ISSN Volume 1 Issue 4 May 2012 FEA Information Engineering Journal

Transcription

1 ISSN Volume 1 Issue 4 May 2012 FEA Information Engineering Journal Honeywell engine Aerospace Journal

2 FEA Information Engineering Journal Aim and Scope FEA Information Engineering Journal (FEAIEJ ) is a monthly published online journal to cover the latest Finite Element Analysis Technologies. The journal aims to cover previous noteworthy published papers and original papers. All published papers are peer reviewed in the respective FEA engineering fields. Consideration is given to all aspects of technically excellent written information without limitation on length. All submissions must follow guidelines for publishing a paper, or periodical. If a paper has been previously published, FEAIEJ requires written permission to reprint, with the proper acknowledgement give to the publisher of the published work. Reproduction in whole, or part, without the express written permissio of FEA Information Engineering Journal, or the owner of of the copyright work, is strictly prohibited. FEAIJ welcomes unsolicited topics, ideas, and articles. Monthly publication is limited to no more then five papers, either reprint, or original. Papers will be archived on For information on publishing a paper original or reprint contact editor@feaiej.com Subject line: Journal Publication Cover: Honeywell engine LS-DYNA Implemented Multi-Layer Fabric Material Model Development for Engine Fragment Mitigation 2 Fea Information Engineering Journal May 2012

3 FEA Information Engineering Journal TABLE OF CONTENTS Volume 1, Issue No. 4 May 2012 Reprint of aerospace papers from the 11th International LS-DYNA Users Conference Modeling Bird Impact on a Rotating Fan: The Influence of Bird Parameters M. Selezneva1, P. Stone2, T. Moffat2, K. Behdinan1, C. Poon1 1Ryerson University, Department of Aerospace Engineering, Toronto, Canada 2Pratt and Whitney Canada, Compressor Structures Department, Mississauga, Canada Investigation of *MAT_58 for Modeling Braided Composites Brina J. Blinzler, University of Akron, Akron Ohio Robert K. Goldberg. NASA Glenn Research Center, Cleveland Ohio Wieslaw K. Binienda. University of Akron, Akron Ohio Comparison of FEM and SPH for Modeling a Crushable Foam Aircraft Arrestor Bed Matthew Barsotti, M.S., Protection Engineering Consultants, LLC LS-DYNA Implemented Multi-Layer Fabric Material Model Development for Engine Fragment Mitigation S. D. Rajan, B. Mobasher and A. Vaidya Civil, Environmental & Sustainable Engineering Program Arizona State University All contents are copyright to the publishing company, author or respective company. All rights reserved. 3 Fea Information Engineering Journal May 2012

4 11 th International LS-DYNA Users Conference Aerospace (1) Modeling Bird Impact on a Rotating Fan: The Influence of Bird Parameters M. Selezneva 1, P. Stone 2, T. Moffat 2, K. Behdinan 1, C. Poon 1 1 Ryerson University, Department of Aerospace Engineering, Toronto, Canada 2 Pratt and Whitney Canada, Compressor Structures Department, Mississauga, Canada Abstract The ability to withstand bird impact is one of the major requirements of the modern aircraft jet engine. In fact, rigorous certification procedures are put in place to assess the engine s ability to sustain severe impact loads developed during bird impact. Full scale bird tests are expensive and time consuming, and call for the use of accurate numerical approximations during the design stages of engine development. The main difficulties encountered in achieving accurate finite element (FE) analysis are related to modeling of the bird which undergoes severe deformations, and modeling of the contact between the bird (soft) and blade (stiff) materials. Thus far Smooth Particle Hydrodynamics (SPH) modeling in LS-DYNA, which is a meshless method, had shown potential in adequately modeling the bird and the bird-blade interactions. Recent publications also show the ability of SPH based models to capture impact strains and forces seen by the rotating fan blades [1, 2]. The current study further investigates the interaction of the SPH bird with the FE blades, and the ability of the model to capture realistic blade deformation. The main emphasis is placed on the effect of the bird related parameters on the damage sustained by the blades. 1 Introduction As airplanes share the sky with birds, they are vulnerable to bird strikes, which could result in serious structural damage and performance loss. An engine is not exempted from such collisions, and has to comply with strict airworthiness standards which are put in place to ensure its safe operation after a bird strike. In fact, before an engine can be certified for service, it has to pass full scale bird ingestion tests, which are expensive and time consuming to perform. To maximize the probability of passing the test, finite element (FE) computer simulations of the impact event are performed during the design process. 1.1 Theory When it comes to modeling a bird strike, FE representation of the blades is rather straightforward since their mechanical properties and geometries are known. On the contrary, properties related to the bird are complex and largely unknown, and thus far, have been the subject of numerous research efforts [5-9]. Some of the earlier experimental work on quantifying bird properties was done by Wilbeck [3]. He concluded that during soft body impact, the yield stress of the projectile is quickly surpassed due to rapid deceleration [3]. Hence, elastic properties are insignificant, and the bird can be treated as a hydrodynamic body which essentially acts like water during impact. Hydrodynamic pressure-volume relation can be defined by an equation of state (EOS) in the form of a third degree polynomial, refer to Equation P = C0 + C1μ + C2μ + C3μ μ = ρ 1 ρ 0 [1] 1-37

5 Aerospace (1) 11 th International LS-DYNA Users Conference In Equation 1 µ is the relative density. For a material such as water which exhibits the linear Hugoniot relation between shock velocity and particle velocity, the EOS can be expressed in terms of the following coefficients [4]: 1-38 C C C = 0 C = ρ c = (2k 1) C = ( k 1)(3k 1) C Where, C o is the initial equilibrium pressure and is considered to be negligible, ρ 0 is the initial density, c o is the speed of sound in the material and k is the experimental constant derived by Wilbeck. Based on experimental results, Wilbeck had proposed to use an EOS corresponding to that of water with 10% porosity (air) [3]. Additional studies were performed to investigate the effect of the EOS on shock pressure, steady-state pressure and radial pressure distribution [5-7]. In fact, A. Nizampatnam [5] showed that 30-40% porosity provides better results. Overall, an EOS of the bird is an approximation of its actual properties and serves as a calibration parameter in the model [4]. Given the large shock pressures developed during impact and the significant mismatch between the mechanical properties of the blades and the bird, it is common place to model the bird as a homogeneous body with simplified shape and properties. Previous publications compared the influence of the bird aspect ratios and basic geometries including cylindrical, spherical, ellipsoidal and cylindrical with two hemispherical ends on the resultant impact pressure profile [5-8]. Overall, the most frequently adopted and recommended shapes are a cylinder with two hemispherical ends [3, 5-8] or an ellipsoid [1, 8, 10] with an aspect ratio of 2 [4-8, 12]. Some effort has been placed in creating more detailed models of the bird, which better mimic its actual shape (head, neck, and torso), density distribution and mechanical properties (i.e. softer lighter lungs vs. denser stiffer bones) [5, 9]. These models have the potential of improving accuracy of the simulation, but they significantly complicate the problem by introducing new parameters. Hence, for this study it was decided to refrain from the use of such models and represent the bird by a hemispherical ended cylinder. 1.2 Motivation and Scope Numerous papers have been found that dealt with modeling of bird impact on flat plates, stationary engine blades, wing leading edges and windshields. In addition, different methods have been applied for bird modeling including Lagrangian, arbitrary Lagrangian-Eulerian and smooth particle hydrodynamics (SPH). The SPH method offers an advantage over other methods, as it is a mesh-less technique that has the potential to properly capture the physics involved in the ingestion of the bird by an engine. However, a limited number of papers have been found that dealt with bird strike analysis of rotating engine fan blades, with even fewer studies employing SPH to model the bird [1, 2, 10]. The main focus of this study was to implement the SPH method for modeling a bird impact on a rotating fan, and to investigate the influence of the bird parameters on the damage sustained by the blades. A comparison was made between the severity of the impact damage and the deformed shape of the blades with respect to different aspect ratios and EOSs of the bird. Also, a sensitivity study was performed regarding the number of SPH particles used. 1 1 [2]

6 11 th International LS-DYNA Users Conference Aerospace (1) 2 Description of the model The computer model was setup to mimic the test conditions of the recent engine bird strike test. This engine has an intermediate size fan and was impacted by a 0.7 kg [1.5 lb] bird. During this test, the blades were rotating at 10,000 rpm, the bird speed was measured to be about 75 m/s [3 in/ms] and the impact occurred at approximately 70% of the blade span. The damage sustained by the blades was qualitatively assessed in terms of the shape of the deformed blades and the severity of the overall damage of the fan. Results of these simulations were compared to the damage sustained by the blades during the actual bird strike test. 2.1 The Fan The fan model was simplified to include only the blades to avoid the complexities associated with detailed modeling of blade-to-hub root attachments. As a result, all boundary conditions and constraints were imposed at the root nodes. To reduce the model size and the computational time, the number of blades included in the model was reduced to 12. This quantity was more than sufficient to fully ingest the bird. The properties of the blades were defined by a comprehensive Johnson-Cook material model which incorporates strain rate sensitivity and temperature effect. Previous studies have shown that Johnson-Cook models are appropriate for capturing blade deformation and failure under conditions prevalent during a bird strike on an engine [11]. The blades were modeled by a fully integrated shell element (ELFORM 16), and in total were made up of 55,000 nodes and 18,000 shell elements. The impact model also took into account the stresses associated with rotation of the blades, and included post-impact damping to minimize blade oscillations. This model was created and imported into LS-DYNA via an in-house software. 2.2 The Bird The bird geometry (cylinder with hemispherical ends) was generated directly in LS-DYNA Prepost 2.2, by creating the spherical and cylindrical shapes, and merging the overlapping SPH nodes. In this study aspect ratios (AR) of 1.5 and 2 were considered, see Figure 1. The number of particles used was varied from 10,000 to 110,000 to assess the sensitivity of the model. The bird density was set to 950 kg/m 3 [0.034 lb/in 3 ], a value which corresponds to the density of gelatin and is within the range of commonly used densities for birds ( kg/m 3 ) [7, 8, 12]. Material properties of the bird were defined as elastic-plastic-hydrodynamic. In the elastic region, the shear modulus and yield stress were set to 2.0 GPa [0.29 Msi] and 0.02 MPa [2.9 psi], respectively. These values were effectively used in previous studies [12]. Overall, these parameters are not expected to have a significant influence on the stresses developed during impact, as the elastic region is quickly exceeded. The hydrodynamic regime was defined by an equation of state corresponding to water with 0%, 10% and 15% porosity; respective coefficients are summarized in Table 1. The coefficients for 0% porosity were calculated based on the Eq. 2 with k = 2 and c o =1480 m/s [12]. Coefficients for 10% porosity are based on the pressuredensity relationship derived by Wilbeck [3]. In the case of 15% porosity, coefficients were chosen to slightly offset the curve to the right, hence making the bird more compressible (compliant), see Figure 2. This approximation was acceptable for the current study, since the 1-39

