements model)
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The triggers tested and the corresponding peak forces (for the high mesh model) are summed up in Table 6. If two peaks were present, only the highest value was kept. After having managed to get results in agreement with the experimental tests, some work was done with a reduced number of elements. The same type of triggers was therefore tested on the 4182-elements model. The same general behaviour of the triggers was noticed, with usually two peak forces before and after the trigger failure. Although the trigger-less configuration gives a way higher peak load than for the 11328 elements model, the same order of loads was observed for most of the configurations. The better configuration is, like before, the reduction of the number of plies (from 6 to 3) at the top of the tube. In order to push further the tests, another type of triggers was designed, with a number of artificially deleted elements in the first row; the results were not conclusive. The results of the tests are given in Table 4.
Trigger type Experiment (no trigger) No trigger Outwards, 1 row, 2.21°
Peak force (kN) 100.938 189.7 163.9
Error (%) 0 87.94 62.38
Outwards, 2 rows, 2.21° Outwards, 3 rows, 2.21° Inwards, 1 row, 2.21°
181.5 155.7 186.7
79.81 54.25 84.97
Inwards, 2 rows, 2.21° Inwards, 3 rows, 2.21°
186.7 145.1
84.97 43.75
Thickness, 3 rows, 3 plies 6 elements deleted on first row
107.3 185.5
6.30
12 elements deleted on second row
178.0
76.35
83.78
Table 7: Peak forces obtained with various triggers (4182 elements model)
Given the mesh sensitivity of the results, no other tests were done in this area with different mesh sizes. Although it could have been interesting to do a real study with several mesh sizes, this was not considered as vital for the rest of the work.
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5.4.4. SOFT parameter The SOFT parameter was tested to evaluate its impact on the trigger peak force. The definition of the parameter SOFT is given in the LS-Dyna Keyboard User’s Manual (21): “Softening reduction factor for material strength in crash front elements (default = 1.0). TFAIL must be greater than zero to activate this option.” As this definition suggested, and as the tests confirmed, the SOFT parameter has no impact on the peak force (TFAIL was of course greater than zero for the tests), because it is applied to elements neighbours to a deleted element during the simulation. No elements are deleted yet when the wall meets the tube, and the SOFT parameter is not applied to the first row.
5.5. Average crushing loads The second step of the study was to calculate the average crushing loads in the best configuration for the peak load, the reduced thickness trigger. The main parameter used to tune the material model was the TFAIL parameter (see section 4.3.2 for an explanation of TFAIL). The influence of this parameter is quite straightforward: increasing it means reducing the number of deleted elements at a given time in the simulation, hence reducing the average crushing load. The experience confirmed more or less this tendency. The tests were made on the two higher mesh density models (11328 and 4182 elements), with the thickness-based trigger and varying TFAIL. Some simulations crashed before the end, with either tubes going through the walls, or elements taking huge sizes.
TFAIL
ACL (kN)
Error (%)
Experimental
29.746
0
0.101 5.10-7
26.2 27.48
3.51 2.24
2. 10-7 1.10-7
30.73 31.73
0.97 1.97
Table 8: Average crushing load results for 11328 elements model
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TFAIL Experimental
ACL (kN) 29.746
Error (%) 0
0.101 1.10-6
29.14 28.12
0.60 1.61
5. 10-7
28.6
1.14
Table 9: Average crushing load results for 4182 elements model
5.6. Coarser mesh In order to be able to run the subfloor model in hard surfaces and get good results, it was necessary to validate first not only the material model, but also the behaviour of the crushing tubes. As we have seen, the material model had to be tuned with nonphysical and mesh-sensitive parameters; and the tuning needs to be re-done for each mesh change. In the subfloor model provided, the crush tubes have around 200 elements, a highly coarse mesh when compared to the 11328 or even the 4182 elements models. It was therefore thought interesting to try to get a good behaviour from a so low-poly mesh. However, without speaking about the peak force which appears to be really difficult to get even below 150 kN, the average crushing force is clearly too inaccurate for the purposes of a simulation, staying around 22 kN.
5.7. Conclusion Simulations were done in order to reproduce results from Perez-Garijo’s work, on composite tubes of 11328, 4182 and 322 elements. In opposition with Perez-Garijo’s work, it was found that only the reduced thickness type of trigger could give acceptable peak forces, within 10% of error compared to the experiments. This error is slightly smaller than the one reached by Perez-Garijo, who had a 16% error on the peak force. It is important to notice that the result of these tests is only the assurance that material model 54-55 is capable of representing a composite material in one very 62
specific experiment. As the study with the coarser mesh shown, this ability is obviously mesh-sensitive, and the conical crush tubes with a coarse mesh present in the subfloor model are likely to have an inaccurate load/time curve response. For this reason, in the absence of any data on the conical crush tubes present in the subfloor, it seems difficult to model accurately the behaviour of this subfloor on hard surfaces.
