Table of Content

30 December 2023, Volume 44 Issue 12

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Contents

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2023, 44(12):  0. 

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The Meso-scale Modeling Method for Concrete Based on Block Division and Parallel Filling and Its Application in High-speed Penetration

LI Xu, LIU Yan, YAN Junbo, SHI Zhenqing, WANG Hongfu, XU Yingliang, HUANG Fenglei

2023, 44(12):  3543-3561.  doi:10.12382/bgxb.2023.0945

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Based on the need for rapid generation of large and complex finite element model in the meso-scale simulation of high-speed deep penetration, a meso-scale modeling method of concrete based on material property identification, block division and parallel filling is proposed. Different interface transition zone (ITZ) characterization methods are used to verify the characterization ability of the meso-scale modeling method under quasi-static and ultra-high speed penetration conditions. The accelerated modeling method has significant advantages in modeling efficiency and accuracy, which can achieve rapid modeling of large and complex shaped concrete structures and precise proportion allocation of microscopic components. Furthermore, the applicable conditions and the initial judgment criteria of material parameters of different ITZ characterization methods (i.e., ITZ solid element method, non-ITZ method and cohesive contact method) are summarized. The ITZ solid element method has the best prediction effect on penetration depth and crater size in ultra-high speed penetration simulation (the deviation is less than 10%); the cohesive contact method has the relatively worst performance in crater size prediction because it does not introduce strain rate effect and is prone to numerical instability. In addition, the response calculation and morphology characterization of the eroded projectile in the meso-scale simulation are highly consistent with the established nose evolution model for high-speed penetration. The research results can solve the difficulties of modeling the large and complex meso-scale targets in engineering practice, and provide the basis for exploring the meso-scale mechanism of ultra-high speed deep penetration.

Research on Dynamic Response and Damage Characteristics of Multi-cabin Structure under the Impact of Underwater Explosion

CHENG Lele, HUANG Fenglei, WU Haijun, TIAN Sichen, CHEN Wenge

2023, 44(12):  3562-3579.  doi:10.12382/bgxb.2023.0276

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The underwater blast tests of multi-cabin structures are conducted to investigate the effects of underwater blast load intensity and blast distance on the damage characteristics of multi-cabin structures under near-surface conditions. The numerical simulation method of S-ALE structured fluid-structure coupling is used to analyze the transfer distribution of flow field pressure load, and the dynamic response and damage characteristics of structures during the near-surface blast. The damage mechanism of underwater blast lioad against multi-cabin structures is claritied based on the numerical simulations of different blast intensities and distances, and the proportion of work done by shock wave and bubble load during the change of blast distance is obtained. The dynamic response characteristics and damage modes of multi-cabin structures under blast load are summarized. The result show that the multi-cabin structure produces the coupled damage forms, such as shear breach, tearing, depression plastic deformation, crush buckling, etc. The damage discontinuity and nonlinear deformation of the structure damage cause the asymmetric expansion motion of explosion bubble, resulting in the pressure distribution in the compartment showing shock wave characteristics and quasi-static characteristics; the shock wave and bubble load together cause the local damage and overall response of multi-cabin structure, and the bubble load induces the structural kinetic energy growth of about 50% or more.

Dynamic Response of Polyurethane-hemisphere Sandwich Structure under Action of Explosive Shock Wave

PAN Teng, BIAN Xiaobing, YUAN Mingzheng, WANG Liangliang, HUANG Yuan, HUANG Guangyan, ZHANG Hong

2023, 44(12):  3580-3589.  doi:10.12382/bgxb.2023.0645

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Improvement of blast resistance of explosion-proof equipment has become a popular research topic. The current explosion-proof equipment is mainly made of metal, generally having considerable weight, the use of lattice sandwich structure can achieve lightweight. Lattice sandwich structure has good energy absorption efficiency and excellent mechanical properties at high strain rates, but the non-deformable hemispherical lattice has not been considered in the previous explosion protection research, and the research on composite polyurethane foam explosion-resistant sandwich structure is even more rare. In view of this, a new type of polyurethane-hemispherical sandwich structure is proposed in considering the energy absorption of polyurethane foam and the arch deformation resistance of hemispherical structure, and a combination of experiment and numerical simulation is used to study the dynamic response of polyurethane-hemispherical sandwich structure under the blast shockwave loading. The results show that the center point displacement of polyurethane-hemisphere sandwich structure with the approximate surface density is the smallest under 0.65m blast impact of 500g TNT, which is 30% and 35% smaller than that of aluminum plate and pure hemisphere sandwich plate, respectively. The pure hemisphere sandwich plate absorbs the most energy but has the largest deformation, and the energy absorption of polyurethane-hemisphere sandwich structure and aluminum plate is 85% and 63% of that of the pure hemisphere sandwich plate, respectively, which shows that the incorporation of polyurethane has a significant role in ensuring the energy absorption. It can be seen that, compared with the aluminum plate, the polyurethane-hemispheres sandwich structure can effectively reduce the speed and stress concentration of the target plate while ensuring the energy absorption efficiency.

Numerical Research on the Power Field of Two-point Array Explosion with Different Spatial Intervals in Air

ZHENG Jian, MAO Zhiyuan, ZHANG Daixin, HU Hongwei, SONG Pu

2023, 44(12):  3590-3600.  doi:10.12382/bgxb.2023.0279

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In order to explore the characteristics of explosive power field formed by simultaneously detonated two explosives with different spatial intervals in infinite air space, a numerical model of two-point explosives with different spacing distances in free field air explosion is established to numerically study the two-point array explosion. The shock wave parameters of each space point in the calculation domain are obtained, and the contours of equal damage region based on overpressure and impulse criteria are drawn, respectively. The geometric characteristics of iso-surface with the change of space distance are studied. Results show that the pressure enhancement effect and multi-peak effect are the main reasons for the reconstruction of explosive power field. With the increase of the separation distance, the equal damage region of two-point explosion field presents three typical shapes. Compared with single point explosion, the volume of two-point explosion power field and the coverage area in specific direction only have gains in the range of partial separation distance. The relevant research conclusions related to the separation distance and criterion threshold can provide a reference for the study of multi-point array explosion power field characteristics and the design of multi-bomb cooperative combat mode. As the most basic mode of array explosion, these results can provide a reference for the study of multi-point array explosion power field characteristics and the design of multi-bomb cooperative combat mode.

