2024 Vol. 44, No. 9
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2024, 44(9): 091411.
doi: 10.11883/bzycj-2023-0473
Abstract:
When shock waves propagate in solid mediums, the internal charge carriers migrate to the electrodes under the action of shock waves to form electric potential and output voltage/current -shock induced polarization (SIP) effect. The development of SIP effect has challenged the traditional understanding of physical response of solid medium. In this paper, the SIP effects of typical solid mediums such as crystals, metals, ceramics and polymers are systematically reviewed. The SIP test methods developed at present are also summarized, and the characteristics of SIP induced by different loading methods such as drop hammer/pendulum, SHPB, light gas gun and explosive detonation are analyzed. The applications of finite element method, molecular dynamics, peridynamic and phase field analysis in the numerical simulation of SIP of solid mediums are summarized. The macroscopic phenomenology theories of SIP of solid mediums are summarized based on Allison theory, Zhang Yuheng theory, shock flexoelectric theory and shock wave theory, and the microscopic mechanism of SIP is explained considering the microstructure of solid medium, carrier transport mode, transport model, mobility and state density. Furthermore, the application prospect of SIP effect in sensors, energy harvesters and actuators are analyzed, also, the development trend and demand of SIP in solid media are also prospected.
When shock waves propagate in solid mediums, the internal charge carriers migrate to the electrodes under the action of shock waves to form electric potential and output voltage/current -shock induced polarization (SIP) effect. The development of SIP effect has challenged the traditional understanding of physical response of solid medium. In this paper, the SIP effects of typical solid mediums such as crystals, metals, ceramics and polymers are systematically reviewed. The SIP test methods developed at present are also summarized, and the characteristics of SIP induced by different loading methods such as drop hammer/pendulum, SHPB, light gas gun and explosive detonation are analyzed. The applications of finite element method, molecular dynamics, peridynamic and phase field analysis in the numerical simulation of SIP of solid mediums are summarized. The macroscopic phenomenology theories of SIP of solid mediums are summarized based on Allison theory, Zhang Yuheng theory, shock flexoelectric theory and shock wave theory, and the microscopic mechanism of SIP is explained considering the microstructure of solid medium, carrier transport mode, transport model, mobility and state density. Furthermore, the application prospect of SIP effect in sensors, energy harvesters and actuators are analyzed, also, the development trend and demand of SIP in solid media are also prospected.
2024, 44(9): 091421.
doi: 10.11883/bzycj-2024-0007
Abstract:
The propagation characteristics of waves are the basis for studying the dynamic behavior of materials, and the theoretical study of waves in continuous media at the macro scale has been well developed. With the widespread application of materials and structures at the micro- and nano- scales, the study of wave propagation characteristics at the lattice scale is receiving increasing attention. In this article, the Tersoff potential interaction between lattices is applied to study the wave propagation characteristics in single-crystal and polycrystalline systems. Firstly, in the case of micro-vibration, the propagation of lattice waves in a single-crystal system is studied based on three potential energy functions between lattices: linear interaction, Tersoff potential, and Tersoff potential with defects. The dispersion relationship in the lattice and the expression of lattice wave velocity are obtained. Secondly, taking carbon lattice and silicon lattice as examples, the finite difference method is applied to study the wave propagation process in the single-crystal system under three potential energies. The differences in lattice motion under compressive and tensile impacts are compared, and the influence of incident velocity on the peak displacement and peak force is discussed, which reveals the difference in wave propagation between single-crystal systems and continuous media. Finally, taking diamond and silicon carbide as examples, molecular dynamics simulations are used to study the wave propagation characteristics in polycrystalline systems, and the differences in atomic motion at different spatial positions are discussed. The results indicate that the lattice structure in polycrystalline systems is more complex, and the wave propagation characteristics in polycrystalline systems are different from those in single-crystal systems. The existence of defects has a significant impact on the propagation law of waves, which is more prominent in polycrystalline systems. This study has good reference significance for the study of material dynamics performance at the micro- and nano- scales.
