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2025,
45(3):
031001.
doi: 10.11883/bzycj-2024-0307
Abstract:
Biological soft materials, often with high water content and ultra-softness, display mechanical properties that non-linearly enhance over a broad range of strain rates. However, existing experimental constraints make it challenging to perform large deformation tests on these materials at intermediate strain rates. This study introduces a 15-meter-long long split Hopkinson pressure bar (LSHPB) system, driven by a dual-bullet electromagnetic mechanism, designed for large deformation intermediate strain rate testing of ultra-soft materials. Comparative tests conducted using both the LSHPB and a high-speed SHPB system validated the reliability of the newly developed system. The LSHPB system was then applied to measure the dynamic mechanical performance of polyvinyl alcohol (PVA) hydrogel at intermediate strain rates. The results, combined with existing data from low and high strain rate analyses, underscore the necessity for intermediate strain rate dynamic performance testing. This work not only broadens our understanding of the mechanical behavior of ultra-soft materials like PVA hydrogel across various strain rates but also introduces an innovative experimental technique for studying materials under intermediate strain conditions, thereby advancing the field of soft material dynamics.
Biological soft materials, often with high water content and ultra-softness, display mechanical properties that non-linearly enhance over a broad range of strain rates. However, existing experimental constraints make it challenging to perform large deformation tests on these materials at intermediate strain rates. This study introduces a 15-meter-long long split Hopkinson pressure bar (LSHPB) system, driven by a dual-bullet electromagnetic mechanism, designed for large deformation intermediate strain rate testing of ultra-soft materials. Comparative tests conducted using both the LSHPB and a high-speed SHPB system validated the reliability of the newly developed system. The LSHPB system was then applied to measure the dynamic mechanical performance of polyvinyl alcohol (PVA) hydrogel at intermediate strain rates. The results, combined with existing data from low and high strain rate analyses, underscore the necessity for intermediate strain rate dynamic performance testing. This work not only broadens our understanding of the mechanical behavior of ultra-soft materials like PVA hydrogel across various strain rates but also introduces an innovative experimental technique for studying materials under intermediate strain conditions, thereby advancing the field of soft material dynamics.
2025,
45(3):
032101.
doi: 10.11883/bzycj-2024-0224
Abstract:
To reasonably describe the reaction evolution behavior of explosives after ignition under mechanical confinement, we conduct in-depth analysis of the deformation and movement characteristics of the shell, and divide the response process of the shell into three stages: elastoplastic stage, complete yield stage, and shell rupture stage with inertial motion constraint. The combustion rate theory and the combustion crack-network theory are employed as pivotal parameters for the reaction evolution of the explosives. In the initial stage, the mechanical properties of the shell are taken into consideration, with the material properties serving as the upper limit for structural constraint strength. During this stage, the deformation of the shell remains relatively small. In the second stage, a generalized equivalent stiffness concept is introduced in order to account for the inertial confinement effect of the shell movement. Furthermore, a mechanical deformation analysis of cylindrical shells and end caps is conducted, which takes into account the coupled effects of combustion crack network reaction evolution and shell deformation movement based on a kinematic theory. The third stage is building upon the foundation established in preceding stages, the impact of gas leakage following shell rupture on the progression of the explosive reaction process is considered, The integration of these three stages yields a formula for pressure, shell velocity, and time in the non-impact ignition reaction evolution process of solid explosives. A model for explosives reaction evolution is established to characterize the inertial confinement effects of the shell movement. This model and the related parameters are verified by comparing the calculating results with typical experimental data. It is found that the velocity of shell motion and the changes in internal pressure fundamentally characterize the relationship between the energy release of the explosives and the work done by the product gas. Considering the inertial confinement effects of shell motion is more indicative for the evolution process of explosives reaction, by using this model, the internal pressure of the shell, reaction rate and reaction degree of solid explosives can be calculated based on the historical changes in the velocity of the shell’s motion, thus providing a theoretical method for the explosive safety design and for evaluation under unexpected stimuli.
To reasonably describe the reaction evolution behavior of explosives after ignition under mechanical confinement, we conduct in-depth analysis of the deformation and movement characteristics of the shell, and divide the response process of the shell into three stages: elastoplastic stage, complete yield stage, and shell rupture stage with inertial motion constraint. The combustion rate theory and the combustion crack-network theory are employed as pivotal parameters for the reaction evolution of the explosives. In the initial stage, the mechanical properties of the shell are taken into consideration, with the material properties serving as the upper limit for structural constraint strength. During this stage, the deformation of the shell remains relatively small. In the second stage, a generalized equivalent stiffness concept is introduced in order to account for the inertial confinement effect of the shell movement. Furthermore, a mechanical deformation analysis of cylindrical shells and end caps is conducted, which takes into account the coupled effects of combustion crack network reaction evolution and shell deformation movement based on a kinematic theory. The third stage is building upon the foundation established in preceding stages, the impact of gas leakage following shell rupture on the progression of the explosive reaction process is considered, The integration of these three stages yields a formula for pressure, shell velocity, and time in the non-impact ignition reaction evolution process of solid explosives. A model for explosives reaction evolution is established to characterize the inertial confinement effects of the shell movement. This model and the related parameters are verified by comparing the calculating results with typical experimental data. It is found that the velocity of shell motion and the changes in internal pressure fundamentally characterize the relationship between the energy release of the explosives and the work done by the product gas. Considering the inertial confinement effects of shell motion is more indicative for the evolution process of explosives reaction, by using this model, the internal pressure of the shell, reaction rate and reaction degree of solid explosives can be calculated based on the historical changes in the velocity of the shell’s motion, thus providing a theoretical method for the explosive safety design and for evaluation under unexpected stimuli.
