Journal of the Mechanics and Physics of Solids

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1 Journal o the Mechanics and Physics o Solids 59 (2) Contents lists available at ScienceDirect Journal o the Mechanics and Physics o Solids journal homepage: Failure mechanisms in composite panels subjected to underwater impulsive loads Félix Latourte a,,2, David Grégoire a,,3, Dan Zenkert b, Xiaoding Wei a, Horacio D. Espinosa a,n a Northwestern University, 245 Sheridan Rd., Evanston, IL 628-3, USA b KTH-Royal Institute o Technology, Sweden article ino Article history: Received 28 August 2 Received in revised orm 9 March 2 Accepted 5 April 2 Available online 2 April 2 Keywords: Composite materials Fluid structure interaction Dynamic ailure Delamination Blast abstract This work examines the perormance o composite panels when subjected to underwater impulsive loads. The scaled luid structure experimental methodology developed by Espinosa and co-workers was employed. Failure modes, damage mechanisms and their distributions were identiied and quantiied or composite monolithic and sandwich panels subjected to typical blast loadings. The temporal evolutions o panel delection and center delection histories were obtained rom shadow Moiré ringes acquired in real time by means o high speed photography. A linear relationship o zero intercept between peak center delections versus applied impulse per areal mass was obtained or composite monolithic panels. For composite sandwich panels, the relationship between maximum center delection versus applied impulse per areal mass was ound to be approximately bilinear but with a higher slope. Perormance improvement o sandwich versus monolithic composite panels was, thereore, established specially at suiciently high impulses per areal mass (I /M 47 m s ). Severe ailure was observed in solid panels subjected to impulses per areal mass larger than 3 m s. Extensive iber racture occurred in the center o the panels, where cracks ormed a cross pattern through the plate thickness and delamination was very extensive on the sample edges due to bending eects. Similar levels o damage were observed in sandwich panels but at much higher impulses per areal mass. The experimental work reported in this paper encompasses not only characterization o the dynamic perormance o monolithic and sandwich panels but also post-mortem characterization by means o both non-destructive and microscopy techniques. The spatial distribution o delamination and matrix cracking were quantiied, as a unction o applied impulse, in both monolithic and sandwich panels. The extent o core crushing was also quantiied in the case o sandwich panels. The quantiied variables represent ideal metrics against which model predictive capabilities can be assessed. & 2 Elsevier Ltd. All rights reserved.. Introduction Glass reinorced plastic (GRP) composite materials are o current interest in naval hull construction (Mouritz et al., 2), because they exhibit low weight and low magnetic signature. These are advantages o particular interest to naval n Corresponding author. address: espinosa@northwestern.edu (H.D. Espinosa). These authors contributed equally. 2 Current ailiation: EDF R&D, MMC, Avenue des Renardieres, 7788 Moret-sur-Loing, France. 3 Current ailiation: LFC-R, UMR55, Université de Pau et des Pays de l Adour, Allée du Parc Montaury, 646 Anglet, France /$ - see ront matter & 2 Elsevier Ltd. All rights reserved. doi:.6/j.jmps.2.4.3

2 624 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) designers interested in ast and stealth marine structures. Two dierent architectures are generally used to build composite hulls: single-skin design and sandwich construction, where a crushable core is encased between iberreinorced ace skins. Both architectures involve the use o rames, stieners and bulkheads that provide the overall structural stiness, and support the GRP monocoque or sandwich hull. In these constructions, the connection between the hull and the bulkhead does not seem to be a weak point when subjected to blast loading. Indeed, no localized shear or tearing was observed in ull scale blast experiments (Hall, 989). These experiments showed that deormation and damage are distributed on the sandwich panel itsel, in which interlaminar delamination occurs. A visible change in opaqueness in the hull skin appeared ater the impulsive loading (Hall, 989). Large scale ield blast experiments have also been conducted. In these experiments, a 3D digital image correlation technique was employed to reconstruct the deormation histories o the tested panels (Dear et al., 29). At the laboratory scale, experimental studies were conducted to study the dynamic response o composite sandwich beams subjected to projectile impact (Tagarielli et al., 27; Johnson et al., 29), the ballistic resistance o 2D and 3D woven sandwich composites (Grogan et al., 27) and the impact response o sandwich panels (Schubel et al., 25; Tekalur et al., 28) with optimized nanophased cores (Bhuiyan et al., 29; Hosur et al., 28). The reader interested in the numerous experimental studies o marine composite subjected to impulsive loadings can reer to Poriri and Gupta (29). These studies present the perormance o dierent composite panels and the most signiicant damage modes involved in blast or ballistic resistance o sandwich structures, whose local degradation can greatly aect the overall structural perormance (Zenkert et al., 25). One limitation o the experiments reported in the literature is that the impacted region is typically small compared to the panel or laminate dimension, resulting in very localized damage. Localized damage is also not representative o the structural eects observed in larger scale blast studies, where clamping tearing is not the most signiicant mechanism responsible or structural ailure, and deormation and damage are spread over a large section o the hull. Scaled down laboratory luid structure interaction experiments have been successully developed and applied to the investigation o monolithic steel plates (Espinosa et al., 26; Rajendran and Narashimhan, 2) and sandwich steel constructions (Mori et al., 27, 29) by Espinosa and co-workers. In the present paper, the luid structure interaction (FSI) setup introduced in Espinosa et al. (26) is utilized to characterize composite monolithic and sandwich plates. The advantage o this setup relies on the scaling o ull ield loads that enable the testing o panels with dimensions (radius L¼76.2 mm) small enough to be easily manuactured and handled in a laboratory setting, but with suicient thickness to investigate layups consistent with ull marine hulls in terms o stacking sequence and number o plies. Moreover, the setup is highly instrumented and allows recording o delection proile histories over the entire span o the panels or a precisely known applied impulse. Composite panels subjected to blast typically present not only extensive interlaminar racture (delamination) but also matrix microcracking and ultimately iber racture at the highest impulses. In sandwich panels, these ailure modes are aected by interactions between the core and the acesheets. Thereore, substantial improvements in the panel perormance rely on the core crushing behavior and the strength o the core-acesheet bond. As a general trend, sot cores are generally preerred since they can enhance energy absorption and blast mitigation, which is key in panel perormance. Foam crushing is typically characterized by a stress plateau ollowed by densiication and sudden increase in hardening. Among core materials, PVC oam and balsa wood cores were investigated because o their suitable crushing strength in naval applications. Unortunately, very limited experimental data exists concerning the perormance and ailure o composite panels subjected to impulsive loading (Tagarielli et al., 27; LeBlanc and Shukla, 2). Thereore, understanding and quantiying ailure modes in composite materials, as a unction o applied impulse, is a topic o research that requires additional attention rom the community. Concerning the prediction o structural behavior and ailure o monolithic and sandwich hulls subjected to impulsive loadings, limited work was reported in the literature (Deshpande and Fleck, 25; Hoo Fatt and Palla, 29; Tilbrook et al., 29; Forghani and Vaziri, 29). Although physically based, most models rely on homogeneous description o the composite material at the scale o the single ply or o the sub-laminate (Hashin, 98; Hashin and Rotem, 973; Puck and Schurmann, 998). A research initiative called world-wide ailure exercise attempted to rank and classiy the numerous models available in the literature based on their perormance to predict ailure under various loading conditions (Hinton et al., 22; Soden et al., 998; Soden et al., 22; Soden et al., 24). Surprisingly, investigated models are unable to predict ailure correctly over a wide range o quasi-static stress paths. Thereore, attempts to establish predictive capabilities or composite materials have to be considered with care. Detailed experimental validation needs irst to be attempted, especially in dynamic situations or which the literature is scarce. In this context, recently introduced multiscale models (Ladeveze and Lubineau, 22; Ladeveze et al., 26; Espinosa et al., 2; Latourte et al., 29; Espinosa et al., 29) accounting or microstructural damage mechanisms developed in the ramework o Hashin s damage mechanics (Hashin, 986) might be o signiicant beneit to the composite modeling community. The objective o the present paper is to characterize composite panel perormance in terms o impulse-delection, using the experimental methodology introduced in Espinosa et al. (26). Failure modes, damage mechanisms and their spatial distributions are identiied and quantiied or composite monolithic and sandwich panels subjected to underwater impulsive loading. The quantiied variables represent ideal metrics against which model predictive capabilities can be assessed. The paper is structured as ollows: irst, the tested composite panels are described and details about the manuacturing are given. Then, the experimental results are presented. These latter sections recap briely the

