Elastic-plastic Wave Research Articles

Численный анализ остаточных напряжений при двухстороннем симметричном лазерном ударном упрочнении тонких пластин из титанового сплава ВТ6

Laser shock peening technology allows residual stresses of the first type (according to Davidenkov) to be generated (at a depth of more than 1 mm) in the near-surface zone of products made of metals and alloys. Extensive experimental studies demonstrate that laser shock peening significantly improves their mechanical properties, increases fatigue life, protects against corrosion. However, when applying this technology to products of rather small thickness (e.g., edges of turbine blades, blades of cutting tools) it is necessary to select such parameters of laser pulse impact that will not cause shape change. This paper presents an approach to numerical modelling of the formation of residual stress fields under laser shock treatment when reducing the thickness of products from 3 to 0.35 mm and by varying the magnitude and sequence of laser pulse application. The Johnson-Cook constitutive relation was used for modelling the propagation of elastic-plastic waves. After that, the static calculation of residual stress distribution was performed taking into account the created plastic strain fields. The obtained residual stress fields were compared with each other under different conditions of impact on the workpiece: single-sided treatment; double-sided sequential treatment; double-sided symmetric treatment. Analysis of the calculated stress fields indicated that double-sided symmetric impact is an effective technique for creating a compressive residual stress field in the near-surface zone of products with a thickness of less than 1 mm. At such hardening, it is possible to avoid bending of products and formation of tensile stress fields. It was revealed that, on the one hand, increasing laser intensity (modulo) increases the value of the minimum main residual (compressive) stress in the treatment zone, and, on the other hand, it also increases the maximum main residual (tensile, balancing) stress at a distance from the impact zone.

Elastic–plastic wave propagation in phononic crystals

Elastic–plastic wave propagation in phononic crystals

Orientation-dependent multi-spall performance of monocrystalline NiTi alloys under shock compression

The primary objective of this work was committed to large-scale non-equilibrium molecular dynamics modeling for the investigation on multiple spall performance, microstructural evolutions, and melting state of NiTi alloys along three typical crystal orientations. We discovered that there was a single-wave structure present in the [100] orientation, whereas elastic-plastic two-wave structures were found in [110] and [111], exhibiting a significant anisotropy in elastic-plastic wave velocity. Compared to [110] and [111] orientations, multi-spallation was more likely to be generated in the [100] direction. During accumulative dynamic damage, there was also a strong sensitivity of void evolution to orientation. For [100], voids tended to be densely distributed in the material and exhibited a strip-shaped manner. In contrast, a more scattered void distribution was observed for the other two orientations, showing a flaky pattern. Interestingly, dislocations in the spall region were almost annihilated before approaching void nucleation. According to void statistics, the peak number of voids, void nucleation rate, and spall region size were identified to be in a good uniformity along [110], [100], and [111]. For all the cases, the samples experienced partial melting in the released state and were followed by a recovery of structural order degree. However, there was an insignificant anisotropy in the melting state for each crystal orientation during multi-spallation.

Influence of the Elastic-Plastic Dynamic Artificial Boundary on the Progressive Collapse Performance of Truss Structures

The traditional fixed boundary could not transmit the elastic-plastic stress waves in the progressive collapse analysis of the truss structures, leading to discrepancies in understanding the true response of structures. To solve the critical problem, a new dynamic artificial boundary is proposed and integrated into the truss structure to transmit elastic-plastic stress waves. The new dynamic artificial boundary is established through the integration of the elastic-plastic constitutive model into the governing equation of the stress wave. This boundary is subsequently implemented within the ABAQUS finite element software for the purpose of conducting progressive collapse analysis of the truss structures. The progressive collapse simulation of the truss structures involves a comparative analysis between the new dynamic artificial boundary and the traditional fixed boundary. Numerical analysis demonstrates that the dynamic artificial boundary led to varied initial failure and collapse compared to the fixed boundary. The failure typically occurs at the mid-span under the dynamic boundary. In contrast, additional failures occur near the support columns under the fixed boundary due to stress wave reflections. The dynamic artificial boundary more closely reflects the physical reality and provides a new method for the progressive collapse analysis of the truss structures in practical applications.