Experiment on dynamic mechanical properties of sandstone based on Lagrangian inverse analysis method
2025,
45(3):
033101.
doi: 10.11883/bzycj-2024-0152
Abstract:
To investigate the dynamic mechanical properties of sandstone in deep strata under impact loads, an improved Hopkinson pressure bar experimental system was established. The traditional Hopkinson pressure bar’s transmission rod was replaced with a long rod specimen made of gray sandstone to better simulate deep geological conditions. Point spalling treatment was applied to the specimen, and strain gauges were meticulously affixed at critical measurement points.Dynamic compression experiments were meticulously conducted on the gray sandstone long rod specimen at various loading rates (9.57, 14.78, 19.32 and 27.60 m/s). Utilizing high-speed digital image correlation (DIC) technology, the evolution of displacement and strain fields on the surface of the specimen throughout each test was closely monitored. This advanced technique enabled a detailed exploration of how the gray sandstone responded to near-field impact loading, particularly focusing on its tensile failure characteristics.Employing the Lagrangian inverse analysis method, displacement-time curves for different mass points derived from the DIC analysis of displacement fields were extracted. These curves provided critical data to compute the stress-strain behavior of the gray sandstone material under dynamic loading conditions. The study reveals several key findings: the gray sandstone long rod specimen predominantly exhibits tensile failure, with distinct patterns of fragmentation near the loading end and layer cracking away from it. Moreover, the dynamic compressive strength factor of the gray sandstone long rod specimen shows a notable increase with higher strain rates, indicating a significant strain rate effect. Correspondingly, both stress and strain peaks observe an upward trend at various measurement points with increasing loading rates. Remarkably, under identical loading rates, stress-strain curves of the gray sandstone long rod specimen exhibit a unique phenomenon where curves from measurement points closer to the loading end envelop those from points farther away. This observation underscores the complex nature of dynamic loading responses in geological materials. Overall, this comprehensive investigation provides essential theoretical insights and methodological references for understanding the dynamic behavior of sandstone within deep geological formations under impact loads. The findings offer valuable contributions to engineering practices concerned with the stability and resilience of underground structures subjected to dynamic loading conditions.
To investigate the dynamic mechanical properties of sandstone in deep strata under impact loads, an improved Hopkinson pressure bar experimental system was established. The traditional Hopkinson pressure bar’s transmission rod was replaced with a long rod specimen made of gray sandstone to better simulate deep geological conditions. Point spalling treatment was applied to the specimen, and strain gauges were meticulously affixed at critical measurement points.Dynamic compression experiments were meticulously conducted on the gray sandstone long rod specimen at various loading rates (9.57, 14.78, 19.32 and 27.60 m/s). Utilizing high-speed digital image correlation (DIC) technology, the evolution of displacement and strain fields on the surface of the specimen throughout each test was closely monitored. This advanced technique enabled a detailed exploration of how the gray sandstone responded to near-field impact loading, particularly focusing on its tensile failure characteristics.Employing the Lagrangian inverse analysis method, displacement-time curves for different mass points derived from the DIC analysis of displacement fields were extracted. These curves provided critical data to compute the stress-strain behavior of the gray sandstone material under dynamic loading conditions. The study reveals several key findings: the gray sandstone long rod specimen predominantly exhibits tensile failure, with distinct patterns of fragmentation near the loading end and layer cracking away from it. Moreover, the dynamic compressive strength factor of the gray sandstone long rod specimen shows a notable increase with higher strain rates, indicating a significant strain rate effect. Correspondingly, both stress and strain peaks observe an upward trend at various measurement points with increasing loading rates. Remarkably, under identical loading rates, stress-strain curves of the gray sandstone long rod specimen exhibit a unique phenomenon where curves from measurement points closer to the loading end envelop those from points farther away. This observation underscores the complex nature of dynamic loading responses in geological materials. Overall, this comprehensive investigation provides essential theoretical insights and methodological references for understanding the dynamic behavior of sandstone within deep geological formations under impact loads. The findings offer valuable contributions to engineering practices concerned with the stability and resilience of underground structures subjected to dynamic loading conditions.
2025,
45(3):
033102.
doi: 10.11883/bzycj-2024-0138
Abstract:
In this study, AlSi10Mg alloy was prepared by selective laser melting (SLM) first, and then subjected to stress relieved annealing treatment. The microstructures of the alloy were analyzed by optical microscope (OM), scanning electron microscope (SEM) and electron backscatter diffraction (EBSD) technology. To understand the influence of coupling effects on the mechanical behavior of AlSi10Mg alloy under wide strain rates and wide temperatures, the mechanical behavior of the alloy under extreme conditions (high and low temperatures, high strain-rate) were analyzed by universal testing machine with an environmental chamber and split Hopkinson pressure bar. The results show that AlSi10Mg alloy possesses fine cellular dendritic microstructure, mainly including α-Al and Si phases, and annealing treatment can result in the discontinuous distribution of eutectic Si particles. AlSi10Mg alloy displays strain-rate strengthening effect under room temperature condition at 0.002–4 800 s−1, and has different strain-rate sensitivity in different strain-rate ranges. The material has higher yield strength and flow stress at 173 K. When the strain-rate is 0.002 s−1, the SLM AlSi10Mg alloy has different temperature sensitivities in different temperature ranges. The alloy does not have temperature sensitivity in the range of 173–243 K; the material exhibits temperature sensitivity ranging from 293 K to 573 K, and the softening effect due to temperature on the material intensifies with increasing temperature. Based on the J-C constitutive model, a modified J-C constitutive model expressed by piecewise functions is constructed and the experimental results are fitted. In addition, experimental verification was conducted on the modified J-C constitutive model, and the predicted results are basically consistent with the experimental results. Within the scope of the study, the modified J-C constitutive model effectively reflects the mechanical behavior of the alloy at high and low temperatures and under different strain-rate.
