1. Small Debris Impact Simulation with MSC.Dytran – Part II Klaus O. Schwarzmeier, Carlos E. Chaves, Franco Olmi Embraer S/A André de Jesus, Eduardo Araújo, Paul Buis MSC.Software Corporation

2. Presentation Contents Introduction Background Strain Rate Sphere Flexibility Failure Model Plate x Solid Model General Conclusions

3. Introduction Embraer – Empresa Brasileira de Aeronáutica S.A. It is one of the world’s leading designer and manufacturer of aircraft for regional airlines, defense and corporate use Founded in 1969 Based in São José dos Campos, 50 miles from São Paulo - Brazil Plant area: 2.51 million sq.ft More than 5,300 aircraft produced and sold in over 30 years

4. Embraer – Empresa Brasileira de Aeronáutica S.A. Introduction

5. Previous work (MSC Aerospace 1999) Steel spheres impacting Al-2024-T3 panels with 1.6 and 3.2 mm thickness Experimental results compared with numerical results from dynamic analysis with MSC.Dytran Background

6. MSC.Dytran Models Characteristics Lagrangian shell elements (CQUAD4) Impacting sphere initially simulated as a rigid ellipsoid. Constitutive model: Johnson-Cook (YLDJC) Failure model: element maximum plastic strain failure (FAILMPS) Material properties: obtained from MSC.Mvision database Previous analysis: all parameters in the Johnson-Cook relation as well as the value of FAILMPS assumed as constants Background

7. Discrepancy between analytical and experimental results (sphere velocities) from the previous work is shown in the figure This work: Influence of parameters used as input for the constitutive equation and failure model, as well as the modeling characteristics, will be addressed Parameters assumed as material constants in the previous work (regardless of the dynamic condition) will be analyzed in detail Background

8. Strain Rate Assuming that actual material stress-strain behavior could differ significantly from the data available, a sensitivity analysis for the strain rate parameter C was carried out Results for 1.6 mm thickness plate shown in the figure Value of C available in the MSC.Mvision database is 0.015

9. Strain Rate In order to have close agreement with the experimental results for the range of velocities analysed, C value of must change more than one order Conversely, small changes in C will imply in small changes in the final velocity CONCLUSION: strain rate parameter does not exert a major influence in analysis results Influence of the sphere flexibility and friction between sphere and plate considered Small reduction in the final velocity due to friction observed This trend seems to be correct only when initial velocities are smaller CONCLUSION: sphere flexibility and friction between sphere and plate do not explain the discrepancies between analytical and experimental results Sphere Flexibility

10. Failure Model Present results showed that the failure parameter (FAILMPS) plays a key role in numerical analysis Starting with FAILMPS = 0.18 (static result for Al 2024-T3), a series of analyses with varying values for this parameter were carried out Results of these analyses for both plates shown in figures below

11. Failure Model CONCLUSIONS: 1. Value of FAILMPS Previous work: FAILMPS assumed as fixed and equals to 0.18 FAILMPS may change significantly, according to the impact velocity and plate thickness (geometry) This work: failure index changes, and can be significantly higher than the one obtained from static tests MSC.Mvision database: failure index FAILMPS = 0.5 supplied for Al 2024-T3 This may correspond to some specific dynamic condition, but will not necessarily cover the impact conditions evaluated in this work

12. CONCLUSIONS (cont.) 2. Stress Triaxiality Sphere penetrating in a plate: stress state is clearly bi-axial It is apparent that a failure parameter based on the effective plastic strain may not be suitable for the dynamic conditions analyzed Desirable to find a correlation between some triaxiality parameter and the strain rate, such that a more adequate failure model can be implemented (for example, by means of an external subroutine in MSC.Dytran) 3. Failure Modes According to the plate thickness, two distinct failure modes observed These failure mechanisms are associated to the triaxial strain state due to plate thickness, and can be interpreted only by means of a more appropriate failure criterion Failure Model

13. LEFT: impact energy = 750 J, thickness = 1.6 mm bulge formation and tearing (petaling) RIGHT: impact energy = 1500 J, thickness = 3.2 mm precipitated plug formation, followed by a plug removal Failure Model

14. Solid x Plate Model Possibility to run the analysis with solid elements also investigated. CHEXA elements along the thickness direction. Plate with thickness 1.6 mm modeled with 12 layers Plate with thickness 3.2 mm modeled with 24 layers Material properties: same as in the previous work, C=0.015, FAILMPS = 0.18

15. In general, plots show decrease in final velocity for model with solid elements, expressing some ability of solid elements to absorb energy during the impact (or to take into account the strain variations along the plate thickness direction) This trend is opposite to the experimental results for the 3.2 mm thickness plate CONCLUSION : solid elements do not to reproduce appropriately experimental results when compared to the shell elements Computational effort: in a NT workstation with 512 Mb of RAM memory and one processor, models with shell elements typically run in about 20 minutes, while models with solid elements last about 20 hours Obviously 2D model is much more economic and should always be used when there are time or CPU constraints Solid x Plate Model

16. General Conclusions PRESENT STUDY: brings some important concepts that were not taken into account previously Influence of the parameters of material constitutive equation is not relevant when compared to the failure index (FAILMPS) Sphere flexibility and friction also do not imply in significant losses of energy Failure index (FAILMPS): can change considerably according to strain rate, and values higher than the one obtained by static tests can be considered Failure mechanism: quite complex, and a parameter based on an equivalent plastic strain will not describe this mechanism completely. There are also stress triaxiality issues that must be considered. The complete understanding of this parameter requires further studies Solid elements: do not result in a major improvement in the analysis results, but imply in a significant increase in the CPU time for the analysis