Emission Of Dislocation Loops Research Articles

Molecular dynamics simulation of nanoindentation on nano-twinned FeCoCrNiCu high entropy alloy

ABSTRACT Twin boundary (TB) plays an important role in the deformation process of materials. In this paper, molecular dynamics (MD) simulation was used to investigate the nanoindentation deformation behaviour of single-crystal FeCoCrNiCu high entropy alloy (SC-HEA) and nano-twinned FeCoCrNiCu high entropy alloy (NT-HEA) with different twin spacings. It is found that the main characteristic of plastic deformation of SC-HEA is the dislocation loop emission. The dislocation movement and distribution of NT-HEA are very different from that of SC-HEA. We found that partial dislocation slip parallel to the twin boundary (PSPTB) and twin partial slip (TPS) can lead to alloy softening. The hindrance of the TB causes the dislocation to slip within a single layer (known as confined layer slip, CLS), which strengthens the material. In the process of nanoindentation, the softening and strengthening mechanisms are constantly competing. When the twin spacing is larger than 1.23 nm, CLS dominates the competition with the hardening mechanism, and the hardness of the material increases with the decrease of the twin spacing. When the twin spacing is less than 1.23 nm, the dominant mechanism of plastic deformation changes to the softening mechanism controlled by TPS, and the hardness thus decreases as twin spacing increases.

Molecular-Dynamics Analysis of the Mechanical Behavior of Plasma-Facing Tungsten.

We report a systematic computational analysis of the mechanical behavior of plasma-facing component (PFC) tungsten focusing on the impact of void and helium (He) bubble defects on the mechanical response beyond the elastic regime. Specifically, we explore the effects of porosity and He atomic fraction on the mechanical properties and structural response of PFC tungsten, at varying temperature and bubble size. We find that the Young modulus of defective tungsten undergoes substantial softening that follows an exponential scaling relation as a function of matrix porosity and He atomic content. Beyond the elastic regime, our high strain rate simulations reveal that the presence of nanoscale spherical defects (empty voids and He bubbles) reduces the yield strength of tungsten in a monotonically decreasing fashion, obeying an exponential scaling relation as a function of tungsten matrix porosity and He concentration. Our detailed analysis of the structural response of PFC tungsten near the yield point reveals that yielding is initiated by emission of dislocation loops from bubble/matrix interfaces, mainly 1/2⟨111⟩ shear loops, followed by gliding and growth of these loops and reactions to form ⟨100⟩ dislocations. Furthermore, dislocation gliding on the ⟨111⟩{211} twin systems nucleates 1/6⟨111⟩ twin regions in the tungsten matrix. These dynamical processes reduce the stress in the matrix substantially. Subsequent dislocation interactions and depletion of the twin phases via nucleation and propagation of detwinning partials lead the tungsten matrix to a next deformation stage characterized by stress increase during applied straining. Our structural analysis reveals that the depletion of twin boundaries (areal defects) is strongly impacted by the density of He bubbles at higher porosities. After the initial stress relief upon yielding, increase in the dislocation density in conjunction with decrease in the areal defect density facilitates the initiation of dislocation-driven deformation mechanisms in the PFC crystal.

Effect of radiation defects on the early stages of nanoindentation tests in bcc Fe and Fe-Cr alloys

Classical molecular dynamics (MD) simulations of nanoindentation tests are performed in defect-free at 300, 600 and 1000 K and defected crystals at 300 and 600 K of pure Fe and Fe-9Cr alloy. The aim of the work is to evaluate the effect of the presence of various defects specific to neutron/heavy ion irradiation (i.e., voids, dislocation loops and Cr precipitates) on the material response during the early stages of nanoindentation (i.e., at indentation depths up to 20 Å). We establish that even a relatively large density of the radiation defects (∼1024 m−3) does not induce any significant change in the material response, i.e., it is not unambiguously detectable at the force-depth curves neither in pure Fe nor in Fe-9Cr alloys. The macroscopic parameters, which can be derived from these curves, such as hardness and reduced modulus, calculated in the crystals with and without radiation defects also cannot clearly reveal the contribution from the presence of the radiation defects given the resulting uncertainty of their extraction. However, several distinct features typical for nanoindentation tests observed in crystals with radiation defects only were identified, such as a) obstruction of emission of dislocation loops under the indenter during loading for crystals with precipitates and dislocation loops, and b) special residual imprint pattern for crystals with dislocation loops. The results of this work provide useful data for the parameterization and validation of the higher-scale methods, such as dislocation dynamics and (crystal plasticity-) finite-element method. The details of the transferability of MD results to these methods are also discussed.

