Misorientation texture development during grain growth. Part II: Theory

A critical event model for the evolution of number- and area-weighted misorientation distribution functions (MDFs) during grain growth is proposed. Predictions from the model are compared to number- and area-weighted MDFs measured in Monte Carlo simulations with anisotropic interfacial properties and several initial orientation distributions, as well as a dense polycrystalline magnesia sample. The steady-state equation of our model appears to be a good fit to all data. The relation between the grain boundary energy and the normalized average boundary area is discussed in the context of triple junction dynamics.     

Grain growth in anisotropic systems: comparison of effects of energy and mobility

Grain growth in systems of anisotropic grain boundary energy and mobility is investigated by computer simulations in a two-dimensional textured polycrystalline system. The energy and mobility are allowed to depend on both grain boundary inclination and misorientation. Mobility anisotropy alone does not significantly change the growth kinetics or statistical distributions of misorientation, grain size and number of grain edges, even though grain shapes evolve in a self-dissimilar fashion where the aspect ratio of grains and inclination distribution of grain boundaries are time dependent. Energy anisotropy, however, causes significant deviation of grain growth kinetics, misorientation and edge-distributions from the ones observed in isotropic systems. Moreover, misorientation distribution is skewed towards low energy (special) boundaries. Size distributions are similar in all cases. Mobility anisotropy influences grain growth kinetics only when energy is also anisotropic. Variation of misorientation distribution with time plays the key role in determining the grain growth behavior.     

Misorientation dependence of intrinsic grain boundary mobility: simulation and experiment

Both experimental and atomistic simulation measurements of grain boundary mobility were made as a function of temperature and boundary misorientation using the same geometry that ensures steady-state, curvature-driven boundary migration. Molecular dynamics simulations are performed using Lennard–Jones potentials on a triangular lattice. These simulations represent the first systematic study of the dependence of intrinsic grain boundary mobility on misorientation. The experiments focus on high purity Al, with 〈111〉 tilt boundaries, which are isomorphic to those examined in the simulations. Excellent agreement between simulations and experiments was obtained in almost all aspects of these studies. The boundary velocity is found to be a linear function of the curvature and the mobility is observed to be an Arrhenius function of temperature, as expected. The activation energies for boundary migration varies with misorientation by more than 40% in the simulations and 50% in the experiments. In both the simulations and experiments, the activation energies and the logarithm of the pre-exponential factor in the mobility exhibited very similar variations with misorientation, including the presence of distinct cusps at low Σ misorientations. The activation energy for boundary migration is a logarithmic function of the pre-exponential factor in the mobility, within a small misorientation range around low Σ misorientations.     

Simulation of microstructural evolution during directional annealing with variable boundary energy and mobility

Microstructural evolution during directional annealing has been investigated with variable grain boundary energy and mobility. The boundary energy and mobility were expressed as a function of misorientation between grains and incorporated into a front-tracking grain-growth simulation model. Development of columnar grain structure becomes more difficult with anisotropic boundary properties with the proportion of low angle boundaries increasing with increasing hot zone width. The critical hot zone velocity for the propagation of a columnar grain structure in an anisotropic system is expressed as a function of the boundary misorientation angle. The grain aspect ratio is shown to increase and the texture becomes more pronounced with decreasing hot zone velocity.     

The annealing behaviour of deformed cube-oriented aluminium single crystals

Single crystals of the {001}〈100〉 cube orientation of a dilute single-phase Al–Si alloy have been deformed in plane strain compression at temperatures between 300 and 500°C at strain rates between 0.5 and 50/s. The stability of the cube orientation was found to be dependent on the deformation conditions, which is in agreement with previous work. The deformed crystals contained bands of subgrains of a range of sizes and misorientations. Detailed EBSD analysis of deformed and annealed crystals revealed a strong correlation between subgrain growth and misorientation, and analysis of the data enabled the mobility of low angle grain boundaries in the misorientation range 5–20° to be determined in the temperature range 300–450°C. It was found that the boundary mobility increased with increasing misorientation up to ∼15–20° and thereafter reached a plateau. The activation energies of migration were consistent with control by lattice diffusion of Si in Al and the activation energy was found to increase with increasing misorientation.     

Assignment of individual orientations by gaussian distribution and monte-carlo grain growth simulation by grain boundary character distribution (GBCD) in Fe-3%Si alloy

In order to investigate the effect of GBCD on microstructural evolution, a Monte-Carlo computer simulation method was developed in which the texture of real material was closely reconstructed in the simulated microstructure. This method consists of extracting a volume fraction and a Gaussian half-width from an experimental ODF of a Fe-3%Si alloy and planting them into the simulated microstructure. Using the reconstructed microstructure, the recrystallization texture formation characteristic of this alloy was studied with a particular focus on the anisotropic mobility of grain boundaries. By deliberately assigning a high anisotropic mobility (1000 times) to the grain boundaries with a misorientation angle in the range of 20 to 45 degrees, the abnormal grain growth phenomenon was analyzed. It was found that a selective growth of grains occurred when they were subjected to such pertinent conditions as their own high mobility accompanied by the presence of the neighboring low-mobility grains. Grains with a Goss orientation conformed to this general pattern of selective coarsening. Therefore, the present result strongly suggests that the theory of Hayakawaet al. - based on the selective growth of the Goss grains with particular boundary misorientation angles - needs to be modified so as to incorporate more general cases.     

