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The shape of a high-explosive is an important factor to consider in the near-field and contact explosion, but this has been rarely studied previously. In this paper, we first conduct experiments to study the directional effects of the underwater explosion shock wave of slender explosives. A numerical model based on the multi-material arbitrary Lagrangian Eulerian (MM–ALE) technique is then developed to study the influence of the explosive slender ratio on the generated shock waves. The numerical model is validated by experiment data. Then, tests are conducted with constant-mass cylindrical explosives with slender ratios ranging from 2.0 to 9.2. By comparing with the center-detonated spherical explosive, the peak pressure, pulse duration, impulse and energy flux of the underwater explosion of slender explosives are analyzed in detail. Furthermore, the effectiveness of the fluid-structure interaction algorithm is verified through the experimental data of a plate subjected to underwater contact explosion. Finally, the response of plates subjected to the underwater explosion of a slender explosive at different azimuths is studied. The interaction between the plate and the directional loads is analyzed. We conclude that the loads and structure responses of the near-field underwater explosion of slender explosives are different from those of spherical explosives. The analyses and results provide a reference for the near-field underwater explosion loads and structural response studies.

Explosion tests were performed underwater to study the blast resistance of water-backed sandwich panels. Effects on the structural response of face-sheet and core configurations, including face-sheet thickness, cell wall thickness of the honeycomb, core thickness and charge mass, were investigated by a large number of experiments. Quantitative results were obtained in the tests with corresponding sensors and further processing. Further results characterized the permanent deformation of sandwich panels. A failure mode map was adopted to identify the effect of design parameters on the structural failure mechanism at this blast magnitude. Finally, a comparison between sandwich panels and monolithic plates was performed. The comparative study provided further experimental evidence for the benefits of sandwich in water-backed configuration. Present study led to the apprehension of blast resistance of water-backed sandwich structure to underwater blast load, thereby developed useful guidelines for the design of blast-resistant structural systems.

In this paper, a coupled scheme utilizing advantages of the Runge–Kutta discontinuous Galerkin (RKDG) method and finite elements is applied to investigate cavitation induced by rarefaction waves during a near-field underwater explosion of cylindrical charge. A high-order RKDG method has advantages of an accurate shock capturing. So, it was used to solve a governing Eulerian equation for a compressible fluid. A finite-element method (FEM) was suitable to deal with problems of a shock response of structures and, therefore, applied for structural analysis. The suggested method was used to study pressure characteristics and cavitation effects of underwater explosions of cylindrical charges near single/double plates. First, a cavitation model was introduced in the RKDG method, and a numerical model of a high-pressure bubble in a cylinder was developed. The obtained numerical results were compared with the known solution in order to verify the validity of the suggested method. Second, a RKDG-FEM model of underwater explosion of a spherical charge near a plate was developed; its results for maximum deflection at the centre of the plate were compared with experimental data to prove the effectiveness of the coupled algorithm. Then, this algorithm was employed to simulate the process of underwater explosions of cylindrical charges near a single plate. Here, effects of different parameters - thickness of the plate and a distance between the charge and the plate - on pressure and cavitation characteristics were studied. Finally, a numerical model of double plates subjected to a near-field underwater explosion was developed. Cavitation evolution and its effect on shock-wave loading were analysed. Additionally, the effect of the distance between two plates was studied. The suggested analysis and its results provide a reference for load characteristics of near-field underwater explosions and shock response of structures.

This paper presents a simplified method for assessing the damage of a non-stiffened immersed cylinder subjected to the primary shock wave produced by an underwater explosion. The interaction between water and cylinder is split into two different phases. In the first phase, the kinetic energy which is transmitted by the shock wave to the cylinder is derived from explosion parameters. In the second phase, the cylinder deforms and the additional pressure created by interaction between water and deforming shell is calculated. To simulate the response of a cylinder clamped at its extremities, an analytical method based on the so-called rigid-plastic string on rigid-plastic foundation model is proposed. Closed-form expression is derived for evaluating the final shell deflection and used to highlight the influence of water added mass on cylinder damage. The proposed method is then validated by comparing, for a given cylinder and different shock factors, the resulting damage with finite element results. It appears that for high shock factors (i.e. K ≥ 2), the method allows for a good estimation of the cylinder shell deflection. It however underestimates significantly the deformed area when the shock factor is around 1.5 or lower. Additional research work is on-going to take into account deep immersion effects as well as ring-stiffening of the cylindrical shell.

