Localised Blast Loading Research Articles

Inelastic dynamic response of square membranes subjected to localised blast loading

Extensive shock and highly localised blast waves generated by detonation of near field explosives (such as improvised explosive devices (IEDs)) are catastrophic to structures and humans, resulting in injury or death, progressive damage, or perforation through the structure and collapse. Mitigating the effects of such waves is paramount in various aspects of design engineering. A theoretical model is presented here to predict the large inelastic deformation of ductile thin square membranes induced by a generic, short pulse pressure load, comprising a piecewise function of spatial and temporal parts. Using the constitutive framework of limit analysis and incorporating the influence of finite displacements, two patterns of kinematically admissible, time dependent velocity profiles were investigated. These patterns included stationery and moving plastic hinges. The results were investigated in two cases: once with the interaction between bending moment and membrane forces retained in the analyses, and then when the response was solely governed by membrane forces.For blast loads of high magnitude, the pressure was replaced by an impulsive velocity and the results were expressed in terms of dimensionless form of initial kinetic energy. The effects of boundary conditions and visco-plasticity have also been investigated. The theoretical results corroborated well with various experimental results in the literature, on ductile metallic plates such as high strength ARMOX steel and mild steel.

Experimental response of high strength steels to localised blast loading

Modern high-strength and armour grade steels have developed continually increasing strength and fracture toughness, but there have been limited experimental investigations into their response to localised blast response. In this work, the response of four modern steels to localised blast loading is experimentally investigated. The deformation and rupture threshold is comprehensively characterised and a detailed fractographic investigation is conducted into the initiation and progression of rupture failure modes. It was found that for the current experimental setup, higher strength steels can outperform more ductile steels, and that steel with a tailored microstructure had a higher rupture threshold than three modern armour steels. All steels studied herein initiate rupture via ductile shear fracture, as opposed to tensile tearing which is common in lower-strength steels. Results showed that the deformation resistance cannot be predicted precisely using only yield strength, and only by considering strain hardening can the deflection response be more accurately predicted. A new non-dimensional impulse correction parameter was also developed that captures the effect of charge stand-off on the target plate deformation and rupture performance. The results demonstrate the suitability of high-strength steels for blast applications, and have application to the design and analysis of safer armour systems for blast protection.

The response of mild steel and armour steel plates to localised air-blast loading-comparison of numerical modelling techniques

This paper presents a comparative study of numerical, experimental and empirical techniques on the effect of localised air blast loads on mild steel and armour steel plates. The blast load effects on monolithic plates have been accounted for by using different approaches provided in the Finite Element hydrocode ABAQUS 6.13, namely an Eulerian Lagrangian and a Coupled Eulerian Lagrangian model. In the first model, the air and the explosive were modelled using multi-material Eulerian grids while the plate was modelled using a rigid Lagrangian mesh, while in the second model the rigid target was replaced with deformable plate.The transient deformation of the plate, strain localisation, pressure distribution on the plate have been investigated in the FE models, which have been validated against small scale experimental data for a limited range of charge sizes for both the mild steel and armoured steel. Despite the lower deflection of armour steel compared to mild steel plates, both plates were shown to undergo rupture upon similar charge mass and stand-off. For this purpose, a non-dimensional analysis was carried out with consideration of stand-off distance and slenderness ratio to predict the rupture impulse.

High strain rate and high temperature response of two armour steels: Experimental testing and constitutive modelling

Under ballistic impact or blast loading, the high strain rate and high temperature behaviour of armour steels is key to their response to a given threat. This experimental and numerical investigation examines the tensile response of a class 4a improved rolled homogenous armour steel (IRHA) and a high hardness armour steel (HHA). Cylindrical tensile specimens were tested at a range of strain rates from 0.001 s-1 to 2700 s-1. Quasi-static, elevated temperature tests were performed from room temperature up to 300° C. While the HHA is strain rate insensitive, the IRHA displays a significant increase in strength across the range of loading rates reducing the ultimate strength difference between the materials from 19% at 0.001s-1 to 4.6% at 2700s-1. An inverse numerical modelling approach for constitutive model calibration is presented, which accurately captured the dynamic material behaviour. The modified Johnson-Cook strength and Cockcroft-Latham (C-L) fracture models were capable of predicting the ballistic limit of each material to within 5% of the experimental result and to within 10% for deformation under blast loading. The blast rupture threshold of both materials was significantly over-estimated by the C-L model suggesting stress state or strain rate effects may be reducing the ductility of armour steel under localised blast loading.