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6. WATER VALIDATION After the validation of the material model, it is necessary to validate the water model itself. The test data used as a reference comes from the work of Pérez-Garijo (2). The simulations included water modelled with solid elements, as in Garijo’s work; and water modelled as SPH particles, as well as “hybrid” water, with both solid and SPH elements. A part of the work was to evaluate the influence of various parameters on the acceleration peak and the pressure history of the elements; another was to choose a good set of parameters for each model (solid, SPH and hybrid) to get a realistic acceleration peak. The data taken as a reference was provided by Kevin Hughes, and is from experiments conducted as part of the CAST program. The idea behind the hybrid water is to have the main strength of the SPH, which is the good modelling of subfloor flooding, while limiting the calculation time by using a good part of solid elements.
6.1. Setting the experiment
6.1.1. Water model The water model is based on an equation of state. The Gruneisen equation was chosen for the purpose of this study, as did Pérez-Garijo. An equation of state is used to calculate the pressure to which an element is submitted. Gruneisen equation is defined as follows in the LS-Dyna keyboard user’s manual (21):
o p ' . 7 . n. ?1 ?1 2' @ . n 2 . n7 @ o' p. n. ' m 7 n7 n6 X1 1. n 7 . n 1 6 . Z n 17
(17)
Where C is the speed of sound in the material; S1, S2 and S3 are coefficients; γ0 is the “Gruneisen gamma”; a is the first order volume correction to γ0; E0 is the internal energy (per volume unit) and n=⁄' 1
64
This equation gives the pressure of the water from its volume. The values used were chosen according to Pérez-Garijo’s values, and are gathered in Table 10. This equation of state was used as well for the SPH elements. Various water block and element sizes were tested in order to find the best compromise between the number of elements and the precision of the result.
C (m/s)
1483
γ0
1
S1
2.037
a
0.5
S2
0
E0 (Pa)
0
S3
0
V0
1
Table 10: Water model parameters (2)
The width (181.5 cm) and length (235.4 cm) of the water block were kept as they were for all the tests. Only the depth was modified, and tests were made with depths between 60 cm and 122.4 cm. In order to reduce the computational cost, the water model was divided by four, using the symmetries of the model.
6.1.2. Impactor model The impactor is a 100 cm long half-cylinder with a 24.2 cm diameter. It has a Young modulus of 1.2 GPa, and a density of 0.87 g/cm3. Again, all the data is taken from (2). Some comparisons were made between an impactor modelled with elastic material 1, and the same body modelled using the rigid body material 20. The variation in acceleration peak was considered as acceptable, and all the following study was performed with a rigid impactor. As for the water, only a quarter of the impactor is modelled. The accelerations of two nodes were recorded, as shown in Figure 22.
65
Sensor #1
Sensor #2
Figure 22: Location of the acceleration sensors on the impactor
6.1.3. Experimental data The final point was to manage to approach as closely as possible the experimental data available for the test. This data consists in the acceleration of the two nodes mentioned earlier. Figure 23 gives the acceleration curve of these points:
66
Figure 23:: Experimental data (CAST program - cylinder drop test in water)
6.1.4. Analysing the results
6.1.4.1.
Filtering
At the beginning of the experiments, the author had some difficulties with the analysis of the results. The amount of noise present in the acceleration data of the chosen nodes was important enough to make mandatory the use of a filter. It was recognized that the amount of filtering used had a great impact on the acceleration peaks registered; actually, it can be said it has a far greater impact than any of the model parameters such as boundary conditions, water depth or mesh size. The author therefore decided ided that all the results would be filtered with exactly the same parameters. A Butterworth filter was used, used with a C/s of 750 and a time in ms. In order to choose ose this value, a water model with a fine water mesh, provided by Kevin Hughes, was used as a reference. eference. The filter was tuned in order to get approximately the same peak as in the experimental data available, and this filter was kept for all the other experiments. The author had at first tried to use the same filter as in the experiment, but did not no manage to reproduce the filter, probably because of the unusual time unit (centiseconds). At that point, it was considered that too much work had been done with the cm, cs, kg unit system to re-do re do all the simulations from the beginning. 67
6.1.4.2.
