Pressure Pulse Loading Research Articles

Double blast loadings of clamped square steel plates

This paper presents a combining experimental, numerical, and analytical efforts to elucidate the resultant effect of synchronised double blast loadings on square steel plates. Blast tests were performed to investigate the effect of the distance between the two identical charges upon the large inelastic deformation of fully-clamped steel plates at various standoff distances. Detailed three-dimensional finite element simulations using LS-Dyna were performed to provide insights into the equal blast wave collision and transient response of the ductile plates under the double blast loading. An analytical model was developed to predict the large inelastic deflection of the fully-clamped thin plate under either pulse pressure loading or impulsive loading (an instantaneous zero-period impulse). Experimental results found that splitting a 1kg TNT into 2 × 0.5 kg TNT (with a certain separating distance) would lead to greater permanent inelastic deformation of the ductile thin plates (by up to 19.6%). Both numerical and analytical results were validated against experimental data. Results from the parametric study showed that an optimum charging distance exists for maximised plate deflection under a given TNT mass and standoff distance. The results presented in this work shall be useful for evaluating the hazards of multiple blast loadings or for demolition applications.

Dynamic plastic response and impulse saturation of rectangular plates subjected to pressure pulse loading

A combination of the Membrane Factor Method (MFM) and Saturation Analysis (SA) has proven to be a simple yet effective theoretical tool to predict the dynamic inelastic response of various structures subjected to long-duration pressure pulse loading. In this study, this theoretical tool is extended to the analysis of rectangular plates. Boundary conditions are treated in a unified manner in the analysis, so that the influence of the boundary conditions on the saturation phenomenon is clarified based on MFM. By taking the transient response phase and the exact yield conditions into consideration, complete solutions of saturation deflection and impulse are obtained, and the effect of the aspect ratio of rectangular plates is examined. Results from the present methods are also compared with finite element simulation utilizing elastic-plastic material behavior and modal solutions. The effects of the yield condition adopted and the transient response phase on the saturation phenomenon of rectangular plates under pressure pulse loading are respectively discussed.

Dynamic instability of fiber composite cylindrical shell with metal liner subjected to internal pulse loading

Thin-walled cylindrical shells are commonly used structures in explosion containment vessels. When subjected to internal blast loading, these cylindrical shells are prone to dynamic buckling failure.In this work the dynamic stability of cylindrical fiber composite shells with metal liner subjected to uniform internal pressure pulse was investigated through both finite element simulations and theoretical modelling. In particular, pulse buckling of the inner metal liner and vibrational buckling of the outer fiber composite shell were observed and studied. Dynamic, Implicit analysis in ABAQUS Standard considering the initial geometric imperfections were conducted to study the mechanisms for the dynamic buckling of the inner metal liner and outer fiber composite shell. The simulated buckled shape using a simplified two-dimensional model could successfully reproduce the previous experimental results. The dynamic pulse buckling of the metal liner was found to occur during the plastic compression process. The effect of the buckling amplitude of the inner metal liner on the dynamic stability of the outer fiber composite shell was also revealed using numerical simulations. Instead of preventing the outer fiber composite shell from buckling instability, severely buckled metal liner with large buckling amplitude may even accelerate the growth of unstable mode of the fiber composite shell. The theoretical solution for the radial deformation of the metal liner was established by modelling the growth of the buckling mode as the amplification of the initial geometric or velocity imperfection. The most amplified mode and corresponding amplification were determined by the derived amplification function. The solutions for the radial deformation of the outer fiber composite shell were represented by a set of Mathieu differential equations. The dynamic instability of the fiber composite shells was determined from the Mathieu stability charts. The dependence of the dynamic instability of the bilayer composite shells on various parameters such as composite layup, thickness-to-radius ratio and impulse of pressure pulse loading was theoretically predicted and compared with the finite element simulation results.

Dynamics of pulse-loaded circular Föppl-von Kármán thin plates- Analytical and numerical studies