Response of Armour Steel Plates to localised Air Blast Load – A Dimensional Analysis

We report on the results of dimensional analyses on the dynamic plastic response of square armour steel plates due to detonation of proximal cylindrical charges and ensued air blast loading. By assuming a generic function for the blast load, which is multiplicative comprising its spatial and temporal parts, a set of 14 dimensionless parameters, representative of the load and plate deformation, were identified and recast in the form of dimensionless functions of stand-off to charge diameter ratio. Parametric studies were performed using commercial code ABAQUS’s module of Finite Element hydrocode using MMALE and MMAE techniques, and combined with regression analyses to quantify the dimensional parameters and the expressions for dimensionless functions. A few numerical studies with various FE mesh types were also performed to validate the transient deflections against the small-scale experiments. For pulse loading due to proximal charges of small orders of stand-off/charge diameter ratio, the magnitude of the transverse deflection increased abruptly with incremental decrease in stand-off, in contradistinction to the plate deformations at higher stand-offs where variations in displacement are smooth. This confirmed the existence of a stand-off at which a transition in behaviour takes place. For stand-off values less than charge diameter, a dimensionless energy absorbing effectiveness factor was considered to investigate the prediction of rupture in the plate corresponding to different charge masses. This factor is measured as a baseline parameter to predict, using solely numerical means, the blast loads which ensue rupture on full-scale prototypes.

Reprint of: Experimental investigation and simplified modeling of response of steel plates subjected to close-in blast loading from spherical liquid explosive charges

Detonations of nitromethane spherical charges have been carried out to study close-in blast loading of steel plates and the effectiveness of several protective solutions. Three types of bare steel plates, namely mild steel, high-strength steel, and stainless steel were subjected to explosive blast loading. Steel plates of the same type with polyurea coating and composite covers were also subjected to localized blast loading. During an explosive field trial, the blast pressures and displacements of steel plates were measured. Additionally, loading of steel plates by the impinging detonation products was captured by high-speed video recordings. This experimental program has produced results which can be used to calibrate numerical models and to refine the simplified models for predicting blast loads and response of structural elements due to close-in detonations. The effectiveness of polyurea coating for enhancing blast protection of steel plated structures is discussed. The engineering-level model for predicting the blast impact impulse of the detonation gases from the charges in close proximity from the target is introduced and validated using the experimental results obtained during the course of the explosive trials.

Deformation and Rupture of Armour Grade Steel Under Localised Blast Loading

A series of 30 blast experiments were conducted on monolithic steel panels of two armour grade steels. The two steels evaluated were a high hardness armour (HHA) and a rolled homogenous armour (RHA). Tests were conducted at two standoff distances using a fixed charge diameter. The charge weight was varied to produce specific magnitudes of blast loading and to isolate the rupture threshold of each material. The results indicated that the HHA steel, generally reserved for ballistic protection, outperformed a more ductile RHA steel in terms of both its deformation resistance and rupture threshold. Optical and scanning electron microscopy was utilised for fractographic analysis of the ruptured plates. The failure of the steels in this investigation was found to be initiated by slant shear fracture with little to no localised thinning. This is in contrast to the tensile instability and ductile tearing predicted by established theories of plate rupture for mild steels under blast loading. The deformation and rupture of the candidate steels was analysed for all experimental conditions and compared to current empirical models based on a non-dimensional impulse parameter. While deformation behaviour is well predicted, the blast rupture threshold of the armour grade steels is poorly captured by current empirical modelling approaches. The identified shear fracture mode leads to lower energy absorption capabilities of the material compared to more ductile tensile failure.