Initial distance to water
Moreover, the initial distance between the cylinder and the water was found to have an impact on the filtered results. Tests were done with the three variants of water (full solid, full SPH and mixed SPH and solid) with the distance ranging from 1 mm to 15 cm.
Figure 24: Variation of load factor history with initial impactor height
Tests showed that the results were quite sensitive to the initial distance of impact, instead of being totally independent from it as they should should be. This is uniquely due to filtering, as the unfiltered curves were compared and are strictly identical. Figure 24 shows an example of this phenomenon: phenomenon: the plain curves are the load factors of the two nodes on an impactor at 2 cm of the water; the dotted curve is the load factor of the two nodes on an impactor at 3 cm of the water. The difference in the load factor peak recorded is near 19 %, which which is more than the influence of some of the parameters studied in the next sections. For all the tests, the SLSFAC parameter (please see section 69) was at 0.55. In order to avoid any influence of the filtering on the results, the author decided to take a good margin and set the initial distance as 15 cm. This considerably increased the calculation time, but it stayed under acceptable limits.
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6.2. Solid elements water: water: sensitivity to various parameters Numerous simulations were run in order to get the better compromise possible between calculation time and results accuracy, to get a proper water model for the simulation of the subfloor crash in water.
6.2.1. Penalty stiffness parameter The contact between, for example, nodes and surfaces, is modelled in LS-Dyna LS by creating springs which resist the penetration of the nodes in the surfaces. The stronger is the penalty stiffness, the higher is the repulsion force for a given penetration. The user has access to the th parameter SLSFAC, defined in the *CONTROL_CONTACT card, to modify this stiffness. By default, SLSFAC equals 0.1. Tests were made with SLSFAC values ranging from 0.02 to 5000. For each value, the two acceleration peaks (one for each node) are recorded, and and a curve giving the acceleration peak as a function of SLSFAC was constructed. This work is shown on Figure 25 for two sizes of elements. For 2x2x2 elements, the values 500 and 5000 gave a negative volume on one of the impactor elements (for an elastic impactor); the same phenomenon appeared for the value 5000 with 3x3x3 elements.
Figure 25:: Influence of SLSFAC on the acceleration peaks
69
The general trend seems to be a slow decrease of the peaks as SLSFAC increases, which would be in contradiction with the conclusion of Pérez-Garijo. Pérez Garijo. However, the influence seems to be of a low magnitude, magnitude, even if it does gives some possibilities to make good a mesh a bit coarser than the 2x2x2 elements. The values were taken for SLSFAC equals to 0.02, 0.1, 0.5, 5, 50, 500, and 5000.
6.2.2. Element size,, water depth The element size is one of the most obvious parameter parameter which can be taken in account. It concerns here only the width and length of each element, the depth being dealt with in the section 6.2.3.. The tests were made with cubic elements of 2x2x2, 2.5x2.5x2.5 and 3x3x3 x3x3 cm, with a water depth of 60 cm. The boundary conditions were with classical restricted movement on the plane axes, and a non-reflective non reflective boundary at the bottom of the water block. The Th penalty stiffness parameter was 0.5.
Figure 26: Influence of water element size on the acceleration peak of a cylindrical impactor
In Figure 26,, a zoom has been made to focus on the peak difference. We can see that the two plain curves for the 2x2x2 elements have a peak inferior to the dotted curves 70
of the 2.5x2.5x2.5 elements and 3x3x3 elements. This difference could however also come from the lower number of elements in depth (as the depth is constant, the number of elements is of course changing Another factor which could have an importance is the size of the mesh compared to the curvature of the impactor surface. As the radius is only 12.1 cm, the water surface cannot match properly the impactor surface with water elements bigger that 2x2 (in width and length). This phenomenon is shown in Figure 27: the left picture is with a 2x2x2 mesh, the right picture with a 3x3x3 mesh.
Figure 27: Quality of mesh and surface draping
In order to validate more efficiently the water model, it would have been interesting to have experimental data for an impactor with dimensions (curve radii) similar to the dimensions of the subfloor.