Experimental Study and Theoretical Analysis of the Size Effect for Scale Model Projectile Penetrating into Rock Target

GAO Fei, DENG Shuxin, ZHANG Guokai, JI Yuguo, LIU Chenkang, WANG Mingyang

2023, 44(12):  3601-3612.  doi:10.12382/bgxb.2023.0014

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The penetration effects of geometrically similar projectiles on high-strength granite targets are tests to study the inherent mechanism of the size effect of the projectile penetrating into rock medium. According to the penetration test results, the applicability of typical empirical formulae for predicting the penetration depth of projectile into high strength rock is evaluated, a penetration depth calculation method with the shape and diameter coefficients as the control variables is developed, and the conversion relationship between the penetration depths of model projectile and prototype projectile under different scale ratios is established. The research results show that the proportional penetration depth of model projectile and the prototype projectile has the caliber effect. The effect coefficient is not only related to the scale ratios, but also related to the diameter of prototype projectile and the material parameters of target. It increases with the increase in the prototype projectile diameter, and decreases with the increase in the scale ratio. The established conversion relation of penetration depth explains the reason for the error between the model test result and the prototype test result caused by the traditional model test method, and reveals the mechanism of the size effect of projectile penetrating into rock-like materials.

Dynamic Response Mechanism of Aluminum Foam Sandwich Plate with Cavity under Shallow-buried Explosive Loading

LIU Wei, MA Honghao, XU Qinming, YAO Xiangyang, ZHAO Yong, YANG Ke, YANG Hui, SHEN Zhaowu

2023, 44(12):  3613-3621.  doi:10.12382/bgxb.2022.1195

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The cavity structure can effectively protect the rear area. In order to study the influence of the cavity structure on the energy attenuation performance of aluminum foam sandwich plate structure, the influence of the cavity size on the deflection of sandwich plate, the secondary shock wave behind the plate and the energy absorption efficiency of aluminum foam core layer under the experimental conditions of explosion loading of shallow-buried explosive is investigated by changing the diameter and thickness of the cavity in the aluminum foam core layer. The results show that the intensity of secondary shock wave behind the structure decreases significantly with the increase of the cavity thickness in the aluminum foam. When the cavity diameter is 0.3D and its thickness is 1/3H, the central pressure intensity is the lowest, which is about 63% of that of the non-porous aluminum foam plate. The volume strain is the largest when the cavity diameter is 0.3D and its thickness ias 2/3H, which is 61% higher than that of the control group. The surface cavity structure can effectively enhance the energy absorption efficiency of aluminum foam sandwich structure.

Research Progress of Transient Photoelectric Measurement Technology for Shock Wave and Detonation Physics Experiments

DU Liangliang, QIAN Weixin, LIU Shouxian, ZHAO Yu, LI Shengfu, ZHAI Zhaohui, CHANG Lihua, ZHU Yu, WENG Jidong, WU Jian, LI Jun, ZHU Liguo

2023, 44(12):  3622-3640.  doi:10.12382/bgxb.2023.0361

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Shock wave physics and detonation physics is the key basis for detonation device physical design, engineering design and effect research, and are focused on researching the mechanical response, effect and engineering technology application of medium, materials and structures under strong dynamic loads such as explosion, shock and transient energy deposition. The advanced transient photoelectric measurement technology for extreme environments is an important driving force for the research and development of shock wave physics and detonation physics. Based on the current situation of transient photoelectric measurement technology for shock wave and detonation experiments at home and abroad, the characteristics and typical technical parameters of the main techniques, such as high-speed photography, X-ray flash photography, holographic imaging, transient pyrometer and Doppler velocimetries, are summarized. The development trend of these techniques is analyzed, which provides some references for the development of transient photoelectric measurement technology for shock wave and detonation experiments in China.

The Failure Patterns of Concrete Slabs with Different Aggregate Gradations under Contact Blast Loading

QI Xiaopeng, ZHANG Jie, ZHAO Tingting, WANG Zhiyong, WANG Zhihua

2023, 44(12):  3641-3653.  doi:10.12382/bgxb.2023.0282

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A three-dimensional meso-scale model of concrete slabs with randomly distributed aggregates based on Voronoi technology is presented, and the finite element software is employed to simulate the dynamic response and damage of concrete slabs under contact blast loading. The proposed model takes into account the mesoscopic factors such as aggregate size, volume fraction and gradation, and provides accurate insights into the influence of high-strength aggregate and low-strength mortar on the dynamic mechanical properties of concrete. Compared with the referenced experimental results, the model can be used to predict the crater size and failure pattern of concrete slab under the contact blast loading. Furthermore, the influence of aggregate gradation on the plastic deformation and failure patterns of concrete slabs is studied, and the influence mechanism of aggregates in the explosion response process of concrete slab is discussed. The results show that the spherical characteristic of the shock wave propagating in concrete slab is disturbed by aggregates, which leads to a random damage distribution. The aggregate gradation has little effect on the concrete slabs with the aggregate distribution of continuous gradation or discontinuous gradation. Both of them have the same failure pattern with obvious spalling characteristics, and the damage degree also has little different. However, the blast response of concrete slab is significantly influenced when only the single gradation of aggregate is considered, and it presents obvious penetrating characteristics. The concrete slab with single gradated aggregate has stronger binding force, which reduces the plastic deformation of the concrete. The research result provides important theoretical and engineering application values for the evaluation of anti-explosion performance and structural optimization design of concrete at the meso-scale level.