7 Aerospace (1) 11 th International LS-DYNA Users Conference actual coefficients are hard to determine and the EOS can be treated as a calibration parameter to adjust the model [4]. Figure 1, Dimensions and positioning of a bird with an aspect ratio of a) 1.5 and b) 2 Table 1, Equation of state coefficients used in the model to represent water with 0%, 10% and 15% porosity Coefficients 0% porosity [MPa/ Ksi] 10% porosity [MPa/ Ksi] 15% porosity [MPa/ Ksi] C / / / 1 C / / / -200 C / / / 4500 Figure 2, Pressure-density relationships as per EOS coefficients given in Table

8 11 th International LS-DYNA Users Conference Aerospace (1) 2.3 Contact An automatic-nodes-to-surface contact was defined between the blades (master) and the bird (slave). This contact type checked for penetration of the master segment by the slave nodes, which was in fact a desired feature due to the nature of the problem at hand. The viscous damping coefficient (VDC) was set to 40% to eliminate any instability due to the difference in the mechanical properties between the two impacted materials which can develop in SPH based models [13]. 3 Discussion of Results Numerous simulations were run with birds having different EOS, AR, number of particles and locations (with respect to the blade) to achieve a better statistical representation of the observed trends. An example of the bird-blade interaction at different time steps is included in the Appendix. The initial step of this study was aimed at assessing the sensitivity of the model to the number of SPH particles used to represent the bird. The particle count was varied from 10,000 to 110,000. Overall, it was found that the minimum number of particles required to achieve smooth blade deformation was about 36, Effect of the Equation of State Equations of state corresponding to the different amounts of porosity were compared in terms of the resultant shapes of the deformed blades and the overall damage to the fan. Implementation of EOS corresponding to 0% porosity [from this point on referred to as EOS 0] led to visibly more damage to the blades than the use of EOS corresponding to 10% or 15% porosity [EOS 10 and EOS 15]. These results were anticipated since EOS 0 represents a stiffer bird which would in turn cause more damage than the softer more porous bird of the same mass. In fact, previous studies have shown that birds modeled by EOS 0 generated a higher impact pressure on the target structure than those modeled by EOS of porous water [6, 7]. Figure 4, Shape of a) an un-deformed blade and of deformed blades obtained with b) EOS 0 and c) EOS 10 Moreover, interesting observations were made regarding the post-impact blade shapes attained by using different EOS. Overall, the use of EOS 0 resulted in well pronounced cupping (Figure 4b) that could be seen in 4-6 blades. On the contrary, implementation of EOS 10 or 15 led to only 1 or 2 blades being substantially damaged. In addition, these blades showed more global deformation (Figure 4c) instead of the localized cupping as in the case with EOS 0. These 1-41

9 Aerospace (1) 11 th International LS-DYNA Users Conference differences are further illustrated by Figure 5, which shows blade deformation in terms of leading edge deflection from the original shape for EOS 0 (5a) and EOS 10 (5b). Figure 5, Blade deformation plots for a bird with a) EOS 0 and b) EOS 10 [Values are relatively scaled] These characteristic differences between the deformed blade shapes can probably be linked to the radial pressure distribution created during impact by a cylindrical projectile. It was shown by R. Jain et al [6] that the contact pressure is the maximum at the center of the projectile and drops quickly towards its sides. Figure 6 shows that pressure at the center is significantly higher for a projectile with no porosity versus that with 10% or 15% porosity. In fact, the cupped shape of a deformed blade resembles the bird shape (hemispherical cylinder) used in the current study. L.-M. L. Castelleti et al [10] also emphasized the influence of the diameter and internal density variations of the projectile on the slicing effect of a rotating blade. Even though these parameters are initially the same for all test cases corresponding to the same AR, they change during impact, and these changes are in part governed by the EOS, which defines the pressure-volume response of a soft projectile. Hence, it can be anticipated that the bird-blade interactions and the resultant pressure distribution profiles are more complex during impact with a rotating structure than during a straight head-on collision. Thus, bird porosity has an intriguing effect on deformation of rotating blades Figure 6, Radial pressure distribution generated during impact of a soft cylindrical projectile [6].

10 11 th International LS-DYNA Users Conference Aerospace (1) 3.2 Effect of the Aspect Ratio The effect of the bird geometry on the deformed blade shape was investigated by considering birds of different aspect ratios, 1.5 vs. 2 [referred to as AR 1.5 and AR 2]. As it was anticipated, more blades are damaged when a bird is modelled by AR 2 (Figure 7a), simply due to the fact that it is longer. Additionally, the shape of the deformed blades was also strongly influenced by the bird AR. Application of a smaller diameter bird, AR 2, led to cupping of all damaged blades (Figure 7a). On the contrary, application of a wider AR 1.5 bird resulted in severe global deformation of 1 or 2 blades, which then shielded the following blades from the bird (Figure 7b). These results are in line with the conclusions drawn regarding the use of different EOS, and reemphasize the influence of the bird diameter and internal pressure or density distribution on the damage sustained by the fan blades during a bird strike. Overall, fan damage predicted by simulations involving AR 1.5 bird matched well with the available test data. Thus far, modeling a bird as an SPH cylinder with hemispherical ends and an aspect ratio of 1.5 shows potential to adequately capture the impact dynamics involved in the problem; however, additional work is necessary to confirm these results. Figure 7, Blade deformation plots for a bird with a) AR 2 and b) AR 1.5 [Values are relatively scaled] 4 Conclusions LS-DYNA was used to simulate a bird strike on an engine and to investigate the effect of bird related parameters on the damage sustained by fan blades. Through numerous simulations it was found that the geometry of the bird and its hydrodynamic properties incorporated into the model strongly influence the bird-blade interaction during the impact, due to the coupled effect of impact and slicing. Overall, blade deformations attained while using an AR 1.5 bird in combination with EOS 10 agreed well with the results of the previously conducted bird strike tests. The present study has further shown the potential of the SPH based impact models to capture damage sustained by the fan blades during a bird strike. Future work will encompass application of the SPH method to bird strike analysis on other Pratt and Whitney engines. 1-43

11 Aerospace (1) 11 th International LS-DYNA Users Conference Acknowledgements The authors would like to thank C. Wojtyczka, C. Mason, D. Chawla, M. Nasr, T. Rose, A. Khorshid, F. Abrari and K. Newell, who are all employees of Pratt and Whitney Canada (P&WC), for their help with creating the models, interpreting the results and understanding the physics of the bird strike event. Additional gratitude is extended to Dean Carpenter, a manager at P&WC, and the Ryerson Institute for Aerospace Design and Innovation (RIADI) for organizing this collaborative project between Ryerson University and P&WC. References [1] Shmotin, Y. N., Chupin, P. V., Gabov, & et al. Bird strike analysis of aircraft engine fan. Proceedings of the 7 th European LS-DYNA Users Conference. [2] Ryabov, A. A., Romanov, V. I. & Kukanov, S. S. Fan blade bird strike analysis using Lagrangian, SPH and ALE approaches. Proceedings of the 6 th European LS-DYNA Users Conference. [3] Wilbeck, J. S. Impact Behavior of Low Strength Projectiles. University of Dayton Research Institute for the Air Force Flight Dynamics Laboratory, Wright-Patterson Air Force Base, OH. Technical Report AFML-TR (1978). [4] Johnson, A. F., & Holzapfel, Numerical prediction of damage in composite structures from soft body impacts. Journal of Material Science 41 (2006): [5] Nizampatnam, L. S. Models and Methods for Bird Strike Load Predictions. Wichita State University, PhD thesis (2007). [6] Jain, R. & Shivayogi, Effect of bird materials and projectile shape on temporal pressure. Proceedings of Altair CAE User s Conference (2006). [7] Airoldi, A. & Cacchione, B. Modelling of impact forces and pressures in Lagrangian bird strike analyses. International Journal of Impact Engineering 32 (2006): [8] Meguid, S. A, Mao, R. H. & Ng, T. Y. FE analysis of geometry effects of an artificial bird striking an aeroengine fan blade. International Journal of Impact Engineering 35 (2008): [9] McCallum, S. C. & Constantinou. The influence of bird-shape in bird-strike analysis. Proceedings of the 5 th European LS-DYNA Users Conference. [10] Castelletti, L.-M. L. & Anghileri, M. Bird strike: the influence of the bird modeling on the slicing forces. 31st European Rotorcraft Forum ( 2005): [11] Lesuer, D. R. Experimental investigation of material models for Ti-6Al-4V titanium and 2024-T3 aluminum. Report No. DOT/FAA/AR-00/25 prepared for U.S. Department of Transportation Federal Aviation Administration (2000). [12] Lavoie, M.-A., Gakwaya, A.& Ensan, M. N. Application of the SPH Method for Simulation of Aerospace Structures under Impact Loading. Proceedings of the 10 th International LS-DYNA Users Conference. [13] Anghileri, M., Castelletti, L.-M. L. & Tirelli, M. Fluid-structure interaction of water filled tanks during the impact with the ground. International Journal of Impact Engineering 31 (2005):

12 11 th International LS-DYNA Users Conference Aerospace (1) Appendix Blade Deformation Un-damaged State Damaged State Time 0 ms Time 0.4 ms Time 0.6 ms Time 0.8 ms 1-45