The propagation characteristics of waves are the basis for studying the dynamic behavior of materials, and the theoretical study of waves in continuous media at the macro scale has been well developed. With the widespread application of materials and structures at the micro- and nano- scales, the study of wave propagation characteristics at the lattice scale is receiving increasing attention. In this article, the Tersoff potential interaction between lattices is applied to study the wave propagation characteristics in single-crystal and polycrystalline systems. Firstly, in the case of micro-vibration, the propagation of lattice waves in a single-crystal system is studied based on three potential energy functions between lattices: linear interaction, Tersoff potential, and Tersoff potential with defects. The dispersion relationship in the lattice and the expression of lattice wave velocity are obtained. Secondly, taking carbon lattice and silicon lattice as examples, the finite difference method is applied to study the wave propagation process in the single-crystal system under three potential energies. The differences in lattice motion under compressive and tensile impacts are compared, and the influence of incident velocity on the peak displacement and peak force is discussed, which reveals the difference in wave propagation between single-crystal systems and continuous media. Finally, taking diamond and silicon carbide as examples, molecular dynamics simulations are used to study the wave propagation characteristics in polycrystalline systems, and the differences in atomic motion at different spatial positions are discussed. The results indicate that the lattice structure in polycrystalline systems is more complex, and the wave propagation characteristics in polycrystalline systems are different from those in single-crystal systems. The existence of defects has a significant impact on the propagation law of waves, which is more prominent in polycrystalline systems. This study has good reference significance for the study of material dynamics performance at the micro- and nano- scales.
2024, 44(9): 091422.
doi: 10.11883/bzycj-2023-0365
Abstract:
Solid mediums, like rocks, concretes, shells and porous materials, etc., has the characteristics of microscopic discontinuity and macroscopic continuity. It is of great significance for material design, safety protection and other fields to reveal the influence of the meso-discontinuity on the dynamic response of the material. In this paper, based on the generalized Taylor’s formula under fractional definition, the governing equation of 1-D wave propagation in discontinuous medium is derived. Equivalent fractional order is introduced and the simplified form of the governing equation is presented for easily calculating. By using the finite difference method, the numerical solution of the governing equation is obtained. The influence of equivalent fractional order on wave propagation are analyzed. By the time domain analysis, the smaller the equivalent fractional order, the greater the degree of attenuation of the calculated waveform. By the frequency domain analysis, both high frequency wave and low frequency wave exhibit attenuation, and the attenuation of high frequency wave is higher than that of low frequency wave, which makes the pulse duration of the wave being larger. It is obvious that the equivalent fractional order has a certain relationship with the spatial structure of discontinuous medium. Based on the structural characteristics of some meso-discontinuous medium, e.g., porous materials and rocks, a randomly distributed pores model is established by using ABAQUS to verify the reliability of the governing equation and study the wave propagation of meso-discontinuous medium. The effects of porosity, material properties and input waves on wave propagation are analyzed. The degree of wave attenuation is positively related to the porosity of the medium, and negatively related to the wave velocity and the pulse duration of input wave. However, the equivalent fractional order is only related to the porosity and pore distribution of the discontinuous medium. When the spatial structure of the discontinuous medium remains unchanged, the corresponding equivalent fractional order does not change with the material property and the pulse duration of the input wave. By the randomly distributed pores model with various porosities, it is found that the equivalent fractional order decreases with the increase of porosity. Under the same porosity, the heterogeneity of pore distribution will result in different waveforms, while with the increase of porosity, this difference becomes more obvious, but the corresponding equivalent fractional order only has little difference. The statistical relation between equivalent fractional order and porosity is approximately linear when the pore distribution is almost the same. Compared with the randomly distributed pores medium, the statistical relation between equivalent fractional order and porosity of discontinuous medium with uniform distribution of different porosity shifts upward, indicating that the attenuation effect of random structure on wave is higher than that of uniform structure. This paper provides a new approach to investigate wave propagation in meso-discontinuous medium such as porous materials, rocks, shells, etc. It can be used as a basis to evaluate the dynamic response of discontinuous medium.
