Anisotropic rheology during grain boundary diffusion creep and its relation to grain rotation,grain boundary sliding and superplasticity

The response of periodic microstructures to deformation can be analysed rigorously and this provides guidance in understanding more complex microstructures. When deforming by diffusion creep accompanied by sliding, irregular hexagons are shown to be anisotropic in their rheology. Analytic solutions are derived in which grain rotation is a key aspect of the deformation. If grain boundaries cannot support shear stress, the polycrystal viscosity is extremely anisotropic. There are two orthogonal directions of zero strength: sliding and rotation cooperate to allow strain parallel to these directions to be accomplished without any dissolution or plating. When a linear velocity/shear stress relationship is introduced for grain boundaries, the anisotropy is less extreme, but two weak directions still exist along which polycrystal strength is controlled only by the grain boundary “viscosity”. Irregular hexagons are characterised by four parameters. A particular subset of hexagons defined by two parameters, which includes regular hexagons as well as some elongate shapes, shows singular behaviour. Grain shapes that are close to that of the subset may exhibit large grain rotation rates and have no well-defined rheology unless there is a finite grain boundary viscosity. This new analysis explains why microstructures based on irregular but near equiaxed grains show high rotation rates during diffusion creep and it provides a framework for understanding strength anisotropy during diffusion creep.     

铜沉淀对直拉硅单晶中洁净区形成的影响

研究普通热处理和快速热处理工艺下直拉单晶硅中过渡族金属铜杂质对洁净区生成的影响. 通过腐蚀和光学显微镜研究发现,常规高-低-高三步洁净区生成热处理样品中, 第一步高温热处理前对样品铜沾污,样品中没有洁净区生成,高密度的铜沉淀布满了样品整个截面. 而第二步、第三步热处理过程中引入铜杂质不影响洁净区的生成. 研究表明,高温热处理过程中生成的铜沉淀不能溶解是导致洁净区不能形成的最主要原因. 另外,由于不同温度下热处理,导致引入铜杂质的平衡浓度不同,会在一定程度上影响洁净区的厚度. 对于快速热处理样品,可以得到相似的结果. 关键词： 直拉单晶硅 铜沉淀 洁净区     

The stability of triple junctions during the grain boundary diffusion process

The grain boundary diffusion in a system with triple junctions is considered in such a geometry, in which the flows of diffusing atoms meet at the triple line. The solutions of the diffusion equation is given in the frameworks of Fisher's model and under the assumption of quasi-stationary distribution of the diffusing atoms along the grain boundaries. The change of the mechanical equilibrium at the triple junction due to the increase of the concentration of solute atoms is considered. It is shown that under some circumstances the triple junction looses its stability with respect to migration in the direction to the diffusion source. The stability diagrams in the segregation-diffusivity parameter space are plotted.     

Effects of grain boundary diffusion of copper on nickel creep

We have investigated the effects of surface copper diffusion on the creep of large-grain nickel (average grain size about 20 m) and submicron crystalline nickel (grain size about 0.3 m). For both structural states of nickel we find an acceleration of creep over its value in vacuum, and an increase in plasticity during creep when copper has diffused deeply into the nickel from the surface. The temperature range over which these effects are observed in the submicron nickel is nearly 300° lower than that for the large-grain samples. This result is probably due to a significant increase in the grain-boundary and bulk diffusion coefficients of copper in submicron nickel when compared with large-grain nickel.Siberian Branch. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 83–86, December, 1994.     

Finite element modelling of creep cavity filling by solute diffusion

In recently discovered self healing creep steels, open-volume creep cavities are filled by the precipitation of supersaturated solute. These creep cavities form on the grain boundaries oriented perpendicular to the applied stress. The presence of a free surface triggers a flux of solute from the matrix, over the grain boundaries towards the creep cavities. We studied the creep cavity filling by finite element modelling and found that the filling time critically depends on (i) the ratio of diffusivities in the grain boundary and the bulk, and (ii) on the ratio of the intercavity distance and the cavity size. For a relatively large intercavity spacing 3D transport is observed when the grain boundary and volume diffusivities are of a similar order of magnitude, while a 2D behaviour is observed when the grain boundary diffusivity is dominant. Instead when the intercavity distance is small, the transport behaviour tends to a 1D behaviour in all cases, as the amount of solute available in the grain boundary is insufficient. A phase diagram with the transition lines is constructed.     