13 Aerospace (1) 11 th International LS-DYNA Users Conference Time 1.2 ms Time 1.4 ms Time 1.8 ms Final deformed shape (damped out) 1-46

14 11 th International LS-DYNA Users Conference Aerospace (1) Investigation of *MAT_58 for Modeling Braided Composites Brina J. Blinzler University of Akron, Akron Ohio Robert K. Goldberg NASA Glenn Research Center, Cleveland Ohio Wieslaw K. Binienda University of Akron, Akron Ohio Abstract An in-depth analysis is needed to simulate the impact behavior of triaxially braided composite materials. Before an impact simulation can be generated, all material input parameters must be found. The objective of this work is to use static tests conducted on axial and transverse coupons to determine these input parameters. In particular, analysis methods that capture the architecturally dependent damage observed in these tests in a computationally efficient manner are required. A macromechanical shell element based model for braided composites has been developed, in which the braid architecture is approximated as a series of four parallel laminated composites with varying fiber orientations. The composite damage model *MAT_58, available within LS- DYNA, is used in this investigation. Careful investigation of the model s global response, and local stress and strain distribution within each element of the composite unit cell are examined parametrically using various input strength parameters. From these studies, relatively small changes in the input parameters have been found to have a significant effect on the overall response, sometimes in non-intuitive ways. Thru this investigation the predictive capability of the developed braid model will be improved and a greater understanding of the functionality of the MAT_58 material model will be obtained. Introduction Textile polymer matrix composite materials are being investigated for use in aerospace applications as a replacement for metals or traditional laminated composites. The goal for this effort is to develop a method to capture the unique failure mechanisms in laminated textile composites. The primary focus for this effort is triaxially braided composites. One application for this type of material is as a jet engine fan blade containment system. In order to create an optimum engine case design, the failure, damage, and deformation needs to be simulated with the use of commercial explicit finite element codes. A design tool was required to capture the structural effect of the braid and damage along fiber bundles while modeling the entire engine case. To balance these needs, a macro scale finite element simulation was developed using the advanced continuum damage mechanics material model *Mat_58 (*Mat_Laminated_ Composite_Fabric) to account for unique structural effects [Ref. 1]. For these aerospace applications the model needed to accurately simulate the textile composite under both static loading and impact situations. This effort looked at a triaxially braided composite with a [0 /+60 /-60 ] layup. Taking efficiency into account, the material was modeled as a membrane and the structure was made up of traditional four noded shell elements. The unique way the fiber architecture was incorporated into the shell elements will be discussed later. There has been a significant amount of research conducted in textile composite modeling and analysis. In most of the previous research homogenized material properties were used. For example Tanov 1-1

15 Aerospace (1) 11 th International LS-DYNA Users Conference and Tabiei used a representative volume cell approach which assigned homogenized material properties to the model elements [Ref. 2]. These types of approaches do not directly account for the textile architecture in the finite element model and work well for small yarn sizes but lack the ability to capture damage in a composite with larger yarn sizes. It has been noted in experimental impact testing, failure in some textile composites propagates in the fiber directions [Ref. 3]. In order to simulate this unique failure propagation, the textile architecture should be directly simulated in the finite element model. This paper will discuss a method developed to capture this unique textile failure. Background Matzenmiller developed a constitutive model for anisotropic damage of fibrous composite materials with non-ductile matrices [Ref. 4]. The method used continuum damage mechanics theory in the material axis system to approximate damage initiation and ultimate material failure. Each lamina was assumed to be a unidirectional composite and any non linearity was assumed to be due to damage mechanisms. The development of damage was completely dependent on the stress and strain states of the individual unidirectional lamina. Matzenmiller then used the Hashin failure criteria which determined a failure envelope based on the five strength properties of the unidirectional lamina: longitudinal tension, longitudinal compression, transverse tension, transverse compression, and shear strengths [Ref. 5]. The equations used in *MAT_58 reflect the Matzenmiller method and assumptions [Ref. 1]. Material T700 PR520 T Material Parameter Name (LS-DYNA name) Value (unit) Value (unit) Axial Modulus (EA) (GPa) (GPa) Transverse Modulus (EB) (GPa) (GPa) In Plane Shear Modulus (GAB) (GPa) (GPa) In Plane Poisson Ratio (PRBA) Axial Tensile Failure Strain (E11T) Axial Compressive Failure Strain (E11C) Transverse Tensile Failure Strain (E22T) Transverse Compressive Failure Strain (E22C) In Plane Shear Failure Strain (GMS) Axial Tensile Stress at Failure (XT) (MPa) (MPa) Axial Compressive Stress at Failure(XC) (MPa) (MPa) Transverse Tensile Stress at Failure (YT) (MPa) (MPa) Transverse Compressive Stress at Failure (YC) (MPa) (MPa) In Plane Shear Stress at Failure (SC) (MPa) (MPa) Stress Limiting Parameter for Axial 0 0 Tension (SLIMT1) Stress Limiting Parameter for Transverse 1 1 Tension (SLIMT2) Stress Limiting Parameter for Axial 0 0 Compression (SLIMC1) Stress Limiting Parameter for Transverse 0 0 Compression (SLIMC2) Stress Limiting Parameter for Shear (SLIMS) 0 0 Table 1: Input Parameters 1-2

16 11 th International LS-DYNA Users Conference Aerospace (1) The inputs for the material model are listed in Table 1. The material inputs required by this model are unidirectional strength and stiffness properties. There are five exceptions. The SLIM inputs are not related to mechanical properties. The SLIM inputs are known as stress limiting factors. These stress limiting factors define the amount of additional stress an integration layer can take after the ultimate strength has been reached. A SLIM of one would allow no further stress in the defined direction after reaching ultimate strength and cause the material to act like a perfectly plastic material. SLIM values less than one simulate the material carrying a percentage of stress after hitting ultimate strength. In the model used in this paper a SLIMT2 of one is used. This effectively simulates a perfectly plastic situation when a fiber bundle in the composite reaches ultimate tensile strength in the transverse direction. Approach Previous research on this topic was conducted by Cheng and Littell [Ref. 6, 7]. Their analytical model discretized the braided composite into a series of parallel shell elements. Each element in this series was modeled as a laminated composite. This allowed for architecturally dependent damage to be modeled while maintaining a large unit cell for efficiency. This model was based on the identification of the repeating unit cell within the triaxial braid architecture seen in Figure 1 (a). The unit cell was further divided into four subcells: A, B, C, and D noted in Figure 1 (b). These four elements were the building blocks of the model and were repeated in both in-plane directions until the desired size was created. The subcells divided the braid architecture into four areas that individually were approximated as uniaxial laminated composites. This can be seen in Figure 1 (c). The braided composite is composed of six layers which can be seen in Figure 2. In this figure the subcell shifting through the thickness of the unit cell was done to account for the nesting effect noted in experimental samples [Ref. 3]. The braid architecture was incorporated in this model by using equivalent unidirectional composite properties found as a result of laboratory experiments. The unidirectional lamina properties are not known for a braided composite and cannot be directly measured. The equivalent unidirectional properties seen in Table 1 were back calculated from the experimental results using micromechanics equations and classical lamination theory. Further explanation of the equivalent unidirectional properties formulation can be found in Ref. 5. There are several advantages for this analytical model. One advantage is that the constitutive model being used is a continuum damage mechanics model. This quality is important for impact analysis. Another advantage is that the experimental data required for the model comes only from the triaxially braided composite samples; no additional inputs are required. In addition, the model is computationally efficient, and it can be used to model large components. 1-3

17 Aerospace (1) 11 th International LS-DYNA Users Conference Fig. 1: Identification of the unitcell Fig. 2: Through thickness view of shell a)specimen photograph, b)four shell elements layers element braided composite unit cell (A,B,C,D), c)through thickness integration The shell element formulation allows each integration layer to have a weight factor and thickness. The braided material consists of [0 /+60 /-60 ] degree fibers. The zero degree fiber bundles are referred to as axial fiber bundles and the plus and minus sixty degree fiber bundles are referred to as bias fiber bundles. In this case all layers were assigned the same thickness but the zero degree fibers were assigned twice the weight factor of the bias fibers because the zero degree fiber bundles contain two times the amount of carbon fibers as the bias bundles. After analyzing the effects of these inputs, it was determined that changing the thickness of the layer is negligible for this case. The weight factor of the layer contributes only slightly more than the thickness. Static simulations were conducted to accurately characterize the material and structure. The axial tension and transverse tension simulations seen in Figure 3 were developed to mimic experimental coupon tests. For these static simulations, the nodes at the very top were fixed. This is noted with black crosses in the figure. Displacement in the static simulations was applied to the nodes at the bottom in the negative Y direction while motion for these nodes was constrained in X and Z. The colorful arrows in Figure 3 are showing the amount of displacement near the beginning of the simulation. The stress-strain curves for these simulations were defined by averaging the elemental stresses and strains for the bottom six rows of elements in each model. This is similar to the previous methods used to create stress-strain curves. 1-4

18 11 th International LS-DYNA Users Conference Aerospace (1) Axial Tension Simulation Transverse Tension Simulation Fig. 3: Simulation Schematics Parametric studies were conducted to aid in modifying previous assumptions and developing a method of modeling based on experimental data that will capture the differences seen in two triaxially braided composites tested. The two composites that were studied were T700/PR520 and T700/3502, wheret700 refers to Toray s TORAYCA T700s carbon fiber, PR520 refers to Cytec s CYCOM PR 520 resin, and 3502 refers to Hexcel s 3502 resin. The interesting thing was that for T700/PR520 while elastic stiffness properties were the same the nominal strains were different. In order to completely understand the model and to accurately predict failure damage patterns and velocity a complete understanding of how the material inputs affect the simulation results had to be achieved. 1-5

