Strain Rate Analysis of Efficient Honeycomb Sandwich Panels under Blast Load

doi:10.21203/rs.3.rs-2704887/v1

Honeycomb sandwich panels are investigated for a broad range of areas as protective structures that can withstand blast loading. The advantage of these panels is that they are light in weight when compared to solid metal plates due to the hollow core and have high energy absorption capabilities. Due to their high bending stiffness, honeycomb sandwich panels have found applications in aerospace, automotive, marine, defense, and railway industries. In order to analyze the effect of blast loading on sandwich panels the experiments that need to be conducted are costly as well as time-consuming. Also, while conducting experiments with explosives, human safety is a major concern. Taking the aforementioned parameters into consideration, modeling and simulation of honeycomb sandwich panels is the better alternative. ABAQUS software has been used in this paper to study the behavior of metallic honeycomb sandwich panels (MHSP) with squared, hexagonal, and circular cores when subjected to blast loads of different kilograms of trinitrotoluene (TNT). The obtained simulation results show that circular core has higher blast resistance as compared to hexagonal and square cores. With the aim of optimizing blast protection characteristics of the sandwich model, effect of gel-filling and addition of Aluminium foamto hollow honeycomb core of the sandwich panelswas investigated.The face plate deflection and energy absorption capacity were found to have improved after these additions. Mass evaluation pertaining to reduction in plate deflection versus increase in weight of the sandwich panel after addition of gel and foam was also performed. The influence of strain rate on the deflection of blast-loaded sandwich panels was also studied. It was found that higher strain rates gave favourable results i.e., lower deformation values. Lastly, energy absorption study of all the various configurations of the sandwich panel was performed.

Blast load

Foam

Gel

Honeycomb

Sandwich panel

Strain rate effect

TNT

In recent times, there is an increasing need for protection against explosions caused either by terrorist activities or due to negligence by humans such as leaks from chemical plants, etc. Honeycomb sandwich structures have been used extensively for protection from these blasts owing to their lightweight, high strength properties. Metallic honeycomb sandwich panels (MHSP) have been extensively used as structural elements that provide protection against blast loading in a wide range of applications, especially in military and aircraft industries [1–3]. This is mainly owing to their unique characteristics, such as high bending stiffness with overall low density and high thermal isolation capacity [4–6]. Conducting experimental research in order to design the optimized sandwich panel is very expensive and time consuming. Numerical simulations are a better alternative to obtain accurate results that requires less time and capital, while also ensuring human safety [7, 8]. Many novel numerical methods to accurately predict the behaviour of different components under blast loading have been developed by several researchers. A numerical simulation for the dynamic behaviours of steel plate identical to the experimental condition was developed coupling analysis of finite element method (FEM) and discrete particle method (DPM) [9]. A Fortran vectorized user-material subroutine (VUMAT) program considering strain rate, stress status and temperature effect which can effectively predict the dynamic response of metallic materials was developed by Li et al. [10]. Fu et al. [11] developed a model that can accurately achieve the scaling of the dynamic response of a steel plate under blast loading. Yang et al. [12] proposed a new method, based on a single-degree-of-freedom (SDOF) system with appropriate modification for strain-rate effect to calculate the dynamic strength of mild steel in the analysis of reinforced concrete structures subjected to air-blast loading.

Dharmasena et al. [3] conducted both experimental and simulation analysis on square core sandwich panels under blast load and compared their performance to solid plates. They found the sandwich panels with suitably strong cores can withstand far bigger impulses than solid plates of the same material and weight. The effects of various honeycomb core topologies on blast performance were investigated by and Patel and Patel [7] and Kumar and Patel [13]. It was concluded that for the same wall thickness, circular core shape gave better results. Liu et al. [14] analyzed a hexagonal honeycomb structure filled with circular tubes using ABAQUS/Explicit; they discovered that sandwich panels with circular tubes had a lower rear face-sheet deflection than ordinary honeycomb panels. A unique hierarchical core structure was simulated on LS-DYNA, in which each vertex of a conventional hexagonal cell was substituted with a smaller hexagonal unit. The results showed that with a higher level of blast load, the maximum deflection at the back face sheet of the hierarchical honeycomb sandwich panels was smaller than the equivalent standard honeycomb [15]. Jing et al. [16] found the foam with highest density was placed at the top followed by lower density foam cores gave better results for energy absorption. Foam filled honeycomb structure with metallic face plates of sandwich panels has also been studied by previous researchers. They found that the foam filled sandwich structure outperforms in comparison to hollow metallic sandwich structures in terms of blast resistance [17–19]. An alternative to addition of foam, which has been used in some studies for optimizing blast protection of sandwich structures is gel. The energy absorption capacity and impact resistance of sandwich panels was improved by filling the honeycomb core with a shear-thickening gel mixed with silica particles [20]. In another research study, better bending strength and modulus were obtained for honeycomb sandwich structure after the honeycombs were filled with magnetic shear-stiffening gel [21]. Faria et al. [22] obtained favourable results when they analyzed sandwich beams having honeycomb cores filled with magnetorheological gel.

