Numerical-experimental Study on Steel Plates Subjected to Blast Loading

Numerical-experimental study of steelplates subjected to blast loading

Daniel Ambrosini1,2 & Abel Jacinto3

1CONICET2Engineering Faculty, Nat. Univ. of Cuyo, Argentina3Politechnical Univ. of Cataluna, Spain

Abstract

The main objective of this paper is the comparison between testing andnumerical responses of metallic plates subjected to air blast loads, in or-der to determine the accuracy of modern calculation methods and compu-tational codes. The secondary objective is to provide data that could beused for checking the accuracy of a variety of calculation methods. A setof four tests at full scale is presented on two non-stiffened metallic steelplates with different boundary conditions (one set up as a cantilever andanother clamped along the four edges), subjected to the action of pressurewaves originating from the detonation of high explosive charges. The timehistory of the acceleration at different points on both plates and the pres-sure waves at selected points, are recorded. In addition, a linear dynamicanalysis of the plate models was carried out (using the codes ABAQUS andCOSMOS). Suggestions about computational modeling of structures underimpulsive loads are discussed arising from the comparison of numerical andexperimental results.

Keywords: air blast waves, unstiffened plates, dynamic response, experimentalanalysis

1 Introduction

In recent years explosive loads have received considerable attention becauseof different events, accidental or intentional, relating to important structuresall over the world. As a consequence, there has been an increased activity

WIT Transactions on Engineering Sciences, Vol 49

Impact Loading of Lightweight Structures, M. Alves & N. Jones (Editors)

c© 2005 WIT Press, www.witpress.com, ISSN 1743-3533

50 Daniel Ambrosini & Abel Jacinto

in explosive loading research in the last decade. Initially, this work wasmostly empirical, but, in recent years, important new methods have begunto be developed. The dynamic loads originating from explosions result instrain rates in the material of about 10−1 to 103 s−1. These extreme loadsproduce a special behaviour in the material that is characterized, amongother effects, by an increase in strength, in comparison with normal, staticproperties. Galiev [1] and Krauthammer et al. [2], among others, describethe behaviour of metals under impulsive load.

According to Smith et al. [3], even nominally identical, well-controlled ex-periments involving explosives can produce results with a significant spread,making data analysis more uncertain than is desirable. For this reason, goodquality experimental data can be useful for theoretical and numerical investi-gations. Moreover, Pan and Louca [4] said that while there has been interestin blast resistance of plates and panels over the past few years, fundamen-tally for use in topside modules in the offshore industry, there is very littledata available on their response characteristics. However, recently, Loucaet al. [5] and Boh et al. [6] present studies about pro?led panels used asblastwalls in typical offshore topsides modules to provide a safety barrierfor working personnel and equipment.

The objectives of this paper are, firstly, to determine the accuracy of mod-ern calculation methods and computational codes and, secondly, to providegood quality data that can be used for checking the accuracy and reliabilityof new calculation methods and procedures. To achieve these objectives,a set of four tests at full scale was performed on two unstiffened metallicsteel plates with different boundary conditions (one set up as a cantilever inthe ground and another clamped around the four edges), subjected to theaction of pressure waves produced by the detonation of explosive chargesequivalent to 1 to 10 kg of TNT. The acceleration time histories at differ-ent points on both plates and the pressure waves at selected points, arerecorded. In addition, numerical analysis using the finite element programsABAQUS/Standard [7] and COSMOS/M [8] were carried out. In previouspapers [9, 10], some results related with different tests and numerical veri-fication were presented. In this paper, results of others tests are presentedjointly with the comparison of results obtained with different computationalcodes.

Related to dynamic response of plates subjected to blast loading, Rudra-patna et al [11] present numerical results for clamped, square stiffened steelplates subjected to blast loading, Nurick et al [12] present experimental re-sults for the prediction of tearing of clamped circular plates subjected touniformly loaded air blast, Louca et al [13] describes numerical results ofnonlinear analysis on both stiffened and unstiffened plates and Shen andJones [14] analyze the nonlinear dynamic response and failure of clampedcircular plates. Recently, Yuen and Nurick [15] present valuables experimen-




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Numerical-experimental study of plates subjected to blast loading 51

tal and numerical studies on the response of quadrangular stiffened platessubjected to uniform blast load and Langdon et al. [16] analyze the case oflocalized blast loading. Moreover, Akus and Yildirim [17] study the effectof thickness on deformation of plates subjected to blast loading.