Dynamic Response and Failure Mechanism of Pre-holed Q235 Steel Plate under Foam Projectile Impact Loading

HAN Jiatong, WANG Xin, ZHANG Lei, LI Zhen, WANG Pengfei, ZHAO Zhenyu, LU Tianjian

2023, 44(12):  3654-3666.  doi:10.12382/bgxb.2023.0359

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A pre-holed Q235 steel plate subjected to foam projectile impact is numerically investigated to assess the structural damage caused by combined blast and fragment loading upon detonation of cased explosives. The validity of the numerical model is checked against experimental measurements. The validated model is then employed to investigate the dynamic response, deformation/failure modes and hole-edge deflection of the pre-holed plate. The physical mechanisms of tearing failure initiated around the pre-hole are revealed using the stress triaxiality and Lode parameter for describing the state of stress. The influences of hole diameter and plate thickness on the impact resistance and failure mechanism are also quantified. Results show that the presence of a pre-formed hole significantly curtails the impact resistance of the steel plate: With increase in hole diameter or decrease in plate thickness, the hole-edge deflection of the steel plate grows, while the projectile momentum causing tearing failure drops.

Behavior of Segmented Projectile Penetrating into Ceramic/Steel Composite Armor

WANG Mingyang, ZHENG Yuxuan, LI Tianpeng, CHEN Chun, WANG Yuanchao

2023, 44(12):  3667-3675.  doi:10.12382/bgxb.2023.0274

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A two-stage segmented core structure is designed for the phenomena of deformation and fragmentation of armor-piercing core during the impact of a high-speed projectile on a target plate, and the finite element analysis software is used to numerically simulate the penetration of two-stage core structure into the ceramic/steel composite target plate. The stage analysis of the penetration process is carried out based on the damage pattern of target and the motion law of two-stage core structure, and the influences of core length ratio, spacing and other factors on the penetration performance of two-stage core structure are discussed. The results show that the increase in the penetration depth of two-stage core structure can reach more than 16% compared with that of the ordinary core. It is found that the length ratio and spacing of two-stage cores have a great influence on the penetration effect, and the selection of reasonable length ratio and spacing can help improve the penetration performance of two-stage segmented projectiles on ceramic/steel composite target plates.

Experiment on Dynamic Mechanical Characteristics and Damage Fractal Law of Crack in Decoupled Charge Scratch Blasting

MA Jun, WANG Xuguang, LI Xianglong, WANG Jianguo

2023, 44(12):  3676-3686.  doi:10.12382/bgxb.2022.1270

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In order to study the dynamic mechanical characteristics and damage law of crack in decoupled charge structure scratch blasting, the dynamic mechanical characteristics of PMMA explosive crack propagation with the decoupled coefficients of 1.00, 1.33, 1.67 and 2.00 are studied by appling the dynamic caustics experimental technology. The damage variable and fractal dimension after blasting are calculated by fractal dimension theory. The results show that, for R_d<1.67, the damage variables of the partitions around a blasthole are larger, and there are more secondary cracks in the non-scratched direction of the blasthole. For R_d=1.67, the dynamic mechanical behaviors of the left and right cracks on the blasthole are similar, and the damage variables and fractal dimension are the smallest. With the increase of the decoupled coefficient, the length of the main crack decreases, the propagation speed of the main crack, the stress intensity factor and the dynamic energy release rate decreases, but the crack propagation time increases and the quasi-static effect of the explosive gas is prolonged. The dynamic mechanical characteristics of reactivation, initiation, propagation and stop of crack under the action of explosive gas have realized the quantitative analysis of dynamic and static separations to a certain extent. The relationship between the damage variable and fractal dimension of PMMA decoupled charge structure scratch blasting under free boundary conditions is ω=0.00175D^9.04.

Explosion Impact Protection Performance of Sandwich Structure with Box-shaped Cores

WANG Hao, XU Bin, WANG Shu, XU Yongjie, WU Hao

2023, 44(12):  3687-3695.  doi:10.12382/bgxb.2023.0256

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In order to improve the crashworthiness of corrugated plate sandwich structure under blast loading, a new type of box-shaped thin-walled structure is proposed as the core of the corrugated plate sandwich structure to improve its energy absorption capacity. The quasi-static crushing tests are performed on the unit cell of the box-shaped thin-walled structure. The energy absorption capacity of box-shaped thin-walled structure, such as energy absorption, specific energy absorption per unit mass, initial peak crushing force, mean crushing force, and crushing force efficiency, are analyzed and compared with that of the Kirigami modified trapezoidal structure. A numerical simulation model is established with finite element software, and calibrated with the experimental results. The energy absorptions and maximum deformations of the corrugated plate sandwich structures with box-shaped cores and Kirigami modified trapezoidal cores with different geometric configurations are analyzed and compared numerically. The numerical results show that the sandwich plate with box-shaped thin-walled structure as core has excellent crashworthiness, such as higher specific energy absorption, uniform and stable deformation pattern, and longer effective energy absorption stroke. These indicate the potential applications of the proposed corrugated plate sandwich structure with box-shaped cores for enhancing the energy absorption capacity under blast loading.

Research on the Viscoelastic Constitutive Model of Composite Solid Propellant Containing Damage Based on Mesostructure

WANG Guijun, WU Yanqing, HOU Xiao, HUANG Fenglei

2023, 44(12):  3696-3706.  doi:10.12382/bgxb.2022.0747

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The macroscopic mechanical properties of composite solid propellant are inseparably linked to its mesoscopic components and damage. A macro and mesoscopic constitutive model of composite solid propellant with void damage was developed based on the evolution of the mesostructure during the deformation process of composite solid propellants. The model takes into account the dependence of propellant temperature and strain rate, and is able to describe the different mechanical responses of propellant in tension and compression. The validity of the constitutive model is verified by tensile and compressive tests at different temperatures and strain rates. The macro and mesoscopic constitutive model is re-developed based on the user material subroutine interface UMAT provided by the finite element software, and applied to the structural integrity analysis of grain under low temperature ignition conditions, indicating that the safety factor of grain under low-temperature ignition conditions is 2.56, and the structural integrity of grain meets the requirements. Finally, compared with the linear viscoelastic constitutive model based on Prony series, the proposed constitutive model can be used to more accurately analyze the structure of composite solid propellant grains.