19 Aerospace (1) 11 th International LS-DYNA Users Conference In order to examine how each of the strength properties (XT, E11T, XC, E11C, YT, E22T, YC, E22C, SC, and GMS from Table 1) affected the failure of the braid model, a full diagnostic was conducted. Axial and transverse tension simulations from Figure 3 were used in this parametric study. The five strengths mentioned above were varied along with their corresponding failure strains. For example, when shear strength was increased 25 percent, shear failure strain was also increased 25 percent to keep the elastic modulus constant. Both the original six layer and a new single layer model were examined with strength values varied up and down at increments of 25 percent. The strengths and failure strains were increased 25 and 50 percent, and decreased 25 and 50 percent for each variation. From this diagnostic, the primary and limiting parameters were identified. The parametric study was first conducted for the baseline simulation, which was the full six layer nested model. A single layer simulation (Figure 4) was developed to help verify the results and compare with the experimental single layer test. Following this, a parametric study was conducted with both the single layer model and a six layer non-nested model (Figure 5). The six layer non-nested model was used to verify the single layer results and compare with the previous study. Fig. 4: Single Layer Through Thickness Fig. 5: Six Layer Non-nested Through Thickness Results In order to capture the unique failure mechanisms of the triaxially braided composites some of the model assumptions may need to be modified. The model sensitivity must be fully understood to scientifically modify these assumptions. A parametric study was conducted to describe the model sensitivity in detail. There were four sets of simulations run during the course of the parametric study: the baseline parametric study, the single layer verses baseline comparison, the single layer parametric study, and the non-nested comparison. The baseline parametric study was conducted first. Below are the stress-strain graphs which show the effects of the changes to the input parameters in the baseline model. During each of these studies, primary failure drivers were identified for the different inputs for the composite materials. The primary failure driver for these studies was defined as the uniaxial input strength which created the largest change in global output strength and stiffness. Uniaxial shear strength was identified as the primary driver for both axial tension specimen failure and transverse tension specimen failure for the T700/PR520 composite simulation (Figures 7 and 8). 1-6

20 11 th International LS-DYNA Users Conference Aerospace (1) Test data noted in Figures 7-18 is from experimental composite coupon tests [Ref. 3]. The accuracy of the test data for the transverse tension tests for both composites is in question. It has been proposed that there is a significant amount of artificial nonlinearity resulting from ungripped bias fibers [Ref. 3]. Because these composites are quasi-isotropic the experimental transverse tension strength and stiffness should be similar to the strength and stiffness of the axial tension test. Fig. 7: Baseline Parametric Study T700/PR520 with Shear Strengths Varied for the Axial Tension Simulation Fig. 8: Baseline Parametric Study T700/PR520 with Shear Strengths Varied for the Transverse Tension Simulation Uniaxial longitudinal tension strength was identified as the primary failure driver for the axial tension specimen failure for the T700/3502 composite simulation (Fig. 9). Uniaxial shear strength was identified as the primary driver for transverse tension specimen failure for the 1-7

21 Aerospace (1) 11 th International LS-DYNA Users Conference T700/3502 composite simulation (Fig. 10). This was different from the T700/PR520 composite and was due to the difference in the ratio of longitudinal strength to other strengths. Fig. 9: Baseline Parametric Study T700/3502 with Longitudinal Strengths Varied for the Axial Tension Simulation 1-8 Fig. 10: Baseline Parametric Study T700/3502 with Shear Strengths Varied for the Transverse Tension Simulation After the baseline parametric study was completed the single layer verses baseline comparison was conducted. This was originally done to validate the baseline parametric study, but ended up prompting further research when the results were seen to differ greatly. Overall the single layer axial tension simulation of T700/PR520 was less stiff and weaker than the six layer simulation (Figure11). Subcells A and C followed the six layer curves and subcells B and D were significantly weaker. The resulting unit cell average had a much lower stiffness and strength than the six ply simulations. The single layer transverse tension simulation of T700/ PR520 (Figure 12) was also less stiff than the six layer simulation. The curve of subcells A and

22 11 th International LS-DYNA Users Conference Aerospace (1) C were closer to the stiffness of the six layer simulation than the average and the curve of subcells B and D were far weaker. These differences in the single layer simulations were attributed to the behavior of the zero degree fibers. Because of the nested nature of the six layer model, all subcells contained the same amount of zero degree fibers. However, in the single layer simulations this was not the case. Subcells B and D contained no zero degree fibers in the single layer simulations. Due to the lack of strength from zero degree fiber layers, the single layer axial tension simulation had a decreased stiffness and strength and the single layer transverse tension simulation had a decreased strength. Fig. 11: Single Layer Comparison T700/PR520 for the Axial Tension Simulation Fig. 12: Single Layer Comparison T700/PR520 for the Transverse Tension Simulation 1-9

23 Aerospace (1) 11 th International LS-DYNA Users Conference The single layer axial tension simulation of T700/3502 (Figure 13) was also less stiff than the baseline simulation. Again, the curve for subcells A and C was in line with the six layer simulation but the curve for subcells B and D was much less stiff. The single layer transverse tension simulations of T700/3502 (Figure 14) had the same stiffness but were weaker than the six layer simulations. Fig. 13: Single Layer Comparison T700/3502 for the Axial Tension Simulation 1-10 Fig. 14: Single Layer Comparison T700/3502 for the Transverse Tension After the differences were noted in the single layer comparison, a single layer parametric study was conducted to characterize the effects of changing the strengths on subcells with and without zero degree fiber layers. In the single layer parametric study the T700/PR520 composite was analyzed first. For this analysis, the uniaxial longitudinal tension strength and failure strain were varied first. When the uniaxial longitudinal tension strength and failure strain (XT & E11T) were varied, the axial tension simulation was affected significantly while the transverse tension simulation was not. During the axial tension simulation, when the uniaxial longitudinal

24 11 th International LS-DYNA Users Conference Aerospace (1) tension strength and failure strain were increased, the global strength increased and the global strength decreased when they were decreased. However, during the transverse tension simulation, there was no significant change. There was only a small decrease in the global strength when the uniaxial longitudinal strength and failure strain were decreased by 50 percent. Next, the uniaxial transverse tension strength and failure strain were varied. When the uniaxial transverse tension strength and failure strain (YT & E22T) were varied, both the axial tension and the transverse tension simulations were affected. During the axial tension simulation, the curve followed a similar path to the baseline, but as the uniaxial transverse tension strength and failure strain decreased the global strength decreased and the stress at which the transition to nonlinearity occurs also decreased. During the transverse tension simulation, when the uniaxial transverse tension strength and failure strain increased the global strength and stiffness of the curve increased and when the uniaxial strength and failure strain decreased the global strength and stiffness decreased. Finally, the uniaxial shear strength and failure strain were varied. When the uniaxial shear strength and failure strain (SC & GMS) were decreased both the axial tension and transverse tension simulations were significantly affected. There was less change when the uniaxial shear strength and failure strain were increased. During the axial tension simulation, when the uniaxial shear strength and failure strain were decreased the global strength decreased and when the uniaxial strength and failure strain were increased the global strength increased. During the transverse tension simulation, when the uniaxial shear strength and failure strain decreased the global strength and stiffness decreased and when the uniaxial strength and failure strain increased the global strength and stiffness increased. The T700/3502 composite was analyzed second. For this analysis, the uniaxial longitudinal tension strength and failure strain were varied first. When the uniaxial longitudinal tension strength and failure strain (XT & E11T) were increased and decreased, both the axial tension and transverse tension simulations were affected. There was some change when the uniaxial longitudinal tension strength and failure strain were increased. During both simulations when the uniaxial strength and failure strain decreased, the global strength decreased significantly. Next, the uniaxial transverse tension strength and failure strain were varied. When the uniaxial transverse tension strength and failure strain (YT & E22T) were varied, both axial and transverse tension simulations were affected. During the axial tension simulation when the uniaxial transverse tension strength and failure strain increased, global stiffness increased, and when the uniaxial strength and failure strain decreased the global stiffness decreased. During the transverse tension simulation when the uniaxial transverse tension strength and failure strain increased, global strength and stiffness increased, and when the uniaxial strength and failure strain decreased the global strength and stiffness decreased. Finally, the uniaxial shear strength and failure strain were varied. When the uniaxial shear strength and failure strain (SC & GMS) were varied, both axial and transverse tension simulations were affected. During the axial tension simulation, when the uniaxial shear strength and failure strain increased the global strength increased and when the uniaxial strength and failure strain decreased the global strength decreased. During the transverse tension simulation, when the uniaxial shear strength and failure strain increased the global strength and stiffness increased significantly and when the uniaxial strength and failure strain decreased the global strength and stiffness decreased significantly. Comparing all these variations, primary failure drivers were found for the transverse tension and axial tension tests for both composites. From the single layer parametric study, primary failure drivers were identified. The stressstrain graphs displaying these primary failure drivers are seen in Figures Uniaxial shear 1-11

25 Aerospace (1) 11 th International LS-DYNA Users Conference strength was identified as the primary driver for both axial tension specimen failure and transverse tension specimen failure for the T700/PR520 composite (Figures 15 and 16). These results were similar to those noted in the parametric study involving the six ply laminate. Fig. 15: Single Layer Parametric Study T700/PR520 with Shear Strengths Varied for the Axial Tension Simulation Fig. 16: Single Layer Parametric Study T700/PR520 with Shear Strengths Varied for the Transverse Tension Simulation The uniaxial longitudinal strength was identified as the primary failure driver for the axial tension specimen failure for the T700/3502 composite simulation (Figure 17). The uniaxial shear strength was identified as the primary driver for transverse tension specimen failure for this composite (Figure 18). These results are also similar to those noted in the parametric study involving the six ply laminate. 1-12

26 11 th International LS-DYNA Users Conference Aerospace (1) Fig. 17: Single Layer Parametric Study T700/3502 with Longitudinal Strengths Varied for the Axial Tension Simulation Fig. 18: Single Layer Parametric Study T700/3502 with Shear Strengths Varied for the Transverse Tension Simulation After the single layer parametric study, six layer non-nested simulations were run to validate the data from the single layer study. The six layer non-nested model behaved very similar to the single layer model. For all four of the T700/PR520 and T700/3502 composite simulations the stress strain curves were nearly identical for the six layer non-nested and the single layer models. In order to identify why the different materials had different simulation responses and different input sensitivity, a number of strength ratios were calculated. In situ uniaxial strengths were compared in the form of tables of ratios (Tables 2 and 3). This showed that the in situ shear and transverse strengths of the T700/PR520 composite were similar while the axial strength was much larger (Table 2). This meant that the specimens could be near failure in either the shear or transverse directions and small changes in uniaxial strength could easily tip the scales. This also 1-13