2 Experimental tests description

2.1 Experimental set-up

The structures analysed in this paper are two unstiffened steel plates subjectto blast loads caused by the detonation of explosives at different stand-offdistances. The explosive used was Gelamon VF80 with a theoretical TNTequivalence of 0.8. Four tests with different amounts of explosive were car-ried out (Figure 1). In order to measure the overpressure generated by theblast waves, four pressure sensors (Honeywell 180PC) were used, located inthe front and back positions of the plates. In addition, three accelerometerswere used to measure the dynamic response of the plates (Figure 2) and a dy-namic strain amplifier amplified the signal generated by the accelerometers.A 100 kHz data acquisition board was mounted on a notebook computerin order to record and process the signals. Seven channels were used in alltests and the signals were sampled at 4000 sps for each channel (28,000 spstotal rate acquisition).

The experimental pressure time history was used as applied load in thecomputational analysis of the plate. A typical pressure-time history is givenin Figure 3, from Test 4.

50.0 m 30.0 m

30.0 m

Plate B

Plate A Equipment

Test 4(10 kg TNT)

Test 3(1 kg TNT)

Test 2(10 kg TNT)

Test 1(0.8 kg TNT)

References

Plate A: Metallic plate clamped at the basePlate B: Metallic plate campled at four edges

10.0 m

5.0 m

4.05 m

5.65

m

0.75

m

0.75

m

Figure 1: Experimental set-up




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2.2 Plates tested

The steel plate A is 1.0 m wide and 1.5 m high and 2.1 mm thick. Thebottom of the plate was set up as a cantilever on a concrete base (Figure2). The accelerometer locations in the tests are shown in Figure 2. For thecase of Test 1, accelerometers were positioned at points 1 and 2, and for theother tests they were positioned at the three points indicated in Figure 2.

The steel plate B is 0.95 m wide, 0.95 m high and 0.9 mm thick. Thefour edges of the plate were clamped to a rigid steel frame of I section of100 x 50 x 4.5 mm. This frame was clamped to a concrete base (Fig. 2).The accelerometer was located in the centre of the plate (Fig. 2). The ex-perimental dynamic response measured for Test 1 is presented in the nextsections.

3 Numerical analysis

The numerical analysis was carried out using the finite element programABAQUS/Standard 5.8 [7] and COSMOS/M 1.7 [8]. The plates were mod-eled using shell elements. In both cases, the boundary conditions were con-sidered as perfectly clamped. The material properties adopted were: Young’sE = 180 GPa (experimental value), Poisson coefficient ν = 0.3, density ρ

= 7850 kg/m3. The dynamic analysis was performed using the modal su-perposition method and integration direct method. The integration step bystep was carried out using the Newmark-β method (β = 1/4 and γ = 1/2)and the time step size was 0.25 ms. The time-history of the acceleration inthe nodes corresponding to the accelerometer position in the test was deter-mined. Only the results corresponding to the modal superposition methodare presented in this paper.

3.1 Metallic plate clamped in the bottom (Plate A)

Numerical models of 150 (10x15 mesh, Model 1) and 600 elements (20x30mesh, Model 2) were used. The damping coefficient adopted was 0.6 %. Thisvalue, obtained experimentally, is similar to other values found in literaturefor steel working under low stresses and was discussed in [10].

The pressure time history shown in Fig. 4b was used as the applied loadfor the numerical analysis. This curve was obtained by the vector additionof the recorded pressures in Sensor 2 (front) and Sensor 4 (back). Thesepressure waves have different arrival times (Figure 4a) and are acting inopposite directions. Moreover, in order to introduce a “soft” variation inthe input pressure, the oscillations observed in the resultant record of theshock wave were smoothed, considering only the upper points of the curve(Figure 4b). In addition, for comparison purposes, the pressure recorded on




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1.0 m

0.4 m

1.2 m

0.5 m

0.5 m

0.5 m 1

2

3

Accelerometers

(a) Plate A

0.95 m

0.95 mSteel plate

Accelerometer

0.2 m

(b) Plate B

Figure 2: Plates tested and accelerometers location

the front face of the plate was also used as the applied load for the numericalanalysis.