Another very important phenomenon that needs to be considered while performing blast load analysis is strain rate effect. Blast loads typically produce very high strain rates in the range of 10² − 10⁴ s^-1, while ordinary static strain rate is within the range of 10^− 6 − 10^− 5 s^-1 [23, 24]. When load with high strain rate is applied to a structure, its dynamic mechanical properties and damage mechanisms itself change [25]. The results of various studies demonstrated that the deformation values obtained under high strain rates were very different from those derived with the static properties of the materials [26–28]. Yin et al. [29] found that with the increase of explosive equivalent (increase of strain rate), the dynamic peak stress and corresponding strain as well as dynamic modulus of elasticity of steel fiber concrete increased. The yielding stress, fracture stress and fracture strain for steel grew by more than 60%, 20% and 50% respectively when the strain rate was changed from the quasi-static regime to the impact one (> 500 s-1) [30]. Dynamic Increase Factor (DIF) due to strain rate effect was examined with documented experimental work done by Razaqpur et al. [31]. DIF is the ratio of the dynamic to static strength, normally reported as function of strain rate. It is used to represent the influence of strain rate on strength enhancement under dynamic conditions. Based on the experimental results, empirical relations have been proposed to determine the values of DIF for steel under high strain rates [32, 33]. It was concluded that when the dynamic increase factor was considered in the numerical analysisof concrete and steel reinforcement materials, the behaviour of model under blast load become closer to experimental work [34].

Above literature shows that very limited work has been done on the dynamic behavior of MHSP with square, hexagonal, and circular cores. Numerical modeling of foam-filled MHSP has been developed to sustain the higher blast loads up to 10 kg TNT. An analysis on gel-filling effect of metallic honeycombs was conducted with the aim of improving the results obtained after foam addition. Mass comparison study was performed for hollow, foam filled and gel filled MHSPs. A strain rate study was carried out using different honeycomb sandwich structures to determine the plastic deformation behavior of the MHSPs. The MHSPs are subjected to conventional weapons effects program (CONWEP) air-blast loads ranging from 1 kg to 10 kg TNT for a fixed stand-off distance of 100 mm. Blast resistance has been evaluated by face deflections and energy absorption due to plastic deformations.

2.1 Air-blast loading

When a bomb detonates, a massive amount of energy is released into an open medium, causing a blast wave to spread out in all directions. As this blast wave travels through the air, the pressure increases to a value that is much higher than the ambient atmospheric pressure. Over pressure is the term for the sudden increase in pressure that occurs as the shock wave moves out from the explosion center and it is followed by a suction or negative phase as the graph in Fig. 1 [1–3].A Friedlander wave equation can be used to explain the free-field pressure–time response as shown in Eq. (1):

$$P(t)={P_0}+{P_{SO}}\left( {1 - \frac{t}{{{t_d}}}} \right){\exp ^{ - \frac{t}{{{t_d}}}}}$$

1

Here,P₀ is the atmospheric pressure, P_SO is the peak positive pressure, t is current time and t_d is time duration of positive pressure.The size of the bomb or the charge weight (m) and the stand-off distance (r) between the blast source and the target are two key characteristics that determine the impact of a bomb [3]. Eq. 2 can be used to approximate the peak pressure of the blast wave (p) for a particular explosive, where K is an explosive material parameter.

The applied pressure–time response during the positive phase, where p is the incident pressure, can be used to compute the impulse load (I) imparted to the structure, as shown in Eq. 3.

$$\int\limits_{{{t_a}}}^{{{t_a}+{t_d}}} {p(t)dt}$$

3

There are three stages to the response of sandwich panels to blast loading. The shock wave strikes the structure's top face plate in the first stage, providing an impulse to the top surface. The upper plate travels downward in the second stage, while the core tries to oppose the movement of the top plate and slow it down [3, 5]. In this step, core crushing takes place. If the impulse load is large enough, the bottom plate will bend in the third stage. Further mechanical energy dissipation occurs at this stage.

2.2 Geometry modelling

MHSP with a square honeycomb core was modeled for validation purposes according to the parameters mentioned in Dharmasena et al. [3]. Due to symmetry of MHSP, only one-quarter of the geometry was modeled to save computation time and reduce the storage space requirement. The material defined for the square honeycomb core and face sheet was a high-ductility stainless steel alloy (AL-6XN), with an approximate composition of 49Fe–24Ni–21Cr–6Mo (wt. %) [3]. The dimensions of the face plate were 305 x 305 x 5 mm³. The honeycomb core had outer dimensions of 305 x 305 x 51 mm³. The core was made up of a 10 × 10 cells square grid made up of 0.76 mm thick strips spaced 30.5 mm [3]. The geometric model can be better understood by Fig. 2.

2.3 Material modeling

The Johnson–Cook (J-C) plasticity modelwas used to model the MHSPfor CONWEP air-blast loading. The J-Cmodel is usedfor estimating the outset of damage and failure in ductile metals, especially for plastic deformations. It can be understood from Eq. 4 [5, 7, 36].

Where, σ_eq and ε^pl_eqare the equivalent plastic stress andstrain, respectively. ὲ is the plastic strain rateandὲ_ois areference strain rate. The material constants are A, B, C, n, and m. A is the yield strengthof the material under reference conditions. B is the strain hardening constant, n is the strain hardening coefficient, C represents the strain rate effect, and m represents the thermal softening effect. T_melt and T_o represent melting temperature and reference temperature, respectively. The values of the above parameters as well as the material properties were taken from literature [7]as shown in Table 1.