27 Aerospace (1) 11 th International LS-DYNA Users Conference helped explain why shear strength and stiffness plays such a significant role in failure in both the axial and transverse tension simulations for the T700/PR520 composite material. This was not the case for the T700/3502 composite. The transverse strength is much lower and the shear strength is much higher in comparison. The uniaxial strengths for the two different composites were also compared by ratios (Table 3). This comparison makes clear the large relative difference in the uniaxial transverse tensile strengths and the small relative difference in the uniaxial shear strengths. This relative difference is important because uniaxial shear strength appears to play a large role in the failure of both composites. ratio (YT/XT) ratio (SC/XT) ratio (SC/YT) T700/PR520 T700/ Table 2: Composite Strength Ratios ratio(xt) T /T700-PR520 ratio (YT) T /T700-PR520 ratio (SC) T /T700-PR Table 3: Composite Strength Ratios Conclusion During this effort to capture the unique failure mechanisms of laminated textile composites, several steps were taken to ensure that the simulation output is a direct result of scientifically implementing experimental data. Through this effort a deeper understanding of the sensitivity of the macromechanical model has been obtained. The parametric studies and layer level integration point analysis are crucial in the definition of a quasi-empirical formula to capture material failure. This empirical formula s more accurate input parameters are being developed exclusively from experimental data. The formula is being implemented in a program that requires experimental data for input, and outputs a set of *Mat_58 material cards. These material cards can then be used in an LS-DYNA analysis. Through this effort the predictive capability of the developed braid model is being improved. This method will create a more accurate and easy to use modeling tool for textile composite materials. 1-14

28 11 th International LS-DYNA Users Conference Aerospace (1) References 1. Hallquist, J.O. et al, LS-DYNA Keyword User s Manual, Livermore Software Technology Corporation, Livermore, CA, May Tanov, R., Tabiei, A. Computationally Efficient Micromechanical models for Woven Fabric Composite Elastic Moduli. J. Appl. Mech Roberts, G. et al. Impact Testing and Analysis of Composites for Aircraft Engine Fan Cases. NASA TM Matzenmiller, A., Lubliner, J., Taylor, R.L. A constitutive model for anisotropic damage in fiber-composites, University of California at Berkeley. Berkeley, California Hashin, Z., Failure Criteria for Unidirectional Fiber Composites, J. Appl. Mech. 47, Cheng, J., Material Modeling of Strain Rate Dependent Polymer and 2D Triaxially Braided Composites, Ph.D. Dissertation. University of Akron. Akron, Ohio Littell, J., The Experimental and Analytical Characterization of the Micromechanical Response for Triaxial Braided Composite Materials, Ph.D. Dissertation. University of Akron. Akron, Ohio

29 Aerospace (1) 11 th International LS-DYNA Users Conference 1-16

30 11 th International LS-DYNA Users Conference Aerospace (2) Comparison of FEM and SPH for Modeling a Crushable Foam Aircraft Arrestor Bed Matthew Barsotti, M.S. Protection Engineering Consultants, LLC Abstract Passenger aircraft can overrun the available runway area during takeoff and landing, creating accidents involving aircraft damage and loss of life. Crushable foam arrestor bed systems are often placed at runway ends to mitigate such overruns. As the aircraft tires roll through the bed, the material compaction dissipates energy, bringing the aircraft to a controlled stop. A detailed two-year analysis was conducted for the TRB Airport Cooperative Research Program to develop improved arresting systems (Barsotti, et al., 2009). A major thrust of the effort was the development of validated numerical models for crushable arrestor bed materials and deformable aircraft tires. Finite element models for the crushable material manifested several problems due to the unusual mode of deformation experienced, which included significant element skewing, heavy compaction (~90%), and high hourglass energies (~19%). Many meshing and hourglass mitigation strategies were attempted, but they produced only marginal improvement. The Smoothed Particle Hydrodynamics (SPH) method was adopted as a replacement, and detailed performance comparisons of the FEM and SPH versions were made. Error convergence studies using mesh refinement were performed for 1-D, 2-D, and 3-D cases, culminating in the comparison of full tire & arrestor models for each formulation. Arrestor Background Overview of Problem The current arrestor technology for civil aircraft utilizes a large bed of crushable material placed at the end of a runway. This arrestor concept is designated by the Federal Aviation Administration (FAA) as an Engineered Material Arresting System (EMAS) (FAA, 2005). If an aircraft overrun occurs, its tires roll through the EMAS bed, compacting the material. The aircraft is slowed by the induced drag load, and the energy absorbed is proportional to the volume of material compacted (Figure 1) (Barsotti, 2008)

31 Aerospace (2) 11 th International LS-DYNA Users Conference Vertical Load Imparted Drag Load Imparted Direction of Travel Material Initial Height Material Compressed Height Pavement Height Energy Consumed Proportional to Volume of Material Crushed Figure 1. Arresting Performance of Crushable Materials Idealized Material Assumptions Only one variant of EMAS is current approved by the FAA, and it uses a cellular cement foam as the principal absorbent material (Barsotti, et al., 2009). However, other crushable foam materials are entirely viable. This research features a generalized foam material featuring the following assumptions: Crushable material with no elastic rebound Nominal compression strength of 50 psi Negligible Poisson s ratio Negligible rate effects Density roughly equivalent to current arrestor systems (18 25 pcf) Idealized step function profile for the compressive stress-strain curve High compressibility (85%) Negligible energy absorption in tension Figure 2 shows a uniaxial compression curve for the idealized material (Barsotti, et al., 2009)

32 11 th International LS-DYNA Users Conference Aerospace (2) Compression Stress (σ) Plateau Slope Energy Absorbed in Compression Compression Strain (ε) Figure 2. Stress-Strain Load Curve for Idealized Material Finite Element Modeling of Material Constitutive Model The arrestor material was modeled using *MAT_CRUSHABLE_FOAM, as shown below in units of lbf-in-sec (Table 1) (LSTC, 2007). The load curve in such cases was similar to Figure 2 with a strength of 50 psi and a bottoming strain of The tensile stress cutoff (TSC) varied depending upon the erosion criterion specified to ensure realistically low energy absorption in tension. Table 1. Parameters for *MAT_063 or *MAT_CRUSHABLE_FOAM Parameter Symbol Description Value Unit MID Material ID number RO ρ Density 3.75E-5 lbf-s 2 /in 4 E E Young s modulus 2.00E+3 psi PR ν Poisson s ratio 0.00 LCID Load curve ID for nominal stress versus strain TSC Tensile stress cutoff 1 to 50 psi DAMP Rate sensitivity via damping coefficient 1.00E-4 *MAT_ADD_EROSION was used in some versions of the model to allow element failure based upon principal or shear strain criteria, with variation of the strain values as described further below. Control and Stability Mesh tangling was problematic due to the highly compressible nature of the material, which routinely underwent 85 to 90% compaction. *CONTACT_INTERIOR was used with a default activation thickness factor F a = 0.10 to prevent mesh tangling in high compression areas. The interior contact carries a computational penalty, however

33 Aerospace (2) 11 th International LS-DYNA Users Conference Hourglass energies were problematic in all finite element versions of the models. As such, fully integrated solid elements were implemented (ELFORM = 2,3), but without success. Stability issues plagued versions using these formulations, which were highly prone to simulation crashes under high compaction. The default single-point solid formulation was used for the majority of cases (ELFORM = 1). Under maximum compression, the element characteristic length decreased by nearly an order of magnitude, causing a proportional decrease in the timestep and increase in overall run time. Mass scaling countermeasures were not considered viable; the tire overruns were to take place at high speed, and mass scaling would have added artificial inertial resistance. Tire and Arrestor Evaluation Figure 3 and Figure 4 illustrate the tire rolling through the arrestor and creating a rut of crushed material. The tire in this case represented a Goodyear H44.5x main gear tire for a Boeing (Goodyear, 2007). The arrestor bed depth was 20 inches, using 2-inch cubic finite elements. High Combined Shear and Tensile Strain at the Vertical Rut Wall Area of Very High Compression, Reduces Time Step: Elements with High Shear and Compressive Strain Figure 3. Overview of FEM Arrestor Bed with Tire Overrun (2-inch Elements) The elements along the vertical sides of the rut deformed substantially, as expected, in both shear and tension (Figure 4). Elements along the bottom of the run underwent high compression. Figure 5 shows a detail of the deformed elements in areas of high compression, where a flattened diamond shape results

34 11 th International LS-DYNA Users Conference Aerospace (2) High Combined Shear and Tensile Strain at the Vertical Rut Wall Area of Very High Compression, Reduces Time Step: Elements with High Shear and Compressive Strain Figure 4. Orthogonal Views of FEM Arrestor Bed with Tire Overrun (2-inch Elements) Initial Deformation Involves Pushing in Leading Corner of Element Final Element Shape is a Flat Diamond Figure 5. Details of Element Distortion in Combined FEM Arrestor/Tire Model Hourglass energy was relatively high. All applicable types of hourglass control were implemented in various strengths, but the overall hourglass energy proved irreducible beyond the level of about 14 to 19% of internal energy. The deformation sequence of the elements precipitated problems when attempting to implement element erosion. Principal strain and shear strain criteria were both used with mixed results. Problematically, the deformation sequence triggered erosion relatively early with either criterion, before the elements had undergone substantial compression or absorbed much energy. These issues were exacerbated by cases involving deep material (Figure 6). In actual overruns, the upper part of the material would break off and form furrows. Erosion criteria with higher 16-41