Solid mediums, like rocks, concretes, shells and porous materials, etc., has the characteristics of microscopic discontinuity and macroscopic continuity. It is of great significance for material design, safety protection and other fields to reveal the influence of the meso-discontinuity on the dynamic response of the material. In this paper, based on the generalized Taylor’s formula under fractional definition, the governing equation of 1-D wave propagation in discontinuous medium is derived. Equivalent fractional order is introduced and the simplified form of the governing equation is presented for easily calculating. By using the finite difference method, the numerical solution of the governing equation is obtained. The influence of equivalent fractional order on wave propagation are analyzed. By the time domain analysis, the smaller the equivalent fractional order, the greater the degree of attenuation of the calculated waveform. By the frequency domain analysis, both high frequency wave and low frequency wave exhibit attenuation, and the attenuation of high frequency wave is higher than that of low frequency wave, which makes the pulse duration of the wave being larger. It is obvious that the equivalent fractional order has a certain relationship with the spatial structure of discontinuous medium. Based on the structural characteristics of some meso-discontinuous medium, e.g., porous materials and rocks, a randomly distributed pores model is established by using ABAQUS to verify the reliability of the governing equation and study the wave propagation of meso-discontinuous medium. The effects of porosity, material properties and input waves on wave propagation are analyzed. The degree of wave attenuation is positively related to the porosity of the medium, and negatively related to the wave velocity and the pulse duration of input wave. However, the equivalent fractional order is only related to the porosity and pore distribution of the discontinuous medium. When the spatial structure of the discontinuous medium remains unchanged, the corresponding equivalent fractional order does not change with the material property and the pulse duration of the input wave. By the randomly distributed pores model with various porosities, it is found that the equivalent fractional order decreases with the increase of porosity. Under the same porosity, the heterogeneity of pore distribution will result in different waveforms, while with the increase of porosity, this difference becomes more obvious, but the corresponding equivalent fractional order only has little difference. The statistical relation between equivalent fractional order and porosity is approximately linear when the pore distribution is almost the same. Compared with the randomly distributed pores medium, the statistical relation between equivalent fractional order and porosity of discontinuous medium with uniform distribution of different porosity shifts upward, indicating that the attenuation effect of random structure on wave is higher than that of uniform structure. This paper provides a new approach to investigate wave propagation in meso-discontinuous medium such as porous materials, rocks, shells, etc. It can be used as a basis to evaluate the dynamic response of discontinuous medium.
2024, 44(9): 091423.
doi: 10.11883/bzycj-2023-0438
Abstract:
Heterogeneous media are very common in nature. Due to the complex internal structure, the heterogeneous compressive shear coupled stress field is inside heterogeneous media, which leads to a mutual influence of compression and shear waves. The study of wave mechanics behavior and description of heterogeneity in heterogeneous media is of great significance and full of challenges. This article establishes a general constitutive relationship that reflects the compression shear coupling characteristics of heterogeneous materials, proposes coupling coefficients to describe material heterogeneity, combines momentum conservation law to establish a generalized wave equation, and provides a general method for solving the generalized wave equation. As an example, expressions for the three characteristic wave velocities of compression shear coupling under the first-order compression shear coupling constitutive relationship are provided, and the finite difference method is employed to obtain the propagation process of coupled compression and shear waves. The effects of four heterogeneous coupling coefficients on stress state, coupled wave velocity, and wave propagation process are studied. The positive and negative values of coupling parameters and their combinations reflect the structural characteristics of heterogeneous media and also determine the properties of compression shear coupling waves. For heterogeneous media with high-pressure effects, shear dilation effects, and shear weakening effects, the coupled compression wave velocity is lower than the elastic compression wave velocity corresponding to uniform media, and the coupled shear wave velocity is higher than the elastic shear wave velocity. The effect of shear on compression delays the propagation of compressive stress, while compression promotes the propagation of shear. Coupled compression wave velocity is the result of the competition between the coupling effect of shear on compression and the volume compaction effect. Coupled shear wave velocity is the result of the competition between the coupling effect of compression on shear and the shear weakening effect caused by continuous distortion of the medium. These mechanisms could be achieved through different combinations of compression shear coupling parameters. A true triaxial experimental testing system was used to measure the longitudinal wave velocity of granite, model materials made of mortar, and materials made of cement mortar with coarse aggregates under different compressive and shear stresses. The results indicate that for heterogeneous media, the longitudinal wave velocity decreases with the increase of static water pressure and equivalent shear stress, and the shear expansion and shear weakening effects dominate. The experimental results and theoretical results have the same trend. The conclusion of this study is expected to provide a physical mechanism explanation for the phenomenon of the variation of wave velocity with stress state in heterogeneous materials.
