Effects of imperfect experimental conditions on stress waves in SHPB experiments

Experimental and numerical simulations were undertaken to estimate the effects of imperfect conditions on stress waves in split Hopkinson pressure bar （SHPB） experiments. The photonic Doppler velocimetry （PDV） measurement results show that the rise and fall times of an incident wave increases with an increasing inclination angle; also, the fluctuations of the incident wave disappear gradually with the increase of inclination angle. The following characteristics for various defects in the SHPB were obtained by numerical simulation： （1） the influence of a curved bar was negligible; （2） misalignment modestly affects the fluctuation characteristics, and bending waves were generated at this condition; （3） inclination and indentation of the impact end- surface had a great impact on the incident waves, and both of them increase the rise time of the incident wave by increasing the degree of defects. In view of the results, misalignment, inclination, and indentation in SHPB experiments should be minimized.

Stress Waves in Polymeric Fluids

This paper demonstrates the existence, propagation, transmission, reflection, and interaction of deviatoric stress waves in polymeric fluids for which the mathematical models are derived using conservation and balance laws (CBL) of Classical Continuum Mechanics (CCM) and the constitutive theories are based on the entropy inequality and representation theorem. The physical mechanisms of deformation in polymeric liquids that enable the stress wave physics are identified and are demonstrated to be valid using Maxwell, Oldroyd-B, and Giesekus polymeric fluids, and are illustrated using model problem studies. We assume polymeric fluids to be isotropic and homogeneous at the macro scale so that the CBL of the CCM can be used to derive their mathematical models. For simplicity, we assume the polymeric fluids to be incompressible in the present work.

Experimental Investigation on Transmission of Stress Waves in Sandwich Samples Made of Foam Concrete

A series of impact tests of sandwich samples were completed using a large-diameter split Hopkinson pressure bar (SHPB)device at different velocities. The interlayer is made of foam concrete, loess or sand. The stress peak value decay, energy decay and waveform dispersion characters are studied by comparing the incident waves with the transmission waves. The tests indicate that the foam concrete has the best capabilities of shock resistance and energy absorption, the loess comes second, and the sand takes third place.

SCATTERING OF HARMONIC ANTI-PLANE SHEAR STRESS WAVES BY A CRACK IN FUNCTIONALLY GRADED PIEZOELECTRIC/PIEZOMAGNETIC MATERIALS

In this paper, the dynamic behavior of a permeable crack in functionally graded piezoelectric/piezomagnetic materials is investigated. To make the analysis tractable, it is assumed that the material properties vary exponentially with the coordinate parallel to the crack. By using the Fourier transform, the problem can be solved with the help of a pair of dual integral equations in which the unknown is the jump of displacements across the crack surfaces. These equations are solved to obtain the relations between the electric filed, the magnetic flux field and the dynamic stress field near the crack tips using the Schmidt method. Numerical examples are provided to show the effect of the functionally graded parameter and the circular frequency of the incident waves upon the stress, the electric displacement and the magnetic flux intensity factors of the crack.

Propagation of combined longitudinal and torsional stress waves in a functionally graded thin-walled tube

An analytical model for the propagation of combined stress waves in a functionally graded thin-walled tube subjected to combined longitudinal and torsional impact loading is established.The material properties of the tube are assumed to be continuously graded along the length according to a power law function with respect to the volume fractions of the constituents.The generalized characteristic theory is used to analyze the main features of the characteristic wave speeds and simple wave solutions in the functionally graded thin-walled tube.The finite difference method is used to discretize the governing equations.Two types of typical solutions are obtained for the functionally graded tube and the homogeneous tube subjected to combined longitudinal and torsional step loading.The numerical results reveal some abnormal phenomena in the stress path and wave process of the functionally graded thin-walled tube.

THE INVESTIGATION ON DYNAMIC FRACTURE BEHAVOUR OF MATERIALS UNDER COMPRESSIVE-SHEAR COMBINED STRESS WAVES

In this paper,an improved plate impact experimental technique is presented for studying dynamic fracture mechanism of materials,under the conditions that the impacting loading is provided by a single pulse and the loading time is in the sub-microsecond range.The impacting tests are carried out on the pressure-shear gas gun.The loading rate achieved is dK/dt～10~8 MPam^(1/2)s^(-1).With the elimination of influence of the specimen boundary,the plane strain state of a semi-infinite crack in an infinite elastic plate is used to simulate the deformation fields of crack tip. The single pulses are obtained by using the 'momentum trap'technique.Therefore, the one-time actions of the single pulse are achieved by eradicating the stress waves reflected from the specimen boundary or diffracted from the crack surfaces.In the current study,some important phenomena have been observed.The special loading of the single pulse can bring about material damage around crack tip,and affect the material behavior,such as kinking and branching of the crack propagation.Failure mode transitions from mode Ⅰ to mode Ⅱ crack are observed under asymmetrical impact conditions.The mechanisms of the dynamic crack propagation are consistent with the damage failure model.