35 Aerospace (2) 11 th International LS-DYNA Users Conference strain limits, as required for the elements at the rut bottom, allowed the upper elements to overstretch and form tunnels. Lower strain limits created more realistic failure in the upper area, but caused premature erosion at the bottom of the rut and cascading material failure beneath the tire. Upper Layer of Deep Material Should Spall Upward, Forming Furrows Inadequate Blend of Erosion Criteria Prevents Furrowing Figure 6. Problematic Furrowing Loading Mode in Deep Material for FEM Arrestor/Tire Model Summary of FEM Model Findings Overall, the FEM model for the material had several shortcomings: The tire overrun produced a shearing distortion of the arrestor elements; Element erosion did not adequately resolve the distortion; Hourglass energy remained high even with best-case settings; The 85% compression of the material reduced the timestep by nearly an order of magnitude; and The FEM approach was not readily adaptable for modeling the plowing action of a tire in deep material. Smoothed Particle Hydrodynamics Modeling of Material The Smoothed Particle Hydrodynamics (SPH) method was applied to the arrestor model in lieu of finite elements. The meshless approach of SPH proved more robust for this high compaction and high dislocation application. The particles of SPH are inherently dissociative, which better matches the actual crushable foam material at a behavioral level. The constitutive model used essentially the same values as given in Table 1. Control and Stability The SPH formulation in LS-DYNA is controlled through three keywords (LSTC, 2007): 16-42

36 11 th International LS-DYNA Users Conference Aerospace (2) *CONTROL_SPH *SECTION_SPH *BOUNDARY_SPH_SYMMETRY_PLANE Default properties were used for most parameters, including the particle formulation (FORM=0). However, the number of cycles between bucket sorts (NCBS) was set to 10 to improve computational time efficiency by 20%. Tire and Arrestor Evaluation The SPH arrestor bed performed well and seemed suited to the modes of deformation experienced. The tire cut a clean rut through the material, leaving a crisp vertical rut wall, while compressing the bottom material. Since the particles could undergo dislocations and separations, erosion was not necessary (nor possible). This provided superior performance along areas of shear failure, such as the rut side-wall. The timestep remained constant throughout the simulation, which was an advantage not shared by the finite element versions of the model

37 Aerospace (2) 11 th International LS-DYNA Users Conference Small Pieces of Glass Foam Fragment Off of Bed Deformable Finite Element Aircraft Tire Model SPH Arrestor Bed Arrestor and Tire Model Uses Half- Symmetry Tire Penetrates Vertically to a Prescribed Depth Material Compressed by Tire Figure 7. Model of Combined Tire & Crushable Foam Arrestor System Summary of SPH Model Findings The SPH formulation proved itself to be a robust, durable representation of the crushable material, including: Natural dislocation and separation of the material without mass/volume losses due to erosion; Constant timestep; and Good shear failure performance at rut side walls

38 11 th International LS-DYNA Users Conference Aerospace (2) Error Convergence Comparison of Methods Qualitatively, the SPH method seemed to provide a superior fit for the problem at hand. A threestage error convergence study was undertaken to compare it side-by-side with the FEM version of the material, in order to determine if SPH would also provide accurate quantitative predictions. The convergence study was conducted in one-, two-, and three-dimensional forms. The FEM and SPH methods did not carry equivalent assumptions of convergence; it has been noted that SPH lacks a rigorous convergence and refinement theory (Li, et al., 2007). As such, newer FEM-specific error estimation methods have been neglected in favor of a simpler analysis of measured functionals (Babuska, et al., 2001). Various performance metrics (energy absorption rate, vertical load, and drag load) were measured at multiple mesh discretizations. Powerfunction convergence trends per Richardson s Extrapolation method were assumed a priori, and later confirmed to be uniformly applicable (eq 1) (Kardestuncer, 1987). Where: (1) Convergence for each case was analyzed using one of two methods: Grid Convergence Index (GCI) (Celik, Undated); this method worked well for three discretizations only and for cases where the scatter in the convergence trend was minimal

39 Aerospace (2) 11 th International LS-DYNA Users Conference Power-function regression fitting; this method worked better for cases with more data scatter and was required if more than three mesh sizes were to be analyzed. In the convergence study that follows, uniform mesh refinement is employed. The FEM approach could feasibly be improved using adaptive remeshing, which would improve the perelement Jacobian in areas of distortion. However, in LS-DYNA, adaptive remeshing for solids is only available for tetrahedrons using essentially incompressible materials. Hence, it is not applicable to this LS-DYNA modeling problem. 1-D Convergence Study The one-dimensional model simulated a platen compression test (zero Poisson ratio). The specimen had dimensions of 12 x12 x24, which was representative of a nominal 24-inch deep arrestor bed (Figure 8). Three mesh densities were used, with elements/particles sized at h = 4, 2, and 1 inch. The specimen was compressed uniaxially to a principal strain of ε 1 = 85%. The boundary conditions included symmetry definitions along the vertical faces of the specimens to ensure one-dimensional behavior. Figure 8. Uniaxial FEM (left) and SPH (right) Compression Specimens Figure 9 shows the performance of the FEM and SPH models. The force plots clearly show that the FEM version has much higher accuracy, closely following the baseline plot of the defined material load curve

40 11 th International LS-DYNA Users Conference Aerospace (2) Baseline Material Curve 4-Inch Force 2-Inch Force 1-Inch Force Baseline Material Curve 4-Inch Force 2-Inch Symm on Bottom 1-Inch Symm on Bottom Pressure (psi) Pressure (psi) Strain (in/in) Strain (in/in) Figure 9. 1-D FEM (left) and SPH (right) Compression Force Performance Table 2 summarizes the convergence of the RMS (root-mean-squared) error for the compressive energy absorption as compared with the integrated material stress-strain curve. Convergence was assessed using via regression analysis. Both the FEM and SPH cases had high convergence rates, with orders p of and 3.293, respectively. A glance at the final converged values for the energy RMSE (φ ext ) underscores the superiority of the FEM method over SPH, since FEM converges to 0.73% RMSE and SPH converges to 3.78%. This apparent superiority is fleeting, however, as the addition of more dimensions makes clear in subsequent sections. Table 2. Convergence Summary for 1-D Case, Regression Power-Function Fit Absorbed Energy RMSE FEM P Order of Convergence φ ext Converged Value 0.73% R 2 Fit Quality SPH P Order of Convergence φ ext Converged Value 3.78% R 2 Fit Quality D Convergence Study The two-dimensional case modeled a planar version of a rigid tire form rolling through the crushable material (Figure 10 and Error! Reference source not found.). Three mesh densities were used, with elements/particles sized at h = 4, 2, and 1 inch

41 Aerospace (2) 11 th International LS-DYNA Users Conference The bed was 24 inches deep and 200 inches long; the rigid roller diameter was 44.5 inches. The roller followed a constrained displacement path to a penetration depth of inches while travelling forward at 1,418 in/s (70 knots). Figure D FEM (top) and SPH (bottom) Rigid Roller Models, 4-inch Elements Table 3 summarizes selected GCI tabular data, including the GCI value, the asymptotic value, and the order of the convergence. The hourglass energy for the FEM version at the predicted convergence was nominally 17% of the internal energy value. Meanwhile, the SPH method showed comparable convergence levels and no hourglass energy. Overall, the SPH method showed GCI values on par with the FEM orthogonal approach. Table 3. Convergence Summary for 2-D Case, Grid Convergence Index Method FEM Vertical Load Drag Load Internal Energy Hourglass Energy P Order of Convergence Hourglass Percentage of Internal φ ext Converged Value 875 lbf (1,091) lbf 110,195 lbf-in 18,711 lbf-in 17.0% GCI Convergence Quality 9.8% 3.8% 2.0% 11.8% e ext 1 Error of Finest Mesh 8.5% 3.1% 1.6% 10.4% SPH P Order of Convergence φ ext Converged Value 845 lbf (1,117) lbf 122,850 lbf-in GCI Convergence Quality 5.0% 5.5% 2.5% e ext 1 Error of Finest Mesh 4.2% 4.6% 2.9% 3-D Convergence Study The three-dimensional study featured a deformable B main gear tire (Goodyear H44.5x ) that was rolled through an arrestor bed strip. The bed was 24 inches deep,

42 11 th International LS-DYNA Users Conference Aerospace (2) inches long, and 12 inches wide, with a symmetry plane defined down the centerline of the tire (Figure 11). Just as in the two-dimensional version, the tire followed a constrained displacement path to a penetration depth of 16.0 inches while travelling forward at 1,418 in/s (70 knots). The bottom and outside nodes of the arrestor were constrained for the FEM method, while the SPH version used partial constraints and an outside SPH symmetry plane. Three discretization densities were originally defined, with elements/particles sized at h = 3, 2, and 1 inch (Figure 11). Additional meshes between these three primary values were also run for the different cases. Figure D FEM (left) and SPH (right) Models with 3-, 2-, and 1-Inch Element Sizes Table 4 summarizes the regression convergence results. As shown, the hourglass energy remains too high for the FEM method: 19% even at a 1-inch mesh density. The drag force for SPH was unusual among the functionals measured, having a low R 2 value due to a very flat trend combined with scatter in the data; the drag force was so consistent across the different meshes that the only significant variations were due to noise (Figure 14). As the table shows for the p values, the SPH version converges at least twice as quickly as the FEM version. Further, the SPH version has nearly an order of magnitude less error than the FEM version for the 1-inch mesh density

43 Aerospace (2) 11 th International LS-DYNA Users Conference Table 4. Method Convergence Summary, Regression Power-Function Fit Vertical Force Drag Force Energy Absorption Hourglass Energy Hourglass Percentage of Internal FEM SPH P Order of Convergence φ ext Converged Value 10,730 lbf 8,144 lbf 7,591 lbf-in/in 1,548 lbfin/in R 2 Fit Quality e ext 1 Error of Finest Mesh 15.3% 23.4% 9.4% 27.6% 19.4% P Order of Convergence φ ext Converged Value 10,400 lbf 10,030 lbf 7,996 lbf-in/in 0% R 2 Fit Quality e ext 1 Error of Finest Mesh 0.3% 1.2% 1.5% Figure 12 through Figure 14 illustrate several examples of measured functional data and their regression curve fits. In these figures, the SPH version follows the power-law convergence form more consistently than the FEM method, converges more quickly, and has less error for any given mesh density. In Figure 14, it is clear that the FEM and SPH methods converge to different values for the drag force. In assessing this discrepancy, the SPH method was deemed more trustworthy for several reasons: The SPH models and measured values were more stable; The FEM method, as an alternative, presented a very low order of convergence (p = 1.16); The FEM method still retained substantial hourglass energy A separate punch test model (not shown) revealed that SPH predicted resulting shear force along failure surfaces better than the FEM, which is present along the rut side wall of this model