In this study, AlSi10Mg alloy was prepared by selective laser melting (SLM) first, and then subjected to stress relieved annealing treatment. The microstructures of the alloy were analyzed by optical microscope (OM), scanning electron microscope (SEM) and electron backscatter diffraction (EBSD) technology. To understand the influence of coupling effects on the mechanical behavior of AlSi10Mg alloy under wide strain rates and wide temperatures, the mechanical behavior of the alloy under extreme conditions (high and low temperatures, high strain-rate) were analyzed by universal testing machine with an environmental chamber and split Hopkinson pressure bar. The results show that AlSi10Mg alloy possesses fine cellular dendritic microstructure, mainly including α-Al and Si phases, and annealing treatment can result in the discontinuous distribution of eutectic Si particles. AlSi10Mg alloy displays strain-rate strengthening effect under room temperature condition at 0.002–4 800 s−1, and has different strain-rate sensitivity in different strain-rate ranges. The material has higher yield strength and flow stress at 173 K. When the strain-rate is 0.002 s−1, the SLM AlSi10Mg alloy has different temperature sensitivities in different temperature ranges. The alloy does not have temperature sensitivity in the range of 173–243 K; the material exhibits temperature sensitivity ranging from 293 K to 573 K, and the softening effect due to temperature on the material intensifies with increasing temperature. Based on the J-C constitutive model, a modified J-C constitutive model expressed by piecewise functions is constructed and the experimental results are fitted. In addition, experimental verification was conducted on the modified J-C constitutive model, and the predicted results are basically consistent with the experimental results. Within the scope of the study, the modified J-C constitutive model effectively reflects the mechanical behavior of the alloy at high and low temperatures and under different strain-rate.
2025,
45(3):
033103.
doi: 10.11883/bzycj-2024-0069
Abstract:
In relation to the application of high-entropy alloy systems containing high-density and high-calorific value elements in the liner of shaped charge warheads, the Ta-Hf-Nb-Zr high-entropy alloy system is investigated. The study employed an INSTRON material testing machine and a split Hopkinson pressure bar testing platform to explore the mechanical response of this high-entropy alloy across a wide range of strain rates from 10−3 to 103 s−1, temperatures ranging from 25 to 900 °C, and stress triaxiality values ranging from 0.33 to 0.89. Yield strength and failure strain data were obtained from static round bar tensile tests and dynamic compression tests conducted under these varying conditions. By using least squares fitting, the parameters of the Johnson-Cook (J-C) constitutive equation as well as the damage failure model parameters, are derived. Subsequently, a simulation model for explosively formed projectile (EFP) made from high-entropy alloys under explosive loading conditions was developed. Pulse X-ray tests of the EFP formation were performed, and numerical simulations of the EFP formation process are conducted using LS-DYNA software. The results show that at 117 μs, the high-entropy alloy EFP remains largely intact, with a length of 51.1 mm and a diameter of 12.27 mm. At 187 μs, three fractures are observed at the tail of the EFP, with the head length measuring 24.3 mm, the diameter at 12.27 mm, and the EFP speed recorded at2496.3 m/s. The numerical simulations demonstrate that the EFP length, diameter, and velocity at these time instants match the test data with errors of less than 8.2%. Moreover, the fracture patterns observed experimentally align closely with those predicted by the simulations. This consistency indicates that the J-C model effectively predicts the formation characteristics of high-entropy alloy EFPs under explosive loading conditions, confirming its utility in accurately simulating the EFP formation process.
In relation to the application of high-entropy alloy systems containing high-density and high-calorific value elements in the liner of shaped charge warheads, the Ta-Hf-Nb-Zr high-entropy alloy system is investigated. The study employed an INSTRON material testing machine and a split Hopkinson pressure bar testing platform to explore the mechanical response of this high-entropy alloy across a wide range of strain rates from 10−3 to 103 s−1, temperatures ranging from 25 to 900 °C, and stress triaxiality values ranging from 0.33 to 0.89. Yield strength and failure strain data were obtained from static round bar tensile tests and dynamic compression tests conducted under these varying conditions. By using least squares fitting, the parameters of the Johnson-Cook (J-C) constitutive equation as well as the damage failure model parameters, are derived. Subsequently, a simulation model for explosively formed projectile (EFP) made from high-entropy alloys under explosive loading conditions was developed. Pulse X-ray tests of the EFP formation were performed, and numerical simulations of the EFP formation process are conducted using LS-DYNA software. The results show that at 117 μs, the high-entropy alloy EFP remains largely intact, with a length of 51.1 mm and a diameter of 12.27 mm. At 187 μs, three fractures are observed at the tail of the EFP, with the head length measuring 24.3 mm, the diameter at 12.27 mm, and the EFP speed recorded at
2025,
45(3):
033104.
