Dislocation transmission across the Cu/Ni interface: a hybrid atomistic–continuum study

The strengthening mechanisms in bimetallic Cu/Ni thin layers are investigated using a hybrid approach that links the parametric dislocation dynamics method with ab initio calculations. The hybrid approach is an extension of the Peierls–Nabarro (PN) model to bimaterials, where the dislocation spreading over the interface is explicitly accounted for. The model takes into account all three components of atomic displacements of the dislocation and utilizes the entire generalized stacking fault energy surface (GSFS) to capture the essential features of dislocation core structure. Both coherent and incoherent interfaces are considered and the lattice resistance of dislocation motion is estimated through the ab initio-determined GSFS. The effects of the mismatch in the elastic properties, GSFS and lattice parameters on the spreading of the dislocation onto the interface and the transmission across the interface are studied in detail. The hybrid model shows that the dislocation dissociates into partials in both Cu and Ni, and the dislocation core is squeezed near the interface facilitating the spreading process, and leaving an interfacial ledge. The competition of dislocation spreading and transmission depends on the characteristics of the GSFS of the interface. The strength of the bimaterial can be greatly enhanced by the spreading of the glide dislocation, and also increased by the pre-existence of misfit dislocations. In contrast to other available PN models, dislocation core spreading in the two dissimilar materials and on their common interface must be simultaneously considered because of the significant effects on the transmission stress.     

界面结构对Cu/Ni多层膜纳米压痕特性影响的分子动力学模拟

金属多层膜调制周期下降到纳米级时,其力学性质会发生显著改变. Cu-Ni晶格失配度约为2.7%,可以形成共格界面和半共格界面,实验中实现沿[111]方向生长的调制周期为几纳米且具有异孪晶界面结构的Cu/Ni多层膜,其力学性质发生显著改变.本文采用分子动力学方法对共格界面、共格孪晶界面、半共格界面、半共格孪晶界面等四种不同界面结构的Cu/Ni多层膜进行纳米压痕模拟,研究压痕过程中不同界面结构类型的形变演化规律以及位错与界面的相互作用,获取Cu/Ni多层膜不同界面结构对其力学性能的影响特征.计算结果表明,不同界面结构的样品在不同压痕深度时表现出的强化或软化作用机理不同,软化机制主要是由于形成了平行于界面的分位错以及孪晶界面的迁移,强化机制主要是由于界面对位错的限定作用以及失配位错网状结构与孪晶界面迁移时所形成的弓形位错之间的相互作用.     

Effect of H impurity on misfit dislocation in Ni-based single-crystal superalloy: molecular dynamic simulations

The effect of H impurity on the misfit dislocation in Ni-based single-crystal superalloy is investigated using the molecular dynamic simulation. It includes the site preferences of H impurity in single crystals Ni and Ni₃Al, the interaction between H impurity and the misfit dislocation and the effect of H impurity on the moving misfit dislocation. The calculated energies and simulation results show that the misfit dislocation attracts H impurity which is located at the γ/γ' interface and Ni₃Al and H impurity on the glide plane can obstruct the glide of misfit dislocation, which is beneficial to improving the mechanical properties of Ni based superalloys.     

Transformation of Slip Dislocations in Σ3 Grain Boundary

Grain boundary processes during plastic deformation of bicrystals were studied by TEM. Two methods were used. In situ straining in the electron microscope followed by post mortem examination and post mortem observation of specimens previously deformed by in situ synchrotron radiation X-ray topography. Two mechanisms governing slip propagation across a coherent twin boundary in a Fe-Si alloy bicrystal were identified. The first mechanism is a dissociation of a slip dislocation with the Burgers vector lying parallel to the boundary into three equal grain boundary dislocations. The second mechanism is a decomposition of a slip dislocation with Burgers vector inclined to the boundary into a dislocation mobile in the other grain and two screw grain boundary dislocations.     