On the Response of Hemispherical Shell under Blast Loading

Blast valve is an important component of protective structures (required for performing critical operations) for ventilation during normal conditions and for protection from blast/ shock during explosion. In blast valves, hemispherical shells are used as part of closure mechanism. The aim of this work is to investigate the response of hemispherical shells under localised blast loads produced by PE4(C4) explosive. For comparison purpose, circular plate is also analysed. Simply supported and clamped hemispherical shells are loaded from both front (concave) and back (convex) sides. The mid-point displacements of shells are compared for different boundary conditions, loadings and shell dimensions.

Experimental investigation and simplified modeling of response of steel plates subjected to close-in blast loading from spherical liquid explosive charges

Detonations of nitromethane spherical charges have been carried out to study close-in blast loading of steel plates and the effectiveness of several protective solutions. Three types of bare steel plates, namely mild steel, high-strength steel, and stainless steel were subjected to explosive blast loading. Steel plates of the same type with polyurea coating and composite covers were also subjected to localized blast loading. During an explosive field trial, the blast pressures and displacements of steel plates were measured. Additionally, loading of steel plates by the impinging detonation products was captured by high-speed video recordings. This experimental program has produced results which can be used to calibrate numerical models and to refine the simplified models for predicting blast loads and response of structural elements due to close-in detonations. The effectiveness of polyurea coating for enhancing blast protection of steel plated structures is discussed. The engineering-level model for predicting the blast impact impulse of the detonation gases from the charges in close proximity from the target is introduced and validated using the experimental results obtained during the course of the explosive trials.

NUMERICAL STUDIES OF CONCRETE PLATES UNDER LOCALIZED BLAST LOADS

An investigation has been carried out to examine the dynamic behavior of concrete plates subjected to localized blast loading. The concrete plate is modeled as a thin plate with finite dimensions sitting on an elastic three-parameter soil foundation model. The localized blast loading is expressed by using the Dirac Delta function for different value of the load’s position. The governing equation of the problem is solved using the modified Bolotin method for determining the natural frequencies and the wave numbers of the system. The orthogonal properties of Eigen functions are used to find the general solution of the problem. Special emphasis is focused on the mid-point displacements. The results obtained allow an insight into the effect of the load’s position, the thickness of the concrete plate on the response of the concrete plate under localized blast loading and indicate that the load’s position and the thickness of the plate can affect their overall behavior.

The analysis of the ultimate blast failure modes in fibre metal laminates

Finite element modelling has been applied to simulate various failure modes in fibre metal laminate (FML) panels under localized high intensity blast loading. A relatively simple material model, based on continuum damage mechanics, has been proposed to describe the constitutive response of the composite material in the FMLs. Simulations of the blast response of FMLs with various stacking configurations has been carried out, capturing both perforation and non-perforation failure modes. Blast loading was modelled by a pressure function applied on the front face of the FML panel. The definition of the pressure function accounts for both the temporal as well as the spatial distribution of the blast. The capability of the models has been assessed by comparing the predictions associated with both low and high intensity blast cases with published experimental data. Good qualitative and quantitative agreement has been observed for lay-ups with similar proportions of aluminium and composite. It is believed that the models can be employed for use in parametric studies that would facilitate the adoption of FMLs in wider engineering design.

Numerical simulation of the dynamic response in pulse-loaded fibre–metal-laminated plates

This article presents a three-dimensional constitutive model to replicate the dynamic response of blast-loaded fibre–metal laminates made of 2024-0 aluminium alloy and woven composite (glass fibre–reinforced polypropylene). Simulation of the dynamic response is challenging when extreme localised loads are of concern and requires reliable material constitutive models as well as accurate modelling techniques. It is well known that back layers in a fibre–metal laminate provide structural support for front layers; thus, proper modelling of constituent failure and degradation is essential to understanding structural damage and failure. The improved developed model to analyse damage initiation, progression and failure of the composite is implemented in finite element code ABAQUS, and a good correlation is observed with experimental results for displacements of the back and front faces as presented by other researchers. The model was also able to predict accurately the tearing impulses. Finally, the concepts of the ‘efficiency of the charge’ and ‘effectiveness of the target’ are proposed in the context of localised blast loading on a structure. Dimensionless parameters are introduced to quantify these parameters.

