Crack–grain boundary interactions in zinc bicrystals

In polycrystalline materials that fail by transgranular cleavage, it is known that crystallographic misorientation of preferred fracture planes across grain boundaries can provide crack growth resistance; despite this, the micromechanisms associated with crack transmission across grain boundaries and their role in determining the overall fracture resistance are not well understood. Recent studies on diverse structural materials such as steels, aluminum alloys and intermetallics have shown a correlation between fracture resistance and the twist component of grain misorientation. However, the lack of control over the degree and type of misorientation in experimental studies, combined with a dearth of analytical and computational investigations that fully account for the three-dimensional nature of the problem, have precluded a systematic analysis of this phenomenon. In this study, this phenomenon was investigated through in situ crack propagation experiments across grain boundaries of controlled twist misorientation in zinc bicrystals. Extrinsic toughening mechanisms that activate upon crack stagnation at the grain boundary deter further crack propagation. The mechanical response and crack growth behavior were observed to be dependent on the twist angle, and several accommodation mechanisms such as twinning, strain localization and slip band blocking contribute to fracture resistance by competing with crack propagation. Three-dimensional finite element analyses incorporating crystal plasticity were performed on a stagnant crack at the grain boundary that provide insight into crack-tip stress and strain fields in the second grain. These analyses qualitatively capture the overall trends in mechanical response as well as strain localization around stagnant crack-tips.     

MOLECULAR DYNAMICS SIMULATION ON LOW ANGLE GRAIN BOUNDARIES

Molecular dynamics simulation has been performed to investigate the microstructure and properties of low angle grain boundaries, employing the embedded atom method(EAM) type interatomic potential for Ni-Al alloy. The energies of the low angle grain boundaries with different dislocation densities were calculated, and the results indicate that the low angle grain boundary energy varies as a function of misorientation angle. The simulation was found in good agreement with the calculation on the basis of the dislocation theories in the low angle scale. The low angle grain boundary energy goes up with the increase of misorientation angle and tends to go down after reaching a maximum. An energy cusp exists when the misorientation angle increases further, but in this scale the dislocation theories are invalid for energy calculation due to the strong interaction of the dislocations at the boundaries. The simulation results also indicate that the microstructure of low angle grain boundaries can still be described as dislocations when the misorientation angle is larger than 10°.     

The study of grain orientation distributions and grain boundary misorientation distributions in 304 and 316L stainless steels

Orientation distribution functions in two recrystallized austenitic stainless steels (AISI types 304 and 316L) with known grain boundary misorientation distributions have been studied. Previously obtained data on grain boundary spectra in these steels have been re-examined and analyzed from the point of view of texture analysis.The results obtained have shown that there is no unambiguous relatonship between grain boundary misorientation distribution and grain orientation distribution (ODF) determined by the X-ray analysis in the materials under study. This ambiguity is due to the following reason. In the grain boundary misorientation statistics only nearest-neighbor grains are taken into account, but in the orientation distribution function orientations are averaged over the entire volume of the specimen independent as to whether the grains are adjacent or not. Two main results were established for the steels under study: (i) Textures of the two steels differ, though their grain boundary misorientation distributions are similar; and (ii) misorientations of the majority of grain boundaries can be described as rotations about the axes close to 110.     

Accurate measurement of grain boundary misorientation by Large Angle Convergent Beam Electron Diffraction

A new method using Large Angle Convergent Beam Electron Diffraction (LACBED) patterns is proposed to measure accurately the grain boundary misorientation. The LACBED patterns which are obtained with a defocused convergent electron beam having a convergence semi-angle in the range 1 to 5^o contain very sharp deficiency lines. Due to the good quality of the LACBED patterns, these sharp deficiency lines can be used to measure with great accuracy the grain boundary misorientation. In addition, since the LACBED method is a defocus mode method, the patterns contain at the same time information on the reciprocal space (the deficiency lines typical of the crystal orientation of the two grains on each side of the grain boundary) and on the real space (the image of the grain boundary). We describe a method which allows the identification of the misorientation from these LACBED patterns. The main point to consider is the accuracy which is about 0.05^o. It is much better than the one obtained from other conventional methods used to measure this misorientation.     

Grain Boundary Dynamics: A Novel Tool for Microstructure Control

The reaction of grain boundaries to a wide spectrum of forces is reviewed. Curvature, volume energy and mechanical forces are considered. The boundary mobility is strongly dependent on misorientation, which is attributed to both grain boundary structure and segregation. In magnetically anisotropic materials grain boundaries can be moved by magnetic forces. For the first time a directionality of boundary mobility is reported. Flat boundaries can also be moved by mechanical forces, which sheds new light on microstructure evolution during elevated temperature deformation. Curvature driven and mechanically moved boundaries can behave differently. A sharp transition between the small and large angle boundary regime is observed. It is shown that grain boundary triple junctions have a finite mobility and thus, may have a serious impact on grain growth in fine grained materials. The various dependencies can be utilized to influence grain boundary motion and thus, microstructure evolution during recrystallization and grain growth.     