Unveiling the local deformation behavior of typical microstructures of nickel-based single crystals under nanoindentation

In the present study, consider the typical microstructures (γ, γ’ and interface phases) in nickel-based single crystal, three ideal simplified atomic models of Ni, Ni3Al and Ni/Ni3Al interface were established. And nanoindentation molecular dynamics (MD) simulations were performed on the above models. Based on the dynamic deformation behavior and mechanism of nickel-based single crystal microstructure under the local loading, the nanoindentation plastic deformation is divided into two stages Pi and Pii. In the initial Pi stage, dislocations only move and react on the contact surface between the indenter and the substrate. Subsequently, in stage Pii, edge dislocations climb away from the contact surface, screw dislocations interact with each other and finally form dislocation shear loops. The local plastic deformation is dominated by the nucleation and emission of dislocation loops, affected by its resistance and dislocation velocity. It is noted that in the interface model, dislocation shear loops inevitably interact with interface dislocations, which will lead to further plastic deformation. Combined with the dislocation theory and the above research, a model based on the movement of dislocations was established better describe the local plastic behavior of the typical microstructure in nickel-based single crystal under indentation.

Atomic-scale mechanisms of He/V ratio effect on helium bubble hardening in iron for neutron irradiated F/M steels

The helium-to-vacancy (He/V) ratio is a key factor related to the helium bubble hardening mechanisms induced by neutron irradiation in ferritic/martensitic (F/M) steels as advanced nuclear structural materials. According to the helium bubble hardening results in F/M steel irradiated in the spallation neutron source, the interactions between a 1/2<111>{110} edge dislocation and helium bubbles with various sizes of 0.7–3.0 nm in bcc-Fe under irradiation temperatures and room temperature was investigated by using molecular dynamics simulation. The effect of various He/V ratios in the ranges of zero to the highest He/V ratios, 1.85–4.0 of stable helium bubbles with no dislocation loop emission, on the interaction mechanisms was analyzed. The results indicated that the critical resolved shear stress (CRSS) drops rapidly to a very low stress level, and immediately bottoms out and rebounds to a very high stress level, when the He/V ratio increases from 1.0 to the highest He/V ratio. The significant change of CRSS values is not only related to the climbing degree of dislocation after releasing, but also related to the moment when the climb appears. A new repulsion mechanism of interaction between dislocation and bubble was proposed to elucidate the abnormal phenomena of the bottoming rebound of CRSS with a great climbing degree, according to the repelling interaction between helium bubble and superjog of dislocation with both strong compressive stress field.

Molecular dynamics simulations for nanoindentation response of nanotwinned FeNiCrCoCu high entropy alloy

Twin boundary (TB) plays an important role on the plastic deformation of high entropy alloy (HEA). The strong effects of TB on the deformation response of HEA are revealed from atomic level based on the defect structure, shear strain and surface morphology, by comparing the nanoindentation behavior of nanotwinned FeNiCrCoCu HEA (nt-HEA) and single-crystal FeNiCrCoCu HEA (single-HEA). The plastic deformation of nt-HEA is mainly dominated by the dislocations slip confined by first twinning layer, the TB migration, the dislocation nucleation at TB and the stacking fault tetrahedron (SFT) formation, while the dislocation loop emission is the main plastic deformation feature of single-HEA. Compared to the case for single-HEA, the nanoindentation induces more dislocations in nt-HEA. The shear strain in nt-HEA mainly distributes in the first twinning layer, due to the obstacle effect of TB. The shear zone is larger in nt-HEA, and the distribution of shear strain on the nt-HEA surface is more symmetric. The nanoindentation generates fewer steps on the nt-HEA surface, and then brings about a relatively smooth surface for nt-HEA. These findings provide an insight into the TB effect on the nanoindentation response of FeNiCrCoCu HEA, and develop the application of nanotwinned HEA systems.

