Amplitude Of Stress Wave Research Articles

Failure characteristics and stress wave propagation of red sandstone under explosion with varying gas energies

AbstractThis study designs a blasting loading device capable of changing the utilization of explosive gas by modifying the constraint conditions. The propagation of crack and stress waves in red sandstone under different explosive gases is recorded using digital image correlation technology and ultra‐dynamic strain gauges. Both methods are effectively validated against each other. The results showed that as the utilization of explosive gas increases, the explosive stress wave induces layer cracking at the specimen's far end and tensile failure at its near end. In addition, the larger the stress wave's amplitude, the greater the spatial attenuation coefficients of the compression and tension waves. The study ultimately deduces the propagation process of the incident wave and analyzes the influence of stress wave propagation on the specimen's failure characteristics.

Stress Wave Propagation and Decay Based on Micro-Scale Modelling in the Topology of Polymer Composite with Circular Particles.

This article deals with stress wave decay performance, analysing the stress wave propagation generated by an impulsive unit load in a 2D representative unit cell (RUC) of a polymer composite with circular particles representing spherical particles, elliptical particles, and short fibres. The micro-scale numerical simulation uses explicit finite element analysis (FEA). The micro-response to an impulsive unit load creates a stress wave amplitude interacting with the material structure and tends to weaken and absorb energy. The stress wave damping is determined by the decaying amplitudes of Mises stress at the front of the stress wave. The stress wave damping is evaluated for different ratios of tensile modules and material densities of matrix and reinforcing material and other factors, such as percentage and particle size, applied to nine topologies of RUCs, and even the presence of an interfacial region is analysed. Moreover, the article visualises the phases of stress wave decay in various particle distributions, i.e., various topologies. Analysing the different topologies of the same particle volume (area) percentage, the study proved that the composite topology and resulting wave-particle and wave-wave interactions are other sources of material damping. The presence of even a small percentage, 3.5 area%, of reinforcing circular particles in the matrix brings a significant increase in stress wave damping up to about 40-43% (depending on the topology) compared to a homogeneous matrix with stress wave damping of 12.5% under the same conditions. Moreover, the topology with the same volume (area) percentage can increase particle stress wave damping by 15.3%.

Damage and Nonlinearity Effects on Stress Wave Propagation in Planar Frame Structures: A Machine Learning Classification Approach Based on Stress Wave Amplitude Solution

Damage and Nonlinearity Effects on Stress Wave Propagation in Planar Frame Structures: A Machine Learning Classification Approach Based on Stress Wave Amplitude Solution

Mesoscale numerical investigation of dynamic spalling fracture in toughness concrete

This study presents a two-phase mesoscale numerical model to investigate the dynamic spalling fracture behaviour of hybrid fibre ultra-high toughness cementitious composites (UHTCC). The model simulated the presence of random steel fibres and ductile UHTCC independently, and accurately incorporated the fibre-matrix bond-slip relationship, with carefully considering the influence of the inclination angle of the steel fibres on the pullout behaviour. Validation of the numerical model involved a meticulous comparison between numerical outcomes and results from spallation tests, encompassing strain-time and velocity-time histories, failure modes, and locations of cracking or fracture. Subsequently, the developed model was employed to analyse the impact of fibre inclination, stress wave amplitude, and waveform (based on the impulse equivalence principle) on the dynamic spalling fracture behaviour of hybrid fibre UHTCC. Evaluation of spalling fracture performance was based on both maximum velocity and pullback velocity of resulting fragments or free surfaces. Findings revealed that fibres parallel to the stress wave propagation direction exhibited optimum performance. It was also observed that stress waveforms with rectangular and sinusoidal shapes presented the highest risk of spalling fracture, while exponentially attenuated waves were comparatively safer. Additionally, stress waveforms with either rise time or duration at maximum pressure were deemed hazardous. Further, the hybrid fibre UHTCC demonstrated multiple spalling cracking/fracture behaviours under all stress waves except rectangular ones. This comprehensive exploration provided insights for the utilization of hybrid fibre UHTCC in impact engineering.