doi: 10.11883/bzycj-2024-0083
Abstract:
Reinforced concrete slabs, as the main load-bearing components in the structure of construction projects, are very likely to suffer serious damage in explosive accidents, while polyurea elastomers, with their better anti-blast and anti-impact properties, have been widely used in the field of protective engineering. It is well known that the mechanical properties and deformation mechanisms of thin slabs in the range from 100 mm to 250 mm and thick concrete slabs above 250 mm are not the same, and the thickness of reinforced concrete substrates studied so far is generally concentrated in the range from 100 mm to 250 mm, and there are relatively few studies on thick slabs of polyurea-coated reinforced concrete with a slab thickness of 250 mm or more. In order to study the anti-blast performance of the polyurea/reinforced concrete thick slab composite structure, firstly, the contact explosion experiments were carried out on the polyurea/reinforced concrete thick slab composite structure with different charges, while the overall and local damage characteristics were analyzed. Secondly, numerical simulations were carried out using LS-DYNA finite element simulation software to verify the correctness of the numerical model by comparing with the experimental results. Based on LS-DYNA finite element simulations, the damage process of polyurea/reinforced concrete thick plate composite structure and the evolution of shock wave inside the polyurea/reinforced concrete thick plate were investigated, which revealed the anti-blast mechanism of the polyurea coating, and further analyzed the damage mode and damage characteristics of the polyurea/reinforced concrete thick plate composite structure. The experimental and finite element results showed that the polyurea/steel-reinforced concrete composite structure exhibited six damage modes under the contact explosion load (i.e., crate; spall; spall and bulge; threshold spall, bulging deformation of the polyurea coating; severe spall, serious bulging deformation of the polyurea coating; perforation). The investigation also demonstrated that the backside polyurea-coated reinforced concrete thick slabs effectively improved the anti-blast performance of the composite structure. The results of the study can provide a basis and reference for the design of blast resistance of polyurea/reinforced concrete thick slab composite structures.
Reinforced concrete slabs, as the main load-bearing components in the structure of construction projects, are very likely to suffer serious damage in explosive accidents, while polyurea elastomers, with their better anti-blast and anti-impact properties, have been widely used in the field of protective engineering. It is well known that the mechanical properties and deformation mechanisms of thin slabs in the range from 100 mm to 250 mm and thick concrete slabs above 250 mm are not the same, and the thickness of reinforced concrete substrates studied so far is generally concentrated in the range from 100 mm to 250 mm, and there are relatively few studies on thick slabs of polyurea-coated reinforced concrete with a slab thickness of 250 mm or more. In order to study the anti-blast performance of the polyurea/reinforced concrete thick slab composite structure, firstly, the contact explosion experiments were carried out on the polyurea/reinforced concrete thick slab composite structure with different charges, while the overall and local damage characteristics were analyzed. Secondly, numerical simulations were carried out using LS-DYNA finite element simulation software to verify the correctness of the numerical model by comparing with the experimental results. Based on LS-DYNA finite element simulations, the damage process of polyurea/reinforced concrete thick plate composite structure and the evolution of shock wave inside the polyurea/reinforced concrete thick plate were investigated, which revealed the anti-blast mechanism of the polyurea coating, and further analyzed the damage mode and damage characteristics of the polyurea/reinforced concrete thick plate composite structure. The experimental and finite element results showed that the polyurea/steel-reinforced concrete composite structure exhibited six damage modes under the contact explosion load (i.e., crate; spall; spall and bulge; threshold spall, bulging deformation of the polyurea coating; severe spall, serious bulging deformation of the polyurea coating; perforation). The investigation also demonstrated that the backside polyurea-coated reinforced concrete thick slabs effectively improved the anti-blast performance of the composite structure. The results of the study can provide a basis and reference for the design of blast resistance of polyurea/reinforced concrete thick slab composite structures.
2025,
45(3):
033201.
doi: 10.11883/bzycj-2023-0343
Abstract:
Facing the challenges on the accurate and effective prediction under extreme loads, machine learning has gradually demonstrated its potential to replace traditional methods. Existing approaches primarily focus on predicting the peak overpressure or impulse of explosive shock waves, with limited research on predicting the reflected overpressure time history. Load-time history prediction encompasses not only the peak overpressure but also embraces various multi-dimensional information including duration, waveform, and impulse, thereby offering a more comprehensive depiction of the dynamic temporal and spatial characteristics of shock waves. To address this issue, a prediction model for bridge surface reflected overpressure time history is proposed, targeting a planar shock wave diffracting around a bridge section. This model is based on principal component analysis (PCA) and back propagation neural network (BPNN) algorithm with multi-task learning. A loss function considering the impact of peak overpressure and maximum impulse is introduced to fully consider the potential correlations between different modes after PCA dimension reduction. This enables the model to effectively predict bridge shock wave load time histories under varying incident overpressure. Through the analysis of three types of BPNN models, multi-task learning model, multi-input single-output model, and multi-input multi-output model. It was found that the multitask learning model has the highest prediction accuracy, while the multi-input multi-output model struggles to effectively adapt to the current predictive task requirements. The multitask learning model, used for predicting, achieves high precision in forecasting the time history of reflected overpressure at various measurement points on the bridge surface and the peak overpressure values, with R2 values of 0.792 and 0.987. It also closely matches the simulation values in predicting the time history of combined forces and torque acting on the box girder. Additionally, this model performs better in interpolative value prediction than in extrapolative value prediction, but it also demonstrates a certain capability in predicting extrapolative values.