镍基单晶高温合金界面位错网在剪切载荷作用下的演化

运用分子动力学方法,研究了镍基单晶高温合金γ/γ' 相界面错配位错网在剪切载荷作用下的演化特征.结果表明:(100),(110) 和 (111) 三种相界面形成的位错网在载荷作用下有不同形式和不同程度的损伤,其变形和损伤随温度的增加而增加.在相同的剪切载荷和温度作用下,(100) 相界面形成的正方形位错网最稳定. 关键词： 镍基单晶高温合金 界面位错网 分子动力学     

Sheared solid materials

We present a time-dependent Ginzburg-Landau model of nonlinear elasticity in solid materials. We assume that the elastic energy density is a periodic function of the shear and tetragonal strains owing to the underlying lattice structure. With this new ingredient, solving the equations yields formation of dislocation dipoles or slips. In plastic flow high-density dislocations emerge at large strains to accumulate and grow into shear bands where the strains are localized. In addition to the elastic displacement, we also introduce the local free volumem. For very smallm the defect structures are metastable and long-lived where the dislocations are pinned by the Peierls potential barrier. However, if the shear modulus decreases with increasingm, accumulation ofm around dislocation cores eventually breaks the Peierls potential leading to slow relaxations in the stress and the free energy (aging). As another application of our scheme, we also study dislocation formation in two-phase alloys (coherency loss) under shear strains, where dislocations glide preferentially in the softer regions and are trapped at the interfaces.     

The activation and the spreading of deformation in a fully lamellar Ti–47 at.% Al–1 at.% Cr–0.2 at.% Si Alloy

The spreading of deformation in a lamellar Ti–47?at.% Al–1?at.% Cr–0.2?at.% Si alloy deformed under compression is studied at 25°C and 600°C. This microstructure is largely dominated by twin-related variants which are separated by either twin interfaces or thin α ₂ slabs. The alloy deforms at both temperatures by ordinary dislocations and twins. Deformation in a particular γ variant and its adjacent twin-related variant involves the same kind of glide system, either ordinary dislocations or twins. This property is found to be true for all twin-related lamellae. The occurrence of this correlated glide is explained by the introduction of the notion of pilot and driven orientations. The lamellar orientation in which the operating glide system is activated on the basis of Schmid factor considerations is termed the pilot orientation. It imposes its deformation system on to the twin-related lamella, called the driven orientation, whose deformation may not involve the slip system most favoured by the applied stress.     

A computational approach towards modelling dislocation transmission across phase boundaries

To study the nanoscopic interaction between edge dislocations and a phase boundary within a two-phase microstructure the effect of the phase contrast on the internal stress field due to the dislocations needs to be taken into account. For this purpose a 2D semi-discrete model is proposed in this paper. It consists of two distinct phases, each with its specific material properties, separated by a fully coherent and non-damaging phase boundary. Each phase is modelled as a continuum enriched with a Peierls–Nabarro (PN) dislocation region, confining dislocation motion to a discrete plane, the glide plane. In this paper, a single glide plane perpendicular to and continuous across the phase boundary is considered. Along the glide plane bulk induced shear tractions are balanced by glide plane shear tractions based on the classical PN model. The model's ability to capture dislocation obstruction at phase boundaries, dislocation pile-ups and dislocation transmission is studied. Results show that the phase contrast in material properties (e.g. elastic stiffness, glide plane properties) alone creates a barrier to the motion of dislocations from a soft to a hard phase. The proposed model accounts for the interplay between dislocations, external boundaries and phase boundary and thus represents a suitable tool for studying edge dislocation–phase boundary interaction in two-phase microstructures.     

Interface dislocation structures at the onset of coherency loss in nanoscale Ni–Cu bilayer films

We have performed a transmission electron microscopy study, using weak beam imaging, of the interface dislocation arrays that form initially at the (001) Ni–Cu interface during coherency loss. Interface dislocations were absent in the 2.5?nm Ni/100?nm Cu bilayers, but were present in the 3.0?nm Ni samples, indicating that the critical Ni film thickness for coherency loss is between 2.5 and 3?nm. The key features of the interface dislocation structure at the onset of coherency loss are: (i) the majority of interface dislocations are 60° dislocations, presumably formed by glide of threading dislocations in the coherently stressed Ni layer, and have Burgers vector in the {111} glide plane; (ii) the interface contained approximately 5% Lomer edge dislocations, with Burgers vector in the {001} interface plane, and an occasional Shockley partial dislocation and (iii) isolated segments of interface dislocations terminating at the surface are regularly observed. Possible mechanisms that lead to these dislocation configurations at the interface are discussed. This experimental study shows that near the critical thickness, accumulation of interface dislocations occurs in a somewhat stochastic fashion with favourable regions where coherency is first lost.     

