Emission Of Shear Loops Research Articles

Towards the ultimate strength of iron: spalling through laser shock

The ultimate strength of materials is reached at strain rates approaching the Debye frequency, when the deformation time at the atomic scale approaches the time for atoms to move away from the equilibrium to their extreme separation position (~5.5 × 1013 s−1 for iron). We conducted high-power pulsed laser experiments on single, poly-, and nanocrystalline iron, generating tensile pulses with strain rates approaching the Debye frequency, 106 s−1 – 107 s−1, and nanosecond time durations. We find iron strengths varying between 5 and 10 GPa, a factor of ten higher than the static tensile strength. Ultrafine-grained iron samples exhibit a lower tensile strength, ~4-6 GPa, than single crystal iron, ~10 GPa. MD simulations show that this is due to differences in the initiation sites for voids, primarily at grain boundaries for the nano- and polycrystalline conditions. Sparse runaway voids (~5 μm diameter) and evidence of surface melting are observed for the single crystal iron and are likely due to strain-induced melting when sufficient deformation occurs. The process of separation leading to spalling is modeled by molecular dynamics, and the mechanisms observed in the experimentally recovered specimens are determined: in single crystals voids nucleate at the intersection of twins, while in nanocrystalline specimens grain boundaries are the principal sources of void nucleation. Analytical calculations are applied to the dislocations generated by the emission of shear loops from the void surfaces and the geometrically necessary dislocation densities are found to be consistent with predictions from molecular dynamics calculations.

The deformation mechanism in cold-welded gold nanowires due to dislocation emission

Though dislocation emission was known to be critical in the deformation and fracture process of metallic nanowires, the corresponding mechanism in cold-welded metallic nanowires has never been clarified. In order to understand the dislocation-mediated deformation mechanism in cold-welded nanowires, large-scale atomistic simulations are employed in this work. During dislocation emission, the formation and motion of only unclosed shear loops are observed inside nanowires. We prove from a theoretical viewpoint that unclosed shear dislocation loops can induce material transport and hence plastically deform cold-welded nanowires. For a better clarification, through running simulation replicates, we propose a novel approach to single out the displacement field solely due to shear loop emission. Regarding the pattern of material transport, our simulated atom arrangement near the dislocation core is found consistent with that captured by high-resolution transmission electron microscopy (HRTEM) of a stressed Au nanocrystal. Our analysis clarifies that the emission of unclosed shear loop plays a crucial role in not only the tensile deformation, but also the fracture process of cold-welded nanowires. It should be regarded as a general mechanism that shear loop emission can induce surface deformation and redistribute mass in the process of plasticity.

Growth mechanism of subsurface hydrogen cavities in tungsten exposed to low-energy high-flux hydrogen plasma

Due to a lack of direct experimental results, the detailed mechanisms that govern the blistering behavior of tungsten (W) exposed to ITER-relevant condition in nuclear fusion remain unclear. The growth mechanism of hydrogen (H) blisters is one example. In this work, recrystallized W was exposed to H plasma at 50 eV, 1.5×1026m−2, and 573 K. Transmission electron microscopy (TEM) samples were prepared using plasma-focused ion beam (FIB) followed by flash-polishing to effectively remove surface damages induced by FIB. The TEM images revealed that the general blisters observed on the exposed surface are associated with underlying cavities. A considerable amount of dislocations were found in the vicinity of the cavities. Prismatic dislocation loop arrays were observed, including small size 'coffee-bean' prismatic loops and large size prismatic loops. Near the tip of surfaces cavities, evidences for the emission of shear loops were also found. Based on the experimental findings, a multi-stage growth mechanism of H cavities was proposed. The loop-punching mechanism is operative for both very small cavities and cavities with sizes larger than several hundreds of nanometers. Whereas at intermediate sizes, cavities grow by emitting shear loops from the cavity tip.

Ductile mechanisms of metals containing pre-existing nanovoids

The void growth in monocrystalline Cu and Fe are investigated by molecular dynamics simulations to reveal the ductile mechanisms based on dislocation emission and propagation. The results show that the void growth in Cu is governed by the collective interaction of stacking faults along four (111) planes. Three dominant mechanisms of void growth in Fe are identified: (i) for small voids, nucleation of twinning boundaries; (ii) for intermediate voids, emission of shear loops; (iii) for large voids, stacking faults nucleate at the void surface and then degenerate into shear loops. The slip-twinning transition rate of Fe at room temperature calculated according to Zerrili-Armstrong model is in the range measured by our atomistic simulations. Vacancy generation which promotes void growth results from the intersection of more than two stacking faults in Cu, while in Fe it is related to the movement of screw dislocations. An analytical model based on nudged elastic band calculation is developed to include the strain rate dependence of the nanovoid-incorporated yielding. This new model demonstrates that the critical stress for dislocation emission will decrease with increasing strain rate and dislocation core width. For both metals, the dislocation density has been calculated to elucidate the plastic hardening coupled with void growth. This work sheds new lights in exploring the atomistic origins of the void size and strain rate dependent mechanisms associated with dislocation activities close to void surface.