Facing the challenges on the accurate and effective prediction under extreme loads, machine learning has gradually demonstrated its potential to replace traditional methods. Existing approaches primarily focus on predicting the peak overpressure or impulse of explosive shock waves, with limited research on predicting the reflected overpressure time history. Load-time history prediction encompasses not only the peak overpressure but also embraces various multi-dimensional information including duration, waveform, and impulse, thereby offering a more comprehensive depiction of the dynamic temporal and spatial characteristics of shock waves. To address this issue, a prediction model for bridge surface reflected overpressure time history is proposed, targeting a planar shock wave diffracting around a bridge section. This model is based on principal component analysis (PCA) and back propagation neural network (BPNN) algorithm with multi-task learning. A loss function considering the impact of peak overpressure and maximum impulse is introduced to fully consider the potential correlations between different modes after PCA dimension reduction. This enables the model to effectively predict bridge shock wave load time histories under varying incident overpressure. Through the analysis of three types of BPNN models, multi-task learning model, multi-input single-output model, and multi-input multi-output model. It was found that the multitask learning model has the highest prediction accuracy, while the multi-input multi-output model struggles to effectively adapt to the current predictive task requirements. The multitask learning model, used for predicting, achieves high precision in forecasting the time history of reflected overpressure at various measurement points on the bridge surface and the peak overpressure values, with R2 values of 0.792 and 0.987. It also closely matches the simulation values in predicting the time history of combined forces and torque acting on the box girder. Additionally, this model performs better in interpolative value prediction than in extrapolative value prediction, but it also demonstrates a certain capability in predicting extrapolative values.
2025,
45(3):
033301.
doi: 10.11883/bzycj-2024-0217
Abstract:
To study the penetration resistance to the projectile by the reinforced concrete, the mechanical response of reinforcing bars under the dynamic constraint of both the projectile and concrete was analysed and the limitation of existing finite-length rigid beam models have been obtained. Based on this foundation, a shear-plastic hinge model was used to analyze the case of a projectile directly hitting the reinforcing bars, and a plastic string model was used to analyze the case of a projectile colliding with the side of the reinforcing bars, resulting in a more accurate equation for penetration resistance. In the shear-plastic hinge model, stress analysis was performed based on the shear sliding of the reinforcing bar before fracture, and energy dissipation was calculated based on the deformation of the plastic hinge after the reinforcing bar fractures. In the plastic string model, the yield criterion of reinforcing bars under the combined action of bending moment and axial force was analyzed, and the plastic energy dissipation equations for reinforcing bar tension and bending were established. At the same time, the influence of changes in reinforcing bar kinetic energy was considered. Based on the theoretical model of cavity expansion and the empirical formula for the depth of projectile penetration, the concrete resistance equation under the indirect influence of steel reinforcement was obtained. By comparing with existing test data, the rationality of the theoretical models was verified. By analyzing the yield strength, diameter, mesh size of reinforcing bars, as well as the impact location of projectile, suggestions for the reinforcement design of the bulletproof layer were given. The adjacent two layers of reinforcing bars mesh should be staggered. The ratio of steel mesh to projectile diameter should be set between 0.5 and 0.8. It is not advisable to simply pursue high-strength reinforcing bars, and the ultimate plastic strain of reinforcing bars should also be considered as an important factor.
To study the penetration resistance to the projectile by the reinforced concrete, the mechanical response of reinforcing bars under the dynamic constraint of both the projectile and concrete was analysed and the limitation of existing finite-length rigid beam models have been obtained. Based on this foundation, a shear-plastic hinge model was used to analyze the case of a projectile directly hitting the reinforcing bars, and a plastic string model was used to analyze the case of a projectile colliding with the side of the reinforcing bars, resulting in a more accurate equation for penetration resistance. In the shear-plastic hinge model, stress analysis was performed based on the shear sliding of the reinforcing bar before fracture, and energy dissipation was calculated based on the deformation of the plastic hinge after the reinforcing bar fractures. In the plastic string model, the yield criterion of reinforcing bars under the combined action of bending moment and axial force was analyzed, and the plastic energy dissipation equations for reinforcing bar tension and bending were established. At the same time, the influence of changes in reinforcing bar kinetic energy was considered. Based on the theoretical model of cavity expansion and the empirical formula for the depth of projectile penetration, the concrete resistance equation under the indirect influence of steel reinforcement was obtained. By comparing with existing test data, the rationality of the theoretical models was verified. By analyzing the yield strength, diameter, mesh size of reinforcing bars, as well as the impact location of projectile, suggestions for the reinforcement design of the bulletproof layer were given. The adjacent two layers of reinforcing bars mesh should be staggered. The ratio of steel mesh to projectile diameter should be set between 0.5 and 0.8. It is not advisable to simply pursue high-strength reinforcing bars, and the ultimate plastic strain of reinforcing bars should also be considered as an important factor.
2025,
45(3):
033302.
doi: 10.11883/bzycj-2024-0158
Abstract:
Combined with the actual distribution characteristics of tungsten fibers and metallic glass matrix, a three-dimensional (3D) mesoscale finite element (FE) geometric model of a long rod of tungsten fiber-reinforced metallic glass composite was established, and the coupled thermo-mechanical constitutive model was used to describe the high strength and high shear sensitivity of metallic glass matrix. FE simulations on the oblique penetration/perforation of composite and tungsten alloy long rods into steel targets were carried out combined with related oblique penetrating tests, and comparative analyses on the deformation and failure characteristics of projectiles and targets were conducted. Furthermore, the influences of oblique angle and impact velocity on the ‘self-sharpening’ behavior of composite long rods and the corresponding ballistic performance were investigated in detail. Related analysis shows that in the oblique impact condition, due to the asymmetrical characteristics of target resistance on the rod, the rod nose gradually sharpens into an asymmetrical pointed configuration, and certain deflection occurs in the trajectory. Consequently, the ‘self-sharpening’ behavior in the composite long rod is weakened to a certain extent, and thus a decay occurs in its penetrating property. Besides, the impact velocity also contributes to the ‘self-sharpening’ characteristics and the corresponding ballistic behavior in the oblique impact condition, and the decay of penetrating capability derived from the oblique angle is more remarkable at lower impact velocities. When the oblique angle increases to 50°, the composite long rod is hard to effectively penetrate the target at an impact velocity lower than 900 m/s, and ricochet becomes easy when it impacts under a higher oblique angle. The results are of good significance in predicting the penetrating ability of tungsten fiber-reinforced metallic glass matrix composite long rods and optimizing its impact attitude.
