Numerical and experimental blast response characterization of sandwich composite structural panels

Abstract

Experimental blast response and quasi-static material property data were obtained for E-glass and carbon face skin sandwich composite panels with balsa, polyvinyl chloride foam, and TYCOR® cores. The pressure versus impulse (P–I) curve methodology enabled the generation of a database of performance envelopes for these sandwich composite panel configurations under different blast loading scenarios. The strength versus deformation properties of various undamaged sandwich composite panels are established numerically and idealized for single-degree-of-freedom modeling. Results show good correspondence between model predictions and experimental results for performance evaluation of the various sandwich composite structural panel configurations that were investigated.

Keywords

Blast sandwich composite panels finite element analysis

Introduction

The goal of this study is to make use of available experimental blast and shock response data for the performance prediction of sandwich composite panels under a wider range of operational loading conditions and threat scenarios, which would facilitate design decisions at the ship superstructure-system level. The available experimental data, which is limited to only specific blast and shock loading scenarios, is used for validating the proposed reduced order computer simulation methodology.

Several detailed studies have been conducted on the blast and shock response of sandwich composite panels [1 –5]. These studies have examined the response and various failure modes of the panels such as core crushing, delamination, bending, and shear response. The focus of these studies has largely been limited to the response of a composite sandwich panel to a unique blast or shock loading scenario.

Our study focuses on implementation of the P–I (pressure vs. impulse) curve computational methodology to enable exploration of the design space, and for evaluating the response of available sandwich composite panel configurations to various blast loads. An attempt has been made to validate the computational methodology for predicting the performance of various sandwich composite panels based on limited available experimental data corresponding to specific blast load histories.

The P–I (pressure–impulse) diagram shown in Figure 1 relates a specific damage level to a combination of blast pressure and impulse imposed on a particular structural element, and allows the reduced order modeling of sandwich composite panel systems. P–I curves are also known as iso-damage curves with each curve representing a certain response level such as mid-span deflection or rotation at supports, etc.

In a particular threat scenario, the pressure and impulse acting on a structure can be determined using scaling laws based on the distance of the structure from the blast source [6]. Knowing the distribution of pressure and impulse due to a specific blast scenario, the damage to individual components in terms of ductility demand can then be determined from the P–I chart [7, 8], and can also be further mapped on to a structure consisting of many such components.

Previous research conducted at the University of Mississippi on nano-particle reinforced composites for critical infrastructure protection involved the evaluation of strength and deformation capacity of civil infrastructure components subject to blast and extreme loading [9]. Pressure vs impulse (P–I) curves were used to represent estimated damage levels in components subjected to blast or shock loadings. The adopted procedure and reflected blast pressure vs distance relation followed the TM 5-1300 Joint Forces military guidance [6]. A database of P–I curves for reinforced concrete components of various cross sections and reinforcement ratios was developed, including the benefits of nano-particle reinforcement. These simulations allow the planner to determine the likely location and extent of damage in building structures subject to blast loadings. This simplified methodology used for rapid damage and vulnerability assessment of critical infrastructure [10], has been adopted here for the performance evaluation of sandwich composite panels for naval ship structural applications [11].

Fabrication of large size sandwich composite panels

Large 1.22 × 1.22 m² (4 × 4 ft²) and 2.44 × 1.22 m² (8′ × 4′) size navy relevant sandwich composites with balsa, polyvinyl chloride (PVC), TYCOR® foam cores, and glass and carbon/vinyl ester face sheets were fabricated for blast, shock, ballistic, and impact characterization by the vacuum assisted resin transfer molding process at the University of Alabama–Birmingham [11]. A total of six variants (two 1.22 × 1.22 m² panels for each variant) were processed with varying face sheet material, core, and stacking sequence. In the work reported here, these six different sandwich composite panels are considered for computational simulation and analysis. The layup and stacking sequence of these panels are described in Table 1.

Table 1.