Correlation between grain size and dynamic response of NiTi alloy during intense shock-induced multi-spallation

This work committed to performing non-equilibrium molecular dynamics simulations to explore the influence of grain size on multi-spall performance of nanocrystalline nickel-titanium (NiTi) alloy. By comparing the calculated Hugoniot relationship with present experimental results, the Finnis-Sinclair (FS) type potential used in this work was verified to be suited for reproducing the shock behavior of NiTi alloy at high strain rate. During shock wave evolution, a single plastic wave was clearly observed in the sample with grain size of 5 nm, while there was a more pronounced elastic-plastic double wave structure at larger grain size. According to the free surface velocity history, the predicted spall strength exhibited a decreasing tendency and subsequently increased when the grain size decreased from 50 to 5 nm, indicative of a critical grain size (10 nm). Correspondingly, there were multiple spall planes appearing in the sample, the grain size of which was not smaller than the critical one. Contrarily, a single spall plane was observed at 5 nm. By counting the void distribution statistic, we found that as the grain size increased, the void-nucleation behavior changed from the intergranular to intergranular/transgranular coexisting pattern. In consequence, more nucleation sites were provided to promote an increase in the number of voids. Interestingly, for intergranular, there were much more voids involved in spallation at smaller grain size, which was attributed to grain boundary effect. The results demonstrated that void evolutions rarely occurred at the grain boundaries parallel to the loading direction. Moreover, when the grain size was larger than 5 nm, the B19 phases were found to be produced around those potential void-nucleation sites. After void nucleation, these B19 phases decreased till disappearance, accompanied by the proliferation of a large number of [100] dislocations. Such dislocations accumulated in the region without voids could block the void growth in this region, which was expected to be the reason for the formation of multiple spall planes. On the contrary, the absence of dislocations at 5 nm was inclined to the fact that the space for dislocation emission and aggregation was preoccupied by nucleated voids.

Direct imaging of shock wave splitting in diamond at Mbar pressure

Understanding the behavior of matter at extreme pressures of the order of a megabar (Mbar) is essential to gain insight into various physical phenomena at macroscales—the formation of planets, young stars, and the cores of super-Earths, and at microscales—damage to ceramic materials and high-pressure plastic transformation and phase transitions in solids. Under dynamic compression of solids up to Mbar pressures, even a solid with high strength exhibits plastic properties, causing the induced shock wave to split in two: an elastic precursor and a plastic shock wave. This phenomenon is described by theoretical models based on indirect measurements of material response. The advent of x-ray free-electron lasers (XFELs) has made it possible to use their ultrashort pulses for direct observations of the propagation of shock waves in solid materials by the method of phase-contrast radiography. However, there is still a lack of comprehensive data for verification of theoretical models of different solids. Here, we present the results of an experiment in which the evolution of the coupled elastic–plastic wave structure in diamond was directly observed and studied with submicrometer spatial resolution, using the unique capabilities of the x-ray free-electron laser (XFEL). The direct measurements allowed, for the first time, the fitting and validation of the 2D failure model for diamond in the range of several Mbar. Our experimental approach opens new possibilities for the direct verification and construction of equations of state of matter in the ultra-high-stress range, which are relevant to solving a variety of problems in high-energy-density physics.

Unraveling Anisotropy in Crystalline Orientation under Shock-Induced Dynamic Responses in High-Entropy Alloy Co25Ni25Fe25Al7.5Cu17.5.

Shock-induced plastic deformation and spall damage in the single-crystalline FCC Co25Ni25Fe25Al7.5Cu17.5 high-entropy alloy (HEA) under varying shock intensities were systematically investigated using large-scale molecular dynamics simulations. The study reveals the significant influence of crystalline orientation on the deformation mechanism and spall damage. Specifically, the shock wave velocities in the [110] and [111] directions are significantly higher than that in the [001] direction, resulting in a two-zone elastic-plastic shock wave structure observed in the [110] and [111] samples, while only a single-wave structure is found in the [001] sample. The plastic deformation is dominated by the FCC to BCC transformation following the Bain path and a small amount of stacking faults during the compression stage in the [001] sample, whereas it depends on the stacking faults induced by Shockley dislocation motion in the [110] and [111] samples. The stacking faults and phase transformation in the [001] sample exhibit high reversibility under release effects, while extensive dislocations are present in the [110] and [111] samples after release. Interestingly, tension-strain-induced FCC to BCC phase transformation is observed in the [001] sample during the release stage, resulting in increased spall strength compared to the [110] and [111] samples. The spall strength estimated from both bulk and free surface velocity history shows reasonable consistency. Additionally, the spall strength remains stable with increasing shock intensities. The study discusses in detail the shock wave propagation, microstructure change, and spall damage evolution. Overall, our comprehensive studies provide deep insights into the deformation and fracture mechanisms of Co25Ni25Fe25Al7.5Cu17.5 HEA under shock loading, contributing to a better understanding of dynamic deformation under extreme environments.

