Elastic Precursor Wave Research Articles

Plastic deformation of [001]-oriented single-crystal iron under shock compression: Effects of void size

The thermomechanical behavior of materials is known to be sensitive to preexisting defects in their microstructure. In this paper, non-equilibrium molecular dynamics simulations have been used to investigate the effects of the microvoid size on the plastic deformation in single-crystal iron shock-compressed along the [001] crystallographic direction. The higher the microvoid radius, the faster the kinetics of dislocations. Thus, as the microvoid radius increases, the plastic activity evolves from a regime where the deformation is dominated by twin activities to a regime where both twin and dislocation activities play an essential role and then to a regime where the deformation is dominated by dislocation slip. Furthermore, in both defect-free and defective initial crystal states, the elastic precursor wave is observed to decay with propagation distance, resulting in a constitutive functional dependence of the yielding pressure, σE, on the plastic deformation rate, ε˙p. In the regime where both deformation twinning and dislocation slip play important roles, the constitutive behavior is consistent with the original Swegle–Grady model and is in overall agreement with experimental data and thermomechanical simulations.

Stress wave propagation and force transmission in polymeric closed cell foams subjected to air shock loading

Polymeric foams are widely used in sandwich structures to withstand blast loadings, serving as energy dissipators and force attenuators. This study explores the mechanics involved when an air shock interacts with closed-cell polymeric foam. The authors provide a comprehensive analysis of stress wave propagation and its evolution across the foam specimen by employing ultra-high-speed imaging and digital image correlation (DIC). Measurement of elastic, plastic, and shock wave velocities inside the impacted foam was conducted. A methodology to predict elastic precursor wave velocity is proposed, that considers the foam material’s behavior at higher strain rates. The predicted values were found to be in excellent agreement with the experimentally obtained values. Furthermore, the authors investigate the force transmission through foams as a function of bulk foam density under unconfined conditions. The results reveal that under shock loading intensities where foam specimens remained in their elastic regime, a transmitted force amplification was observed relative to the input load. However, when subjected to higher-intensity shock loading, substantial foam deformation occurs during the initial propagation of the shock wave. In these cases, the transmitted force measured was found to rely on the plastic and shock waves generated within the material. Additionally, as the loading persists, the force transmissibility ratio decreases beyond the initial stress wave propagation phase, thus demonstrating the material’s suitability for blast mitigation applications.

Understanding the So Called “Anomalous Thermal Strengthening” of Elastic Precursor Decay Tests

Some time ago a Russian shock physics group performed planar impact tests on thin metal targets (1mm or less) at different temperatures. They were able to observe the elastic precursor wave amplitudes at different target thicknesses and for different target temperatures. They concluded from the test results that the elastic precursor wave decay rate was lower for higher test temperatures, or as they phrased it, dynamic strength increases with temperature. Such a behavior is counter intuitive, as we are used to believe from our experience with quasistatic viscoplastic response, that strength should decrease with temperature. Accordingly, these results of the Russian group were referred to by them as "Anomalous Thermal Strengthening". Our purpose here is to reproduce such test results using a hydrocode. To this end we do the following: 1) we change the way our hydrocode computes dynamic viscoplastic response, from the usually used radial return approach to the more appropriate overstress approach; 2) we compute a planar impact example and reproduce an elastic precursor decay behavior; 3) we show how the quasistatic part of the response can be separated from dynamic part; and 4) we make the quasistatic and the dynamic response parts depend separately on temperature, and in this way we’re able to reproduce the elastic precursor wave increase with temperature, as observed in the above mentioned tests. &nbsp

A comparative investigation of shock response in high entropy Cantor alloys by MEAM and LJ type potentials

We assess the effect of interatomic potential in determining the shock response of the high entropy Cantor alloy through large scale non-equilibrium molecular dynamics simulations. In literature, two different potentials have been suggested for modelling Cantor alloys at atomic scale – the 2NN MEAM potential, henceforth termed as the MEAM potential, and the Lennard-Jones (LJ) type-potential. We show that the MEAM potential results in a different shock response than the LJ type-potential – (i) the shock wave speed and the pressure behind the shock front are smaller for MEAM than the LJ type-potential, (ii) no twinning is observed with the MEAM potential along the [100] direction unlike that with the LJ type-potential, and (iii) the shock induced phase transition from FCC to HCP is observed along the [100] direction only with the LJ type-potential. Our numerical results with the LJ type-potential are in agreement with the experiments as well, where twinning and phase transition have been observed. Looking at the morphology of the post-shocked samples at different times, we identify the mechanism behind the phase transition. Lastly, we subject the post-shocked structure to uniaxial tensile tests to show that for the [111] direction, a greater fracture strain than the unshocked structure is obtained, suggesting a higher fracture toughness. • Used 2-NN MEAM and LJ-type potential to study the effect of shock loading in Cantor alloy. • The LJ-type potential results in higher shock pressure and shock speed as compared to MEAM. • The elastic precursor wave is overdriven by the plastic wave along [100], unlike the [110] and [111] directions. • Plastic deformation by slipping and twinning in [100] direction is observed with LJ-type, consistent with experiments, unlike the MEAM potential. • Disordered phases along [110] and [111] directions increases the fracture toughness in after-shocked samples.

