dynamic behavior of a steel plate subjected to blast loading · test results were compared with the...

DYNAMIC BEHAVIOR OF A STEEL PLATE SUBJECTED TO BLAST LOADING

Jong Yil Park1, Eunsun Jo2, Min Sook Kim2, Seung Jae Lee3 and Young Hak Lee2,41Department of Safety Engineering, Seoul National University of Science and Technology, Seoul, Korea

2Department of Architectural Engineering, Kyung Hee University, Yongin, Korea3The 8th R&D Institute, Agency for Defense Development, Korea

E-mail: [email protected]

IMETI 2015 SA5011_SCINo. 16-CSME-14, E.I.C. Accession Number 3900

ABSTRACTThis paper presents the results of an experimental test conducted on the blast resistance of a steel plate. Asupporting steel frame on a concrete foundation was designed for testing a steel plate target against blastloading. A 1220 mm × 2140 mm × 10 mm steel plate was tested and subjected to the explosion of 50 kg ofTNT (tri-nitro toluene) at a stand-off distance of 20 m. Data collected from the specimen included the strainand deflection of the steel plate. The test data were analyzed to evaluate the performance of the plate. Thetest results were compared with the results of Autodyn, which is a finite element method-based commercialsoftware. The analytical results showed minor differences from the test results when the boundary conditionsof the steel plate assumed that the upper and lower sides were fixed and the other sides were free.

Keywords: blast loading; hydro code; steel plate; finite-element analysis; Autodyn.

COMPORTEMENT DYNAMIQUE D’UNE PLAQUE D’ACIER EXPOSÉE AU SOUFFLE D’UNECHARGE EXPLOSIVE

RÉSUMÉCet article présente les résultats d’un test expérimental effectué sur la résistance d’une plaque d’acier ausouffle d’une charge explosive. On a conçu un cadre en acier supporté par une structure de béton pour éva-luer le comportement d’une plaque d’acier soumise au souffle d’une charge explosive. Elle a été soumiseà une charge explosive de 50 kg of TNT (trinitrotoluène) à une distance de sécurité de 20 m. Les donnéesrecueillies du spécimen comportaient la déformation et la flexion de la plaque d’acier. Ces données furentanalysées pour évaluer la performance de la plaque. Les résultats ont été comparés avec les résultats pro-venant d’Autodyn, un logiciel commercial basé sur la méthode des éléments finis. Les résultats analytiquesont montré que des différences minimes dans les résultats des tests quand les conditions limites de la plaqued’acier supposaient que les côtés supérieure et inférieure étaient fixes et les autres côtés étant libres.

Mots-clés : souffle d’une charge explosive; plaque d’acier; analyse des éléments finis; Autodyn.

Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 4, 2016 575

1. INTRODUCTION

When a blast occurs, immediate damage is caused to structural members. This can lead to the loss of livesand result in secondary damage caused by progressive collapse and fragment accidents over a short periodof time. When performing experiments on blast loading, there can be problems related to the safety of theexperimental processes and/or related to the cost because of the large expense associated with these exper-iments. As such, because there are limited experimental environments that can be used for blast loading,few experimental models have been used, and only a small amount of experimental data has been obtained.In this study, an experiment was performed and the simulation results were examined by comparing thesimulated and experimental results in an attempt to increase the reliability of the simulation.

Ngo et al. [1] conducted an experiment in which equivalent explosives containing 6 ton of TNT weredetonated at a stand-off distance of 30 to 40 m to demonstrate the behavior of ultra-high-strength pre-stressedconcrete panels. Through this experiment, it was determined that the pre-stressed panels exhibited excellentblast resistance and that the damage level varied according to the thickness of the specimens. Concretestructures that were affected by blasts and impact loading were also analyzed by finite element analysisfor verifying experimental results. Carriere et al. [2] examined the changes in the resistance capacity ofconcrete columns affected by blast loading; for this purpose, they applied steel polymer reinforcements tothe concrete structure test samples. By analyzing the experimental and simulation results, they confirmedthat the concrete column that was strengthened by the steel polymer reinforcement showed better resistanceperformance compared to typical concrete columns. In an experiment performed by Jacob et al. [3], mildsteel plates were completely fixed with stand-off distances of 13 to 300 mm, and the degree of damage wasexamined.

In this study, 50 kg of TNT was detonated at a stand-off distance of 20 m and a height of 1 m above theground. Then, the incident pressure that was measured during the experiment was compared with the resultsobtained by modeling the explosion pressure simulated by Autodyn (version 15.0). The central displacementand the central and horizontal strains were also measured. The experimental results were compared with thesimulation results obtained from Autodyn in order to validate the simulation method that was used in thisstudy.

2. BLAST LOADING

2.1. The Material Model2.1.1. Explosive and airAutodyn expresses air with an equation of state using an ideal gas and the energy-related pressure, as shownin Eq. (1). In this equation, γ is a constant, ρ is the density of air, and e is the specific internal energy. Thesevalues are set as 14, 1.225 kg/m3, and 206800 kJ/kg, respectively.

