Initial dislocation density effect on strain hardening in FCC aluminium alloy under laser shock peening

Abstract

The effect of initial dislocation density on subsequent dislocation evolution and strain hardening in FCC aluminium alloy under laser shock peening (LSP) was investigated by using three-dimension discrete dislocation dynamics (DD) simulation. Initial dislocations were randomly generated and distributed on slip planes for three different dislocation densities of 4.21 × 10¹², 8.12 × 10¹² and 1.26 × 10¹³ m^?2. Besides, variable densities of prismatic loops were introduced into the DD cells as nanoprecipitates to study the dislocation pinning effect. The flow stresses as a function of strain rate obtained by DD simulation are compared with relevant experimental data. The results show a significant dislocation density accumulation in the form of dislocation band-like structures under LSP. The overall yield strength in FCC aluminium alloy decreases with increasing initial dislocation density and forest dislocation strengthening becomes negligible under laser induced ultra-high strain rate deformation. In addition, yield strength is enhanced by increasing the nanoprecipitate density due to dislocation pinning effect.     

Effects of the AlN nucleation layer thickness on the crystal structures of an AlN epilayer grown on the 6H-SiC substrate

The influence of the LT-AlN(NL) growth times on the mosaic structure parameters of the AlN layer grown on the LT-AlN(NL)/6H-SiC structures as well as the dislocation densities and the strain behaviours in the AlN epilayers has been investigated using XRD measurements. The growth times of the LT-AlN(NL) were changed to 0, 60, 120, 180, and 240?s. We observed that the mosaic structure parameters of the AlN epilayers were slightly affected by the LT-AlN(NL) growth times. However, the dislocation densities in the AlN layer are affected by the growth times of the LT-AlN(NL) layer. The highest edge dislocation density (5.48?×?10¹⁰?±?2.3?×?10⁹?cm^?2) was measured for the sample in which 120?s grown LT-AlN(NL) was used. On the other hand, highest screw type dislocation density (1.21?×?10¹⁰?±?1.7?×?10⁹?cm^?2) measured in the sample E that contains 240?s growth LT-AlN(NL). The strain calculation results show that the samples without LT-AlN(NL) suffered maximum compressive in-plane strain (?10.9?×?10^?3?±?1.8?×?10^?4), which can be suppressed by increasing the LT-AlN(NL) growth times. The out-of-plane strain also has a compressive character and its values increase with LT-AlN(NL) growth times between 60 and 180?s. Same out-of-plane strain values were measured for the LT-AlN(NL) growth times of 180 and 240?s. Furthermore, the form of the biaxial stress in the AlN epilayer changed from compressive to tensile when the LT-AlN(NL) growth times were greater than 120?s.     

Void growth via atomistic simulation: will the formation of shear loops still grow a void under different thermo-mechanical constraints?

Abstract

Molecular dynamics (MD) simulations under different mechanical and thermal constraints are carried out with a nanovoid embedded inside a single-crystal, face-centred-cubic copper. The dislocation emission angles measured from MD plots under 0.1 K, uniaxial-strain simulation are in line with the theoretical model. The dislocation density calculated from simulation is qualitatively consistent with the experimental measurement in terms of a saturation feature. The ‘relatively farthest-travelled’ atoms are employed to reflect the correlation between the dislocation structure and the void growth. At a smaller scale, the incomplete shear dislocation loops on the slip plane contribute to the local material transport. At a larger scale, the dislocation structures formed by those incomplete shear loops further facilitate the growth of nanovoid. Compared to the uniaxial-strain case, the void growth under the uniaxial-stress is very limited. The uniaxial-strain loading results in an octahedron void shape. The uniaxial-stress loading turns the nanovoid into a prolate ellipsoid along the loading direction. In the simulation, the largest specimen contains 12 million atoms and the lowest strain rate applied is 2 × 10⁶ s^?1. Under all the different thermomechanical constraints concerned, the formation of incomplete shear dislocation loops are found capable of growing the void.     

