2024 Vol. 44, No. 8
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2024, 44(8): 081411.
doi: 10.11883/bzycj-2024-0086
Abstract:
Cellular materials are structures with a large number of internal cavities and cells, which have the properties of lightweight and high specific energy absorption, and they are widely used in the collision/explosion protection, such as aerospace, transportation, and human protection. Introducing a gradient design to cellular materials helps the materials to meet the protection requirements in different scenarios and conditions with the properties of orderly dissipation of energy and manipulation of loads. A review of research advances in the dynamic analysis and design on mechanical behavior of graded cellular materials is presented. Three cases of the applications of graded cellular materials/structures, i.e., impact resistance, blast resistance, and blast-mimicking loading, are elaborated. Firstly, graded cellular materials are briefly described from various aspects, such as natural vs. artificial, layered vs. continuous, strength gradient vs. density gradient, and conventional manufacturing vs. additive manufacturing. The studies of the deformation characteristics, shock wave models, and protective properties of graded cellular materials under dynamic loading are then reviewed systematically. A competitive mechanism of density/strength gradients and inertial effects exists in graded cellular materials to synergistically modulate collapse deformation modes. According to the stress-strain curve characteristics of cellular materials, choosing the appropriate constitutive model could increase the characterization accuracy for its dynamic mechanical behavior. Secondly, the shock wave models are used as a mechanical tool to guide the design of graded cellular materials/structures. Some strategies are elaborated, such as the backward design of graded cellular materials for impact resistance, the design of several types of anti-blast sandwich structures, and the design of blast-load simulators with the projectile-beam coupling effect being taken into account. The optimal protection effect or precise load control had been realized efficiently, which provides a theoretical basis and technical support for the protection design and rapid evaluation of impact/explosion resistance structures. Finally, for the applications in the scenarios of extreme environmental loading, large energy impacts, and strong nonlinear load manipulation, the investigations of graded cellular materials are full of challenges and expectation.
Cellular materials are structures with a large number of internal cavities and cells, which have the properties of lightweight and high specific energy absorption, and they are widely used in the collision/explosion protection, such as aerospace, transportation, and human protection. Introducing a gradient design to cellular materials helps the materials to meet the protection requirements in different scenarios and conditions with the properties of orderly dissipation of energy and manipulation of loads. A review of research advances in the dynamic analysis and design on mechanical behavior of graded cellular materials is presented. Three cases of the applications of graded cellular materials/structures, i.e., impact resistance, blast resistance, and blast-mimicking loading, are elaborated. Firstly, graded cellular materials are briefly described from various aspects, such as natural vs. artificial, layered vs. continuous, strength gradient vs. density gradient, and conventional manufacturing vs. additive manufacturing. The studies of the deformation characteristics, shock wave models, and protective properties of graded cellular materials under dynamic loading are then reviewed systematically. A competitive mechanism of density/strength gradients and inertial effects exists in graded cellular materials to synergistically modulate collapse deformation modes. According to the stress-strain curve characteristics of cellular materials, choosing the appropriate constitutive model could increase the characterization accuracy for its dynamic mechanical behavior. Secondly, the shock wave models are used as a mechanical tool to guide the design of graded cellular materials/structures. Some strategies are elaborated, such as the backward design of graded cellular materials for impact resistance, the design of several types of anti-blast sandwich structures, and the design of blast-load simulators with the projectile-beam coupling effect being taken into account. The optimal protection effect or precise load control had been realized efficiently, which provides a theoretical basis and technical support for the protection design and rapid evaluation of impact/explosion resistance structures. Finally, for the applications in the scenarios of extreme environmental loading, large energy impacts, and strong nonlinear load manipulation, the investigations of graded cellular materials are full of challenges and expectation.
2024, 44(8): 081421.
doi: 10.11883/bzycj-2023-0437
Abstract:
To study the thermal relaxation behavior of graded media that satisfies the power law, a one-dimensional hyperbolic non-Fourier heat conduction equation of the graded material which satisfies the power law was derived from the Cattaneo-Vernotte linear hyperbolic heat transfer equation with the thermal relaxation coefficient and graded exponent induced. The equation was first treated dimensionless. Based on the Laplace transformation, the new heat conduction equation was found to conform to the general form of the Bessel equation called the Lommel equation in the frequency domain, and the Bessel series solution of the temperature field in the frequency domain was obtained. With the asymptotic expansion of the Bessel series, a simplified expression of the temperature field in the frequency domain containing trigonometric function was obtained. The inverse Laplace transformation of the temperature field in the frequency domain was employed to get the first analytical solution of the temperature field in the time domain. Besides the first analytical solution, the new heat conduction equation in the frequency domain was simplified to the Euler equation, and the second kind of analytical solution was obtained by the pole residue method. The second analytical solution exhibits similar fluctuation attenuation and diffusion features, and both the waveform and response time are sensitive to the relaxation time coefficient. However, the second kind of analytical solution differs from the first kind of solution in terms of waveform elements which are highly related to the graded structure. The accuracy of the analytical result is verified by numerical calculation. Taking Mo-ZrC graded composite as an example, the thermal relaxation behavior of graded material that satisfies power law under the first kind of temperature boundary and temperature pulse loading are discussed in detail. The temperature field shows both fluctuation attenuation and conduction characteristics. With the increase of the thermal relaxation coefficient, the response time and temperature wave amplitude increase, the unit waveform develops from a trapezoidal wave to a rectangular wave, and the oscillation approaching the boundary shows an obvious bias.