Shock-induced dynamic response in single and nanocrystalline high-entropy alloy FeNiCrCoCu

The high-entropy alloys (HEAs) exhibit some unique atomic-scale plastic deformation mechanisms under extreme loading conditions (e.g., shock). Here, four samples are characterized and compared, including nanocrystalline and single-crystal samples in [001], [110], and [111] directions, in terms of their shock-induced dynamic plasticity and failure. Extensive molecular dynamics (MD) simulations show that the anisotropic crystal properties of FeNiCrCoCu HEA significantly affect the Hugoniot elastic limit and the corresponding two-zone elastic-plastic shock wave structures. Importantly, the plastic deformation mechanisms are also tuned by crystal anisotropy. The plastic deformation of the single-crystal sample along [001] direction is dominated by nanotwins and dislocation slip, while those of the other samples only exhibit dislocation slip. The nanotwins are formed by two adjacent stacking faults. In terms of the spallation, the critical shock intensities are different for the four samples. The shock speed threshold of spallation along the [001] and [111] directions is 0.7 km/s, while the [110] direction of 0.6 km/s. Nanocrystalline HEA shows a similar shock speed threshold with the single crystal along [110] direction. The simulation results of spall strength exhibit little discrepancy with the increase of shock velocity. In nanocrystalline HEA, the presence of grain boundaries leads to a low spall strength. During the spall evolution, the voids of single crystals nucleate in the amorphous region formed by the interaction of stacking faults. The spall defects of nanocrystalline samples display a heterogeneous nucleation mechanism at the grain boundaries.

An analytical method for the spherical stress wave equation in linear hardening materials

An analytical method for the spherical stress wave equation in linear hardening materials under impact loading is given in this paper. In this method, the elastic, unloading and plastically loading wave equations are solved, separately. In the elastic region, the solutions under different wave velocity ratio conditions are given. In the unloading region and the plastically loading region, the general solutions of the equations are given and the ordinary differential equations of the arbitrary functions are obtained. And then the exact solutions of the equations are given. The stress contour diagrams in the medium under typical loading conditions are given by the analytical method. The correctness of the analytical method is verified by comparing with the numerical results. On the stress contour diagrams, the discontinuities of the analytical results are clearer than that of the numerical results. A parametric study is conducted to show the effects of the parameters on the behaviour of stress distributions. This method can be useful for the rapid calculation of the elastic-plastic spherical stress waves in engineering and the theoretical analysing and law studying of the elastic-plastic spherical stress wave researches.

Attenuation and inflection of initially planar shock wave generated by femtosecond laser pulse

Evolution of wavefront geometry during propagation and attenuation of initially planar shock waves generated by femtosecond laser pulses in aluminum is studied. We demonstrate that three stages of shock front inflection take place in consistent hydrodynamics and molecular dynamics simulations.During the first stage, the distance traveled by a near-planar wave DSW≲RL is smaller than the radius of heated laser spot RL. Wave attenuation is associated with one-dimensional plane (1D) rarefaction wave coming from the free surface. Such rarefaction wave shapes the shock wave to a 1D triangular pressure profile along direction normal to target surface with a shock front followed by an unloading tail. The second transitional stage starts after propagation of DSW∼RL, at which the unloading lateral waves begin to arrive to a symmetry axis of flow and initiate inflection of the initially planar shock front. Next at the third stage, the wavefront geometry is finally rounded and rapid attenuation of shock pressure begins at DSW≳RL.It is shown that such divergent shock wave cannot generate plastic deformations in aluminum shortly after propagation of DSW∼RL. Thus, we may estimate the maximal peening depth as a radius of focal spot, which sets an upper limit for the laser shock peening.The cessation of plastic deformation is caused by the fall of the shockwave amplitude below the elastic limit. In this case, the elastic-plastic wave transitions to a purely elastic mode of propagation. For large-sized light spots, this transition ends in the 1D mode of propagation.

Method of theoretically calculating spherical stress wave field in linear-hardening materials under impact load

Based on the linear hardening plastic constitutive model, the theoretical solution of the elastic-plastic spherical stress wave field under impact load is established. Firstly, the influence of the impact load unloading rate on the propagation of the spherical stress wave is analyzed, and three different types of propagation images are obtained. On this basis, the method of theoretically calculating the spherical wave equation in elastic stage, plastic loading stage and unloading stage is established separately, and the calculation scheme of particle displacement, particle velocity, stress and strain is given. Compared with the existing theoretical methods, this method takes into account the different propagation patterns of the stress waves under different unloading rates, and shows how to calculate the stress wave parameters in unloading stage, which is more applicable. This method is used to calculate the elastic-plastic spherical stress wave field under constant shock load and exponential attenuation shock load. The calculated results are in good agreement with those from the existing theoretical method and numerical simulation results in the elastic stage and also in the plastic loading stage. In the unloading stage, the existing theoretical method is no longer applicable, while the results obtained in this paper are in good agreement with the numerical simulation results, which verifies the correctness of the theoretical method.