Table 1

J-C parameters and material properties for AL-6XN[7]
E(GPa)	υ	ρ (kg/m³)	A (MPa)	B (MPa)	C	n	m	ὲ_o(s^-1)	T_o(K)	T_melt (K)
161	0.35	7850	400	1500	0.045	0.4	1.2	0.001	293	1800

2.4 Boundary conditions and meshing characteristics

The top and bottom plates were discretized using 30 Continuum 3 Dimensional 8 noded Reduced integration (C3D8R) solid elements. 31 C3D8R elements and 5 C3D8R elements were defined for the plate surface and through the plate thickness respectively. Shell 4 noded Reduced integration (S4R) elements were used to discretize the core. 30 S4R shell elements along the core height were used. Enhanced hourglass control was applied to avoid element distortion in numerical simulations. At a temperature of 273 K, the sandwich structure was in its initial undeformed state. The boundary conditions, stand-off point distance, and dimensions are applied for the MHSP are shown in Fig. 2. In the sandwich structure, tie constraints were used between the honeycomb web and inner surfaces of the plates. A mesh convergence and validation study were also performed to validate the present numerical results with the experimental results available in literature [3] using the CONWEP air-blast loading.

2.5 Numerical validation study

Dynamic explicit analysis of honeycomb sandwich structure was performed with a square core under blast loadings of 1 to 3 kg TNT. The front face deflection results of present simulation were compared to the experimental results obtained by Dharmasena et al. [3] at 1, 2, and3 kg TNT as shown in Fig. 3 (a). The comparison of numerically and experimentally deformed structures are represented in Fig. 3 (b). A good match was found between the deflections of front plate, as can be seen from the graph shown in Fig. 3 (a). Similarly, if we look at Fig. 3 (b), we can see the deformation of sandwich panels at 1, 2, and 3 kg TNT blast by Dharmasena et al. [3] and present deformed MHSPs with square honeycomb. A very close resemblance is observed.

3.1 Effect of core geometry for hollow honeycomb core

The hexagonal and circular cores were also modeled for the same dimensions, material properties, and boundary conditions as the square panels. The meshing conditions were also kept exactly the same. The honeycomb core structures were compared on the basis of front face deflection for a blast load of 1, 2, and 3 kg TNT. The deformations of various honeycomb sandwich structures are shown in Fig. 4. The front face center point deflections for different honeycomb sandwich structures are tabulated below in Table 2.

For a load of 1 kg TNT, it can be observed that the front face deflections decreased by 20.45% and 37.01% after substituting the square honeycomb core with hexagonal and circular cores, respectively. A similar reduction is observed for 2 kg and 3 kg loads as well. The front face deflections show a decrement of about 7.35% and 30.09% when the square core is replaced by hexagonal and circular cores respectively, for 2 kg TNT load. Similarly, for a load of 3 kg TNT, front face deflections reduce by 6.02% and 28.98% respectively, when hexagonal and circular cores are used instead of square.

Table 2

Centre point deflection for the different honeycomb sandwich structures
Mass of TNT used for blast load	Centre point deflection
Mass of TNT used for blast load	Square core	Hexagonal core	Circular core
1 kg	69.298	55.121	34.272
2 kg	110.482	102.362	71.558
3 kg	141.244	132.745	100.311

It can be seen from the simulated results that a circular core sandwich panel gives the best results (i.e., least deformation) as compared to square and hexagonal cores when subjected to the same blast load. Hence, the circular core is the strongest core among all the modeled cores of same wall thickness. One possible reason for this occurrence can be that stress concentration takes place at sharp corners of square and hexagonal cores, along which then the material fails. Absence of sharp edges makes circular core better suited to resist blast loads. It can be further concluded from the results presented in Table 1 that amongst hexagonal and square cored sandwich panels, hexagonal cored MHSP perform better. This can be in part because, in case of hexagonal core, there are six walls of a single core unit supporting each other whereas, in case of square core there are only four.

Substantial front plate bending and core crushing can be seen at the center of the panel closest to the detonation source at all blast loads. It can be observed from Fig. 4, that the honeycomb core is only partially crushed at 1 kg and 2 kg TNT for square and hexagonal cored sandwich panels. However, the core is almost completely crushed at 3 kg TNT for the square and hexagonal panels.In contrast, the core crushing is very limited for circular cored sandwich panel, even at 3 kg TNT.

3.2 Effect of Foam Filled Metallic Honeycomb Sandwich Panel (FFMHSP)

Addition of foams to hollow cores of the honeycomb sandwich structure is a constructive way of improving its blast resistant performance while also keeping the panel lightweight. In this section, analysis was conducted by filling the honeycomb core with aluminium foam. Only circular core sandwich panels were considered for this analysis as they gave the most optimum result with respect to deformation as seen in previous section. For this purpose, the material properties of crushable Al foam given by Novak et al.[37] were used. The temperature was kept constant at 296K. 30 linear solid C3D8R elements were used for meshing of foam. The material and plastic curve properties are shown in Tables 3 and 4. Where; ρ is density, E is Young’s modulus, ν is Poisson's ratio, k is compression yield stress ratio and k_t is hydrostatic yield stress ratio.

Table 3

Parameters for crushable Aluminium foam material[37]
ρ (kg/m³)	E (MPa)	Ν	k	k_t
681	5023.8	0.11	1.53	0.45

Table 4

Hardening curve definition for crushable Al foam [37]
Plastic Strain	0	0.03	0.12	0.15	0.25	0.42	0.51	0.60	0.9	1.07	1.8
Stress (MPa)	11	11.9	15.35	16.12	18.39	20.93	23.05	25.18	29.7	69.82	2100

It can be observed from Fig. 5 that, after the addition of foam, the plastic deformation of the sandwich panel is moderately reduced. The center point deflection of the front face sheet obtained for the foam filled circular core is 31.49 mm, 66.97mm and 97.56 mm at loads of 1, 2 and 3 kg TNT respectively. The center point deflection reduces by 8.23%, 6.41% and 2.75% for blast loads of 1, 2 and 3 kg TNT respectively after the addition of foam.

