Elsevier

Engineering Structures

Volume 29, Issue 10, October 2007, Pages 2723-2736
Engineering Structures

The effect of stand-off distance on the failure of fully clamped circular mild steel plates subjected to blast loads

https://doi.org/10.1016/j.engstruct.2007.01.021Get rights and content

Abstract

The effect of stand-off distance and charge mass on the response of fully clamped circular mild steel plates, of radius 53 mm, subjected to blast loads travelling along tubular structures is reported. The procedure consists of creating a blast load using plastic explosive mounted onto the end of mild steel tubes. The stand-off distance is varied, from 13 to 300 mm, using different tube lengths.

The plate responses range from large inelastic deformation to complete tearing at the boundary. Different loading regimes are observed, depending on the stand-off distance between the explosive charge and the plate, and are classified according to the plate response. At stand-off distances less than the plate radius (13–40 mm), the blast load is considered to be focused (localized). For stand-off distances greater than the plate radius (100–300 mm), the loading is considered uniformly distributed over the entire plate area. Theoretical and empirical analyses are performed, to enable predictions of the mid-point deflection. Appropriate modifications are introduced to account for the effect of stand-off distance on plate deformation. The modified analyses show satisfactory correlation with experimental results.

Introduction

The response of fully clamped metal plates subjected to uniform and localized blast loads has been studied for many years. Experimental work on beams, plates and shells has been widely reported. Nurick and Martin [1] presented an overview of theoretical and experimental results, up to 1989, that dealt mostly with uniformly loaded plates. In subsequent years, mild steel plates subjected to localized blast loads are reported by Nurick et al. [2], [3], [4].

The failure of circular plates subjected to uniform blast loads was investigated by Teeling-Smith and Nurick [5]. It was reported that permanent midpoint deflection increased with increasing impulse, resulting in thinning at the boundary. Further increases in impulse led to partial tearing along the plate boundary, followed by complete tearing. The mid-point deflection decreased as impulse was increased beyond the threshold of complete tearing, as the failure tended towards complete shear at the boundary edge. The effect of different edge fixations on mild steel plates subjected to uniform blast loads was reported by Thomas and Nurick [6]. Fully clamped plates were compared to built-in plates machined from 20 mm thick steel. For plates without tearing, the mid-point deflections were identical, that is within experimental error, regardless of edge fixation. Tearing along the boundary occurred at lower impulses for built-in plates compared to clamped plates, as the clamps did not fully prevent in-plane movement of the plate and hence delayed tearing. Schleyer et al. [7] also examined the effect of boundary clamping on the response of mild steel plates subjected to dynamic loading. The loading took the form of a triangular pressure pulse applied over 50 ms and was not impulsive considering the long load duration with respect to the natural period of the test plates. In-plane movement along the clamped edge was observed, confirming the observations reported in [6].

Nurick et al. [8] investigated the onset of thinning for different diameter circular mild steel plates clamped between frames with different edge conditions. The clamps featured sharp edges or fillet radii of 1.5 and 3.2 mm. Observations from the experiments showed that thinning occurred for all plate diameters with sharp edged clamps, however, plates secured using frames with fillets allowed larger deflections to occur before the onset of thinning and tearing. Plates restrained with sharp edged clamps exhibit sharp indentation within the necked region due to the clamp followed thereafter by stretching and thinning. In the case of curved edge boundary, the thinning is similar to that observed in a uniaxial tensile test.

Experiments on fully clamped circular mild steel plates subjected to localized blast loads were reported by Nurick and Radford [2]. The plate deformation was characterised by an inner dome superimposed on a larger global dome, later reported in Reference [3] for built-in circular plates and [4], [9] for quadrangular plates subjected to localised loads. At higher impulses, thinning at the central area and boundary of the plate was observed. Tearing in the central area of the plate occurred with further increases in impulse after the onset of thinning. The tearing observed was characterized by a cap torn away from the plate. Tearing at the boundary was observed for larger load diameter — plate diameter ratios.