Failure Simulation in the Reinforced V-Shape Plates Subjected to Localized Blast Loading

This paper presents a numerical approach to predict failure in the reinforced V-shape plates subjected to blast loading. V-shape plates are commonly used in the vehicle’s hull to mitigate the blast pressure effects. In the current research, V-shape plates were reinforced using multiarch surfaces and honeycomb energy absorbers. Ductile and shear damage parameters were introduced to simulate failure in the finite elements models. Results of this study show that applying V-shape plates along with reinforcing elements significantly enhance the energy dissipating capacity of the V-shape hulls without overloading the vehicle. Also, based on the numerical calculations, upward reaction force was reduced by five times in the reinforced V-shape plate compared to the simple V-shape plate. Finally, it was shown that weight reduction by 2.5 times is achieved by the reinforcing V-shape plates in comparison to flat plates imposed to 50 g TNT explosive.

Experimental and numerical studies on the deformation and tearing of X70 pipelines subjected to localized blast loading

The dynamic response of X70 grade steel pipeline under localized blast loading is studied by experimental and numerical investigations. The steel pipelines with large diameter and high grade are concerned in the paper. The influences of the explosive mass, contact area and wall thickness on the deformation/failure mechanisms of the X70 pipelines were investigated. The post-failure motion of the fragment was also observed during the experiment. Four different failure modes were observed during the experiment namely Mode I, Mode II, Mode IIIa and Mode IIIb. The features of each mode are analyzed concretely. Results revealed that the deflection and damage level of pipeline increased with the increase of explosive mass and contact area. The wall thickness plays an important role on the damage and post-failure motion. Numerical simulations based on the experimental results were conducted. The damage process, midpoint deflection, pressure distribution, energy changes and the post-failure fragment velocities were analyzed. The results of numerical simulations show good correlation with the experiments

Experimental Study of the Effectiveness of Sacrificial Cladding Using Polymeric Foams as Crushable Core with a Simply Supported Steel Beam

The present paper focuses on the study of the effectiveness of the sacrificial cladding using polymeric foam as crushable core to reduce the delivered blast energy using a simplified structure. The latter consists of a simply supported steel beam under a localized blast load. The tested sacrificial cladding has a cross-sectional area of 80 × 80 mm2. The effect of the front plate mass and the crushable core properties (plateau stress and thickness) is studied. Three polymeric foams are investigated: (a) the expanded polystyrene foam (PS13) with a density of 13 kg/m3, (b) the closed-cell polyurethane (PU30) with a density of 30 kg/m3, and (c) the open-cell polyurethane (PU50) with a density of 50 kg/m3. Four front plate masses are used: 144, 188, 336, and 495 g. All possible combinations are tested to determine their absorption capacity. The obtained results show that the absorption capability increases by increasing the front plate mass, the plateau stress, and the thickness of the crushable core. The open-cell polyurethane PU50 performs better. Disintegration problems are observed on the expanded polystyrene PS13 after the end of the compression process.

The effects of blast-induced fragments on cellular materials

This paper presents the results of an experimental study to characterise blast-induced fragments and to understand how different cellular materials alleviate the damage caused by the blast-induced fragment. In the experimental arrangement, a front plate, 106 mm in diameter, is subjected to a localised blast load to generate a cap fragment (Mode IIc failure) to impact a rear plate of similar dimensions, located parallel and offset from the front plate. Different charge diameters and masses are used to create fragments of different sizes and masses (4.1 g to 12.5 g) propelled at different speeds (244 m/s to 741 m/s). Various cellular materials (aluminium foam, aluminium honeycomb, balsa wood, Corecell M80 foam, Divinycell H200 PVC foam and polyurethane 200 foam) of thicknesses 40 mm and 60 mm are placed in front of the rear plate to act as energy absorbers. The damage caused by the fragment and the protective performance of the cellular materials are quantified by means of the maximum deflection of the rear plate. The results indicate that the cellular materials alleviate the damage incurred to the rear plate, with different materials absorbing different amounts of impact energy. For the range of experiments carried out and foam investigated, the Divinycell foam provided the best protection while Corecell foam offered the least resistance to damage.