Experimental and numerical study on the effect of electrohydraulic shock wave on concrete fracturing

In order to apply electrohydraulic shock wave (EHS) technology to oil and gas stimulation or assisted rock fracture, it is necessary to analyze how the crack propagation behavior of the rock subjected to the EHS. For this purpose, experiments and numerical simulations are carried out respectively. In the experiment, the relevant parameters of electrical characteristics and acoustic radiation characteristics were given based on the established discharge platform, and 30 times impacts tests are carried out on cubic concrete. The results show that the corner areas of the upper surface of the concrete are the first to be broken; with the increase of impact time, the shape and number of cracks on the surface of the concrete sample change in two stages. In the first stage, the number of microcracks increased rapidly, the cracks are interconnected, and the existing pores gradually become bigger. In the second stage, the growth rate of the number of microcracks gradually decreases, and the width of the formed cracks gradually increases; the damage variable of the concrete obtained by the acoustic test increases sharply first and then increase slowly throughout the impact test. In the numerical simulation, the history match of the EHS pressure is implemented based on the equivalent explosion method (EEM); a two-dimensional numerical model is established to simulate the interaction process between the EHS and the concrete sample; a three-dimensional TNT-water-concrete numerical model is built to simulate the concrete fracturing. The results show that it is reliable to use the equivalent explosion method to simulate the EHS. The concrete sample subjected to the EHS is affected by four aspects: bubble; transmitted wave and reflected wave; diffraction wave; elastic precursor wave and plastic loading wave. When the element deletion method is used to simulate crack generation, adopting the maximum tensile stress failure criterion can accurately simulate the final distribution of cracks, but it is difficult to simulate the evolution process of cracks under cyclic impact loads.

Simulation of Non-Shock Loading of Tantalum

We discuss and perform hydrocode simulations of gradual dynamic loading of tantalum. We show that using the generally accepted approach to viscoplastic response, it’s not possible to reproduce some features of the test results. But when we use our overstress approach, we’re able to reproduce those features, including the initial spike of the elastic precursor wave.  

Shock Hugoniot of porous nanosized nickel

The shock compression of porous nickel from nanosized particles nNi was studied at a pressure range of 4–61 GPa. The average size of the nNi particles was 50 nm, and the porosity of the samples was 50%. Plane shock waves in the samples were generated by the impact of aluminum plates accelerated to velocities ranging from 0.8 to 5 km/s. Laser interferometry was used to monitor particle velocity histories at the interface between the samples and water or LiF windows. The data obtained at pressures below 8 GPa showed a complex shock wave profile with the formation of an elastic precursor wave. The shock Hugoniot and data on the expansion isentropes were obtained. The Hugoniot of nanosized nNi coincided within the experimental errors with the Hugoniot of micron-sized nickel. The Hugoniot calculated on the basis of the equation of state for porous nickel was in good agreement with that of experimental data. It has been established that in the middle pressure range (20–35 GPa), the expansion isentropes in the “pressure–particle velocity” coordinates become noticeably flatter with a significant increase in the particle velocity. The reason for this phenomenon is still unclear. An assumption was made about the onset of particle melting upon reaching pressures above 15 GPa.

Numerical modeling of dynamic response and microcracking in shock-loaded polycrystalline transparent ceramic

Transparent ceramics are promising materials in the fields of high pressure and high temperature. Based on a lattice-spring simulation method, a novel polycrystalline model for shock-wave compression is established to explore the dynamic response and damage evolution of yttrium aluminum garnet (YAG) under shock loading. The macro-response and micro-fracture process under impact loading can be obtained simultaneously, and a correlation between the macroscopic response and mesoscale damage is shown. The process of crack propagation along a grain boundary and through grain-boundary deflection is observed in the simulation. A change in deformation behavior from intergranular fracture to transgranular fracture in the vicinity of grain boundaries, associated with the transition from an elastic response to a plastic response, is observed, as the shock stress increases from below to above the Hugoniot elastic limit. Computational results demonstrate a clear, exponential attenuation of the elastic precursor wave with the propagation of shock waves. The reasons for the elastic precursor decay and the transition from an elastic response to a plastic response are the stress relaxation and energy dissipation caused by internal transgranular fracture. The polycrystalline model will aid in microstructure design and provide a reference for the development of polycrystalline transparent ceramics in the fields of engineering and scientific research.