Numerical Analysis of Cyclic Impact Damage Evolution of Rock Materials under Confining Pressure

To study the effect of cyclic impacts and confining pressure on the damage evolution of rock materials, numerical simulations of cyclic impact tests on rock materials under confining pressure were carried out by LS-DYNA using dynamic relaxation and full restart analysis. The static confining pressure was applied by dynamic relaxation, and cyclic impacts were realized by full restart analysis. As the crack generation and propagation result in the failure of elements in the finite element model, the damage variable defined by the crack density method was characterized by volume reduction. Numerical simulation indicates that both the confining pressure and amplitude of incident stress waves significantly affect the damage evolution of rock materials. High incident stress waves lead to severe damage, while large confining pressure results in minor damage. Under confining pressure, the damage to rock materials is alleviated due to the constraint effect on crack propagation. The number of cyclic impacts before macroscopic fracture increases as the confining pressure increases and decreases when the amplitude of the incident stress waves increases. The cumulative damage of rock materials under confining pressure progressively increases with the number of cyclic impacts, and the damage evolution exhibits three distinct stages: rapid rising, steady development, and sharp rising.

Numerical simulations of fatigue failure processes in intermittent jointed rock masses under the action of repeated stress waves

To study the fatigue failure of an intermittent jointed rock mass under repeated stress waves, numerical models of jointed rock masses with different joint angles were created using Autodyne software, and crack propagation behavior was simulated using the Drucker–Prager strength model and cumulative damage failure criteria. In this numerical simulation, the influence of stress wave amplitude and the mode of disturbance on fatigue failure of the rock mass were analyzed. The simulation results showed a significant difference between the failure process of jointed rock masses subjected to repeated stress waves and those exposed to a single stress wave, including crack initiation locations, propagation paths, and rock mass failure patterns. With increasing angles of inclination, the fatigue life of the rock mass first decreased and then increased under repeated stress waves. As the joint inclination angle, β, increased from 20° to 50°, it had a significant influence on the fatigue life of the rock mass, which decreased rapidly with increases in β. The variation in the disturbance form (the change in amplitude of the stress waves from small to large, or from large to small) did not affect the final macro failure pattern of the rock mass; but the extent of damage to the rock mass was affected.

Effect of Different Tunnel Distribution on Dynamic Behavior and Damage Characteristics of Non-Adjacent Tunnel Triggered by Blasting Disturbance

When a blasting is executed near two tunnels, the blasting wave will trigger a dynamic response and damage to the tunnels. Depending on the tunnel distribution, the path of the blasting wave to the remote non-adjacent tunnels will change. The aim of this study is to analyze the effect of the tunnel distribution on the dynamic response characteristics of a remote non-adjacent tunnel. Numerical models of two tunnels were established by PFC2D and three different tunnel distributions were considered. The two tunnels were divided into the adjacent tunnel and the non-adjacent tunnel according to their relative distance to the blasting source. The dynamic stress evolution, damage characteristics and the evolution of strain energy of the non-adjacent tunnel were initially analyzed. The results show that the stress wave amplitude of the non-adjacent tunnel is closely related to the tunnel distribution, but only near the sidewalls of the non-adjacent tunnel is the stress wave waveform sensitive to the tunnel distribution. The larger the tunnel dip, the more severe the damage to the non-adjacent tunnel. In addition, as the tunnel dip increases, the maximum strain energy densities (SEDs) in the roof, floor and sidewalls of the non-adjacent tunnel exhibit different trends. The influence of the wavelength of the blasting wave is further discussed. It is shown that the dynamic stress amplification factor and damage degree around the non-adjacent tunnel is usually positively correlated with the wavelength of the blasting wave. Moreover, the release of strain energy around the non-adjacent tunnel has a positive correlation with the wavelength. The SED variations in different areas around the non-adjacent tunnel also exhibit different trends with the increase of tunnel dip.