Combined with the actual distribution characteristics of tungsten fibers and metallic glass matrix, a three-dimensional (3D) mesoscale finite element (FE) geometric model of a long rod of tungsten fiber-reinforced metallic glass composite was established, and the coupled thermo-mechanical constitutive model was used to describe the high strength and high shear sensitivity of metallic glass matrix. FE simulations on the oblique penetration/perforation of composite and tungsten alloy long rods into steel targets were carried out combined with related oblique penetrating tests, and comparative analyses on the deformation and failure characteristics of projectiles and targets were conducted. Furthermore, the influences of oblique angle and impact velocity on the ‘self-sharpening’ behavior of composite long rods and the corresponding ballistic performance were investigated in detail. Related analysis shows that in the oblique impact condition, due to the asymmetrical characteristics of target resistance on the rod, the rod nose gradually sharpens into an asymmetrical pointed configuration, and certain deflection occurs in the trajectory. Consequently, the ‘self-sharpening’ behavior in the composite long rod is weakened to a certain extent, and thus a decay occurs in its penetrating property. Besides, the impact velocity also contributes to the ‘self-sharpening’ characteristics and the corresponding ballistic behavior in the oblique impact condition, and the decay of penetrating capability derived from the oblique angle is more remarkable at lower impact velocities. When the oblique angle increases to 50°, the composite long rod is hard to effectively penetrate the target at an impact velocity lower than 900 m/s, and ricochet becomes easy when it impacts under a higher oblique angle. The results are of good significance in predicting the penetrating ability of tungsten fiber-reinforced metallic glass matrix composite long rods and optimizing its impact attitude.
2025,
45(3):
033303.
doi: 10.11883/bzycj-2024-0096
Abstract:
An experimental investigation of typical projectiles penetrating multi-layer spaced Q355B steel targets was conducted to study the trajectory characteristics of elliptical cross-section projectiles penetrating multi-layer spaced steel targets. Numerical simulations were performed on LS-DYNA finite element software and typical results obtained were validated by experimental results. The attitude and trajectory parameters in the penetration process and the deflection mechanism of the projectile were obtained. The influence of cross-section shape, the minor-to-major axis length ratio of the projectile cross-section, initial velocity, rotation angle, and incident angle on the penetration trajectories and attitude deflection was investigated. The research results show that the penetration trajectory stability of the circular cross-section projectile is better than the elliptical and asymmetric elliptical cross-section projectiles when the rotation angle is 0°. As the minor-to-major axis length ratio increases, the trajectory is more stable. The trajectory deflection reduces with a higher initial velocity. When the rotation angle is 90°, the penetration trajectory of both symmetric and asymmetric elliptical cross-section projectiles in the incident plane is the most stable, and the trajectory deflection of the two projectiles in the horizontal plane reaches its maximum at rotation angles of 45° and 90°, respectively. The trajectory stability of an asymmetric elliptical projectile, when the rotation angle is obtuse, is better than that at the acute angle. When the incident angle is in the range of [0°, 50°], the trajectory instability and attitude deflection of the projectile increase with the increase of incident angle and then decrease, and both reach the largest when the incident angle is about 30°. It is also found that the projectile will separate from the target during the penetration stage of the projectile nose when penetrating a thin steel target in a stable attitude. When the projectile penetrates a thin steel target at a large attack angle, the attachment of the projectile and target mainly occurs on the upper surface of the projectile.
An experimental investigation of typical projectiles penetrating multi-layer spaced Q355B steel targets was conducted to study the trajectory characteristics of elliptical cross-section projectiles penetrating multi-layer spaced steel targets. Numerical simulations were performed on LS-DYNA finite element software and typical results obtained were validated by experimental results. The attitude and trajectory parameters in the penetration process and the deflection mechanism of the projectile were obtained. The influence of cross-section shape, the minor-to-major axis length ratio of the projectile cross-section, initial velocity, rotation angle, and incident angle on the penetration trajectories and attitude deflection was investigated. The research results show that the penetration trajectory stability of the circular cross-section projectile is better than the elliptical and asymmetric elliptical cross-section projectiles when the rotation angle is 0°. As the minor-to-major axis length ratio increases, the trajectory is more stable. The trajectory deflection reduces with a higher initial velocity. When the rotation angle is 90°, the penetration trajectory of both symmetric and asymmetric elliptical cross-section projectiles in the incident plane is the most stable, and the trajectory deflection of the two projectiles in the horizontal plane reaches its maximum at rotation angles of 45° and 90°, respectively. The trajectory stability of an asymmetric elliptical projectile, when the rotation angle is obtuse, is better than that at the acute angle. When the incident angle is in the range of [0°, 50°], the trajectory instability and attitude deflection of the projectile increase with the increase of incident angle and then decrease, and both reach the largest when the incident angle is about 30°. It is also found that the projectile will separate from the target during the penetration stage of the projectile nose when penetrating a thin steel target in a stable attitude. When the projectile penetrates a thin steel target at a large attack angle, the attachment of the projectile and target mainly occurs on the upper surface of the projectile.