Honeycomb sandwich panels without foam were not able to sustain loads greater than 3 kg TNT and when subjected to higher loads, the core was completely crushed. However, after the filling of AL foam in the hollow cores, the panels were able to provide protection against blast loads of up to 10 kg TNT. Thus, sandwich panels with Al foam can be used for high blast load applications.

Figure 6. shows the front plate deflections of FFMHSPs at 5 and 10 kg TNT blast loads. Here too a similar pattern is observed wherein the circular cored MHSP gives the least value of front plate deflection followed by hexagonal and then square cored panels. For FFMHSP, when a load of 5 kg TNT was applied, the front face deflections for the circular, hexagonal, and square cored panels obtained were 117.07 mm, 124.54 mm, and 135.52 mm respectively. Similarly, when 10 kg TNT blast load applied for the same FFMHSP, the front face deflections for the circular, hexagonal, and square core obtained were 194.82 mm, 202.46 mm and 215.71 mm respectively.

The cores crushing of FFMHSPs are shown in Fig. 7.It can be observed that the foam filled circular core is crushed to a lesser extent than the foam filled hexagonal core.And similarly, the foam filled hexagonal core is less severely crushed compared to the foam filled square core for both 5 and 10 kg TNT. Hence, it can be concluded that, Al foam filled circular, hexagonal and square MHSP, can all sustain high blast loads, but circular core panel provides superior blast protection i.e., minimum deflection. It can be observed that the order of preferred blast performance for all the cases is circular cored MHSPs, followed by hexagonal cored MHSPs and then finally squared core MHSPs.

3.3 Effect of Gel Filled Metallic Honeycomb Sandwich Panel (GFMHSP)

It was concluded in the previous section that addition of foam improved the performance of sandwich panel w.r.t. front face deflection. In an attempt to further improve the blast resistance of the panel, gel filled metal honeycomb sandwich panels (GFMHSP) was analysed. The properties of gel available in Shalchy et al. [38] were used for this purpose. In the experimental study done by Shalchy, commercial gelatine powder (42 g) was mixed in 1 L of water to prepare the gel. For modelling purposes, the gel was considered to be an isotropic elastic material of density 1000 kg/m³. Young’s modulus (E) of 6.9 MPa and Poisson’s ratio (υ) of 0.4999 were defined for the gel. The plastic deformation curve for the gel was acquired from graphs available in Shalchy et al. [38]. Continuum 3 Dimensional 8 noded Reduced Integration (C3D8R) hexahedral elements were used for meshing of the gel. Tie constraints were used to bind the gel elements to the cell walls of the core and face sheets.

It can be observed from the bar graph in Fig. 8. that addition of gel caused a significant reduction in the front face deflection, giving better results than the Al foam filled honeycombs. The deformation models of GFMHSPs can be observed in Fig. 9. It can be noted that the panels in this case are not as severely deformed as the ones with hollow core. The front face deflection at the center point of the sandwich panel obtained after addition of gel to the honeycomb was 20.52 mm, 47.6 mm and 72.34 mm for loads of 1, 2 and 3 kg TNT respectively. The performance of foam and gel filled honeycomb panels can be better evaluated based on percentage reduction w.r.t hollow core. The center point deflection reduced by 8.23% for a load of 1 kg TNT when foam was filled in the honeycomb core; whereas it reduced by 40.12% when the same core was filled with gel. For a load of 2 kg TNT, the face plate deflection reduced by 6.41% when foam was used, compared to 33.48% when gel was used. For 3 kg TNT as well, the reduction in deflection was substantially higher for gel at 27.88% as compared to foam at 2.75%.

3.4 Mass Evaluation

It is evident from the previous sections that addition of foam and gel are constructive to optimizing the blast resistance performance of the sandwich panel. The front face sheet deflection of the panels reduces after these additions. But on the flip side, the weight of the panel increases. Depending upon the application, the appropriate configuration of the sandwich panel must be chosen. If high blast resistance is required of the panel, then a compromise is to be made on its weight; the weight of the panel will go up in such a case. On the other hand, if keeping the panel lightweight is a priority, then it will not be able to sustain high loads. Mass evaluation of MHSP, FFMHSP and GFMHSP has been performed for a load of 1 kg TNT in this section to study this problem in detail.

Table 5

Mass Evaluation of MHSP, FFMHSP and GFMHSP
	Mass of Quarter Model (kg)	Front Face Deflection (mm)
MHSP	7.59	34.27
FFMHSP	16.76	31.49
GFMHSP	21.05	20.52

If MHSP and FFMHSP are considered, it can be observed from Table 5 that the mass of the panel increases considerably after addition of foam but the reduction in deflection is only 8.23%. In such a case, for light weight applications, it is prudent to go with MHSP, albeit only for low or moderate blast loads. But as seen in section 3.2, FFMHSP are able to sustain very high blast loads (up to 10 kg TNT) and can be used in cases where high blast protection is necessary. If FFMHSP and GFMHSP are compared, it can be perceived that GFMHSPs are 25.59% heavier than FFMHSP but the face sheet deflection is improved by 34.84%. Thus, it is pragmatic in this case to compromise on the weight of the panel (if possible, according to application) as superior blast protection is provided by using gel instead of foam. The mass of the panel is increased by approximately 3 times when MHSPs are replaced by GFMHSPs, but there is an exponential decrease in face sheet reduction as well of about 40.12%. Thus, GFMHSPs are suitable for high blast applications where weight is not an issue.

