Relaxation of interphase stresses on the later stages of the heterogeneous decomposition of solid solutions. II. Variational problem

The study of relaxation processes upon the decomposition of solid solutions at the stage of coalescence in the regime of dislocation-matrix diffusion is performed using a “precipitated-phase-particle-feeding-dislocations” system as an example. Within the framework of the variational approach, the cases of the independent and interdependent variation of the fraction of the relaxed regions of the interphase surface and of the number of edge dislocations which supply the alloying component to the precipitated phase have been investigated. Under the assumption that implies the linearity of the possible connection between these parameters, the model approximation of the continuous nucleation of epitaxial defects, and the absence of free matrix dislocations near the particle in the initial state, it is shown that the decrease in the number of edge feeding dislocations in the process of relaxation of interphase stresses can occur only by means of “leakage” of dislocation segments localized in the precipitate outside the limits of the precipitate with the formation of structural dislocation loops on the interphase surface.     

Relaxation of interphase stresses on the later stages of the heterogeneous decomposition of solid solutions. I. Functional of the energy

For describing the isomorphic heterogeneous decomposition of binary supersaturated solid solutions at the stage of coalescence under conditions of dislocation-matrix diffusion with a relaxation of stresses caused by phase separation, we consider a system representing a precipitation-phase particle in a surrounding matrix + dislocations intersecting the interphase surface and supplying an alloying component to it. In the approximations based on the continuity of the distribution of misfit dislocations on the interphase surface and of the average concentration field, we obtained an expression for the total energy of the system in the form of a functional which depends on the fraction of the relaxed regions of the interphase surface, the number of supplying (feeding) dislocations, and their mutual arrangement. The need for the use of a model functional appears within the framework of the variational problem for determining the equilibrium parameters of the system.     

Nucleation of ordered particles at dislocations and formation of split patterns

We investigated the effect of nucleation of ordered precipitates at dislocations and the subsequent growth of particle morphology through computer simulations using a phase-field model. The model treats simultaneously precipitates, dislocations and precipitate–dislocation interactions within a single algorithm. In particular, the model takes into account the structural discontinuity associated with a dislocation that leads to the formation of antiphase domains if the dislocation is within an ordered particle. Three long-range order parameters are used to describe the antiphase domains associated with L1₂ ordering and an additional set of non-conserved order parameters is introduced to characterize dislocations. We show that heterogeneous nucleation and subsequent growth of ordered precipitates at dislocations yield various “split” patterns, whose formation has been attributed to different mechanisms in literature.     

On particle size effects: An internal length mean field approach using field dislocation mechanics

A mean field approach including an internal length scale is developed in order to capture the particle size effects on the overall mechanical behavior of particle-reinforced alloys. A generalized self-consistent scheme (with coated particles) is employed, with a new “phase” representing the “layers” where orderly dislocations between the matrix and the particles are present. The thickness of these “layers” is the internal length scale introduced in the model. It is determined dynamically by using a one-dimensional field dislocation mechanics model, where localized geometrically necessary dislocation densities accommodate the lattice incompatibility between matrix and inclusions. The beneficial influence of this scheme, as compared to classical mean field approaches, is shown from comparisons with experimental data on the particle size effects in Al/SiC composites.     

Homogeneous nucleation of dislocation loops in nanocrystalline metals and ceramics

A special mechanism of dislocation nucleation in deformed nanocrystalline metals and ceramics is theoretically described. The mechanism represents non-local homogeneous nucleation of a nanoscale loop of “non-crystallographic” partial dislocation whose Burgers vector magnitude continuously grows during the nucleation process. The dislocation loop nucleation is accompanied by nucleation and evolution of a generalized stacking fault bounded by the loop. It is shown that the special mechanism can effectively produce nanoscale loops of lattice dislocations in nanocrystalline metals (Al, Ni) and ceramics (3C–SiC) deformed at high mechanical stresses achieved in shock-wave and indentation load regimes.     

