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.     

Climb via vacancy diffusion of edge dislocations in 2D dislocation microstructures

The prevention of strength degradation of components is one of the great challenges in solid mechanics. In particular, at high temperatures material may deform even at low stresses, a deformation mode known as deformation creep. One of the microstructural mechanisms that governs deformation creep is dislocation motion due to the absorption or emission of vacancies, which results in motion perpendicular to the glide plane, called dislocation climb. However, the importance of the dislocation network for the deformation creep remains far from being understood. In this study, a climb model that accounts for the dislocation network is developed, by solving the diffusion equation for vacancies in a region with a general dislocation distribution. The definition of the sink strength is extended, to account for the contributions of neighbouring dislocations to the climb rate. The model is then applied to dislocation dipoles and dislocation pile-ups, which are dense dislocation structures and it is found that the sink strength of dislocations in a pile-up is reduced since the vacancy field is distributed between the dislocations. Finally, the importance of the results for modelling deformation creep is discussed.     

Dislocation dynamics in multiwalled carbon nanotubes at high temperatures

Dislocation dynamics dictate the mechanical behavior of materials. Dislocations in periodic crystalline materials have been well documented. On the contrary, dislocations in cylindrical carbon nanotubes, particularly in multiwalled carbon nanotubes (MWCNTs), remain almost unexplored. Here we report that a room temperature 1/2<0001> sessile dislocation in a MWCNT becomes highly mobile, as characterized by its glide, climb, and the glide-climb interactions, at temperatures of about 2000 degrees C. The dislocation glide leads to the cross-linking of different shells; dislocation climb creates nanocracks; and the interaction of two 1/2<0001> dislocations creates kinks. We found that dislocation loops act as channels for mass transport. These dislocation dynamics are drastically different from that in conventional periodic crystalline materials due to the cylindrical, highly anisotropic structures of MWCNTs.     

镍铬合金中的位错运动与位错反应

对镍铬合金中单一滑移面内和两个滑移面间的位错反应,特别是动态下的反应,进行了透射电子显微镜观察,并对其中的一些位错组态进行了衍衬分析。1.六角位错网络主要是单一滑移面内柏氏矢量相差120°的两组位错间反应的结果;2.与螺型位错一样,刃型或混合型位错也能在两个滑移面间交滑移;3.两个滑移面间的位错反应有时在其截线方向生成不滑动的位错(如L.C.位错锁)并不能完全阻挡住这两个滑移面上的位错运动;4.在含铝、钛的镍铬合金中,超点阵位错的反应与不含铝、钛的合金或无序固溶体中的位错反应相似。 关键词：     

Defect structure in EuS single crystals grown from the melt

The defect structure in EuS single crystals grown form the melt is studied by etch pitting, scanning and high-voltage electron microscopy. Circular and square etch pits and a second phase in the shape of thin hexagonal platelets are observed by etching. Microprobe analysis indicates the platelets to consist of Eu metal. In the transmission electron microscope, smoothly curved dislocations and helical dislocations, small dislocation loops and inclusions associated with dislocations are observed. The possible origin of the detected dislocation structure is considered with reference to climb and glide processes occurring during cooling down the grown crystals. The results corroborate the glide geometry of the NaCl lattice for EuS. On leave from Institute of Physics, Academic Sinica, Peking, VR China     

Dislocations and mechanical properties of icosahedral quasicrystals

In this article we interpret the mechanical properties of icosahedral quasicrystals with the dislocation theory. After having defined the concept of dislocation in a periodic crystal, we extend this notion to quasicrystals in the 6-dimensional space. We show that perfect dislocations and imperfect dislocations trailing a phason fault can be defined and observed in transmission electron microscopy (TEM). In-situ straining TEM experiments at high temperature show that dislocations move solely by climb, a non-conservative motion-requiring diffusion. This behavior at variance with that of crystals which deform mainly by glide is explained by the atypical nature of the atomic structure of icosahedral quasicrystals.     

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.     