Study on the Mechanism of Secondary Penetration of Long-rod Projectile and Its Influencing Factors

TANG Kui, WANG Jinxiang, LIU Liangtao, YANG Ming

2023, 44(12):  3707-3718.  doi:10.12382/bgxb.2023.0035

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A 3D SPH-FEM finite element model is established to further investigate the penetration mechanism of long-rod projectile at the third penetration stage. On the basis of verifying the effectiveness of the model, a penetration of gold rod against a semi-infinite thick 7075-T6 aluminum target is studied, the mechanism of the third penetration stage is explored, and the influence law of projectile/target density and strength, and L/D of projectile on penetration is also analyzed. The calculated results show that the reason why the P/L vs. striking velocity curve for gold rod penetrating 7075-T6 aluminum target is broken is the secondary penetration of the inverted rod debris. A tubular fragment is formed after the gold rod is eroded. At high initial velocity, its velocity is higher, its direction is consistent with the penetration direction, and its density is large. Therefore, it will continue to penetrate the target after the projectile body is completely eroded. The secondary penetration depth of the gold rod increases in an “S” shape with the increase in striking velocity, and its contribution to the total penetration depth is even as high as 15.6% at striking velocity of 3km/s. When there is a secondary penetration, it is more appropriate to divide the third penetration stage into residual and secondary penetration stages. High projectile-target density ratio is beneficial for the formation of secondary penetration. The influence of the target density and strength on the penetration capability significantly exceeds that of the projectile. Under the conditions of the unchanged length or mass of the projectile, the effect of length-to-diameter ratio on the hydrodynamics and total penetration depth is significant, but its effect on the secondary penetration is small.

The Damage Effect of Reinforced Concrete Beams Subjected to Synchronous Explosion of Double Charges

XU Yingliang, LIU Yan, YAN Junbo, BAI Fan, YU Hao, LI Xu, WANG Hongfu

2023, 44(12):  3719-3732.  doi:10.12382/bgxb.2023.0286

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To study the damage effect of synchronous explosive loading of double charges on reinforced concrete (RC) beams, the experiments were conducted on RC beams subjected to the synchronous explosive loading of double charges. The damage characteristics and displacement response of RC beams were obtained through the experiments. Based on the experimental results, a corresponding RC beam synchronous explosion simulation model with double charges is established using finite element simulation software, considering the influence of simply supported boundary conditions. The reliability of the simulation model is verified by comparing the local failure characteristics and maximum displacement responses of RC beams from experiments and simulation. Based on this, the effects of charge spacing and blast height on the failure characteristics and displacement of concrete beams during synchronous explosion of double charges are further studied. In addition, the damage effects of double charges and equivalent single charges on the concrete beams at the same blast height are compared. The results show that the failure mode of concrete beams gradually changes from local failure to punching shear failure with the increase of charge spacing. As the charge spacing increases, the displacement response and front surface failure of concrete beam shows a trend of first increasing and then decreasing, mainly due to the enhancement effect of shock wave superposition during synchronous explosions of two charges. Besides, compared to the destructive effect of a single charge with the same total mass on concrete beams, the local damage of RC beams under the action of double charges is more uniform. Moreover, there exists a range of intervals related to charge spacing, within which the displacement response of RC beams under double charges is greater than that under equal mass single charge: the smaller the blast height, the larger the range of this interval; The larger the charge mass, the larger the range of this interval.

Damage Effect of Plasma Produced by High-velocity Impact of Reactive Fragments

XU Ruize, XIAO Jianguang, MA Junyang, AN Delong, XIE Zhiyuan, WANG Yanxin

2023, 44(12):  3733-3742.  doi:10.12382/bgxb.2023.0048

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The damage test of reactive fragments hitting aluminum plate at high speed is carried out to investigate the plasma characteristics and the electromagnetic damage effect on target caused by high-speed impact of reactive fragments. The reactive material fragments of different formulas and ordinary aluminum fragment are used to impact the aluminum plate. The electron density and temperature of plasma generated from thereactive and inert fragments at specific spatial location were obtained by usingatriple Langmuir probe system. The electromagnetic damage effect of 74HC04 logic chip under the action of plasma was obtained by usinga logic chip signal-acquisition system. The results show that the plasma electron density produced by the reactive fragments is higher than that produced by the inert fragments due to the unique penetration effect of the reactive fragments and the release of more energy. When the reactive fragment containingtantalum/magnesium/tetrafluoroethylene-hexafluoropropylene-vinylidene fluoride copolymer(Ta/Mg/THV,70%Ta+9.26%Mg+20.74%THV) impact the double aluminum plates with 2mm thickness at the speed of 1.4km/s, the plasma electron density can reach 5.89×10¹⁵m^-3, andit also causes thetransient soft damage with transient distortion of logic relation and theirreversible damage with complete failure of logic working ability to the 74HC04 logic-chip.