Emission of Dislocation Loops from Nanovoids in an FCC Crystal Subjected to Shear Deformation under Post-Cascade Shock Waves

The method of molecular dynamics is applied to the study of the effect of post-cascade shock waves generated in a solid irradiated by high-energy particles on the heterogeneous formation of dislocation loops in a simulated gold crystal containing a spherical nanovoid, which is subjected to shear deformation. The interaction between atoms is described with the use of a potential calculated by the embedded atom method. Shock waves are created by assigning a velocity exceeding the speed of sound in the simulated material to the boundary atoms of the computational cell. It is shown that two regions of increased mechanical stress are formed under shear deformation near the surface of a nanovoid, which are the sources of emerging partial dislocations. The main mechanism for the formation of dislocations is the displacement of a group of atoms towards the inner surface of the void, which does not contradict modern ideas about the heterogeneous formation of dislocations. It is shown that, when the values of shear stress are insufficient for the formation of dislocations, loop emission can be initiated by a post-cascade shock wave generated in the computational cell. As temperature increases, the number of nucleated dislocation loops increases, and, in addition, the formation of Lomer–Cottrell dislocations is observed, which is attributed to the additional tangential stresses created by the unloading wave. In this case, the formation of a stable dislocation loop in which the linear tension is balanced by the Peach–Koehler force due to external stress requires that the shock wave front affect the regions of increased stress near the void surface while propagating through the simulated crystal.

Effect of void defect onc-axis deformation of single-crystal Ti under uniaxial stress conditions: Evolution of tension twinning and dislocations

Abstract

Indentation response of γ-TiAl(111) and influence of True-twin interface

Nanoindentation response of γ-TiAl(111) face is investigated by classical molecular dynamics simulation. The evolution of dislocation is observed, and the result indicate that the dislocation emission is not central symmetry like ordinary FCC crystal. What’s more, dislocation loop emission can be observed during the indentation process. In addition, influence of TT interface is also discussed. The interface has little influence on the elastic modulus but it is effective obstacle to the motion of dislocations. Dislocation nucleate from the TT interface can also be observed.

Molecular dynamics simulations on size dependent tensile deformation behaviour of [110] oriented body centred cubic iron nanowires

Tensile deformation behaviour of 〈110〉/{111} oriented body centred cubic (BCC) iron nanowires has been examined using molecular dynamics (MD) simulations at 10K. MD simulations were performed on nanowires with cross section width in the range 1.42–24.27nm. The results indicated that the deformation behaviour in BCC Fe nanowires is governed by full dislocation slip irrespective of nanowire size. The initiation of plastic deformation occurred by the collective emission of dislocation loops originating from the corner of the nanowires. Following yielding, accumulation of straight screw dislocations with increasing plastic deformation has been observed. Presence of curved slip steps observed in the surface morphology suggested the occurrence of cross slip in large size nanowires. Evidence of cross slip was not noticed in small size nanowires. The variations of Young’s modulus, yield strength and flow stress with nanowire size displaying strong size effects in BCC Fe nanowires have been presented.

Plastic deformation in nanoporous aluminum subjected to high-rate uniaxial compression

The mechanical behavior of nanoporous monocrystal aluminum subjected to uniaxial compressive loading at a rate of 2109 s- 1 along [110] crystallographic orientation is studied using molecular dynamics simulations. Subjected to such a loading, nanovoids act as the effective sources of dislocation nucleation and emission, four of the twelve {111}110 slip systems may be activated. With the same strain of 3.8%, dislocation nucleation will occur in both the sample of multiple voids and that with a single void. The configuration of multiple voids decreases the required stress for the onset of dislocation nucleation and emission in comparison with the sample with an isolated void of the same size. Because of the emission of trial partials, the accumulation of dislocation density can be changed into a piecewise linear process by the dislocation density propagation rate dd/d: in the initial stage of plastic deformation we obtain dd/d1.071018 m-2, but this changes to dd/d5.361018 m-2 at higher deformation. The velocity of dislocation is calculated to be subsonic and is a variable value during the plastic deformation. Dislocation loop pairs emit from the same void, glide and approach to each other, leading to the reduction of dislocation velocity. Then one loop of each pair continues to glide to intersect mutually and finally interact with the loops emitted from other voids, causing a strain hardening to reach the peak flow stress of 4.3 GPa. There is a post-yield softening corresponding to the onset of rapid dislocation density proliferation at higher dislocation densities. With the temperature evolution of the sample with multiple voids during plastic deformation, the density of mobile dislocations is calculated to be one magnitude lower than the total dislocation density. There is a decrease of mobile dislocation densities at large strains, showing that the mobile dislocation are diminished by the formation of dislocation forest and junctions. At the onset of their nucleation, the dislocations are all Shockley partials, however, when dislocation intersection happens, the majority are still Shockley partials, while the rest consists of Frank partials, perfect fcc dislocations and other dislocation ingredients. Voids collapse at the strain of 11.8%. No twins are found in the present simulation due to the high stacking-fault energy of aluminum. Prismatic dislocation loop emission is observed in this simulation.