6.2.3. Water depth and element aspect ratio In order to limit the influence of the bottom boundary condition, it is possible to increase the depth. This can be done either by increasing the number of elements, or by increasing the depth of each element. It would also be possible to keep cubic 71
ce, and then to increase progressively the depth of the elements near the surface, elements as we move away from the surface. The study was focused on the idea of increasing the depth of each element in order to increase the total depth. This solution is totally cost-free cost free in terms of calculation time, and could increase the accuracy of the results. Several tests were done, with a SLSFAC of 0.5, and a SLSFAC of 50. The baseline model has an 80 cm depth (2.5x2.5x4 elements); then, keeping the same number of elements, their depth was put at 5 cm, with a 100 cm depth. All the tests were made with SLSFAC at 50.
Figure 28: Influence of water depth (4cm and 5cm elementelement-depth) on the acceleration peak of the two sensors
It seems that to increase the depth could give better results, even without changing the number of elements. However, the study should be broadened broadened to include more mesh sizes before taking any definitive conclusion. conclusion. The time allocated did not allow conducting such a study, and therefore squared elements were kept. Moreover, the use of coupled SPH-Solid SPH Solid elements is better with a regular SPH mesh in the 3 directions, and therefore squared elements were anyway nearly mandatory for the tests. 72
6.2.4. Boundary conditions The boundary conditions for the impactor are straightforward: all the nodes in the planes of symmetry are blocked in the translation orthogonal orthogonal to this plane. The rotations having their axis in the plane of symmetry are also blocked, which gives three degrees of freedom blocked. For the block of water, an alternative exists: the non-reflecting non reflecting boundary condition. This can be only applied on surfaces, and is supposed to stop the reflection of the pressure waves on the surfaces. Three different boundary conditions were therefore tested for the block of water: •
Option 1: Non-reflecting reflecting boundary conditions for the planes of symmetry and the bottom of the block of water;
•
Option 2: Non-reflecting reflecting boundary conditions for the bottom of the block, and standard boundary conditions for the planes of symmetry;
•
Option 3: Standard boundary conditions for the planes of symmetry and the bottom of the block of water.
In order to compare the effect of the boundary conditions, the pressure in the elements was monitored for the column of elements at the junction of the two planes of symmetry. etry. With a high sampling rate, it is possible possible to record the passage of the pressure waves in the elements. All the tests described in this section were made with SLSFAC at 0.5, a depth of 60 cm and 2x2x2 elements.
Figure 29:: Pressure history with varying boundary conditions
73
The result of the pressure monitoring is shown on Figure 29.. The left picture corresponds to Option 1,, with all non-reflecting non reflecting boundary conditions. The right picture represents the pressure history for the two other options, as it is, surprisingly, identical. We can see that the pressure waves are slightly dampened in the left picture. The author had anticipated icipated that the bottom boundary condition would be the most important, but it appears from this short test that it is actually not quite the case. It is possible that a more thorough study of the propagation of the pressure waves could have given a broader er view of the phenomenon, but this study was not done in the time allocated. The acceleration of the nodes was also monitored, in order to confirm the trend shown by the pressure study. The results were so similar for options 2 and 3 that the curves are difficult to discriminate. The acceleration curves for options 1 and 2 are displayed in Figure 30;; it can be seen that the difference is not dramatic, and affects only one of the extremities.
Figure 30:: Acceleration for various boundary conditions
Option 1, although it was maybe the better in theory, was not appropriate for the coarser meshes (3x3x3).. Indeed, it gave odd behaviour haviour of the water near the planes of 74
symmetry in some conditions (the water behaving as if there was no boundary at all). Therefore, the second option was used for most of the other tests.
6.3. Behaviour of SPH particles The next step was to replace some or all the water solid elements by SPH particles, in order to check their behaviour and their impact on the acceleration peaks.
6.3.1. Combined SPH-Solid elements As usual, two main outputs can be monitored to check the influence of the introduction of SPH on the model: the acceleration peak and the pressure in the elements. Unfortunately, the author did not manage to get good pressure information on the SPH particles: there is a way to export the particles date (sphout), but not to create a set of SPH elements… It was tried to create such a set by hand in the keyboard file, but in vain. It is still possible to get the pressure from the history plots, but the sampling rate is too low to record properly the pressure waves.
Figure 31: Elements monitored
75
Therefore, the pressure is compared for solid elements at the same place in two models: one with only solid elements, the other with solid and SPH elements. The elements monitored are shown sho in grey in Figure 31.. They are all in the axis of symmetry of the model (intersection of the two planes of symmetry): symmetry) It is difficult to draw any conclusion conclusion from these graphs. It is true that the wave in the SPH elements seems to be delayed, but this can be accounted for by the exact time of the impact. Although a contact thickness (of 1 cm) has been defined, which is supposed to give a simultaneous impact, the small difference is not surprising.