To study the thermal relaxation behavior of graded media that satisfies the power law, a one-dimensional hyperbolic non-Fourier heat conduction equation of the graded material which satisfies the power law was derived from the Cattaneo-Vernotte linear hyperbolic heat transfer equation with the thermal relaxation coefficient and graded exponent induced. The equation was first treated dimensionless. Based on the Laplace transformation, the new heat conduction equation was found to conform to the general form of the Bessel equation called the Lommel equation in the frequency domain, and the Bessel series solution of the temperature field in the frequency domain was obtained. With the asymptotic expansion of the Bessel series, a simplified expression of the temperature field in the frequency domain containing trigonometric function was obtained. The inverse Laplace transformation of the temperature field in the frequency domain was employed to get the first analytical solution of the temperature field in the time domain. Besides the first analytical solution, the new heat conduction equation in the frequency domain was simplified to the Euler equation, and the second kind of analytical solution was obtained by the pole residue method. The second analytical solution exhibits similar fluctuation attenuation and diffusion features, and both the waveform and response time are sensitive to the relaxation time coefficient. However, the second kind of analytical solution differs from the first kind of solution in terms of waveform elements which are highly related to the graded structure. The accuracy of the analytical result is verified by numerical calculation. Taking Mo-ZrC graded composite as an example, the thermal relaxation behavior of graded material that satisfies power law under the first kind of temperature boundary and temperature pulse loading are discussed in detail. The temperature field shows both fluctuation attenuation and conduction characteristics. With the increase of the thermal relaxation coefficient, the response time and temperature wave amplitude increase, the unit waveform develops from a trapezoidal wave to a rectangular wave, and the oscillation approaching the boundary shows an obvious bias.
2024, 44(8): 081422.
doi: 10.11883/bzycj-2023-0469
Abstract:
The diffusion behavior of shear instability control under dynamic load is the inducement for the development of local large deformation and the deterioration of macroscopic mechanical properties of rock. Firstly, the energy function of the unstable interface was established; and then based on the generalized variational principle, the interface disturbance analysis was carried out, while the first and second-order variances of the function were taken into consideration. Thus the governing equation of dynamic instability of the interface under shear load was established. Based on the discriminant equation, the influence of shear force and dynamic effect on the angle of the unstable interface is obtained. The results show that the angle of the shear deformation zone increases to a certain extent with the increase of external shear force. With the increase of the local dynamic coefficient, that is, the increase of the local inertial force, the shear band angle decreases obviously. By solving the diffusion equation with the edge displacement, the analytical expression of displacement was obtained, showing that the displacement increases gradually with the increase of loading time. To verify the reliability of the theoretical model and further study the deformation behavior of interface instability and its influence on wave propagation, the evolution of the fine and microscopic morphology of the contact surface during dynamic shear was described by combining with the SHPB rod-beam experiment technique, and an evaluation method for the influence of the evolution of surface contact parameters on mechanical parameters during interface instability was proposed. The numerical analysis model was established, and its result shows that interface instability is the leading condition of local shear failure slip. With the increase of interface thickness and shear force, the local displacement increases. The interfacial shear diffusion behavior greatly reduces the amplitude and changes the frequency of the transmitted wave. This study provides a good theoretical reference for the study of localization deformation and dynamic strength of rocks.
The diffusion behavior of shear instability control under dynamic load is the inducement for the development of local large deformation and the deterioration of macroscopic mechanical properties of rock. Firstly, the energy function of the unstable interface was established; and then based on the generalized variational principle, the interface disturbance analysis was carried out, while the first and second-order variances of the function were taken into consideration. Thus the governing equation of dynamic instability of the interface under shear load was established. Based on the discriminant equation, the influence of shear force and dynamic effect on the angle of the unstable interface is obtained. The results show that the angle of the shear deformation zone increases to a certain extent with the increase of external shear force. With the increase of the local dynamic coefficient, that is, the increase of the local inertial force, the shear band angle decreases obviously. By solving the diffusion equation with the edge displacement, the analytical expression of displacement was obtained, showing that the displacement increases gradually with the increase of loading time. To verify the reliability of the theoretical model and further study the deformation behavior of interface instability and its influence on wave propagation, the evolution of the fine and microscopic morphology of the contact surface during dynamic shear was described by combining with the SHPB rod-beam experiment technique, and an evaluation method for the influence of the evolution of surface contact parameters on mechanical parameters during interface instability was proposed. The numerical analysis model was established, and its result shows that interface instability is the leading condition of local shear failure slip. With the increase of interface thickness and shear force, the local displacement increases. The interfacial shear diffusion behavior greatly reduces the amplitude and changes the frequency of the transmitted wave. This study provides a good theoretical reference for the study of localization deformation and dynamic strength of rocks.