The paper reviews some salient research works on load characterization and structural response of thin walled metallic structures subjected to Underwater Explosion (UNDEX), while highlighting the critical gaps and scope for further research work. The key aspects of an UNDEX phenomenon including Fluid Structure Interaction (FSI) and loading mechanisms on air backed fully submerged structures has been elucidated. Expressions for estimation of an early time far field UNDEX loading history on a plated structure considering FSI effects based on Taylor's theory, have been presented. With an objective to assess the consistency of published results and categorization of observed failure modes in UNDEX experiments, a composite plot of displacement response of clamped circular and rectangular plates in comparison to the response trends for impulsive blast loads have been presented. The comparisons presented in terms of non-dimensional parameters bring out the need and significance of more UNDEX experiments. Salient aspects in numerical modelling of UNDEX loading with increasing Shock Factor and simulations of associated highly non-linear structural response and experimentally observed ductile fracture modes have also been discussed. Various simple and complex phenomenological damage models, relevant in the numerical simulations of observed failure and fracture modes have been highlighted, with an emphasis on simple uncoupled strength models, which are relatively simple to calibrate. Approach towards FEA numerical simulations of UNDEX structural response using simple uncoupled damage models, including calibration of involved failure parameters, has been discussed in detail.

A shape of charge liners has a great effect on formation of a metal jet and its penetration into a target. In this paper, three different shapes of a charge liner, namely, conical, hemispherical and spherical-segment, are chosen to investigate their effect on damage response of a plate to underwater explosion. A Smooth Particle Hydrodynamic (SPH) method based on mesh-free Lagrange formulation is applied to simulate an entire process of a shaped-charge detonation, formation of a metal jet as well as penetration on a steel plate. Initially, a SPH model of the shaped charge with a spherical-segment liner is developed, and its results are compared with experimental data to verify the effectiveness of this method. Then, numerical simulations of shaped charges with different liners are performed to study the damage characteristics of a steel plate subjected to underwater-explosion shock loading and the metal jet. It was found that for the shock wave the peak value of the radial pressure is larger than that of the axial pressure during the detonation process; the level of pressure in the spherical-segment case was higher than that of the other two cases. After the detonation, the metal jet was gradually produced under the effect of the detonation wave. Three types of the metal jet - a shaped charge jet (SCJ), a jetting projectile charge (JPC) and an explosive formed projectile (EFP) – were formed corresponding to three cases with conical, hemispherical and spherical-segment liners. The obtained results show that the velocity and length of the SCJ in the conical case are greater than that of the other cases, and it therefore may lead to a larger penetration depth. In addition, the EFP has a better motion stability for a velocity difference in the spherical case is lower than that of the other two cases. Subsequently, the shock wave arrives at the plate earlier than the metal jet, which will cause deformation of the plate. Due to higher pressure, the shock wave in the spherical-segment case has a stronger damaging effect on the plate than that in the other two cases. Finally, the metal jet reaches the plate causing a hole. Because of a wider jet head, the EFP results in a more serious damage to the plate. The suggested analysis and its results provide a reference for structural design of shaped charge warheads.

A fluid model is developed and used in combination with Abaqus/Explicit to investigate the effects of graded foam cores on the loading of a sandwich spherical shell subject to underwater explosion from the inner side, after having validated the modeling technique by reproducing results by other authors. Based on the relation between the core strength and the stiffness of the outer face sheet (OFS), four different situations are considered to discuss the graded effects. It is demonstrated that for the case of relatively strong cores and the OFS with low stiffness or soft cores and the OFS with high stiffness, the core arrangement of low/medium/high (relative density from the inside to the outside) has the best performance to shock loadings which is a consequence of the effects of the fluid–structure interaction and the energy absorption capability; on the other hand, for the case of intermediate core strengths and stiffness of the OFS where the pulling-back force due to the stretching of the OFS is close to the core strength, the configuration of high/medium/low has the best performance due to its higher energy absorption efficiency of the foam and lower transmitted stress.

A series of close-in underwater blast tests were performed on sandwich panels consisting of two aluminum alloy face-sheets and a honeycomb core to investigate blast resistance of metallic sandwich panels. The blast resistance of sandwich panels was assessed in terms of structural deformation resistance represented by back face-sheet deflection and intensity of the secondary pressure wave, which is determined by the maximum velocity of the back face-sheet. It was found that the secondary pressure wave shows an inverse trend with face-sheet thickness while a positive relationship with core density, which is determined by foil thickness in this study. A failure mode map was adopted to indentify the effect of design parameters on the structural failure mechanism at this blast magnitude. Finally, a comparison of underwater blast resistance between sandwich panels and monolithic plates of equivalent mass was performed. The comparative study provided further experimental evidence for the benefit of sandwich construction in terms of deformation resistance and secondary pressure wave intensity even at high blast magnitude. It was also suggested that the benefit of deformation resistance was amplified with increase in equivalent thickness.