44 11 th International LS-DYNA Users Conference Aerospace (2) Energy per Distance (lbf-in/in) 20,000 15,000 10,000 5,000 FEM Internal Energy y= x (0.995) FEM Hourglass Energy y=1548x x (0.999) SPH Internal Energy y=7996x x (0.998) Mesh Size (in) Figure D Convergence of Internal and Hourglass Energy 30,000 25,000 FEM Vertical Force (lbf) y= x x (0.999) SPH Vertical Force (lbf) y= x x (0.993) 20,000 Force (lbf) 15,000 10,000 5, Mesh Size (in) Figure D Convergence of Vertical Force 16-51

45 Aerospace (2) 11 th International LS-DYNA Users Conference 20,000 15,000 Force (lbf) 10,000 5,000 FEM Drag Force (lbf) y=8144x x (0.999) SPH Drag Force (lbf) y= x x (0.786) y= x (0.423) Mesh Size (in) Figure D Convergence of Drag Force Conclusions For the modeling of high-compaction foam materials as used in aircraft overrun applications, the finite element method proved to have several shortcomings that were difficult to resolve. The nature of the crushable foam featured cracking and dislocations preceding full compaction, which rendered erosion criteria ineffective at capturing the overall behavior at low, medium and upper areas through the arrestor bed thickness. The smoothed particle hydrodynamics (SPH) formulation was found to provide better results due to its inherently meshless dissociative nature, which more closely reflected the actual material s behavior during an overrun. Because the SPH method lacks the foundational convergence theory inherent to the FEM approach, great care was taken to ensure that the SPH method was sufficiently accurate for the modeling effort. A three-stage convergence study examined the two methods in one-, two-, and three-dimensional forms. In cases where the crushable foam material underwent fairly orthogonal compression, as in the uniaxial model, the FEM version had superior accuracy and computational efficiency. Substantial hourglass effects appeared in the FEM version for the two-dimensional case, however, and the SPH method drew even with the FEM method in terms of convergence performance. In three dimensions, SPH took a strong lead over FEM with: No hourglassing; No element skewing; Convergence rates of double or higher; 16-52

46 11 th International LS-DYNA Users Conference Aerospace (2) Error levels nearly an order of magnitude less; Constant timestep regardless of compaction; and Similar overall computational efficiency. Therefore, SPH was selected as the LS-DYNA modeling method of choice for the larger research effort, where it was incorporated into a broad set of parametric investigations using LS- OPT. The robustness of the SPH model allowed a broad range of material parameters to be explored with stability surpassing the more fickle FEM version of the model. References [1] Babuska, Ivo and Strouboulis, Theofanis The Finite Element Method and its Reliability. Oxford : Oxford University Press, [2] Barsotti, Matthew A Optimization of a Passive Aircraft Arrestor with a Depth-Varying Crushable Material Using a Smoothed Particle Hydrodynamics (SPH) Model. University of Texas at San Antonio. Austin, TX : UMI, Graduate Thesis. [3] Barsotti, Matthew, Puryear, John and Stevens, David Developing Improved Civil Aircraft Arresting Systems. Washington, DC : Transportation Research Board, Airport Cooperative Research Program, Report 29. [4] Celik, Ismail. Procedure for Estimation and Reporting of Discretization Error in CFD Applications. Mechanical and Aerospace Engineering Department, West Virginia University. Morgantown, WV : West Virginia University. [5] FAA AC a: Engineered Materials Arresting Systems (EMAS) for Aircraft Overruns. s.l. : Federal Aviation Administration, [6] Goodyear Aircraft Tire Data Book. Akron, OH : Goodyear Tire & Rubber Company, [7] Kardestuncer, Hayrettin, [ed.] Finite Element Handbook. New York : McGraw-Hill Book Company, [8] Li, Shaofan and Liu, Wing Kam Smoothed Particle Hydrodynamics (SPH). Meshfree Particle Methods. s.l. : Springer Berlin Heidelberg, 2007, pp [9] LSTC LS-DYNA Keyword User's Manual. v971. Livermore : Livermore Software Technology Corporation, p

47 Aerospace (2) 11 th International LS-DYNA Users Conference 16-54

48 11 th International LS-DYNA Users Conference Aerospace (1) LS-DYNA Implemented Multi-Layer Fabric Material Model Development for Engine Fragment Mitigation S. D. Rajan, B. Mobasher and A. Vaidya Civil, Environmental & Sustainable Engineering Program Arizona State University Tempe, AZ Abstract The development of a robust and reliable material model for dry fabrics is the main subject of this paper. Dry fabrics are used in a number of applications such as propulsion engines fan-containment systems, and soft body armor. A mechanistic-based material behavior model capturing the behavior of fabrics when subjected to impacts from high-velocity projectiles would make a powerful predictive tool. In this paper, the constitutive model for Kevlar 49 is developed. Experimental static and high strain rate tensile tests have been conducted at Arizona State University (ASU) to obtain the material properties of Kevlar fabric. Results from laboratory tests such as Tension Tests including high-strain rate tests, Picture Frame Shear Tests, and Friction Tests yield most of the material properties needed to define a constitutive model. The material model is incorporated in the LS-DYNA commercial program as a user-defined subroutine. The validation of the model is carried out by numerically simulating actual ballistic tests conducted at NASA-GRC. 1.0 Introduction High strength woven fabrics are ideal candidate materials for use in structural systems where high energy absorption is required. Their high strength to weight ratio and the ability to resist high speed fragment impacts enable them to be very efficient compared to metals. One of the more widely used applications for woven fabrics is in propulsion engine containment systems. The engine containment system is typically constructed by wrapping multiple layers of Kevlar 49 around a thin aluminum encasement (Fig. 1). The fabric is then covered with a protective layer. Figure 1. Honeywell engine Designing the containment system consists of determining the type of fabric, the number of fabric layers and fabric width required. Currently the FAA s certification standards require that a full-scale test be completed to qualify an engine. Because of the extensive pre and post-test analysis, and the fact that equipment is unusable after testing, a typical fan blade out (FBO) test can cost several million dollars. With today s advanced numerical techniques, modeling a propulsion engine and simulating a FBO event can be accomplished using an appropriate hydrocode. While there are proven constitutive models that can simulate the behavior of most of the materials [Ishikawa and Chou, 1982; Scida et al., 1999; Jiang et. al., 2000], the difficulty lies 1-47

49 Aerospace (1) 11 th International LS-DYNA Users Conference in the fact that there is no mechanistic based constitutive model for woven Kevlar 49 (or any other) fabric, especially one that can be used to predict the fabric s behavior when subjected to high-speed impact loads. The challenge is to represent the actual fabric as an equivalent continuum element as shown in Fig = 1 Fabric Continuum Equivalent Figure 2. Modeling the dry fabric as a continuum 2.0 Experimental Program for Constitutive Model Our constitutive model is developed using a combination of experimental test data and virtual testing [Naik et. al., 2009; Stahlecker et. al., 2009]. We take material direction 11 as the main longitudinal direction of the fabric (warp direction), direction 22 as the direction along the width of the fabric (fill direction), and direction 33 refers to the direction perpendicular to both warp and fill directions. The fabric has negligible stiffness perpendicular to both fabric material directions and hence those properties were assumed to be zero. The constitutive behavior suitable for use in an explicit finite element analysis in stiffness incremental form is shown below. Δσ11 E Δε11 σ 22 0 E ε Δ Δ 22 Δσ Δε 33 = Δσ G Δε12 Δσ G 0 Δε Δσ G Δε23 (1) No coupling effect between the material directions was assumed the Poisson s ratios were assumed to be zero. Gasser and co-workers [Gasser et. al, 2000] using biaxial tests and threedimensional finite element simulations show that υ 12, υ 13 and υ 23 are negligibly small. The decoupled stress-strain relationship has been successfully used to model dry fabric structural systems [Duana et.al., 2005; Raftenberg, 2004]. E 33 is taken as zero simply because the shell element formulation (shell elements are used to model the fabric). The values for E 11, E 22, G 12, G 31, and G 23 are a function of several factors including the current stress and strain, the stress and strain history, and the strain rate. Tensile Behavior Uniaxial tension tests were conducted in both the warp and fill directions. The results for the warp direction are shown in Fig. 3. The primary mode of failure of Kevlar 49 is the breakage of the warp or fill direction yarns. Hence, once the element representing the fabric experienced a critical level of strain in either the warp or fill directions, the element is considered to have failed 1-48

50 11 th International LS-DYNA Users Conference Aerospace (1) in that direction. To simplify and simulate this in the material model, the post-peak region is approximated with a linear region followed by a non-linear region up until fabric failure (Fig. 3) Warp Direction Experimental Tests ASU V1.1 Stress, psi Experimental Values Linear Postpeak Region σ * Non-linear Postpeak Region ε crimp Strain, in/in ε max ε fail Figure 3. Kevlar 49 warp (11) direction uniaxial stress-strain results Unloading/Reloading and Compressive Behavior When the fabric is subjected to impact loads, it can load and unload many times throughout the event. It is important to determine its cyclic behavior and model it correctly. Cyclic tests in the warp direction for three Kevlar 49 samples were conducted to determine the fabric s unloading and reloading behavior. The test results show that in the elastic region, the fabric unloads and reloads approximately along the same path but at a slope that is about one and a half times the elastic stiffness. In the post-peak region, the unloading and reloading stiffness decreases as the strain increases likely resulting from an increase in the breakage of fibers. The cyclic test fabric samples showed that the warp direction had an average strain at peak stress of approximately whereas the uniaxial test samples showed an average of approximately This could be due to the variability in the stress-strain response of the fabric. Since cyclic testing of the fill direction was not conducted, it was assumed that the unloading and reloading stiffness of the fill direction was similar to the warp direction. For simplicity and due to the lack of experimental data, the unloading and reloading stiffness were assumed to be independent of strain rate. 1-49