Resistance to high-rate deformation and fracture of lead at normal and elevated temperatures in the sub-microsecond time range

Using measurements of the evolution of shock compression pulses and the rise time of plastic shock waves, the dependences of the yield stress and dynamic tensile strength (spall strength) of lead were determined depending on the strain rate in a range of 104 to 107 s−1 at room temperature and at 280–310 °C. Similar to other metals with a face-centered cubic structure, the dynamic yield stress of lead under these conditions increased abnormally as the temperature increased. At room temperature, the plastic strain rate in the shock wave did not significantly differ from the initial rate in the elastic precursor wave at the same value of the shear stress, but significantly exceeded it at 280 °C.

Shock wave characterization of precipitate strengthening of PH 13–8 Mo stainless steel

The shear stresses required for dislocations passage of highly coherent NiAl-based precipitates, formed in commercial PH 13–8 Mo steel after homogenization, quenching and aging for different duration of time at 510 °C, were determined in a series of planar impact experiments using samples with different thickness. The experiments revealed two regimes of decay of the elastic precursor waves: a fast one, at the shear stress τ greater than some threshold τ*, associated with the interaction of moving dislocations with lattice phonons, and a slow one, at τ < τ*, corresponding to the precipitates' cutting with the help of thermal fluctuations. Consequently, the stress τ* can be regarded as the stress which permits the passage of the precipitate by a dislocation without thermal support. Precipitates' geometry and size, determined based on the activation volume at thermally-activated regime, are in a reasonable agreement with precipitates dimensions estimated from High Resolution Transmission Electron Microscopy images.

Shock wave compression behavior and dislocation density evolution in Al microstructures at the atomic scales and the mesoscales

Molecular dynamics simulations are carried out to investigate the deformation response during shock compression of nanocrystalline Al microstructures at the atomic scales. The shock response is investigated for various grain sizes (18 nm–100 nm) and impact velocities (700 m/s to 1500 m/s). The simulations suggest an increase in shock front width and a decay in the velocity and the amplitude of the elastic precursor wave (Hugoniot elastic limit) as the wave travels through the microstructure. For a limited sample depth of 500 nm of polycrystalline Al, the Hugoniot elastic limit (HEL) values are higher for larger grain sizes due to a lower density of grain boundaries and higher for higher piston velocities/shock pressures. Quasi-coarse-grained dynamics (QCGD) simulations are carried out to extend this investigation of the shock response of polycrystalline microstructures to the mesoscales. The capability of QCGD simulations to reproduce the atomic scale evolution of dislocation density fractions and shock wave structures is first demonstrated for a 100 nm grain-sized Al system. The evolution of shock front width, HEL, and dislocation densities are investigated for microstructures with grain sizes ranging from 100 nm to 800 nm and system lengths ranging from 600 nm to 9.6 μm. The MD and QCGD simulations indicate that the decay behavior is attributed to the capability of the shock wave to generate Shockley partial dislocations in the compressed microstructure. The simulations indicate that grain size and impact velocities affect the rates of generation of Shockley partials and hence affect the decay of the HEL. The MD and QCGD predicted values for HEL reported here show excellent agreement with the experimentally observed sample thickness dependence for Al. An empirical model is developed to predict the HEL of Al microstructures with grain size, shock pressure and sample depth as variables.

Shock wave determination of the strengthening of commercial aluminum alloy 6061 by point defects

The strengthening of aluminum alloy 6061 (AA6061) by different point defects was determined experimentally using a shock wave technique. Decay of the amplitude of elastic precursor wave τel with propagation distance h was studied in four groups of AA6061 samples, namely, that in the super-saturated solid solution state (SSSS), and those strengthened by atomic clusters (short-range order), by Guinier-Preston zones I and by Guinier-Preston zones II after, respectively 7.5, 240 and 960 min aging of the SSSS samples at 145 °C. The dependences τel(h) were found to be kinked at stress τ*, corresponding to the transition of the control of dislocation motion from phonon viscous drag at τel>τ* to thermally activated obstacle passage at τel<τ*. The values of strengthening by atomic clusters, GP-I, and GP-II zones were found equal to τsro=67, τGP-I=67, and τGP-II=124MPa, respectively. Activation volumes corresponding to the interaction of dislocations with the studied defects, estimated based on τel<τ* segments of the measured dependences τel(h), were found to be in reasonable agreement with existing concepts of dislocation/defect interactions.