Underwater explosion shock loadings can seriously damage the vitality and fighting capacity of warships. Plastering a layer of sacrificial coating on the ship hull is one of effective strategies to isolate shock impulses and absorb shock energy. In this paper, the shock mitigation effects of sacrificial coatings plastered on a stiffened double cylindrical shell are analyzed numerically. The numerical models are validated by conducting a series of physical experiments of a stiffened double cylindrical shell under noncontact underwater explosion. Three different configurations are considered: both the pressure and thin hulls are plastered with sacrificial coatings; only the thin hull is plastered with sacrificial coatings; and only the pressure hull is plastered with sacrificial coatings. The total pressure field in water and the dynamic response of the stiffened double cylindrical shell are obtained. The results indicate that the deformation and motion of the sacrificial coatings can more easily generate rarefaction wave, which can decrease the total shock impulse acting on the structure. Among three configurations, the configuration of the coating plastered on the thin hull has a better capability of isolating the shock impulse and reducing the shock loadings transmitted to the pressure hull. The dynamic stress and velocity responses of the shell are effectively decreased. Comparisons between different configurations suggest that the coating on the thin hull plays a key role in mitigating shock loadings, while the coating on the pressure hull has limited effects. Moreover, comparison results between the bare hull and the equivalent model which increases the thickness of the thin or pressure hulls under the same mass conditions indicate that the method of using a sacrificial coating is more effective in improving the blast resistance of the structure. The research results are useful in guiding the shock resistance design of stiffened double cylindrical shells.

The response of a submerged structure to an underwater explosion (UNDEX) involves complex interactions between the structure and surrounding fluid. This study describes a numerical modelling methodology for calculating the structural response of an internally stiffened submerged aluminum cylinder to a close-proximity UNDEX. The simulations account for the effects of both the shock wave and bubble jetting on the deformation of the cylinder. The accuracy of the simulations is demonstrated by comparison of calculated pressure, bubble motion, structural displacement and strain with experimental measurements. The simulated migration and jetting of the gas bubble agrees well with experimental observations. The magnitude of calculated strains is consistent with measurements and the calculated depth of permanent deformation in the shell plating is within 3% of the experimental value.

This paper presents numerical simulations of dynamic responses of a ship section to non-contact underwater explosion using ABAQUS. The finite element model of the ship section including the size of fluid mesh, initial and boundary conditions etc. has been built up. Comparisons of the acceleration and velocity response between the experimental and numerical results have been investigated. The numerical results agree well with the measured results. Furthermore, the effect of the mass proportional damping factor on the velocity response have been investigated numerically. The dynamic response modes of the ship section subjected to a side-on non-contact underwater explosion are discussed.

In order to evaluate the strength and comparability of impulsive environment of model and practical structure in the water when subjected to underwater explosion, a new shock factor based on energy acting on the structure is presented to describe the loading of underwater explosion. To test the validity of this new factor, numerical experiments of double stiffened cylindrical shells are carried out a series of cases designed by the new factor and two other standard shock factors respectively. The results of the cases designed by the new factor indicate that the kinetic energy, potential energy and shock response spectrums of the structures agree well with each other in different cases designed by the equal new shock factor. However, the results of the cases designed by the two other standard shock factors are rather diverse. The analysis considers that the old shock factors do not take the spherical characteristics of shock wave front and relative position between detonation and structure into account, which can hardly reflect the similarity of underwater explosion loadings. The new shock factor can make up for such limitations.

The response of a lightweight torpedo when subjected to an underwater explosion (UNDEX) is an important criterion for multidisciplinary design. This paper investigates the effect of structural stiffeners on the performance of a lightweight torpedo. The finite element package ABAQUS was used to model the UNDEX and the fluid–structure interaction (FSI) phenomena, which are critical for accurate evaluation of torpedo stress levels. The pressure wave resulting from an underwater explosion was modeled using similitude relations and it was assumed to be a spherical wave. Various explosive weights and explosion distances were explored to determine the critical distance both for an un-stiffened and a stiffened torpedo. Once it was established that the stiffened torpedo performed better under explosive pressure loads, various configurations were studied to determine the optimal number of ring and longitudinal stiffeners. A final configuration was obtained for the torpedo that had minimum weight and was least sensitive to small manufacturing variations in the dimensions of the stiffeners. This paper presents details of the torpedo and fluid models and the finite element analysis method for FSI.