Research on the Dynamic Damage Properties and Determination of the Holmquist–Johnson–Cook Model Parameters for Sandstone

During blasting in engineering construction, the surrounding rock becomes unstable and is damaged under the impacts of multiple low-amplitude stress waves. It is of great practical significance to understand the damage evolution characteristics and the attenuation of the mechanical properties of rocks subjected to multiple stress waves. Single impact and repeated impact tests for sandstone were carried out using a split Hopkinson pressure bar (SHPB) loading system. The single impact test results showed that the sandstone materials were strain-rate-dependent, and the dynamic constitutive curve could be divided into four stages, namely the linear elastic stage, the new crack formation stage, the plastic strengthening stage and the unloading stage. The failure pattern mostly indicated splitting tensile failure, and the impact damage threshold was 45 J. The relationship between the damage and stress wave amplitude was D = 0.0029·exp\({\boxed{f_{()}}}\)(5.4127•σ/76.13) − 0.0504. The repeated impact test results showed that the dynamic compressive strength and the dynamic elastic modulus decreased, while the failure strain increased gradually as the number of impacts (n) increased. The sandstone specimen under repeated impacts had only one fracture surface compared with the single impact failure pattern. The cumulative damage presented the development form of ‘rapid rise–steady development–rapid rise’, and the damage evolution law could be expressed by D = 0.265 − 0.328·ln⁡⁡⁡\({\boxed{f_{()}}}\)(ln13.989/n). Finally, a set of methods to determine the Holmquist–Johnson–Cook (HJC) model parameters for sandstone was proposed based on a single impact test, repeated impact test, uniaxial compression test and triaxial compression test. The numerical simulation results of the SHPB test showed that the dynamic constitutive curves of sandstone were in good agreement with the experimental results.

Experimental Study of the Effect of Axial Load on Stress Wave Characteristics of Rock Bolts Using a Non-Destructive Testing Method

Traditional rock bolt inspection methods are destructive and limited. Non-destructive testing (NDT) based on the stress wave method can realize a fast and convenient quality detection of rock bolts. To verify the effectiveness of the stress wave-based anchor NDT method, a multi-functional experimental bench was customized on the basis of a bench-pull tension testing machine. Stress waves can be generated by applying axial loads on rock bolts and then collected using a non-destructive tester. The VMD decomposition method and Hilbert–Huang signal processing method were used to filter and analyze the stress wave signal. The influence of the axial loads of different magnitudes on the stress wave was then investigated. The results showed that the stress wave characteristics of the rock bolt changed with the increase in the axial load. It was found, correspondingly, that the stress wave amplitude decreased gradually and there was a trend of rapid decrease at the beginning and then a slower decline. The change in the time domain amplitude of the stress wave after noise reduction can be used to determine the magnitude of the load on the rock bolt during the elastic deformation stage. Further studies showed that the axial load on rock bolts inversely calculated by the stress-wave time-domain amplitude method is accurate and reliable, which can be validated by comparing the data measured by the rock bolt dynamometer. The research results shed light on the development of the NDT technology on rock bolt inspection, and make this testing method more convenient, efficient, and accurate.

Effect of pulse duration and confinement on laser-induced stress waves for high strain-rate material testing

Laser-induced stress waves have been a powerful technique for high strain-rate material characterization. The stress amplitude and duration can be strongly influenced by both laser characteristics and sample configuration. In this study, stress histories of silicon substrates loaded by pico- and nanoseconds laser pulses, with and without confinement of the interaction volume, were investigated. Shorter pulse duration and confinement of the absorbing medium have been found to increase the amplitude of laser-induced stress waves, but they may also alter the stress evolution. Without confinement or at low energy densities the stress wave profile is similar to that of the laser pulse. At high energy densities with confinement shock loading with stretched unloading is observed.

