DYNAMIC BEHAVIOR OF A STEEL PLATE SUBJECTED TO BLAST LOADING Jong Yil Park 1, Eunsun Jo 2, Min Sook Kim 2, Seung Jae Lee 3 and Young Hak Lee 2,4 1 Department of Safety Engineering, Seoul National University of Science and Technology, Seoul, Korea 2 Department of Architectural Engineering, Kyung Hee University, Yongin, Korea 3 The 8th R&D Institute, Agency for Defense Development, Korea E-mail: leeyh@khu.ac.kr IMETI 2015 SA5011_SCI No. 16-CSME-14, E.I.C. Accession Number 3900 ABSTRACT This paper presents the results of an experimental test conducted on the blast resistance of a steel plate. A supporting steel frame on a concrete foundation was designed for testing a steel plate target against blast loading. A 1220 mm 2140 mm 10 mm steel plate was tested and subjected to the explosion of 50 kg of TNT (tri-nitro toluene) at a stand-off distance of 20 m. Data collected from the specimen included the strain and deflection of the steel plate. The test data were analyzed to evaluate the performance of the plate. The test results were compared with the results of Autodyn, which is a finite element method-based commercial software. The analytical results showed minor differences from the test results when the boundary conditions of 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 UNE CHARGE EXPLOSIVE RÉSUMÉ Cet article présente les résultats d un test expérimental effectué sur la résistance d une plaque d acier au souffle d une charge explosive. On a conçu un cadre en acier supporté par une structure de béton pour évaluer le comportement d une plaque d acier soumise au souffle d une charge explosive. Elle a été soumise à une charge explosive de 50 kg of TNT (trinitrotoluène) à une distance de sécurité de 20 m. Les données recueillies du spécimen comportaient la déformation et la flexion de la plaque d acier. Ces données furent analysées pour évaluer la performance de la plaque. Les résultats ont été comparés avec les résultats provenant d Autodyn, un logiciel commercial basé sur la méthode des éléments finis. Les résultats analytiques ont montré que des différences minimes dans les résultats des tests quand les conditions limites de la plaque d 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 lives and result in secondary damage caused by progressive collapse and fragment accidents over a short period of time. When performing experiments on blast loading, there can be problems related to the safety of the experimental processes and/or related to the cost because of the large expense associated with these experiments. 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 the simulated 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 were detonated at a stand-off distance of 30 to 40 m to demonstrate the behavior of ultra-high-strength pre-stressed concrete panels. Through this experiment, it was determined that the pre-stressed panels exhibited excellent blast resistance and that the damage level varied according to the thickness of the specimens. Concrete structures that were affected by blasts and impact loading were also analyzed by finite element analysis for verifying experimental results. Carriere et al. [2] examined the changes in the resistance capacity of concrete columns affected by blast loading; for this purpose, they applied steel polymer reinforcements to the concrete structure test samples. By analyzing the experimental and simulation results, they confirmed that the concrete column that was strengthened by the steel polymer reinforcement showed better resistance performance compared to typical concrete columns. In an experiment performed by Jacob et al. [3], mild steel plates were completely fixed with stand-off distances of 13 to 300 mm, and the degree of damage was examined. In this study, 50 kg of TNT was detonated at a stand-off distance of 20 m and a height of 1 m above the ground. Then, the incident pressure that was measured during the experiment was compared with the results obtained by modeling the explosion pressure simulated by Autodyn (version 15.0). The central displacement and the central and horizontal strains were also measured. The experimental results were compared with the simulation results obtained from Autodyn in order to validate the simulation method that was used in this study. 2. BLAST LOADING 2.1. The Material Model 2.1.1. Explosive and air Autodyn expresses air with an equation of state using an ideal gas and the energy-related pressure, as shown in Eq. (1). In this equation, γ is a constant, ρ is the density of air, and e is the specific internal energy. These values are set as 14, 1.225 kg/m 3, 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; the JWL equation of state is shown in Eq. (2). The JWL algorithm is defined based on data of constants obtained from an experiment. η = ρ/ρ 0, where ρ 0 is the reference density, and A, B, R 1, R 2, and ω are constants determined by dynamic experiments. P = A ( 1 ωη R 1 ) ( e R1/η + B 1 ωη ) e R2/η + ωρe. (2) R 2 2.1.2. Steel plate The Johnson Cook model was utilized for modeling the steel plates; this model is appropriate for materials influenced 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/m 3 ] 7850 Poisson s ratio 0.26 Yield strength [MPa] 252.5 Modulus 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. ε P is the effective plastic strain, ε P n normalized effective plastic strain rate, and T H is the temperature. is the 2.2. Numerical Model [ Y = [A + BεP] n 1 +C ln ε ] P [1 TH m ]. (3) ε 0 Simulation was performed by directly applying the blast loading as a piecewise stress to a 3D simulation model. In this simulation, steel plates were modeled using a Lagrange solver. In addition, fixed conditions were 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 Properties The material properties of the steel plate are summarized in Table 1. The average yield strength and modulus of elasticity of the steel plate were measured to be 252.5 and 207829 MPa, respectively. Therefore, the standard values of Steel 4340, which are provided in the properties library of Autodyn, were applied to the simulation. The properties for this material are as follows: the density is 7.85 g/cm 3, the bulk modulus is 159 GPa, the shear modulus is 81.8 GPa, the reference temperature is 300 K, and the specific heat is 477 J/kg K. Additionally, the yield strength of the material model was set to be 252.2 MPa same as the yield strength of the steel plate in this experiment. Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 4, 2016 577