Exponent for Hall–Petch behaviour of ultra-hard multilayers

Elastically inhomogeneous multilayer films are being exploited for use as ultra-hard coatings. These films exhibit a strong dependence between the compositional wavelength of the film, Λ, and the hardness, H=KΛ^?a+H₀ where the scaling exponent a depends on the elastic properties of the individual layers (shear moduli and Poisson ratios). The dislocation pileup model can explain this trend and form a bridge between the microscopic strength of multilayer interfaces and the macroscopic strength of the multilayer. A semianalytic solution to the pileup model of multilayer strength is presented. All parameter dependencies are solved analytically except a single dimensionless coefficient which is found from numerical simulation. The predictions are compared to data from a 2D discrete dislocation model and to experimental Cu/Ni data. Coefficients and exponents are given for some additional material systems.     

Mechanisms of high-temperature creep of nickel-based superalloys under low applied stresses

[001] single-crystal specimens of the superalloys CMSX-4 and CMSX-10 were tested for creep at 1100°C under tensile stresses between 105 and 135?MPa, where they show pronounced steady creep. The deformed superalloys were analysed by density measurements, scanning electron microscopy and transmission electron microscopy which supplied information about porosity growth, evolution of the γ–γ′ microstructure, dislocation mobility and reactions during creep deformation. It is shown that, under the testing conditions used, steady creep strain mostly results from transverse glide–climb of (a/2) ?011? interfacial dislocations. A by-product of the interfacial glide–climb are vacancies which diffuse along the interfaces to growing pores or to a ?100? edge dislocations climbing in the γ′ phase. Climb of a ?100? dislocations in the γ′ phase is a recovery mechanism which reduces the constraining of the γ phase by the γ′ phase, thus enabling further glide of (a/2) ?011? dislocations in the matrix. Moreover the γ′ dislocations act as vacancy sinks facilitating interfacial glide–climb. The creep rate increases when the γ–γ′ microstructure becomes topologically inverted; connection of the γ′ rafts results in extensive transverse climb and an increase of the number of a?100? dislocation segments in the γ′ phase.     

Shape memory behaviour of annealed Ti48.5Ni(51.5− x )Cu x (x = 6.2–33.5) thin films

The shape memory behaviour of (Ni,Cu)-rich Ti–Ni–Cu thin films (Ti_48.9Ni_44.9Cu_6.2, Ti_48.5Ni₄₀Cu_11.5, Ti_48.6Ni_35.9Cu_15.5, Ti_48.3Ni_28.4Cu_23.3, Ti_48.3Ni_23.9Cu_27.8 and Ti_48.5Ni₁₈Cu_33.5) annealed at 773, 873 and 973 K for 1 h was investigated. The films with 6.2, 11.5–15.5 and 23.3–33.5 at% Cu showed a single-stage deformation due to a B2 ? B19′ transformation, a two-stage deformation due to the B2 ? B19 ? B19′ transformation and a single-stage deformation due to the B2 ? B19′ transformation, respectively. The martensitic transformation start temperature (M _s) increased with increasing Cu content and then levelled off for more than 15 at% Cu, indicating a high Ms temperature of 345 K. Temperature hystereses were almost 15 K for all films with more than 10 at% Cu. The critical stress for slip increased with increasing Cu content and increased significantly for the Ti_48.5Ni₁₈Cu_33.5 film, whereas the maximum recoverable strain significantly decreased for the Ti_48.5Ni₁₈Cu_33.5 film. With decreasing annealing temperature, the critical stress for slip increased, but the M _s temperature decreased. It was found that films with 11.5 at% Cu or more, annealed at 873 K, showed a high martensitic transformation temperature and a high critical stress for slip.     

Disconnections in simple and complex structures

Disconnections are interfacial defects with dislocation and step character; for example, twinning dislocations in homo-phase and transformation dislocations in hetero-phase materials. They play important structural roles and are classified as either ‘perfect’, separating energetically degenerate regions of interface, or ‘partial’, bounding a faulted region. In kinetic mechanisms, disconnection motion can be glissile, by conservative climb or climb. In the present paper, disconnection mobility is analyzed in terms of shear and shuffle-type atomic displacements and diffusional flux. This is applied to a sequence of hetero-phase materials with increasing structural complexity, namely the β to α transformation in Ti, θ′ precipitation in Al(Cu) and the orthorhombic to monoclinic martensitic transformation in ZrO₂. A disconnection source mechanism in Ti, involving conservative climb, is also described.     