Materials such as modern armour steel, benefit from appreciably high elastic energy storage capacity prior to failure. Such a capacity contributes to absorption of the impulse generated during an extreme pulse pressure loading event such as a localised blast. As the plate deforms within the bounds of the elastic region without plastic dissipation, the probability of catastrophic failure is mitigated while large deformations compared to conventional metallic panels are encountered. No studies have proposed, to date, a closed-form solution for nonlinear elastic response of thin circular plates subject to localised pulse loads.The present work aims at deducing, from the minimization of the Föppl-von Kármán (FVK) energy functional, explicit solutions for the response of dynamically (pulse) loaded thin clamped circular plates undergoing large deformations. The solutions were derived from a presumed kinematically admissible displacement field together with an associated stress tensor potential as an infinite polynomial series, which was truncated into a multiplicative decomposition of temporal parts and spatial parts, representative of a Multiple Degrees-of-Freedom (MDOF's) system.In the case of static loading, using the Frobenius method, an exact recursive solution to each mode of defamation was obtained. In the event of dynamic loading, useful expressions for stress tensor components were delineated, corresponding to a multimode multiplicative product, and a series of coupled Ordinary Differential Equations (ODE's) were derived, using the Ritz-Galerkin variational method. The explicit solutions were sought using the Poincaré-Lindstedt (PL) perturbation method. The closed-form solutions obtained were corroborated with FE results including the Fluid-Structure Interaction (FSI) effects and showed convergence when the first few modes were considered. The influence of higher modes, however, on the peak deformation was negligible and the solution with 3 DOF's conveniently estimated the blast response to a satisfactory level of precision. The influence of element type on the response was also examined and discussed in the context of the problem.

A new crushable foam model for polymer-foam core sandwich structures

An elastic-plastic, viscoelastic damage model to accurately describe the crushing and energy absorption of polymer foams in sandwich panels was implemented in ABAQUS Explicit. Good agreement was found between ABAQUS predictions and experimental results with Divinycell H100 foams under triaxial compression, triaxial compression-tension and triaxial compression-shear. The elastic-plastic viscoelastic damage model was used to simulate the response of a doubly curved foam core composite sandwich shell subjected to direct pressure pulse and water pressure pulse loading. Results using the new crushable foam model were compared to those using the ABAQUS built-in isotropic crushable foam model. It was found that sandwich panels with the more commonly used, isotropic crushable foam model overestimated the stiffness, strength and energy dissipation of sandwich shells with Divinycell H100 foam cores. The proposed elastic-plastic-viscoelastic-damage model would provide more accurate results and offer better protection of composite sandwich structures than the isotropic crushable foam model.

On the saturated impulse for a circular hollow beam under pressure pulse loading

The saturated impulse phenomenon, which may occur in a hollow beam with a circular cross-section, is examined when a rectangular pressure pulse loading is applied uniformly on the upper surface of the beam. A simplified 2DoF model of the dynamic response of a relatively long circular hollow section beam is developed to explore the role of the local and global deformations build up simultaneously during the beam response. In order to simplify the analytical formulation, the elastic deformations of the hollow beam are neglected, and a rigid-plastic method of analysis is applied. Finite element simulations using an elastic, perfectly plastic material model are carried out to verify the proposed analytical model and to reveal the influence of the elasticity on the beam response. The limit of the pressure pulse loading, beyond which saturated impulse is not defined for a hollow beam, is obtained numerically. The responses of hollow beams with lengths between 800 and 1200 mm, radius of 40 mm and several wall thicknesses are analysed. It is observed that the proposed 2DoF model can predict satisfactory the local and global saturated deflections while the saturated pressure pulse duration is underestimated due to the disregard of the stored elastic energy in the beam. It is suggested that the analytically predicted saturated impulse can be used as a lower bound estimate for the saturated impulse for a given beam geometry.

Large deformation of square plates under pulse loading by combined saturation analysis and membrane factor methods

Thin plates will experience large deformation under intense pulse loading, which may result in serious consequences. Numerous research work has been conducted since 1950s and some theoretical methods have been developed to predict the large deformation of plates based on Rigid-Plastic Idealization of material behavior. However, even with this idealization, it is often difficult to obtain complete solutions. Membrane Factor Method (MFM) has proved a powerful method to solve this problem, resulting in solutions taking into account of the effects of the transient phase and the interaction between membrane force and bending moment through a relatively simple procedure. On the other hand, Saturation Analysis (SA) based on the saturation phenomenon is more rational and accurate than the traditional analyses using total impulse of pulse loading. This paper combines these two approaches to study the dynamic plastic response of square plates under rectangular pressure pulse and linear decay pressure pulse loading, and then the results are compared with modal solutions and FE simulations. Meanwhile, the solutions of this combined method, which merely considers the modal phase are also provided to identify the effect of the transient phase. Finally, two sets of simple calculation formulae are proposed for the permanent deformation of plates so as to facilitate engineering applications.