3.5 Strain rate effect analysis of MHSP

Strain rate refers to the rate at which a material deforms when subjected to an external load. The strain rate of a material can be affected by several parameters such as the applied load, temperature and microstructure of the material. A material can exhibit different strain rates under the same load due to variations in its microstructure. Generally, a material with fine-grained microstructure will deform at a higher strain rate than a coarse-grained material under the same load. This is because smaller grains will provide more barriers to dislocation motion, which increases the strength of the material and makes it more resistant to plastic deformation[39].

The high strain rate dependence of the flow stress of metals and alloys from a dislocation mechanics viewpoint has been extensively studied.At higher strain rates, transition from plastic flow (that is controlled by the mobility of the resident dislocation density) to plasticity (that is controlled by dislocation or twin generations at the shock front) is observed [39–41]. The increase of the elongation to fracture and tensile strength with the strain rate could be ascribed to the formation of mechanical twins [42]. Thus, increasing the rate of deformation of the sandwich panel by making changes to its microstructure isan effective way of optimizing the sandwich panel. The plastic deformation obtained in such a case will be considerably lower.This theory has been numerically tested using Abaqus software in this section. It was noted upon studying previous research work that experimental analysis in relation to strain rate effect under blast loading is close to nil.

The MHSP of square and circular cores at a strain rate of 0.1/s and 3500/s were simulated on FEA, for loads of 1, 2, and 3 kg TNT, in order to observe how strain rate affects deformation. The temperature was kept constant at 296K. To analyze the effect of strain rate, the plastic deformation properties ascribed in Nemat-Nassera et al. [35] at two different strain rates (0.1/s and 3500/s) were used. The results obtained are plotted in Fig. 10. for all three loads of 1, 2, and 3 kg TNT, for both the square and circular core shapes.When the strain rate was increased from 0.1/s to 3500/s, there was a significant reduction in the front plate deformation. For a load of 1 kg TNT, in circular core MHSP, as the strain rate was increased from 0.1/s to 3500/s, there was an 18.71% decrease in front plate deflection. In a similar manner, when the strain rate was increased for square panel, from 0.1/s to 3500/s, for a load of 1 kg TNT, the front plate deflection reduced by 14.82%. In the same manner, for 2 Kg TNT there was a 15.32% and 26.54% decrease in the front plate deflection for square and circular core panels, respectively as the strain rate was modified from 0.1/s to 3500/s. For a load of 3kg TNT, an 18.55% and 37.24% decrease in front plate deflection was observed for square and circular panels with the increase in strain rate.

These reductions in front face deflection can be attributed to changes in microstructure of the material as the strain rate increases. AL6XN being a ductile material has time to stretch at low strain rates before fracture. As a result, the maximum load is restricted. At a rapid strain rate, a material has less time to deform, which causes a bigger measured load.The two forms of atomic mobility that affect the yield phenomena in ductile materials are dislocation glide and twinning. High strain rates interfere with the dislocation glide, which hinders twinning. Due to the increased energy required to move atoms, the face sheet deflection is smaller in the case of high strain rate for the same mass of TNT blast [44–48]. It is to be noted that reduction in deformation is more for circular MHSP. Thus, it can be inferred that circular core is more favorable, which is consistent with previous results.

Strain rate analysis was also conducted for Al foam. The strain-rate effect on the crushing stress of both open-cell and closed-cell aluminium foams was investigated by Yu et al. [49], using Split Hopkinson Pressure Bar method. It was concluded that structural heterogeneity induces the strain-rate effect of circular-cell honeycombs. Under dynamic compression tests, it was observed that the damage mode of the aluminium honeycomb structure was plastic buckling, collapse and folding of the cell wall. The folding length of the cell wall at a higher strain rate was found to be longer than that at a lower strain rate [50]. Figure 11. shows the strain rate analysis of Aluminium FFMHSP under two different strain rates of 0.004/s and 12,000/s respectively.

As the strain rate increased from 0.004/s to 12,000/s for 1 kg TNT blast load, the center point deflection obtained changed from 31.51 mm to 16.65 mm. Likewise for a load of 2 kg TNT as well, a reduction from 69.81 mm to 37.36 mm was observed after increasing the strain rate. In a similar fashion, the front face deflection reduced from 100.74 mm to 58.67 mm for 3 kg TNT blast load following increment in strain rate. It can be concluded that, for high strain rate (12,000/s) FFMHSP shows lower deflection in comparison to low strain rate foam filled structure (0.004/s). There was a 121.55%, 46.48% and 41.76% decrease in the front plate deflection as the strain rate was increased from 0.004/s to 12000/s, at 1, 2 and 3 kg TNT loads, respectively.

3.5 Energy Analysis

Table 6

Energy Absorption for MHSP and FFMHSP at varying loads
	Internal Energy (kJ)
		MHSP		FFMHSP
	1 kg TNT	2 kg TNT	3 kg TNT	5 kg TNT	10 kg TNT
Circular	21.58	76.48	149.17	166.76	514.86
Hexagonal	30.16	107.45	203.15	189.55	579.76
Square	34.18	120.26	149.68	202.71	613.94

It can be seen upon observing the data in Table 6, that energy absorbed goes on increasing with increase in the load; this is obvious. Another interesting pattern to noted is that the internal energy is proportional to the deformation of the panel. It can be discerned from the data given in Table 6, that the panel which undergoes most amount of deformation has absorbed the maximum amount of energy. As concluded in previous sections, the order of deformation of the panels according to their geometric core configurations were circular, hexagonal, and square. Square cored MHSP underwent the most deformation and accordingly, the energy absorbed by it was the largest followed by hexagonal MHSP and then circular MHSP. This order of energy absorption is consistent for FFMHSPs as well.