2024, 44(8): 081423.
doi: 10.11883/bzycj-2023-0454
Abstract:
The scattering of seismic waves by shallow-buried underground structures has significant theoretical value in the engineering field. However, previous studies have mainly focused on the case of plane waves or the case of complete bonding between lining and surrounding rock, with little consideration of the effects of source distance and non-complete bonding between lining and surrounding rock. In order to deepen the understanding of the influence of source distance and non-complete bonding on seismic wave scattering, the series solution of the dynamic response of shallow-buried circular non-complete bonded tunnels under the loading of anti-plane line source was derived based on the displacement discontinuity model, wave function expansion method, Graf formula and mirror method. The accuracy of the obtained solution was verified by the relationship between the residuals of the inner and outer boundary conditions of the lining and the number of truncated terms in the series solution. By systematically analyzing the parameters of this series solution, the influence of factors such as the contact stiffness between lining and surrounding rock, lining modulus, lining thickness, tunnel depth and source distance on the displacement and circumferential shear stress on the inner surface of the lining was discussed. The results show that the contact stiffness between lining and surrounding rock has a significant influence on the dynamic response of the tunnel, especially in cases with relatively low contact stiffness, where the amplitude of the dynamic response of the tunnel can be very large. Increasing the lining modulus reduces the displacement but increases the circumferential shear stress. Increasing the lining thickness can simultaneously reduce the displacement and circumferential shear stress. As the tunnel depth increases, the maximum displacement and circumferential shear stress on the inner surface of the lining shifts towards the apex of the tunnel. Increasing the horizontal distance between the line source and the tunnel increases the relative amplitude of the tunnel's back wave side.
The scattering of seismic waves by shallow-buried underground structures has significant theoretical value in the engineering field. However, previous studies have mainly focused on the case of plane waves or the case of complete bonding between lining and surrounding rock, with little consideration of the effects of source distance and non-complete bonding between lining and surrounding rock. In order to deepen the understanding of the influence of source distance and non-complete bonding on seismic wave scattering, the series solution of the dynamic response of shallow-buried circular non-complete bonded tunnels under the loading of anti-plane line source was derived based on the displacement discontinuity model, wave function expansion method, Graf formula and mirror method. The accuracy of the obtained solution was verified by the relationship between the residuals of the inner and outer boundary conditions of the lining and the number of truncated terms in the series solution. By systematically analyzing the parameters of this series solution, the influence of factors such as the contact stiffness between lining and surrounding rock, lining modulus, lining thickness, tunnel depth and source distance on the displacement and circumferential shear stress on the inner surface of the lining was discussed. The results show that the contact stiffness between lining and surrounding rock has a significant influence on the dynamic response of the tunnel, especially in cases with relatively low contact stiffness, where the amplitude of the dynamic response of the tunnel can be very large. Increasing the lining modulus reduces the displacement but increases the circumferential shear stress. Increasing the lining thickness can simultaneously reduce the displacement and circumferential shear stress. As the tunnel depth increases, the maximum displacement and circumferential shear stress on the inner surface of the lining shifts towards the apex of the tunnel. Increasing the horizontal distance between the line source and the tunnel increases the relative amplitude of the tunnel's back wave side.
2024, 44(8): 081431.
doi: 10.11883/bzycj-2024-0004
Abstract:
A 1D SPH (smoothed particle hydrodynamics) and approximate HLLC (Harten-Lax-van Leer-contact) Riemann solver coupled method for elastic-perfectly plastic model is proposed through elastic and plastic wave analysis. In SPH simulations, each particle pair in the supporting domain generates a Riemann problem, whose solutions are substituted into governing equations. The philosophy of HLLC approximate Riemann solver is to divide the procedure into three steps: assume the whole state in elastic deformation and compute Riemann problem, and then reconstruct flux under von Mises yielding conditions and compute the final HLLC Riemann solution with reconstructed fluxes. We compare the new SPH-HLLC method with the traditional SPH method in several numerical tests, which show that this method can effectively simulate collision and reflected rarefaction waves between the materials, and it can profoundly suppress oscillations of pressure and deviatoric stress at contact interface between different materials, which the traditional SPH method finds difficult to realize. Moreover, the new SPH-HLLC scheme shows better energy performance than the traditional SPH method in 2D test case where initial kinetic energy is successfully transformed into internal energy with new SPH-HLLC scheme while total energy significantly decreases with time using the traditional SPH method.