2025,
45(3):
033401.
doi: 10.11883/bzycj-2023-0395
Abstract:
The propeller is a critical component of a ship’s propulsion system that significantly influences the vessel’s performance through its stability and efficiency. Current research on the propulsion shaft system’s anti-shock properties often oversimplifies the propeller as a uniform circular disk, which disregards its structural intricacies and leads to inaccuracies in the transient damage characteristics during underwater explosions. This research focused on the propeller’s structural details and developed both an equivalent shell model and a more intricate solid model. Through structural wet modal numerical simulations, the study had determined that solid modeling outperforms shell modeling in accuracy. This finding is corroborated by comparisons with empirical formulas, thereby validating the fluid-structure coupling analysis model. Building upon this foundation, the research examines the propeller’s transient shock response and damage characteristics when subjected to far-field shockwaves. Utilizing the total wave algorithm in ABAQUS, the investigation extends to the cavitation and damage patterns of the propeller under such conditions, with confirmation provided by the one-dimensional Bleich-Sandler finite element model. To delve deeper into the phenomenon of hydrodynamic cavitation caused by the propeller’s high-speed rotation, the coupled Eulerian-Lagrangian (CEL) method was applied. Initially, a simplified propeller model was created to confirm the cavitation bubble layer’s fragmentation due to the flow field load resulting from explosive product expansion. Subsequent modifications to the propeller’s transient fluid-structure coupling calculation model allow for a more thorough analysis of its transient damage characteristics. The findings indicate that at attack angles of 0° and 90°, the propeller surface experiences heightened shockwave loads, albeit with a threshold linked to the propeller’s structural properties. When hydrodynamic cavitation is factored in, the stress distribution on the propeller blade tends to be more uniform; the blade’s primary plastic damage is localized at the root, exhibiting both localized and complete plastic deformation patterns. This research elucidates the damage and cavitation effects on propellers due to far-field explosions, offering valuable insights for enhancing the anti-shock defenses of both the propulsion shaft system and the propeller itself.
The propeller is a critical component of a ship’s propulsion system that significantly influences the vessel’s performance through its stability and efficiency. Current research on the propulsion shaft system’s anti-shock properties often oversimplifies the propeller as a uniform circular disk, which disregards its structural intricacies and leads to inaccuracies in the transient damage characteristics during underwater explosions. This research focused on the propeller’s structural details and developed both an equivalent shell model and a more intricate solid model. Through structural wet modal numerical simulations, the study had determined that solid modeling outperforms shell modeling in accuracy. This finding is corroborated by comparisons with empirical formulas, thereby validating the fluid-structure coupling analysis model. Building upon this foundation, the research examines the propeller’s transient shock response and damage characteristics when subjected to far-field shockwaves. Utilizing the total wave algorithm in ABAQUS, the investigation extends to the cavitation and damage patterns of the propeller under such conditions, with confirmation provided by the one-dimensional Bleich-Sandler finite element model. To delve deeper into the phenomenon of hydrodynamic cavitation caused by the propeller’s high-speed rotation, the coupled Eulerian-Lagrangian (CEL) method was applied. Initially, a simplified propeller model was created to confirm the cavitation bubble layer’s fragmentation due to the flow field load resulting from explosive product expansion. Subsequent modifications to the propeller’s transient fluid-structure coupling calculation model allow for a more thorough analysis of its transient damage characteristics. The findings indicate that at attack angles of 0° and 90°, the propeller surface experiences heightened shockwave loads, albeit with a threshold linked to the propeller’s structural properties. When hydrodynamic cavitation is factored in, the stress distribution on the propeller blade tends to be more uniform; the blade’s primary plastic damage is localized at the root, exhibiting both localized and complete plastic deformation patterns. This research elucidates the damage and cavitation effects on propellers due to far-field explosions, offering valuable insights for enhancing the anti-shock defenses of both the propulsion shaft system and the propeller itself.
2025,
45(3):
034201.
doi: 10.11883/bzycj-2024-0073
Abstract:
To improve the accuracy and robustness of the explicit finite element algorithm based on penalty method for simulating large deformation impact-contact problem, a new large-deformation non-penetration contact algorithm based on forward incremental displacement central difference (FIDCD) is developed. On the one hand, according to FIDCD, the solving step of the dynamic equation is decomposed into an estimated step without considering contact and a correction step considering contact constraint. At the current moment, a contact force is applied through the penalty method to make the deformation of entities satisfy the non-penetration condition. The contact force is calculated by a soft constraint penalty stiffness, which helps to maintain stability of contact localization. It refines the numerical accuracy of the explicit contact computation. On the other hand, to accurately calculate the large-deformation internal force of the next moment while only obtaining the displacement, the internal force term of the dynamic equation is mapped to a known configuration for solution based on the arbitrary reference configurations (ARC) theory. It avoids using the values of variables at intermediate configuration to approximate them, thereby improving the numerical accuracy of the large deformation computation. More rigorous contact algorithms and geometric nonlinear solution strategy can effectively suppress mesh distortion and non-physical penetration between entities during large-deformation impact simulation. This thus improves the robustness of the new explicit algorithm. Finally, the computational program written according to the new developed algorithm is applied to simulate several impact and penetration examples with different impact velocities. By comparing the simulation results with those obtained from commercial software, the correctness of the developed algorithm and computational program is verified. At the same time, it can also be proven that the algorithm proposed is more robust in simulating high-speed and large-deformation impact problems than the classical explicit impact-contact algorithm based on the frog jump center difference scheme combining with penalty method.