Mechanism of formation of cellular dislocation structures during propagation of intense shock waves in crystals

The mechanism of formation of a cellular dislocation structure in face-centered cubic (fcc) metal crystals subjected to shock compression at strain rates \(\dot \varepsilon \) > 10⁶ s^?1 has been considered theoretically within the dislocation kinetic approach based on the kinetic equation for the dislocation density (dislocation constitutive equation). A dislocation structure of the cellular type is formed in the case of a two-wave structure of the compression wave behind its shock front (elastic precursor). It has been found that, at pressures σ > 10 GPa, the dislocation cell size Λ _c depends on the pressure σ and the density ρ _G of geometrically necessary dislocations generated at the shock front according to the relationship Λ _c ～ ρ _G ^?n ～ σ^?m , where n = 1/4–1/2, m = 3/4–3/2, and m = 1, for different pressures and orientations of the crystal. It has been shown that, in copper and nickel crystals with the shock loading axis oriented along the [001] direction, the cellular structure is not formed after reaching the critical pressures σ _c equal to 31 and 45 GPa, respectively.     

Influence of temperature and strain on the amplitude-dependent internal friction of high-purity aluminum

The dislocation amplitude-dependent friction (ADIF) of high-purity (99.999%) polycrystalline aluminum is investigated in the temperature range 7–300K at vibrational strain amplitudes of 10⁻⁷–10⁻⁴ for samples in the annealed and deformed (by quasistatic, shock, and ultrasonic loading) states. The ADIF is a multistage effect in the indicated temperature and vibration amplitude ranges. Analysis of the amplitude-temperature spectra of the ADIF permits separation of components attributable to: interaction between dislocations, the interaction of dislocations with pinning points, and pure dislocation relaxation (the interaction of dislocations with the Peierls relief). ADIF is observed to depend nonmonotonically on the initial quasistatic strain determined by strain hardening and recovery processes. Fiz. Tverd. Tela (St. Petersburg) 40, 1839–1844 (October 1998)     

Dislocation motion in high strain-rate deformation

We present a systematic investigation of dislocation motion, dislocation interactions, and the collective behaviour of dislocations in high strain-rate deformation. Based on results from three-dimensional dislocation dynamics simulations, we find that employing the accurate, full-dynamics, equation of motion (i.e. that includes inertial effects) significantly changes the predictions of microstructural evolution and the macroscopic response compared to the commonly used overdamped equation of motion (i.e. with no inertial effects), especially at high strain rates (10³–10⁶ s^?1). While we find that inertial effects cannot be neglected, the net velocities are not high enough that ‘relativistic’ effects are important. We also present results on the effects of high strain rates on single-crystal deformation, which show good agreement with experimental trends, including increased hardening with increasing strain rate.     

Determination of elastic strain fields and geometrically necessary dislocation distributions near nanoindents using electron back scatter diffraction

The deformation around a 500-nm deep Berkovich indent in a large grained Fe sample has been studied using high resolution electron back scatter diffraction (EBSD). EBSD patterns were obtained in a two-dimensional map around the indent on the free surface. A cross-correlation-based analysis of small shifts in many sub-regions of the EBSD patterns was used to determine the variation of elastic strain and lattice rotations across the map at a sensitivity of ～±10^?4. Elastic strains were smaller than lattice rotations, with radial strains found to be compressive and hoop strains tensile as expected. Several analyses based on Nye's dislocation tensor were used to estimate the distribution of geometrically necessary dislocations (GNDs) around the indent. The results obtained using different assumed dislocation geometries, optimisation routines and different contributions from the measured lattice rotation and strain fields are compared. Our favoured approach is to seek a combination of GND types which support the six measurable (of a possible nine) gradients of the lattice rotations after correction for the 10 measurable elastic strain gradients, and minimise the total GND line energy using an L¹ optimisation method. A lower bound estimate for the noise on the GND density determination is ～±10¹² m^?2 for a 200-nm step size, and near the indent densities as high as 10¹⁵ m^?2 were measured. For comparison, a Hough-based analysis of the EBSD patterns has a much higher noise level of ～±10¹⁴m^?2 for the GND density.     

On the homogeneous nucleation and propagation of dislocations under shock compression