3 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) h R h 45 9 h R h 3 h 2 h 2L µm -45 2D Fig.. Schematic o tested composite panels: (a) monolithic panel o thickness h bonded to a steel ring o thickness h R, (b) sandwich panel with acesheet thicknesses h and h 3 and core thickness h 2, (c) optical photograph o the solid panel cross section highlighting the dierent abrics, (d) optical photograph o the sandwich panel cross section and (e) optical microscopy image o an E-glass/vinylester quasi-isotropic abric used in the manuactured panels. luid structure interaction experimental apparatus, and report impulse delection perormance and dynamic behavior o composite panels. A section is devoted to the study o damage modes identiied post-mortem rom an ultrasonic pulse-echo technique and optical microscopy. A summary o main indings and their implications is discussed in the closing section. 2. Description o composite panels Composite solid, symmetrical sandwich and asymmetrical sandwich panels are considered in this study. The composite acesheets are comprised o quasi-isotropic Devold DBLT85-E glass-iber (/45/9/ 45) non-crimp abric iniltrated by vinylester Reichhold DION 95 and the sandwich panels are built based on a 5 mm Diab H25 divinycell PVC oam core. Each composite abric is composed o our laminas comprised o unidirectional E-glass ibers and assembled ollowing the sequence: /45/9/ 45. The iber diameter, lamina and abric thicknesses are 5, 5 and 6 mm, respectively. Fig. a andb describes the composite monolithic and sandwich panel geometries tested under the FSI experiment. Optical photography o the cross-sections are shown in Fig. c and d and an optical micrograph o an iniltrated abric is shown in Fig. e. Composite monolithic and sandwich panels o approximately the same weight per unit area were manuactured at KTH-Royal Institute o Technology, Sweden. Ater the manuacturing, the panels were cut with a water jet in order to obtain the inal circular geometry ( 292. mm). Once the circular cut was perormed, the panels were bonded to a steel ring o thickness h R ¼25.4 mm (or h R ¼9 mm or monolithic panels tested at low impulse) with a 3M Scotch-Weld TM DP46 epoxy adhesive. The three dierent specimen designs are Composite monolithic panels consisting o nine composite abrics iniltrated by the resin: (/45/9/ 45) 4 (45/9/ 45/) 5. The inal thickness obtained or solid panels was h¼5.8 mm. Symmetrical sandwich panels consisting o six composite abrics separated by a oam core: (/45/9/ 45) 3 - Core - (45/9/ 45/) 3. The inal thickness obtained or symmetrical sandwiches was h¼9 mm (h ¼2 mm, h 2 ¼5 mm and h 3 ¼2 mm). Asymmetrical sandwich panels consisting o six composite abrics separated by a oam core: (/45/9/ 45) 2 Core - (45/9/ 45/) 4. Final thickness obtained or asymmetrical panels was h¼9 mm (h ¼.33 mm, h 2 ¼5 mm and h 3 ¼2.66 mm). The three designs listed above provide a similar areal mass to that o sandwich steel panels previously tested with the same luid structure interaction setup (Espinosa et al., 26; Mori et al., 27; Mori et al., 29). The areal masses M o the monolithic, the symmetrical sandwich and the asymmetrical sandwich panels were.7,.3 and.2 kg m 2, respectively. The principal mechanical properties o the constituents used in the manuactured panels are summarized in Table. 3. Fluid structure interaction experiments 3.. Experimental setup, perormances and deormation histories In order to reproduce in a laboratory setting underwater explosive loading conditions, a scaled luid structure interaction experimental setup was developed by Espinosa et al. (26). During underwater blast loading, the impulsive load is characterized by an exponential decay pressure history depending on two parameters: the peak pressure p and the time decay t (Fig. 2). In the FSI experimental setup, the shell o a naval hull is scaled down to a composite panel specimen (Fig. 2). As described in Espinosa et al. (26), the scaling is achieved by setting the same luid structure interaction as the one expected in the ull scale application. In other words, the same raction o the ar ield momentum, I, should be transmitted to the specimen. Deining the scaling actor, K, as the panel thickness in the ull scale naval structure over the panel thickness in the experiment, i.e., K¼h F /h E, the analysis shows that applied impulse should scale down by K (Espinosa et al., 26).

4 626 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) Table Constituent material properties. E-glass a Resin b Core b Density (kg/m 3 ) 85 c 25 Tensile modulus (MPa) 73, 33 7 Tensile strength (MPa) Compressive modulus (MPa) 3 Compressive strength (MPa) 5.8 Shear modulus (MPa) Shear strength (MPa) a Properties estimated rom experiments. b Properties as certiied by manuacturer. c Mean density estimated on the actual panels ater iniltration. Fig. 2. (a) Schematics o underwater explosion conditions and pressure proile history; (b) schematic o blast simulator (Espinosa et al., 26) and (c) example o pressure decay history as obtained rom one-dimensional analysis (Espinosa et al., 26) (blue curve) and FEA (red curve). (For interpretation o the reerences to color in this igure legend, the reader is reerred to the web version o this article.) As pressure does not scale down because it is an intensive quantity, impulse scaling is achieved by adjusting decay time t through the dimensions o projectile and water piston. Another important consideration in the experimental design is the panel boundary condition. In the FSI setup, a steel ring is used to clamp the composite panels. The inertia o the steel ring simulates the structural bulkheads in a ull scale naval structure. Moreover, this boundary condition allows or boundary core crashing in sandwich structures. A water piston seals the other extremity o the chamber and the exponentially decaying pressure history is produced by impacting the water piston with a lyer plate launched by a gas gun (Espinosa et al., 26). Ater impact, pressure waves propagate through the water column and reach the composite panel. The circular part o the composite panel in contact with the water column is subjected to the impulsive load. When the panel deorms, water cavitation is elicited at the specimen water interace. The delection history o the loaded panel is characterized by means o shadow Moiré and high speed photography (Espinosa et al., 26; Mori et al., 27, 29). In previous experiments carried out on solid stainless steel panels (Espinosa et al., 26), pressure histories recorded with pressure transducers were consistent with the predicted exponential decay associated with blast loading. The pressure wave created by the impact o the lyer plate on the water piston is a unction o lyer initial velocity V, material impedance and lyer plate/water piston dimensions. As shown in Fig. 2c, the pressure decay history, at the anvil entrance, predicted by the one-dimensional analytical solution given in Espinosa et al. (26), exhibits overall agreement with the pressure history obtained rom a coupled Eulerian Lagrangian inite element analysis (FEA) perormed using ABAQUS/ Explicit v6.9. However, we ound rom FEA simulations that at impact velocities in excess o 2 m/s, the generated impulse is also sensitive to other eatures, such as the geometry o the anvil tube, and dimensions and plastic low o