Heterogeneous media are very common in nature. Due to the complex internal structure, the heterogeneous compressive shear coupled stress field is inside heterogeneous media, which leads to a mutual influence of compression and shear waves. The study of wave mechanics behavior and description of heterogeneity in heterogeneous media is of great significance and full of challenges. This article establishes a general constitutive relationship that reflects the compression shear coupling characteristics of heterogeneous materials, proposes coupling coefficients to describe material heterogeneity, combines momentum conservation law to establish a generalized wave equation, and provides a general method for solving the generalized wave equation. As an example, expressions for the three characteristic wave velocities of compression shear coupling under the first-order compression shear coupling constitutive relationship are provided, and the finite difference method is employed to obtain the propagation process of coupled compression and shear waves. The effects of four heterogeneous coupling coefficients on stress state, coupled wave velocity, and wave propagation process are studied. The positive and negative values of coupling parameters and their combinations reflect the structural characteristics of heterogeneous media and also determine the properties of compression shear coupling waves. For heterogeneous media with high-pressure effects, shear dilation effects, and shear weakening effects, the coupled compression wave velocity is lower than the elastic compression wave velocity corresponding to uniform media, and the coupled shear wave velocity is higher than the elastic shear wave velocity. The effect of shear on compression delays the propagation of compressive stress, while compression promotes the propagation of shear. Coupled compression wave velocity is the result of the competition between the coupling effect of shear on compression and the volume compaction effect. Coupled shear wave velocity is the result of the competition between the coupling effect of compression on shear and the shear weakening effect caused by continuous distortion of the medium. These mechanisms could be achieved through different combinations of compression shear coupling parameters. A true triaxial experimental testing system was used to measure the longitudinal wave velocity of granite, model materials made of mortar, and materials made of cement mortar with coarse aggregates under different compressive and shear stresses. The results indicate that for heterogeneous media, the longitudinal wave velocity decreases with the increase of static water pressure and equivalent shear stress, and the shear expansion and shear weakening effects dominate. The experimental results and theoretical results have the same trend. The conclusion of this study is expected to provide a physical mechanism explanation for the phenomenon of the variation of wave velocity with stress state in heterogeneous materials.
2024, 44(9): 091424.
doi: 10.11883/bzycj-2024-0046
Abstract:
Under pure bending, a brittle slender beam may undergo sudden fracture, leading to the occurrence of secondary fractures near the initial fracture point. Studies suggest that the secondary fractures are induced by the unloading bending wave released from the initial fracture. Unloading causes an overshoot of the bending moment near the location of the initial fracture. Traditional Euler-Bernoulli beam theory cannot describe the wave propagation phenomena resulting from sudden loading or unloading. In this paper, the bending fracture problem is analyzed based on Timoshenko beam theory. In this theory, the bending wave velocity is finite, and it possesses an intrinsic characteristic time. Utilizing Timoshenko beam theory and incorporating a brittle cohesive bending fracture model containing fracture energy, an initial-boundary value problem is established for the one-dimensional propagation of bending waves. The problem with three boundary conditions is solved using the characteristic line method: (1) the beam is suddenly applied with a boundary transverse velocity; (2) the beam is suddenly applied with a boundary bending moment; (3) the beam initially bears a constant moment, which is released according to a cohesive bending fracture law. Through numerical calculations, the dynamic responses of the beam under these three conditions are presented. Initially, the problems (1) and (2) are calculated using the characteristic line method, validating the feasibility of this approach. Subsequently, by calculating problem (3), the impact of fracture energy on fracture time and peak moment is analyzed. The study reveals that once a beam in a pure bending state undergoes instantaneous fracture, the shortest distance between the point of secondary fracture and the point of primary fracture is 5 times characteristic length. When the non-dimensional fracture energy is 1.4×10−4, the location at 17.7 characteristic lengths from the initial fracture point exhibits a peak moment with an amplitude of 1.67, making it the most likely position for secondary fracture. Larger fracture energy prolongs the fracture time, resulting in a more distant peak moment position and a corresponding reduction in peak load.
Under pure bending, a brittle slender beam may undergo sudden fracture, leading to the occurrence of secondary fractures near the initial fracture point. Studies suggest that the secondary fractures are induced by the unloading bending wave released from the initial fracture. Unloading causes an overshoot of the bending moment near the location of the initial fracture. Traditional Euler-Bernoulli beam theory cannot describe the wave propagation phenomena resulting from sudden loading or unloading. In this paper, the bending fracture problem is analyzed based on Timoshenko beam theory. In this theory, the bending wave velocity is finite, and it possesses an intrinsic characteristic time. Utilizing Timoshenko beam theory and incorporating a brittle cohesive bending fracture model containing fracture energy, an initial-boundary value problem is established for the one-dimensional propagation of bending waves. The problem with three boundary conditions is solved using the characteristic line method: (1) the beam is suddenly applied with a boundary transverse velocity; (2) the beam is suddenly applied with a boundary bending moment; (3) the beam initially bears a constant moment, which is released according to a cohesive bending fracture law. Through numerical calculations, the dynamic responses of the beam under these three conditions are presented. Initially, the problems (1) and (2) are calculated using the characteristic line method, validating the feasibility of this approach. Subsequently, by calculating problem (3), the impact of fracture energy on fracture time and peak moment is analyzed. The study reveals that once a beam in a pure bending state undergoes instantaneous fracture, the shortest distance between the point of secondary fracture and the point of primary fracture is 5 times characteristic length. When the non-dimensional fracture energy is 1.4×10−4, the location at 17.7 characteristic lengths from the initial fracture point exhibits a peak moment with an amplitude of 1.67, making it the most likely position for secondary fracture. Larger fracture energy prolongs the fracture time, resulting in a more distant peak moment position and a corresponding reduction in peak load.
