Stress dependence of cross slip energy barrier for face-centered cubic nickel

The energy barrier for the cross slip of screw dislocations in face-centered cubic (FCC) nickel as a function of multiple stress components is predicted by both continuum line tension and discrete atomistic models. Contrary to Escaig's claim that the Schmid stress component has a negligible effect on the energy barrier, we find that the line tension model, when solved numerically, predicts comparable effects from the Schmid stress and the Escaig stress on the cross slip plane. When the line tension model is compared against an atomistic model for FCC nickel, a good agreement is found for the effect of the Escaig stress on the glide plane. However, the atomistic model predicts a stronger effect than the line tension model for the two stress components on the cross slip plane. This discrepancy is larger at higher stresses and is also more severe for the Escaig stress component than for the Schmid stress component.     

Derivation of Orowan's Law from the Peierls–Nabarro Model

In this paper we consider the time dependent Peierls-Nabarro model in dimension one. This model is a semi-linear integro-differential equation associated to the half Laplacian. This model describes the evolution of phase transitions associated to dislocations. At large scale with well separated dislocations, we show that the dislocations move at a velocity proportional to the effective stress. This implies Orowan's law which claims that the plastic strain velocity is proportional to the product of the density of dislocations by the effective stress.     

Threading dislocation densities in semiconductor crystals: A geometric approach

In this Letter, we introduce a geometric model to explain the origin of the observed shallow levels in semiconductors threaded by a dislocation density. We show that a uniform distribution of screw dislocations acts as an effective uniform magnetic field which yields bound states for a spin-half quantum particle, even in the presence of a repulsive Coulomb-like potential. This introduces energy levels within the band gap, increasing the carrier concentration in the region threaded by the dislocation density and adding additional recombination paths other than the near band-edge recombination.     

Line-integral representations for the elastic displacements,stresses and interaction energy of arbitrary dislocation loops in transversely isotropic bimaterials

The elastic displacements, stresses and interaction energy of arbitrarily shaped dislocation loops with general Burgers vectors in transversely isotropic bimaterials (i.e. joined half-spaces) are expressed in terms of simple line integrals for the first time. These expressions are very similar to their isotropic full-space counterparts in the literature and can be easily incorporated into three-dimensional (3D) dislocation dynamics (DD) simulations for hexagonal crystals with interfaces/surfaces. All possible degenerate cases, e.g. isotropic bimaterials and isotropic half-space, are considered in detail. The singularities intrinsic to the classical continuum theory of dislocations are removed by spreading the Burgers vector anisotropically around every point on the dislocation line according to three particular spreading functions. This non-singular treatment guarantees the equivalence among different versions of the energy formulae and their consistency with the stress formula presented in this paper. Several numerical examples are provided as verification of the derived dislocation solutions, which further show significant influence of material anisotropy and bimaterial interface on the elastic fields and interaction energy of dislocation loops.     

Quantifying dislocation microstructure evolution and cyclic hardening in fatigued face-centered cubic single crystals

Discrete dislocation dynamics simulations were performed to investigate the dislocation microstructure evolution and cyclic hardening during the early stages of fatigue loading in nickel single crystals. The effects of the crystal size and initial dislocation densities on both the mechanical response and the evolution of dislocation microstructure were quantified. Crystals having an initial dislocation density of 10¹²  m⁻² and diameter less than $2.0\mathrm{\mu }\mathrm{m}$ do not show any dislocation density multiplication or cyclic hardening. In contrast, crystals having the same initial dislocation density and diameters larger than $2.0\mathrm{\mu }\mathrm{m}$ show a significant dislocation density accumulation in the form of dislocation cell-like structures, even after only a few number of loading cycles. This dislocation density accumulation was also accompanied by considerable cyclic hardening. The dislocation cell size and its wall thickness increase with increasing crystal size. With increasing dislocation density the critical crystal size, at which dislocation cell-structures form, decreases. The information theoretic entropy is utilized as a metric to quantify the extent of dislocation patterning and the formation and evolution of dislocation cell structures over time. Cross-slip was found to play a dominant role in the dislocation cell-structure formation. Further insights on the mechanisms contributing to the observed behavior are presented and discussed.     

