Dislocations In Fcc Metals Research Articles

Peierls–Nabarro modeling of twinning dislocations in fcc metals

Metals with fcc structure may exhibit deformation twinning under specific conditions, which is an interesting but somewhat elusive aspect of their deformation behavior. It is well acknowledged that the phenomenon occurs through the activities of twinning partial dislocations. However, the lack of a comprehensive understanding of their fundamental properties obstructs the development of detailed multiscale plasticity models for the fcc metals. Here, we explore the core-structures and lattice friction of twinning partials through atomistically informed numerical modeling. To this end, we choose four fcc crystals with widely differing stacking fault energies. Using the semi-discrete variational Peierls–Nabarro model with non-local and surface corrections, we compute the core-widths and Peierls stresses of edge and screw twinning dislocations. In particular, the alternate-shear mode of twinning has been considered in addition to the regular layer-by-layer mechanism. In the former case, the stable disregistry energy of the middle layer is observed to be significantly less than the unsheared configuration, which is enough to overcome the Peierls barrier spontaneously. This study also highlights the significance of incorporating the correction terms, the absence of which may lead to significant inaccuracy in estimating the intrinsic lattice resistance of the twinning partials.

An atomistically-informed phase-field model for quantifying the effect of hydrogen on the evolution of dislocations in FCC metals

A new atomistically-informed phase-field model is developed to quantify the effect of hydrogen on the evolution of dislocations. In this model, the long-range interaction between dislocation and hydrogen is considered through the elastic interaction energy due to their eigenstrain fields, and the short-range interaction is taken into account by the hydrogen-affected dislocation core energy. The non-conserved phase-field order parameters describing the evolution of dislocations are controlled by the time-dependent Ginzburg-Landau equations, while the conserved order parameter representing the distribution of hydrogen atoms is governed by the Cahn-Hilliard diffusion equation. To explore the capability of this newly developed phase-field model, it is employed to simulate the hydrogen effect on both the static dissociation of dislocations and the dynamics shrinkage of a dislocation glide loop at zero applied stress in nickel (Ni). The simulation results show that, on the one hand, hydrogen can enhance the equilibrium spacing between two partial dislocations mainly due to the short-range interaction. On the other hand, hydrogen can impede the shrinkage of the glide loop by reducing its line energy. These results are well consistent with the atomistic calculations and theoretical predictions. It means that this new model can well capture both the hydrogen-affected dislocation dynamics influenced by long-range interaction and the hydrogen-affected equilibrium configurations of dislocations dominated by short-range interaction. Finally, with minor modifications, this new model can be further employed to study the effect of hydrogen on the evolution of various microstructures beyond dislocation networks at the mesoscale, which is crucial for a thorough understanding of the hydrogen-induced premature failure mechanisms.

Atomistic dislocation core energies and calibration of non-singular discrete dislocation dynamics

The total energy of an atomistic dislocation includes contributions from the inelastic/large-distortion ‘core’ region. Capturing this inelastic ‘core’ energy is important, especially for dislocations with a curvature in the 10–100 nm scale. Current implementations of discrete dislocation dynamics (DDD) mesoscale simulations either approximate or neglect the core energy and so do not provide consistency with fully-atomistic studies. Using established interatomic potentials for FCC metals, the total dislocation energy is computed directly in atomistic simulations of straight dislocations and a core energy at any desired cut-off core radius is obtained as a function of dislocation character. A proper introduction of the atomistic core energy into the ParaDiS DDD code that uses a non-singular theory (Cai et al 2006 J. Mech. Phys. Solids 54 561–87) is then presented. The resulting atomistically-informed ParaDiS DDD is used to simulate the periodic bow-out of edge and screw dislocations in near-elastically-isotropic aluminum at various length and stress, with comparisons to fully-atomistic simulations. Generally good agreement is obtained between DDD and atomistics, with the best agreement achieved using a non-singular regularization parameter in the range of a = 5 – 10b. The analysis is then extended to compute the core energy of the Shockley partial dislocations that arise in the dissociation of perfect dislocations in fcc metals.