How to moderate ship the damages caused by the underwater explosions is of great interest to the modern ship designers. This investigation explores the protective effects of a layer of rubber sandwich with the square honeycomb core coated onto ship hull. Two slender steel scaled ship models were manufactured and tested. One model was coated with a layer of rubber coating while the other kept intact. A series of comparative tests were carried out to comprehend the dynamic performance of the protective layer when both shock wave and bubble pulse loading were considered. Modal characteristics of both models were measured firstly and then live UNDEX tests were made on the free floating ship models. The acceleration and strain peaks were selected as the major comparative criterions. The free field and wall pressure were also monitored. Detailed discussions on test results show that the protective rubber layer is capable of moderating damage of the ship body caused by shock wave while not very effective in reducing the whipping damage excited by bubble pulse.

Behaviour of plate specimens subjected to underwater explosion is of interest to metal forming community and ship designers. The break down of the original molecule of an explosive into product molecules associated with the evolution of large amount of heat generates a shock front in the water medium, followed by a gas bubble pulsation. The interaction of the shock wave with a plate imparts energy to it, which is dissipated in the form of deformation. The intensity of explosion determines whether a plate undergoes elastic deformation, yielding, plastic deformation or fracture. When the deformation is in the elastic range, the stress developed in the plate is given as a function of the material and shock wave parameters. As the intensity of explosion progressively increases, the elastic to plastic transition occurs over a specific shock factor. Plastic deformation is predicted as a function of geometric and material properties of the plate and shock pulse impulse. Deflection-time history reveals the reloading effects of the shock wave. As the deforming plate absorbs maximum energy, depending on its strength and ductility, it undergoes fracture. Terminal strain to fracture is considered as the criterion for explosive shock performance of ship materials.

This paper presents an analysis on attenuation of floating structures response to underwater shock. An explicit finite element approach interfaced with the boundary element method is used for the shock-fluid–structure interaction. The bulk cavitation induced by underwater shock near the free surface is considered in this study. Two types of floating structural configurations are modeled: one is the two-layered panel and the other is the sandwich panel, both of which are extracted from the typical floating hulls—the former corresponds the single hull with coating material and the latter corresponds to the double hull with different material fillings. Their effective structural damping and stiffness are formulated and incorporated in the fluid–structure-coupled equations, which relate the structure response to fluid impulsive loading and are solved using the coupled explicit finite-element and boundary element codes. The cavitation phenomenon near free surface is captured via the present computational procedure. The attenuation effects of the floating structure response to underwater explosion are examined. From the results obtained, some insights on the improvement of floating structures to enhance their resistance to underwater shock are deduced.

An underwater explosion (UNDEX) validation methodology was presented in O’Daniel et al. (2002, Int. J. Impact. Eng. 27, 919), describing a process where precision impact tests were used to generate a response equivalent to the underwater structural response of a flat panel subjected to a blast wave. A critical part of the methodology was to validate the code LS-DYNA3D (LSTC 936 (1995)) for the explicit finite element analyses of the short duration elastic responses of aluminum and composite panels subjected to low velocity, line and distributed impact loadings. A line impact was used as a base to perform preliminary tests of the precision impact test system, and the distributed impact configuration was necessary to generate a response similar to an underwater blast wave loading. Once validated for that range of structural response under impact loading conditions, LS-DYNA3D could then be used to predict impact tests to find responses that were equivalent to the UNDEX response of the target. This paper presents a detailed description of the precision impact events, and a comprehensive coverage of the validation of LS-DYNA3D for those impact events. O’Daniel et al. [1] provides an explanation of the equivalence between impact and UNDEX, as well as the overall methodology. A precision impact test machine was designed and fabricated, and low velocity impact tests were conducted to experimentally determine the panel responses for each impact configuration. Overall, the numerical predictions correlated well with the experimental results. However, better correlation may be achievable if more complex hyperelastic material models are used for the rubber materials in the composite and the impactor, a more detailed representation of the test frame-distributed impactor interface is included, and a static preload is numerically included in the panel-to-support interface. Details of the panel configurations, general impact solution methods, numerical simulations, precision impact equipment and impact tests, and comparisons between simulation and test results are presented.