5 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) projectile and water piston. Furthermore, impulse losses with propagation distance are also expected due to luid viscosity. Thereore, here the ree-ield impulse near the panel is obtained rom FEM simulations using an equation o state or water (Espinosa et al., 26) and viscoplastic properties or the lyer and water piston. Contact between lyer and anvil, as well as between water piston and anvil, are also modeled with a riction coeicient o.. Separate coupled Eulerian Lagrangian simulations were perormed on water columns extending beyond the location o the specimen. Hence, by speciying the experimental conditions, such as lyer plate velocity, anvil, lyer plate and water piston materials and geometries, the applied impulse or each experiment was obtained by numerically integrating the pressure history at the location o the tested panels. The decay time t was obtained by dividing the impulse by the peak pressure. In the work reported here, the panels are labeled by coniguration and test number. Solid panel, symmetrical sandwich and asymmetrical sandwich coniguration are respectively numbered as irst, second and third. Hence, experiment 2-3 reers to the test #3 or the symmetrical sandwich coniguration. In Table 2, panel conigurations and corresponding impulse parameters are summarized. For all the experiments, except 2-4 and 3-2, the thickness o the water piston was.42 mm. Experiments 2-4 and 3-2 were conducted with lyer plates and water pistons o matching thicknesses. Impulses were varied rom I ¼233 Pa s (panel -) to I ¼6672 Pa s (panel 3-2). Applied impulses per areal mass (I =M) are also listed in Table 2 or each perormed test. In order to examine the inluence o the panel architecture on the delection perormance, panels with dierent construction types (monolithic and sandwich) were tested at comparable impulses. The last column o Table 2 provides the normalized peak delection d max /L. For experiment -5, no peak delection was obtained because the grating used in the shadow Moiré was damaged by lying debris. For experiment -4, the reported peak delection was obtained prior to the panel massive delamination and ailure as observed rom high speed camera pictures and post-mortem imaging. The perormance o the composite panels in terms o normalized maximum delection measured or an applied impulse per areal mass is shown in Fig. 3. Plotting on the same igure experimental results obtained on composite monolithic panels, composite sandwich panels and previous results obtained on A34SS sandwich panels with various core topologies (Mori et al., 27; Mori et al., 29), a comparison o perormances is obtained. For sandwich panels, the maximum delection on the airside is employed. This delection is indeed a relevant perormance indicator or blast protection in which personnel and equipment must be shielded. The experimental results or all tested panels are plotted in Fig. 3. From the experimental results plotted in Fig. 3, the ollowing observations can be drawn: The perormance o composite solid panels ollows a linear trend, as shown by the dashed line, leading to the ollowing relation as determined rom a least square linear it: I =M ¼ð935 d max =L 3Þðms Þ, ðþ where I is the applied impulse X, M is the panel areal mass, d max is the peak delection and L is hal the panel span. The impulse delection behavior o sandwich panels 2-, 2-2, 2-3, 3- and 3-2 shows a bilinear relationship given by I =M ¼ð556 d max =L 884Þðms Þ or I =M o43 I =M ¼ð42 d max =L 633Þðms Þ or I =M 443: ð2þ Note the higher slope as compared to monolithic panels. The advantage o the sandwich architecture at high impulse per areal mass is thereore established. The eect o pressure history is illustrated by the perormance o experiments 2-3 and 2-4. While both panels have been subjected to the same impulse but dierent peak pressure and decay time, their perormance (see Fig. 3) and ailure modes (see Section 3.3) exhibited quite distinct eatures. Table 2 List o conducted experiments reporting impulse parameters and normalized peak delections recorded during the experiments. Geometry Labels Flyer plate thickness (mm) Projectile velocity (m/s) p (MPa) t (ls) Impulse I (Pa s) I =M (m s ) Normalized peak delection d max /L Solid panel a Symmetrical sandwich Asymmetrical sandwich a a Peak delection preceding massive panel ailure.

6 628 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) Fig. 3. Impulse per areal mass versus normalized delection or monolithic and sandwich composite panels. The experimental results obtained on A34 stainless steel sandwich panels, reported in Mori et al, (27, 29), are overlaid or comparison. Fig. 4. Panel center delection histories or monolithic panels (tests - to -5). During tests -4 and -5, panel ailure prevented the observation o Moiré ringes ater the last point plotted on the graph. The perormance o composite monolithic panels in terms o impulse-delection is comparable to the one observed or A34SS I-beam core steel sandwiches, which was identiied as optimal core topology among all the dierent designs reported in Mori et al. (27, 29). By contrast, composite monolithic panels perorm much better than A34SS panels with honeycomb or pyramidal cores. This highlights the perormance-to-weight advantages o composite solid panels. Experiments -4, 2-3 and 3-2 exhibited extensive delamination and iber ailure with loss o impermeability as will be discussed later in Section Deormation histories in composite solid panels (tests - to -5) Delection proiles were calculated or all solid panels; typical results are presented in Appendix A. From the ull proile sequence corresponding to each experiment, delection at the panel center was extracted to plot delection histories. In Fig. 4 the delection history or all tested monolithic panels is given. In this igure, several eatures are noticeable: At the lowest impulse, experiment -, I =M ¼6 m s, the peak delection is reached slowly at 35 ms. A permanent deormation, recorded ater the test, was less than 2 mm. Hence, the elastic recovery occurs at a very slow rate, and is not ully captured by the recorded images.

7 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) At higher impulses (experiment -2 at I =M¼66 and experiment -3 at 227 m s ), the peak delection d max is reached aster, at approximately 25 ms. An even aster rate o deormation is observed at higher impulses (I =M ¼34 and 46 m s ). The spring back eect is more pronounced at I =M¼66 and 227 m s than at I =M ¼6 m s.ati =M ¼227 m s the permanent delection d perm was 5.2 mm, which is very close to the last value recorded using high speed photography in the rame at t¼592 ms. For the two highest impulses I =M ¼34 and 46 m s, no spring back eect was measured because o the extreme nature o these experiments. As it will be shown later in the ailure analysis section, extensive delamination and iber ailure occurred under these impulses, which prevented the recording o Moiré ringes beyond the initial increasing deormation phase Deormation histories in composite sandwich panels (tests 2- to 2-4 and 3, 3 2) Composite sandwich panels were also subjected to underwater blast loading using the same methodology (c. Table 2). Center delection histories were computed and plotted in Fig. 5 or symmetric sandwich panels and in Fig. 6 or asymmetric sandwich panels. An additional result showing complete delection proiles is presented in Appendix A. Fig. 5. Panel center delection histories or composite symmetric sandwich panels. Fig. 6. Panel center delection histories or composite asymmetric sandwich panels (exp. 3- and 3-2) at two dierent impulse levels. Center delection history o experiment 2-2 (symmetric coniguration) is also shown or comparison. Note that experiments 2-2 and 3- were perormed at approximately the same impulse per areal mass.

8 63 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) Several eatures can be observed in Figs. 5 and 6: Delection proile shapes in sandwich panels were similar over the range o applied impulses. Delection proiles exhibit a symmetrical parabolic shape (Fig. 24). In the early increasing delection stage (to3 ms), characteristics shoulders are observed on the center delection histories. The symmetrical (test 2-2) and the asymmetrical (test 3-) sandwich panels show a similar response up to peak delection when subjected to comparable impulses per unit areal mass (I =M ¼35and 35 m s, respectively). The maximum delections are almost identical and occur at approximately the same time. A dierence in the rate o recovery is observed, with the asymmetric coniguration exhibiting a slower rate, which can be associated to less damage in the airside acesheet. In all the sandwich panels, the peak delection is reached in approximately 3 35 ms, while in most o the monolithic panels it was reached earlier in 25 ms. This delay to reach the peak delection can be explained by core compaction, which absorbs part o the impulsive load beore it is transerred to the airside acesheet. During the initial increasing deormation phase, several distinct rates are observed. A irst rapid increase in delection, up to 2 ms, is observed in experiments 2-, 2-3 and 3-2. Then, a slower rate o increase ollowed by another high rate up to peak delection is observed. In the other experiments, 2-2, 2-4 and 3-, the irst initial increase in delection is ollowed by a continuous and smooth reduction in the delection rate leading to a peak delection at approximately 35 ms. This dierence in phase can be correlated to peak and decay time o the applied impulses (c. Table 2). As such these eatures can be attributed to the FSI eect. In act, in experiments 2-, 2-3 and 3-2 peak stresses are high and decay times short when compared to experiments 2-2, 2-4 and 3-. At ixed applied impulse, peak pressure and decay time greatly aect the response o sandwich panels as suggested by the delection histories in sandwich panels 2-3 and 2-4 tested at I =M¼495and 48 m s, respectively. Although the applied impulses are comparable, the decay time in the pressure history corresponding to test 2-4 was 58% longer than the one in experiment 2-3. This results in a peak delection 26% larger in panel 2-3 than in panel 2-4. Moreover, ailure mechanisms in these two panels were quite dierent (c. Section 3.3) Comparison in deormation histories between solid and sandwich panels Fig. 7 compares center delection proile histories or experiment -3 (solid panel) and experiment 2- (symmetrical sandwich panel) subjected to comparable impulses per areal mass, I =M¼227 and 27 m s, respectively. The plot highlights the clear improvement in perormance resulting rom the sandwich construction. The delection in the sandwich panel is reduced by 23% to the one in the solid panel, and correspondingly, the amount o damage in the back ace sheet is highly reduced. The spring back rate is much slower in the sandwich case Non-destructive damage identiication A 3-D damage evaluation was perormed on the tested panels by the pulse-echo technique, which has already been proven successul in the identiication o damage o thick GRP laminates (Mouritz et al., 2). In this study, ultrasonic Fig. 7. Comparison between panel center delection histories or solid (exp. -3) and symmetrical sandwich (exp. 2-) panels at impulse per areal mass o I =M22 m s.