Study on Physical Characteristics and Shock Wave Behavior of Aluminum Powder Suspension Ignited by Electrical Wire Explosion

HAN Ruoyu, YUAN Wei, LI Chen, CAO Yuchen, BAI Jie

2023, 44(12):  3743-3754.  doi:10.12382/bgxb.2023.0244

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Underwater electrical wire explosion driven by a high-power electric pulse is accompanied by physical effects such as shock wave, plasma and strong light radiation. Therefore, it has achieved remarkable results in the underwater explosion simulation and the exploition of unconventional oil and gas. Due to the skin effect and the limited electrical insulation of the equipment, it is often impossible to obtain the required shock wave by increasing the stored energy and load quality without limitation. In this paper, the underwater electrical explosion of copper wire is used to ignite the aluminum powder suspensions with particle sizes of 10μm and 1μm to find the mechanism of detonation of aluminum powder suspension to enhance shock wave. The details of space-time evolution of aluminum powder suspension ignited by the electrical explosion are obtained through the diagnosis of electrical physical parameters and high-speed backlight images. The discharge characteristics and ignition mechanism of aluminum powder suspension under electric-hydraulic breakdown and electrical explosion are studied, and the relationship between the stored energy and shock wave is established. It is found that the ignition of aluminum powder suspension by electrical wire explosion is a result of the joint action of near-field shock wave, plasma and strong light radiation, and then the continuously combusting aluminum powder injects energy into the surrounding compressed water layer, which enhances the amplitude, positive action time and impulse of shock wave.

Equivalent Strength of Armour Steel against High-velocity Penetration of Long-rod Projectile

WANG Jirui, WANG Chengxin, WANG Yini, TANG Kui, BO Qile

2023, 44(12):  3755-3770.  doi:10.12382/bgxb.2023.0619

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Armour grade steel is one of the main components of composite armour. A 3D SPH-FEM coupling model is developed to investigate the equivalent strength of armour grade steel against the penetration of long-rod projectile. On the basis of verifying the reliability of the model, a simulation study on tungsten alloy long-rod projectiles penetrating a semi-infinite 300-600HBW armour steel in the initial velocity range of 1000-1800m/s is carried out. The equivalent strength of armour steel under high strain rate-adiabatic conditions is explored based on the resistance force and Walker-Anderson model. The calculated results show that the penetration process of tungsten long-rod projectiles into semi-infinite steel targets can be divided into three stages: initial transient, quasi-steady and residual penetration. In most conditions, Walker-Anderson model can be used to accurately calculate the depth of penetration and head velocity of quasi-steady stage. the diameter of rod body and the equivalent strength of target are approximately constant in the quasi-steady stage, thus the penetration resistance can be described by the Poncelet formula. According to the above analysis, a nonlinear conversion model for the equivalent strength and hardness of armour steel is developed. Combined with Walker-Anderson model, it can accurately predict the depth of penetration of long-rod projectiles against semi-infinite targets. The model shows that equivalent strength is positively related to hardness, but its increase slows down due to the enhancement of thermal softening and the weakening of strain rate hardening.

Machine Learning-based Models for Predicting the Penetration Depth of Concrete

LI Meng, WU Haijun, DONG Heng, REN Guang, ZHANG Peng, HUANG Fenglei

2023, 44(12):  3771-3782.  doi:10.12382/bgxb.2023.0291

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The test data about concrete penetration are often limited in quantity and unevenly distributed, which leads to the poor accuracy of machine learning-based models for predicting the penetration depth. This study aims to mitigate the unevenness of data distribution and increase the amount of available data to obtain an optimal machine learning model under the limitation of limited penetration test data. Based on collecting a large amount of penetration test data, the penetration data are extended by data augmentation methods such as linear interpolation and adding Gaussian noise. The genetic algorithm and greedy algorithm are used to optimize the hyperparameters of four common machine learning models: multilayer perceptron, radial basis neural network, support vector regression and extreme gradient boosting tree. The prediction of concrete penetration depth based on machine learning is realized. Sensitivity analysis method is used to analyze the influence of input factors on the penetration depth. The results show that the problem of insufficient data can be effectively alleviated by using linear interpolation and adding Gaussian noise. The accuracies of multilayer perceptron, radial basis neural network, support vector regression and extreme gradient boosting tree are improved by 2.49%, 0.99%, 0.74%, and 0.72%, respectively, after using data augmentation. The diameter, impact velocity and mass of projectile have the dominant influence on penetration depth. In addition, the average error of the optimal concrete penetration depth prediction machine learning model is 8.28%, and its global accuracy is better than the commonly used empirical formulas for predicting the penetration depth.

Design of Layered Metal Embedded Stress Sensing Structure and Testing of Microstructure and Properties in Ultrasonic Additive Manufacturing

WANG Yu, BAI Shule, WANG Ziqi, LIU Bin, FENG Li, ZHAO Wenjuan, HAO Junhui

2023, 44(12):  3783-3792.  doi:10.12382/bgxb.2023.0349

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A diaphragm type layered metal embedded stress sensing structure is proposed to address the issues of low accuracy and difficulty in detecting the internal stresses in metal structures using traditional patch testing. Material selection and structural design are carried out from aspects of the thickness of diaphragm layer and the material of diaphragm. Ultrasonic additive manufacturing is used to manufacture Cu/Al layered diaphragm structures. The mutual diffusion, phase composition, and microstructure of the diaphragm/substrate interface after ultrasonic consolidation are studied. Finite element impact simulation is used to simulate the strain of traditional patch structures and the layered embedded stress sensing structures obtained from manufacturing, Strain testing is conducted on layered embedded stress sensing structures to investigate the strain response effect of layered metal embedded stress sensing structures. The research results indicate that the shape of diaphragm designed by the diaphragm layer is a circular membrane, of which the film material is a pure copper with a film diameter of 20mm and a film thickness of 0.1mm. After ultrasonic additive manufacturing of Cu film/Al matrix, a small amount of Cu atoms diffuse towards the Al layer without generating new intermetallic compounds, forming a mechanically bonded toothed morphology. The results of impact simulation and strain testing both indicate that the strain response effect of the embedded stress sensing structure is more accurate than that of the traditional patch structure.