异常晶粒长大的Monte Carlo模拟

采用作者提出的Monte Carlo Potts新模型，模拟研究了高纯铝在各向异性晶界能和晶界迁移率条件下晶粒长大的组织、动力学和晶粒尺寸分布特征，揭示初始组织织构强度对异常晶粒长大的影响规律。结果表明：各向异性晶界能和晶界迁移率使晶粒尺寸不均匀、形状不规则，降低了晶粒长大指数，晶粒尺寸分布偏离对数正态分布；异常晶粒长大只出现在中等强度的织构组织中，而不会在太强或太弱织构组织中出现。理论分析认为各向异性晶界能和晶界迁移率是异常晶粒长大的内因，织构是引起异常晶粒长大的外因，其强度决定了异常晶粒长大是否出现。     

Effect of deformation mode and grain orientation on misorientation development in a body-centered cubic steel

Strain-induced misorientation development was studied in an IF steel as a function of strain for two deformation modes, plane strain compression and simple shear. Using electron back-scattered diffraction, orientation maps of “large” areas were obtained, from which several individual grains associated with the principal texture components could be extracted so that only intragranular misorientations could be estimated for these orientations. It was observed that the increase of the misorientation angle was more prominent in simple shear than in plane strain compression and that the orientation influence was different for each mode. Considering texture evolution as a possible source of misorientation development, the lattice spin tensor was estimated with the Taylor model for the two deformation modes; both reorientation axis and angle were compared with misorientation angle and axis. The striking concordance of both quantities allows us to conclude that there is a direct contribution of texture evolution to misorientation accumulation with strain.     

Texture evolution in FCC metals from initially different misorientation distributions under shear deformation

We applied the crystal plasticity finite element method (CPFEM) based on a rate sensitivity model to examine the subgrain texture evolution of FCC metals under shear deformation. We used two kinds of microstructure models with the same orientation distribution function (ODF) but different spatial arrangements or misorientation distributions (MDs). One contained a great high frequency around low misorientation angles and the other a great high frequency near high misorientation angles. Different misorientation angles among neighboring crystals caused different interactions among them, particularly at the subgrain scale. The difference in MD affected the evolution of texture and average misorientation angles during deformation. The average misorientation angles of the subgrain boundaries increased with shear strain.     

Inclination dependence of grain boundary energy and its impact on the faceting and kinetics of tilt grain boundaries in aluminum

The shape evolution and migration of <1 0 0> and <1 1 1> tilt grain boundaries with rotation angles θ in the range between 6° and 24° were investigated in situ in a scanning electron microscope at elevated temperatures. The results revealed that boundaries with misorientation θ < 15° did not attain a continuously curved shape in the entire temperature range up to the melting point and, thus, did not move under a capillary driving force. Instead, they remained straight or formed several facets which were inclined to the initial boundary orientation. Molecular statics simulations suggest that the observed behavior of low-angle boundaries is due to the anisotropy of grain boundary energy with respect to boundary inclination. This anisotropy diminishes with increasing misorientation angle, and high-angle boundaries assume a continuously curved shape and move steadily under the curvature driving force.     

Simulations of anisotropic grain growth: Efficient algorithms and misorientation distributions

An accurate and efficient algorithm, closely related to the level set method, is presented for the simulation of Mullins’s model of grain growth with arbitrarily prescribed surface energies. The implicit representation of interfaces allows for seamless transitions through topological changes. Well-resolved large-scale simulations are presented, beginning with over 650,000 grains in two dimensions and 64,000 grains in three dimensions. The evolution of the misorientation distribution function (MDF) is computed, starting from random and fiber crystallographic textures with Read–Shockley surface energies. Prior work had established that with random texture the MDF shows little change as the grain network coarsened whereas with fiber texture the MDF concentrates near zero misorientation. The lack of concentration about zero of the MDF in the random texture case has not been satisfactorily explained previously since this concentration would decrease the energy of the system. In this study, very-large-scale simulations confirm these previous studies. However, computations with a larger cut-off for the Read–Shockley energies and an affine surface energy show a greater tendency for the MDF to concentrate near small misorientations. This suggests that the reason the previous studies had observed little change in the MDF is kinetic in nature. In addition, patterns of similarly oriented grains are observed to form as the MDF concentrates.     