9 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) s 2 s 2 I R..8.6 s 2 s 4.4 z y x.2. Fig. 8. C-scans obtained or solid panels - and -3 tested at impulses per areal mass o I =M¼6 m s (a) and I =M¼227 m s (b), respectively. C-scans obtained or the two acesheets o sandwich panel 2-3 tested at I =M¼495 m s, (c) waterside acesheet (gate s 2 ) and airside acesheet (gate s 4 ). Gates are deined in Appendix B. C-scans o the panels were perormed by Sonoscan Inc., using a D95 TM C-SAM s apparatus. The scans were done in water-immersed conditions, with MHz transducers. The scan speed was 38 mm/s and the monitored area was 82 by 82 mm covered by 768 by 768 pixels. This corresponds to a pixel size o.23 mm, which is suicient to capture local variation within the panel section, o diameter 2L¼52.4 mm, subjected to the underwater blast loading. Details on the technique and employed data reduction procedures are discussed in Appendix B. A summary o the main results obtained with the ultrasonic scanning technique are given in Fig. 8. At low impulse (subplot (a)), solid panels did not exhibit localized eatures associated with delamination, which was conirmed by optical microscopy on cross-sectional cuts (see below). At higher impulses per areal mass, I =M ¼ 227 m s (subplot (b)), a bright ring on the periphery was identiied, which corresponds to bending induced delamination near the clamped boundary (the signal appears bright because o shadowing above the scanned region). Darker patches correspond to delamination within the mapped gate, while a brighter hourglass-shaped patch is noticed in the center o the panel where delamination is not present. Hence, the non-destructive evaluation (NDE) technique revealed delamination eatures, at suiciently high impulse, that are more prominent on the periphery o the panels. The same type o delamination was ound on the airside o sandwich panels subjected to I =M ¼495 m s (Fig. 8c), although its extent was much smaller. This is a remarkable sign o perormance improvement resulting rom the sandwich construction since delamination is reduced while the impulse per areal mass was doubled. At the same time, a cross shaped eature was revealed on the waterside, and correspond to visible cracks. We should note here that this type o crack is oten not detrimental to the overall perormance o the sandwich panels, as long as their integrity is preserved. In the ollowing section, we report post-mortem optical microscopy observations that will provide conirmation and urther insight into the trends inerred rom the pulse-echo scans Post-mortem microscopy Ater having perormed non-destructive evaluation with the pulse-echo technique, ive panels (monolithic - and -3 and sandwich 2-3, 2-4 and 3-2) were sectioned along a diameter, oriented along the or 9 axis, using a water jet machine. The two solid panels - and -3 were chosen to show the inluence o the impulse magnitude, and because their dynamic delection responses exhibited signiicant dierences (see Fig. 4). The sandwich panels 2-3 and 2-4 were o interest because visible iber ailure was observed post-mortem but at dierent locations. The sandwich panel 3-2 was o interest because o its asymmetric coniguration and because the panel was subjected to the highest tested impulse. Photographs o the panel waterside taken beore the cut are shown in Figs. 9a, 3a, 4a, 7a and 8a or experiments -3, -4, 2-3, 2-4 and 3-2, respectively. A dash line was superimposed to the cross section location where the cut was perormed. Cross sectional views taken ater the cut are shown in Figs. 7b, 3b, 4b, 7b and 8b. In some o these crosssections, dierent areas, AM i, where microscopy observations were conducted are shown. Photographs o the cross section o panel - are not reported but are similar in every aspect to the ones reported in Fig. 9 or panel -3. A Nikon inverted DIC microscope Eclipse ME6 was used at 5 magniication, itted with a ProgRes Capture Pro 2.5 cooled CCD camera, to acquire sequence o images on the surace o the dierent panel cross-sections. These sequences covered the areas AM i, and are shown in Figs., 2, 5 and 6. Each individual picture has a resolution o 36 by 24 pixels, with a pixel size o 2.55 mm. Higher magniication pictures were also acquired to image matrix microcracking. Two ailure mechanisms were identiied and analyzed based on the cross-sectional microscopy study. We will start by discussing trends in delamination or monolithic and sandwich panels subjected to increasing impulses. Second, an analysis o matrix microcracking distributions will be conducted or two solid panels, experiments - and -3.

10 632 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) r = L r = A A x y z A-A r = L r = air side AM AM 2 clamping ring 25mm L/3 L/3 2L/3 water side Fig. 9. Optical photography o solid panel tested at I =M¼227 m s (exp. -3). (a) impacted side (waterside) o the panel showing whitened areas within the region subjected to water pressure. The line A A corresponds to the cross-sectional cut. (b) Panel cross section A A showing the steel ring bonded to the composite panel. A permanent delection is observed, with a center residual delection o 5.35 mm. The regions AM and AM 2 correspond to the micrographs reported in Figs. a and 2a, respectively. AM AM Fig.. Optical microscopy pictures in the clamped region AM o solid panels - (a) and -3 (b), tested at I =M¼6 and 227 m s, respectively. Delaminated interaces are clearly observed, which typically propagate somewhat in the clamped region. In the case o panel -, the tip o the delaminated interace is indicated by an arrow. 5 N d /3 r/l 2/3 Fig.. The number o delaminated interaces N d in the monolithic panel -3 tested at I =M ¼227 m s (experiment -3) versus normalized radial position r/l Cross-sectional microscopy: monolithic panels The clamping regions o monolithic panels - and -3 are shown in Fig. a and b, respectively. These regions cover around one quarter o the panel radius, L. The edge o the clamping ring, located at r¼l, corresponds to the white dashed line. Tested at an impulse o I =M¼6 m s, panel - exhibits a single delamination plane located at the panel hal thickness. The delamination propagated within the clamped region o the sample, over a distance o approximately 5 mm.