Mechanical and tribological properties of Ni/Al multilayers—A molecular dynamics study

Mechanical and tribological properties of multilayers with nanometer thickness are strongly affected by interfaces formed due to mismatch of lattice parameters. In this study, molecular dynamics (MD) simulations of nanoindentation and following nanoscratching processes are performed to investigate the mechanical and tribological properties of Ni/Al multilayers with semi-coherent interface. The results show that the indentation hardness of Ni/Al multilayers is larger than pure Ni thin film, and the significant strength of Ni/Al multilayers is caused by the semi-coherent interface which acts as a barrier to glide of dislocations during nanoindentation process. The confinement of plastic deformation by the interface during nanoscratching on Ni/Al multilayers leads to smaller friction coefficient than pure Ni thin film. Dislocation evolution, interaction between gliding dislocations and interface, variations of indentation hardness and friction coefficient are studied.     

Which stresses affect the glide of screw dislocations in bcc metals?

By direct application of stress in molecular statics calculations we identify the stress components that affect the glide of 1/2?111? screw dislocations in bcc tungsten. These results prove that the hydrostatic stress and the normal stress parallel to the dislocation line do not play any role in the dislocation glide. Therefore, the Peierls stress of the dislocation cannot depend directly on the remaining two normal stresses that are perpendicular to the dislocation but, instead, on their combination that causes an equibiaxial tension-compression (and thus shear) in the plane perpendicular to the dislocation line. The Peierls stress of 1/2?111? screw dislocations then depends only on the orientation of the plane in which the shear stress parallel to the Burgers vector is applied and on the magnitude and orientation of the shear stress perpendicular to the slip direction.     

Diffusive fluxes associated with interfacial defeet motion and interaction

The diffusional flux associated with the motion of interfacial defects is described by an equation expressed in terms of the topological parameters which characterise defects, namely their Burgers vectors and step heights, the defect velocity and the concentration of each atomic species in the two adjacent crystals. This expression demonstrates that glide/climb behaviour of grain boundary defects is analogous to motion of dislocations in single crystals; climb motion results if a component of b is perpendicular to the interface plane. However, the situation is more complex in the case of interphase interface defects, but the present approach, which considers the step and dislocation portions of defects separately, enables a straightforward analysis. Several examples are illustrated to show the various possibilities, such as climb motion even when b is parallel to the interface, and glide motion when b is not. The latter case arises in martensitic transformation where the existence of an invariant-plane-strain relation at the interface leads to equal and opposite fluxes to the step and dislocation portions of transformation defects so that overall the motion is diffusionless.Interfacial processes involve the motion and interaction of defects. The present analysis facilitates the consideration of diffusive fluxes associated with defect interaction since the step and dislocation portions can be treated independently. A general expression is derived for the total flux arising, and a particular case, the interaction of transformation dislocations with crystal dislocations which have reached the interface during lattice-invariant deformation in martensite formation, is considered.     

Evolution of dislocation structure during deformation of γ-irradiated LiF crystals

The effect of γ irradiation on the mechanical characteristics and dislocation structure of slip bands in LiF crystals is studied at doses D⩽7.3×10⁸ R. Irradiation causes a substantial increase (up to a factor of 30) in the yield stress τ _y of the crystals, with τ _y ∝ D ^0.4 in the first approximation. The deformation shear increases in the slip bands of irradiated crystals, as do the densities of the screw and edge dislocation components, while the dislocation mean free paths decrease. Irradiation also raises the probability of twinning cross slip for screw dislocations. The observed effects are assumed to be related to the formation of a different kind of defects in the irradiated crystals, primarily clusters of implanted atoms. Fiz. Tverd. Tela (St. Petersburg) 39, 1072–1075 (June 1997)     

Stress field and interaction forces of dislocations in anisotropic multilayer thin films

Utilizing Fourier transforms, the elastic field of three-dimensional dislocation loops in anisotropic multilayer materials is developed. Green's functions and their derivatives, obtained first in the Fourier domain and then in the real domain by numerical inversion, are used in integrals to determine the elastic field of dislocation loops. The interaction forces between dislocations and free surfaces or interfaces in multilayer thin films are then investigated. The developed method is based on rigorous elasticity solutions for dislocations approaching to within one to two atomic planes from the interface. For a dislocation in one layer, the interface image force is determined mainly by the elastic moduli and thicknesses of neighbouring layers. When a dislocation approaches an interface between two layers, within 10–20 atomic planes, the image force changes rapidly. Interaction forces are then kept constant up to the interface. The model shows that, when a dislocation crosses an interface from a soft to a hard layer, additional external forces must be applied to overcome an elastic mismatch barrier. The developed method extends the concept of the Kohler barrier in 2D, and shows that the interface force barrier not only depends on the relative ratio of the elastic moduli of neighbouring layers, but also on the 3D shape of the dislocation, the number of interacting adjacent layers, and on layer thicknesses.