2024, 44(9): 091425.
doi: 10.11883/bzycj-2023-0368
Abstract:
Shape memory alloys undergo phase transformation under strong impact loads, and the phase transformation has a significant impact on the dynamic mechanical response of their structural components. Based on the phase transformation critical criterion considering both hydrostatic pressure and deviatoric stress effects, an incremental constitutive model of phase transformation is derived. The analytical expression of characteristic wave speed under complex stress state is obtained based on the generalized characteristic theory. The characteristic wave speed is not only related to the mechanical parameters of the material itself (such as the tension-compression asymmetry and the modulus of the mixed phase), but also related to the stress state of the material. For TiNi alloys with volume expansion due to phase transformation, the increase of tensile-compressive asymmetry coefficient will increase the wave speed of slow waves, while having almost no effect on fast waves. At the short axis of the phase transformation ellipse (α = 90°), the wave speed of slow waves is the lowest and decreases significantly with the increase of the dimensionless modulus of the mixed phase. When the dimensionless modulus of the mixed phase increases from 2 to 5, the wave speed decreases by 36.2%, while the wave speed of fast waves reaches the maximum value c0, which is independent of the modulus of the mixed phase; at the long axis of the phase transformation ellipse (α = 180°), the speed of slow waves reaches the maximum value, and the wave speed of fast waves reaches the minimum value c2.
Shape memory alloys undergo phase transformation under strong impact loads, and the phase transformation has a significant impact on the dynamic mechanical response of their structural components. Based on the phase transformation critical criterion considering both hydrostatic pressure and deviatoric stress effects, an incremental constitutive model of phase transformation is derived. The analytical expression of characteristic wave speed under complex stress state is obtained based on the generalized characteristic theory. The characteristic wave speed is not only related to the mechanical parameters of the material itself (such as the tension-compression asymmetry and the modulus of the mixed phase), but also related to the stress state of the material. For TiNi alloys with volume expansion due to phase transformation, the increase of tensile-compressive asymmetry coefficient will increase the wave speed of slow waves, while having almost no effect on fast waves. At the short axis of the phase transformation ellipse (α = 90°), the wave speed of slow waves is the lowest and decreases significantly with the increase of the dimensionless modulus of the mixed phase. When the dimensionless modulus of the mixed phase increases from 2 to 5, the wave speed decreases by 36.2%, while the wave speed of fast waves reaches the maximum value c0, which is independent of the modulus of the mixed phase; at the long axis of the phase transformation ellipse (α = 180°), the speed of slow waves reaches the maximum value, and the wave speed of fast waves reaches the minimum value c2.
2024, 44(9): 091441.
doi: 10.11883/bzycj-2024-0030
Abstract:
Quantitative investigation of stress wave effects during the elastic compression stage of split Hopkinson pressure bar (SHPB) tests is fundamental for decoupling accurate elastic curve of material. Based on the assumption of plane waves and utilizing the generalized wave impedance theory, a quantitative theoretical analysis of the structural effects caused by the evolution of stress waves during the elastic compression stage of specimens with mismatched bar/specimen cross-sectional areas is conducted. The characteristics and main influencing factors of the deviation between engineering stress-strain curves of specimens during the elastic stage and the actual material stress-strain curves under different conditions are explored. It further reveals the governing rules and mechanisms influencing these deviations. The analysis indicates that for linearly incident loading waves, when the dimensionless time is a multiple of 0.5, even if other parameters change, the engineering stress-strain values of the specimen correspond approximately to the actual material stress-strain values. Even when there is a significant stress difference at both ends of the specimen, if the variation of stress difference tends to stabilize, the difference between the engineering stress-strain curve of the specimen and the actual material stress-strain curve is relatively small. The study calculates the maximum stress deviation value of the specimen and its corresponding dimensionless time, as well as the trend of the maximum stress deviation value of the specimen within different fluctuation intervals. Moreover, the study investigates the scenario where the incident wave is a bilinear combination wave. The results show that when a bilinear incident wave is present, the two linear intervals can be independently analyzed. Regardless of the combination or the variation of stress difference, only when the stress difference at both ends of the specimen reaches an approximately constant curve, the corresponding engineering stress-strain curve of the specimen is relatively accurate. This study provides theoretical references for the refined design of SHPB tests and the accurate data processing.