Phase-field-based calculations of the disregistry fields of static extended dislocations in FCC metals

ABSTRACTIn the continuum context, the displacements of atoms induced by a dislocation can be approximated by a continuum disregistry field. In this work, two phase-field (PF)-based approaches and their variants are employed to calculate the disregistry fields of static, extended dislocations of pure edge and pure screw character in two face-centred cubic metals: Au and Al, which have distinct stable stacking fault energy and elastic anisotropy. A new truncated Fourier series form is developed to approximate the generalised stacking fault energy (GSFE) surface, which shows significant improvement over the previously employed Fourier series form. By measuring the intrinsic stacking fault (ISF) width and partial dislocation core size in different ways, the PF-based disregistry fields are quantitatively compared against those predicted by molecular statics. In particular, two new measures for the ISF widths are proposed and shown to overcome drawbacks of the more commonly used standards in the literature. Our calculations also show that continuum formulation of the elastic energy and the GSFE for a homogeneous surface can successfully characterise the core structure. Last, our comparisons highlight the significance of including the gradient energy in the free energy formulation when an accurate description of the dislocation core structure is desired.

Effects of the stacking fault energy fluctuations on the strengthening of alloys

In alloys and high entropy alloys the stacking fault energy varies with the local composition. The effects of these energy fluctuations on the strengthening are studied using dislocation dynamics simulations that track the evolution of partial dislocations in FCC metals at zero temperature. Different values of the intrinsic stacking fault energy are assigned to regions with size in the range of 0.5 nm–12 nm in the slip plane, while the other mechanical properties are left constant. A theoretical model is derived and compared to the simulation results. In the model and the simulations the predicted value of the yield stress grows with larger fluctuations of the stacking fault energy. Furthermore, a strong size dependency is observed, with a maximum in the strength attained when the mean region size approaches the average equilibrium stacking fault width. In summary, the strength of high entropy alloys can be improved by introducing disorder in the chemical misfit with a characteristic length scale of the order of the average stacking fault width.

Mechanism of intrinsic diffusion in the core of screw dislocations in FCC metals – A molecular dynamics study

The mechanism of self-diffusion in the absence of any pre-existing point defects (intrinsic diffusion) along an a/2 〈1 1 0〉 screw dislocation in FCC metals is studied using molecular dynamics simulations. High diffusivity along the dislocation core at elevated temperatures is found to be due to the constriction of partial dislocations, where a vacancy-interstitial pair forms. The two point defects separate and start to migrate along the core, giving rise to diffusion. Formation energy for both vacancy and self-interstitial are found to be much lower on the constricted node of partial dislocations compared to other atomic sites, indicating the important role of the constriction in enhancing the diffusion.

Dynamic behaviour of mixed dislocations in FCC metals under multi-oriented loading with molecular dynamics simulations

Conventional models of plastic deformation are based on linear elastic approximations with respect to the empirical results obtained from pure screw or pure edge dislocations. In real materials, however, mixed dislocations are far more commonly observed and their motion carries the bulk of the plastic deformation. Molecular dynamics (MD) simulations are useful to ‘unlock’ the temperature and structure dependence of the phonon drag effect, and the phonon drag strongly influences the mobility of dislocations in FCC metals. The Burgers vector of a dislocation dictates the necessary orientation of the stress required to control the glide behaviour. Hence, the mobility of mixed dislocations can only be studied once the stress can be carefully controlled for both the τxy and τyz components simultaneously. It is non-trivial to accurately control the global stress components effectively under multi-orientation testing. To this end, the present study evaluates the effectiveness of utilising a well-tuned barostat to show the influence of stress loading orientation on the mobility of a mixed 30° dislocation dipole. Self-consistent results with two different EAM potentials and size-independent steady-state velocities (excluding only the lowest stress and smallest size case), suggest that this approach is valid. The glide stress, τg, is contrasted with the shear component in a perpendicular orientation within the glide plane, referred to as the Escaig stress, τe. When the appropriate stress control regime and cell dimensions were applied, the influence of dipole image forces were mitigated down to stresses as low as 5MPa. The stacking fault width was influenced by τe in an identical manner for the two different EAM potentials, once compensation was made to offset the discrepancy in the stacking fault energy. The stacking fault width was effected in a non-linear relationship with τe, which caused either an increase or decrease depending on the orientation and magnitude of τe. The phonon dissipation and radiative damping exhibited by the mixed dislocations was qualitatively better matched to the characteristics of pure edge dislocations, and the calculated drag coefficient was significantly smaller than has been found for pure screw dislocations in the literature. Results show that when the appropriate methodology is applied, the stress-velocity curve can follow a smoothly linear function of the τg component for mixed stress conditions with any combination of τe.