Figure 32: Pressure recordings for solid and hybrid models
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Similarly, the maximum pressure registered is not really meaningful, as the sampling rate, even if it is really fast, might not allow an accurate recording of the pressure peaks. The only conclusion possible from these results is maybe that the SPH pressure pressur is noisier than the solid elements pressure. Apart from this, the readings seem to be rather consistent. The study of the acceleration peaks (Figure 33) seems to confirm this observation. The introduction of the SPH hardly changes the peaks, but delays them a little bit. It is estimated as largely acceptable given the other advantages of the SPH particles.
Figure 33: Comparison of acceleration curves for solid and hybrid models
6.3.2. All SPH particles A part of the study included the run of a full SPH water model. The idea was to try to get a good acceleration peak (i.e. approximately 80 g, cf. section 6.1.3). 6.1.3 Therefore, tests used a mode important height of 120 cm, with varying penalty stiffness parameters and particle densities. Two main models were run, with respectively respec 40x40x40 (i.e. 64000) particles and 60x60x60 (i.e. 216000) particles. Penalty stiffness parameters were modified, but did 77
not have more impact than for solid elements. The following figures show that even if the dispersion of results is greater for the 60x60x60 model, the lower peak approaches more accurately the actual acceleration, which makes sense from a bigger model. To give a basis of comparison, the solid model with 2x2x2 elements had around 76000 elements, which is not so different from the SPH 40x40x40 model.
Figure 34:: Acceleration curves for a 40x40x40 SPH water block (SLSFAC=10)
Figure 35:: Acceleration curves for a 60x60x60 SPH water block (SLSFAC=0.55) 78
Although the author believes it would be possible to get accurate response from allall SPH models, this is not a practical way for the experiment we try to simulate, because the SPH elements are quite time-consuming time consuming during the calculations. Their use would however wever be necessary if it was found that the interaction between the SPH water elements and the solid water elements raises issues. Such issues were not discovered in section 6.3.1.
6.4. Final models Two water models were selected for the subfloor impact, one solid and one hybrid model. Both use basically the same parameters, the baseline being the solid model with 2x2x2 elements, SLSFAC at 50, a 60 cm depth and a non-reflecting non reflecting bottom boundary condition (as well well as standard boundary conditions on the planes of symmetry). Figure 36 and Figure 37 compare the acceleration peak of this model with the experiment:
Figure 36:: Water model results - solid model
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Figure 37:: Water model results - hybrid model
6.5. Conclusion Tests were conducted on three different water models in order to validate the capacity of LS-Dyna to model accurately a pool of still water; and to evaluate the coupling between FE and SPH. The data from the experiments has been filtered, due to a high level of noise. It was noticed that the unfiltered signal from simulations involving SPH was different in amplitude from the unfiltered signal of other simulations without SPH particles. Studies were made on various parameters to evaluate their impact impact on the acceleration peaks, and in some occasions on the pressure wave propagation. The results show that with 2x2x2 solid elements it is possible to get a very accurate answer from the model, when compared to the experiment, even with only 60 cm depth. depth. The introduction of SPH to create a hybrid model is working well, and only introduces sometimes a difference between the two accelerations recorded.
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7. SUBFLOOR CRASH In order to test the difference between the two alternatives, a subfloor drop test was simulated. The geometrical model of the subfloor was provided by the author’s supervisor and is from the CAST program. Pérez-Garijo used this model for his tests in Dyna-3D. The author created all the materials according to his work, with the necessary properties, using the *Part_Composite card. Some values were corrected when necessary. All the details are available in (2).
7.1. Solid model The water model in this case consists in a 300x250x60 cm “pool” of water, with 3x3x3 elements. Although all the previous tests show that 3x3x3 elements are less accurate than 2x2x2 elements, the number of 2x2x2 elements needed to fill the pool was far too important to be considered.
Figure 38: Acceleration plot, subfloor drop test – 3x3x3 solid elements water – initial impact speed 8m/s
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The acceleration was recorded for the 6 elements situated at the exterior corner of the fittings, as shown below. The acceleration recording (filtered with the same filter as the water tests) is shown in Figure 38. The maximal acceleration peak recorded is around 14 g, which is really lower than the peak recorded in the experiments (2), which is around 24 g.