Anisotropic tensile behavior and related yield point phenomena in annealed ultrafine-grained pure aluminum

It is found that tensile flow curves of samples of annealed ultrafine-grained aluminum AA1090 show the development of a yield point and a significant mechanical anisotropy. To rationalize the anisotropic tensile behavior, the orientation data of the annealed material were measured using electron backscatter microscopy. It is found that the inferior mechanical properties of samples tested at 45° to the rolling direction may be attributed to a strong rolling texture effect and that the anisotropic magnitude of the yield drop may be related to the proportion of grains with soft orientations (defined as those with Schmid factor greater than 0.45) in the sample. Additionally, it is found that the anisotropy in tensile ductility is in general agreement with a Considère criterion analysis and that the mechanical anisotropy in the samples is only partly explained by the crystallographic texture, where microstructural anisotropy may also play a role.     

激光电弧热源复合模式对301L不锈钢焊接接头性能的弱化机制

激光电弧复合焊在传统的激光填丝焊基础上加入了电弧形成复合热源,导致电弧区产生热量积累,造成焊缝晶粒粗大,并弱化了焊接接头的强度和断后伸长率,促使焊接结构的服役安全性能大幅降低. 通过建立三维熔池温度模型及力学性能分析阐明了激光与电弧协同热作用对焊接接头强度和断后伸长率的影响规律. 结合焊缝的晶粒尺寸、晶界取向差分布、织构强度从微观晶体学角度揭示了焊接接头强度和断后伸长率的弱化机制. 结果表明,电弧介入促使复合热源产生热积累,降低熔池温度梯度,强化了晶粒的择优取向生长及织构强度,导致接头各向异性,从而使焊接接头的断后伸长率降低2%. 较低的温度梯度会延长熔池冷却时间,促使晶粒长大和大角度晶界减少,不利于阻碍位错滑移,导致焊接接头平均屈服强度降低35 MPa,极限抗拉强度降低66 MPa. 并且随着焊接电流的升高,熔池高温停留时间延长,接头晶粒及织构强度增大,接头强度和断后伸长率继续降低.     

On misorientation distribution evolution during anisotropic grain growth

In order to study the development of texture and boundary character during annealing, three-dimensional grain crystallography and crystallographically mediated grain boundary properties were incoporated into a finite temperature Monte Carlo model for grain growth. Randomly textured microstructures evolve normally, with growth exponent n=0.96. While texture remains random, the steady-state boundary misorientation distribution favors low-angle boundaries. To first order, low-angle boundaries increase by lengthening, not by proliferating. In contrast, microstructures with a strong single-component texture develop four-grain junctions and highly curved grain boundaries, which alter evolution. The boundary misorientation distribution narrows and shifts to low angles, and no steady state is observed. The accompanying decrease in mean boundary mobility causes growth to slow, resulting in a growth exponent n=0.62. The dependence of the growth exponent on average boundary mobility may explain experimental observations of exponents less than unity.     

Correlations between the crystallographic texture and grain boundary character in polycrystalline materials

A method is presented to determine the misorientation probability distribution function in polycrystalline materials based on a known, analytical or numerical, representation of the associated orientation probability distribution function, i.e., texture. The proposed formulation incorporates the local grain-to-grain orientation correlations by combining local or macroscopic statistical information, and finds a natural interpretation through the well-known stereographic projection (pole-figure) representation. The proposed formulation distinguishes between antiparallel crystallographic orientations, as well as cone-angle and polar angle misorientations. For fiber-textured samples, it is quantitatively shown that highly oriented samples are equivalent to polycrystals with a high density of low-angle misorientations, while completely random (untextured) materials are equivalent to microstructures with a high probability of large-angle misorientations.     

Selective Laser Melting of Carbon-Free Mar-M509 Co-Based Superalloy: Microstructure,Micro-Cracks,and Mechanical Anisotropy

In this work,the microstructural evolution,micro-crack formation,and mechanical anisotropy of the selective laser melted(SLM) carbon-free Mar-M509 Co-based superalloy were systematically studied under different linear energy densities(LED).Observation shows that the SLM Mar-M509 superalloy possesses a fully dense structure,whereas some microcracks exist along the building direction.The electron backscatter diffraction results reveal that dominant columnar grains tend to elongate along the buildi...     

Analysis of microstructure and texture evolution in pure magnesium during symmetric and asymmetric rolling

Asymmetric rolling of commercially pure magnesium was carried out at three different temperatures: room temperature, 200 °C and 350 °C. Systematic analysis of microstructures, grain size distributions, texture and misorientation distributions were performed using electron backscattered diffraction in a field emission gun scanning electron microscope. The results were compared with conventional (symmetric) rolling carried out under the same conditions of temperature and strain rate. Simulations of deformation texture evolution were performed using the viscoplastic self-consistent polycrystal plasticity model. The main trends of texture evolution are faithfully reproduced by the simulations for the tests at room temperature. The deviations that appear for the textures obtained at high temperature can be explained by the occurrence of dynamic recrystallization. Finally, the mechanisms of texture evolution in magnesium during asymmetric and symmetric rolling are explained with the help of ideal orientations, grain velocity fields and divergence maps displayed in orientation space.