Sandwich composite panels subjected to blast loads

S. no.	Material code	Face sheet material	Core material	Face skin stacking sequence
1	E1B3VNB1	E-glass/vinyl ester	Balsa core type 9.7 pcf PB standard	[0°/90°]/45°/[0°/90°]/45°/[0°/90°] – five plies
2	C3B3VNB1	T-700 carbon F0E-treated/vinyl ester	Balsa core type 9.7 pcf PB standard	[0°/90°]/45°/[0°/90°]/45°/[0°/90°] – five plies
3	C3B3V0B1	T-700 carbon F0E-treated/vinyl ester	Balsa core type 9.7 pcf PB standard	[0°/90°]/45°/[0°/90°]/45°₂/[0°/90°]/45°/[0°/90°] – eight plies
4	C3P2V0B1	T-700 carbon F0E-treated/vinyl ester	PVC core type 8.1 pcf Divinycell H130	[0°/90°]/45°/[0°/90°]/45°₂/[0°/90°]/45°/[0°/90°] – eight plies
5	E1T7VMB2	E-glass/vinyl ester	Stitched TYCOR	[0°/90°]/45°/[0°/90°]/45°/[0°/90°] – five plies
6	E1T8VPB1	E-glass/vinyl ester	Non-stitched TYCOR	[0°/90°]/45°/[0°/90°]/45°/[0°/90°] – five plies

PVC: polyvinyl chloride.

Blast testing

The six large 1.22 × 1.22 × 0.057 m³ (4 ft × 4 ft × 2.25 in) thick panels with balsa, PVC, TYCOR foam cores, and E-glass and T700 F0E-treatedⁱ carbon face sheets were mounted in the US Army Corps of Engineers ERDC Blast Load Simulator (Vicksburg, MS) such that the top and bottom were fixed and the other two sides were free (Figure 2). The blast simulator uses a He/Air mixture to simulate the effects of an explosion. Stiff steel edge plates of width 152 mm (6″) are used as front and back of the loading frame. These panels were subjected to blast load waveforms of 106.8–129.6 kPa (15.5–18.8 lbf/in²) peak over-pressures and 1.28–1.38 kPa s (185–200 lbf/in² ms) impulse which represents an approximate threat level of 907.2 kg (2000 lbs) of trinitrotoluene (TNT) at 42.7 m (140 ft) (Figures 3 and 4). Four high speed Phantom® cameras with a sampling rate of 1000 frames per second were positioned to capture the response of the rear face of the panel from various angles. A laser range finder (Acuity® AR4000-LIR) was used for recording the deflection time-history of the back face of the panels. Kulite® high pressure ruggedized dynamic response IS pressure transducer (HKS-11-375-100SG(M) series) was used for measuring the pressure time-histories at various locations around the panel (as shown in Figure 3). A HiTechniques® (HT600) data acquisition system sampled the events at 1 MHz and recorded for 131 ms for the pressure gages and 2 s on the laser.

These blast tested panels underwent about 12.7–38.1 mm (0.5–1.5 in.) of mid-point deflection, with no visible signs of external damage.

Figure 5 compares the experimental blast response characteristics of these sandwich panels [11]. To accommodate specific weight requirements, the reported experimental and numerical data have been normalized to areal density (NTAD) (kg/m²); with respect to both mid-point deflection (m/kg/m²) and the energy absorption (kJ/kg/m²) capabilities.

Finite element modeling

Various failure mechanisms may influence the response during blast loading of a sandwich composite panel. This study focuses only on the global flexural mode of failure, with the sandwich composite panel under a fixed–fixed boundary condition at each support. The methodology described here, however, can be easily extended to accommodate other failure modes and boundary conditions.

The SAP2000® [12] finite element (FE) model consists of layered nonlinear shell elements (Figure 6(a)) and allows multiple layers of different thicknesses, each with a different material property, while avoiding shear locking behavior. The shell element also includes the effects of transverse shear deformation. Bulk material nonlinear–stress strain data obtained from quasi-static tensile and compressive testing of corresponding face sheet and core materials, respectively, is used as input for the material constitutive models. The quasi-static experimental data shows some variation in material properties for the face skin and core materials (Figures 7 to 9); hence both the averaged experimental and published material data that are consistent with the SAP2000 program requirements are used as input for the FE model [13 –16].

A parameter study was initially conducted with the FE model, for closely similar boundary conditions, in order to simulate the complex interactions that occur during the actual blast tests (Figure 6(b)). The bolt locations are modeled as being fixed against displacement and rotation. The stiff back plate near the bolts (Figure 2) extends the support to the panel by 76 mm (3″). Figure 6(b) shows the effect of three different boundary conditions (simulating different degrees of restraint at the edge of the back plate) on the quasi-static force–deformation response (stiffness) of the panel. The free boundary condition at the plate edge was finally chosen, based on comparison of dynamic response of the equivalent single-degree-of-freedom (SDOF) system with experimental observations for maximum back-face deflection.

The strength versus deformation capacity of undamaged sandwich composite panels shown in Table 1 are established by nonlinear quasi-static FE analysis [12], with each panel subjected to about 1.5 in. (38.1 mm) of mid-span deformation under displacement control.