Factors affecting the dissociation width of dissociated dislocations in FCC metals and alloys

Dislocations in FCC structure are dissociated into two partial dislocations. The dissociation width of a dissociated dislocation controls the mechanical behavior of the alloy. Experimental work using transmission electron microscopy on factors determining the dissociation width is reviewed with special reference to the Suzuki segregation.

Atomistic simulations of the interactions of hydrogen with dislocations in fcc metals

The interactions of hydrogen with both edge and screw dislocations in face-centered-cubic (fcc) metals are investigated using molecular statics simulations of nickel-hydrogen as a model system. It is shown that the most energetically favorable sites for H occupation are octahedral sites in the perfect fcc lattice, tetrahedral sites in the stacking fault, and both octahedral and tetrahedral sites in the Shockley partial cores of dislocations. Moreover, the diffusion barrier for H is relatively high except for pipe diffusion near the Shockley partial cores. It is also shown that partial dislocation cores have the strongest interactions with hydrogen. The hydrogen-dislocation interactions (attractive or repulsive) and the change in stacking width (increase or decrease) depend on the hydrogen-occupying sites (octahedral or tetrahedral) and the positions of the hydrogen atoms relative to the strongest binding energy sites. In particular, on the dislocation glide plane, only hydrogen atoms in both of the Shockley partial core regions can result in increasing the stacking fault width, while those in the stacking fault region or in the perfect fcc lattice region have no observable effects. On the other hand, uniformly distributed hydrogen in the tension region near the center of a dislocation can result in decreasing the stacking fault width. The stable stacking fault energy also decreases with increasing hydrogen concentration due to the resulting negative binding energy of hydrogen to the stacking fault, while the unstable stacking fault energy increases with increasing hydrogen concentration. This may result in pinning the dislocation due to the nature of short-range interaction between interstitial hydrogen atoms and their neighboring Ni atoms.

Influence of the stacking fault energy surface on partial dislocations in fcc metals with a three-dimensional phase field dislocations dynamics model

We present simulations of the dissociation of perfect dislocations into extended partial dislocations in aluminum, palladium, and nickel using a phase field dislocation dynamics (PFDD) theory that incorporates the $\ensuremath{\gamma}$ surface. As expected from dislocation theory, the simulations show that increasing the intrinsic stacking fault energy, normalized by the product of the shear modulus and Burgers vector, decreases the equilibrium stacking fault width. Significantly, it is also found that increasing the unstable stacking fault energy has the same effect when the intrinsic stacking fault energy is held constant. Furthermore, our results show that the equilibrium configurations cannot be described only by the ratio between the intrinsic and unstable stacking fault energies as previously suggested but rather by their product.

Analysis of defect structural evolution in fcc metals irradiated with neutrons under well defined boundary conditions

Defect structural evolutions near pre-existing defects such as surfaces, grain boundaries and dislocations in fcc metals are studied to clarify point defect processes during irradiation. By the comparison of Au irradiated as thin foils with fission neutrons and fusion neutrons, the PKA energy to produce a stacking fault tetrahedron is determined to be 80 keV with a production efficiency of 0.05. Grain boundaries are effectively used to detect the existence of one-dimensional motion of interstitial clusters. In Ni and Ni binary alloys (2 at.% Si, Cu, Ge or Sn), there is a good coincidence between the void growth and one-dimensional motion of interstitial clusters. The coincidence is, however, not good for Cu. Screw dislocations with jogs turn into helical dislocations by absorbing one type of point defects. The difference of freely migrating defects between fission and fusion neutron irradiation is measured as a function of irradiation dose and it is concluded that the same number of freely migrating defects is generated from each subcascade in fission and fusion neutron irradiated Ni.