Deformable Special-Shaped Projectile Impacting a High-strength Rock:Experiments and Analysis

REN Guang, WU Haijun, DONG Heng, LÜ Yingqing, HUANG Fenglei

2023, 44(12):  3793-3804.  doi:10.12382/bgxb.2023.0278

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Fracturing a high-strength rockto collect the fragment samples by the kinetic energy of deformable special-shaped projectile has attracted much attention in the Near-Earth Asteroid (NEA) sampling scheme. Three types of deformable special-shaped projectiles,i.e., petal penetrating, petal non-penetrating and oval penetrating, are designed to study theprojectile-target interaction and rock fracture mechanism. Based on 57mm lightgas gun and 14.5mm ballistic gun, the low-speed (71.4-280.0m/s) and high-speed (453.0-612.0m/s) impact experiments are carried out for a rock with uniaxial compression strength of 180MPa to obtain the reflected velocity of projectile, mass of rock fragments, and diameter and depth of fracturing zone. Experimental results show that, in the low-speed impact experiments, two types of petal projectiles have lower reflected kinetic energy ratio and its reflection speed is reduced by 21.9%-42.8% compared to other projectiles; In the high-speed impact experiments, the projectile-target interaction of petal projectile is two-phase processes: multi-point simultaneous impact and Taylor rod impact, which increase the mass of fragments about three times than petal penetrating projectiles. The research inspires the designing of deformable special-shaped projectile and the comprehending of fracture mechanism of rocks under impact.

Dynamic Mechanical Properties and Damage Constitutive Model of Copper-bearing Garnet-biotite Schist

ZHAO Zehu, LI Xianglong, HU Qiwen, WANG Jianguo

2023, 44(12):  3805-3814.  doi:10.12382/bgxb.2023.0690

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The dynamic mechanical properties and damage law of deep ore rock under different loading conditions are explored by taking the copper-bearing garnet biotite schist in deep mining as an object of study. A combined dynamic and static impact test is performed under the conditions of six kinds of axial pressure σ_ap (0MPa, 6MPa, 12MPa, 18MPa, 24MPa, 30MPa), six kinds of confining pressure σ_p (0MPa, 4MPa, 8MPa, 12MPa, 16MPa, 20MPa) and six kinds of impact velocity v (18.68m/s, 20.93m/s, 23.54m/s, 26.63m/s, 29.26m/s, 31.95m/s), and the factors of impact velocity, axial pressure, confining pressure and strain rate are considered. Based on the statistical damage theory and Drucker-Prager failure criterion, a dynamic damage constitutive model of copper-bearing garnet-biotite schist under combined static and dynamic loading is established. The results show that there is almost no compaction stage in the stress-strain curve of ore rock specimen. When the stress increases to 65%-80% of peak stress, the stress-strain curve of this stage shows a step phenomenon. The dynamic failure mode of deep surrounding rock is significantly affected by the stress state and impact velocity of ore rock at different buried depths.When σ_p=12MPa and v=31.95m/s, the dynamic compressive strength increases first and then decreases with the increase of axial compression σ_ap, while the peak strain decreases linearly. When σ_p=12MPa and σ_ap=24MPa, the dynamic compressive strength increases linearly with the increase of strain rate, while the peak strain increases as quadratic polynomial with the increase of strain rate. The theoretical curve of the model is in good agreement with the experimental curve, which verifies the reliability of the dynamic constitutive model, and can provide some reference for the research and engineering application of the dynamic constitutive model of deep buried rock mass.

Study on the Evolution Characteristics of Pressure Pulse in Shock Tube and a Method of Simulating Air Explosion Shock Wave

ZHOU Yuelan, PEI Lu, LONG Renrong, ZHANG Qingming, LIU Bowen, REN Jiankang

2023, 44(12):  3815-3825.  doi:10.12382/bgxb.2023.0284

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The evolution characteristics of pressure pulse in the shock tube are studied to generate a shock wave similar to the air explosion shock wave in the tube. The process of forming a shock wave similar to air explosion shock wave in shock tube driven by high pressure gas is analyzed through the experimental study and numerical simulation of pressure pulse characteristics in shock tube, and the relationship between shock wave characteristics and shock tube parameters is established. The results show that the shock wave generated in the shock tube is a plane wave. When the length of the low pressure section of shock tube is long enough, the reflected rarefaction wave in the low pressure section can catch up with the right shock wave front, and form a shock wave similar to the air explosion shock wave at the overtaking position. The decrease in the driving pressure and length of the high pressure section makes the rarefaction wave easier catch up with the shock wave. As the pressure in the low pressure section increases, the velocity of the shock wave decreases, and the reflected rarefaction wave catches up with the shock wave faster. At the same time, the shock wave travels shorter in the low pressure section, and the positive pressure duration of the shock wave pressure is shorter. The characteristic parameters such as peak overpressure and positive pressure duration of shock wave are related to the driving pressure and length of the low pressure section of the shock tube. Combined with dimensional analysis, the minimum length of low pressure section required to form simulated air explosion shock wave is established, and the relationship among the characteristic parameters such as peak overpressure and positive pressure duration of shock wave and the parameters such as pressure and length in shock tube is established, which provides basic theory and data support for the design of simulated air explosion shock tube.

Study on Preparation and Properties of TiW/Ni/Au Exploding Foil

LI Siyu, DONG Xiaofen, WANG Yunpeng, LI Shuai, WANG Duan, WANG Qinghua

2023, 44(12):  3826-3835.  doi:10.12382/bgxb.2023.0238

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Exploding foil initiator is very popular in all kinds of tactical weapons because of its high reliability and security, but its initiation requires high input energy and voltage, so it needs to be equipped with special initiation circuit, which leads to high cost and large volume. Its application in conventional weapons is limited. In order to comply with the development trend of low energy and miniaturization of exploding foil initiator and obtain and exploding foil initiator with charging voltage below 1.5kV, a kind of exploding foil with TiW/Ni/Au composite film was designed and prepared, and its electric explosion performance and driving ability were studied deeply. The results show that the TiW/Ni/Au exploding foil with bridge size of 0.15mm×0.15mm has the best performance. It can reliably explode when the charging voltage is 800V and the energy storage capacitance is 0.1μF, so that the 25μm-thick polyimide flyer is accelerated to 3920m/s within 0.4μs under the shear action of an accelerated bore with a diameter of 350μm. Compared with Cu foil, the energy utilization efficiency of TiW/Ni/Au exploding foil is increased from 3.11% to 12.76% at 800V charging voltage.