A 1D SPH (smoothed particle hydrodynamics) and approximate HLLC (Harten-Lax-van Leer-contact) Riemann solver coupled method for elastic-perfectly plastic model is proposed through elastic and plastic wave analysis. In SPH simulations, each particle pair in the supporting domain generates a Riemann problem, whose solutions are substituted into governing equations. The philosophy of HLLC approximate Riemann solver is to divide the procedure into three steps: assume the whole state in elastic deformation and compute Riemann problem, and then reconstruct flux under von Mises yielding conditions and compute the final HLLC Riemann solution with reconstructed fluxes. We compare the new SPH-HLLC method with the traditional SPH method in several numerical tests, which show that this method can effectively simulate collision and reflected rarefaction waves between the materials, and it can profoundly suppress oscillations of pressure and deviatoric stress at contact interface between different materials, which the traditional SPH method finds difficult to realize. Moreover, the new SPH-HLLC scheme shows better energy performance than the traditional SPH method in 2D test case where initial kinetic energy is successfully transformed into internal energy with new SPH-HLLC scheme while total energy significantly decreases with time using the traditional SPH method.
2024, 44(8): 081432.
doi: 10.11883/bzycj-2024-0026
Abstract:
To investigate the wound effectiveness of cross-medium bullets, gelatin is chosen as a simulated human target. The numerical simulation of the penetration process of the designed 7.62 mm multi-environment bullet into the simulated target is conducted using LS-DYNA software. The motion of the bullet and the changes in the target cavity are analyzed. By utilizing a three-degree-of-freedom rigid body motion model, the theoretical variations of bullet motion are obtained. In the same time, the penetration experiment was carried out by using multi-parameter synchronous measurement techniques. The results show that the numerical simulation agrees well with the experimental observations, effectively reproducing the penetration process and the wound effects of the multi-environment bullet. The theoretical model exhibits small errors compared to the experimental results but accurately predicts the motion characteristics of the bullet in the target. By employing a cavity structure, the stability of the bullet's motion across different media is improved. Compared to the traditional 56-type 7.62 mm rifle bullet, the designed bullet demonstrates longer stable flight time, greater distance, slower velocity decay, smaller deflection angle during tumbling phase, and comparable maximum cavity, permanent cavity, and energy transfer efficiency. It also exhibits a certain killing effect on the target. The research findings enrich the design theory of bullets and provide data support for the optimization design of new lightweight ammunition.
To investigate the wound effectiveness of cross-medium bullets, gelatin is chosen as a simulated human target. The numerical simulation of the penetration process of the designed 7.62 mm multi-environment bullet into the simulated target is conducted using LS-DYNA software. The motion of the bullet and the changes in the target cavity are analyzed. By utilizing a three-degree-of-freedom rigid body motion model, the theoretical variations of bullet motion are obtained. In the same time, the penetration experiment was carried out by using multi-parameter synchronous measurement techniques. The results show that the numerical simulation agrees well with the experimental observations, effectively reproducing the penetration process and the wound effects of the multi-environment bullet. The theoretical model exhibits small errors compared to the experimental results but accurately predicts the motion characteristics of the bullet in the target. By employing a cavity structure, the stability of the bullet's motion across different media is improved. Compared to the traditional 56-type 7.62 mm rifle bullet, the designed bullet demonstrates longer stable flight time, greater distance, slower velocity decay, smaller deflection angle during tumbling phase, and comparable maximum cavity, permanent cavity, and energy transfer efficiency. It also exhibits a certain killing effect on the target. The research findings enrich the design theory of bullets and provide data support for the optimization design of new lightweight ammunition.
2024, 44(8): 081433.
doi: 10.11883/bzycj-2023-0470
Abstract:
The wave propagation and pressure distribution during the interaction between long duration blast waves and structures are important foundations for the large scale explosion protection design and safety assessment. In order to understand the interaction mechanism between long duration blast waves and cylindrical shells, as well as the distribution law of the surface load on the cylindrical shells under their action, the overpressure histories on the cylindrical structure surface were obtained through the 150 ms long duration blast wave shock tube experiment, and the shock wave evolution and the pressure load distribution were investigated numerically using the large eddy simulation and hybrid WENO-TCD (weighted essentially non-oscillatory-tuned centered difference) method. The results show that the overpressure load of the calculation results is in good agreement with the experimental results, and the overpressure load on the cylindrical shell appears a clear angle and height correlation. The pressure on the back shell is higher than that on the side surface or even comparable to the blast on the facing surface, which exhibit different pressure attenuation modes from the traditional short duration blast wave propagation. The sudden expansion on the side surface is the main reason for the initial oscillation of pressure, and has a lower pressure than that at the windward and leeward sides. On the other hand, a series of diffracted shock waves collides and reflects on the symmetry plane of the shell leeward, as well as the stationary and superimposed effects of the series of decelerating shock waves near the 135° phase, which are the main mechanisms that cause the overall increase of the pressure load on the cylindrical shell. In addition, the formation and evolution of wake vortex structures on the leeward side due to the boundary effects is a key factor leading to differences in the load distribution along the height direction. The above analysis methods and related results lay the foundation for the subsequent study of load distribution models for typical structural components under long duration blast waves.