This work compares experimental and numerical results concerning the elastic dynamic response of an air-backed rectangular aluminum plate subjected to an underwater explosion. Experiments were executed in a 4 m ×4 m ×4 m water tank. A small quantity of charge was applied to ensure the dynamic response of the target plate remained within the elastic range. A highly sensitive combined charge, which consists of a DP60 detonator and a Detasheet, was selected to enable a small quantity of charge to react fully when it explodes in the small water tank. The shock parameters of the combined charge were determined experimentally. Subsequent experiments on a plate panel were affected by an explosion of the aforementioned combined charge at various standoff distances. The plate panel under the same experimental conditions was numerically analyzed using the package USA/DYNA. The acceleration, velocity and strain histories of the target plate obtained from both experimental tests and numerical analysis were compared. The experimental and numerical results correlate well with each other.

Linear elastic shock response of plane plates subjected to underwater explosion is of importance to warship designers. Underwater explosion experiments were carried out with small quantity of explosive charges on air-backed 4 mm high strength low alloy (HSLA) steel circular plates of 290 mm diameter and rectangular plates of 300×250 mm with varying stand off. Strain gauges were fixed at regular intervals from the centre to the edge of the plates and dynamic strains were recorded. Strain distribution function was formed from the experimental data using which semi-analytical models were derived for predicting the elastic strain. The models showed good agreement with the experiments, © Elsevier

Experimental and numerical investigations were carried out on clamped rectangular plates subjected to underwater explosion loading. Experiments were conducted on rectangular plates of size 0.55×0.45×0.004 m using a box model set-up under air-backed conditions in a water tank detonating small charge weights of PEK-I explosive. Corresponding plastic deformation of the plates were measured for different charge weights and stand off distances. Numerical analysis was carried out using the MARC finite element code for various test conditions and the results are compared with experimental results.

The paper presents selected results of a study concerning the protective capacity of containment structures subjected to impulsive loading, produced by an underwater explosion of a spherical charge. The main application of these structures lies in design of underwater structures of great importance (tunnels, pipelines), which should also be protected against exceptional loads of this kind. In this study, a nonlinear finite-element computer code ABAQUS/Explicit was applied to determine the permanent effects of explosion in a protective containment structure and in bearing elements of the main, protected structure. The numerical results obtained for various structural configurations of a protective structure were compared and discussed in order to find the best protection in terms of its effectiveness, weight and simple realization.

Numerical simulations of the anomalous behavior of a plate/liquid/underwater explosion system are presented. The term “anomalous” implies that the final deflection of a plate is in the opposite direction to the direction of the explosion pressure. It is shown that anomalous behaviour takes place in a certain narrow range of the explosion pressure variation if the elastic unloading of the plate material and the liquid cavitation occur simultaneously. Small disturbances of the system parameters within this sensitive range can change the plate deformation history dramatically.

This paper examines changes to the flexural properties of a monolithic glass reinforced polymer (GRP) laminate when impulsively loaded by an underwater shock wave produced by an explosion. The laminate was experimentally tested using shock waves having a wide range of impulse pressures, and the residual flexural strength and stiffness was measured by the four-point bend technique. When dynamically loaded by a shock wave with relatively low pressure, the laminate experienced comparatively little microstructural damage, and consequently the flexural properties remained unchanged. Increasing the shock wave pressure beyond a threshold value caused severe damage, resulting in a significant loss in flexural strength and stiffness. This paper also presents measurements of the flexural strength of GRP at strain rates between 2 x 10−6 and 2 x 10−1 s−1 It is proposed that the four-point bend test method can be used to evaluate the resistance of GRP to damage by underwater shock loading, providing the strain sensitivity of the laminate is considered.

Summary This paper examines the plastic deformation and failure behaviour of mild steel bolts subjected to tensile loads exerted at strain rates ranging from about 10 −5 to 10 2 s −1 . Three experimental techniques were used to generate different strain rates; these being tensile testing (for a strain rate of 2.5 × 10 −5 s −1 ), drop tower impact testing (~ 1–10 s −1 ), and underwater explosion shock testing (~ 10 2 s −1 ). Measurements of the tensile failure strengths of the shank and threads of the bolt revealed that the threads fail at loads which are significantly lower than the breaking strength of the shank. The threads were damaged under loading in a two-stage process: firstly their tips were sheared off, and then the remaining thread was severely plastically deformed. These findings are important considerations when determining the load-bearing capacity of bolted joints and structures under impact conditions.