P = (γ −1)ρ. (1)

Also, the explosive is represented by the Jones–Wilkins–Lee (JWL) [4] physical property algorithm; theJWL equation of state is shown in Eq. (2). The JWL algorithm is defined based on data of constants obtainedfrom an experiment. η = ρ/ρ0, where ρ0 is the reference density, and A, B, R1, R2, and ω are constantsdetermined by dynamic experiments.

P = A(

1− ωη

R1

)eR1/η +B

(1− ωη

R2

)eR2/η +ωρe. (2)

2.1.2. Steel plateThe Johnson Cook model was utilized for modeling the steel plates; this model is appropriate for materialsinfluenced by high strain, strain speed, and temperature. [5] The yield stress Y of this model is defined

576 Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 4, 2016

Table 1. Material properties of the steel plate.Density [kg/m3] 7850Poisson’s ratio 0.26Yield strength [MPa] 252.5Modulus of elasticity [MPa] 207829

Fig. 1. Schematic view of the test frame.

as shown in Eq. (3). A,B,C,n and m are material constants. εP is the effective plastic strain, ε̇nP is the

normalized effective plastic strain rate, and TH is the temperature.

Y = [A+BεnP]

[1+C ln

ε̇P

ε̇0

][1−T m

H ]. (3)

2.2. Numerical ModelSimulation was performed by directly applying the blast loading as a piecewise stress to a 3D simulationmodel. In this simulation, steel plates were modeled using a Lagrange solver. In addition, fixed conditionswere applied to the top and bottom sides of the steel plate. The size of the element was 61 mm × 42.8 mm× 2.5 mm.

3. EXPERIMENT

3.1. Material PropertiesThe material properties of the steel plate are summarized in Table 1. The average yield strength and modulusof elasticity of the steel plate were measured to be 252.5 and 207829 MPa, respectively. Therefore, thestandard values of Steel 4340, which are provided in the properties library of Autodyn, were applied to thesimulation. The properties for this material are as follows: the density is 7.85 g/cm3, the bulk modulus is159 GPa, the shear modulus is 81.8 GPa, the reference temperature is 300 K, and the specific heat is 477 J/kgK. Additionally, the yield strength of the material model was set to be 252.2 MPa same as the yield strengthof the steel plate in this experiment.


Fig. 2. Test setup.

Fig. 3. Pressure sensor locations.

3.2. Test SetupFigure 1 shows the frame used to install the specimen. The dimensions of the frame supporting the specimenwere 1800 mm × 2200 mm. The concrete foundation was placed on the ground to prevent the frame frombeing pushed away by the explosion pressure. Both the top and bottom sides of the specimen were fixed byhigh strength bolts at an interval of 150 mm.

The dimensions of the concrete foundation were 4000 mm × 4000 mm × 200 mm, and its averagemeasured compressive strength was 35 MPa. Rebars with a diameter of 16 mm were also placed at intervalsof 150 mm, both horizontally and vertically, as flexural reinforcements. Figure 2 shows the front view ofthe specimen installed for the test.

Figure 3 shows the detonation of 50 kg of TNT at a stand-off distance of 20 m. The explosive was deto-nated from the point 1 m above the ground, and a cube of TNT explosive (320 mm × 320 mm × 320 mm)


Fig. 4. Scheme of the strain gauges.

Fig. 5. Notation to indicate each type of result.

was used in the test. In Fig. 3, S1 stands for the steel plate specimen. The specimen was located 20 m awayfrom the detonation point. Incident pressure sensor IP_1500 mm, IP_2000 mm, and IP_2500 mm, whichare depicted in Fig. 3, indicate the locations of the sensors used to measure the incident pressure at threedifferent stand-off distances. Figure 4 shows the location of the strain gauges attached to the steel plate. Thenotations which identify each result (both experimental and analytical) are shown in Fig. 5.

4. COMPARISON BETWEEN EXPERIMENTAL RESULTS AND ANALYTICAL PREDICTIONS

4.1. Explosion PressureIn terms of the explosion pressure, the incident pressures measured in the experiment were compared withthose simulated by Autodyn. This was done in order to verify the simulation method used in this study.Figure 6 shows the actual explosion of 50 kg of TNT in the test field.

In the 2D environment of Autodyn, the entire air size was modeled to be 10000 mm ×30000 mm, andthe mesh size was set to be 25 mm; thus, there are 400 elements ×1200 elements = 480000 elements usedto form the air. Figure 7 shows the blast loading modeled in the 2D environment of Autodyn. Boundaryconditions were not applied to the lower y-axis (x = 0) to consider the surface blast simulation, and flow-outconditions were applied to the other air boundaries to prevent reflection.

The experimental and simulated results for the maximum incident pressure at three different stand-off dis-tances were compared. The simulation results were smaller than the experimental results by approximately


Fig. 6. Detonation of 50 kg of TNT.

Fig. 7. Explosion pressure modeling by Autodyn.

