Three-dimensional numerical modeling of composite panels subjected to underwater blast
Introduction
The design and manufacture of lightweight yet stiff and strong materials has attracted a lot of attention recently due to fast-growing military and civilian needs. A number of applications require high strain-rate behavior, e.g., marine hulls subjected to underwater explosions (Porfiri and Gupta, 2010, Chen et al., 2009) or automobile parts designed for crash absorption (Lee et al., 2000, Zarei and Kröger, 2008). The use of sandwich structures (e.g., two solid face sheets with a foam core in the middle) in blast mitigation became a topology of choice as designers realized that a crushable core, which can dissipate a substantial amount of energy, could attenuate the impulse transmitted to the back-side face sheet and therefore protect it from catastrophic failure. Numerous metallic sandwich architectures have been extensively studied and were shown to outperform monolithic structures of equal areal mass (Xue and Hutchinson, 2003, Xue and Hutchinson, 2004, Fleck and Deshpande, 2004, Qiu et al., 2004, Deshpande and Fleck, 2005, Hutchinson and Xue, 2005, Qiu et al., 2005, Liang et al., 2007, Mori et al., 2007, Mori et al., 2009, Vaziri et al., 2007; ). Fleck and Deshpande (2004) suggested that the dynamic response of sandwich panels can be discretized into three stages: Stage I, fluid–structure interaction before first fluid cavitation; Stage II, core compression; Stage III, panel bending and stretching. Adopting Fleck and Deshpande's model, Hutchison and Xue (2005) studied the relationship between the ratio of the momentum transferred to the core and the back-side face sheet over the total imparted momentum and the compressive core crushing strength. Having shown better performance (i.e., higher energy absorbance per unit areal weight) than monolithic structures (Rathbun et al., 2006, Dharmasena et al., 2010), metallic sandwich structures still suffer from shortcomings. For example, the dramatic variation in the stiffness of a metallic core when subjected to buckling and followed by re-strengthening (fully collapsed core) makes optimized design of sandwich structures, over a wide range of applied impulses, very difficult (Hutchinson and Xue, 2005, Vaziri et al., 2006, Lee et al., 2006, McShane et al., 2010).
Recently, fiber reinforced polymer composite materials and cellular polymer foams have been utilized to replace metals in sandwich architectures. Because they have strength comparable to high strength steels, yet much lower material density, fiber reinforced composites are used as skin materials in composite ships (LeBlanc and Shukla, 2011, Dear and Brown, 2003). Polymer foams are chosen as core materials because of their high energy absorption capabilities during compression (Andrews and Moussa, 2009, Tagarielli et al., 2010, Wang and Shukla, 2011, Gardner et al., 2011, LeBlanc and Shukla, 2011). Despite the large volume of literature on sandwich structures (Hoo Fatt and Palla, 2009, Abrate, 2005, Abrate, 2011, Massabò and Cavicchi, 2011, Hoo Fatt and Surabhi, 2012, Arora et al., 2011, Arora et al., 2012, Dear et al., 2005), numerical studies of fluid–structure interaction (FSI) problems that occur when underwater blast is applied to these structures are limited.
In an earlier study (Latourte et al., 2011), we reported experiments on monolithic and sandwich composite panels subjected to a wide range of impulsive loading using a scaled-down FSI apparatus (Espinosa et al., 2006), as shown in Fig. 1a. Each composite lamina in the panels contained four unidirectional plies consisting of Devold DBLT850-E10 glass-fibers infiltrated by vinylester Reichhold DION 9500 resin aligned in a sequence of either (0°/45°/90°/−45°) or (45°/90°/−45°/0°). Four monolithic (solid) panels (panel configuration 1), four symmetric sandwich panels (panel configuration 2), and two asymmetric sandwich panels (panel configuration 3) were tested at impulses ranging from 1233 to 6672 Pa s. Postmortem characterization was also performed to identify different damage mechanisms, such as inter-lamina delamination, fiber and matrix damage in the composite plies, and foam crushing. The performances of the three types of panels were summarized by plotting the applied impulse per areal mass vs. the observed central deflection (Fig. 1b).
In this paper, we report models used to simulate the FSI experiments to assess their accuracy and predictive capabilities. We start by examining various approaches to simulate the FSI effect. Next we introduce the failure models used for the fibers and the matrix, a rate-dependent cohesive law to model inter-lamina delamination, and a foam crush model. We then present the model validation using test ♯1–3 (the 3rd monolithic composite panel) and a discussion of model predictions for both monolithic and sandwich panels over a wide range of impulses. We close with remarks on remaining issues and future work needs.
Section snippets
Numerical model
Three approaches have been widely used to simulate the fluid–structure interaction in air/water blast problems. The first approach is to simulate both the fluid media and solid structure with Lagrangian meshes (L-L model) (Espinosa et al., 2006). The fluid behavior is described with a Mie-Grüneisen equation of state (EOS) with a linear Hugoniot relation. An adaptive remeshing technique is required to prevent large distortion of the fluid mesh during wave propagation and interaction with the
Strain-rate sensitive cohesive law and composite model calibration
With the material properties listed in Section 2, the remaining task was to assess the strain-rate sensitivity of the vinylester resin, which was calibrated by comparing the inter-lamina delamination patterns from simulations with those observed in experiments. In this study, test ♯1-3 (at an impulse of 2425 Pa s) was chosen as the control experiment to calibrate the strain-rate sensitivity cohesive model because it gives a complex delamination pattern with no catastrophic fiber rupture. A
Conclusion
In this study, we have developed a fluid–structure interaction numerical model using a coupled acoustic-solid technique capable of accurately describing the interaction between water and composite panels. In addition, the FSI model is able to depict the various material deformation and damage mechanisms in monolithic and sandwich composite panels, such as inter-lamina delamination, fiber and matrix damage, and foam crushing. Numerical simulations on monolithic composite panels suggest that:
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Acknowledgments
This research was carried out under the financial support of the Office of Naval Research (ONR) under grant number N00014-08-1-1055. The support and encouragement provided by Dr. Rajapakse through the study is greatly appreciated.
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Current affiliation: EDF–R&D, MMC, Avenue des Renardières, 77818 Moret-sur-Loing, France.