Pulse pressure loading and erosion pattern of cavitating jet

Various erosion patterns generated through the cavitating water jet impacts under ambient pressure conditions were investigated in experiments and numerical simulations. A series of normalized stand-off distances ∈ [2.5 13.5] were studied during the erosion acceleration period. Two ring-like erosion areas were observed for comparatively low ∈ [2.5 6.5]. To gain insight into the pulse pressure loading on the erosion area, numerical calculations were performed using the volume of fluid (VOF) interface capturing methodology combined with the large-eddy simulation turbulence model. The erosion patterns are clarified based on the mass loss and distribution features of the eroded regions. The first ring, generated by the cavitation clouds impingement outside the central stagnation area, mainly contributes to the mass loss. The second ring moves inward, merges into the inner ring and eventually vanishes with increasing . High pressure pulsation is found around the locations of the maximum erosion and the approximate intermediate radius of the second ring. The pressure pulsation in the first ring area are dominated by the frequency of the vortices shedding from the jet nozzle. Several higher frequencies are found as the spectral features of the eroded regions in each pattern.

Laboratory Explosive System for Cylindrical Compression

One method of studying materials or plasma under pressure pulse loading is axisymmetric compression using a convergent cylindrical detonation wave. Such waves are often generated by multipoint initiation and have a number of specific features that may affect the properties of the test objects. To solve specific problems, it is proposed to use a laboratory explosive system based on a converging cylindrical detonation wave with 12–48 initiation points. The TNT equivalent of the charge is less than 1 kg. The main method of research is visualization using a domestic high-speed Nanogeit camera with a nanosecond time resolution. The structure of the converging detonation wave is shown, and its velocity along the radius is determined. It is shown that for a charge of limited thickness, the curvature of the detonation wave front for various explosives depends only on the distance to the initiation point.

Blast response of aluminium/thermoplastic polyurethane sandwich panels – experimental work and numerical analysis

This article presents experimental and numerical results following blast tests on a polyether grade thermoplastic polyurethane (TPU). Aluminium alloy (AA) 2024-T3 skins were used as facings to enhance the blast resistance of sandwich structures with TPU cores and varying thicknesses. The experimental results highlighted an improvement in blast resistance with the addition of skins to the TPU core. Increasing the thickness of the TPU core in the sandwich panels served to increase the blast resistance of the structure. For example a 20 mm core offered a blast resistance that was 50.2% higher than an equivalent 5 mm core and 71.2% higher than a plain (i.e. no skin) 5 mm TPU core. Numerical simulations of the blast response of the TPU panels were conducted by converting the explosive loading regime applied to the panels to a simplified pressure pulse loading. Good agreement was obtained between the numerical and experimental results for the back face deflection profiles through the central cross-sections of the panels.

Dynamic plastic response of beams subjected to localised pulse loads

Localised blast loads give rise to high gradients of overpressure detrimental to structural elements as beams and plates. This article presents an analytical study on the dynamic plastic response of beams made of a ductile metallic material due to close-in pulse pressure loading. The close-in pressure load is characterised by a spatially varying function constant over a central region and exponentially decaying beyond it. The temporal pulse shape is assumed to take different forms. The exact static plastic collapse load was obtained for the characteristic load using the framework of plastic limit analysis, whereby the analysis was then extended to the dynamic case by considering the appropriate yield surface and inclusion of inertia forces. The yield surfaces considered were representative of pure bending, the interactions between the bending moment and transverse shear, and bending moment and membrane force, each corresponding to a special case depending on the geometry of the beam. A time-dependent, kinematically admissible velocity profile was assumed to treat the dynamic formulations in interaction of each phenomenon. A study on the strain-rate sensitivity was also presented, and existence of a critical pressure triggering the apparition of travelling plastic hinges was hence highlighted. For blast loads of high magnitude, the expressions for normalised deflection were furnished in terms of the impulsive velocity. The analytical models were validated by performing a parametric study on the two-dimensional representative of the beam model in commercial finite element software ABAQUS 6.14. The numerical results show a good correlation with the analytical results in each case.

Pressure–impulse diagrams for elastoplastic beams subjected to pulse-pressure loading

Pressure–impulse (or p−I) diagrams are developed for fully-clamped elastic-plastic beams subjected to pulse-pressure loading with varying degree of negative phase. Unlike traditional p−I diagrams, the loading parameter space are instead divided into re´gimes, corresponding to the three modes of deformation (I, II and III) observed in blast experiments. The effects of pulse shape, beam aspect ratio and negative phase loading on the isodamage curves that delineate the different re´gimes are investigated. In addition, it is further demonstrated that contour lines of structural performance (maximum deflection, total work done, partitioned energy and saturated) can also be incorporated into the non-dimensionalised pressure-impulse space to provide further information for the design, and assessment, of elastic-plastic beams to blast loading.