The wave propagation and pressure distribution during the interaction between long duration blast waves and structures are important foundations for the large scale explosion protection design and safety assessment. In order to understand the interaction mechanism between long duration blast waves and cylindrical shells, as well as the distribution law of the surface load on the cylindrical shells under their action, the overpressure histories on the cylindrical structure surface were obtained through the 150 ms long duration blast wave shock tube experiment, and the shock wave evolution and the pressure load distribution were investigated numerically using the large eddy simulation and hybrid WENO-TCD (weighted essentially non-oscillatory-tuned centered difference) method. The results show that the overpressure load of the calculation results is in good agreement with the experimental results, and the overpressure load on the cylindrical shell appears a clear angle and height correlation. The pressure on the back shell is higher than that on the side surface or even comparable to the blast on the facing surface, which exhibit different pressure attenuation modes from the traditional short duration blast wave propagation. The sudden expansion on the side surface is the main reason for the initial oscillation of pressure, and has a lower pressure than that at the windward and leeward sides. On the other hand, a series of diffracted shock waves collides and reflects on the symmetry plane of the shell leeward, as well as the stationary and superimposed effects of the series of decelerating shock waves near the 135° phase, which are the main mechanisms that cause the overall increase of the pressure load on the cylindrical shell. In addition, the formation and evolution of wake vortex structures on the leeward side due to the boundary effects is a key factor leading to differences in the load distribution along the height direction. The above analysis methods and related results lay the foundation for the subsequent study of load distribution models for typical structural components under long duration blast waves.
2024, 44(8): 081441.
doi: 10.11883/bzycj-2023-0389
Abstract:
The reflected and transmitted waves in split Hopkinson pressure bar (SHPB) tests provide crucial information for obtaining the stress-strain relationship of materials. Accurately analyzing the formation process and influencing mechanisms of the reflected and incident waves is a key prerequisite for precise experimental design and accurate data processing. In this paper, the propagation and evolution of one-dimensional elastic-plastic waves in the loading stages of the SHPB test are presented particularly for a sandwich bar system consisting of the incident wave, specimen, and transmitted bar. Based on the theory of elastic-plastic incremental waves and numerical simulation calculations, the propagation of elastic-plastic waves in the specimen, the transmission and reflection of elastic-plastic waves at the two interfaces, and the interaction of the resulting series of transmitted and reflected waves are quantitatively investigated. The research findings are as follows. Firstly, although the design principle of the SHPB apparatus is based on linear elastic wave theory, the elastic-plastic waves, especially the stress waves, have a major influence on the transmission and reflection at the elastic-plastic interface, while the transmission and propagation of purely elastic waves have a relatively minor effect. Secondly, when the loading interval of the incident wave has a certain width, the multiple transmission and reflection of elastic waves at the two interfaces in bar 2 attenuate the reflected wave while further strengthening the transmitted wave. This attenuation causes the peak of the reflected wave for the half-sine wave to occur earlier than at 0.5 nondimensional time. Thirdly, in contrary to the preliminary laws of elastic wave transmission and reflection at interfaces in traditional SHPB analysis, variations in the Young’s modulus and density of the specimen material have little effect on the waveform and peak intensity of the transmitted wave, regardless of whether the incident wave is rectangular, trapezoidal, or half-sine. This investigationprovides a scientific basis for the refined design of SHPB experiments and precise analysis of data.