11 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) AM 2 AM 2b AM 2 AM 2b Fig. 2. Optical microscopy pictures in the center region AM 2 o solid panels - (a) and -3 (b), tested at I =M¼6 and 227 m s, respectively. These sets o micrographs highlight the presence o delamination mostly located in the middle plane o the panel in both cases. (c) Magniied view o the central region AM 2b o panel -3 showing matrix cracking patterns in several abrics. A A-A A y x z air side water side Fig. 3. Post-mortem photography o monolithic panel -4 tested at I =M ¼34 m s : (a) waterside acesheet photography showing the location o the cross section A-A and (b) cross sectional view highlighting massive iber ailure and delamination. The delamination path is not constrained to a unique interlaminate interace but it rather jumps across interaces within the laminate. A much larger number o delaminated interaces, N d, is ound in panel -3 tested at a higher impulse o I =M ¼227 m s. At the clamping edge, r¼l, eight delaminated interaces are present but the delamination intensity and N d decrease as the radial coordinate r decreases. The number N d ¼8 corresponds to the number o interabric interaces, since nine abrics were used in the panel construction. Once again, the delaminated interaces are not strictly ollowing the interabric interaces but more generally ollowing interply interaces, crossing plies reely all over the monitored cross section. In the central regions o the two solid panels, less noticeable dierences are observed in delamination trends (see Fig. 2a and b). In panel -, a straight delaminated plane at hal thickness is clearly observed over the whole area AM 2 (Fig. 2a). In panel 3, multiple delaminated planes coexist but are also located mostly at hal thickness and in the upper region o the cross section. Unlike the delamination pattern observed in the clamping region, at r¼, N d ¼ in both cases. The delamination observed in the solid panels is consistent with bending and stretching states (Jones, 989). Bending o circular plates is maximal in the clamping region, inducing shear deormations, while equi-biaxial stretching is prominent in the plate center. In panel -3, the higher delamination observed at the clamping region decreasing progressively toward

12 634 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) B r = r = L 5mm B x y z air side r = r = L B-B AM 6 clamping ring water side AM 5 AM 4 AM 3 2L/3 L/4 25mm Fig. 4. Optical photography o sandwich panel 2-3 tested at the impulse o I =M ¼495 m s, ater the experiment. (a) Impacted side (waterside) o the panel showing cross-shaped racture within the central region, together with a ew debonded ibers in the clamped area. The proile B-B corresponds to the cross-sectional cut. (b) Panel cross section B-B showing the plastically deormed steel ring debonded rom the composite panel. Permanent center delections are observed (5.65 mm or the airside acesheet and 4.2 mm or the waterside acesheet). The areas AM i correspond to the micrographs reported in Figs. 5 and 6. (c) Magniied view o the cross section B-B taken in the panel center section. Arrows highlight the presence o slanted cracks in the oam. AM 4 AM 3 Fig. 5. Optical microscopy pictures or sandwich panel 2-3, tested at I =M¼495 m s, in the airside clamped region AM 4 (a) and waterside clamped region AM 3 (b). The airside clamped region shows delamination patterns, while no delamination can be observed on the waterside. AM 6 AM 5 Fig. 6. Optical microscopy pictures or sandwich panel 2-3, tested at I =M¼495 m s, in the airside central region AM 6 (a) and waterside central region AM 5 (b). The airside clamped region seems intact, while massive delamination and iber ailure can be observed on the waterside acesheet.

13 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) AM A r = L r = + A mm x y z A-A air side AM water side Fig. 7. Post-mortem images o symmetric sandwich panel tested at I =M¼482 m s (exp. 2-4): (a) intact waterside acesheet image and location o the cross section A-A, (b) cross sectional view highlighting severe delamination and boundary racture in the airside acesheet and (c) magniied view o area AM at the vicinity o the steel ring. A mm x y z A A-A air side clamping ring water side Fig. 8. Post-mortem images o asymmetric sandwich panel tested at I =M¼592 m s (exp. 3-2): (a) waterside acesheet image showing cross pattern and location o the cross section A-A; (b) cross sectional view revealing extensive delamination in the airside (see white arrow) and core crushing; and (c) magniied view o the cross section in the panel center showing delamination and iber racture in the water acesheet. the center is a direct consequence o the bending mode, which develops at the early stages o deormation (see Fig. 23). For this panel, the evolution o the number o delaminated interaces N d, as a unction o normalized position, is shown in Fig.. It is worth noting that observations rom NDE are consistent with delamination observed by post-mortem microscopy. Indeed, delamination laws are the only detectable deects rom the NDE signatures. Matrix cracking was not captured due to their size and orientation. Both, NDE and microscopy techniques reveal that delamination is more signiicant in the boundary than in the center o the panel beyond a threshold applied impulse. In the case o the monolithic panel tested at I =M¼34 m s (exp. -4), a cross-shaped damage region extending the ull length, 2L, is observed in Fig. 3a. The cross sectional view o the panel shows that this macroscopic maniestation o ailure is associated with severe delamination and massive iber racture along the path o the macroscopic cracks Cross-sectional microscopy: sandwich panels Optical microscopy was also perormed or several o the tested sandwich panels. Fig. 4 shows optical images o sandwich panel 2-3 tested at I =M ¼495 m s. An image o the waterside acesheet is shown in Fig. 4a. A cross-shaped racture pattern is observed in the central region o the panel. The residual deormed shape and extend o core compaction are shown in Fig. 4b. Details o the waterside acesheet iber racture and delamination, as well as cracks in the PVC core, are shown in Fig. 4c. Microscopy images o the clamped region are shown in Fig. 5a and b and images o the central region are shown in Fig. 6a and b. Similarly to solid panels, a bending induced delamination can be observed in the airside acesheet o the sandwich panel, in contact with the clamping ring. However, the delamination extent o approximately 3.5 mm is small when compared to the one observed in solid panels subjected to similar levels o impulse (Fig. b). A ring that

14 636 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) corresponds to the delaminated interaces observed by microscopy was also revealed by NDE in the airside acesheet o panel 2-3 (see maps s 4 and s 6 in Fig. 29). No delamination is observed near the support on the waterside acesheet, Fig. 6b. Interestingly, edge bending eects are limited on the waterside, as a result o extensive oam crushing. Similar behavior was observed in sot core steel sandwich panels tested with the same experimental apparatus (Mori et al., 29). In all solid and sandwich panels, the presence o delamination corresponds to bending eects with transverse waves traveling rom the support to the panel center. This bending eect was also revealed by real time measurement during the experiment, and is provided by classical closed orm solution o panels, clamped at the edges, and subjected to impulsive loads (Jones, 989). Comparison o Figs. and 5 shows that the delamination extent is signiicantly reduced in sandwich panels when compared to solid panels. In the central region o the sandwich panel, massive ailure (delamination, matrix cracking and iber racture) is observed on the waterside acesheet, see Figs. 4c and 6b. In addition to extensive damage in the waterside acesheet, two slanted cracks propagated in the core over a ew millimeters (see arrows in Fig. 4c). Despite the extensive damage exhibited by the waterside acesheet, in the central region, no signiicant cracking or delamination could be ound on the airside acesheet (Fig. 6a). The eect o decay time on ailure modes can be assessed when comparing experiments 2-3 (I =M ¼495 m s, p ¼.5 MPa, t ¼55 ms) and 2-4 (I =M ¼482 m s, p ¼62.4 MPa, t ¼87 ms). As highlighted in the discussion o Fig. 4, in experiment 2-3 the composite panel exhibits a cross shape macroscopic crack on its waterside acesheet, while the airside acesheet remains intact. By contrast, in sandwich panel 2-4, no appreciable iber ailure is observed on the waterside acesheet o the specimen, Fig. 7a. Likewise, no signiicant core crushing in the central region, typical o strong cavitation associated to luid structure interaction, is observed. On the airside, the acesheet exhibits a high degree o delamination and iber ailure along the periphery, where the steel ring provides inertial support. The eect o a non-symmetric weight distribution in sandwich construction was assessed through comparison o experiments 2-4 (I =M ¼482 m s, p ¼62.4 MPa, t ¼87 ms) and 3-2 (I =M ¼592 m s, p ¼75.8 MPa, t ¼88 ms). These two experiments were both conducted with long pressure decay time but the asymmetric panel was subjected to a higher impulse. As seen in Fig. 8, a cross-shaped racture pattern was induced on the waterside acesheet. Delamination on the airside acesheet o the asymmetric panel is noticed but much reduced when compared to the symmetric panel (experiment 2-4). However, extensive oam crashing and iber racture on part o the boundary o the airside acesheet and in the center o the water acesheet are observed (Fig. 7b and c) Quantiication o stress-induced matrix cracking Matrix damage in composites materials results rom iber/matrix interactions and can precede delamination (Marshall et al., 985). Matrix damage and delamination are the two most signiicant damage mechanisms in composite materials; thereore their spatial characterization is essential in understanding the perormance degradation o impacted structures. At high stresses, when matrix strength is exhausted and delamination has occurred, ibers can ail leading to ultimate ailure o the structure. Hence, assessing matrix damage and particularly its distribution is an essential part o the damage identiication. It also provides useul inormation about the structural state o the panel ater having been subjected to impulsive loading. Macroscopically, matrix cracking results in a loss o structural stiness since local load bearing capacity is reduced. A literature review o research conducted to build relationships between matrix cracking and stiness loss was reported in (Lim and Hong, 989), which presents several inite racture mechanics approaches encompassing shear lag models (Lim and Hong, 989) and the variational approach proposed by Hashin (985, 986). All these analyses were developed in the ramework o symmetrical cross-ply laminates loaded in tension in which cracks appear in the transverse layer. Hashin s method provided an accurate prediction o the stiness loss o tensile samples that were successully compared to experiments conducted on samples o dierent materials. It also provides a local estimation o stresses, and predicts the degradation o the transverse modulus and the shear modulus. Thereore, in this work we will employ Hashin s model. The reader interested in the ormulation o the model can reer to Hashin (985). In short the energy attributed to the crack perturbation is ormulated or compatible stresses, and the complementary energy theorem is applied to ind stress intensity actors and residual stiness coeicients or a given intercrack distance. Evolution o matrix cracking in laminated composite typically stops when the Characteristic Damage State (CDS) is attained. Observed experimentally (Abrate, 99), such state corresponds to a saturation in crack density (minimal distance between cracks) and total stiness reduction o a laminate cracked layer. Hashin s model is able to capture this asymptotic behavior with high precision due to the ormulation o close crack interaction. From high magniication images, acquired using optical microscopy, it was possible to measure the crack spacing as a unction o radial position and ply in the cross-section o specimens - and -3. The crack distribution was identiied separately on each lamina with ibers crossing the observation plane aligned with the orientation o the layup. For this reason, cracks were only counted in plies o orientation 45,9 and 45 (3 every 4 plies). Intervals o 4 mm were deined and a crack density c (number o cracks per mm in the direction transverse to the ibers) was obtained or each measured lamina and each interval covering the radius. Cracks were only counted when showing a suicient contrast on the picture and crossing the lamina entire thickness. To relate the measured crack density, c, and crack distance 2a, to the damage variable, d, we use Hashin s ormulas or axial stiness degradation.