Quantitative investigation of stress wave effects during the elastic compression stage of split Hopkinson pressure bar (SHPB) tests is fundamental for decoupling accurate elastic curve of material. Based on the assumption of plane waves and utilizing the generalized wave impedance theory, a quantitative theoretical analysis of the structural effects caused by the evolution of stress waves during the elastic compression stage of specimens with mismatched bar/specimen cross-sectional areas is conducted. The characteristics and main influencing factors of the deviation between engineering stress-strain curves of specimens during the elastic stage and the actual material stress-strain curves under different conditions are explored. It further reveals the governing rules and mechanisms influencing these deviations. The analysis indicates that for linearly incident loading waves, when the dimensionless time is a multiple of 0.5, even if other parameters change, the engineering stress-strain values of the specimen correspond approximately to the actual material stress-strain values. Even when there is a significant stress difference at both ends of the specimen, if the variation of stress difference tends to stabilize, the difference between the engineering stress-strain curve of the specimen and the actual material stress-strain curve is relatively small. The study calculates the maximum stress deviation value of the specimen and its corresponding dimensionless time, as well as the trend of the maximum stress deviation value of the specimen within different fluctuation intervals. Moreover, the study investigates the scenario where the incident wave is a bilinear combination wave. The results show that when a bilinear incident wave is present, the two linear intervals can be independently analyzed. Regardless of the combination or the variation of stress difference, only when the stress difference at both ends of the specimen reaches an approximately constant curve, the corresponding engineering stress-strain curve of the specimen is relatively accurate. This study provides theoretical references for the refined design of SHPB tests and the accurate data processing.
2024, 44(9): 091442.
doi: 10.11883/bzycj-2024-0045
Abstract:
Cellular projectiles are widely used in the impact tests of protective structures, but the actual loads of cellular projectiles acting on the tested sandwich structures are still unclear. To explore the coupling response process between the uniform/graded cellular projectile and the foam sandwich beam and the loading effect of cellular projectiles, theoretical analysis, numerical simulations, and impact tests were carried out. The foam sandwich beam was equivalent to a monolithic beam to simplify the analysis. Based on the shock wave model of the cellular projectile and the equivalent response model of the foam sandwich beam, a coupling analysis model of the cellular projectile impacting the foam sandwich beam was developed, and its governing equations were presented and solved numerically by the Runge-Kutta method. Meso-finite element simulations of a uniform/graded cellular projectile impacting a foam sandwich beam were carried out based on the 3D Voronoi technique. Impact tests were performed on the test platform of cellular projectiles, and the velocity response of the cellular projectiles and the foam sandwich beams was obtained by using a high-speed camera and a digital image processing technique. It is found that the coupling analysis model can accurately predict the velocity history curves of the cellular projectile and the foam sandwich beam, as well as the impact pressure of the cellular projectile. Subjected to cellular projectiles with the same initial momentum but different density distribution or initial velocity, foam sandwich beams with the same configuration present different mechanical response processes, which demonstrates that the impact of cellular projectiles cannot be simply equivalent to impulse loading, and the coupling effect between the projectile and the sandwich beam cannot be ignored. Compared with uniform cellular projectiles, the impact pressure waveform of the graded cellular projectile is sharper and shows stronger nonlinearity during its attenuation. This study clarifies the loading effect of cellular projectiles on foam sandwich beams and lays a theoretical foundation for the optimal design of cellular projectiles simulating blast loads.