The dynamic response of crystalline materials subjected to extreme shock compression is not well understood. The interaction between the propagating shock wave and the material’s defect occurs at the sub-nanosecond timescale which makes in situ experimental measurements very challenging. Therefore, computer simulation coupled with theoretical modelling and available experimental data is useful to determine the underlying physics behind shock-induced plasticity. In this work, multiscale dislocation dynamics plasticity (MDDP) calculations are carried out to simulate the mechanical response of copper reported at ultra-high strain rates shock loading. We compare the value of threshold stress for homogeneous nucleation obtained from elastodynamic solution and standard nucleation theory with MDDP predictions for copper single crystals oriented in the [0 0 1]. MDDP homogeneous nucleation simulations are then carried out to investigate several aspects of shock-induced deformation such as; stress profile characteristics, plastic relaxation, dislocation microstructure evolution and temperature rise behind the wave front. The computation results show that the stresses exhibit an elastic overshoot followed by rapid relaxation such that the 1D state of strain is transformed into a 3D state of strain due to plastic flow. We demonstrate that MDDP computations of the dislocation density, peak pressure, dynamics yielding and flow stress are in good agreement with recent experimental findings and compare well with the predictions of several dislocation-based continuum models. MDDP-based models for dislocation density evolution, saturation dislocation density, temperature rise due to plastic work and strain rate hardening are proposed. Additionally, we demonstrated using MDDP computations along with recent experimental reports the breakdown of the fourth power law of Swegle and Grady in the homogeneous nucleation regime.     

Two-wave structure of plastic relaxation waves in crystals under intense shock loading

The mechanism of formation of a two-wave structure of plastic relaxation waves at shock wave stresses σ > 1 GPa (plastic strain rates $\dot \varepsilon $ > 10⁶ s^?1) has been theoretically considered using the dislocation kinetic equations and relationships. It has been shown that, under intense shock loading, two plastic relaxation waves are generated in the crystal. Initially, there arises the first wave (in the traditional terminology, it is an elastic precursor) associated with the generation of geometrically necessary dislocations at the boundary between the compressed and uncompressed parts of the crystal. Then, there arises the second wave due to the dislocation multiplication on geometrically necessary dislocations of the first wave in the form of forest dislocations. The dependences of the stresses on the plastic strain rate σ ～ $\dot \varepsilon ^{1/4} $ in the first wave and σ ～ $\dot \varepsilon ^{2/5} $ in the second wave, as well as the dependences of the stresses on the thickness of the target D, i.e., σ ～ D ^?1/3 and σ ～ D ^?2/3, respectively, have been determined by solving the relaxation equations. The obtained relationships have been confirmed by the experimental data available in the literature.     

Effect of preliminary strain hardening on the flow stress of titanium and a titanium alloy during shock compression

The effect of preliminary strain hardening of VT1-0 titanium and a Ti-6 wt % Al-4 wt % V alloy on their mechanical properties under quasi-static and high-rate (τ;10⁵ s^?1) loading is studied. Preliminary hardening is accomplished using equal-channel angular pressing (which results in a significant decrease in the grain size and a twofold increase in the quasi-static yield strength) and shock waves. High-rate deformation is attained via shock-wave loading of samples. The experimental results show that structural defects weaken the dependence of the yield strength on the strain rate. The difference in the rate dependences can be so high that the effect of these defects on the flow stress can change sign when going from quasi-static to high-rate loading.     

Dislocation-density-based constitutive modelling of tensile flow and work-hardening behaviour of P92 steel

The flow and work-hardening behaviour of tempered martensitic P92 steel have been investigated using phenomenological constitutive model in the temperature range 300–873 K for the strain rates ranging from 3.16 × 10^?5 to 1.26 × 10^?3 s^?1. The analysis indicated that the hybrid model reduced to Estrin–Mecking (E–M) one-internal-variable model at intermediate and high temperatures. Further, the analysis also indicated that dislocation dense martensite lath/cell boundaries and precipitates together act as effective barriers to dislocation glide in P92 steel. The flow behaviour of the steel was adequately described by the E–M approach for the range of temperatures and strain rates examined. Three distinct temperature regimes have been obtained for the variations in work-hardening parameters with respect to temperature and strain rate. Signatures of dynamic strain ageing in terms of the anomalous variations in work-hardening parameters at intermediate temperatures and the dominance of dynamic recovery at high temperatures have been observed. The evaluation of activation energy suggested that deformation is controlled by the dominance of cross-slip of dislocations at room and intermediate temperatures, and climb of dislocations at high temperatures.     

