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Poster Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011

Assessment of Sandwich Plates Subject to Blast Loads Chitralekha Dey1 Sunil Nimje 2 1. Research & Development Establishment (Engrs.) Defence Research & Development Organization Dighi, Pune 411 015 2. Defence Institute of Advanced Technology (DEEMED UNIVERSITY) Defence Research & Development Organization Girinagar, Pune-411025 (Email: chitralekha.dey@gmail.com, sunil.nimje@diat.ac.in) Abstract - In today’s date, the impact resistance of engineering structures subjected to blast and impact is of great interest and concern to the engineering community and government agencies against possible terrorist threats. Structures subject to blast loading usually undergo large plastic deformation and absorb energy before collapsing to a stable configuration or fracture. Sandwich beams with cellular core structures are found to be efficient blast resistant structures due to their high compressive strength to weight ratio and high bending stiffness. The paper outlines in brief the finite element analysis of a sandwich plate with a tetrahedral core subjected to blast loads. They were then verified against literature results from the paper “Preliminary assessment of sandwich plates subject to blast loads” by Zhenyu Xue et all published in the International Journal of mechanical sciences. In the present paper, the results are in very good agreement to the published data with a different methodology of load application.

I. INTRODUCTION During explosion, the peak pressure produced by shock wave is much greater than the static collapse pressure of structures. An insight into the relationship between explosion loads and structure deformation behavior can offer a structure with significant energy absorption and blast impact resistance performance. Cellular solids with metal foam and honeycombs can absorb considerable energy by plastic dissipation in compression. Their cellular microstructure, endows them with the ability to undergo large deformation at nearly constant nominal stress. Periodic cellular metals are highly porous structures with 20% or less of their interior volume occupied by metals. Their high stiffness to weight and strength to weight ratio as compared to that of a single solid plate of the same total weight and same material makes them as a more attractive and better alternative for blast mitigation purposes. Hence they are used as the cores of sandwich structures to absorb impacts and shocks. There are three classes of periodic cellular metals-honeycomb, corrugated and lattice truss.

Fig 1

II. APPLICATIONS Sandwich construction with honeycomb and corrugated topology cores are widely used for the cores of light weight sandwich panel structures. Corrugated core provide cross flow heat exchange properties, because their cores are continuous in one direction. Cellular metals with open cell topologies are highly attractive heat exchange media where dissipation of high intensity heat in relatively small space is required. The need to protect structures from high intensity dynamic loads created by air or water explosions has simulated interest in the periodic cellular structures to replace the monolithic load supporting structures. The cellular metals mitigation approach utilizes the sandwich panels concepts to disperse the mechanical impulse transmitted to the structures, thereby reducing the transmitted pressure impulse to the protected structure located behind. The ballistic properties of cellular metals is also been investigated. Use of closed cell aluminum foams in layered integral armour concepts finds potentially significant improvement in system performance due to the delay and attenuation of stress wave propagation. Layers of foams are found to decouple the underlying structure from the high intensity stress waves produced by ballistic projectiles. 44

Poster Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011 IV. PROBLEM DEFINITION

III. BLAST LOADING

Finite element analysis of solid circular plates and sandwich plates of equal mass subject to blast loads had been carried out. They were then verified against literature results from the paper “Preliminary assessment of sandwich plates subject to blast loads” by Zhenyu Xue, John W Hutchinson published in the International Journal of mechanical sciences. In the referred paper, blast loads of sufficient magnitude were applied to metal sandwich plates and solid plates of same mass and material, such that the plates undergo permanent deflections. The zero period impulse resulting due to blast is applied as an initial velocity of the top plate. Whereas the procedure followed in load application is different in the present paper. The load was applied as a pressure time curve where the load ceases to exist after t = τ. The material is taken to be elastic-perfectly plastic with no strain rate dependence. Detailed descriptions of the core were not pursued in the paper, where core properties representative of tetrahedral truss cores were considered. Computations were performed using the explicit time integration version of ABAQUS.The problems which had been attempted are as follows:  Clamped solid circular plate loaded impulsively (zero period impulse)  Clamped circular sandwich plate with a truss core (High strength steel)  Clamped circular sandwich plate with truss core (aluminum alloy)

Fig 2

When an explosive charge is detonated gaseous reaction products compress the surrounding air and structure located behind. The rapid expansion of the detonation products creates a shock wave with discontinuities in pressure, density, temperature and velocity. The shock wave that travels through the air consists of highly compressed air particles that exert pressure on all surfaces they encounter. There is a discontinuous ‘jump’ of the shock front pressure, with the

V. IDEALIZED BLAST LOADING Explosives create a pressure wave with a triangular like profile known as blast. The blast exerts an impulse I on the circular plate, which is equal to the integral of the total force over time. In the present case the pressure pulse applied to the plate was idealized to be uniform over the entire plate with amplitude po and duration τ

Fig 3

pressure rising from ambient (pa) to ps. The pressure difference is referred to as the blast overpressure. At a fixed location in space, the pressure decays exponentially with time after the arrival of the shock and is followed by a negative (i.e. suction) phase. The detonation of explosive creates a shock wave in the surrounding air, which is known as a blast wave. One significant blast wave parameter is the specific impulse of the wave during the positive phase Is, as given by

Fig 4 2

The impulse I=πR poτ.The family of loads corresponds to zero period impulse (τ 0) VI. CLAMPED SOLID CIRCULAR PLATE LOADED IMPULSIVELY (ZERO PERIOD IMPULSE) A circular solid plate with outer radius R and uniform thickness h, which is fully clamped at the outer boundary, was subjected to a blast load. The pressure pulse applied to the plate was idealized to be uniform over the entire plate with amplitude p0 and duration τ, such that the impulse is

Where P (t) is overpressure as a function of time and ta is the time of arrival of the blast wave and ta+td is the time when the pressure falls to the pre-shock level.