Grain-boundary faceting at a = 3, [110]/{112} grain boundary in a cubic zirconia bicrystal

The atomic structure of a = 3, [110]/{112} grain boundary in a yttria-stabilized cubic zirconia bicrystal has been investigated by high-resolution transmission electron microscopy (HRTEM). It was found that the grain boundary migrated to form periodic facets, although the bicrystal was initially joined so as to have the symmetric boundary plane of {112}. The faceted boundary planes were indexed as {111}/{115}. The structure of the {111}/{115} grain boundary was composed of an alternate array of two types of structure unit: {112}- and {111}-type structure units. HRTEM observations combined with lattice statics calculations verified that both crystals were relatively shifted by (α/4)[110] along the rotation axis to form a stable grain-boundary structure. A weak-beam dark-field image revealed that there was a periodic array of dislocations along the grain boundary. The grain-boundary dislocations were considered to be introduced by the slight misorientation from the perfect = 3 orientation. The fact that the periodicity of the facets corresponded to that of the grain-boundary dislocations must indicate that the introduction of the grain-boundary dislocations is closely related to the periodicity of the facets. An atomic flipping model has been proposed for the facet growth from the initial = 3, {112} grain boundary.     

双模晶体相场研究形变诱导的多级微结构演化

本文采用双模晶体相场模型,计算了双模二维相图;模拟了形变诱导六角相向正方相转变过程的多级微结构演化,详细分析了位相差、形变方向对位错、晶界、晶体结构、新相形貌的影响规律.模拟结果表明:形变方向影响正方相晶核的形核位置和生长方向,拉伸时正方相优先在变形带上形核,垂直于形变方向长大,而压缩时正方相直接在位错和晶界的能量较高处形核,平行于形变方向长大;位相差对形变诱发晶界甄没过程有显著影响,体现在能量峰上为,小位相差晶界位错的攀滑移和甄没形成一个能量峰,大位相差晶界位错攀滑移和甄没因分阶段完成而不出现明显的能量峰;形变诱导相变过程中各种因素相互作用复杂,是相变与动态再结晶的复合转变.     

Boundary Mobility and Energy Anisotropy Effects on Microstructural Evolution During Grain Growth

We have performed mesoscopic simulations of microstructural evolution during curvature driven grain growth in two-dimensions using anisotropic grain boundary properties obtained from atomistic simulations. Molecular dynamics simulations were employed to determine the energies and mobilities of grain boundaries as a function of boundary misorientation. The mesoscopic simulations were performed both with the Monte Carlo Potts model and the phase field model. The Monte Carlo Potts model and phase field model simulation predictions are in excellent agreement. While the atomistic simulations demonstrate strong anisotropies in both the boundary energy and mobility, both types of microstructural evolution simulations demonstrate that anisotropy in boundary mobility plays little role in the stochastic evolution of the microstructure (other than perhaps setting the overall rate of the evolution. On the other hand, anisotropy in the grain boundary energy strongly modifies both the topology of the polycrystalline microstructure the kinetic law that describes the temporal evolution of the mean grain size. The underlying reasons behind the strongly differing effects of the two types of anisotropy considered here can be understood based largely on geometric and topological arguments.     

Coupled motion of [10−10] tilt boundaries in magnesium bicrystals

Magnesium bicrystals were grown with symmetric and asymmetric tilt boundaries about the [10–10] axis using the vertical Bridgman technique. Isothermal constant load tensile tests were conducted on these bicrystals in the temperature range 300–500°C and relative displacements of the two grains were measured to obtain an appreciation for grain boundary motion characteristics. Coupled grain boundary motion was noted in almost all cases with the degree of tangential motion versus migration changing with tilt misorientation, temperature and applied stress. Specifically, within the family of symmetric bicrystals evaluated, a minimum in grain boundary displacement in the specimen plane was observed at a tilt misorientation of 20°. In specific stress/temperature regimes, rigid body sliding was observed for the particular case of a 35° asymmetric tilt misorientation. The ease of basal and prism slip in magnesium at the temperatures considered and the consequential impingement of intragranular dislocations on the bicrystal boundary and their decomposition and motion along the boundary are thought to play an important role in the observed coupled motion of these tilt boundaries.     

Grain boundary misorientation changes during grain growth in pure aluminium

A new method is described for data-logging large amounts of grain boundary misorientation information from channelling patterns in the scanning electron microscope (SEM). The method relies on producing specimens where the grain size is larger than the specimen thickness and where the grain boundary planes are perpendicular to the specimen plane (the so-called columnar structure). Results for grain growth in pure aluminium at 460 and 500°C are presented. There is an increase in the proportion of low angle boundaries at the expense of high angle boundaries during growth times of up to a few hours. The reasons are thought to be partly connected with lower low angle boundary mobility compared with high angle boundaries. However, the growth kinetics appear to be normal over the entire growth time range.     