Experiments and numerical simulations of microelectronic devices subjected to multipoint impact loading

Microelectronic devices in projectiles are usually fixed with multiple solder joints or screws. When the overall structure is subjected to an impact load, the devices will suffer multi-point impact at the connection points. This paper proposes a multi-point impact loading technique to simulate the loading environment of microelectronic devices in transient impact processes such as projectile perforation and penetration. In the experiment, a sleeve with convex plates was fixedly connected to the end of a bar. The impact of a striker on the bar produced an incident stress wave, which was transmitted into the convex plates to realize multi-point impact loading. The magnitude of the stress wave's amplitude transmitted into the convex plate was obtained through theoretical analysis. Then two-point and four-point impact loading tests were performed on specific microelectronic devices. The experimental results show that the microelectronic devices are more likely to be damaged under two-point impact loading. Furthermore, the multi-point impact loading tests were simulated by LS-DYNA software. The mechanical response and damage mechanism of the microelectronic devices were analyzed. The results indicate that the two-point impact loading cause larger deflections of the ceramic plates, making the microelectronic devices prone to damage. This novel loading and analysis method can be used for impact damage analysis of other electronic components as well.

Energy absorption within elastic range for AZ31 magnesium alloy

Energy absorption for AZ31 magnesium Alloy was investigated with Split Hopkinson Pressure Bar using single stress wave so as to avoid multiple stress wave loading. The stress wave amplitude, which was in elastic stress range and propagated along the AZ31 magnesium bar, was reduced with increasing propagating distance, and with increasing stress wave amplitude, the stress wave amplitude reduction along the magnesium bar was increased losing more energy as compared with that of the stress wave with lower amplitude. The drastically decreased stress wave amplitude could be explained based on dislocations movements, which was similar to the established theory of damping for the explanation of the energy loss during cyclic loading. However, it was not the case for LY12 aluminum alloy: the stress wave amplitude changed slightly without drastic energy loss regardless of the variation of stress wave amplitude.

The quality evaluation of the grout in rock bolts based on the stress wave propagation

Nondestructive testing of rock bolt is essential for evaluating the grouted quality in rockmass. The stress wave propagation in the fully grouted rock bolts and defectively anchored bolt was investigated, where the mortar between the rock and bolt is subjected to different curing ages and stress wave induced by a dynamic excitation hammer impacting the bolt. First of all, it is found that both velocity and amplitude decrease with the increment of curing age of the anchor agent, based on the experiment of stress wave propagation in the fully grouted rock bolts. Velocity and amplitude attenuation decrease drastically within the first 14 curing ages and maintain steadily thereafter. The energy proportion manifests no change in the same waveform with the increment of curing ages, but the proportion taken by high-frequency harmonic wave increases. The crossing point of energy proportion curves moves towards low-frequency area, whereas the decrease of total energy tends to be stable. Secondly, the experiment of stress wave propagation in anchored bolt with different size of defects is also investigated. The variation of velocity and amplitude of stress wave in the defectively anchored bolt is similar to that of stress wave propagation in the fully grouted rock bolts. The crossing point of energy proportion curves moves towards low-frequency area, which is similar to the fully grouted rock bolts. But the velocity and amplitude attenuations in defectively anchored bolt are less than those in fully grouted rock bolts. The larger the defect size is, the smaller the amplitude attenuation is. Finally, the experiment of stress wave propagation in anchored bolt with different location of defects is also conducted. The magnitude of amplitude attenuation increases with the increase of distance. But the crossing point of energy proportion curves remains unchanged. The anchoring quality of bolts can be evaluated by the anchoring effect of anchoring agent, which can be estimated by the attenuation amplitude of stress wave velocity and amplitude, based on the experiment of stress wave propagation in defectively anchored bolt.