Material transport via the emission of shear loops during void growth: A molecular dynamics study

The growth of a nanovoid in single-crystal copper has been studied via molecular dynamics (MD) method. The objective is to build the correlation between material transport pattern and dislocation structures. MD results are examined by characterizing the material transport via the “relative displacement” of atoms, where the homogenous elastic deformation has been excluded. Through this novel approach, we are able to illustrate the feasibility of void growth induced by shear loops/curves. At a smaller scale, the formation and emission of shear loops/curves contribute to the local mass transport. At a larger scale, a new mechanism of void growth via frustum-like dislocation structure is revealed. A phenomenological description of void growth via frustum-like dislocation structure is also proposed.

Effect of nanograin boundary sliding on nanovoid growth by dislocation shear loop emission in nanocrystalline materials

A theoretical model is suggested to describe the effect of nanograin boundary (NGB) sliding at triple junctions of grain boundaries on nanovoid growth by incipient emission of dislocation shear loop from its surface in mechanically loaded nanocrystalline materials. In the framework of the model, NGB sliding deformation represents generation of disclination dipoles at triple junctions of NGBs. The analytical expression of critical stress for the first dislocation emission is derived. The effects of NGB sliding deformation, the sizes of nanograin and nanovoid on critical stress and the corresponding most favorable slip plane for dislocation emission are evaluated quantitatively in the deformed nanocrystalline materials. The results indicate that NGB sliding deformation releases, in part, the high stresses near the nanovoid, thereby nanovoid growth is slowed down or even arrested with the increment of the strength of NGB sliding deformation in nanocrystalline solids. There exists a range of nanovoid size to make critical stress keep almost unchanged with the appearance of NGB sliding deformation. There is also a critical nanograin size to make critical stress reach the maximum value, at which dislocation emission and nanovoid growth occur most difficultly. • Suggest a theoretical model to describe effect of NGB sliding on nanovoid growth. • Derive analytical expression of critical stress for the first dislocation emission. • Nanovoid growth is slowed down or even arrested due to NGB sliding deformation. • Effect of NGB sliding deformation on critical stress is evaluated. • Effect of sizes of nanograin and nanovoid on critical stress is studied.

Molecular dynamics simulations of void growth in γ-TiAl single crystal

Molecular dynamics simulation was performed to study the growth of spherical nano-voids and the fracture properties of γ-TiAl single crystal. It is found that the emission of shear loops is the primary mechanism of the void growth: continued production of dislocation cores and the propagation of shear loops make the void grow. Cracks originate from the deformed area near the void surface. As the cracks propagate to the void surface and to the crystal boundaries, γ-TiAl single crystal finally fractures. The dependence of the void growth on the specimen size, strain rate, and void volume fraction was also investigated. The incipient yield strength decreases as the specimen size or void volume fraction increases, but increases with the increase of the strain rate. Young’s modulus is only sensitive to the void volume fraction.

Nanovoid growth in nanocrystalline metal by dislocation shear loop emission

Experimental evidence and molecular dynamics simulations of void growth indicate that dislocation shear loop emission is a viable mechanism of void growth. Based on this mechanism, a theoretical model to describe the growth of nanovoid at triple junction of nanocrystalline metal under equal biaxial remote stress is suggested. In this model, it is proposed that emission of dislocation is caused by the interaction between applied stress and image stress introduced by existing nanovoids. The critical stress is derived for emission of dislocation by considering the effects of surface stress. Within our description, dislocations emitted from surface of nanovoid are stopped at grain boundaries and the stress field generated by arrested dislocations can prevent further dislocation emission. The maximum number of dislocations emitted from surface of nanovoid, as a representation of the nanovoid growth, is analyzed as a function of grain size.

Growth and collapse of nanovoids in tantalum monocrystals

The growth and collapse of nanoscale voids are investigated for tantalum (a model body-centered cubic metal) under different stress states and strain rates by molecular dynamics (MD). Three principal mechanisms of deformation are identified and quantitatively evaluated: (i) shear loop emission and subsequent expansion from the surface of the void; (ii) cooperative shear loop emission from slip planes that are parallel to the same 〈111〉 slip direction and their combination, forming prismatic loops; (iii) twinning starting at the void surface. The generation and evolution of these defects are found to be functions of stress state and strain rate. Dislocations are found to propagate preferably on {110} and {112} planes, with Burgers vectors 1/2 〈111〉. The dislocation shear loops generated expand in a crystallographic manner, and in hydrostatic tension and compression generate prismatic loops that detach from the void. In uniaxial tensile strain along [100], the extremities of the shear loops remain attached to the void surface, a requisite for void growth. In uniaxial compressive strain, the extremities of the shear loops can also detach from the void surface. The difference in defect evolution is explained by the equal resolved shear stress in the hydrostatic loading case, in contrast with uniaxial strain loading. Nanotwins form preferably upon both uniaxial tensile strain and hydrostatic stress (in tension) and there is a slip-to-twinning transition as the strain rate exceeds 108s−1. A simplified constitutive description is presented which explains the preponderance of twinning over slip in tension beyond a critical strain rate. The formation of both dislocations and twins is confirmed through laser compression experiments, which provide strain rates (∼108s−1) comparable to MD. The dislocation velocities are determined by tracking the edge component of the expanding loops and are found to be subsonic even at extremely high stress and strain rates: 680ms−1 for 108s−1 and 1020ms−1 for 109s−1.