Cellular projectiles are widely used in the impact tests of protective structures, but the actual loads of cellular projectiles acting on the tested sandwich structures are still unclear. To explore the coupling response process between the uniform/graded cellular projectile and the foam sandwich beam and the loading effect of cellular projectiles, theoretical analysis, numerical simulations, and impact tests were carried out. The foam sandwich beam was equivalent to a monolithic beam to simplify the analysis. Based on the shock wave model of the cellular projectile and the equivalent response model of the foam sandwich beam, a coupling analysis model of the cellular projectile impacting the foam sandwich beam was developed, and its governing equations were presented and solved numerically by the Runge-Kutta method. Meso-finite element simulations of a uniform/graded cellular projectile impacting a foam sandwich beam were carried out based on the 3D Voronoi technique. Impact tests were performed on the test platform of cellular projectiles, and the velocity response of the cellular projectiles and the foam sandwich beams was obtained by using a high-speed camera and a digital image processing technique. It is found that the coupling analysis model can accurately predict the velocity history curves of the cellular projectile and the foam sandwich beam, as well as the impact pressure of the cellular projectile. Subjected to cellular projectiles with the same initial momentum but different density distribution or initial velocity, foam sandwich beams with the same configuration present different mechanical response processes, which demonstrates that the impact of cellular projectiles cannot be simply equivalent to impulse loading, and the coupling effect between the projectile and the sandwich beam cannot be ignored. Compared with uniform cellular projectiles, the impact pressure waveform of the graded cellular projectile is sharper and shows stronger nonlinearity during its attenuation. This study clarifies the loading effect of cellular projectiles on foam sandwich beams and lays a theoretical foundation for the optimal design of cellular projectiles simulating blast loads.
2024, 44(9): 091443.
doi: 10.11883/bzycj-2023-0380
Abstract:
The stress-strain data obtained from split Hopkinson pressure bar (SHPB) tests include both strain rate effects and structural effects, where the structural effects result in non-uniform stress in the elastic phase of the stress-strain curve. The elastic phase is a critical focus of study for materials like concrete with low sound velocity or certain metals under high strain rate loading conditions. In this paper, we focus on one-dimensional rod systems and employ one-dimensional elastic incremental wave theory to derive analytical expressions for stress-strain curves and Young’s modulus under one-dimensional stress wave conditions with linear incident waves. We investigate the effects and mechanisms of stress difference and velocity difference at both ends of the specimen on the accuracy of stress-strain curves and Young’s modulus. Furthermore, we provide a method for determining stress-strain curves and tangent Young’s modulus during the elastic phase for arbitrary incident waveforms. We analyze the influence of the incident wave slope and shape characteristics on the stress uniformity in specimens and stress-strain curves. We establish the inherent relationship between stress uniformity and experimental stress-strain curves, and clarify the relative accuracy and applicability conditions of tangent modulus and secant modulus. The results indicate that stress uniformity is a key factor affecting the accuracy of stress-strain curves and Young’s modulus. However, the accuracy of Young’s modulus is not solely dependent on the change in stress difference at both ends of the specimen; it is also related to the factors such as the incident wave slope, shape characteristics, and the elastic segment range of the specimen. An increase in the linear wave slope leads to a greater difference between the tangent modulus and the secant modulus from the actual values. For larger slopes, the accuracy of the secant modulus is higher than that of the tangent modulus. When the incident wave shape is considered as a reference, curves with low initial slopes, such as sine waves, have higher accuracy for the tangent modulus compared to the secant modulus, whereas curves with high initial slopes show the opposite trend. For concrete specimens, we verify the influence of incident wave slope on Young’s modulus and evaluate the maximum incident wave slopes for concrete specimens to reach accurate values, which are 0.128 MPa/μs for the tangent modulus and 0.319 MPa/μs for the secant modulus.
The stress-strain data obtained from split Hopkinson pressure bar (SHPB) tests include both strain rate effects and structural effects, where the structural effects result in non-uniform stress in the elastic phase of the stress-strain curve. The elastic phase is a critical focus of study for materials like concrete with low sound velocity or certain metals under high strain rate loading conditions. In this paper, we focus on one-dimensional rod systems and employ one-dimensional elastic incremental wave theory to derive analytical expressions for stress-strain curves and Young’s modulus under one-dimensional stress wave conditions with linear incident waves. We investigate the effects and mechanisms of stress difference and velocity difference at both ends of the specimen on the accuracy of stress-strain curves and Young’s modulus. Furthermore, we provide a method for determining stress-strain curves and tangent Young’s modulus during the elastic phase for arbitrary incident waveforms. We analyze the influence of the incident wave slope and shape characteristics on the stress uniformity in specimens and stress-strain curves. We establish the inherent relationship between stress uniformity and experimental stress-strain curves, and clarify the relative accuracy and applicability conditions of tangent modulus and secant modulus. The results indicate that stress uniformity is a key factor affecting the accuracy of stress-strain curves and Young’s modulus. However, the accuracy of Young’s modulus is not solely dependent on the change in stress difference at both ends of the specimen; it is also related to the factors such as the incident wave slope, shape characteristics, and the elastic segment range of the specimen. An increase in the linear wave slope leads to a greater difference between the tangent modulus and the secant modulus from the actual values. For larger slopes, the accuracy of the secant modulus is higher than that of the tangent modulus. When the incident wave shape is considered as a reference, curves with low initial slopes, such as sine waves, have higher accuracy for the tangent modulus compared to the secant modulus, whereas curves with high initial slopes show the opposite trend. For concrete specimens, we verify the influence of incident wave slope on Young’s modulus and evaluate the maximum incident wave slopes for concrete specimens to reach accurate values, which are 0.128 MPa/μs for the tangent modulus and 0.319 MPa/μs for the secant modulus.