Poster Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011 I= πr2p0 τ .The impulse per area is I1= p0 τ .The limit of this family of loads corresponding to a zero period impulse. The elastic–plastic behavior of the plate is described by an elastic-perfectly plastic model with Young’s modulus E, Poisson’s ratio ν and uniaxial tensile yield stress σy.The Von Misses criterion is used to specify the yield surface. The plate was modeled as a three dimensional solid

Fig.7 Comparative representation of deflection values

Fig 5 In the referred paper, the authors had carried out numerical analysis of the plate subject to blast loading and compared the same with standard theoretical results. Several graphs have been shown depicting the variation of the response time and maximum deflection with the variation of different material parameters.

Fig.8 V0"ρ=4000. The time of load application is 0.0015ms δmax.=0.12m,published value=0.16m.

Variation of maximum deflection with relative core density

Fig.9 V0"ρ=10,000. The time of load application is 0.002ms , δmax.=0.32m , published value =0.35m.

Variation of maximum deflection with Young’s modulus

Fig.6 Influence of relative core density on the normalized maximum deflection. E=200GPa,ν =0.3, σy =580MPa,R=1m,h=0.02m T ABLE 1

Poster Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011 T ABLE II

The tetragonal truss core had not been modeled. Instead the core was modeled as a solid whose effective properties mimic those of the tetragonal truss. A constitutive model developed for metal foams had been adopted .The model permits to set the crushing strength of the core to match values appropriate to the tetragonal truss. The relative density of the core ρc1 defined as the ratio of equivalent core density ρc to the density of the material ρ.The crushing yield stress of the regular tetragonal core σcy is defined as the normal force per unit area applied to the face sheet which is required in bringing down the truss members to compressive yield. It is related to the relative density by



2 y c



1 c

y

Young’s modulus of the core under normal loading of the face sheets Ec is

Fig. 11 Graphical representation of deflection values

The poisons ratio ν =0 is motivated by the fact that its compressive behavior normal to the faces is essentially independent of deformations parallel to the faces. Fig.12 E=500GPa. The time of load application is 0.003ms .δmax.=0.088m , Published value =0.093m

VII. CLAMPED CIRCULAR SANDWICH PLATE WITH A TRUSS CORE ( HIGH STRENGTH STEEL) The response of a clamped circular sandwich plate with a tetrahedral truss core had been verified for a uniformly distributed impulsive load applied to the top face sheet of the plate towards the blast. The radius of the sandwich plate is R.The plate has two identical face sheets of thickness h f bonded to a tetragonal truss structure core of thickness Hc.The face sheets and the truss elements are made from the same elastic-perfectly plastic material with density ρ, Young’s modulus E, tensile yield stress σy and poisons ratio ν.The yield surface of the face sheets is again taken to be the Von misses surface.

Fig.14

The normalized maximum deflection of top and bottom face sheets of a sandwich plate versus relative density of core for three zero period impulses. E=200GPa, ν =0.3, σy =580MPa, R=1m, hf=0.008m, Hc=0.10m

Fig.15 Graphical representation of deflection values.Table 1

Fig 13

Poster Paper Proc. of Int. Conf. on Advances in Robotic, Mechanical Engineering and Design 2011 T ABLE – 3

Fig. 16

I=32KN-s. Relative density=0.08 The time of load application is 0.0005ms δmax.=0.11m , published value

Fig. 17 Time histories of plastic dissipation in the whole model with I=32KN-s., relative density=0.08

VIII. CLAMPED CIRCULAR SANDWICH PLATE WITH TRUSS CORE (ALUMINUM ALLOY) Aluminum-silicon alloy is approximated as an elastic,

ideally plastic solid with Young’s modulus ES=70GPa, yield

CONCLUSION

strength σy=170MPa.

The challenging tasks of analysis of sandwich plates with tetrahedral core subject to blast loading had been accomplished successfully. ACKNOWLEDGEMENT Authors gratefully acknowledge the guidance and the encouragement given by Dr. S Guruprasad, Director, R&DE (Engrs) and Shri N.B.Vijayakumar, Joint Director, Combat Engineering in carrying out this work. REFERENCES Fig. 18 Graphical representation of deflection values

1. Zhenyu Xue, John W. Hutchinson “Preliminary assessment of sandwich plates subject to blast loads , International Journal of Mechanical Sciences 45 (2003) 687–705 2. F. Zhu & G. Lu, A Review of Blast and Impact of Metallic and Sandwich Structures, EJSE Special Issue: Loading on Structures (2007) 3. Haydn N. G. Wadley, Multifunctional periodic cellular metals, Phil. Trans. R. Soc A, 2006, 364, 31-68 4. Allen H.G, 1969, Analysis and design of structural sandwich panels 5. V.S.Deshpande, N.A Fleck, Collapse of truss core sandwich beams in 3-point bending, International journal of solids and structures 38(2001), 6275-6305 6. Jones, N. (1989) Structural Impact. Cambridge University Press, UK.