钼单晶体中亚晶界位错结构的研究

本文应用蚀象法对电子束浮区区熔法制得的原生态钼单晶体中的亚晶界位错结构进行了直接观测。对于实验结果进行了细致的分析,并与亚晶界的Frank公式的一些预期结果比较,全面地证实了理论预测。对(111)面上平行蚀线方向的测量表明,它们大体沿着1/2〈111〉刃型位错的滑移面及攀移面的交线,从而证实了它们是这种位错所组成的一组位错倾侧型晶界。通过对蚀斑三叉亚晶界的分析,检验了推广后的Read-Shockley公式,同时表明存在着两组位错的倾侧晶界。对于(111)面上观察到的15组蚀线网络进行了分析,结果表明其中5组是1/2〈111〉/〈100〉网络,9组是〈100〉/〈110〉网络。分析中,除去应用Carrington等所发展的极图分析法以外,我们还根据Frank公式所规定的网线间距的关系式,提出了进一步定量检验的分析方法。实践证明,当极图分析不能获得唯一的结果时,这种定量检验法可以有效地确定位错网络的Burgers矢量。此外,我们还观察到奇位错和亚晶界交互作用的事例,特别是奇位错在亚晶界上引起“台阶”以及夹杂物和亚晶界交互作用的迹象。不同类型的亚晶界交接以及非平衡态的亚晶界也是经常可以观察到的。以上结果表明,蚀象法对于定量地研究原生态晶体中的亚晶界位错结构是极其有效的,其能力并不亚于电子显微镜薄膜透射法。     

Inhomogeneity of misfit stresses in nickel-base superalloys: Effect on propagation of matrix dislocation loops

It is shown experimentally that, during annealing and creep under low applied stresses, matrix dislocation loops frequently cross-glide. The periodic length of the zigzag dislocations deposited in the interfaces is equal to that of the γ/γ′-microstructure. Initially, the zigzag dislocations move in the (001) interface by a combination of glide and climb but then they stop near the γ′-edges and align along ?100?. Reactions of such dislocations lead to the formation of square interfacial networks consisting of ?100? oriented edge dislocations. The complex dislocation movement is explained by the inhomogeneity of the misfit stresses between γ- and γ′-lattices. The tensile components of the stress tensor drive the dislocations through the channel, whereas the shear components near the γ′-edges cause the zigzag movement and the ?100? alignment. The total effect is the most efficient relaxation of the misfit stresses. The results are relevant, especially for single-crystal superalloys of the newest generations, which have an increased γ/γ′-misfit due to the high level of refractory elements.     

Numerical calculation of the rate of strain of interstitial solid solutions under irradiation. I. Model of radiation creep

A model of radiation creep of interstitial solid solutions is developed on the basis of the combined motion of dislocations, including their glide and climb past obstacles. The obstacles considered are forest dislocations and pileups of radiation-induced point defects. A computational formula for the rate of strain is derived which describes creep at high stresses, when the gliding dislocations overcome some of the barriers by force, and a method is described for determining the average distance traversed by a dislocation in the glide plane under the influence of the stress until it is stopped by barriers. The results are compared with those of other authors. It is shown that the formula obtained for the rate of strain goes over in particular cases to those given by the previously known SIPA, Gittus-Mansur, and glide-climb models of radiation creep. Zh. Tekh. Fiz. 69, 64–71 (January 1999)     

Surface stress mediated image force and torque on an edge dislocation

The proximity of interfaces gives prominence to image forces experienced by dislocations. The presence of surface stress alters the traction-free boundary conditions existing on free-surfaces and hence is expected to alter the magnitude of the image force. In the current work, using a combined simulation of surface stress and an edge dislocation in a semi-infinite body, we evaluate the configurational effects on the system. We demonstrate that if the extra half-plane of the edge dislocation is parallel to the surface, the image force (glide) is not altered due to surface stress; however, the dislocation experiences a torque. The surface stress breaks the ‘climb image force’ symmetry, thus leading to non-equivalence between positive and negative climb. We discover an equilibrium position for the edge dislocation in the positive ‘climb geometry’, arising due to a competition between the interaction of the dislocation stress fields with the surface stress and the image dislocation. Torque in the climb configuration is not affected by surface stress (remains zero). Surface stress is computed using a recently developed two-scale model based on Shuttleworth’s idea and image forces using a finite element model developed earlier. The effect of surface stress on the image force and torque experienced by the dislocation monopole is analysed using illustrative 3D models.     

A dislocation network model of creep transients after a stress dip

The transient creep behaviour which follows a sudden decrease in stress is predicted by using simple equations for the rates of creation and annihilation of dislocations. It is shown that a variety of transient types can occur, depending on the relative values of the dislocation glide and climb mobility and the magnitude of the stress dip.The work was carried out at the Berkeley Nuclear Laboratories of the Technology Planning and Research Division and the paper is published with permission of the Central Electricity Generating Board.     