To improve the accuracy and robustness of the explicit finite element algorithm based on penalty method for simulating large deformation impact-contact problem, a new large-deformation non-penetration contact algorithm based on forward incremental displacement central difference (FIDCD) is developed. On the one hand, according to FIDCD, the solving step of the dynamic equation is decomposed into an estimated step without considering contact and a correction step considering contact constraint. At the current moment, a contact force is applied through the penalty method to make the deformation of entities satisfy the non-penetration condition. The contact force is calculated by a soft constraint penalty stiffness, which helps to maintain stability of contact localization. It refines the numerical accuracy of the explicit contact computation. On the other hand, to accurately calculate the large-deformation internal force of the next moment while only obtaining the displacement, the internal force term of the dynamic equation is mapped to a known configuration for solution based on the arbitrary reference configurations (ARC) theory. It avoids using the values of variables at intermediate configuration to approximate them, thereby improving the numerical accuracy of the large deformation computation. More rigorous contact algorithms and geometric nonlinear solution strategy can effectively suppress mesh distortion and non-physical penetration between entities during large-deformation impact simulation. This thus improves the robustness of the new explicit algorithm. Finally, the computational program written according to the new developed algorithm is applied to simulate several impact and penetration examples with different impact velocities. By comparing the simulation results with those obtained from commercial software, the correctness of the developed algorithm and computational program is verified. At the same time, it can also be proven that the algorithm proposed is more robust in simulating high-speed and large-deformation impact problems than the classical explicit impact-contact algorithm based on the frog jump center difference scheme combining with penalty method.
2025,
45(3):
035101.
doi: 10.11883/bzycj-2024-0150
Abstract:
The protection level and domestic standard test level of commonly used passive flexible barriers against rockfall impact are not higher than 5 000 kJ, while bridges in mountains and other important transportation infrastructures are facing rockfall disaster threats with higher impact energy levels. Considering that the design method for passive flexible barriers with higher impact energy levels is lacking, to provide a feasible and reliable tool for the infrastructure engineers, the analysis and design of 8 000 kJ-level passive flexible barrier against rockfall impact were carried out at present based on the numerical simulation method. Firstly, by adopting the explicit dynamic software ANSYS/LS-DYNA, quasi-static tests, including the tensile test on single wire ring and three-ring chain, net puncturing test, and the dynamic impact test, i.e., 2 000 kJ rockfall impacting the full-scale passive flexible barrier, were numerically reproduced, and the reliability of the numerical simulation method was fully verified by comparing with the test data, i.e., the maximum breaking force and breaking displacement of the wire ring and its failure characteristics, the whole impact process of rockfall, and the cable force-time history curves, the influencing factors, i.e., the inclining angle, span, and height of the steel post and different specifications of energy dissipating devices ranging from 50 kJ to 70 kJ, on the dynamic behavior of the passive flexible barrier were further analyzed. The results show that the specification of the energy dissipation device is the most critical parameter controlling the internal force and displacement of the passive flexible barrier. The inclining angle of the steel post is recommended to be 10°. An increase in the post spacing can reduce the in-plane stiffness of the structure while having less effect on the transverse anchorage. An increase in the post height will cause a significant increase in the support reaction force at the post bottom. A reasonable adjustment of the anchorage position of each wire rope is required when the post height and spacing are changed. Finally, based on the results of parameter analysis, two design schemes for a passive flexible barrier against 8 000 kJ rockfall impact were given by adjusting the geometry of the structure, the specification of the energy dissipating device, and the addition of transmission support ropes. Both of them passed the test of the European standard EAD 340059-00-0106.
The protection level and domestic standard test level of commonly used passive flexible barriers against rockfall impact are not higher than 5 000 kJ, while bridges in mountains and other important transportation infrastructures are facing rockfall disaster threats with higher impact energy levels. Considering that the design method for passive flexible barriers with higher impact energy levels is lacking, to provide a feasible and reliable tool for the infrastructure engineers, the analysis and design of 8 000 kJ-level passive flexible barrier against rockfall impact were carried out at present based on the numerical simulation method. Firstly, by adopting the explicit dynamic software ANSYS/LS-DYNA, quasi-static tests, including the tensile test on single wire ring and three-ring chain, net puncturing test, and the dynamic impact test, i.e., 2 000 kJ rockfall impacting the full-scale passive flexible barrier, were numerically reproduced, and the reliability of the numerical simulation method was fully verified by comparing with the test data, i.e., the maximum breaking force and breaking displacement of the wire ring and its failure characteristics, the whole impact process of rockfall, and the cable force-time history curves, the influencing factors, i.e., the inclining angle, span, and height of the steel post and different specifications of energy dissipating devices ranging from 50 kJ to 70 kJ, on the dynamic behavior of the passive flexible barrier were further analyzed. The results show that the specification of the energy dissipation device is the most critical parameter controlling the internal force and displacement of the passive flexible barrier. The inclining angle of the steel post is recommended to be 10°. An increase in the post spacing can reduce the in-plane stiffness of the structure while having less effect on the transverse anchorage. An increase in the post height will cause a significant increase in the support reaction force at the post bottom. A reasonable adjustment of the anchorage position of each wire rope is required when the post height and spacing are changed. Finally, based on the results of parameter analysis, two design schemes for a passive flexible barrier against 8 000 kJ rockfall impact were given by adjusting the geometry of the structure, the specification of the energy dissipating device, and the addition of transmission support ropes. Both of them passed the test of the European standard EAD 340059-00-0106.