The reflected and transmitted waves in split Hopkinson pressure bar (SHPB) tests provide crucial information for obtaining the stress-strain relationship of materials. Accurately analyzing the formation process and influencing mechanisms of the reflected and incident waves is a key prerequisite for precise experimental design and accurate data processing. In this paper, the propagation and evolution of one-dimensional elastic-plastic waves in the loading stages of the SHPB test are presented particularly for a sandwich bar system consisting of the incident wave, specimen, and transmitted bar. Based on the theory of elastic-plastic incremental waves and numerical simulation calculations, the propagation of elastic-plastic waves in the specimen, the transmission and reflection of elastic-plastic waves at the two interfaces, and the interaction of the resulting series of transmitted and reflected waves are quantitatively investigated. The research findings are as follows. Firstly, although the design principle of the SHPB apparatus is based on linear elastic wave theory, the elastic-plastic waves, especially the stress waves, have a major influence on the transmission and reflection at the elastic-plastic interface, while the transmission and propagation of purely elastic waves have a relatively minor effect. Secondly, when the loading interval of the incident wave has a certain width, the multiple transmission and reflection of elastic waves at the two interfaces in bar 2 attenuate the reflected wave while further strengthening the transmitted wave. This attenuation causes the peak of the reflected wave for the half-sine wave to occur earlier than at 0.5 nondimensional time. Thirdly, in contrary to the preliminary laws of elastic wave transmission and reflection at interfaces in traditional SHPB analysis, variations in the Young’s modulus and density of the specimen material have little effect on the waveform and peak intensity of the transmitted wave, regardless of whether the incident wave is rectangular, trapezoidal, or half-sine. This investigationprovides a scientific basis for the refined design of SHPB experiments and precise analysis of data.
2024, 44(8): 081442.
doi: 10.11883/bzycj-2023-0392
Abstract:
Compared to the reflection and transmission analysis process during the incident wave loading phase, the incident wave plateau phase lasts longer, and the elastic-plastic propagation and evolution behavior are much more complex. The effects of elastic-plastic wave interactions within the specimen during this phase are very pronounced. Using the elastic-plastic incremental wave theory, combined with numerical simulation, the calculations of elastic-plastic wave’s interactions inside the specimens under rectangular incident wave action and its elastic-plastic transmission and reflection behavior at the two interfaces are carried out. The attenuation characteristics of the reflected waves in the sandwich rod system are investigated. The results show that under strong incident wave action, the specimen internally forms a curve-shaped elastic-plastic interface due to the interactions of elastic-plastic waves. This causes the transmission end to reach the yield state significantly earlier. This elastic-plastic interface propagates towards the reflection end at a speed greater than the elastic sound speed. The attenuation of the reflected wave during the plastic phase is the sum of the increase in generalized wave impedance due to the increase in the specimen’s cross-sectional area and the increase in the number of back-and-forth plastic waves caused by compression. Calculations also show that although the change of the specimen density significantly affects its wave speed and wave impedance, the sum of the attenuations caused by these two factors is close to zero. Hence, the effect of density changes on the transmission and reflection wave plateau phase can be ignored. An increase in the plastic modulus causes the reflection wave plateau to attenuate faster, but the effect of the specimen’s diameter is not monotonous. When it increases from 4 mm to 10 mm, the reflection wave attenuation speed increases, but when it further increases to 12 mm, the attenuation amount decreases. This study has certain reference value for in-depth analysis of split Hopkinson pressure bar test for the transmission waveforms as well as for the detailed test design and data processing.
Compared to the reflection and transmission analysis process during the incident wave loading phase, the incident wave plateau phase lasts longer, and the elastic-plastic propagation and evolution behavior are much more complex. The effects of elastic-plastic wave interactions within the specimen during this phase are very pronounced. Using the elastic-plastic incremental wave theory, combined with numerical simulation, the calculations of elastic-plastic wave’s interactions inside the specimens under rectangular incident wave action and its elastic-plastic transmission and reflection behavior at the two interfaces are carried out. The attenuation characteristics of the reflected waves in the sandwich rod system are investigated. The results show that under strong incident wave action, the specimen internally forms a curve-shaped elastic-plastic interface due to the interactions of elastic-plastic waves. This causes the transmission end to reach the yield state significantly earlier. This elastic-plastic interface propagates towards the reflection end at a speed greater than the elastic sound speed. The attenuation of the reflected wave during the plastic phase is the sum of the increase in generalized wave impedance due to the increase in the specimen’s cross-sectional area and the increase in the number of back-and-forth plastic waves caused by compression. Calculations also show that although the change of the specimen density significantly affects its wave speed and wave impedance, the sum of the attenuations caused by these two factors is close to zero. Hence, the effect of density changes on the transmission and reflection wave plateau phase can be ignored. An increase in the plastic modulus causes the reflection wave plateau to attenuate faster, but the effect of the specimen’s diameter is not monotonous. When it increases from 4 mm to 10 mm, the reflection wave attenuation speed increases, but when it further increases to 12 mm, the attenuation amount decreases. This study has certain reference value for in-depth analysis of split Hopkinson pressure bar test for the transmission waveforms as well as for the detailed test design and data processing.