Sensor #5
Sensor #4
Sensor #3 Sensor #6 Sensor #2 Sensor #1
Figure 39: Location of the sensors
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7.2. Hybrid model
Figure 40: Acceleration plot, subfloor drop test – hybrid (solid + SPH) water – initial impact speed 8m/s
The hybrid model was created using the solid model as a base. Some solid elements were replaced in their centre by SPH particles. The results of the simulation can be seen in Figure 40 (with the same sensors as with the previous model). Here again, the acceleration recorded seems to be too low. The acceleration records are quite different from the solid model. Following is a set of pictures taken from the post-processing of the files:
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Figure 41: 3D plot, subfloor, hybrid water, t=0, 0.6, 1.2, 1.8, 2.4, 3.0 cs
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8. CONCLUSIONS
8.1. Discussion The objective was to evaluate the capacity of LS-Dyna to give accurate results in the field of helicopter crash into water, and specifically the performances of the SPH/FE coupling. This evaluation was done by comparison with real tests and the work of Pérez-Garijo, who used Dyna-3D. It appears that it is possible to simulate in a very precise way the characteristics of composite tubes when crushed. However, this could be done only by the use of nonphysical parameters, and this technique cannot allow having any predictive analysis. On the other hand, Pérez-Garijo own material model did not need non-physical parameters, and therefore is more useful for simulations. This last remark should be pondered by the fact that more physical material models exist in LS-Dyna, but only under license (they are the MAT_COMPOSITE_MSC materials). These materials can model delamination, for example. It seems difficult to have any predictive capability without modelling properly the main energy absorption mechanisms in tube crushes: delamination and friction. The modelling of the impactor drop into water showed the efficiency of LS-Dyna in this domain. SPH particles were not as easy to use as standard elements, but this is probably partly due to the Hypermesh interface. It was for example impossible to create SPH elements from Hypermesh, and the author had to use LS-Prepost for this. The FE/SPH coupling seems to work effectively, even if a thorough study of the pressure waves should be conducted to take any definitive conclusion. The last drop test, of the subfloor in the two water models, did not give the expected accurate results. This could be due to a lot of parameters, but the author could not identify the cause. Although it is true that the water is shallow and the elements coarser than ideal, the elements used by Pérez-Garijo were coarser (3x3x5) and its water as shallow. Further tests with the model itself would be needed to draw any conclusion on that matter. It is however possible to compare the results obtained with solid elements and the hybrid model: although the shape of the acceleration curves is quite different, the acceleration peaks are similar. The fact that the acceleration curves differ is quite
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normal, as SPH does not have the accuracy problems met with highly distorted elements.
8.2. Conclusion It appears that LS-Dyna is now an efficient crash simulation code. Its material choice is wide, allowing the user to model easily any situation. However, it is believed that only composite material models taking in account all the energy-absorption mechanisms might be able to give a predictive capability. Such models do not exist yet in LS-Dyna. The coupling between FE and SPH particles was working well, even if it was difficult to get accurate results for only-SPH models. Generally speaking, the results obtained are in the same margin of error than the results of Pérez Garijo. The author has no explanation for the surprisingly low acceleration level of the subfloor, but believes the subfloor model would have needed more work, especially on the material side.
8.3. Further work The author recognizes that this work is only a first step in the successful modelling of a helicopter subfloor crash. A lot of work is to be done on the conical tubes of the model if it is to be dropped on hard surfaces. Some simulations were run on hard surfaces, but the crush cones were not solicited as they should be. The lack of experimental data on the crush cones hampered any further research on this topic. It would be interesting to investigate the behaviour of the same subfloor in the case of soft soils. It is recognized that the soft soils are less critical than water or hard surfaces, but the evaluation of the capacity of LS-Dyna to model such soils would be interesting. However, it is possible that the apparent lack of data on the crush cones could prevent such a research to be successful. More importantly, the topic of the bottom sandwich delamination (which is one of the main energy-absorption mechanisms for the water impact) has been totally overlooked in this work. The author believes that the current state of LS-Dyna allows the modelling of the delamination between the sandwich and the bottom skin. Such a work would provide probably better results. As a summary, further work could include: 86