Dynamic structural response of laminated glass panels to blast loading

This paper presents an analytical model of ‘fully-clamped’ laminated glass panel subjected to pulse-pressure loading in an air-blast. The dynamic structural response of the laminated glass panel is decoupled into two distinct phases of motion: phase I is controlled by the elastic deformation of the brittle glass plies whilst phase II is dominated by the large inelastic deformation of the Polyvinyl Butyral (PVB) interlayer. Transition between the two phases follows the large scale fragmentation of the glass plies – this will be captured through a stress-based damage criterion. Following the work of others, the PVB interlayer is idealised as a rigid-perfectly plastic material which allows its large inelastic response to be modelled within the constitutive framework of limit analysis. An interactive yield criterion is adopted to capture the simultaneous influence of bending and membrane stretch that governs plastic flow in the interlayer. Predictions by the analytical model are validated against existing experimental data and they will be shown to be in good agreement. Parametric studies were performed to elucidate the effects of total mass (per unit area) and thickness ratio on the maximum transverse deflection. The efficacy of Youngdahl’s technique on desensitising pulse shape effects is also studied.

Marine composite sandwich plates under air and water blasts

Fluid-structure interaction solutions for the air and water blast response of marine composite sandwich panels with crushable foam cores are presented in this paper. Reflected and radiated acoustic pressure waves were introduced using Taylor's FSI method into Lagrange's equations of motion for the sandwich plate. In comparison to air blast, water-structure interactions diminished deflection and slowed down the response of the sandwich panel for a given pressure pulse loading. The predicted elastic-plastic transient response of the sandwich panel from the analytical model was shown to be fairly consistent results with ABAQUS Explicit. Pressure amplitudes to initiate damage in a sandwich panel with E-glass/Vinyl Ester facesheets and PVC H250 foam core were calculated under water blast/air back, water blast/water back, and air blast/air back conditions. It took significantly higher pressures to initiate damage in the panels under water blast/air back and water blast/water back conditions than in the air blast/air back plate because of fluid damping and higher plastic work dissipation in the core. A parametric study showed that on a per unit areal weight basis, panels with softer, more ductile foams were more blast resistant than panels with strong and stiff cores because of work dissipation during core plasticity. In the water blast cases, foam yielding was affected by transverse compression and not only transverse shear, as is usually case in air blast-loaded sandwich panels.

The saturated impulse of fully clamped square plates subjected to linearly decaying pressure pulse

Saturated impulse refers to the critical value, beyond which the deflection of a beam or plate under pulse loading will no longer increase with further applied load. Previous studies have explored the saturated impulse for structures under rectangular pressure pulse loading. The present paper investigates the saturated impulse for fully clamped square plates subjected to linearly decaying pressure pulse, which is closer to the pulse produced by explosive loading. Both rigid-plastic model and elastic-plastic model are employed to study the saturated duration, saturated impulse, saturated deflection, etc. The results indicate that the saturated impulse exists if the decaying duration is greater than a certain value (i.e. the minimum decaying duration), and a saturation regime map is constructed accordingly. To facilitate engineering designs, an empirical expression for saturated duration is provided based on the elastic-plastic numerical results. In addition, a method is proposed to predict the deflection of fully clamped square plates, which replaces the linearly decaying pressure pulse with an equivalent rectangular pressure pulse. Inspired by Youngdahl's pioneering work, the proposed method has explicit physical meaning and wide range of application.

Experimental simulation of blast loading on structural elements using rarefaction waves – theoretical analysis

An experimental approach aiming at producing blast loading on structural elements without using either an explosive charge or an impact load, shock waves or compression waves, was investigated theoretically. The transient pressure pulse loading is produced by a transient differential pressure gradient created by a timely sudden pressure release from two connected chambers in between which a target plate is placed. It was shown that this test facility is capable of producing uniform pulse loading on the face of the tested element. An effective model with lumped parameters has been developed to simulate the problem and calculate the resulting blast pulses. The model allows analysis of the basic characteristics of the blast pulses depending on a predefined initial pressure, on the chambers volumes and on the exit air release opening areas. The following characteristics of a blast pulse are studied with that model: peak pressure, built-up duration and pressure drop to zero duration. Both short pulses and pulses with a plateau segment and with an infinite duration are considered.The effect of the filling gas properties on the resulting blast pressures acting on the target was investigated including a diatomic (air) and monatomic (helium) gases. The analytical results are compared with computational results obtained from simulations using the AUTODYN software. Comparisons are also made with experimental data. Excellent agreement is obtained between the calculated pressure time histories predicted by the proposed model and the computational and measured experimental pressure signals. The new presented model with lumped parameters allows an effective analysis of any experiment using that experimental system and definitely will help in planning experiments with specific blast characteristics through proper selection of the suitable parameters to achieve the planned experiment goal.