Low-defect metamorphic Si (Ge) epilayers on Si (001) with a buried template of nanocavities for multiple-junction solar cells

Si (001)-oriented substrates (p-type) were implanted at 10keV with He+ ion doses in the 5×1015cm−2 range. They were annealed at 973K for 1h to create a buried layer of nano-sized bubbles. Layers of Si0.77Ge0.23 about 215nm thick were grown by low pressure chemical vapor deposition at 848K on these silicon wafers. The surface roughness and morphology were checked by atomic force microscopy and optical microscopy before and after etching with a modified Shimmel recipe to reveal etch pit dislocations. The thickness, composition, crystalline quality and relaxation-state of the SiGe layer were assessed by Rutherford backscattering spectroscopy and high-resolution X-ray diffraction. A fully relaxed strain-state was obtained for Si0.77Ge0.23 layers that did not exhibit the classical cross-hatched pattern morphology while having a threading-dislocations density below 103cm−2. This low dislocation density was confirmed by photoluminescence spectroscopy. From high resolution transmission electron microscopy observations, the quasi-total strain-relief is assumed to take place by emission of dislocation loops protruding down into the Si substrate from the SiGe/Si interface and terminating at void surfaces of the buried-nanoporous layer. Possible annihilation of dislocation segments coming from either the SiGe/Si interface or punched out in glide planes by overpressurized nanobubbles may also occur. This near surface porous Si is well adapted for multiple junction solar cell manufacturing.

Atomistic modeling of penny-shaped and through-thickness cracks in bcc iron

Atomistic simulations of penny-shaped embedded cracks in body-centered cubic (bcc) iron are performed using molecular dynamics. The results reveal that the original circular crack geometry can change shape gradually upon loading, depending on the crystallographic orientation. This new geometry generally favors emission of dislocation loops instead of unstable fracture. A comparison is made between through-thickness cracks in six different orientations and penny-shaped cracks on the same crack planes. We find that changes in crack shape and the interaction of events in different directions play an important role in how fracture mechanisms evolve when cracks in full 3D simulations extend, and that dislocation emission and mechanical twins ‘win’ over unstable crack growth by bond breaking.

Ductile tensile failure in metals through initiation and growth of nanosized voids

We here reveal the initiation of ductile failure in metals at the nanometer scale by molecular dynamics simulations coupled with a novel analytical model. This proceeds by the emission of a special type of dislocation shear loop, which can expand as a partial or perfect dislocation, evolve into a prismatic loop through reaction, or develop into twins. Molecular dynamics (MD) simulations predict a strong dependence of the stress required for the initiation of plastic flow at the surface of the void for both Cu (a model fcc metal) and Ta (a model bcc metal). The decrease in stress with increasing void size is also analyzed in terms of a new analytical approach based on the energetics of dislocation loop emission. For both fcc (copper) and bcc (tantalum) metals initiation of plastic flow in MD simulations takes place at voids as small as a tri-vacancy (radius R≈0.1nm). Extensive calculations for tantalum combined with the analytical model, which tracks the simulations, enable extrapolation to R≈300nm, in the realm of second phase particles and inclusions. Thus we conclude that this is a general mechanism of tensile failure in pure monocrystalline metals where other initiation sites are absent.