2024, 44(8): 081443.
doi: 10.11883/bzycj-2023-0449
Abstract:
To study the strength, deformation characteristic and damage mechanism of freeze-thaw treated rock mass under the action of cyclic dynamic disturbance, the cyclic impact tests of freeze-thaw treated red sandstone under two kinds of impact pressure were carried out to investigate the effects of cyclic impact number and freeze-thaw number on stress wave propagation, dynamic stress-strain curve, peak stress, and peak strain. In addition, the calculation method of cumulative damage factor, which can comprehensive consider the effects of cyclic impact and freeze-thaw, is proposed based on the Lemaitre strain equivalence principle. Finally, the microstructure characteristics of red sandstone after freeze-thaw and cyclic impact are analyzed in detail. Results show that red sandstone specimens treated with different freeze-thaw number show tensile failure mode under cyclic impact load. The cyclic impact number that red sandstone specimen can withstand is negatively correlated with freeze-thaw cycle number, and red sandstone specimen after 75 freeze-thaw cycles treatments reaches the failure state after the first impact loading. Moreover, the cyclic impact number mainly affects the jump point, abscissa corresponding to peak point and amplitude of transmitted waves, and the amplitude of reflected waves. While the freeze-thaw number shows a great effect on the jump point, abscissa corresponding to peak point, and amplitude of transmitted waves during the first impact process. The cumulative damage factor of red sandstone specimen exhibits a good negative correlation with the dynamic peak stress. After the combination effects of freeze-thaw and cyclic impact, the cracks inside red sandstone spread along the grain boundary and connect with the pores to form a complex network.
To study the strength, deformation characteristic and damage mechanism of freeze-thaw treated rock mass under the action of cyclic dynamic disturbance, the cyclic impact tests of freeze-thaw treated red sandstone under two kinds of impact pressure were carried out to investigate the effects of cyclic impact number and freeze-thaw number on stress wave propagation, dynamic stress-strain curve, peak stress, and peak strain. In addition, the calculation method of cumulative damage factor, which can comprehensive consider the effects of cyclic impact and freeze-thaw, is proposed based on the Lemaitre strain equivalence principle. Finally, the microstructure characteristics of red sandstone after freeze-thaw and cyclic impact are analyzed in detail. Results show that red sandstone specimens treated with different freeze-thaw number show tensile failure mode under cyclic impact load. The cyclic impact number that red sandstone specimen can withstand is negatively correlated with freeze-thaw cycle number, and red sandstone specimen after 75 freeze-thaw cycles treatments reaches the failure state after the first impact loading. Moreover, the cyclic impact number mainly affects the jump point, abscissa corresponding to peak point and amplitude of transmitted waves, and the amplitude of reflected waves. While the freeze-thaw number shows a great effect on the jump point, abscissa corresponding to peak point, and amplitude of transmitted waves during the first impact process. The cumulative damage factor of red sandstone specimen exhibits a good negative correlation with the dynamic peak stress. After the combination effects of freeze-thaw and cyclic impact, the cracks inside red sandstone spread along the grain boundary and connect with the pores to form a complex network.
2024, 44(8): 081444.
doi: 10.11883/bzycj-2024-0003
Abstract:
In order to study the effects of free surface on underwater explosion shock wave, bubble behavior and water plumes formed by strong coupling between bubble and free surface, a small yield pentaerythritol tetranitrate (PETN) spherical charge near water surface underwater explosion experimental system was designed, five typical conditions of underwater explosion experiments were carried out, and the evolution process of bubble and water plumes, as well as time history of pressure at the gauge were obtained by high-speed camera and pressure sensor respectively. Based on the characteristics of shock waves and bubble time series, their free surface effects were analyzed separately. The shock wave mainly manifests as truncation effects. The interaction between bubble and free surface is manifested as complex bubble evolution and water plume generation and evolution, which were mainly analyzed through high-speed images, appropriately combined with pressure values. The free surface effects of the bubble were further quantitatively analyzed by the horizontal radius of the bubble, the offset displacement of the bubble, and the maximum height of water plume. The results show that with the decrease of the detonation depth , the difference of the surface reflection wave path decreases, and the truncation effect of the free surface on shock wave increases, that is, the time of the positive pressure of shock wave decreases, and the maximum deviation between the measured truncation time difference and the calculated time difference is 6.81%. With the decrease of the scaled detonation depth, the free surface effects increase, and the shapes of bubble and water plumes become more complicated. The bubble evolves from a sphere to an oval shape, even more complex shapes. The water plume gradually changes from a single water spike to a complex form such as a water spike-top splash column, a water spike-vertical jet column-water jet, etc. The change of the horizontal radius of the bubble no longer retain pulsation characteristics from the second pulsation period to the first pulsation period and even to the first bubble expansion stage. The offset displacement of the center of the bubble’s horizontal radius shows a two-stage variation law, and in the early rapidly-increasing stage (0–20 mm), the offset displacements at 4 scaled detonation depths show a linear variation law, and the linear coefficients are close.