Equivalent SDOF idealization

The nonlinear force–deflection relationship obtained from FE modeling for each sandwich panel configuration is initially idealized to an elastic-perfectly plastic force–deflection relationship by equating the work done, which is the area under the respective force–deflection curves (Figures 10 to 15). The equivalent elastic stiffness, k_e, and the equivalent maximum elastic deflection, y_o, are then computed. Since there are non-unique solutions for these idealized curves; in this study the, k_e_, is constrained such that the elastic stiffness of the SDOF system is similar to the initial stiffness of the composite panel obtained from quasi-static nonlinear analysis. Based on these assumptions, the component is idealized as an equivalent SDOF system [17].

The energy balance method (based on principle of conservation of mechanical energy) is commonly employed to obtain the quasi-static and impulsive asymptotes of P–I curves [17]. To obtain the impulsive asymptote, the maximum deflection of an SDOF system subject to a very short duration loading (relative to the natural period) is considered. The total energy imparted to the system is assumed to be in the form of kinetic energy and is equated to the total strain energy stored in the system at its maximum response. The loading is considered to be a pure impulse as shown below

i = F \cdot t_{d}

(1)

This impulse imparts an initial velocity (v) to the system of mass M

v = \overset{•}{y} = \frac{i}{M}

(2)

Therefore, the kinetic energy imparted to the system is given by

K . E . = \frac{{Mv}^{2}}{2} = \frac{i^{2}}{2 M}

(3)

Since resistance is bilinear, strain energy at maximum deflection (i.e. total energy absorbed by the system) is equal to the area under the resistance curve given by

U = R_{max} \cdot (y_{max} - \frac{y_{el}}{2})

(4)

where U is the strain energy at maximum deflection,

R_{max}

the maximum resistance of the equivalent SDOF system,

y_{max}

the maximum deflection of the equivalent SDOF system, and

y_{el}

the maximum elastic deflection of the equivalent SDOF system.

At maximum deflection the external energy is assumed to be completely absorbed by the SDOF system. Thus, equating external kinetic energy (equation (3)) to internal strain energy (equation (4)) and normalizing with respect to area, we obtain

i = \frac{(R_{max} / R_{max} A A) \cdot (\sqrt{2 μ - 1})}{ω}

(5)

where A is the exposed area (36″ × 42″) of the sandwich panel,

μ = \frac{y_{max}}{y_{el}}

the ductility ratio, and

ω = \sqrt{\frac{K}{M}}

K = \frac{R_{max}}{y_{el}}

To obtain the pressure asymptote, the quasi-static regime is considered; where the load can be assumed to be constant before the maximum deformation is achieved. Accordingly, the quasi-static (pressure) asymptote is obtained by equating the work done by the load and total strain energy in the system at maximum deformation as shown below

W = F \cdot y_{max}

(6)

Equating the external energy (equation (6)) to internal energy (equation (4)) and normalizing with respect to area, we obtain

P = \frac{R_{max}}{A} \cdot (\frac{μ - 0.5}{μ})

(7)

P–I curves can also be generated numerically by simulating the dynamic response of the SDOF system to a large number of triangular impulse loads using the implicit generalized Newmark method of time integration in Matlab®. The time duration of the impulse (t_d); the time of rise (t_r), peak load, and the impulse applied onto the component are varied. The maximum values of response to each loading are then computed, and if they match a certain desired response level, they are stored in an array along with the peak pressure and corresponding impulse. A comparison of the energy balance method and the numerical approach (Figure 16) for a typical case shows that similar P–I curves are obtained by both these methods.

However, given the large variation in the material properties of the sandwich panel materials, as well as the complex boundary conditions, only the asymptotes of the P–I curves are computed in this study. These numerical simulations of reduced order enable the rapid construction of iso-damage curves that are suitable for damage prediction over a wider range of blast pressure and impulse combinations.

Results and discussion

The quasi-static and impulsive asymptotes for different ductility ratios (µ_i = y_i/y_o) corresponding to critical stages in component response for the six different composite sandwich panel configurations investigated are plotted in the respective P–I space (Figures 17 to 22). Figure 23 shows the comparative performance, in P–I space, of these six sandwich panel configurations, corresponding to first yield displacement (µ = 1). The simulated responses are observed to concentrate under three groupings corresponding to relatively high, medium, and low overall blast resistance, in terms of the pressure and impulse these panels can withstand before undergoing plastic deformation. The first group consisting of eight ply carbon/balsa (C3B3VOB1) and eight ply carbon/PVC (C3P2VOB1) shows the greatest overall resistance. The second group with five ply E-glass/balsa (E1B3VNB1), five ply E-glass/TYCOR® (unidirectional), and five ply E-glass/TYCOR® (stitched), each of which show relatively moderate resistance to blast. The five ply carbon/balsa (C3B3VNB1) is predicted to have the lowest overall blast resistance of all six sandwich panel configurations, as per this P–I curve methodology.