The effect of preferential diffusion on soot formation in a laminar ethylene/air diffusion flame

The influence of preferential diffusion on soot formation in a laminar ethylene/air diffusion flame was investigated by numerical simulation using three different transport property calculation methods. One simulation included preferential diffusion and the other two neglected preferential diffusion. The results show that the neglect of preferential diffusion or the use of unity Lewis number for all species results in a significant underprediction of soot volume fraction. The peak soot volume fraction is reduced from 8.0 to 2.0 ppm for the studied flame when preferential diffusion is neglected in the simulation. Detailed examination of numerical results reveals that the underprediction of soot volume fraction in the simulation neglecting preferential diffusion is due to the slower diffusion of some species from main reaction zone to PAH and soot formation layer. The slower diffusion of these species causes lower PAH formation rate and thus results in lower soot inception rate and smaller particle surface area. The smaller surface area further leads to smaller surface growth rate. In addition, the neglect of preferential diffusion also leads to higher OH concentration in the flame, which causes the higher specific soot oxidation rate. The lower inception rate, smaller surface growth rate and higher specific oxidation rate results in the lower soot volume fraction when preferential diffusion is neglected. The finding of the paper implies the importance of preferential diffusion for the modeling of not only laminar but maybe also some turbulent flames.     

Grain boundary interdiffusion in the case of concentration-dependent grain boundary diffusion coefficient

The grain boundary diffusion in a binary system which exhibits a grain boundary phase transition is considered in the framework of Fisher's model. The kinetic law of the growth of the grain boundary phase and the distribution of the diffusant near the grain boundary are calculated. The method of determining of the concentration dependence of the grain boundary diffusion coefficient from the experimentally measured penetration profiles of the diffusant along the grain boundaries is suggested. The experimental results on Zn diffusion in Fe(Si) bicrystals, Ni diffusion in Cu bicrystals and grain boundary grooving in Al in the presence of liquid In are discussed in light of the suggested model.     

低杂波电流驱动中径向扩散效应的数值模拟

应用改进后的程序详细计算了不同径向扩散系数对低杂波电流驱动剖面分布的影响。通过计算发现:考虑径向扩散效应后,驱动电流分布变平展宽,电流驱动的分布随着扩散系数的增大逐渐向外层移动,由局域性分布演化成非局域性分布;驱动电流的大小和效率随着扩散系数的增大而降低。     

Theory of grain boundary motion during high-temperature DIGM

A theory of diffusion induced grain boundary migration (DIGM) is presented for high temperatures where volume diffusion of solute atoms out of the grain boundary is important. It is shown that due to the presence of a gradient term in the expression for the free energy of solid solution, even a relatively small discontinuity in the solute distribution across the gain boundary provides enough driving force for grain boundary migration. From the expression obtained for the grain boundary velocity the coefficient for the Ni diffusion across the grain boundaries in a Cu(Ni) polycrystal has been estimated.     

低杂波电流驱动中径向扩散效应的数值模拟

应用改进后的程序详细计算了不同径向扩散系数对低杂波电流驱动剖面分布的影响。通过计算发现:考虑径向扩散效应后，驱动电流分布变平展宽，电流驱动的分布随着扩散系数的增大逐渐向外层移动，由局域性分布演化成非局域性分布；驱动电流的大小和效率随着扩散系数的增大而降低。     