15 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) According to the variational approach introduced by Hashin (985), the longitudinal stiness E x (c) o a cross-ply /9/ laminate can be computed rom the undamaged (initial) stiness E x, the axial and transverse moduli EA and E T, the axial and transverse Poisson ratio n A and n T, and the axial and transverse ply thicknesses t and t 2 according to the ollowing set o equations: r E x E þ 4 x E T k2 ZðlÞaða 2 þb 2 Þt c, when ða=t Þb, ð3þ E r þ k2 þ, when ða=t x E Þ-, ð4þ x lþ E T le A with k ¼ t h þ ET E A t 2h p ¼ðC 2 C Þ=C 22 ZðlÞ¼ð3l 2 þ2lþ8þ=6 q ¼ C =C 22 l ¼ðt 2 =t Þ, h ¼ t þt 2 a ¼ p =4 cosðy=2þ b ¼ q =4 sinðy=2þ piiiiiiiiiiiiiiiiiiiiiii y ¼ tan ð4q=p 2 Þ C ¼ =E T þ=l E A C 2 ¼ðn T =E T Þðlþ2=3Þ n A l=3e A C 22 ¼ðlþÞð3l 2 þ2lþ8þ=6e T C ¼ 3 ð=g T þl=g A Þ ð5þ The stiness reduction given by Eqs. (3) and (4) is valid or cross-ply laminates. While Eq. (3) gives the lower bound o n the degraded stiness or ar apart cracks, Eq. (4) provides the expression o degraded stiness E x associated to the Characteristic Damage State (CDS) when the smallest intercrack distance is observed and the stiness loss in the cracked layer is maximal (d¼). One diiculty o quantiying damage in the material tested in this work is the absence o analytical solutions rom matrix cracking in non-orthogonal laminates, which lack symmetry. However, inite element simulations have been compared to experiments on quasi-isotropic laminates (Singh and Talreja, 29), and comparable matrix cracking mechanisms to those in orthogonal laminates were predicted. For this reason, the Hashin model or orthogonal laminates is assumed to provide a reasonable estimation o damage induced by matrix cracking in a quasi-isotropic laminate. Relationships between matrix damage d and crack density c in each ply o the quasi-isotropic abric used in the composite panels studied in this work could then be obtained. In the specimens investigated here, the thicknesses t and t 2 o the axial and transverse plies were chosen to be.225 and.75, respectively, based on a laminate thickness h o.6 mm, corresponding to the abric thickness, and a ply thickness o one quarter the abric thickness. Eqs. (3) and (4) were then employed using the lamina elastic constants E T, E A, n T, n A, G T and G A listed in Table 3. These material coeicients were obtained rom Daniel et al. (26). E x ¼5.7 GPa is obtained experimentally or our quasi-isotropic layup. In the ollowing, Eqs. (3) and (4) are considered to be true at the limit, providing thus a lower bound estimation o degraded stiness. The local matrix tensile damage variable d o the cracked ply is inally obtained by interpreting the stiness reduction o the cross-ply lamina using the relationship: dðcþ¼min E x E x, : ð6þ E x E x n Note that the damage variable is bounded by d(c)¼ at the initial state (E x ¼E x) and d(c)¼ when Ex re x (complete stiness loss o the cracked layer). The matrix damage d as a unction o radius r, or specimen -3, is given in Fig. 9. In this plot, 8 sets o points and curves are shown corresponding to the abrics i that were measured using microscopy. Among the 9 abrics o the monolithic abric, corresponds to the waterside while 9 corresponds to the airside o the panel. Each point corresponds to an averaged d computed in each 4 mm long interval within a given abric. Some scattering is observed in the data, which could be attributed to measurement noise and low typical number o cracks per ply in each measured interval (2 6 in average). Smoothing splines are plotted together with the experimentally sampled data to better represent variations in mean damage values. Such variations are noticeable: higher d values close to (complete loss o stiness) are observed in the central part o the specimen or or/lo/3, while damage progressively diminishes towards the supported boundary. A high damage is also seen in the vicinity o the supporting ring (r/l¼), which indicates some eect o local shear and Table 3 Lamina elastic constants or E-glass/vinylester. Coeicient Axial stiness E A (GPa) Poisson ratio n A Shear modulus GA (GPa) Value Coeicient Transverse stiness E T (GPa) Poisson ratio n T Shear modulus G T (GPa) Value 2 ðe T =E A Þn A ¼.862 3

16 638 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) matrix damage d matrix damage d Normalized position r/l Normalized position r/l 2 Fig. 9. Distribution o matrix damage in each analyzed abric i in the composite monolithic panel tested at I =M¼227 m s (exp. -3) as a unction o the normalized radial position r/l: (a) waterside abrics and (b) airside abrics. matrix damage d matrix damage d Normalized position r/l..2.3 Normalized position r/l Fig. 2. Distribution o matrix damage, as a unction o the normalized radial position r/l, in each analyzed abric i o the composite monolithic panel tested at I =M ¼6 m s (exp. -): (a) waterside abrics and (b) airside abrics. stress concentrations induced by the support. It is interesting to notice that delamination (see Fig. ) and matrix damage vary in opposite directions along the radius o panel -3: the matrix damage d(c) is the highest in the center where biaxial stretching is maximal and decreases towards the boundary o the panel, A higher number o delaminated interaces N d are observed near the boundary, where bending-induced transverse loading is maximal, with a continuous reduction towards the panel center. The damage distribution was also computed in the central section o the monolithic panel - tested ati =M¼6 m s (see Fig. 2). A signiicant reduction in matrix damage, d, as the normalized position r/l increases can be observed. Dierences between airside and waterside abrics appear: more damage is observed in the airside abrics ( 6 9 ) than in the waterside abrics ( 5 ), which is consistent with the act that stretching is higher on the airside because o the structural response o the panel. By contrast, less variations in damage were observed in experiment 3 (I =M¼227 m s ), where damage values were higher in the central section and very close to. 4. Discussion and concluding remarks An assessment o the perormance o composite monolithic and sandwich panels was presented in this article. Using a luid structure interaction experimental apparatus, the delection proile histories o composite panel specimens were recorded by shadow Moiré and high speed photography. The perormance o each panel was identiied by plotting the peak center delection versus applied impulse per areal mass. A linear relationship between center peak delection versus applied impulse per areal mass was obtained or composite monolithic panels, similar to the behavior experimentally observed or steel monolithic panels (Rajendran and Narashimhan, 2; Xue and Hutchinson, 23; Nurick and Martin, 989; Nurick and Shave, 996; Teeling-Smith and Nurick, 99; Rajendran and Narasimhan, 26). For composite sandwich panels, the relationship between center peak delection versus applied impulse per areal mass is also linear but