Influence of the Radial Inertia Effect on the Propagation Law of Stress Waves in Thin-Walled Tubes

This investigation focused on the influence of the radial inertia effect on the propagation behavior of stress waves in thin-walled tubes subjected to combined longitudinal and torsional impact loads.Generalized characteristics theory was used to analyze the main features of the characteristic wave speeds and simple wave solutions in thin-walled tubes.The incremental elastic-plastic constitutive relations described by the rate-independent plasticity were adopted,and the finite difference method was used to investigate the evolution and propagation behaviors of combined elasticplastic stress waves in thin-walled tubes when the radial inertial effect was considered.The numerical results were compared with those obtained when the radial inertia effect was not considered.The results showed that the speed of the coupled stress wave increased when the radial inertia effect was considered.The hardening modulus of the material in the plastic stage had a greater impact on the coupled slow waves than on the coupled fast waves.

Macro Meso Response and Stress Wave Propagation Characteristics of MCT High-Voltage Switch Under Shock load

In order to study the dynamic and electrical coupling response characteristics of Metal Oxide Semiconductor Controlled Thyristor(MCT)high-voltage switch under the synergic action of mechanical load and high voltage,the separated Hopkinson pressure bar(SHPB)test system was used to simulate different impact load environments,and combined with the multi-layer high-voltage ceramic capacitor charging and discharging system,the instantaneous electrical signals of MCT high-voltage switch were collected.Combined with numerical simulation and theoretical analysis,the failure mode and stress wave propagation characteristics of MCT high voltage switch were determined.The mechanical and electrical coupling response characteristics and failure mechanism of MCT high voltage switch under dynamic load were revealed from macroscopic and microscopic levels.The results show that the damage modes of MCT high-voltage switches can be divided into non-functional damage,recoverable functional damage,non-recoverable damage and structural damage.Due to the gap between the metal gate and the oxide layer,the insulating oxide layer was charged.After placing for a period of time,the elastic deformation of the metal gate partially recovered and the accumulated charge disappeared,which induced the recoverable functional damage failure of the device.In addition,obvious cracks appeared on both sides of the monocrystalline silicon inside the MCT high-voltage switch,leading to unrecoverable damage of the device.

Effect of Blasting Stress Wave on Dynamic Crack Propagation

Stress waves affect the stress field at the crack tip and dominate the dynamic crack propagation.Therefore,evaluating the influence of blasting stress waves on the crack propagation behavior and the mechanical characteristics of crack propagation is of great significance for engineering blasting.In this study,ANSYS/LS-DYNA was used for blasting numerical simulation,in which the propagation characteristics of blasting stress waves and stress field distribution at the crack tip were closely observed.Moreover,ABAQUS was applied for simulating the crack propagation path and calculating dynamic stress intensity factors(DSIFs).The universal function was calculated by the fractalmethod.The results show that:the compressive wave causes the crack to close and the reflected tensile wave drives the crack to initiate and propagate,and failure mode is mainly tensile failure.The crack propagation velocity varies with time,which increases at first and then decreases,and the crack arrest occurs due to the attenuation of stress waves and dissipation of the blasting energy.In addition,crack arrest toughness is smaller than the crack initiation toughness,applied pressure waveforms(such as the peak pressure,duration,waveforms,wavelengths and loading rates)have a great influence on DSIFs.It is conducive to our deep understanding or the study of blasting stress waves dominated fracture,suggesting a broad reference for the further development of rock blasting in engineering practice.

Stress wave analysis of high-voltage pulse discharge rock fragmentation based on plasma channel impedance model

High-voltage pulse discharge(HVPD)rock fragmentation controls a plasma channel forming inside the rock by adjusting the electrical parameters,electrode type,etc.In this work,an HVPD rock fragmentation test platform was built and the test waveforms were measured.Considering the effects of temperature,channel expansion and electromagnetic radiation,the impedance model of the plasma channel in the rock was established.The parameters and initial values of the model were determined by an iterative computational process.The model calculation results can reasonably characterize the development of the plasma channel in the rock and estimate the shock wave characteristics.Based on the plasma channel impedance model,the temporal and spatial distribution characteristics of the radial stress and tangential stress in the rock were calculated,and the rock fragmentation effect of the HVPD was analyzed.