Nonlinear quasi-static analysis indicates that the five ply carbon/balsa has the highest energy absorption (NTAD) capability followed by five ply E-glass/balsa and five ply E-glass/TYCOR® (unidirectional)-Long., respectively, based on area under the simulated quasi-static load–deflection curves (Figure 24). From these force–deformation simulations it appears that for the eight ply carbon/balsa and eight ply carbon/PVC panels (which have the same face sheet material, but different cores of same thickness) the type of core material dictates the deformation up to yield (NTAD), being higher for PVC foam than the balsa core (Figure 24(a)). However, the energy absorption (NTAD) under quasi-static loading is marginally higher with balsa than PVC core (Figure 24(b)). A similar comparison between the five ply E-glass/balsa, five ply E-glass/TYCOR® (unidirectional) Long., and five ply E-glass/TYCOR® (stitched) Long., (which have the same face sheet materials, but different cores of same thickness) indicates that the five ply E-glass/balsa has the highest deformation up to yield (NTAD) among these three panel configurations, with the five ply E-glass TYCOR® (stitched) Long. panel having the lowest deformation up to yield (NTAD). Figure 24(b) indicates highest energy (NTAD) absorption, among these three, by the five ply E-glass panel with a balsa core. It is also observed that the five ply E-glass TYCOR® (stitched) panel absorbs less energy (NTAD) as compared to the five ply E-glass TYCOR® (unidirectional) Long. panel.

Comparison of all the panels with five ply E-glass face sheets and different cores of same thickness mentioned in the previous paragraph, gives similar values of peak load resistance (Figures 10, 14, and 15). Conversely, the eight ply carbon/balsa panel gives a higher peak load resistance (Figure 11) than a five ply E-glass/balsa panel (Figure 10) (which have the same core, but different face sheet materials of same thickness). This indicates correlation between the type of face sheet material and the peak load resistance of the panel. Overall these trends shown in Figure 24 are similar to those obtained from the experimental blast tests (shown previously in Figure 5).

In the pressure–impulse space, these simulations predict that the eight ply carbon/balsa and the eight ply carbon/PVC sandwich panels would require considerably higher blast pressure and impulse values to cause permanent deformation (as defined by the equivalent SDOF system), when compared with the five ply E-glass/balsa and five ply carbon/balsa and five ply E-glass/TYCOR® (both stitched and unidirectional) sandwich panels. For the experimental blast loading conducted at 106.8–129.6 kPa (15.5–18.8 lbf/in²) peak pressures and 1.38 kPa s (200 lbf/in² ms) impulse, the five ply carbon/balsa panel absorbs the most energy (NTAD) by virtue of plastic deformation at these blast pressure–impulse combinations, while the eight ply carbon/PVC panel absorbs the least energy as it responds more elastically.

Further implications of these findings are that in case of relatively stiffer panels, the supporting structural framing and connections need to be carefully designed such that they allow the maximum demand to be achieved in the panel so as to take full advantage of its energy absorption capability. The framing should also be designed to withstand the higher blast forces transmitted from these panels.

Conclusions

In this study, pressure versus impulse (P–I) curves are developed for sandwich composite panels with a variety of skin and core material combinations, to enable the generation of a database of performance envelopes under various blast loading scenarios.

The strength versus deformation properties of the undamaged sandwich composite panels are established by nonlinear quasi-static FE analysis of the component subjected to mid-span deformation under displacement control, with boundary conditions simulating the actual blast tests and idealized to facilitate SDOF modeling.

The analytical predictions are consistent with the experimental data obtained from blast tests. The computational methodology described in this study can also be adopted for comparing the performance characteristics of various other hypothetical sandwich composite panel configurations with no experimental data corresponding to blast loading.

Footnotes

Funding

This study was funded by ONR grant no. N00014-7-1-1010, Office of Naval Research, Solid Mechanics Program (Dr Yapa Rajapakse, Program Manager).

Acknowledgment

The sandwich composite panels were fabricated by Dr Uday Vaidya and Dr Selvum Pillay at the University of Alabama, Birmingham.

Note

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