Структура волны сжатия при плоском ударном деформировании монокристалла молибдена [100] с различной начальной плотностью дислокаций

The features of the evolution of the elastic-plastic compression wave in Mo single crystals along the crystallographic plane [100], having a different initial dislocation structure formed by small deformations of varying degrees of static compression at room temperature, have been studied. The analysis of wave profiles recorded using the VISAR laser interferometer in samples of different thicknesses showed a non-monotonic change in the hugoniot elastic limit depending on the initial dislocation density – pre-strain of a single crystal by compression reduces the hugoniot elastic limit by 3 times.

Compression wave structure under plane impact deformation of a molybdenum single crystal [100] with different initial density of dislocations

The features of the evolution of the elastic-plastic compression wave in Mo single crystals along the crystallographic plane [100], having a different initial dislocation structure formed by small deformations of varying degrees of static compression at room temperature, have been studied. The analysis of wave profiles recorded using the VISAR laser interferometer in samples of different thicknesses showed a non-monotonic change in the Hugoniot elastic limit depending on the initial dislocation density pre-strain of a single crystal by compression reduces the Hugoniot elastic limit by 3 times. Keywords: Single crystal, small deformations, compression wave evolution, wave profile, VISAR interferometer.

Structural phase transition and amorphization in hexagonal SiC subjected to dynamic loading

Understanding the dynamic behavior of silicon carbide (SiC) at extreme conditions is critical for applications such as coatings and armor. Revealing the plasticity and phase transition in SiC under intensive dynamic loading is among the key concerns. However, the effects of polytypes in SiC as well as the various loading conditions on its dynamic material responses are still not well understood. Here we carry out a series of large-scale molecular dynamics (MD) simulations to explore the inelastic responses of hexagonal SiC subjected to shock and ramp compression along the [0001] direction. The shock responses present three regimes sequentially as the shock particle velocity is increased from 0.5 km/s to 6 km/s: a single elastic wave, a multi-wave structure consisting of an elastic-plastic wave followed by two consecutive phase transition waves, and finally, an overdriven structural phase transformation wave. The original wurtzite structure is observed to transform into a 6-coordinated rock salt structure through a 5-coordinated intermediate structure. Furthermore, slip along the <112‾0> direction on the (0001) plane causes multiple stacking faults and amorphization when subjected to intense shock compression. The effects of temperature and strain rate on the material responses of hexagonal SiC are decoupled by performing ramp loading simulations. The results reveal that a lower temperature rise impedes atomic motion while a lower strain rate promotes it, highlighting a competitive effect. Besides, due to the limited availability of slip planes, dynamic compression can lead to the formation of nanograins in hexagonal SiC, and nanograins refinement with increasing shock intensity is observed. These results provide important insights into the deformation of SiC polytypes under extreme conditions and promote the understanding of the dynamic properties of hexagonal structure covalent materials.

Atomistic-model informed pressure-sensitive crystal plasticity for crystalline HMX

Cyclotetramethylene-Tetranitramine (HMX) is a secondary explosive used in military and civilian applications. Its plastic deformation is of importance in the initiation of the decomposition reaction, but the details of plasticity are not yet fully understood. It has been recently shown that both the elastic constants and the critical resolved shear stress for plastic deformation are pressure sensitive. Since initiation takes place during shock loading, the pressure sensitivity of plasticity is highly relevant. In this work, we examine the pressure-sensitivity of the dynamic mechanical behavior of HMX. To this end, we use an elastic–plastic continuum constitutive model of single crystal HMX in which the anisotropic elastic constants and direction-dependent yield stress are rendered pressure-sensitive. The pressure sensitivity is calibrated based on input from molecular models. We observe that accounting for pressure sensitivity changes significantly the profile of the elastic–plastic wave and the wave propagation speed upon impact. The accumulated dissipation profile and the total dissipation also exhibit profound differences between the simulations that take account of the pressure-dependence of the plastic deformation and the pressure independent counterpart.