In a previous paper by the authors [9], it was demonstrated that, in thiscase, it is equivalent to use the superposition modal method or the direct in-tegration method because, for the pressures involved, the structures behavein a linearly elastic manner and the results obtained with both methods aresimilar.




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-4.0

-2.0

0.0

2.0

4.0

6.0

8.0

10.0

12.0

6.05 6.07 6.09 6.11 6.13 6.15

Time (s)

Pre

ssur

e (k

Pa)

Figure 3: Record of the time history of the overpressure. Test 4. Sensor 3.

3.2 Metallic Plate clamped around the four edges (Plate B)

Numerical models of 100 (10x10 mesh, Model 1) and 400 elements (20x20mesh, Model 2) were used. The damping coefficient, experimentally deter-mined, was 2.2 %. Again, this value was discussed in [10]. As in the case ofplate A, the response of the plate was determined using as loading the blastwave shown in Fig. 4a and the pressure recorded on the front face of theplate for comparison purposes. The acceleration in the centre of the platewas determined using the modal superposition method and the response isshown in the next section.

4 Results and discussion

Firstly, recorded air blast reflected overpressures were compared with pre-dicted values [18] based on empirical findings. Table 1 show measured andestimated values including the positive phase duration. The agreement be-tween the values, except for test 2, is very good and consistent with hemi-spherical air blast loading.

4.1 Natural frequencies

In order to validate the numerical models, firstly, measured and numericalnatural frequencies were compared and the results are presented in Table 2for the first four modes.




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-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

5.95 5.96 5.97 5.98 5.99 6.00

Time (s)

Pres

sure

(kP

a)

Sensor 2 Sensor 4 (a) Measured pressures

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

3.0

5.95 5.96 5.97 5.98 5.99 6.00

Time (s)

Pre

ssur

e (k

Pa)

Resultant Smoothed

(b) Resultant pressures

Figure 4: Applied load used in the analysis

In the case of the plate A, the second mode (torsional) is missing in the ex-perimental determination and there are some differences between measuredand numerical values, particularly in higher modes. This behaviour can beexplained by the second order effects due to the dimensions of the plate





Table 1: Blast pressure and duration estimated and recorded. Sensor 3

TestMeasured Estimated

Overpressure Duration Overpressure Duration

Pr (kPa) td (ms) Pr (kPa) td (ms)

1 4.6 5.5 4.6 5.7

2 10.0 12.2 7.9 10.8

3 3.6 6.5 3.5 6.1

4 14.8 10.0 15.0 10.1

(very low thickness/width ratio) and the support conditions that affect thestability of the plate and make it sensitive to imperfections. Nevertheless,the differences between experimental and numerical modes of vibration donot affect the dynamic response significantly, as is shown in the next point,probably because the pressure is symmetrical and so the influence of anti-symmetrical modes in the response is of minor importance. There are minordifferences between the two numerical modes in this case.

In Plate B, there is a better agreement between the numerical and ex-perimental values and consequently the computational model (mesh andmaterial properties) can be used for the next step of the analysis, that isthe forced vibration. It is interesting to note that the refineshment of thenumerical model lead to a more flexible model in case of ABAQUS andmore stiff in case of COSMOS. However, in all cases the model obtainedwith ABAQUS is dynamically more stiff that the model of COSMOS. Thisdifference can be explained by the different Shell elements used by bothcodes.

4.2 Dynamic response

To meet the objectives of the paper, a comparison between the computa-tional and the experimental results of the acceleration time history will becarried out at this point. At first, as an example, a complete accelerationrecord is showed in Figure 5.

In Figure 6, a comparison between the results obtained experimentallyand with the two codes used, is showed. It can be seen that both codesoverestimate the peak acceleration record but shows a good qualitativelyadjust in the forced vibration zone. In the free vibration zone, more differ-ences between the programs is founded.