A similar trend is observed when MHSPs are compared on the basis of energy absorption at different strain rates. Panels which undergo deformation at a higher rate are less severely deformed compared to panels deformed at low strain rate. And therefore, panels undergoing deformation at low strain rate of 0.1/s show greater energy absorption than panels which deformed at a higher strain rate of 3500/s. This can be observed from Table 7 and holds true for all core geometries.

Table 7

Energy Absorption for MHSPs at varying strain rates
	Circular cored MHSP		Square cored MHSP
Mass of TNT (kg)	Strain rate- 3500/s	Strain rate- 0.1/s	Strain rate- 3500/s	Strain rate- 0.1/s
1	23.42	26.93	35.38	36.51
2	85.45	95.97	124.27	127.09
3	167.39	206.39	232.11	237.36

Numerical modeling of MHSPs, FFMHSP and GFMHSP weredeveloped considering the effect of strain rate using the CONWEP air-blast loads ranging from 1 kg to 10 kg TNT. The following points are concluded from this study:

Circular honeycomb core was found to have thelowest deflection in comparison other honeycomb cores such as square and hexagonal for same the blast loading.
There is a noticeable reduction in the deformation of sandwich panels as well as face deflection after the addition of Aluminium foam.
Sandwich panels with foam are able to resist higher blast loads, up to 10kg TNT, which was not possible without the addition of foam.
Addition of gel improved the deflection results obtained by foam-filling by a significant amount.
Mass comparison study showed that MHSPs are suitable for lightweight, low blast load applications, while FFMHSPs and GFMHSPs are suitable for high blast protection.
When the strain rate was increased while keeping the temperature constant, front plate deflections decreased for both with or without foam filled MHSPs. Thus, higher strain rates are favorable for sandwich panels under blast loads.
The energy absorbed by all the panel configurations is proportional to their deformation.

t	Current time	T_melt	Melting Temperature
t_d	Positive phase time duration	FE	Finite Element
P₀	Atmospheric pressure	FFMHSP	Foam Filled Metallic Honeycomb Sandwich Panel
P_SO	Peak positive pressure	GFMHSP	Gel Filled Metallic Honeycomb Sandwich Panel
σ_eq	Equivalent plastic stress	MHSP	Metallic Honeycomb Sandwich Panel
ὲ_o	Reference strain rate	PDE	Plastic Deformation Energy
ε^pl_eq	Equivalent plastic strain	J-C	Johnson-Cook
ὲ	Plastic strain rate	CONWEP	Conventional Weapons Effects Program
T_o	Reference Temperature	TNT	Trinitrotoluene

The authors declare that they have no conflicts of interest.