51 Aerospace (1) 11 th International LS-DYNA Users Conference Warp Direction (11) Stress, psi E 11 unl Unloading/Reloading Compression E 11 comp Strain, in/in Figure 4. Unloading/Reloading and compression behavior assumed in material model for warp direction Kevlar 49 fabric has negligible compressive stiffness. If a zero (or numerically tiny) compressive stiffness is used, the model behavior in an explicit finite element analysis is unrealistic the projectile simply cuts through the fabric. To avoid this problem, a very small stiffness was assumed. The compressive stiffness was taken as 0.5% of the elastic stiffness. Fig. 4 shows the general unloading, reloading, and compressive behavior of the fabric s warp direction as assumed for the constitutive model. A similar behavior is used for the fill direction. Shear Behavior The experimental setup is shown in Fig. 5. Typical results are shown in Fig. 6. The shear resistance increases with an increase in shear strain. At low shear strains the fabric has little resistance to shear deformation. The yarns rotate and the warp and fill directions are no longer orthogonal. At some point there is a very rapid increase in the shear stress value. This is caused by the re-orientation and packing of the fabric yarns as the shear strain increases. Initial finite element simulations discussed in the following section were run using shear modulus values based on these results. The simulations were highly inaccurate as the fabric experienced large local deformations around the contact area that were not seen in the experimental tests. A further examination of the fabric s deformation during the tests revealed that the fabric was wrinkling at the edges during the initial stages of loading and experienced buckling during the final stages of loading. Based on these observations, we corrected the shear-stress strain curve to include only the behavior captured by yarn reorientation. In the material model, a piecewise linear approximation of the corrected results is used and is shown in Fig. 6. The fabric is assumed to unload and reload along the same path. The in-plane shear stress increment is computed as follows. Δ σ = 2Δ ε G (2)

52 11 th International LS-DYNA Users Conference Aerospace (1) Kevlar AS-49 Experimental Results Adjusted Linear Approximation Engineering Shear Stress, psi Engineering Shear Strain, radians Figure 5. Picture frame shear test setup Figure 6. Engineering shear stress-strain results Strain Rate Effects The high strain rate testing system, shown as Fig. 7, includes MTS 5 kip servo-hydraulic tensile testing machine, MTS Flex SE control panels, laser extensometer, and data acquisition system. A typical 2 test specimen is shown in Fig. 8. The high strain rate tests were conducted to about 200/s, the capacity of the machine. Using other publicly available data [Xia and Wang, 1999], the Cowper-Symonds type of strain rate dependent model is constructed as shown in Fig. 9. Figure 7. High strain-rate test setup 1-51

53 Aerospace (1) 11 th International LS-DYNA Users Conference Figure 8. Test specimen Normalized σ max Warp Direction w/ CS Model Fill Direction w/ CS Model Yarn Experimental Results Strain Rate, ms -1 Figure 9. Normalized peak stress as a function of strain rate Fabric-on-fabric Friction Tests The test setup is shown in Fig. 10. For the experiment, a layer of fabric was pulled using a 55 kip horizontal actuator. This fabric layer was sandwiched between another layer of the same fabric. Normal loads were applied on the fabrics such that the maximum normal load was 800 pounds for a contact area of square inches (60 psi). These normal loads were applied through another actuator mounted vertically on an I beam resting on to channel sections connected to the four columns as shown in figure 10. The second layer of fabric was allowed to move using zinc ball joint rod ends that were fixed to an I-beam. Fig. 11 shows the coefficient of the friction for samples tested with a loading rate of 2.0 inches per minute. Average Pull, lbf Kevlar Friction Test Dynamic Static Coefficient of friction ( Static ) = 0.23 Coefficient of friction ( Dynamic ) = 0.23 Loading Rate = 2.0 in/min Figure 10. Friction Test setup Normal Load, lbf Figure 11. Coefficient of friction for loading rate of 2.0 in/min 1-52

54 11 th International LS-DYNA Users Conference Aerospace (1) 3.0 Ballistic Tests To validate the developed constitutive model that is implemented in LS-DYNA as a usersupplied material model, ballistic tests were carried out at NASA-GRC using a gas gun and aiming a steel projectile at a ring wrapped with Kevlar fabric (see Fig. 12). The event was monitored closely including taking pictures using a high-speed camera. A total of 20 tests were carried out where the number of fabric layers, the projectile velocity and orientations were varied. (a) (b) Fig. 12. Ballistic Test Setup (a) Gas gun (b) Steel ring wrapped with several layers of Kevlar The stainless steel projectiles used in the tests are shown in Fig. 13 and henceforth referred to as old (O) and new (N). (a) (b) Figure 13. Stainless steel projectile (a) Old (b) New The old projectile is a rectangular shaped, 304L stainless steel article, 10.2 cm (4 in) long, 5.1 cm (2 in) high and 0.8 cm (5/16 in) thick, with a nominal mass of 320 gm. The front edge and the corners of the projectile are machined with a full radius. The new projectile is also 304L stainless steel, but had a length of 17.8 cm (7 in), a height of 3.8 cm (1.5 in), a thickness of 0.54 cm (.2135 in) and the same nominal mass as the old projectile. The front edge and corners also were machined with a full radius. The gas gun used to accelerate the projectile consisted of a pressure vessel with a volume of 0.35 m3 (12.5 ft3), a gun barrel with a length of 12.2 m (40 ft) and an inner diameter of cm (8 in). A photograph of the gun is shown in Fig. 12(a). The pressure vessel and the gun barrel were mated by a flange on each side with a number of layers of Mylar sheet sandwiched between the flanges to seal the pressure vessel and act as a burst valve. Helium gas was used as the propellant. The pressurized helium was released into the gun barrel by applying a voltage across a Nichrome wire embedded in the Mylar sheets, causing the Mylar sheets to rupture. The projectile was supported inside an aluminum can-shaped 1-53

55 Aerospace (1) 11 th International LS-DYNA Users Conference cylindrical sabot that was machined to fit snugly inside the gun barrel. The orientation of the projectile was controlled by supporting the projectile either with rigid foam or with an aluminum wedge welded to the bottom of the sabot. The sabot was stopped at the end of the gun barrel by a thick steel plate with a rectangular slot large enough to allow the projectile to pass through. The gun barrel was evacuated to reduce blast loading on the specimen and to reduce the amount of pressure required to achieve the desired impact velocity. 4.0 Numerical Results The FE model of each ballistic test was created using shell finite elements for the fabric and solid finite elements for the steel ring and the projectile. Two models were built the single FE layer (SL model) refers to the model where a single FE shell element is used to model all the Kevlar fabric layers, the multiple FE layer (ML model) refers to the model where a single FE shell element is used to model 4 Kevlar fabric layers. The SL model is computationally efficient. On an average, it takes between 25-50% of the wall clock time required for the corresponding ML model. The ML model provides a more detailed picture of the fabric wrap as a containment system and is designed to predict the extent of the fabric wrap damage. For one of the models (LG612), the comparison between the experiment and the FE simulation is shown in Fig. 14. Table 1 shows the summary of the 18 ballistic tests. The absorbed energy is given as Ea = m( vi vf ) (3) 2 where m is the mass of the projectile, v i and v f are the initial and final velocities respectively. The percent absorbed energy is given as E % a 2 2 ( vi vf ) = 100 (4) 2 v i Table 2 shows the comparison between the experimental results and the FE model predictions. The % difference between the experimental and the FE model prediction are computed as % % ( a ) ( a ) D= E E (5) exp FE where exp refers to the experimental value and FE refers to the FE model value. Hence a positive D corresponds to the FE simulation under predicting the absorbed energy and a negative D corresponds to the FE simulation over predicting the absorbed energy. The results show that the SL model on an average under predicts the absorbed energy. Generally, the predictions are better for smaller number of layers. As the number of layers increases, the predictions get progressively worse with the worst overprediction with LG618 (8 layer model) and the underprediction with LG656 (32 layers). The performance of the ML model is comparatively worse. The two models that define the extreme error values as LG618 where the energy absorbed is overpredicted and LG656 where the energy absorbed is underpredicted. 1-54

56 11 th International LS-DYNA Users Conference Aerospace (1) (a) (b) Fig. 14. (a) Experimental result (b) FE Simulation for LG612 Finally, the developed model is used as a tool in predicting the ballistic limit. Table 3 shows the results for 4, 12, 16, 24 and 32 layers for a direct hit (zero roll, pitch and yaw values). The orientation of the projectile was measured from the location of three points on the projectile that defined a local moving coordinate system and three points at a fixed location in the background that defined a laboratory coordinate system. The laboratory coordinate system consisted of the X axis in the direction of the gun axis, a Z axis in the vertical upward direction and Y axis defined by the vector product of Z and X. The orientation of the projectile was defined by a set of three Euler angles defined by a rotation θ (roll), about the laboratory X axis, followed by a rotation ψ (pitch) about the rotated y-axis, followed by a rotation φ (yaw) about the (twice) rotated z-axis. The roll, pitch and yaw angles are defined as the rotation about the e 1 axis, e 2 axis, and the e 3 axis, respectively, as shown in Fig. 15 where the local coordinate system is shown at the center of the projectile. A right hand rule is used to define positive and negative rotations. Model Fabric Layers Projectile Mass (g) & Type (O/N) Table 1. Ballistic Test Data Roll, Pitch and Yaw (degrees) Initial Velocity Final Absorbed Velocity Energy (ft/s) (ft/s) (%) LG (O) 0,0, LG (O) 0,0, LG (O) 0,0, LG (O) 0,0, LG (O) 0,0, LG (O) 0,0, LG (O) 0,0, LG (N) 27.0,6.6, LG (N) 37.35,0.8, LG (N) 25.3,0.7, LG (O) 30.89, LG (O) 22.78,-3.74, LG (N) LG (N) LG (O) 8.98,-2.31,

57 Aerospace (1) 11 th International LS-DYNA Users Conference LG (O) ,9.73, LG (O) , LG (O) 38.24,2.31, e 3 e 1 Pitch Roll e 2 Figure 15. Roll, Pitch, And Yaw Angles of the Projectile Table 2. Experimental Versus FE Model Predictions Experimental Absorbed Energy Model SL Absorbed Energy Diff., D ML Absorbed Energy Diff., D (%) (%) (%) LG LG LG LG LG LG LG LG LG LG LG LG LG