Mechanism of induced nucleation of misfit dislocations in the Ge-on-Si(0 0 1) system and its role in the formation of the core structure of edge misfit dislocations

Ge-on-Si(0 0 1) films are grown by molecular beam epitaxy via a three-step epitaxial growth method (Ge/Ge seed/GeSi buffer/Si(0 0 1)). The dislocation structure of the Ge/GeSi buffer interface is studied by high-resolution electron microscopy. Misfit dislocations on the interface are edge dislocations and are aligned regularly with a period of 9–10 nm. A variety of atomic structures of the dislocation core is observed, known in the literature as dissociated or asymmetric Lomer edge dislocations. The assumption that atomic structures of various degrees of complexity are intermediate states in the formation of a perfect edge misfit dislocation in the course of plastic relaxation of a stressed film is justified. A model is proposed which explains the intermediate states in terms of statistical variation of the nucleation site of the complementary 60° dislocation which forms, together with the primary dislocation, a Lomer dislocation at the interface.     

Al−Li−S4合金多相析出和多阶段蠕变时效行为的统一本构模型

提出统一的本构模型,以预测最近观察到的Al?Li?S4合金的"多阶段"蠕变行为.通过X射线衍射(XRD)和透射电子显微镜(TEM),详细表征蠕变时效过程中与合金的屈服强度和蠕变变形相关的微观结构变量,包括位错和多种析出相.对于合金的屈服强度,该模型基于强化机制考虑多相强化行为,包括可剪切的T1析出相强化,不可剪切的T1...     

A dislocation dynamics study of the transition from homogeneous to heterogeneous deformation in irradiated body-centered cubic iron

Low temperature irradiation of crystalline materials is known to result in hardening and loss of ductility, which limits the usefulness of candidate materials in harsh nuclear environments. In body-centered cubic (bcc) metals, this mechanical property degradation is caused by the interaction of in-grown dislocations with irradiation defects, particularly small dislocation loops resulting from the microstructural evolution of displacement cascades. In this paper, we perform dislocation dynamics simulations of bcc Fe containing various concentrations of dislocation loops produced by irradiation in an attempt to gain insight into the processes that lead to hardening and embrittlement. We find that a transition from homogenous to highly localized deformation occurs at a critical loop density. Above it, plastic flow proceeds heterogeneously, creating defect-free channels in its wake. We find that channel initiation and size are mediated by loop coalescence resulting from elastic interactions with moving dislocations.     

Oxygen–molybdenum interaction with dislocations in Nb-Mo single crystals at elevated temperatures

A study using a transmission electron microscope was performed for the deformation microstructures of Nb-20mol%Mo single crystals containing from 0.03 to 0.65 mol% oxygen and a Nb-40mol%Mo-0.05mol%O single crystal, compressed to approximately 4% plastic strain at 298 K, 973 K and 1473 K. At 298 K, screw dislocations are predominant in all alloys. At 973 K, in Nb-20Mo-0.03O and Nb-40Mo-0.05O, the dislocation microstructure contains the same amount of edge dislocations and small edge dipoles that tend to aggregate into clusters. In Nb-20Mo-0.65O, however, the arrangement consists of long glide loops parallel to the screw direction. At 1473 K, edge dislocations are dominant in all alloys. From the results, the following conclusions are made: (1) Oxygen atoms impede screw dislocation motion at 298 K and 973 K; (2) The influence of oxygen on screw segments is significantly strong at 973 K; (3) At 1473 K, oxygen atoms impede edge dislocation motion. It is inferred that O-Mo atmosphere is formed around dislocations.     

Effect of climb on dislocation mechanisms and creep rates in γ′-strengthened Ni base superalloy single crystals: A discrete dislocation dynamics study

Creep of single-crystal superalloys is governed by dislocation glide, climb, reactions and annihilation. Discrete three-dimensional (3D) dislocation dynamics (DDD) simulations are used to study the evolution of the dislocation substructure in a γ/γ′ microstructure of a single-crystal superalloy for different climb rates and loading conditions. A hybrid mobility law for glide and climb is used to map the interactions of dislocations with γ′ cubes. The focus is on the early stages of creep, where dislocation plasticity is confined to narrow γ channels. With enhancing climb mobility, the creep strain increases, even if the applied resolved shear stress is below the critical stress required for squeezing dislocations into the γ channels. The simulated creep microstructure consists of long dislocations and a network near the corners of the γ′ precipitate in the low-stress regime. In the high-stress regime, dislocations squeeze into the γ channels, where they deposit dislocation segments at the γ/γ′ interfaces. These observations are in good agreement with experimentally observed dislocation structures that form during high-temperature and low-stress creep.     