A dipole model for the cross-slip of screw dislocations in fcc metals

Abstract An attempt is made to reconcile observations and theories of cross-slip with recent models of cyclic plasticity and the fatigue endurance limit of crystals. According to this view, the stress required to separate two screw dislocations of opposite signs, which are just on the point of mutual annihilation by cross-slip, controls both the stress τIII at the end of linear (stage II) hardening and the saturation stress [sgrave]sat in the cyclic stress-strain curve. It is shown, in confirmation of conclusions by many earlier researchers, that direct annihilation of the dislocations cannot account for the temperature dependence of the stress, although it might account for observations on silver and copper at liquid-helium temperature. Based on the work of Hirsch, a model of stress-aided migration of jogs is proposed, which seems able to account for the observations if the activation energy for the migration is about 0.1 eV in copper, nickel and aluminium. A by-product of the model is a possible reinter...

The dynamics of dislocation interaction with sessile self-interstitial atom (SIA) defect cluster atmospheres

The interaction dynamics between dislocations and radiation induced sessile self-interstitial atom (SIA) dislocation loops in FCC metals are investigated. As a result of dislocation line flexibility, its equilibrium configuration is found to be sensitive to the elastic field of nearby SIA dislocation loops. Dislocation line flexibility also influences the critical stress to free trapped dislocations from pinning atmospheres (i.e. the critical resolved shear stress (CRSS)). Calculated CRSS values differ by up to 100% from the estimates of Trinkaus et al. [J. Nucl. Mater. 249 (1997) 91; J. Nucl. Mater. 251 (1997) 172], which are based on cluster forces exerted on static rigid dislocations. The mechanism of dislocation unpinning from random cluster atmospheres is shown to be a consequence of morphological instabilities on the dislocation line. The initial location of the unlocking instability is always associated with regions of minimum line tension in the vicinity of the lowest cluster density. The growth of dislocation shape fluctuations leads to a sequence of unzipping events, freeing the dislocation from the elastic field of cluster atmospheres. The relative critical shear stress to unlock dislocations in FCC metals, ( τ C/ μ), is found to be in the range: 0.001–0.002, for random atmosphere cluster densities of 10 24–10 25 m 3 , and in the range: 0.0014–0.003, for coherent cluster atmospheres of the same density range. These values are factors of 4–6 smaller than Kroupa's estimates. Implications of these results to the determination of the upper yield point of irradiated FCC metals are discussed.

A strain-gradient thermodynamic theory of plasticity based on dislocation density and incompatibility tensors

In this work, we discuss a thermodynamic theory of plasticity for self-organization of collective dislocations in FCC metals. The theory is described by geometrical tensor quantities of crystal defect fields such as dislocation density tensor, representing net mobile dislocation density and geometrically necessary boundaries, and the incompatibility tensor representing immobile dislocation density. Conservation laws for the two kinds of dislocation density are formulated with dislocation products and interactions terms. Based on the second law of thermodynamics, we drive basic constitutive equations for the dislocation flux, production and interaction terms of dislocations. We also derive a set of reaction-diffusion equations for the dislocation density tensor and incompatibility tensor which describes the vein and persistent slip band (PSB) ladder structures. These equations are analyzed using linear stability and bifurcation analysis. An intrinsic mesoscopic length scale is determined which provides an estimate for the wavelength of the PSBs. The basic aspects of the model are motivated and substantiated by analyzing the stress fields of various possible dislocation configurations using discrete dislocation dynamics.