A parametric simulation method for discrete dislocation dynamics

A new computer simulation method employed in discrete dislocation dynamics is presented. The article summarizes results of an application of the method to elementary interactions among glide dislocations and dipolar dislocation loops. The glide dislocations are represented by parametrically described curves moving in glide planes whereas the dipolar loops are treated as rigid objects. All mutual force interactions are considered in the models. As a consequence, the computational complexity rapidly increases with the number of objects considered. This difficulty is treated by advanced computational techniques such as suitable accurate numerical methods and parallel implementation of the algorithms. Therefore the method is able to simulate particular phenomena of dislocation dynamics which occur in crystalline solids deformed by single slip: generation of glide dislocations from the Frank-Read source, interaction of glide dislocations with obstacles, their encounters in channels of the bands, sweeping of dipolar loops by glide dislocations and a loop clustering.     

Asymptotic behaviors of the stress fields in the vicinity of dislocations and dislocation segments

We obtain the singular asymptotic behavior of the stress field in the vicinity of a non-planar dislocation in three dimensions and the nearly singular behavior of the full self-force of the dislocation including both glide and climb forces, using asymptotic analysis. We also derive asymptotic formulas for the stress field in the vicinity of a curved dislocation segment. Numerical examples are presented to examine the asymptotic formulas. The obtained formulas can be used for qualitative understanding of the stress tensor associated with dislocations and efficient and accurate calculation of the stress tensor in dislocation dynamics simulations.     

The dislocations in graphene with the correction from lattice effect

The dislocation widths and Peierls stresses of glide dislocations and shuffle dislocations in graphene have been studied by the improved Peierls-Nabarro (P-N) equation which contains the discrete correction. The discrete parameter is obtained from a simple dynamic model in which the interaction attributed to the variation of bond length and angle was considered. The restoring force in the improved P-N equation is given by the gradient of the generalized stacking fault energy surface (γ-surface). Our calculation shows that the widths of the shuffle dislocation and the glide dislocation are narrow and the width of the shuffle dislocation is about twice wider than the glide dislocation. The Peierls stress of a shuffle dislocation is one order of magnitude smaller than that of a glide dislocation. As a consequence, the shuffle dislocation moves more easily than the glide dislocation.     

Degradation of DH lasers caused by growth of dislocation networks

The features of the process of rapid degradation of (GaAl) As-GaAs DH lasers are discussed. The existing models for dislocation networks growth during the device operation are critically analysed. A new approach to the mechanism of degradation is proposed according to which the dislocation dipoles in the active layer of the device develop by conservative climb due to the pipe diffusion along helical dislocations.     

Positron annihilation in alpha- and beta-cyclodextrin

A new type of misfit dislocation multiplication is deduced from high-voltage electron micrographs of thin Ge layers on GaAs substrates. Two misfit dislocations with the same Burgers vectors on different glide planes cross and annihilate at the intersection point resulting in the formation of two angular dislocations. The tip of one of these dislocations may reach the growth surface by glide breaking into two separate dislocation segments. These segments may glide to form additional misfit dislocations, which may undergo the same multiplication process.     

纯物质晶界结构及运动的晶体相场法模拟

采用晶体相场模型,分别模拟了纯物质小角度晶界和大角度晶界结构及变形过程中的晶粒转动及晶界迁移.结果表明,小角度晶界迁移的主要机理是构成晶界的位错的滑移和攀移,而大角度晶界的迁移主要依靠晶界两侧原子的跳动及晶界位错等缺陷的运动. 关键词： The phase field crystal model was used to simulate the structure of the small angle and the large angle grain boundary (GB) the grain rotation and the GB migration during deformation. Simulated results show that the dislocation glide and climb are the ma     

Topological kinematic constraints: dislocations and the glide principle

Topological defects play an important role in the physics of elastic media and liquid crystals. Defect kinematics in elastic media is restrained by rigid constraints of purely topological origin. An example is the glide motion of dislocations, a topic which has been extensively studied through the years by metallurgists. To date, most theoretical investigations of this phenomenon were heuristic or numerical. Here, we outline a mathematical derivation of this universal effect and report on new generalizations. Our formalism makes it possible to address the full non-linear theory of relevance at short distance where violations of the standard glide constraint become possible. Our new derivation enables us to systematically predict and estimate corrections to the standard, linear order, glide motion. Our analysis is very broad and pertains to both classical and quantum media. To fully capture the generality of this effect, we arrive at a mathematical definition of the glide constraint which has a universal status. When fused with the mass continuity equations, this then dictates glide motion within linear elasticity and leads to new non-linear corrections in a general elastic medium. It further enables us to study the kinematics of dislocations in arbitrary spatial dimensions (or space-time dimensions in the quantum arena). As an example, we analyze the restricted climb associated with edge dislocations in 3±1D. Quite generally, the climb constraint is equivalent to the condition that dislocations do not communicate with compressional stresses at long distances.