In Figures 7 and 8, the experimental values of the time history of the ac-celeration of plate A are compared with those obtained using the ABAQUS




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Table 2: Natural frequencies of the Plates (Hz)

ModePlate A

Meas.ABAQUS COSMOS

Model 1 Model 2 Model 1 Model 2

1 0.72 0.74 0.74 0.74 0.74

2 - 2.51 2.51 2.49 2.50

3 4.99 4.67 4.63 4.59 4.61

4 7.62 8.52 8.48 8.38 8.44

Plate B1 7.98 8.45 8.32 8.21 8.26

2 16.22 17.98 17.14 16.69 16.83

3 23.70 26.29 25.23 24.34 24.76

4 27.94 35.03 31.32 29.76 30.15

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

5.95 6.15 6.35 6.55 6.75 6.95

Time (sec)

Acc. (g)

Figure 5: Acceleration record. Plate A. Test 1. Location 1.

program. These results were obtained using the modal superposition methodinvolving 60 modes because it was founded in previous papers [9, 10] thatthis amount of modes it is necessary in order to reproduce the measuredresponse. It is important to note that the response is shown for a long time(50 ms), that is, approximately 4 and 2.5 times the duration of the applied





-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

0.00 0.01 0.02 0.03 0.04 0.05

Time (sec.)

Acc

eler

atio

n (g

)

Measured values COSMOS ABAQUS

Figure 6: Acceleration time histories. Plate A. Test 1. Location 2.

-20.0

-15.0

-10.0

-5.0

0.0

5.0

10.0

15.0

20.0

0.00 0.01 0.02 0.03 0.04 0.05

Time (s)

Acc

eler

atio

n (g

)

Measured Numerical

Forced vibration Free vibration


load for the tests 3 and 4 respectively.In addition, in Table 3 the acceleration peak values of both responses are





-120.0

-80.0

-40.0

0.0

40.0

80.0

120.0

0.00 0.01 0.02 0.03 0.04 0.05

Time (s)

Acc

eler

atio

n (g

)

Measured Numerical

Forced vibration Free vibration


-80.0

-60.0

-40.0

-20.0

0.0

20.0

40.0

60.0

80.0

0.00 0.01 0.02 0.03 0.04 0.05

Time (s)

Acc

eler

atio

n (g

)

Measured Numerical

Figure 9: Acceleration time histories. Plate B. Test 1.

presented. For both locations 2 and 3 an excellent agreement was achievedfor the peak values of acceleration in the forced vibration zone. For both





tests in the location 3 there are a very good adjustment for the two firstpulses of the response and for the first pulse in the location 2. In the freevibration zone, for both positions and both tests, there was not completecoincidence for high frequencies and only a qualitative agreement is founded.However, these differences are not important for the design stage.

Table 3: Peak acceleration (g). Plate A.

PositionTest 3 Test 4

Measured Numerical Diff. (%) Measured Numerical Diff. (%)

2 13.44 13.60 1.2 99.40 99.80 0.4

3 14.38 15.18 5.6 100.01 111.52 11.5

In Figure 9 the experimental values of the acceleration time history ofplate B are compared with those obtained using the ABAQUS code when20 modal forms are considered.

Finally, in Table 4 the acceleration peak values of responses measured andobtained with ABAQUS and COSMOS codes are presented. Again, there isa good prediction for the peak value of acceleration as well as the first pulseof the response and a qualitative agreement in the free vibration zone.

Table 4: Peak acceleration (g). Plate B.

PositionTest 1

Measured ABAQUS COSMOS

Center 61.08 57.21 55.25

5 Conclusions

A set of experimental results for unstiffened steel plates, with differentboundary conditions, subjected to air blast loading is presented. The experi-mental work has provided data on the dynamic response of these structures.For comparison purposes, a numerical analysis was carried out.

When the superposition modal method it is used, it is extremely impor-tant the number of vibration modes considered in the analysis because, ingeneral, this type of loading, unlike earthquake or wind loading, excites thehigh frequencies. Then, for numerical analysis prediction, it is necessary to





carry out numerical tests to determine the appropriate number of modesthat will be used in the numerical analysis. Moreover, the element size ofcomputational models should agree with the number of modes that will beincluded in the response. As more refined meshes capture the high frequen-cies with minor error and these frequencies have a significant participationin the obtained response, it is therefore very important to determine itsvalues accurately.