In order to study the effects of free surface on underwater explosion shock wave, bubble behavior and water plumes formed by strong coupling between bubble and free surface, a small yield pentaerythritol tetranitrate (PETN) spherical charge near water surface underwater explosion experimental system was designed, five typical conditions of underwater explosion experiments were carried out, and the evolution process of bubble and water plumes, as well as time history of pressure at the gauge were obtained by high-speed camera and pressure sensor respectively. Based on the characteristics of shock waves and bubble time series, their free surface effects were analyzed separately. The shock wave mainly manifests as truncation effects. The interaction between bubble and free surface is manifested as complex bubble evolution and water plume generation and evolution, which were mainly analyzed through high-speed images, appropriately combined with pressure values. The free surface effects of the bubble were further quantitatively analyzed by the horizontal radius of the bubble, the offset displacement of the bubble, and the maximum height of water plume. The results show that with the decrease of the detonation depth , the difference of the surface reflection wave path decreases, and the truncation effect of the free surface on shock wave increases, that is, the time of the positive pressure of shock wave decreases, and the maximum deviation between the measured truncation time difference and the calculated time difference is 6.81%. With the decrease of the scaled detonation depth, the free surface effects increase, and the shapes of bubble and water plumes become more complicated. The bubble evolves from a sphere to an oval shape, even more complex shapes. The water plume gradually changes from a single water spike to a complex form such as a water spike-top splash column, a water spike-vertical jet column-water jet, etc. The change of the horizontal radius of the bubble no longer retain pulsation characteristics from the second pulsation period to the first pulsation period and even to the first bubble expansion stage. The offset displacement of the center of the bubble’s horizontal radius shows a two-stage variation law, and in the early rapidly-increasing stage (0–20 mm), the offset displacements at 4 scaled detonation depths show a linear variation law, and the linear coefficients are close.
2024, 44(8): 081445.
doi: 10.11883/bzycj-2023-0442
Abstract:
Theoretical study on the attenuation law of underwater explosion shock waves plays a crucial role in predicting the underwater explosion power. The attenuation law of underwater explosion shock waves could be analyzed from the shock waves pressure-time curve. The pressure-impulse (p-I) model has usually been used to assess damage on material and structure. In this paper, the pressure-time formula is analytically derived according to the p-I model. To verify the accuracy of the formula, the pressure-time relation curve was obtained by experiments with various explosive charges and distances. The experimental data was fitted in accordance with the theoretical equations of Cole and Орленко, and also with the developed pressure-time formula. The parameters of the formula are thus obtained. The accuracy could be described by the fitting coefficient R-squared (R2) value. The R-squared value of the developed pressure-time formula exceeds 0.988, which is greater than the R-squared values calculated by the equations of Cole and Орленко. In order to further validate the formula, the impulse and energy of underwater explosion shock waves are derived from the developed pressure-time formula, experimental data, and the equations of Cole and Орленко, respectively. Compared with the experimental results, the error of impulse derived from the developed pressure-time remains below 4%, which is 5%−10% lower than the errors of impulse between the experimental results and the equations of Cole and Орленко. The energy of the shock waves is similarly analyzed. Compared with the experimental results, the error of energy derived from the developed pressure-time remains below 1%, approximately the same as the errors of energy between the experimental results and the equations of Cole and Орленко. Compared with the calculation by equations of Cole and Орленко, it is seen that there is better correlation between the developed pressure-time formula and the experimental results. The developed pressure-time formula can be used to calculate the impulse and energy of underwater explosion shock waves.
Theoretical study on the attenuation law of underwater explosion shock waves plays a crucial role in predicting the underwater explosion power. The attenuation law of underwater explosion shock waves could be analyzed from the shock waves pressure-time curve. The pressure-impulse (p-I) model has usually been used to assess damage on material and structure. In this paper, the pressure-time formula is analytically derived according to the p-I model. To verify the accuracy of the formula, the pressure-time relation curve was obtained by experiments with various explosive charges and distances. The experimental data was fitted in accordance with the theoretical equations of Cole and Орленко, and also with the developed pressure-time formula. The parameters of the formula are thus obtained. The accuracy could be described by the fitting coefficient R-squared (R2) value. The R-squared value of the developed pressure-time formula exceeds 0.988, which is greater than the R-squared values calculated by the equations of Cole and Орленко. In order to further validate the formula, the impulse and energy of underwater explosion shock waves are derived from the developed pressure-time formula, experimental data, and the equations of Cole and Орленко, respectively. Compared with the experimental results, the error of impulse derived from the developed pressure-time remains below 4%, which is 5%−10% lower than the errors of impulse between the experimental results and the equations of Cole and Орленко. The energy of the shock waves is similarly analyzed. Compared with the experimental results, the error of energy derived from the developed pressure-time remains below 1%, approximately the same as the errors of energy between the experimental results and the equations of Cole and Орленко. Compared with the calculation by equations of Cole and Орленко, it is seen that there is better correlation between the developed pressure-time formula and the experimental results. The developed pressure-time formula can be used to calculate the impulse and energy of underwater explosion shock waves.