Slip band formation and mobile dislocation density generation in high rate deformation of single fcc crystals

The mechanisms for the nucleation, thickening, and growth of crystallographic slip bands from the sub-nanoscale to the microscale are studied using three-dimensional dislocation dynamics. In the simulations, a single fcc crystal is strained along the [111] direction at three different high strain rates: 10⁴, 10⁵, and 10⁶?s^??1. Dislocation inertia and drag are included and the simulations were conducted with and without cross-slip. With cross-slip, slip bands form parallel to active (111) planes as a result of double cross-slip onto fresh glide planes within localized regions of the crystal. In this manner, fine nanoscale slip bands nucleate throughout the crystal, and, with further straining, build up to larger bands by a proposed self-replicating mechanism. It is shown that slip bands are regions of concentrated glide, high dislocation multiplication rates, and high dislocation velocities. Cross-slip increases in activity proportionally with the product of the total dislocation density and the square root of the applied stress. Effects of cross-slip on work hardening are attributed to the role of cross-slip on mobile dislocation generation, rather than slip band formation. A new dislocation density evolution law is presented for high rates, which introduces the mobile density, a state variable that is missing in most constitutive laws.     

Behavior of aluminum near an ultimate theoretical strength in experiments with femtosecond laser pulses

The dynamics of the motion of the free surface of micron and submicron films under the action of a compression pulse excited in the process of femtosecond laser heating of the surface layer of a target has been investigated by femtosecond interferometric microscopy. The relation between the velocity of the shock wave and the particle velocity behind its front indicates the shock compression to 9–13 GPa is elastic in this duration range. This is also confirmed by the small (≤1 ps) time of an increase in the parameters in the shock wave. Shear stresses reached in this process are close to their estimated ultimate values for aluminum. The spall strength determined at a strain rate of 10⁹ s⁻¹ and a spall thickness of 250–300 nm is larger than half the ultimate strength of aluminum.     

High strain rate deformation and fracture of the magnesium alloy Ma2-1 under shock wave loading

This paper presents the results of measurements of the dynamic elastic limit and spall strength under shock wave loading of specimens of the magnesium alloy Ma2-1 with a thickness ranging from 0.25 to 10 mm at normal and elevated (to 550°C) temperatures. From the results of measurements of the decay of the elastic precursor of a shock compression wave, it has been found that the plastic strain rate behind the front of the elastic precursor decreases from 2 × 10⁵ s^?1 at a distance of 0.25 mm to 10³ s^?1 at a distance of 10 mm. The plastic strain rate in a shock wave is one order of magnitude higher than that in the elastic precursor at the same value of the shear stress. The spall strength of the alloy decreases as the solidus temperature is approached.     

Laser ablation loading of a radiofrequency ion trap

The production of ions via laser ablation for the loading of radiofrequency (RF) ion traps is investigated using a nitrogen laser with a maximum pulse energy of 0.17?mJ and a peak intensity of about 250?MW/cm². A?time-of-flight mass spectrometer is used to measure the ion yield and the distribution of the charge states. Singly charged ions of elements that are presently considered for the use in optical clocks or quantum logic applications could be produced from metallic samples at a rate of the order of magnitude 10⁵ ions per pulse. A linear Paul trap was loaded with Th⁺ ions produced by laser ablation. An overall ion production and trapping efficiency of 10^?7 to 10^?6 was attained. For ions injected individually, a dependence of the capture probability on the phase of the RF field has been predicted. In the experiment this was not observed, presumably because of collective effects within the ablation plume.     

Full-scale atomistic simulations of dislocations in Ni crystal by embedded-atom method

Full-scale atomistic simulations by the nudged elastic band method are performed to determine the energetics and core structures of dislocations in a Ni lattice using an embedded-atom method potential. We find that for an edge dislocation, the potential yields very weak coupling between the partials which move almost individually. For a screw dislocation, the coupling between the partials is somewhat stronger and the partials move with some dependence. As expected, the results indicate that stacking fault energy has a controlling influence on the coupling behaviour of the partials. The effective Peierls energies and stresses are 1.30?×?10^?6?eV/Å and 2.79?×?10^?6?μ for the edge dislocation, and 1.62?×?10^?4?eV/Å and 2.02?×?10^?4?μ for the screw dislocation.     