•
Validation of coarse crushing tubes (for hard-surfaces crashes)
•
Validation of various structural parts (frames, longerons) against test data
•
Soft soils simulations
•
Investigate the sandwich behaviour in delamination
•
Simulations with varying angles of roll and pitch
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REFERENCES 1. industries, NAHEMA. NH Industries - NH90, The New Reference for the Armed Forces. [Online] 2009. [Cited: 9 November 2010.] http://www.nhindustries.com/site/FO/scripts/myFO_contenu.php?noeu_id=42&page _id=12&lang=EN. 2. Pérez Garijo, German. Simulation of composite helicopter subfloor impact on water. s.l. : Cranfield University, 2004. 3. The History of Helicopter Safety. Fox, Roy G. Montréal, Québec, Canada : American Helicopter Society Symposium, 2005. 4. Caussade, Laurent. Improvement of a helicopter frame design regarding to crash absorption. s.l. : Cranfield University, 1998. 5. Herrera, Ivonne A., et al. Helicopter Safety Study. Trondheim : SINTEF Technology and Society, 2010. 978-82-14-04833-4. 6. America, Departement of Defense - United States of. Military Standard Light Fixed and Rotary-Wing Aircraft Crash Resistance. 1988. 7. W.Jiang, J.L.Yang. Energy-absorption behavior of ametallic double-sine-wave beam under axial crushing. Thin-walled structures. 2009, Vol. 47, 11. 8. Beral, Bruno and Souquet, Jean-Marc. Composite beam with integrated rupture initiator and aircraft fuselage including such beams. US 6948684 B2 US, 27 September 2005. 9. Michielsen, A.L.P.J., et al. Design, Test and Analysis of Tensor Skin Panels for Improved Crashworthiness in Case of Water Impact. s.l. : National Aerospace Laboratory NLR, 1998. 10. Ubels L.C., Wiggenraad, J.F.M. Increasing the survivability of helicopter accudents over water. s.l. : National Aerospace Laboratory NLR, 2002. 11. Jackson, Karen E., Fuchs, Yvonne T. and Kellas, Sotiris. Overview of the NASA Subsonic Rotary Wing Aeronautics Research Program in Rotorcraft Crashworthiness. s.l. : Langley Research Center (NASA), 2009. 12. Campbell, Rod. Helicopter subfloor design and modelling for crash into water. s.l. : Cranfield University, 2009. 88
13. Bansemir, Horst. Subfloor structure of an aircraft airframe. US 6427945 United States of America, 6 August 2002. 14. Composite Demonstrator Test/Analysis Correlation Report. s.l. : CAST, 2003. 15. Tho, Cheng-Ho and Wang, B.P. An Effective Crashworthiness Design Optimization Methodology to Improve Helicopter Landing Gear Energy Absorption. Journal of the American Helicopter Society. 2009, Vol. 54, 4. 16. Farley, Gary L. and Jones, Robert M. Crushing Characteristics of Continuous Fiber Reinforced Composite Tubes. Journal of Composite Materials. 1992, Vol. 26, 1. 17. Brighton, Aaron, et al. Strain Rate Effects on the Energy Absorption of Rapidly Manufactured Composite Tubes. Journal of Composite Materials. 2009, Vol. 43. 18. Farley, G. L. Energy Absorption of Composite Materials. Journal of Composite Materials. 1983, Vol. 17, 3. 19. Farley, Gary. Effect of Fiber and Matrix Maximum Strain on the Energy Absorption of Composite Materials. Journal of Composite Materials. 1986, Vol. 20, 4. 20. Farley, Gary L. The Effects of Crushing Speed on the Energy-Absorption Capability of Composite Tubes. Journal of Composite Materials. 1991, Vol. 25, 10. 21. Compiled by Hallquist, John O. LS-Dyna Keyboard User's Manual. Livermore : Livermore Software Technology Corporation, 2007. ISBN 0-9778540-2-7. 22. Monaghan, J.J. Smoothed Particle Hydrodynamics. Annual Review of Astronomics and Astrophysics. 1992, Vol. 30. 23. Vignjevic, R. Review of Development of the Smooth Particle Hydrodynamics (SPH) Method. Cranfield : Cranfield University, UK. 24. Compiled by Hallquist, John O. LS-Dyna Theory Manual. Livermore : Livermore Software Technology Corporation, 2006. ISBN 0-9778540-0-0. 25. Tabiei, Ala, Yi, Weitao and Goldberg, Robert. Non-linear strain rate dependent micro-mechanical composite material model for finite element impact and crashworthiness simulation. International Journal of Non-Linear Mechanics. 2005, Vol. 40.