Penetration Characteristics and Plate Failure Modes of Asymmetrically Shaped Projectiles Penetrating Thin Metal Targets

DENG Ximin, TIAN Ze, WU Haijun, WANG Hao, HUANG Fenglei

2023, 44(12):  3836-3850.  doi:10.12382/bgxb.2022.0724

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In order to support the theoretical design of terminal damage of hypersonic missile and the basic theory of armor-piercing mechanics of special-shaped projectile, the penetration ability of asymmetrically shaped projectile penetrating metal target and the damage mechanism of target plate need to be solved. The velocity variation and deflection characteristics of the projectile are analyzed through the experiment of asymmetrically shaped projectile penetrating the multi-layer spaced 921A steel plate and the numerical simulation based on Abaqus/Explicit, VUMAT and Python subroutines. The damage mechanism of target plate is analyzed from damage morphology and energy dissipation, and the applicability of the research results in practical engineering application is discussed. The results show that the asymmetric structure has the ability to maintain the stability of projectile attitude. When the initial velocity is lower than 600 m/s, the velocity drop and the ballistic limit increase with the increase of the oblique angle, and the failure modes of the target plate are shear plugging, pealing and transverse deformation. When the initial velocity is higher than 600 m/s, the ballistic limit curves of different oblique angles overlap, the dimensionless velocity drop decreases with the increase of the initial velocity, and the failure mode of target plate changes to ductile enlargement, pealing and fragmentation. During the penetration progress, the tangential component of plastic work done has the largest proportion, the circumferential component is the smallest, and the axial and radial plastic works are similar. During the high-speed penetration, the kinetic energy of plate fragments is 25%-50% of the plastic work done. The scaled model based on geometric similarity can reflect the speed change of the prototype projectile during the high-speed penetration and the damage characteristics of trget plate.

A Comparison of Damage Effectivenesses of Reinforced Concrete Beams by Single-point and Three-point Array Damage Patterns

XIA Liu, WU Weichao, PAN Aigang, WANG Yafei, WANG Qiang, YAN Shen

2023, 44(12):  3851-3861.  doi:10.12382/bgxb.2023.0021

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The single-point and three-point array contact explosion tests and numerical simulations of reinforced concrete beams are investigated to obtain the destruction law and the gain effect of three-point array contact explosion. The local failure characteristics under the same total mass of explosives were observed, and the effects on the local damage effect under different damage patterns were analyzed. The results show that, when the total mass of explosives is the same, multiple blast compressive waves propagate inside the beam member during the explosion of the three-point array and occur a coupling enhancement effect, effectively enhancing the damage power. Four local damage patterns of front cratering, side breakdown, back collapsing and section punching occur in the three-point array damage, and three local damage patterns of front cratering, side breakdown and back collapsing occur in the single-point damage under the action of contact explosion load. Combined with the finite element simulation results, it is found that,the depth of destruction in the beam span is higher, but the damage area of blast-face decreases as the distance between the explosives decreases; and the damage area of blast-face increases, but the damage depth decreases accordingly as the quantity of explosives increases. This indicates that the damage of reinforced concrete beams under contact blast loads is not only related to the distance of charge array and the quantity of charges, but also to the mass of individual explosives in the array. The research results can provide a certain reference for studying the efficient damage of reinforced concrete beams and improving the utilization of explosive energy.

Damage Effect of W/Zr/Ti Reactive Fragments on Spaced Targets

WANG Zaicheng, XU Yi, JIANG Chunlan, HU Rong, HE Zheng

2023, 44(12):  3862-3871.  doi:10.12382/bgxb.2023.0289

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In order to study the coupling damage mechanism of W/Zr/Ti reactive fragments after penetrating a target, a ballistic gun experiment is conducted to investigate the penetration of W/Zr/Ti reactive fragments into a spaced target composed of 6mm-thick Q235 steel plate and 1.5mm-thick aluminum plate. Combined with the impact reaction theory of reactive fragments and the principle of energy conservation, the target deformation energy is calculated and the contributions of chemical energy and kinetic energy to coupled damage are analyzed from the perforation mode of steel targets, the damage mode of after-effect aluminum targets, and high-speed photography of reactive fragments penetrating the spaced targets. The research results show that, the slug and debris cloud cause bulge, perforation, and ablation damage on the aluminum target when an active fragment hits the target at a speed of less than 800m/s. When the target hits the target at a speed of more than 1187m/s, the aluminum target undergoes shear perforation under the action of the front steel target plug, resulting in bulge, cracks, and petal warping under the coupling damage of kinetic and chemical energies of debris cloud. With the increase of the target velocity, the damage area of rear target and the reaction degree of active fragment show an increasing trend, and the contribution of chemical energy to coupled damage gradually increases.

Dynamic Tensile Deformation and Failure Mechanism of β-HMX Single Crystal With Defect Distribution

HUANG Longjie, LIU Rui, GAO Feiyan, CHEN Pengwan

2023, 44(12):  3872-3883.  doi:10.12382/bgxb.2023.0737

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The deformation, damage and failure process of β-HMX single crystal with different defect characteristics (porosity, void number and void distribution morphology ) under dynamic tension are simulated by molecular dynamics method based on Smith force field. The influence of internal defects in β-HMX single crystal on its mechanical behavior is studied through simulation. The results show that, when the porosity increases from 1% to 2%, the tensile strength of β-HMX single crystal is decreased by 5.3%-11.2% compared with the perfect single crystal, and the Young’s modulus is decreased by 3.6%-13.4%. When the porosity is constant, the tensile strength of the crystal decreases with the increase in the nuer of void. When the distance between the voids is small, the interaction between the voids is presented during the tensile process, resulting in the decrease of the tensile strength.The distribution of voids has a significant effect on the tensile strength of β-HMX single crystal. The failure mechanism of β-HMX single crystal under different strain rates is obviously different. Small cracks are formed around the voids at the tensile strain rate of 5×10⁹s^-1, and the cracks gradually expand, which leads to the fracture of β-HMX single crystal. The material has obvious fracture. Multiple cracks were formed inside the β-HMX single crystal under the tensile strain rate of 1×10¹¹s^-1, resulting in the failure of the material. The dynamic tensile deformation and failure mechanism of β-HMX single crystal with defect distribution are obtained, which provides a theoretical basis for optimizing the preparation process of β-HMX and its mixed explosives and improving their mechanical properties.