According to table 1, the air blast wave was consistent with hemisphericalair blast loading and the pressure applied over the plates could be consideredas uniform, but the results obtained improved significantly when the loadapplied was considered as the temporal superposition of the pressure overthe front and back faces of the plates and this effect could not be ignoredin this type of thin structures. However, the definition of the load appliedshould be improved, considering a different spatial distribution over bothfaces.

Modern computational codes can predict the dynamic response of unstiff-ened steel plates accurately, specially the forced vibration zone and the firstpulses of the response (see figs. 6-9 and tables 3-4). However, there are dif-ferences between different codes because its shell elements definition. Thesedifferences could result in different predictions, particularly in free vibrationzone and in nonlinear studies.

References

[1] Galiev, U., Experimental observations and discussion of counterintu-itive behavior of plates and shallow shells subjected to blast loading. In-ternational Journal of Impact Engineering, 18(7-8), pp. 783–802, 1996.

[2] Krauthammer, T. & Ku, C., A hybrid computational approach for theanalysis of blast resistant connections. Computer & Structures, 61(5),pp. 831–843, 1996.

[3] Smith, P., Rose, T. & Saotonglang, E., Clearing of blast waves frombuilding facades. Proceedings of Institution of Civil Engineers: Struc-tures & Buildings, volume 134, pp. 193–199, 1999.

[4] Pan., Y. & Louca, L., Experimental and numerical studies on the re-sponse of stiffened plates subjected to gas explosions. Journal of Con-structional Steel Research, 52, pp. 171–193, 1999.

[5] Louca, L., Boh, J. & Choo, Y., Design and analysis of stainless steelprofiled blast barriers. Journal of Constructional Steel Research, 60,pp. 1699–1723, 2004.

[6] Boh, J., Louca, L. & Choo, Y., Numerical assessment of explosion re-sistant profiled barriers. Marine Structures, 17, pp. 139–160, 2004.

[7] ABAQUS/Standard 5.7-3; User´s Manual, 1997.





[8] COSMOS/M; Version 1.71. User Guide, 1994.[9] Jacinto, A., Ambrosini, D. & Danesi, R., Experimental and computa-

tional analysis of plates under air blast loading. International Journalof Impact Engineering, 25, pp. 927–947, 2001.

[10] Jacinto, A., Ambrosini, D. & Danesi, R., Dynamic response of platessubjected to blast loading. Proceedings of the Institution of Civil Engi-neers: Structures and Buildings; SB152, volume 3, pp. 269–276, 2002.

[11] Rudrapatna, N., Vaziri, R. & Olson, M., Deformation and failure ofblast-loaded stiffened plates. International Journal of Impact Engineer-ing, 24, pp. 457–474, 2000.

[12] Nurick, G., Gelman, M. & Marshall, M., Tearing of blast loaded plateswith clamped boundary conditions. International Journal of ImpactEngineering, 18, pp. 803–827, 1996.

[13] Louca, L. & Pan, Y., Response of stiffened and unstiffened plates sub-jected to blast loading. Engineering Structures, 20(12), pp. 1079–1086,1998.

[14] Shen, W. & Jones, N., Dynamic response and failure of fully clampedcircular plates under impulsive loading. International Journal of ImpactEngineering, 13, pp. 259–278, 1993.

[15] Yuen, S. & Nurick, G., Experimental and numerical studies on theresponse of quadrangular stiffened plates. part i: subjected to uniformblast load. International Journal of Impact Engineering, 31(1), pp. 55–83, 2005.

[16] Langdon, G., Yuen, S. & Nurick, G., Experimental and numerical stud-ies on the response of quadrangular stiffened plates. part ii: localisedblast loading. International Journal of Impact Engineering, 31(1), pp.85–111, 2005.

[17] Akus, Y. & Yildirim, R., Effect of thickness on deformation of platessubjected to transient high pressures. Proceedings of ESDA 2004: 7th

Biennial Conference on Engineering Systems Design and Analysis,Manchester, United Kingdom, pp. 1–6, 2004.

[18] Smith, P. & Hetherington, J., Blast and Ballistic Loading of Structures.Butterworth-Heinemann Ltd: Great Britain, 1994.




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Numerical-experimental Study on Steel Plates Subjected to Blast Loading