Split Hopkinson pressure bar test and cell model of the damage threshold of siltstone

Study the damage threshold of siltstone, we conducted the large-diameter series of split Hopkinson pressure bar cyclic impact tests on siltstone samples. When the damage value of siltstone was 0.16-0.4, increased exponentially with an increase in stress wave amplitude. Damage evolution in siltstone obeys the power-law distribution. This feature is consistent with the self-similarity theory in fractal mechanics. Thus, self-organized criticality theory can be used to determine the rock damage threshold. Combined with the microscopic tectonic features of siltstone, a 2 × 3 cell model was established by based on the renormalization group method, and the failure probability of seven 2 × 3 cell models was established by combining the force transfer coefficients among cell units. The seven damage models, showed that the damage accumulation threshold of siltstone without damage is 0.119, and the damage threshold during failure is 0.4, which is consistent with the SHPB test results. Thus, the cellular model established based on the renormalization group method can be used to study the damage evolution of siltstone.

Lubrication effects on the peristaltic motion of a couple stress fluid in an asymmetric channel

The present article deals with theoretical analysis on the peristaltic transport of a couple stress fluid with lubrication on the walls of the channel. The walls are coated with thin layer of power-law lubricant and the condition arised by the coating is modelled by taking the continuity of velocity and shear stresses of both the fluids at the fluid–fluid interface. The flow problem is discussed in two-dimensional asymmetric medium assuming long wavelength and low Reynolds number. Closed form solutions for velocity, stream function and flow rate are discussed. The numerical solutions for pressure rise, trapping and reflux are discussed. The effects of lubricant parameter, couple stress parameter, phase difference, wave amplitudes and flow rate are discussed for symmetric and asymmetric channels. It is observed that by increasing the lubrication effects, pressure rise increases in the pumping region and for trapping, boluses disappear and streamlines become parallel to the walls of the channel. From the given flow problem, the limiting cases of no-slip and viscous flow are presumed and found to be in excellent agreement with the existing literature.

Stress wave propagation across jointed rock mass under dynamic extension and its effect on dynamic response and supporting of underground opening

Rock joints are prone to open and fail when subject to severe dynamic extension, which might result in spalling of surrounding rock and collapse of underground openings. However, the understanding of dynamic response of rock joints and underground openings subject to tensile stress wave is still at its infancy. To investigate the effect of tensile wave on the response, stability and supporting of underground openings in jointed rock mass, numerical modelling was carried out herein with the DEM-based universal distinct element code (UDEC) after its validation using explosion testing measurements. Results showed that joint tensile strength has significant effects on stress wave propagation if it is lower than the amplitude of tensile stress wave in the shallow rock mass, where joint opening will occur, no significant portion of wave energy could transmit through the joint, and the transmission coefficient for tension-first wave is lower than that for compression-first wave. The buried depth of underground opening and joint properties including stiffness, spacing and dip angle as well as crossing angle between joint sets could significantly influence stress wave propagation and dynamic responses of underground openings under dynamic extension. In addition, installation of rock bolts with appropriate number and length and shotcreting with sufficient thickness could effectively reinforce the surrounding rock and reduce the area of disturbed zones when against dynamic extension. The findings in this study could be of great significance for the design, supporting and stability evaluation of underground openings.

Effect of Nonlinear Deformational Macrojoint on Stress Wave Propagation Through a Double-Scale Discontinuous Rock Mass

The overall dynamic mechanical behavior of a double-scale discontinuous rock mass with a nonlinear deformational macrojoint was investigated. A method of combining the split three characteristic lines with the piecewise linear displacement discontinuity model (DDM) was proposed. The method was applied to investigate the transmission coefficient of P-wave propagation normally through a double-scale discontinuous rock mass with a nonlinear deformational macrojoint. The results were verified by comparison with the results of P-wave propagation normally through a double-scale discontinuous rock mass with a linear deformational macrojoint. The results showed that for a small amplitude stress wave, the nonlinear deformational macrojoint can be simplified as a linear deformational form to study the stress wave propagation, whereas for a large amplitude stress wave, the effects of the nonlinear deformational behavior of the macrojoint must be considered. The difference of the effects of nonlinear and linear deformational macrojoints on large amplitude stress wave propagation can be overlooked in the low-frequency or high-frequency regions. In addition, when the incident stress wave amplitude and initial macrojoint stiffness are sufficiently large, the effects of the nonlinear deformational macrojoint on stress wave propagation can be overlooked, and the effects of microdefects must be considered. The influence degree of microdefects on the stress wave propagation increases with the increase of incident stress wave frequency.