A Dynamics Model of PVC Foam Sandwich Panels under Close-in Blast Loading

ZHAO Meng, DAI Kaida, XIANG Zhao, JIANG Tao, ZHAO Xiaosong, XU Yuxin

2023, 44(12):  3884-3896.  doi:10.12382/bgxb.2022.0729

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Threedeformation stages of PVC foam sandwich panel are analyzed to study the dynamic response of polyvinyl chloride (PVC) foam sandwich panels under close-in blast loading. The deflection surface function is derived, which can reflect the localization characteristics of the panels under close-in blast loading. A single-degree-of-freedom rigid-plastic dynamics model is established, considering the effects of bending moment and membrane force on deformation of panels and core. The dynamic responses of PVC foam sandwich panels with different panel and core thicknesses under close-in blast loading are calculated using the nonlinear numerical calculation software, and the panel deformation and velocity variation are analyzed to verify the force and motion of the panels and core in each stage of the dynamic model. The result shows that the established deflection surface function can reflect the localization characteristics of panel under close-in blast loading, and the localization of panel decreases constinuously during the deformation process. The panel midpoint deflection and velocity-time curves based on the dynamics model fit well with the numerically calculated results, and the difference between the panel midpoint deflection and the experimental result is small. The dynamics model can be used to effectively predict the dynamic response of PVC foam sandwich panels under close-in blast loading.

The Loading Discrepancies in CONWEP and Fluid-structure Interaction Methods and the Dynamic Response Characteristics of Masonry Wall

SHANG Yulu, XU Xuan, ZHANG Di, YANG Jun

2023, 44(12):  3897-3908.  doi:10.12382/bgxb.2023.0285

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The dynamic response behavior of masonry walls under large equivalent blast loading is investigated using a full-scale numerical model of windowed and windowless double-sided masonry walls, which is etablished by a cohesive zone method (CZM). A field experiment with a TNT equivalent of 500kg and blast distance of 13m is used as the basis for the study. The numerical simulations are carried out using two blast load application methods, conventional weapons effects program (CONWEP) and coupled-Eulerian-Lagrangian (CEL). The results indicate that the peak incident overpressures calculated by CONWEP and CEL methods are consistent with the experimental result compared to the swept overpressure data measured at the ground surface. However, the arrival time calculated by CEL method is 7.1% earlier than the test, and the rise time is four times that of the test. On the other hand, the overpressure decay calculated by CONWEP method is slower, and the positive pressure time and impulse volume are 50.7% and 42.56% of the test, respectively. It can be seen by comparing the load curve differences of the two blast loading methods that the rise time of overpressure-time curve calculated by CONWEP method is always constant, but the arrival time and rise time of shock wave calculated by CEL method are affected by the distance from explosive source and mesh size, and the larger the distance from explosive source and mesh size are, the longer the rise time is. The differences in the spatial and temporal distributions of shock wave flow field are reflected in the ideal hemispherical shape of wavefront calculated by CONWEP method and the oblate spherical shape of wavefront loaded by CEL method. For the reflected overpressure peak applied to the wall, the peak of CONWEP method loading is larger in each region and the decay rate is the same in all directions, while the decay rate loaded by CEL method in the y (vertical) direction is greater than that in the z (horizontal) direction. In the study of progressive damage law of wall, CEL loading can simulate the local damage characteristics of the wall more accurately. Moreover, the final damage pattern of the wall under CEL loading is closer to that of the test, while CONWEP method has a greater degree of damage.

Response Characteristics of Curved Fiber Composite Protective Shelter under the action of Explosive Shock Wave

YUAN Mingzheng, PAN Teng, BIAN Xiaobing, YANG Lei, ZHOU Hongyuan, HUANG Guangyan, ZHANG Hong

2023, 44(12):  3909-3920.  doi:10.12382/bgxb.2023.0735

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A significant number of unexploded bombs have remained on the battlefield since World War II. To handle these unexploded bombs effectively and efficiently, it is crucial to provide a robust protection and lightweight explosion-proof shelter that ensures the safety of bomb disposal experts. In this study, three materials were selected: aluminum alloy 6061-T6, ultra-high molecular weight polyethylene (UHMWPE) fiber laminates and carbon fiber laminates. The deformation resistance and shock wave overpressure attenuation effects of curved and square explosion-proof shelters under the action of shock wave are compared through real explosion experiment and finite element simulation. The test results indicate that, for target plate with equal surface density, the carbon fiber laminates exhibit superior deformation resistance compared to UHMWPE fiber laminates and aluminum plates. Furthermore, the simulated results demonstrate that the curved structures offer better deformation resistance than square structures. Finally, when the curved explosion-proof shelter is subjected to an explosive impact at a distance of 3m from a 2kg TNT charge at a height of 0.5m, it generates lower transmission overpressure than the square counterpart due to its enhanced deformation resistance. In the case of minimal deformation observed in this scenario, the overpressure within the shelter remains below 20kPa—ensuring personnel safety without any injuries incurred. Material selection has minimal influence on the clipping effect of curved explosion-proof shelter, however, the carbon fiber laminates yield the optimal explosion-proof effect for square explosion-proof shelters.