Asymmetric tilt grain boundary structure and energy in copper and aluminium

Atomistic simulations were employed to investigate the structure and energy of asymmetric tilt grain boundaries in Cu and Al. In this work, we examine the Σ5 and Σ13 systems with a boundary plane rotated about the ? 100 ? misorientation axis, and the Σ9 and Σ11 systems rotated about the ? 110 ? misorientation axis. Asymmetric tilt grain boundary energies are calculated as a function of inclination angle and compared with an energy relationship based on faceting into the two symmetric tilt grain boundaries in each system. We find that asymmetric tilt boundaries with low index normals do not necessarily have lower energies than boundaries with similar inclination angles, contrary to previous studies. Further analysis of grain boundary structures provides insight into the asymmetric tilt grain boundary energy. The Σ5 and Σ13 systems in the ? 100 ? system agree with the aforementioned energy relationship; structures confirm that these asymmetric boundaries facet into the symmetric tilt boundaries. The Σ9 and Σ11 systems in the ? 110 ? system deviate from the idealized energy relationship. As the boundary inclination angle increases towards the Σ9 (221) and Σ11 (332) symmetric tilt boundaries, the minimum energy asymmetric boundary structures contain low index {111} and {110} planes bounding the interface region.     

Grain Boundary Migration in Metals: Recent Developments

Current research on grain boundary migration in metals is reviewed. For individual grain boundaries the dependence of grain boundary migration on misorientation and impurity content are addressed. Impurity drag theory, extended to include the interaction of adsorbed impurities in the boundary, reasonably accounts quantitatively for the observed concentration dependence of grain boundary mobility. For the first time an experimental study of triple junction motion is presented. The kinetics are quantitatively discussed in terms of a triple junction mobility. Their impact on the kinetics of microstructure evolution during grain growth is outlined.     

Misorientation Dependence of the Grain Boundary Energy in Magnesia

Geometric and crystallographic data obtained from a well annealed magnesia polycrystal have been used to specify the five macroscopic degrees of freedom for 4665 grain boundaries. The results indicate, that for this sample, the five parameter grain boundary character space is fully occupied. A finite series of symmetrized spherical harmonics has been used to approximate the misorientation dependence of the relative grain boundary energy. Best fit coefficients for this series were determined by assuming that the interfacial tensions at each triple junction are balanced. The grain boundary energy function shows Read-Shockley behavior at small misorientations and a broad minimum near the 3 misorientation. Furthermore, misorientations about the ‹100› axis create boundaries with relative energies that are less than those created by misorientations about the ‹110› or ‹111› axes.     

Triple Junction Mobility: A Molecular Dynamics Study

We present a molecular dynamics simulation study of the migration of individual grain boundary triple junctions. The simulation cell was designed to achieve steady state migration. Observations of the triple junction angle and grain boundary profiles confirm that steady state was achieved. The static, equilibrium grain boundary triple junction angles and the dynamic triple junction angles were measured as a function of grain size and grain boundary misorientation. In most cases, the static and dynamic triple junction angles are nearly identical, while substantial deviations were observed for low boundary misorientations. The intrinsic, steady-state triple junction mobilities were extracted from measurements of the rate of change of grain boundary area in simulations with and without triple junctions. The triple junction velocity is found to be inversely proportional to the grain size width. The normalized triple junction mobility exhibits strong variations with boundary misorientation, with strong minima at misorientations corresponding to orientations corresponding to low values of . The triple junctions create substantial drag on grain boundary migration at these low mobility misorientations.     

Grain boundary transitions in binary alloys

A thermodynamic diffuse interface analysis predicts that grain boundary transitions in solute absorption are coupled to localized structural order-disorder transitions. An example calculation of a planar grain boundary using a symmetric binary alloy shows that first-order boundary transitions can be predicted as a function of the crystallographic grain boundary misorientation and empirical gradient coefficients. The predictions are compared to published experimental observations.     

Effect of secondary relaxations on diffraction from high-Σ [001] twist boundaries

The types of diffraction effects which may be expected from secondary relaxations in high-Σ [001] twist boundaries are calculated and discussed. An idealized two-plane model is used which incorporates secondary relaxations by rotating patches of boundary about coincident site lattice elements normal to the boundary. Local relaxations within the patches are also employed using rotational relaxations about local O-lattice elements in a manner consistent with earlier results. The main effect of secondary relaxations is the splitting of grain boundary reflections into small clusters which fall on a “grain boundary dislocation lattice”. This localized splitting is significant only when the deviation of the boundary from a nearby low-Σ misorientation becomes sufficiently large. Under these circumstances a noticeable distortion of the diffraction pattern can also occur. The results are compared with some X-ray diffraction observations from twist boundaries in gold.     

Anisotropy of P Grain Boundary Segregation in a Rapidly Solidified Fe-0.6wt%P Alloy

P grain boundary segregation in an Fe-0.6wt%P alloy quenched from the melt was quantified by X-ray Mapping (XRM) in a Scanning Transmission Electron Microscope (STEM). The misorientation across the boundaries was determined by using ACT (Automatic Crystallography for TEM (Transmission Electron Microscopy)) and CBED (Convergent Beam Electron Diffraction). A significant range of the degree of P segregation to individual grain boundaries was found. Combination of chemical and structural studies provides evidence that P segregation to low-angle grain boundaries is reduced.