Research on propagation law of one-dimensional stress wave in jointed rock mass under in-situ stress

The propagation law of stress wave in jointed rock mass under in-situ stress has important engineering significance on blasting excavation and protection engineering design of deep rock mass. Based on theoretical analysis, the propagation law of stress wave across multiple nonlinear deformation joints under the initial stress is studied. Firstly, the propagation equation of stress wave across multiple nonlinear joints considering the influence of initial stresses is established, through the discontinuous deformation method (DDM) and the recursive analysis method of stress wave in time domain. On this basis, parametric studies are conducted for the effects of stress wave propagation, such as initial stress, the amplitude of stress wave, the distance and the number of joints. The results show that the existence of initial stress will affect the propagation of stress wave, the geometric distribution of joints, such as spacing and number, can also cause the change of stress wave transmission coefficients, and the amplitude of incident wave varies can also lead to the change of stress wave propagation.

An Analytical Research on Stress-Wave Propagation and Comparison of Experiments and Theory of Zonal Disintegration in Rock Masses around Deep Tunnels

The zonal disintegration mechanism in rock masses around deep tunnels is totally controversial. Because this phenomenon basically depends on the stress-wave amplitude, fluctuating and declining in rock masses particularly around deep tunnels. This paper intends to theoretically solve the problem of stress-wave propagation. For this purpose, a physical model of stress-wave propagation is established in rock masses around the deep tunnels. Further, the wave equation is solved for rock masses of deep tunnels. Taking Dingji Tunnel in southern of China as a case-study, the central radius of partition is calculated theoretically and compared with the measured results in rock masses around deep tunnels. The research results of this paper gives a certain promotes to the theory of zonal disintegration in rock masses and have certain guiding significance for deep rock engineering.

Experimental study on stress wave attenuation and energy dissipation of sandstone under full deformation condition

Excavation behaviours not only destroy the balance of original stress in rock mass but lead to the redistribution of initial stress, resulting in rock mass in a new stress environment. The static stress in rock mass has the characteristics of dynamic change. For the purpose of investigating the effect of increasing static stress on attenuation mechanism and energy dissipation of stress wave in sandstone under the overall deformation condition, small disturbance experiments on sandstone bar are carried out with a modified split-Hopkinson pressure bar test system. The stress waveform, p wave velocity, temporal and spatial attenuation of amplitude, and energy dissipation are studied under various static stresses. Results show that stress waveforms at different locations are approximately the same, those at the same locations vary greatly, and the tensile waves that appeared at the tails of stress waves are larger with increasing static stress. With increasing static stress, p wave velocity experiences a dramatic increase, then develops gently, and finally a sharp decrease; the stress demarcation points are σs/σc = 30% and σs/σc = 55%, respectively. P wave velocity can be predicted by a quadratic equation when σs/σc > 63.69%. The relation between longitudinal wave velocity and static stress can be described by a quadratic function. Stress wave amplitudes decrease exponentially with increasing distance and time. Values of temporal spatial response intensity (RI) and spatial RI are approximately equal and present the same development tendency of nonlinear and linear stages due to the same dimensions. Values of temporal attenuation characteristic (AC) and spatial AC are differed by 2 or 3 orders of magnitude although they present the same development tendencies. Ratios of RI and AC can indicate the sensitivity of temporal and spatial attenuation to different static stresses. Full-wave energy declines in an exponential function with increasing static stress and decays as a logarithmic function with increasing distance. Widespread attenuation characteristics like these should provide a theoretical basis for rock mass stability analysis.