In situ dynamic compression wave behavior in additively manufactured lattice materials

The dynamic response of structured materials, such as regular lattices, is nontrivial partly due to the interaction of mechanical waves throughout the structure and free surfaces as the material is dynamically compressed. The existence of an elastic precursor wave in additively manufactured lattices was recently shown to match theoretical predictions and simulation results. Following up on this work, we have investigated the behavior of the elastic precursor with propagation distance, impact speed, and impact material. Through a series of gas gun experiments coupled to X-ray phase contrast imaging measurements and complementary simulations, the elastic precursor wavespeed appears to be nearly independent of impact speed and impact material. We observed evidence for the sustained elastic wave propagation through many unit cells at four significantly different impact conditions. We compared these results with direct numerical simulations of the experiments and found good agreement.

Abnormal temperature effects on the dynamic yield stress of alpha-brass

The evolution of elastic-plastic wave in 70Cu-30Zn brass was measured so as to obtain information about its dynamic strength properties at normal and elevated temperatures. The different propagation velocities of plastic shock recorded in as-rolled and annealed brass can be explained in terms of a strong work-hardening. Measuring the decay of an elastic precursor wave revealed a transition from high-rate to low-rate mechanisms of plastic deformation. Unexpectedly, the flow stresses grow with increasing the temperature in both regimes. While at high strain rates this effect can be explained by phonon drag mechanisms, abnormal thermal hardening at a lower strain rate is apparently associated with different levels of short range order in the alloy at normal and elevated temperatures.

Elastic precursor wave decay in shock-compressed aluminum over a wide range of temperature

The effect of temperature on the dynamic flow behavior of aluminum is considered in the context of precursor wave decay measurements and simulations. In this regard, a dislocation-based model of high-rate metal plasticity is brought into agreement with previous measurements of evolving wave profiles at 300 to 933 K, wherein the amplification of the precursor structure with temperature arises naturally from the dislocation mechanics treatment. The model suggests that the kinetics of inelastic flow and stress relaxation are governed primarily by phonon scattering and radiative damping (sound wave emission from dislocation cores), both of which intensify with temperature. The manifestation of these drag effects is linked to low dislocation density ahead of the precursor wave and the high mobility of dislocations in the face-centered cubic lattice. Simulations performed using other typical models of shock wave plasticity do not reproduce the observed temperature-dependence of elastic/plastic wave structure.

Peculiarities of evolutions of elastic-plastic shock compression waves in different materials

In the paper, we discuss such unexpected features in the wave evolution in solids as strongly nonlinear uniaxial elastic compression in a picosecond time range, a departure from self-similar development of the wave process which is accompanied with apparent sub-sonic wave propagation, changes of shape of elastic precursor wave as a result of variations in the material structure and the temperature, unexpected peculiarities of reflection of elastic-plastic waves from free surface.

Invariability of rate dependences of normalized flow stress in niobium and molybdenum under conditions of shock compression

The evolution of elastic-plastic shock waves has been studied in pure molybdenum and niobium at normal and elevated temperatures over propagation distances ranging from 0.03 to 5 mm. The experiments revealed that annealing of the metals substantially increases their Hugoniot elastic limits and, to a lesser degree, their spall strengths. Variations in the resistance of both the metals to fracture in tension with the test temperature can be described as modest. Measuring the decay of the elastic precursor waves with a propagation distance in the two metals has allowed a determining of the relationships between a flow stress τ and an initial plastic strain rate γ̇p. It was found that, at the plastic strain rates greater than 3÷4×104s−1, the temperature sensitivity of the transient values of τ is much lower than that at the strain rates below this range. The τ(γ̇p) data normalized on shear moduli of the metals have been approximated by simple functions that, despite substantial differences between the moduli and yield stresses, were found to be virtually identical for the two metals.