17 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) with a higher slope and negative intercept (see Fig. 3). Perormance improvement o sandwich versus solid composite panels was, thereore, established specially at suiciently high impulses per areal mass (I =M 42 m s ). The perormance o composite monolithic panels in terms o impulse-delection was similar to the one observed or A34SS I-beam core steel sandwiches, which was identiied as an optimal core topology among all the investigated designs (Mori et al., 27, 29; Hutchinson and Xue, 25; Dharmasena et al., 2; Liang et al., 27). By contrast, composite monolithic panels perorm better than A34SS panels with honeycomb or pyramidal cores. This highlights the properties to weight advantages o composite solid panels. Because o the low weight o glass-polymer composites, higher thicknesses h are obtained at ixed areal mass, which results in a higher bending stiness. The study also shows that dierent through thickness weight distributions, asymmetric versus symmetric, do not result in signiicant perormance improvements. In this investigation, symmetrical (test 2-2) and asymmetrical (test 3-) sandwich panels showed a similar response when subjected to comparable impulses per areal mass, 35 and 35 m s, respectively. This is in part because even when a thinner ront sheet results in overall less transmitted momentum (Vaziri et al., 27; Xue and Hutchinson, 24), enhanced luid structure interaction eect, the kinetic energy that has to be absorbed by the structure is higher. Severe ailure was observed in solid panels subjected to impulses per areal mass I =M 43 m s. Extensive iber racture occurred in the center o the panels, where cracks ormed a cross pattern through the plate thickness, and delamination was very extensive on the sample edges due to bending eects. Similar levels o damage were observed in sandwich panels but at a much higher impulse per areal mass. The eect o pressure history was illustrated by the perormance characterized through experiments 2-3 and 2-4. While both panels were subjected to approximately the same impulse per areal mass, although with dierent peak pressure and decay time, their perormance and ailure modes exhibited distinct eatures. For the shorter decay time and higher peak pressure, a higher peak delection was observed and ailure occurred in the waterside acesheet. For the longer decay time and lower peak pressure, ailure was due to shear tearing near the boundary resulting in delamination and iber ailure on the airside acesheet. The ailure mechanisms, damage types and delection trends are summarized in Table 4. The table highlights a ew correlations, e.g., the correlation between iber damage and development o visible cracks. In the case o solid panels, conical delection proiles correlate with panel massive ailure including ormation o cracks, while more parabolic shapes were not associated to such ailure. The experimental work reported in this paper encompasses not only characterization o the dynamic perormance o monolithic and sandwich panels, but also post-mortem characterization by means o both non-destructive and destructive techniques. Firstly, a non-destructive evaluation (NDE) was conducted by means o a C-scan pulse-echo technique. Then, optical microscopy was conducted on samples obtained by cutting the panels along their diameter. The NDE pulse-echo technique was employed to identiy the presence o delamination on the entire panel. From the pulse-echo technique, qualitative inormation was obtained on the distribution o laws in the panels. In solid panels, laws appeared with more clarity at higher impulses (panel -3). Deects were detected at dierent depths, mostly in the periphery o the panel. When screening the specimen rom the boundary to the center, deects were detected closer to the middle plane o the Table 4 Summary o experiments. Geometry Labels I =M (m s ) Normalized peak delection d max /L Delection rate b Delection proile shape Failure c Damage d Solid panel Parabolic M Parabolic M Conical Mþ, Dþ center Conical Total (cracks) Mþ, Dþ, Fþ total Conical Total (cracks) Mþ, Dþ, Fþ total Symmetrical sandwich Asymmetrical sandwich 2- WS a Parabolic M AS a D 2-2 WS Parabolic cracks (boundary) M, F-, AS D 2-3 WS Parabolic cracks (center and M,Dþ,Fþ boundary) AS D Parabolic 3- WS Parabolic cracks (boundary) M,F AS D 3-2 WS Parabolic total Mþ,Dþ,Fþ AS shearing (boundary) Mþ,Dþ,F a WS and AS stand or the panel airside and waterside, respectively. b The delection rate is represented by a qualitative number varying between and 5 (rom the lowest to the highest rate). c Absence o ailure corresponds to a minus sign. d Each damage mechanism is labeled with a letter: M stands or matrix damage, D or delamination and F or iber damage. Damage intensity is described with plus and minus signs.

18 64 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) panel. In sandwich panels, the most signiicant eature detected by NDE was a delamination ring ( mm wide) on the airside o the panel. Delamination on the waterside acesheet was conined to the center region where the luid structure interaction eect is dominant. The technique did not provide precise inormation on through thickness position and total number o delaminated interaces. Such inormation was later obtained by optical microscopy perormed on selected cross-sections together with a quantitative estimation o matrix damage or dierent applied impulses. Matrix damage was estimated rom measured crack densities by applying a variational ormulation introduced by Hashin (985). The quantiied matrix damage was maximal in the center o solid panels, where biaxial stretching is the highest, and decreases towards the boundary o the panel. At low impulse (experiment -, I =M ¼6 m s ) the damage distribution was spread through the thickness. At higher impulses damage was higher on the airside where higher superposition o bending and stretching occurred. At suiciently high impulses (e.g., experiment -3, I =M ¼227 m s ), more uniorm through thickness damage was identiied with values in some abrics reaching d¼ at the center and near the panel edge. This saturation is likely associated with an exhaustion o dissipated energy by matrix damage. This is consistent with the pronounced iber ailure observed at high impulses (experiments -4 and -5, I =M 43 m s ). The experimental data here reported should be highly useul to those interested in developing models capable to predict the dynamic behavior and damage evolution o iber composite laminated panels o solid and sandwich construction. Models or the experiments here reported are currently being developed (Latourte et al., 29; Espinosa et al., 29) and employed to assess their predictive capabilities. A detailed description o the model calibration procedure, comparison to experimental results and assessment o their predictive capabilities will be presented in a companion paper. Acknowledgments This research was carried out under the inancial support o the Oice o Naval Research (ONR) under grant number N The support and encouragement provided by Dr. Rajapakse through the study is greatly appreciated. D. Grégoire is grateul to the French Ministry o Deense (DGA/D4S) or its support through Grant no. 862 to visit Northwestern University as a research associate. We acknowledge Alex Ray at Sonoscan Inc. or conducting the pulse-echo C-scan measurements. Special thanks go to Arnaud Blouin or the assistance provided to set up and conduct the Fluid Structure Interaction experiments during his Northwestern internship. Appendix A. Delection proile histories in solid and sandwich panels A.. Deormation histories in solid panels A set o shadow Moiré images recorded during experiment -2 is shown in Fig. 2. Using the ringe processing technique introduced in Espinosa et al. (26), delection proiles associated with each image were obtained. The same procedure was used in all experiments. Figs. 22 and 23 present, respectively, the delection proile histories (increasing and spring back phases) obtained by the shadow Moiré method or experiments - and -3 (impulses per areal mass I =M o 6 and 227 m s, respectively). Delection proiles were computed or each experiment but here we plot only the complete proile evolutions related to experiments - and -3 to highlight dierent eatures associated with variations in impulse level. Both delection d and dimensionless delection d/l versus the normalized radial position r/l are plotted. μs μs 5μs 2μs 3μs 4μs 5μs Fig. 2. Example o high speed camera pictures acquired during the dynamic event. Images shown here correspond to the monolithic panel tested at I =M¼66 m s. Time t¼ is set when the pressure wave reaches the specimen.