The attenuation of stress waves in fluid saturated porous rock

The dynamic mechanical frequency spectrum and temperature spectrum measurements of dry and saturated sandstone with three different porosity are conducted by use of the viscoelastic spectrum instrument in the 0.01～100 Hz frequency region. The frequency responses of the attenuation and modulus at different temperature peaks are obtained. With increase of the porosity and the loss of the complex modulus, the attenuation in the saturated sandstones is increased, and the frequency dispersion is enhanced. The relation between the frequency spectrum and the temperature spectrum are also discussed.

Improving tree health assessment accuracy at low temperatures:considering the effect of trunk ice content on electrical resistance and stress wave tomography

Accurate decay detection and health assessment of trees at low temperatures is an important issue for forest management and ecology in cold areas.Low temperature ice formation on tree health assessment is unknown.Because electric resistance tomography and stress wave tomography are two widely used methods for the detection of tree decay,this study investigated the effect of ice content on trunk electrical resistance and stress wave velocity to improve tree health assessment accuracy.Moisture content,trunk electrical resistance and stress wave velocity using time domain reflectometry were carried out on Larix gmelinii and Populus simonii.Ice content is based on moisture content data.The ice content of both species showed a trend of increasing and then decreasing.This was opposite with ambient temperatures.With the decrease of temperatures,daily average ice content increased,but the range narrowed gradually and both electrical resistance and stress wave velocity increased.Both increased rapidly near 0℃,mainly caused by ice formation(phase change and freezing of free water)in live trees.In addition,both are positively correlated with ice content.The results suggest that ice content should be considered for improving the accuracy of tree decay detection and health evaluation using electric resistance tomography and stress wave velocity methods under low temperatures.

The nonlocal solution of two parallel cracks in functionally graded materials subjected to harmonic anti-plane shear waves

In this paper, the dynamic interaction of two parallel cracks in functionally graded materials （FGMs） is investigated by means of the non-local theory. To make the analysis tractable, the shear modulus and the material density are assumed to vary exponentially with the coordinate vertical to the crack. To reduce mathematical difficulties, a one-dimensional non-local kernel is used instead of a twodimensional one for the dynamic problem to obtain stress fields near the crack tips. By use of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present at the crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tips. The present result provides theoretical references helpful for evaluating relevant strength and preventing material failure of FGMs with initial cracks. The magnitude of the finite stress field depends on relevant parameters, such as the crack length, the distance between two parallel cracks, the parameter describing the FGMs, the frequency of the incident waves and the lattice parameter of materials.

A STUDY ON THE EFFECT OF RADIAL INERTIA ON THE ELASTO-PLASTIC COMBINED STRESS WAVE PROPAGATION IN THIN-WALLED TUBES

An in-depth analysis of propagation characteristics ofelasto-plastic combined stress waves in circular thin-walled tubeshas been made. In obtaining the simple-wave solution, however, mostresearches have ignored the influence of the circumferential stressrelated to the radial inertial ef- fect in the tubes. In this paperthe incremental elasto-plastic constitutive relations which areconve- nient for dynamic numerical analysis are adopted, and thefinite-difference method is used to study the evolution adpropagation of elasto-plastic combined stress waves in a thin-walledtube with the radial inertial effect of the tube considered. Thecalculation results are compared with those obtained when the radialinertial effect is not considered. The calculation results show thatthe radial inertial effect of a tube has a fairly great influence onthe propagation of elasto-plastic combined stress waves.

Effect of sensor quantity on measurement accuracy of log inner defects by using stress wave

Wood nondestructive testing （NDT） is one of the high efficient methods in utilizing wood. This paper explained the principle of log defect testing by using stress wave, and analyzed the effects of sensor quantity on defect testing results by using stress wave in terms of image fitting degree and error rate. The results showed that for logs with diameter ranging from 20 to 40 cm, at least 12 sensors were needed to meet the requirement which ensure a high testing accuracy of roughly 90% of fitness with 0.1 of error rate. And 10 sensors were recommended to judge the possible locations of defects and 6 sensors were sufficient to decide whether there were defects or not.