All of the work by Nurick et al. [2], [3], [4], [5], [6], [8], [9] was performed using plastic explosive sited 13 mm away from the plate structure, using a polystyrene pad to prevent spalling. The effect of stand-off distance was not considered. Although there are numerous empirical relationships relating stand-off distance to blast overpressure for free-field explosions, the relationship between stand-off distance and plate deformation due to air blast is not widely reported. There are no established relationships for predicting either the response of plate or the characteristics of the blast loading when the explosion is partially confined.

Experimental studies using air blast loading to understand the effect of stand-off distance on plate deformation were reported by Akus and Yildirim [10]. Square steel plates were loaded with air pressure waves generated by detonating C4 explosive at different stand-off distances. The results indicated that the maximum permanent midpoint deflection occurred at the closest stand-off distance, followed by a rapid decrease as stand-off distance increased until an asymptote value was reached (for a given charge mass). Marchand and Alfawakhiri [11] examined the loading on steel buildings subjected to explosions and suggested a guide for the assumption of a uniform blast load over a structure. It was assumed that if the stand-off distance exceeded one-half of the largest dimension of the structure, then the loads could be reasonably averaged over the structure (provided the charge is centred on the structure).

Despite these two studies [10], [11] there remains a paucity of systematically generated experimental data demonstrating the effect of stand-off distance on structural loading and response. This paper presents new experimental results for fully clamped circular plates subjected to blast loads detonated at various stand-off distances. The stand-off distances vary from 13 to 300 mm, while the plate and load geometry are kept constant. The range of stand-off distances provides a spectrum of experimental data that is used to study the effect of stand-off on plate response. The paper also proposes a modification to existing dimensionless analysis to incorporate the effect of stand off distance into the response of blast loaded circular plates. This work will be useful to those involved in research into the response of structures to explosive loading, a subject that has become increasingly important with heightened public awareness of potential explosive threats to civilian safety. It is also applicable to the study of explosion loading of underground facilities linked to the atmosphere via tunnels.

Section snippets

Failure modes of thin plates subjected to blast loads

It is important when investigating the effect of stand-off distance upon plate response that load localization causes a change in failure mode. This section describes the failure modes observed in blast-loaded structures.

The failure modes of structures subjected to uniformly distributed blast loading were first classified by Menkes and Opat [12] for beams, as shown in Fig. 1. The different modes of failure were defined as: large inelastic deformation of the entire beam (Mode I), tearing

Dimensional analysis

Theoretical predictions of plates subjected to impulsive loading have been reported for many years [1]. Jones [13] proposed a dimensionless impulse λ and an analytical solution to predict large inelastic deformation of fully clamped circular plates loaded by a uniformly distributed velocity. Nurick and Martin [1] proposed modified dimensionless numbers for both uniformly and locally loaded circular plates, based on Johnson’s damage number [14]. In this paper, an extension modification to both

Experimental procedure

The test specimens are 244 mm by 244 mm by 1.9 mm thick. The specimens are clamped in a test rig, comprising two (244 mm×244 mm) frames made from 20 mm thick mild steel plating. A tube of required length, selected from the range shown in Fig. 2, is screwed onto the front clamping frame and the rear clamping frame has a hole of diameter 106 mm, the same as the internal diameter of the tube as shown in Fig. 3. Therefore, each test specimen has a circular exposed area with a diameter of 106 mm. In

Results and discussion

The experimental data are presented in Table 4.

Concluding remarks

The experimental results presented in this paper, for a specific specimen and load geometry, provide an insight into the relationship between stand-off distance and response of circular plates subjected to blast loads travelling through tubular structures. It is shown that stand-off distance influences the type of loading condition applied to a structure. This is illustrated by different plate profiles observed at various stand-off distances. An inner dome superimposed on a larger global dome

Acknowledgements

The authors wish to thank P. Park-Ross, L. Watkins and G. Newins at the University of Cape Town for their technical assistance, and Dr. S. Chung Kim Yuen for his experimental assistance. The financial support of the National Research Foundation (South Africa) and the 1851 Royal Commission (UK) is gratefully acknowledged.

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