19 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) Delection δ (mm) µs 52 µs 252 µs Normalized delection δ/l Normalized position r/l Delection δ (mm) inal 352 µs 652 µs 752 µs 452 µs 552 µs Normalized delection δ/l Normalized position r/l Fig. 22. Delection proile history or experiment - tested at I =M¼6 m s : (a) increasing deormation phase and (b) spring back deormation phase, including inal proile measured post-mortem. Delection δ (mm) Delection δ (mm) µs 92 µs 242 µs Normalized position r/l µs 292 µs 392 µs 492 µs 242 µs inal Normalized position r/l Normalized delection δ/l Normalized delection δ/l Fig. 23. Delection proile history or experiment -3 tested at I =M¼227 m s : (a) increasing deormation phase and (b) spring back deormation phase, including inal proile measured post-mortem.

20 642 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) Delection δ (mm) Delection δ (mm) Normalized position r/l µs 75 µs 525 µs inal 325 µs 325 µs 275 µs 425 µs 225 µs Normalized delection δ/l Normalized delection δ/l Normalized position r/l Fig. 24. Delection proile histories corresponding to experiment 2-3 tested at I =M¼495 m s : (a) increasing deormation phase and (b) spring back deormation phase, including inal proile measured post-mortem. Parameters are normalized by the composite panel radius L¼76.2 mm. The increasing and spring back phases o the deormation are separately plotted or the sake o clarity. It is interesting to note that in experiment - (Fig. 22), the deormed shape is more parabolic, which is an indication o more bending-type deormation. By contrast, in experiment -3 (Fig. 23) ater 92 ms the panel deormed shape is more conical consistent with a membrane dominated deormation regime. A.2. Deormation histories in sandwich panels Fig. 24 shows delection proile histories (increasing and spring back phases) obtained by the shadow Moiré method or a symmetrical sandwich panel, experiment 2-3 with impulse per areal mass o 495 m s. Both delection d and normalized delection d/l versus dimensionless radial position r/l are plotted. The radial position is normalized by the composite panel radius L¼76.2 mm. Similar delection proile histories were obtained or all the tested sandwich panels. Appendix B. Non-destructive evaluation technique and damage maps In the NDE technique introduced in Section 3.2, or each pixel, a pulse is emitted by a MHz transducer. The generated wave propagates through the scanned material and detects changes in acoustic impedance. For example, a large planar void (delamination) will relect the entire wave. The relected signal is captured by the same transducer used or emission. The scanning sequence used in solid and sandwich panels is illustrated in Fig. 25a and b, respectively. Scanning rom both waterside and airside o the FSI experimental setup were perormed. An example o two signals I s recorded by the transducer at dierent locations is shown in Fig. 26a. The irst noticeable spike corresponds to the interace between the water medium and the sample. Several spikes ollow, o decaying amplitude. The captured signals are decomposed into time domains reerred to as gates 6 and labeled {s i, i¼,y,6}. Within each gate, the pixel value I R is taken as the absolute value o the signal peak ampliied by a gain actor calibrated such that an intensity I R o corresponds to a total relection o the signal. Such conditions are obtained when a large void (low impedance medium) is encountered within the gate. On the other hand, an intensity I R o corresponds to the absence o signal relection. This will occur when the scanned medium is uniorm within the gate (no change in impedance), but also i a deect above the current gate already relected the signal (shadowing eect). As a consequence, the pulse-echo technique will detect the outer envelope o deects in the composite panel. In other words, when delamination occurs at multiple interaces, only the outermost delamination patches will be seen by the pulse-echo technique.

21 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) z (mm) 3-3 s s 2 layup by abric scan sequence s 4 s s 5 3 s6 airside waterside scan sequence z (mm) oam core layup by abric s s 2 s 3 s 6 s 5 s 4 airside acesheet waterside acesheet Fig. 25. Representation o the gate sequence s i or C-scans perormed by pulse-echo technique on monolithic (a) and symmetrical sandwich (b) panels. The characteristic times related to the gates s i are detailed in Table 5. For illustrative purpose, the abrics i are shown on the graphs. I s (P,t) I s (P 2,t) s 4ns/div s s I I P P I Fig. 26. (a) Relected signals I s obtained at two dierent pixels positions P and P 2 or solid panel -2. The panel/water interace corresponds to the red dashed line, and the solid red lines deine the gate bounds. (b) C-scan or gate s 2 and location o pixel positions P and P 2. (For interpretation o the reerences to color in this igure legend, the reader is reerred to the web version o this article.) Table 5 Gates selected to generate the C-scan maps rom the pulse-echo scans. Times t i and t correspond to the beginning and the end o each record. Gate# t i (ms) t (ms) Solid panels Sandwich panels z i () (mm) z () (mm) z i(2) (mm) z (2) (mm) s s s s s s Each specimen was imaged separately rom both its waterside and airside. For each scan, the relected signal captured by the transducer at each position was processed to generate three distinct images corresponding to dierent gate times summarized in Table 5. These times were then translated into height z assuming a group wave velocity o 239 m/s calculated rom the GRP density and transverse modulus. This assumption is valid here since the wave number is high enough to prevent dispersive eects (Nayeh and Anderson, 2). From the dierent gate times and the group velocity, one can obtain relative scan depths. The panel surace position was irst identiied rom the signal to obtain the absolute scan depth z given in the coordinate system o the panel. In the case o monolithic panels, the surace was located using the signal I s plotted in Fig. 26, and assuming that the irst spikes correspond to the specimen surace. In the case o sandwich panels, the position o the surace was calculated by correlating the measured I R maps and the microscopy analysis presented in Section 3.3.

22 644 F. Latourte et al. / J. Mech. Phys. Solids 59 (2) s s2 s 3 I R..8.6 s 4 s 5 s 6.4 y z x.2. Fig. 27. C-scans obtained or experiment - at the impulse per areal mass o I =M¼6 m s, waterside (gates s s 3 ) and airside (gates s 4 s 6 ). s s 2 s3 I R..8.6 s 4 s 5 s z y x. Fig. 28. C-scans obtained or solid panel tested at the impulse per areal mass o I =M¼227 m s, exp. 3, waterside (gates s s 3 )andairside(gatess 4 s 6 ). s s 2 s 3 I R..8.6 s 4 s 5 s 6.4 y z x.2. Fig. 29. C-scans obtained or sandwich panel 2-3 tested at the impulse per areal mass o I =M¼495 m s, waterside (gates s s 3 ) and airside (gates s 4 s 6 ). The scans corresponding to the monolithic panel - tested at low impulse (I =M ¼6 m s ) are shown in Fig. 27. The maps have been cropped to conorm to the circular section o the panel subjected to water pressure during the FSI experiment. All images show a textured pattern consistent with the abric weave o the composite. No signiicant eature except the texture can be noticed or the outermost gates s and s 4, and most o the eatures are seen in gates s 2 and s 6.As illustrated in Fig. 25, there is an overlap between these two gates, which could explain the similitude in the observed I R patterns. Although the behavior o the material is expected to be isotropic (the layup is quasi-isotropic) and the applied impulse is symmetric, the I R patterns (associated to delamination) are asymmetrical and are more pronounced in the top region o the panel. The scans corresponding to the monolithic panel tested at higher impulse (I =M ¼227 m s, exp. -3) are shown in Fig. 28. I R maps corresponding to the outermost gates s and s 4 show a bright ring in the periphery. These low values o I R