Fig. 2. Test setup. Fig. 3. Pressure sensor locations. 3.2. Test Setup Figure 1 shows the frame used to install the specimen. The dimensions of the frame supporting the specimen were 1800 mm 2200 mm. The concrete foundation was placed on the ground to prevent the frame from being pushed away by the explosion pressure. Both the top and bottom sides of the specimen were fixed by high strength bolts at an interval of 150 mm. The dimensions of the concrete foundation were 4000 mm 4000 mm 200 mm, and its average measured compressive strength was 35 MPa. Rebars with a diameter of 16 mm were also placed at intervals of 150 mm, both horizontally and vertically, as flexural reinforcements. Figure 2 shows the front view of the 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 detonated from the point 1 m above the ground, and a cube of TNT explosive (320 mm 320 mm 320 mm) 578 Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 4, 2016
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 away from the detonation point. Incident pressure sensor IP_1500 mm, IP_2000 mm, and IP_2500 mm, which are depicted in Fig. 3, indicate the locations of the sensors used to measure the incident pressure at three different stand-off distances. Figure 4 shows the location of the strain gauges attached to the steel plate. The notations which identify each result (both experimental and analytical) are shown in Fig. 5. 4. COMPARISON BETWEEN EXPERIMENTAL RESULTS AND ANALYTICAL PREDICTIONS 4.1. Explosion Pressure In terms of the explosion pressure, the incident pressures measured in the experiment were compared with those 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, and the mesh size was set to be 25 mm; thus, there are 400 elements 1200 elements = 480000 elements used to form the air. Figure 7 shows the blast loading modeled in the 2D environment of Autodyn. Boundary conditions were not applied to the lower y-axis (x = 0) to consider the surface blast simulation, and flow-out conditions 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 distances were compared. The simulation results were smaller than the experimental results by approximately Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 4, 2016 579
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 results decreased. Additionally, the arrival times of the incident pressure obtained from the experimental and simulated results were very similar, with a difference of approximately 0.4 to 2.9%. The main purpose of the 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 plate behavior. Table 2 presents the maximum incident pressure and arrival time of the blast waves derived from the experimental and simulated results for the three different stand-off distances. 580 Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 4, 2016
Table 2. Comparison between simulation and experimental results. Stand-off Distance 15 m 20 m 25 m Peak Incident Pressure [kpa] Autodyn 69.67 41.70 28.72 Experiment 90 50 34 Difference 23% 17% 16% Arrival Time [ms] Autodyn 20.88 32.92 45.71 Experiment 21.5 32.8 46.5 Difference 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. The explosion pressure reached the specimen after approximately 33 ms at a stand-off distance of 20 m. The maximum displacement of S1 was measured to be 33.55 mm after approximately 51 ms. Alternatively, the maximum displacement simulated in Autodyn was 31.22 mm at 44 ms, showing a difference of 6.7% from the 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 derived via simulation, indicating that the strains at gauges G1, G2, and G3 were similar. The simulation results also showed that the strains of the three gauges were very similar in the horizontal direction. Figure 9 presents the experimental and simulation strain results. The maximum simulated strain was 0.001. The experimental strain of G3 was 0.0010, showing a difference of approximately 10% from the simulated strain. The maximum strains were found to be 0.0010 (experimental) and 0.0011 (simulation). Given that the strain values derived from both experiments and simulations did not reach the yield strain value, it was confirmed that the steel plate maintained elastic behavior. The strains obtained experimentally and from simulation are summarized in Table 3. Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 4, 2016 581
Fig. 9. Simulation and experimental strain results for S1. 582 Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 4, 2016
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 examine the validity of the simulation method. According to stand-off distances of 15, 20, and 25 m, the incident pressure 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, showing differences 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, which was found to be 33.55 mm in the specimen. In the simulation by Autodyn, the maximum displacement was found 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) among all of the strain gauges, while a strain of 0.0011 was the biggest value in the simulation result. The yield strain of the steel plate used in this experiment was 0.0012; because neither the experimental nor simulated strain 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 National 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 subjected to 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 strengthened RC 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 clamped circular 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, Lawrence Livermore 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 strain rates and high temperatures, in Proceedings of the Seventh International Symposium on Ballistics, The Hague, The Netherlands, pp. 541 548, 1983. Transactions of the Canadian Society for Mechanical Engineering, Vol. 40, No. 4, 2016 583