Peierls Potential for dislocations in fcc metals

This paper provides a new value for the Peierls Potential for a (100) dislocation in Copper. The calculation is based on the Second Moment Tight Binding approach. The lattice is let to relax in the neighborhood of the dislocation and minimum energy configurations are found for both the Peierls Stress curve minimum and maximum. The energy difference, converted to pressure, between the two cases is the Peierls Potential. We found a value of 28 MPa, quite in agreement with experimental results, which vary from 20 to 30 MPa. Numerical conditions are discussed.

3D simulation of a nanoindentation test at a mesoscopic scale

A 3D simulation of the dynamics and interactions of dislocations in FCC metals has been developed in the last few years. This simulation is based on discretization of both time and space at a mesoscopic scale. The model has been validated on results coming from the dislocation theory in the case of the bulk crystal behaviour. In order to compare the simulation to experimental results, we choose to apply full complex boundary conditions to the simulated volume. Following that goal, the 3D dislocation simulation has been linked to a finite element code CASTEM2000. The heterogenous stress field is computed on every segment through a finite element resolution. Through this method, we present first results of a nano-indentation simulation.

Edge dislocations in fcc metals: Microscopic calculations of core structure and positron states in Al and Cu.

Structures of edge dislocations (dislocation line direction [11\ifmmode\bar\else\textasciimacron\fi{}2], Burgers vector (a/2)[110]) in aluminum and copper are studied with the molecular-dynamics simulation method which incorporates the effective-medium theory extended to include atomic interactions beyond the nearest neighbors. The observed equilibrium distance between the Shockley partial dislocations in both metals agrees well with the estimate evaluated from elasticity theory by using known values for the stacking-fault energy and the bulk modulus. Effective-medium theory leads to a dislocation core which is narrower than the previous results of the pair-potential calculations for simple metals. The vacancy formation energy in copper is higher at the center of the stacking-fault region than in the bulk, which suggests that pipe diffusion can take place only in the narrow partial dislocation core. In the second part of the work, the role of the dislocation line and of the associated point defects as positron traps are studied in both metals. The pure dislocation line forms only a shallow trap but it can be a precursor state for deeper traps, like vacancies and single jogs on the dislocation line. The calculated lifetimes for these defects are in good agreement with the experimentally observed lifetime components coming from dislocations.

A MODEL FOR ULTRASONIC EFFECTS DURING AN FCC-HCP MARTENSITIC TRANSFORMATION

A MODEL FOR ULTRASONIC EFFECTS DURING AN FCC-HCP MARTENSITIC TRANSFORMATION

Anisotropic elastic interaction between misfit defects and extended screw dislocations in fcc metals

The energy and force of interaction of an extended screw dislocation with spherical and tetragonal defects were calculated for several fcc metals using anisotropic and isotropic elasticity theories. It is shown that anisotropy has a large effect on the magnitude of interaction energy and interaction force, as well as on the shape of the energy-distance and force-distance curves. The maximum value of the interaction energy was always smaller in the anisotropic case than in the isotropic case. But the maximum resisting force to dislocation motion due to defect-dislocation interaction is not always smaller in the anisotropic crystal. Computation of the hardening coefficient at 0 °K for several fcc metals indicates that tetragonal defects cause significantly larger hardening than spherical defects.

Solute segregation under irradiation

Recent calculations of substitutional solute segregation to planar surfaces, voids, and dislocations in fcc metals during irradiation are reviewed. The calculations were based on a kinetic model that included the effects of vacancy and dumbellinterstitial diffusional encounters with solute atoms, diffusion of point defects and bound complexes, and spatially dependent reaction terms. Solute segregation is found to be significant in the temperature range from 0.2 to 0.6 Tm. The temperature for maximum segregation is appreciably higher for heavy-ion bombardment or high-voltage-electron-microscope irradiation rates than for fast-reactor irradiation rates. Segregation is also found to be maximum when the interstitialsolute binding energy is sufficiently high so that the migration energies of the vacancy and interstitial-solute complex become comparable. Furthermore, the magnitude of the segregation effect varies with foil thickness, void size, void number density, dislocation-capture radius, and dislocation density.