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26. Bisagni, Chiara and Giavotto, Vittorio. Experiments and Analyses on Postbuckling Behavior of Stringer-Stiffened Laminated Composite Helicopter Tailplane. Journal of the American Helicopter Society. 2009, Vol. 54, 2. 27. Bisagni, Chiara and Mirandola, Cecilia. Experimental and Numerical Investigation of Crash Behavior of Composite Helicopter Cruciform Elements. Journal of the American Helicopter Society. 2005, Vol. 50, 1. 28. Electronic Code of Federal Regulations. GPO Access. [Online] 26 August 2010. http://ecfr.gpoaccess.gov/cgi/t/text/textidx?sid=c6fff022e42916ce84a6dd58573915a4&c=ecfr&tpl=%2Findex.tpl.
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APPENDICES APPENDIX A UNIT SYSTEM One of the first tasks of the modelling was to choose a consistent system of units. At first, the system (mm, s, T) was used, but the geometrical subfloor model was given with distances stated in cm. As a lot of data had been created when the geometrical subfloor was made available, and because at the moment he did not think about the “scale” function of Hypermesh, the author decided to keep as much data in common as with the first unit system chosen. Therefore, the unit system chosen for most of the models was: cm, cs (centiseconds), kg. This allows having pressures, stresses and strengths in MPa, as with the previous system. The forces are in hN (hectonewtons). This system gave some difficulties when the filtering problem arose, which are detailed in section 6.1.4.1.
1
APPENDIX B MATERIAL DATA (2) Aramid/Epoxy 3
Density (Kg/m )
1400
G1 (MPa)
2000
Ply thickness (mm) E1 (GPa)
0.17 25.5
G2 (MPa) G3 (MPa)
800 800
E2 (GPa) E3 (GPa)
25.5 3
S (MPa) Xt (MPa)
57 380
ν12
0.02
Xc (MPa)
140
ν23 ν13
0.008 0.008
Yt (MPa) Yc (MPa)
380 140
Carbon/Epoxy 3
Density (Kg/m ) Ply thickness (mm)
1600 0.25
G1 (MPa) G2 (MPa)
3450 1200
E1 (GPa) E2 (GPa) E3 (GPa)
62.9 62.9 3 (?)
G3 (MPa) S (MPa) Xt (MPa)
1200 69 880
ν12
0.06
Xc (MPa)
500
ν23
0.008 (?)
Yt (MPa)
880
ν13
0.008 (?)
Yc (MPa)
500
Density (Kg/m )
Honeycomb 48
G1 (MPa)
E1 (MPa)
Neglect.
G2 (MPa)
E2 (MPa)
Neglect.
G3 (MPa)
E3 (MPa)
Neglect. (?)
ν12 ν23
0.03 (?) 0.03 (?)
ν13
0.03 (?)
3
Aluminium Clad 2024-T3
Foam Rohacell 71
Density (Kg/m3)
2800
71
E (GPa)
72.4
105
ν
0.33
0.49
2
APPENDIX C PART DATA (2) Bottom skin monolithic
Aramid
[0, 0, 45, 0]s
Bottom skin sandwich
Aramid, Foam 15mm
[0, 0, 45, 0, Foam, 0, 45, 0, 0]
Bottom skin doubler
Alu. 1mm, Aramid
[Alu, 0, 0, 45, 0, 0, 45, 0, 0]
Bulkhead stable C-shape
Carbon
[0, 0, 45, 0]s
Bulkhead lower monolithic
Carbon
[0, 0, 45, 0] (Symmetric?)
Bulkhead sandwich
Carbon, Hon. 10mm
[0, 0, 45, 0, Hon., 0, 45, 0, 0]
Bulkhead upper monolithic
Carbon
[0, 0, 45, 0]s
Keel beam monolithic
Carbon
[0, 0, 45, 0, 0, 45, 0, 0, 0, 45, 0, 0]
Keel beam sandwich
Carbon, Hon. 10mm
[0, 0, 45, 0, 0, 45, 0, 0, Hon., 0, 45, 0, 0]
Keel beam
Carbon
[0, 0, 45, 0, 0, 45, 0, 0]s
Keel beam lower solid
Carbon, Alu 1.6 mm
Alu, [0, 0, 45, 0, 0, 45, 0, 0]s
Ribs monolithic
Carbon
[0, 0, 45, 0]s
Floor monolithic
Carbon
[0, 0, 45, 0]s
Floor sandwich
Carbon, Hon. 25 mm
[0, 0, 45, 0, Hon., 0, 45, 0, 0]s
Crush cone upper part
Alu 6 mm
-
Crush cone lower part
Carbon (C),
[C0, C45, A45, C0, C0, A45, C45,
Aramid (A)
C0]
Hinge
Alu 1.6 mm
-
Fitting
Alu 25 mm
-
upper monolithic
3