2024, 44(9): 091444.
doi: 10.11883/bzycj-2023-0433
Abstract:
In order to deal with the difficulty of measuring the transmitted wave in the backfilling SHPB (split Hopkinson pressure bar) test, rock bars are used to instead of steel bar as the incident bar and transmitted bar for improving the pendulum hammer driven SHPB system. The wave impedance matching formula and viscoelastic wave propagation in SHPB test is proposed. Based on the study of stress wave propagation in rock bar systems, the viscosity attenuation coefficients of stress wave propagation in the incident and transmitted rock bars and the reflection and transmission attenuation coefficient of the rock bar-backfilling body are defined. Based on the Kelvin-Voigt model, the effects of rock bar density and wave velocity on the transmitted wave measured of the filling body in the SHPB tests were simulated and analyzed by using a one-dimensional wave propagation analysis procedure. The relationship between the wave impedance matching coefficient and the reflection and transmission attenuation coefficient of the rock bar-backfilling body were obtained. According to the characteristics of field backfilling, the wave impedance matching coefficient and the reflection and transmission attenuation coefficient, four long rock bars were selected to modify the pendulum hammer driven SHPB system. The viscosity coefficient of the rock bar was measured and stresses and strains on the interfaces of rock bar and backfilling body were calculated by using the one-dimensional wave propagation analysis procedure. The stress waveform characteristics and signal-to-noise ratio of the transmitted waves were analyzed. The matching degree of four kinds of rock bars and backfilling wave impedance from good to poor is obtained, which is green sandstone, granite, marble and basalt. The dynamic impacting experiment on the filling body was conducted and the stress balance in the sample was verified. The pendulum hammer driven SHPB system with green sandstone incident bar and transmission bar is established, which provides support for the dynamic mechanical characteristics of the backfilling.
In order to deal with the difficulty of measuring the transmitted wave in the backfilling SHPB (split Hopkinson pressure bar) test, rock bars are used to instead of steel bar as the incident bar and transmitted bar for improving the pendulum hammer driven SHPB system. The wave impedance matching formula and viscoelastic wave propagation in SHPB test is proposed. Based on the study of stress wave propagation in rock bar systems, the viscosity attenuation coefficients of stress wave propagation in the incident and transmitted rock bars and the reflection and transmission attenuation coefficient of the rock bar-backfilling body are defined. Based on the Kelvin-Voigt model, the effects of rock bar density and wave velocity on the transmitted wave measured of the filling body in the SHPB tests were simulated and analyzed by using a one-dimensional wave propagation analysis procedure. The relationship between the wave impedance matching coefficient and the reflection and transmission attenuation coefficient of the rock bar-backfilling body were obtained. According to the characteristics of field backfilling, the wave impedance matching coefficient and the reflection and transmission attenuation coefficient, four long rock bars were selected to modify the pendulum hammer driven SHPB system. The viscosity coefficient of the rock bar was measured and stresses and strains on the interfaces of rock bar and backfilling body were calculated by using the one-dimensional wave propagation analysis procedure. The stress waveform characteristics and signal-to-noise ratio of the transmitted waves were analyzed. The matching degree of four kinds of rock bars and backfilling wave impedance from good to poor is obtained, which is green sandstone, granite, marble and basalt. The dynamic impacting experiment on the filling body was conducted and the stress balance in the sample was verified. The pendulum hammer driven SHPB system with green sandstone incident bar and transmission bar is established, which provides support for the dynamic mechanical characteristics of the backfilling.