An extended displacement discontinuity method for analysis of stress wave propagation in viscoelastic rock mass

An extended displacement discontinuity method (EDDM) is proposed to analyze the stress wave propagation in jointed viscoelastic rock mass (VRM).The discontinuities in a rock mass are divided into two groups.The primary group with an average geometrical size larger than or in the same order of magnitude of wavelength of a concerned stress wave is defined as 'macro-joints',while the secondary group with a high density and relatively small geometrical size compared to the wavelength is known as 'micro-defects'.The rock mass with micro-defects is modeled as an equivalent viscoelastic medium while the macro-joints in the rock mass are modeled explicitly as physical discontinuities.Viscoelastic properties of a micro-defected sedimentary rock are obtained by longitudinally impacting a cored long sedimentary rod with a pendulum.Wave propagation coefficient and dynamic viscoelastic modulus are measured.The EDDM is then successfully employed to analyze the wave propagation across macro-joint in VRM.The effect of the rock viscosity on the stress wave propagation is evaluated by comparing the results of VRM from the presented EDDM with those of an elastic rock mass (ERM) from the conventional displacement discontinuity method (CDDM).The CDDM is a special case of the EDDM under the condition that the rock viscosity is ignored.Comparison of the reflected and transmitted waves shows that the essential rock viscosity has a significant effect on stress wave attenuation.When a short propagation distance of a stress wave is considered,the results obtained from the CDDM approximate to the EDDM solutions,however,when the propagation distance is sufficiently long relative to the wavelength,the effect of rock viscosity on the stress wave propagation cannot be ignored.

Tomography of the dynamic stress coefficient for stress wave prediction in sedimentary rock layer under the mining additional stress

In this study,the tomography of dynamic stress coefficient(TDSC)was established based on a mechanical model of stress wave propagation in bedding planes and a mathematical model of the stress wave attenuation in rock masses.The reliability of the TDSC was verified by a linear bedding plane model and field monitoring.Generally,the TDSC in the dynamic stress propagation of bedding planes increases with the following conditions:(1)the increase of the normal stiffness of the bedding plane,(2)the increase of the incident angle of the stress wave,(3)the decrease of the incident frequency of the stress wave,or(4)the growth of three ratios(the ratios of rock densities,elastic moduli,and the Poisson’s ratios)of rocks on either side of bedding planes.The additional stress weakens TDSC linearly and slowly during the stress wave propagation in bedding planes,and the weakening effect increases with the growth of the three ratios.Besides,the TDSC decreases exponentially in the rock mass as propagation distance increases.In a field case,the TDSC decreases significantly as vertical and horizontal distances increase and its wave range increases as vertical distance increases in the sedimentary rock layers.

Influences of Stress Wave Propagation upon Studying Dynamic Response of Materials at High Strain Rates

How the wave propagation analysis plays a key role in the studies of dynamic response of materials at high strain rates is analyzed. For the wave propagation technique, the followings are important: the loading and unloading constitutive relation presumed, the positions of the sensors embedded, the interactions between loading waves and unloading waves. For the split Hopkinson pressure bar (SHPB) technique, the assumption of one-dimensional stress wave propagation and the assumption of stress uniformity along the specimen should be satisfied. When the larger diameter bars are employed, the wave dispersion effects should be considered, including the high frequency oscillations, non-uniform stress distribution across the bar section, increase of rise time, and amplitude attenuation. The stress uniformity along the specimen is influenced by the reflection times in specimen, the wave impedance ratio of the specimen and the bar, and the waveform.

Numerical simulations of stress wave propagation and attenuation at arc-shaped interface inlayered SiC/Al composite

The effects of interface shape on stress wave distribution and attenuation were investiga- ted using finite element method （ FEM ）. The simulation results indicate that when the stress wave propagates from SiC ceramic to A1 alloy, the tensile stress decreases and the attenuation coefficient of the stress wave increases with increasing central angle of the concave interface between SiC and A1. But for the convex interface, the tensile stress increases and attenuation coefficient decreases with increasing central angle. As the stress wave propagates from A1 alloy to SiC ceramic, the atten- uation coefficient of stress wave decreases with increasing the central angle of the concave interface. For the convex interface, the attenuation coefficient increases with increasing central angle.

SCATTERING OF THE HARMONIC STRESS WAVE BY CRACKS IN FUNCTIONALLY GRADED PIEZOELECTRIC MATERIALS

The present paper considers the scattering of the time harmonic stress wave by a single crack and two collinear cracks in functionally graded piezoelectric material （FGPM）. It is assumed that the properties of the FGPM vary continuously as an exponential function. By using the Fourier transform and defining the jumps of displacements and electric potential components across the crack surface as the unknown functions, two pairs of dual integral equations are derived. To solve the dual integral equations, the jumps of the displacement and electric potential components across the crack surface are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the influences of material properties on the dynamic stress and the electric displacement intensity factors.