Crystal plasticity and multiscale modelling of superalloy creep

A crystal plasticity approach for superalloy creep has been presented which employs a finite element-based representative volume element (RVE) methodology. The γ channels are assumed to undergo crystal slip and the γ′ particles to deform elastically. A range of superalloys has been studied. Thermocalc computations provide the γ′ volume fraction and an automated scheme for generating the resulting RVE has been developed. It has been shown that primary creep response in a wide range of superalloys over high stress, low temperature regimes is represented excellently by the model, by determination of just an activation energy and an alloying element density. It has been hypothesised that the transition from primary to secondary creep results from the development of geometrically necessary dislocations within the γ channels at the γ′ interfaces. Without the need of further material parameters, it has been shown that secondary creep rates over a broad range of stress and temperature can be accurately predicted, hence supporting the hypothesis. An empirical relationship has been established between the alloying element density and the atomic weight percentages of the alloying elements, using a range of superalloy data. It is hypothesised that a role of the alloying elements within the γ channels is to act as inhibitors of ribbon dislocation motion, hence leading to the large range of macro-level primary and secondary creep responses observed in the alloys with variations in constituent alloys. The empirical relationship established, when combined with the crystal RVE methodology, then allows the prediction of superalloy creep rates from knowledge of alloying constituents.     

Filtering for partially observed diffusion and its applications

This paper provides an analytic method of filtering for partially observed diffusions, which can be also used for parameter estimation with the quasi-maximum likelihood method. The filtering is shown to have consistency in a weak sense. In addition, using the stochastic volatility models, a comparative simulation study is carried out to see how well the proposed method numerically works. The performance of the proposed method is basically better than that of the extended Kalman filtering.     

Monte Carlo simulation of the effect of atomic diagonal transition on cluster diffusion

The effect of atomic diagonal transition on the cluster diffusion and its size dependence is simulated by kinetic Monte Carlo method. The thresholds of atomic diagonal transition barriers E_{dt} are found to be 0.2eV and 0.4eV, corresponding to with and without evaporation and condensation mechanism, respectively. The results indicate that the cluster diffusion is controlled primarily by the atomic diagonal transition, and the cluster diffusion coefficient D decreases drastically with increasing E_d when E_dE_{dt}, and the relationship between D and N changes into D∝N^{-1.08±0.027}.     

稀土La对bcc-Fe中Cu扩散行为影响的第一性原理研究

采用基于密度泛函理论的第一性原理,研究了稀土La对bcc-Fe中Cu析出行为的影响.计算了α-Fe中La原子和Cu原子与空位之间,以及La原子和Cu原子之间的点缺陷结合能;在此基础上,讨论了α-Fe中La对Cu扩散激活能的关系.结果表明:La原子与空位之间有较强的相互吸引作用,且对近邻Cu原子也有一定的束缚.此外,La的加入使Cu原子近邻的空位形成能显著升高,这表明La,Cu偏聚区形成空位较为困难.与此同时,由于La原子对近邻空位和Cu原子的吸引作用,使Cu原子向近邻空位跳跃的迁移能有所升高.迁移能与空位形成能变化的计算结果显示,La原子的加入能够使α-Fe中Cu的扩散激活能显著升高,从而延缓了铁素体区富铜相的偏聚和析出.     