NANOSCALE VOID GROWTH IN MAGNESIUM: A MOLECULAR DYNAMICS STUDY

Molecular dynamics calculations were carried out in single crystal magnesium specimens to reveal the dependence of strain rate, temperature, and orientation of the crystal on damage evolution as defined by pore growth. Two specific crystallographic orientations [0001] and [Formula: see text] were examined. During a [0001] tensile test, twin boundaries developed at the void surface leading to a constraint on the [Formula: see text] crystallographic orientation. On the other hand, during the [Formula: see text] tensile deformation, emission of shear loops in the prismatic slip planes arose when void growth initiated. Furthermore, analysis of the damage components (nucleation, growth and coalescence) revealed that a large number of small voids nucleated that rapidly grew and fractured the specimens independent of the temperature and the strain rate.

Response to “Shear Impossibility—Comments on ‘Void Growth by Dislocation Emission’ and ‘Void Growth in Metals’”

We thank the authors of Ref. [1] for their comments and interest in our work [2–6]. We agree that the emission of shear loops on one single shear plane cannot lead to void growth. However, our simulations suggest that coordinated shear on non-parallel planes can lead to void growth/shrinkage [3–5]. Detailed descriptions of this process are still being worked out and represent an exciting area for future research. Thus, there seem to be two separate dislocation mechanisms operating either sequentially or simultaneously: shear and prismatic loop emission. Whereas prismatic loops are well known and have been extensively documented, the postulation of “special” shear loops is novel. The authors [1] have correctly pointed out that special restrictions need to be applied to these shear loops, something not mentioned in Refs. [2–6]. On the subject of shear impossibility, the authors [1] bring some good points in their comments of our papers. Indeed, the closed loop emitted from the surface of the void does not by itself expand the void. This is obvious from our papers, in which we considered a growth of a cylindrical void by emission of an edge dislocation [2], and a collapse of the void by an emission of an opposite-signed edge dislocation [5]. Thus, if both (positive and negative) dislocations were emitted (which is a 2-D counterpart of a dislocation loop), no net effect on the void growth would take place. Void growth takes place by the outward transfer of the material, which is possible even in an incompressible case due to the outward movement of the remote boundary of the body (the plastically deformed region around the void is surrounded by an elastically deformed region). Eq. (1) of the Comments on our papers [1] nicely states that the net amount of added material associated with the crea-

Void growth in metals: Atomistic calculations

Molecular dynamics simulations in monocrystalline and bicrystalline copper were carried out with LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) to reveal void growth mechanisms. The specimens were subjected to tensile uniaxial strains; the results confirm that the emission of (shear) loops is the primary mechanism of void growth. It is observed that many of these shear loops develop along two slip planes (and not one, as previously thought), in a heretofore unidentified mechanism of cooperative growth. The emission of dislocations from voids is the first stage, and their reaction and interaction is the second stage. These loops, forming initially on different {1 1 1} planes, join at the intersection, if the Burgers vector of the dislocations is parallel to the intersection of two {1 1 1} planes: a 〈1 1 0〉 direction. Thus, the two dislocations cancel at the intersection and a biplanar shear loop is formed. The expansion of the loops and their cross slip leads to the severely work-hardened region surrounding a growing void. Calculations were carried out on voids with different sizes, and a size dependence of the stress threshold to emit dislocations was obtained by MD, in disagreement with the Gurson model which is scale independent. This disagreement is most marked for the nanometer sized voids. The scale dependence of the stress required to grow voids is interpreted in terms of the decreasing availability of optimally oriented shear planes and increased stress required to nucleate shear loops as the void size is reduced. The growth of voids simulated by MD is compared with the Cocks–Ashby constitutive model and significant agreement is found. The density of geometrically necessary dislocations as a function of void size is calculated based on the emission of shear loops and their outward propagation. Calculations are also carried out for a void at the interface between two grains to simulate polycrystalline response. The dislocation emission pattern is qualitatively similar to microscope observations.

Atomistic modeling of shock-induced void collapse in copper

Nonequilibrium molecular-dynamics (MD) simulations show that shock-induced void collapse in copper occurs by emission of shear loops. These loops carry away the vacancies which comprise the void. The growth of the loops continues even after they collide and form sessile junctions, creating a hardened region around the collapsing void. The scenario seen in our simulations differs from current models that assume that prismatic loop emission is responsible for void collapse. We propose a dislocation-based model that gives excellent agreement with the stress threshold found in the MD simulations for void collapse as a function of void radius.