Atomistic study of temperature and strain rate-dependent phase transformation behaviour of NiTi shape memory alloy under uniaxial compression

Molecular dynamics simulation was conducted to investigate the phase transformation behaviour of nickel–titanium (NiTi, 50%-50% at.%) nanopillar under uniaxial compression at loading rates varying from 3.30 × 10⁷ to 3.30 × 10⁹ s^?1 and at temperatures varying from 325 to 600 K. The phase transformation of NiTi was observed to be sensitive to loading rates and temperatures. The phase transformation stress of B2 → B19 increased with increasing temperature while it was insensitive to loading rate. The phase transformation stress of B19 → B19′ → BCO increased with increasing strain rate and decreasing temperature. In addition, reverse phase transformation was observed during compression due to the interaction between the phase transformation of B19 → B19′ → BCO and the deformation twinning/dislocation slide-induced plasticity of the BCO phase, leading to different residual crystal structures after loading. Moreover, a diagram for the phase transformation behaviour of NiTi in the simulated ranges of strain rate and temperature was obtained, from which the contrary experimental observations on the phase transformation behaviour of NiTi from the studies of Nemat-Nasser et al. (Mech. Mater. 37 (2005) p.287) and Liao et al. (J. Appl. Phys. 112 (2012) p.033515) at various strain rates could be well explained.     

The influence of strain rate on the visibility of dislocations in transmission electron microscopy images of deformed Ti–6 wt% Al–4 wt% V and in Timet 550

Samples of Ti–6?wt%?Al–4?wt%?V and Timet 550 (Ti–4?wt%?Al–4?wt%?Mo–2?wt%?Sn–0.5?wt%?Si) have been subjected to strain rates between 10^?1 and 10³?s^?1and detailed examination of the dislocation structure in the α grains has been carried out using transmission electron microscopy (TEM). For samples deformed to a strain of 0.1 at 10^?1?s^?1, detailed analysis of the defects can be carried out using all diffracting vectors and the presence of (c +?a) dislocations and a dislocations thus confirmed. In contrast, for samples strained to the same strain of 0.1 but at 5?s^?1, it is not possible to obtain images of dislocations when using any diffracting vectors other than 0002. Thus the presence of dislocations which have a Burgers vector containing a c component can be confirmed in the samples strained at 5?s^?1 but the presence of a-component dislocations can only be inferred from TEM of these samples because of the difficulty of obtaining images with diffracting vectors other than 0002. Limited observations on samples strained at 10³?s^?1 show that similar difficulties are found in imaging dislocations as are found in samples deformed at 5?s^?1 but at this strain rate, the highest used, the difficulties are reduced since images can be obtained in some grains using diffracting vectors other than 0002. These results are discussed in terms of the nature of damage as a function of strain rate and the factors that influence contrast from dislocations in crystals.     

Ramp compression of tantalum to 330 GPa

We report on the stress–density and rate-dependent response for Ta, ramp compressed to 330?GPa with strain rates up to 5?×?10⁸?s^?1. We employ temporally shaped laser drives to compress Ta stepped foils over several to tens of nanoseconds. Lagrangian wave-profile analysis reveals a stress–density relationship which falls below the Hugoniot, above the hydrostat, and is consistent with ramp-compression experiments at lower strain rates. We also report on the peak elastic stress prior to plastic deformation as a function of strain rate for laser-driven ramp and shock-compression data spanning the 1–50?×?10⁷?s^?1 strain-rate range. When combined with previously published lower strain data (10¹–10⁷?s^?1), we observe a change in rate dependence, suggesting a transition from thermally activated to defect-limited (phonon drag) dislocation motion occurring at a strain rate of about 10⁵?s^?1.     

Molecular dynamic simulation of stress evolution analysis in Cu nanowire under ultra-high strain-rate simple tension

This study analyses the behaviour of atoms associated with the propagation of stress waves in Cu nanowires (NWs) during uniaxial tensile deformation using molecular dynamic simulation. Maximum local stress (MLS) and virial stress (VS) methods are adopted to express dynamic stress in ?100? Cu NWs under tension. Simulation results indicated that the VS method enhances the averaging effect at ultra-high strain rates (above 10¹⁰ s^?1), leading to serious undervaluation of yield stress. However, the MLS method provides superior prediction results for the dynamic mechanical responses of NWs under tension at the ultra-high strain rate than does the VS. At a strain rate of 7 × 10¹⁰ s^?1, the double-peak stress phenomenon was observed in the stress–strain curve using the MLS method. The response time (T_rs) to wave propagation, observed at an ultra-high strain rate, is responsible for the accumulation of the elastic stress that is applied at the beginning of tensile loading in a short period, producing the first stress peak. Following plastic deformation, the encounter of the wavefronts with the reduced tensile stress causes the fully constructive interference effect in the middle of the tensile NWs, producing the second stress peak. The results explain the dynamic mechanical behaviour of NWs, contributing to future applications of subsonic manufacturing.