On the dynamic plastic response of steel membranes subjected to localised blast loading

Permanent plastic deformation is expected when close-in blasts due to e.g. detonation of Improvised Explosive Devices (IED's) hit thin metallic targets. A circular thin steel plate i.e. a membrane is studied in the present work subject to a general form of a localised blast loading. The spatial shape of the pulse is fixed and different temporal shapes are investigated. Dynamic analyses are conducted and the permanent transverse displacements are found for each case.For high amplitude pulse loads of short duration, it was found that the permanent transverse displacement can be found by replacing the load by an impulse without the loss of accuracy. Excellent correlation with numerical simulations obtained from ABAQUS/Explicit is achieved. The predicted final displacements for different pulse shapes are also found to be similar, thus where membrane action is dominant, the response is insensitive to pulse shape.

On dimensionless loading parameters for close-in blasts

Close-range blasts pose a threat through severe damage to structures and injury or death. In this work, the spatial and temporal descriptions of a localised blast load are presented using 6 non-dimensional parameters. These are found to be solely functions of the charge stand-off distance to diameter ratio for a cylindrically-shaped charge. Numerical simulations of a localised blast are performed using AUTODYN, where the pressure variation on a rigid barrier for various charge stand-off/diameter combinations is obtained. The least-square regression is then utilised to obtain the relationship between stand-off/diameter ratio and dimensionless loading parameters. The relevant expressions and dimensionless charts are presented. The proposed equations are verified by comparing experimental data with numerical results obtained by finite element analysis (FEA) of blast loaded steel plates (using the user-defined subroutine VDLOAD implemented in the FEA package ABAQUS/Explicit). Excellent correlation of the measured permanent displacement with numerically predicted results is obtained.

NUMERICAL DYNAMIC ANALYSIS OF ORTHOTROPIC PLATES UNDER LOCALIZED BLAST LOADING

This paper analyzes the dynamic response of fixed supported orthotropic plates under localized blast loading using the method of modal superposition. The analysis procedure is used to quantify the linear transient response of such plates to the localized blast load at different positions. Many studies are currently available, in which the blast load is considered to be spatially uniform across the plate, with a temporal distribution described by a Dirac delta function. The novel aspect considered here is the case for which the blast load is modeled as a linear triangular function, and the orthotropic plate is fixed along its edges. A Mathematica program is used to solve the first and the second auxiliary Levy-type problem to determine the values of the natural frequencies of the system. The results presented here are collected from the results of analyses performed on localized blast-loaded orthotropic plates, for a variety of parameters important with regard to the dynamic response. Conclusions are drawn concerning the influence of the various parameters on the nature of the orthotropic-plate response.

Dynamic response of Dyneema® HB26 plates to localised blast loading

This paper reports on the dynamic response of a potential blast-resistant lightweight alternative to steel for military applications, namely ultra-high molecular weight polyethylene (UHMwPE) fibre composites known as Dyneema®. The results of localised air-blast loading tests on Dyneema HB26 panels are reported and analysed.Various failure modes were observed, including permanent deformation, delamination, in-plane shear, buckling around the boundary, localised melting and matrix damage. Total penetration (rupture) at the highest charge masses was also exhibited by the Dyneema panels.The experimental results are compared to the numerically simulated responses of mild steel and armour steel plates of equal areal density and reasonable correlation was observed in most cases. Dimensional analysis was used to compare the responses and showed that there is a possibility of unifying all the results i.e. the responses for all materials once a newly proposed slenderness ratio was incorporated into the formulation. Simple dimensionless expressions are proposed to predict permanent midpoint transverse displacements, irrespective of the particular material type.It was also observed that armour steel and Dyneema HB26 offer potential displacement reductions of almost 50% and 30%, respectively for the range of impulses tested.