Ultrasonic vibration-induced severe plastic deformation of Cu foils: effects of elastic-plastic stress wave bounce, acoustic softening, and size effect

Ultrasonic vibration-induced severe plastic deformation of Cu foils: effects of elastic-plastic stress wave bounce, acoustic softening, and size effect

Shock compression of molybdenum single crystals to 110 GPa: Elastic–plastic deformation and crystal anisotropy

To investigate the role of crystal anisotropy on the elastic–plastic deformation of BCC single crystals at high shock stresses, molybdenum (Mo) single crystals were shock compressed along the [100], [111], and [110] orientations at elastic impact stresses between 20 and 110 GPa. Laser interferometry was used to measure shock wave velocities and particle velocity histories. Along the [100] and [111] orientations, elastic–plastic waves (two wave structure) were observed up to 110 GPa. Along the [110] orientation, the two wave structure was observed only up to 90 GPa. The measured elastic wave amplitudes were analyzed to determine crystal anisotropy effects, impact stress dependence, and the activated slip systems on the Hugoniot elastic limit. The findings from our work have provided insight into the role of crystal anisotropy on the elastic–plastic deformation under shock compression at high stresses.

Wave propagation in elastic–plastic material with voids

Constitutive relations and governing equations have been developed for an elastic–plastic material with voids having single slip-plane and direction. The plasticity of the material is considered through the dislocation of slip-plane. The propagation of unidirectional plane waves has been explored in an infinite elastic–plastic material with voids, and it has been found that there exist four basic waves consisting of three coupled elastic–plastic waves and a lone transverse wave. The speeds of propagation of all the coupled elastic–plastic waves are found to be affected by the plasticity and void parameters, in general, while the transverse wave is not affected by the plasticity and void parameters at all and travels with the speed of classical transverse waves. Out of the three coupled elastic–plastic waves, two waves are the counterpart of the waves existing in elastic materials with voids, while the third wave is new and has appeared due to the presence of plasticity in the material. One of the coupled elastic–plastic waves that is least affected by the plasticity faces a critical frequency, below which the wave is a nonpropagating wave. This critical frequency arises due to the presence of voids in the medium. The speed of various waves is computed for a specific model and the results that are obtained are presented graphically. At large frequencies, all the coupled elastic–plastic waves propagate with constant speeds, but at low frequencies, they propagate with speeds less than that of the longitudinal wave of classical elasticity. Several earlier known results have been recovered as special cases from the present formulation.

Effects of temperature on the flow stress of aluminum in shock waves and rarefaction waves

Elastic–plastic waves of shock compression and unloading in annealed AD1 aluminum were recorded at room temperature, 508 °C, and 610 °C. Using measurements of the parameters of the plastic shock waves and quasi-elastic rarefaction waves at the peak shock stresses from about 1.5 to 4.2 GPa, the strain rate dependences on the stress, the temperatures, and the loading histories were obtained in the range of 105–107 s−1. The initial resistance to high-rate deformation was found to increase anomalously with increasing temperature, but even a small deformation in the shock wave and the accompanying multiplication of dislocations changed the sign of the temperature dependence of the flow stress.

ТЕОРЕТИЧНІ ПЕРЕДУМОВИ ЕКСПЛУАТАЦІЇ КОНСТРУКЦІЙ З МЕТАЛ-СКЛЯНИМИ ЗАХИСНИМИ ПОКРИТТЯМИ В УМОВАХ СУДНОВИХ ВІБРАЦІЙ

The article is devoted to looking for a solution for the scientific and technical issue of reducing vibrations on vessels. It is considered to be achieved with the application of the vibration-absorbing composite coatings. The purpose of the work is to theoretically substantiate the possibility of operation of structures with metal-glass coatings taking into consideration the vibration environment of a vessel. The formulation of the research includes the discovery of the solution for the micromechanics issue set up on the model of a two-layer plate St3 ‒ metal-glass coatings, taking into account their structural features, and experimental tensile tests. The influence of the polydisperse structure of coatings on the mechanisms of absorption of elastic-plastic waves of dynamic oscillations has been analyzed with the help of the analytical description of microdisplacement deformations. The influence of morphology and volume content of glass fillers, specifically hollow glass microspheres, powders of sodium silicate and lead-containing glass on the vibration coefficient, strength limit and yield strength has been investigated. Calculations have shown the feasibility of using metal-glass coatings in conditions of vessel vibration, which is due to the absorption of energy by glass inclusions of spherical and angular shape. It has been experimentally proven that coated plates are slightly inferior in tensile strength to samples with St3; the destruction of coatings occurs between glass inclusions. The obtained results have scientific and practical significance for the design of ship structures using composite materials and coatings.