Emission of Dislocation Loops at Zero Indentation Load in Adhesive Nanocontacts

In this article, by characterizing the energetic lower bound for dislocation emission, we demonstrate that there exists an indenter-geometry-dependent criterion for the onset of plasticity, wherein dislocation emission can occur even at zero indenter loads in adhesive nanocontacts. By characterizing this mechanism for the conversion and restorage of surface energy into dislocation loops, we discuss its implications for the use of instrumented nanoindentation for studying incipient plasticity phenomena in the presence of indenter-bulk adhesive interactions.

A Quasicontinuum study of nanovoid collapse under uniaxial loading in Ta

The mechanisms underlying the deformation of nanovoids in Ta single crystals are analyzed when they are subjected to cyclic uniaxial deformation using numerical simulations. Boundary and cell-size effects have been mitigated by means of the Quasicontinuum (QC) method. We have considered ≈1 billion-atom systems containing 10.9 nm voids. Two kinds of simulations have been performed, each characterized by a different boundary condition. First, we compress the material along the nominal [0 0 1] direction, resulting in a highly symmetric configuration that results in high stresses. Second, we load the material along the high-index [ 4 ¯ 8 19 ] direction to confine plasticity to a single slip system and break the symmetry. We find that the plastic response under these two conditions is strikingly different, the former governed by dislocation loop emission and dipole formation, while the latter is dominated by twinning. We calculate the irreversible plastic work budget derived from a loading–unloading cycle and identify the most relevant yield points. These calculations represent the first fully three-dimensional, fully non-local simulations of any body-centered cubic metal using QC.

Threshold condition of dislocation loop emission from microvoids

This study examines the micromechanics of dislocation loop emission, aiming at determining the threshold condition associated with microvoid growth. The closed form of threshold stress is obtained for edge dislocation in the vicinity of cylindrical void in a general planar macroscopic stress state. The effects of surface energy and lattice friction are accounted for; the former is found to be significant. A prolate-to-oblate shape transition in uniaxial strain due to a higher driving force on slip plane transverse to the loading direction is observed. In the asymptotic condition of a large void, threshold condition is dictated by planar mean stress for general macroscopic stress state.

Void growth by dislocation-loop emission

Experimental results from spall tests on aluminum reveal the presence of a dense dislocation structure in an annulus around a void that grew under the tensile pulse when a shock wave was reflected at the free surface of the specimen. The proposition is that dislocation emission from the void surface under load is a viable mechanism for void growth. To understand void growth in the absence of diffusive effects, the interstitial-loop emission mechanism under tensile hydrostatic stress is investigated. First, the micromechanics of pile-up formation when interstitial loops are emitted from a void under applied macroscopic loading is reviewed. Demand for surface energy expenditure upon void-surface change is taken into consideration. It is demonstrated that in face-centered cubic metals loop emission from voids with a radius of ∼10 nm is indeed energetically possible in the hydrostatic stress environment generated by shock loading. On the other hand, the levels of hydrostatic stress prevalent in common structural applications are not sufficient to drive loops at equilibrium positions above a ∼10 nm void. However, for voids larger than about 100 nm, the energetics of loop emission are easily met as a necessary condition even under the low stress environment prevalent in structural applications.

Lattice orientation effect on the nanovoid growth in copper under shock loading

Molecular-dynamics (MD) simulations have revealed that under shock loading a nanovoid in copper grows to be of ellipsoidal shape and different loading directions ([100] and $[1\overline{1}1]$) change the orientation of its major axis. This anisotropic growth is caused by preferential shear dislocation loop emission from the equator of the void under [100] loading and preferential shear dislocation loop emission deviating away from the equator under $[1\overline{1}1]$ loading. A two-dimensional stress model has been proposed to explain the anisotropic plasticity. It is found that the loading direction changes the distribution of the resolved shear stress along the slip plane around the void and induces different dislocation emission mechanisms.

Plastic Deformation Instabilities: Lambert Solutions of Mecking-Lücke Equation with Delay

The aim of this paper is the study of instabilities during plastic deformation at constant cross‐head velocity. The deformation is supposed to be controlled by the emission of dislocation loops. Under some hypothesis analogous to the Mecking‐Lücke relation, we derive a linear delay differential‐difference equation. The “retarded” time term appears as the phase shift between the time of loop nucleation and the time at which the mean strain is recorded. We show the existence of the solution of strain equation. We give an analytic approach of solution using Lambert functions. The stability is also investigated close to the stable solution using a linearization of the number of nucleated loops functions.