Experimental investigation on blast response of cellular concrete

A test setup consisting of a shock-tube with an instrumented short rod is developed for investigating the blast response of cellular concrete foams. In the shock tube facility, blast pressure wave is generated by the rupture of a notched aluminum membrane. An instrumented rod is calibrated for measuring transmitted stress from the cellular foam. Experiments are conducted on brittle cellular concrete foam, which exhibits non-linear stress–strain behavior associated with crushing of the cellular structure and subsequent densification. Crushing is initiated when the stress exceeds the crushing strength and continued crushing produces an upward concave stress–strain curve leading to densification of the material. Foams with two different crushing strengths are evaluated. The influence of the length of the foam is investigated. For an applied blast pressure amplitude, which is higher than the crushing strength of foam, the wave structure in the foam consists of an elastic precursor wave followed by a compaction front that produces crushing of the cellular structure of the material. From the experimental investigation, the existence of a critical length for completely attenuating the applied blast pressure wave is established. For a given blast pressure loading, when the length of foam is larger than the critical length, the applied blast pressure wave is transmitted as a rectangular pulse of nominally constant magnitude, which is slightly higher than the crushing strength of the foam. The foam is compacted without significant densification. The critical length depends on the crushing strength of the foam and the blast pressure amplitude and duration. If the length of the foam is smaller than the critical length, there is an enhancement in the transmitted stress amplitude. If the length of foam is significantly smaller than the critical length, the transmitted stress is enhanced to a magnitude higher than the applied blast pressure amplitude and the compaction of foam leads to significant densification of the material.

Rate and temperature dependences of the yield stress of commercial titanium under conditions of shock-wave loading

The evolution of elastic-plastic shock waves with the propagation distance has been studied in annealed titanium of commercial purity at temperatures 20 °C and 600 °C. The free surface velocity histories of the shock-loaded samples 0.25–4.0 mm in thickness have been recorded using the Velocity Interferometer System for Any Reflector. The measured decays of the elastic precursor waves have been converted into relationships between the shear stress and the initial plastic strain rate at the Hugoniot elastic limit. It has been found that the temperature practically does not influence on the resistance to high-rate plastic deformation: the plastic strain rate varies with the shear stress as γ̇=2.5×106(τ/τ0)4.8 s−1 at 20 °C and γ̇=2.9×106(τ/τ0)4.9 s−1 at 600 °C. An analysis of the rise times of the plastic shock waves has shown that for the same level of shear stress, the plastic strain rate after small compressive strain is more than by order of magnitude higher than the initial plastic strain rate at the wave's foot. Such acceleration of the plastic deformation seems to be a result of an intense multiplication of the mobile dislocations or twins.

Mesomechanism of elastic precursor decay in alumina under plate impact loading

The Hugoniot elastic limit (HEL) of ceramics is explained as the limit of elastic response and the onset of failure under dynamic uniaxial strain loading, which is an important parameter for understanding the dynamic properties of ceramic materials. Previous experimental impact studies showed an interesting phenomenon that the HEL decreases with the increase of sample thickness, which is termed the elastic precursor decay. This phenomenon has not been explained by a suitable mechanism to date. Recently it has become apparent that mechanical response of polycrystalline ceramics is governed by mechanism operating at a grain level. So the objective of the present work is to develop a mechanism that can illustrate this phenomenon on a mesoscale. In this paper, the plate impact experiments of alumina with varying thickness values are conducted by using one-stage light gas gun. The histories of the rear free surface velocity of the samples are recorded by a Velocity Interferometer System for Any Reflector (VISAR). The HELs of alumina samples with different thickness values are obtained from turning point of elastic phase to inelastic phase in the temporal curves of free surface velocity. It is confirmed that the HEL of alumina decreases with increasing the sample thickness obviously, namely elastic precursor decay phenomenon. It is considered that this phenomenon is related to the failure mechanism of shocked alumina at a grain level. Thus, the mesoscopic model of alumina, including alumina grain phase and glass binder phase, is developed according to the microstructure properties of tested sample observed experimentally. Mesoscale simulations are presented to study the mesoscale failure properties of alumina at various impact velocities. The results show that inelastic responses, such as microcracking, grain plasticity, are observed in microstructure of alumina even when the peak-shock stress is less than the magnitude of HEL. As is well known, the evolution process of cracking or plasticity is the energy dissipation process essentially, which will reduce the amplitude of elastic wave. Furthermore, the properties of elastic precursor wave propagation in microstructure of alumina are also captured in the present simulations. Since the acoustic impedance of glass binder phase is much lower than that of alumina grain phase, complex reflection and transmission of elastic wave will occur at grain boundaries. Due to a large number of randomly oriented crystals, the wave front, well defined at the continuum, is dispersed to lateral or reverse directions at these length-scales, which can also decay the elastic precursor amplitude in the initial propagating direction. Therefore, the results suggest that energy dissipation caused by the failure process should occur below HEL and energy dispersion due to reflection and transmission of elastic wave at grain boundaries should play a dominant role in the phenomenon of elastic precursor decay.