16 to 23%. As the stand-off distance increased, the difference between the experimental and simulated re-sults decreased. Additionally, the arrival times of the incident pressure obtained from the experimental andsimulated results were very similar, with a difference of approximately 0.4 to 2.9%. The main purpose ofthe predicting pressure was to set the sensing range of the pressure gauge before testing.

The pressure difference between the field test and analysis results comes from the ground conditions,TNT shape, and sensor direction change. The measured pressure history was used to analyze the platebehavior. Table 2 presents the maximum incident pressure and arrival time of the blast waves derived fromthe experimental and simulated results for the three different stand-off distances.


Table 2. Comparison between simulation and experimental results.Stand-off Distance

15 m 20 m 25 mPeak Incident Pressure [kPa] Autodyn 69.67 41.70 28.72

Experiment 90 50 34Difference 23% 17% 16%

Arrival Time [ms] Autodyn 20.88 32.92 45.71Experiment 21.5 32.8 46.5Difference 2.9% 0.4% 1.7%

Fig. 8. The simulated strains of S1.

4.2. Evaluation of the Displacement

The experimental and simulation results on the central displacement of the steel plate were compared. Theexplosion pressure reached the specimen after approximately 33 ms at a stand-off distance of 20 m. Themaximum displacement of S1 was measured to be 33.55 mm after approximately 51 ms. Alternatively, themaximum displacement simulated in Autodyn was 31.22 mm at 44 ms, showing a difference of 6.7% fromthe maximum displacement of S1 in the experiment.

4.3. Strain of S1

The horizontal strains were measured at the center of S1. Figure 8 presents the strains in S1 that were derivedvia simulation, indicating that the strains at gauges G1, G2, and G3 were similar. The simulation resultsalso showed that the strains of the three gauges were very similar in the horizontal direction. Figure 9presents the experimental and simulation strain results. The maximum simulated strain was 0.001. Theexperimental strain of G3 was 0.0010, showing a difference of approximately 10% from the simulatedstrain. The maximum strains were found to be 0.0010 (experimental) and 0.0011 (simulation). Given thatthe strain values derived from both experiments and simulations did not reach the yield strain value, it wasconfirmed that the steel plate maintained elastic behavior. The strains obtained experimentally and fromsimulation are summarized in Table 3.


Fig. 9. Simulation and experimental strain results for S1.


Table 3. Strain of S1.Experiment Autodyn Difference in Peak Strain

E_S1_G1 0.0008 A_S1_G1 0.0011 28%E_S1_G2 0.0007 A_S1_G2 0.0011 37%E_S1_G3 0.0010 A_S1_G3 0.0011 10%

5. CONCLUSIONS

In this study, a blast experiment was performed and compared with simulation results in order to examinethe validity of the simulation method. According to stand-off distances of 15, 20, and 25 m, the incidentpressure indicated that the simulation values were less than the experimental values by approximately 23, 17,and 16%, respectively. The arrival time of the explosion pressure was very similar in both results, showingdifferences of approximately 2.9, 0.4, and 1.7% for stand-off distances of 15, 20, and 25 m, respectively.

The LVDT was installed at the center of the steel plate to measure the maximum displacement, whichwas found to be 33.55 mm in the specimen. In the simulation by Autodyn, the maximum displacement wasfound to be 31.22 mm, which was smaller than the experimental value by 2.29 mm.

The strain measured in the experiment indicated that G3 of S1 showed the greatest strain (0.0010) amongall of the strain gauges, while a strain of 0.0011 was the biggest value in the simulation result. The yieldstrain of the steel plate used in this experiment was 0.0012; because neither the experimental nor simulatedstrain values reached the yield strain, the steel plate would maintain elastic behavior.

ACKNOWLEDGEMENTS

This work was supported by the Agency for Defense Development, Korea (2014-1294) and the Na-tional Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2013R1A2A2A01067754).

REFERENCES

1. Ngo, T., Mendis, P. and Krauthammer, T., “Behavior of ultra high-strength prestressed concrete panels subjectedto blast loading”, Journal of Structural Engineering, Vol. 133, No. 11, pp. 1582–1590, 2007.

2. Carriere, M., Heffernan, P.J., Wight, R.G. and Braimah, A., “Behavior of steel reinforced polymer strengthenedRC members under blast load”, Canadian Journal of Civil Engineering, Vol. 36, pp. 1356–1365, 2009.

3. Jacob, N., Nurick, G.N. and Langdon, G.S., “The effect of stand-off distance on the failure of fully clampedcircular mild steel plates subjected to blast loads”, Engineering Structures, Vol. 29, pp. 2723–2736, 2007.

4. Lee, E.L., Horning, H.C. and Kury, J.W., “Adiabatic expansion of high explosives detonation products”, LawrenceLivermore National Laboratory, University of California, Livermore, TID 4500-UCRL 50422, 1968.

5. Johnson, G.R. and Cook, W.H., “A constitutive model and data for metals subjected to large strains, high strainrates and high temperatures”, in Proceedings of the Seventh International Symposium on Ballistics, The Hague,The Netherlands, pp. 541–548, 1983.


dynamic behavior of a steel plate subjected to blast loading · test results were compared with the...

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