Multiscale diffusion method for simulations of long-time defect evolution with application to dislocation climb

In many problems of interest to materials scientists and engineers, the evolution of crystalline extended defects (dislocations, cracks, grain boundaries, interfaces, voids, precipitates) is controlled by the flow of point defects (interstitial/substitutional atoms and/or vacancies) through the crystal into the extended defect. Precise modeling of this behavior requires fully atomistic methods in and around the extended defect, but the flow of point defects entering the defect region can be treated by coarse-grained methods. Here, a multiscale algorithm is presented to provide this coupling. Specifically, direct accelerated molecular dynamics (AMD) of extended defect evolution is coupled to a diffusing point defect concentration field that captures the long spatial and temporal scales of point defect motion in the presence of the internal stress fields generated by the evolving defect. The algorithm is applied to study vacancy absorption into an edge dislocation in aluminum where vacancy accumulation in the core leads to nucleation of a double-jog that then operates as a sink for additional vacancies; this corresponds to the initial stages of dislocation climb modeled with explicit atomistic resolution. The method is general and so can be applied to many other problems associated with nucleation, growth, and reaction due to accumulation of point defects in crystalline materials.     

Atomistic simulation analysis of the effects of void interaction on void growth and coalescence in a metallic system

Material deformation caused by the interaction between defects is a significant factor of material fracture failure. The present study employs molecular dynamics simulations of single-void and double-void crystalline Ni atomic systems to investigate inter-void interactions. Furthermore, simulations showing the evolution of dislocations for three different crystallographic orientations are conducted to study the void growth and coalescence. The simulations also consider the effect of the radius of the secondary void on dislocation evolution. The results show that double-void systems are more prone to yield than single-void systems. Further microstructural analysis indicates that the interaction between voids is realized by dislocation reactions. The simulation results of the dislocation evolution of the three orientations reveal that a relationship exists between the evolution of the dislocation density and the stress-strain curve. At the initial stage of dislocation, the dislocation grows slowly, and consists of Shockley partial dislocation. The dislocation growth rate then increases significantly in the sharply declining stage of the stress-strain curve, where most of dislocations are Shockley partial dislocation. Analysis of the dislocation length during the overall simulation indicates that the dislocation length of the [110] orientation is the longest, followed by that of the [111] orientation and the [100] orientation, which has the shortest dislocation length.     

New phenomena concerning a screw dislocation interacting with two imperfect interfaces

Dislocation mobility and stability in nanocrystals and electronic materials are influenced by the material composition and interface conditions. Its mobility and stability then affect the mechanical behaviors of the composites. In this paper, we first address, in detail, the problem of a screw dislocation located in an annular coating layer which is imperfectly bonded to the inner circular inhomogeneity and to the outer unbounded matrix. Both the inhomogeneity-coating interface and coating-matrix interface are modeled by a linear spring with vanishing thickness to account for the possible damage occurring on the interface. An analytic solution in series form is derived by means of complex variable method, with all the unknown constants being determined explicitly. The solution is then applied to the study of the dislocation mobility and stability due to its interaction with the two imperfect interfaces. The most interesting finding is that when the middle coating layer is more compliant than both the inner inhomogeneity and the outer unbounded matrix and when the interface rigidity parameters for the two imperfect interfaces are greater than certain values, one stable and two unstable equilibrium positions can exist for the dislocation. Furthermore, under certain conditions an equilibrium position, which can be either stable or unstable (i.e., a saddle point), can exist, which has never been observed in previous studies. Results for a screw dislocation interacting with two parallel straight imperfect interfaces are also presented as the limiting case where the radius of the inner inhomogeneity approaches infinity while the thickness of the coating layer is fixed.     

Size and strain rate effects in tensile strength of penta-twinned Ag nanowires

Penta-twinned Ag nanowires(pt-AgNWs) have recently attracted much attention due to their interesting mechanical and physical properties. Here we perform largescale atomistic simulations to investigate the influence of sample size and strain rate on the tensile strength of pt-AgNWs. The simulation results show an apparent size effect in that the nanowire strength(defined as the critical stress for dislocation nucleation) increases with decreasing wire diameter. To account for such size effect, a theoretical model involving the interaction between an emerging dislocation and the twin boundary has been developed for the surface nucleation of dislocations. It is shown that the model predictions are in quantitative agreement with the results from atomistic simulations and previous experimental studies in the literatures. The simulations also reveal that nanowire strength is strain-rate dependent, which predicts an activation volume for dislocation nucleation in the range of 1–10b~3,where b is the magnitude of the Burgers vector for a full dislocation.