Effect of thermomechanical processing on the creep behaviour of Udimet alloy 188

Udimet alloy 188 was subjected to grain-boundary engineering involving thermomechanical processing in an attempt to improve the creep performance and determine the effects on creep deformation processes. The as-received sheet was cold-rolled to either 10, 25 or 35% reduction per pass followed by a solution treatment at 1191°C for 1 h plus air cooling. This sequence was repeated four times and the resultant microstructure and grain-boundary character distribution were described using electron backscatter diffraction. The fraction of general high-angle grain boundaries tended to increase with increased cold rolling. The 10 and 25% cold-rolled materials exhibited lower creep rates than the 35% cold-rolled material. The measured creep stress exponents and activation energies suggested that dislocation creep with lattice self-diffusion was dominant at 760°C for stresses ranging between 100 and 220 MPa. A transition in the creep exponent below the applied stresses of 100 MPa indicated that a different secondary creep mechanism was rate-controlling at low stresses. A significant amount of grain-boundary cracking was observed both on the surface and subsurface of deformed samples, but surface cracks were greater in number and size than those within the bulk. The cracking behaviour was similar in both vacuum and air environments, indicating that grain-boundary cracking was not caused by environment. To assess the mechanisms of crack nucleation, in situ scanning electron microscopy was performed during elevated-temperature (T ≤ 760°C) tensile-creep deformation. Sequential secondary electron imaging and electron backscatter diffraction orientation mapping were performed in situ to allow the evolution of crack nucleation and linkage to be followed. Cracking occurred preferentially along general high-angle grain boundaries and less than 15% of the cracks were found on low-angle grain boundaries and coincident site lattice boundaries. A fracture initiation parameter analysis was performed to identify the role of slip system interactions at the boundaries and their impact on crack nucleation. The parameter was successful in separating the population of intact and cracked general high-angle boundaries at lower levels of strain, but not after crack coalescence dominated the fracture process. The findings of this work have significant implications regarding grain-boundary engineering of this alloy and potentially for other alloy systems.     

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提出了一种利用ANSYS软件模拟单轴扩散焊过程的仿真计算方法,主要研究采用单轴扩散焊工艺制备聚变实验包层模块冷却管板中的管道变形问题,同时采用低活性马氏体钢进行了相关实验研究,并将实验结果与仿真结果进行对比以验证计算方法的可靠性。结果表明,在单轴扩散焊过程中,管道出现较大变形;仿真计算结果与实验结果吻合良好。这表明本方法将有助于单轴扩散焊制造冷却板的工艺改进。     

The influence of tensile stress on grain and cell boundary precipitation in supersaturated Al-Zn alloys during creep

The results are presented of the optical microscopic and X-ray diffraction study of the stress-induced nucleation and growth of (Zn) precipitates at grain and cell boundaries (GB's and CB's) during uniaxial creep at 200 °C of supersaturated AlZn20 and AlZn30 alloys. The rate of precipitation is increased mainly owing to the modifying effect of tensile stress on diffusion processes in alloy samples during their anneal. The diffusion of Zn atoms toward GB's and CB's from adjacent regions of grains is accompanied during creep by diffusive flux of Zn along boundaries parallel or nearly parallel to the tensile creep axis toward boundaries with near to normal orientation to that axis. Enhanced precipitation of results then preferentially at the latter and is supressed at the former boundaries where even the dissolution of preexisting has been found during a later application of tensile stress. The stress-induced precipitation of at GB's gradually ceases with prolonged creep exposures due to the lengthening of duffusion paths of Zn atoms from grain interior to GB's.Dissolution of lamellae by their regress toward GB's and CB's is assisted with the stress-induced diffusion of Zn along epitaxial / lamellar interfaces. Copious precipitation of at the parts of GB's and/or CB's with near to normal orientation to the creep axis is then observed on account of Zn from dissolved lamellae. Creep strain also leads to the fragmentation of lamellae and thus also to breaking down of the paths for diffusion of Zn along / interfaces. Spheroidization of fragmented parts of lamellae is then observed. Spheroids of remain embedded within the former lamellar regions.Large creep strains and high strain rates observed on fine-grained alloy samples may be associated with an enhanced viscous GB sliding due to the stress-dependent flow of Zn along GB's and/or CB's.     

The Gorskii effect and diffusion creep in alloys of the V-H system under bending

A phenomenological theory is proposed for diffusion theory under bending, caused by the Gorskii effect. The theory predicts a three-stage creep curve for two-phase alloys and a one-stage curve for one-phase solid solutions. Formulas derived make it possible to determine the diffusion coefficient in the first two stages of the creep curve. Results from experimental studies of creep of a two-phase alloy of the V-Zr-H system under bending support the conclusions of the theory. Theory has substantiated and experiment has confirmed the existence of a shape memory effect caused by the redistribution of the phase during diffusion creep.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 26–33, August, 1993.