Amulani, A., Pratap, H., & Thomas, B. (2021). Investigation of static and fatigue behavior of honeycomb sandwich structure: a computational approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 43, 1-19. https://doi.org/10.1007/s40430-021-03195-y
Du, J., Su, H., Bai, J., Zhang, Y., & Zhang, J. (2023). On dynamic response of double-layer rectangular sandwich plates with FML face-sheets and metal foam cores under blast loading. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 45(1), 31. https://doi.org/10.1007/s40430-022-03956-3
Dharmasena, K. P., Wadley, H. N., Xue, Z., & Hutchinson, J. W. (2008). Mechanical response of metallic honeycomb sandwich panel structures to high-intensity dynamic loading. International Journal of Impact Engineering, 35(9), 1063-1074. https://doi.org/10.1016/j.ijimpeng.2007.06.008
Galehdari, S. A., & Kadkhodayan, M. (2019). Collapse of honeycomb cell as a result of buckling or plastic hinges, analytical, numerical and experimental study. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41, 1-9. https://doi.org/10.1007/s40430-019-1646-6
Patel, M., & Patel, S. (2022). Novel design of honeycomb hybrid sandwich structures under air-blast. Journal of Sandwich Structures & Materials, 24(8), 2105-2123. https://doi.org/10.1177/10996362221127967
Chandra, S., Amulani, A., Thomas, S. B., Soni, S. K., & Thomas, B. (2022). Influence of CNT volume fractions on static and dynamic behavior of aluminum honeycomb-cored carbon-fiber-reinforced honeycomb sandwich structure. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 44(11), 507. https://doi.org/10.1007/s40430-022-03825-z
Patel, S., Patel, M. (2022). The efficient design of hybrid and metallic sandwich structures under air blast loading. Journal of Sandwich Structures & Materials, 24, 1706-1725. https://doi.org/10.1177/10996362211065748
Sawant, R., Patel, M., Patel, S. (2022). Numerical analysis of honeycomb sandwich panels under blast load. Materials Today: Proceedings.https://doi.org/10.1016/j.matpr.2022.09.547
Saburi, T., Kubota, S., Wada, Y., Kumaki, T., & Yoshida, M. (2014). High Strain Rate Test of a Steel Plate under Blast Loading from High Explosive. In Materials Science Forum (Vol. 767, pp. 144-149). Trans Tech Publications Ltd. https://doi.org/10.4028/www.scientific.net/MSF.767.144
Li, Y., Wu, W., Zhu, H., Wu, Z., & Du, Z. (2017). The influence of different pre-formed holes on the dynamic response of square plates under air-blast loading. Engineering Failure Analysis, 78, 122-133. https://doi.org/10.1016/j.engfailanal.2017.03.002
Fu, T., Zhang, M., Zheng, Q., Zhou, D., Sun, X., & Wang, X. (2021). Scaling the response of armor steel subjected to blast loading. International Journal of Impact Engineering, 153, 103863. https://doi.org/10.1016/j.ijimpeng.2021.103863
Yang, G., & Lok, T. S. (2007). Analysis of RC structures subjected to air-blast loading accounting for strain rate effect of steel reinforcement. International journal of impact engineering, 34(12), 1924-1935. https://doi.org/10.1016/j.ijimpeng.2006.11.009
Kumar, R., Patel, S. (2021). Failure analysis on octagonal honeycomb sandwich panel under air blast loading. Materials Today: Proceedings, 46, 9667-9672.https://doi.org/10.1016/j.matpr.2020.07.525
Liu, J., Wang, Z., & Hui, D. (2018). Blast resistance and parametric study of sandwich structure consisting of honeycomb core filled with circular metallic tubes. Composites Part B: Engineering, 145, 261-269. https://doi.org/10.1016/j.compositesb.2018.03.005
Sun, G., Zhang, J., Li, S., Fang, J., Wang, E., & Li, Q. (2019). Dynamic response of sandwich panel with hierarchical honeycomb cores subject to blast loading. Thin-Walled Structures, 142, 499-515. https://doi.org/10.1016/j.tws.2019.04.029
Jing, L., Liu, K., Su, X., & Guo, X. (2021). Experimental and numerical study of square sandwich panels with layered-gradient foam cores to air-blast loading. Thin-Walled Structures, 161, 107445. https://doi.org/10.1016/j.tws.2021.107445
Sun, G., Wang, E., Zhang, J., Li, S., Zhang, Y., & Li, Q. (2020). Experimental study on the dynamic responses of foam sandwich panels with different facesheets and core gradients subjected to blast impulse. International Journal of Impact Engineering, 135, 103327. https://doi.org/10.1016/j.ijimpeng.2019.103327
Zang, S., Zhou, X., Wang, H., & You, Z. (2016). Foldcores made of thermoplastic materials: Experimental study and finite element analysis. Thin-Walled Structures, 100, 170-179. https://doi.org/10.1016/j.tws.2015.12.017
Kumar, V., Kartik, K. V., & Iqbal, M. A. (2020). Experimental and numerical investigation of reinforced concrete slabs under blast loading. Engineering Structures, 206, 110125. https://doi.org/10.1016/j.engstruct.2019.110125
Lin, G., Li, J., Li, F., Chen, P., Sun, W. (2022). Low-velocity impact response of sandwich composite panels with shear thickening gel filled honeycomb cores. Composites Communications; 32, 101136.https://doi.org/10.1016/j.coco.2022.101136
Huang, S., Liu, Y., Wen, K., Su, X., Liang, C., Duan, H., Zhao, G. (2023). Optimization design of a novel microwave absorbing honeycomb sandwich structure filled with magnetic shear-stiffening gel. Composites Science and Technology, 232, 109883.https://doi.org/10.1016/j.compscitech.2022.109883
Faria, L., Gomes, G., Gomes de Sousa, S., Bombard, A., Ancelotti, A. (2020). Dynamic experimental behavior of sandwich beams with honeycomb core filled with magnetic rheological gel: a statistical approach. Smart Materials and Structures, 29, 115044.https://doi.org/10.1088/1361-665X/abb8e7
Ehinger, D., Krüger, L., Martin, U., Weigelt, C., & Aneziris, C. G. (2011). Strain Rate Effect on Material Behavior of TRIP‐Steel/Zirconia Honeycomb Structures. steel research international, 82(9), 1048-1056. https://doi.org/10.1002/srin.201100076
Tao, Y., Chen, M., Pei, Y., & Fang, D. (2015). Strain rate effect on mechanical behavior of metallic honeycombs under out-of-plane dynamic compression. Journal of Applied Mechanics, 82(2). https://doi.org/10.1115/1.4029471