Application of the Peierls-Nabarro Model to Symmetric Tilt Low-Angle Grain Boundary with Full <a> Dislocation in Pure Magnesium

Three types of symmetric (11\(\bar{2}\)0) tilt low-angle grain boundaries (LAGBs) with array of basal, prismatic, and pyramidal edge full dislocations in pure Mg have been studied by using the improved Peierls-Nabarro model in combination with the generalized stacking fault energy curve. The results show that with decreasing distance between the dislocations in all the three types of tilt LAGBs, the stress and strain fields are gradually suppressed. The reduction extent of the stress and strain fields decreases from the prismatic to basal to pyramidal dislocations. The variation of dislocation line energy (DLE) for all tilt LAGBs is divided into three stages: DLE changes slightly and linearly when the distance is larger than 300 Å, ~10%; DLE declines exponentially and quickly when the distance goes from 300 to 100 Å, ~70%; and finally, the descent speed lowers when the distance is smaller than 100 Å and the dislocation core energy is nearly half of the DLE. The grain boundary energy (GBE) decreases when the tilt angle of LAGB increases from 1° to 2° for all cases. The tilt LAGB consists of pyramidal dislocations always has the largest GBE, while that with array of prismatic dislocations has the smallest one in the whole range. The Peierls stress of dislocation in tilt LAGB is nearly unchanged, the same as that of single dislocation. This work is useful for further study of dissociated dislocation, solute segregation, precipitate nucleation in tilt LAGB and its interaction with single dislocations.     

Effects of temperature on structure and mobility of the 〈1 0 0〉 edge dislocation in body-centred cubic iron

Dislocation segments with Burgers vector b = 〈1 0 0〉 are formed during deformation of body-centred-cubic (bcc) metals by the interaction between dislocations with b = 1/2〈1 1 1〉. Such segments are also created by reactions between dislocations and dislocation loops in irradiated bcc metals. The obstacle resistance produced by these segments on gliding dislocations is controlled by their mobility, which is determined in turn by the atomic structure of their cores. The core structure of a straight 〈1 0 0〉 edge dislocation is investigated here by atomic-scale computer simulation for α-iron using three different interatomic potentials. At low temperature the dislocation has a non-planar core consisting of two 1/2〈1 1 1〉 fractional dislocations with atomic disregistry spread on planes inclined to the main glide plane. Increasing temperature modifies this core structure and so reduces the critical applied shear stress for glide of the 〈1 0 0〉 dislocation. It is concluded that the response of the 〈1 0 0〉 edge dislocation to temperature or applied stress determines specific reaction pathways occurring between a moving dislocation and 1/2〈1 1 1〉 dislocation loops. The implications of this for plastic flow in unirradiated and irradiated ferritic materials are discussed and demonstrated by examples.     

双相TiAl基合金γ相中螺旋状普通位错的形成

利用自行开发的精确立体显微术研究了800℃压缩变形2％的双相TiAl基合金γ相中普通位错的空间形态。研究结果表明，同一位错往往并不处于同一晶面，其中一些位错段靠近（111）晶面，另一些则靠近（112）晶面，构成三维螺旋状曲线。普通位错形成这种螺旋状曲绠交滑移的结果，即原先在（111）密排面滑移的螺位错的部分位错段交滑移到（112）非密排面。随着处于不同晶面的位错段的进一步滑移，靠近位错段交界处的位错线方向将发生变化，具有较大刃型分量的部分可通过攀移而偏离（111）或（112）晶面。     

TiCp／Ti复合材料的熔铸法制备及微观组织研究

用熔铸法制备了原位自生钛合金基复合材料,为减少复合材料的成分波动,熔炼前先用混合均匀的TiC粉和铝制备TiCp-Al中间合金,然后用中间合金制取复合材料,研究了复合材料中TiC的形貌。结果表明所制备的复合材料的成分易控制,波动小。对其TEM的研究表明,其TiC形态为初生树枝晶和短棒状共晶。此外还发现在0．3-0．6μm的规则块状TiC颗粒析出,多分布在晶界上,与其体界面干净,无反应层,HRTEM也证明不存在反应层。基体中存在较多位错,且位错线上有阻碍位错运动的TiC析出物。     

Study of precipitation and growth of γ′ and dislocation structure in Inconel X-750

The precipitation of the γ′ (Ll₂) phase in Inconel X-750 has been studied in the 704–871°C ageing temperature range using transmission electron microscopy. The morphology of γ′ was observed to be cuboidal for all ageing temperatures, deviating from this only at long ageing times. The loss of coherency of γ′ precipitate occurred by nucleation of dislocation loops at and around the precipitate, interaction of dislocations at the interface, and the attraction of dislocations toward the particle/matrix interface.     