The Saturated Impulse for Fully Clamped Square Plates Subjected to Linear-Decay Pressure Pulse

Saturated impulse refers to the critical value beyond which the deflection of the beam or plate under pulse loading will no longer increase with further applied load. Previous effort has been made to study the saturate impulse for structures under rectangular pressure pulse loading. Through theoretical analysis, the present paper investigates the saturated impulse for fully clamped square plates subjected to linear-decay pressure pulse, which is closer to explosive loading pulse. The results indicate that the saturated impulse does exist if the decay duration is greater than a certain value (i.e. the minimum decay duration). The saturated impulse, saturated deflection and saturated duration all have nonlinearly relations with the dimensionless applied pressure, and grow with the increase of the decay duration.

Large deformation, damage evolution and failure of ductile structures to pulse-pressure loading

In this paper, a model is developed for an elastic perfectly-plastic structural beam system subjected to general pulse-pressure loadings - this may be either impulsive or non-impulsive - which is capable of capturing large non-linear deformation, ductile damage evolution and its consequential failure. The proposed model is an extension of Schleyer and Hsu (2000) by incorporating interactions between bending, membrane stretch and transverse shear in the fully plastic stress state, and uses damage mechanics to capture the loss of integrity at the supports and the subsequent beam detachment. Predictions by the model were validated against existing experimental data from literature and to three-dimensional finite element models developed in this paper. Parametric studies were performed to elucidate the effects of loading duration on the mode of deformation by the beam and the critical conditions governing their transition. The efficacy of Youngdahl’s (1970; 1971) technique on desensitising pulse shape effects is also investigated using different pressure pulse profiles and it will be shown that the technique is successful only for monotonically decaying pulse-pressures.

The influence of intraluminal thrombus on noninvasive abdominal aortic aneurysm wall distensibility measurement.

Abdominal aortic aneurysm wall distensibility can be estimated by measuring pulse pressure and the corresponding sac volume change, which can be obtained by measuring wall displacement. This approach, however, may introduce error if the role of thrombus in assisting the wall in bearing the pulse pressure loading is neglected. Our aim was to introduce a methodology for evaluating and potentially correcting this error in estimating distensibility. Electrocardiogram-gated computed tomography images of eleven patients were obtained, and the volume change between diastole and systole was measured. Using finite element procedures, we determined the equivalent pulse pressure loading that should be applied to the wall of a model where thrombus was digitally removed, to yield the same sac volumetric increase caused by applying the luminal pulse pressure to the model with thrombus. The equivalent instead of the measured pulse pressure was used in the distensibility expression. For a relative volumetric thrombus deposition (V ILT) of 50%, a 62% distensibility underestimation resulted when thrombus role was neglected. A strong linear correlation was observed between distensibility underestimation and V ILT. To assess the potential value of noninvasive wall distensibility measurement in rupture risk stratification, the role of thrombus on wall loading should be further investigated.

A non-explosive test method for generating wide area dynamic blast-type pressure pulse loading on armored panels

The ever-changing face of modern warfare drives the need for improved vehicle armor and the means of testing new protection systems. Test methods to-date have been based on explosive loading or using apparatus such as shock tubes and gas guns to produce representative loading. Each methodology comes with its own set of limitations, such as poor visibility and remote facilities required for explosive testing or limited impact area for the gas gun based methods. A new impact-based method has been developed to address some of these limitations by employing the UC San Diego Blast Simulator, a system composed of high-speed (up to 66 m/s) actuators and a tuned pressure pulse generating projectile. The system has been used to impact a wide area (406 × 406 mm) on large-sized (610 × 610 mm) armor panels at a specific impulse of 7520 Pa s. Panels tested using the non-explosive Blast Simulator were compared to panels subjected to actual blasts with C4 explosive. Metrics of interest were damage modes, extent of damage, and pressure pulse attenuation relative to steel. Results indicate similar damage modes but larger degree of internal damage for the actual blast-tested composite sandwich panels, but a similar level of permanent deformation for the steel panels. The sandwich panels exhibited up to 37% reduction in initial-average transmitted acceleration and 76% reductions in peak transmitted acceleration compared to steel armor panels, at a weight savings of up to 49%. This non-explosive test allows for generating consistent and repeatable wide area pressure pulse loads to facilitate performance comparison and optimization of armor panel designs.