Ngo, T., Mendis, P., Gupta, A., & Ramsay, J. (2007). Blast loading and blast effects on structures–an overview. Electronic journal of structural engineering, (1), 76-91. https://doi.org/10.56748/ejse.671
Hashemi, S. K., & Bradford, M. A. (2014). The strain-rate effects on the numerical simulation of steel beams under blast loads. WIT Transactions on the Built Environment, 141(1743-3509), 311-322.
Stochino, F., & Carta, G. (2014). SDOF models for reinforced concrete beams under impulsive loads accounting for strain rate effects. Nuclear Engineering and Design, 276, 74-86. https://doi.org/10.1016/j.nucengdes.2014.05.022
Tavakoli, H. R., & Kiakojouri, F. O. A. D. (2014). Numerical dynamic analysis of stiffened plates under blast loading. Latin American Journal of Solids and Structures, 11, 185-199. https://doi.org/10.1590/S1679-78252014000200003
Yin, H., & Ouyang, Y. (2022). Experimental and Numerical Study on Steel Fiber Concrete under Blast Loading. Buildings, 12(12), 2119. https://doi.org/10.3390/buildings12122119
Cadoni, E., Asprone, D., & Prota, A. (2007). High strain-rate testing of concrete and steel for the assessment of the Tenza Bridge under blast loading. New trends in fractures mechanics of concrete, 627-635.
Razaqpur, A. G., Tolba, A., & Contestabile, E. (2007). Blast loading response of reinforced concrete panels reinforced with externally bonded GFRP laminates. Composites Part B: Engineering, 38(5-6), 535-546. https://doi.org/10.1016/j.compositesb.2006.06.016
Malvar, L. J. (1998). Review of static and dynamic properties of steel reinforcing bars. Materials Journal, 95(5), 609-616. https://doi.org/10.14359/403
Nassr, A. A. (2012). Experimental and analytical study of the dynamic response of steel beams and columns to blast loading (Doctoral dissertation). http://hdl.handle.net/11375/12249
Kandil, K. S., Nemir, M. T., Ellobody, E. A., & Shahin, R. I. (2014). Strain Rate Effect on the Response of Blast Loaded Reinforced Concrete Slabs. World Journal of Engineering and Technology, 2(04), 260. https://doi.org/10.4236/wjet.2014.24027
Trajkovski, J., Kunc, R., Perenda, J., Prebil, I. (2014). Minimum mesh design criteria for blast wave development and structural response – MMALE method. Latin American Journal of Solids and Structures, 11 (11). https://doi.org/10.1590/S1679-78252014001100006
Gaur, B., Patel, M., Patel, S. (2023). Strain rate effect on CRALL under high-velocity impact by different projectiles. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 45(2), 103. https://doi.org/10.1007/s40430-023-04031-1
Novak, N., Vesenjak, M., Duarte, I., Tanaka, S., Hokamoto, K., Krstulović-Opara, L., ... & Ren, Z. (2019). Compressive behaviour of closed-cell aluminium foam at different strain rates. Materials, 12(24), 4108. https://doi.org/10.3390/ma12244108
Shalchy, F., Carlsson, J., Deshpande, V., Fleck, N. (2022). Pinching of gel-filled honeycomb. International Journal of Solids and Structures 2022, 257, 111728. https://doi.org/10.1016/j.ijsolstr.2022.111728
Li, L., Wang, R., Zhao, H., Zhang, H., Yan, R. (2021). Combined effects of elevated temperatures and high strain rates on compressive performance of S30408 austenitic stainless steel. Structures, 34, 1-9.https://doi.org/10.1016/j.istruc.2021.07.063
Armstrong, R., Walley, S. (2008). High strain rate properties of metals and alloys. International Materials Reviews, 53 (3), 105-128. https://doi.org/10.1179/174328008X277795
Chen, A., Ruan, H., Wang, J., Chan, H., Wang, Q., Li, Q., Lu, J. (2011). The influence of strain rate on the microstructure transition of 304 stainless steel. Acta Materialia, 59 (9), 3697-3709.https://doi.org/10.1016/j.actamat.2011.03.005
Xu, D., Wan, X., Yu, J., Xu, G., Li, G. (2018). Effect of strain rate on microstructures and mechanical properties of Fe–18Cr–8Ni steel. Materials Science and Technology, 35(2), 195-203. https://doi.org/10.1080/02670836.2018.1548113
Nemat-Nasser, S., Guo, W. G., & Kihl, D. P. (2001). Thermomechanical response of AL-6XN stainless steel over a wide range of strain rates and temperatures. Journal of the Mechanics and Physics of Solids, 49(8), 1823-1846. https://doi.org/10.1016/S0022-5096(00)00069-7
Xiao, L., Xu, X., & Wang, H. (2022). A comparative study of finite element analysis of single-particle impact on mild steel with and without strain rate considered. International Journal of Impact Engineering, 159, 104029. https://doi.org/10.1016/j.ijimpeng.2021.104029
He, Z. F., Jia, N., Wang, H. W., Liu, Y., Li, D. Y., & Shen, Y. F. (2020). The effect of strain rate on mechanical properties and microstructure of a metastable FeMnCoCr high entropy alloy. Materials Science and Engineering: A, 776, 138982. https://doi.org/10.1016/j.msea.2020.138982
Hund, J., Granum, H. M., Olufsen, S. N., Holmström, P. H., Johnsen, J., & Clausen, A. H. (2022). Impact of stress triaxiality, strain rate, and temperature on the mechanical response and morphology of PVDF. Polymer Testing, 114, 107717. https://doi.org/10.1016/j.polymertesting.2022.107717.
Kun, Q., Li-Ming, Y., & Shi-Sheng, H. (2009). Mechanism of strain rate effect based on dislocation theory. Chinese Physics Letters, 26(3), 036103. https://doi.org/10.1088/0256-307X/26/3/036103.
Seo, J. M., Kim, H. T., Kim, Y. J., Yamada, H., Kumagai, T., Tokunaga, H., & Miura, N. (2022). Effect of strain rate and stress triaxiality on fracture strain of 304 stainless steels for canister impact simulation. Nuclear Engineering and Technology. https://doi.org/10.1016/j.net.2022.02.002
Yu, J., Li, J., Hu, S. (2006). Strain-rate effect and micro-structural optimization of cellular metals. Mechanics of Materials, 38 (1-2), 160–170.https://doi.org/10.1016/j.mechmat.2005.05.018
Zhang, S., Chen, W., Gao, D., Xiao, L., Han, L. (2020). Experimental Study on Dynamic Compression Mechanical Properties of Aluminium Honeycomb Structures. Applied Sciences,(10) 3, 1188. https://doi.org/10.3390/app10031188

Strain Rate Analysis of Efficient Honeycomb Sandwich Panels under Blast Load

Status:

Version 1

Abstract

Figures

1. Introduction

2. Numerical Modeling Of The Metallic Honeycomb Sandwich Panel (Mhsp)