LOW ENERGY DISLOCATION STRUCTURES DUE TO FATIGUE SOFTENING

The evolution of dislocation structures in 6% prestrained steel 1018 during fatigue has beenstudied by TEM.The dislocations are quite movable,the loose cells quickly change to“checkboard”structures,in which the main cell walls lie about {100}.Then,the low energydislocation structures i.e.dipolar walls and abyrinth structures are evolved.The characteristicof labyrinth and the orientation of dipolar walls are quite similar to fcc crystal.This indicatesthe energy state of system and the moving ability of dislocations are important factors affect-ing softening process,rather than the slip geometric characteristic of dislocations and detailsof dislocations.The decreasing in misorientation between adjoining cells and internal stressare discussed.     

Dislocation decorrelation and relationship to deformation microtwins during creep of a γ′ precipitate strengthened Ni-based superalloy

The evolution of microtwins during high temperature creep deformation in a γ′ strengthened Ni-based superalloy has been investigated through a combination of creep testing, transmission electron microscopy (TEM), theoretical modeling, and computer simulation. Experimentally, microtwin nucleation sources were identified and their evolution was tracked by characterizing the deformation substructure at different stages of creep deformation. Deformation is highly localized around stress concentrators such as carbides, borides and serrated grain boundaries, which act as sources of a/2〈1 1 0〉 matrix-type dislocations. Due to fine channels between the γ′ particles, coupled with a low γ matrix stacking fault energy, the a/2〈1 1 0〉 matrix dislocations dissociate into a/6〈1 1 2〉 Shockley partials, which were commonly observed to be decorrelated from one another, creating extended intrinsic stacking faults in the γ matrix. Microtwins are common and form via Shockley partial dislocations, cooperatively shearing both the γ and γ′ phases on adjacent {1 1 1} glide planes. The TEM observations lead directly to an analysis of dislocation–precipitate interactions. The important processes of dislocation dissociation and decorrelation were modeled in detail through phase field simulations and theoretical analyses based on Orowan looping, providing a comprehensive insight into the microstructural features and applied stress conditions that favor the microtwinning deformation mode in γ′ strengthened Ni-based superalloys.     

The evolution of dislocation density during heat treatment and creep of tempered martensite ferritic steels

The evolution of dislocation density in two tempered martensite ferritic steels (a 12% and a 9% chromium steel, “X20” and “P91”) during heat treatment and creep is analyzed using transmission electron microscopy (TEM) and X-ray diffraction (XRD); both methods yield results which are in good agreement when rationalizing the XRD-data based on densities of free dislocations. It is shown that due to the intermediate formation of martensite, standard heat treatments produce very high dislocation densities in tempered martensite ferritic steels (TMFSs). Long term tempering and creep are characterized by a decrease of dislocation density; but dislocation densities are still high as compared to alloys where the formation of microstructure does not involve a martensitic transformation. A heterogeneous microstructure after long term tempering and creep is a characteristic feature of TMFSs. Micro grains with high dislocation densities co-exist next to micro grains without dislocations. The XRD method yields average data and cannot account for this microstructural heterogeneity; but it supports the TEM results which in isolation suffer from providing insufficient statistics. The results of the present study are discussed in the light of earlier work published in the literature and contribute to a better understanding of the role of free dislocations in TMFSs during tempering, creep and high temperature low cycle fatigue.     

Nanoscale phase field microelasticity theory of dislocations: model and 3D simulations

The first Phase Field model of evolution of a multi-dislocation system in elastically anisotropic crystal under applied stress is formulated. The model is a modification and extension of our Phase Field Microelasticity approach to the theory of coherent phase transformations. The long-range strain-induced interaction of individual dislocations is calculated exactly and is explicitly incorporated in the Phase Field formalism. It also automatically takes into account the effects of “short-range interactions”, such as multiplication and annihilation of dislocations and a formation of various metastable microstructures involving dislocations and defects. The proposed 3-dimensional Phase Field model of dislocations does not impose a priori constraints on possible dislocation structures or their evolution paths. Examples of simulation of the FCC 3D system under applied stress are considered.