Grain Boundary Configuration Research Articles

冷間加工した純鉄試料における粒界のフラクタル次元

The effects of the amount of cold work on the fractal dimension of grain boundary were investigated using specimens of the commercial pure iron cold-upsetted in the range from 0% to about 85%. The fractal dimension of grain boundary was estimated principally by approximating the length of the grain perimeter (the length of grain boundaries which belonged to a grain) by line segments.The length of the grain perimeter, L, in each specimen decreased with an increase of the scale of the analysis, r, in the range from about 5×10−7m to about 3×10−6m (region I) and above about 1×10−5m (region III) of r, while it showed a constant value, Lp, between about 3×10−6m and about 1×10−5 m of r. Total datum points of several grains were unified by dividing L by Lp and by plotting L⁄Lp against r. The fractal dimension of grain boundary was obtained by using the datum points in region I, since the change in the grain-boundary configuration with cold work was associated with the slip in the grains. The fractal dimension of grain boundary increased from about 1.05 to about 1.15 with increasing amount of cold work in the range from 0% to about 50% of cold reduction, but it was almost constant above 50% cold work. The box-counting method gave a little larger values of the fractal dimension of grain boundary than the coarse-graining using line segments. The shape change of grains with cold work was also examined and interpreted by a simple analysis in this study.

The fractal dimension of grain-boundary fracture in high-temperature creep of heat-resistant alloys

The fractal dimension of the grain-boundary fracture in high-temperature creep was estimated by the vertical section method on several creep-ruptured specimens of the cobalt-nickel- and iron-based heat-resistant alloys. Grain-boundary microcracks linked to the fracture surface were also taken into account in the present analysis by the box-counting method. In the specimens containing many grain-boundary microcracks linked to the fracture surface, the fractal dimension of the grain-boundary fracture was larger in the scale range of more than about one grain-boundary length than in the scale range less than this length. Thus, there was a cross-over in the fractal dimension of the grain-boundary fracture at about one grain-boundary length in these specimens. In the specimens containing much fewer microcracks, there was no clear cross-over in the fractal dimension of the grain-boundary fracture with regard to the scale of the analysis, irrespective of creep-ductility and grain-boundary configuration of the specimens. The fractal dimension of the grain-boundary fracture was generally larger in specimens with serrated grain boundaries than in specimens with straight grain boundaries in these heat-resistant alloys, because the fractal dimension of the grain boundary and the number of the grain-boundary microcracks were larger in the former specimen. The fractal dimension of the grain-boundary fracture did not tend to converge to unity when the scale of the analysis approached the specimen size. The inclusion of near-specimen size data with regard to the scale of the analysis did not affect the fractal dimension of the grain-boundary fracture in these alloys. Thus, the grain-boundary fracture in the creep-ruptured specimens exhibited a fractal nature, at least in the scale range below specimen size, although there was a cross-over in the fractal dimension of the grain-boundary fracture in specimens containing a large number of grain-boundary microcracks.

Low-energy configurations of symmetric and asymmetric tilt grain boundaries

High-resolution electron-microscopy experiments are combined with computer simulations of tilt grain boundaries (GBs) in Au to investigate the preferred GB planes in ∑ = 9 and ∑ = 11 bicrystals. Th...

Characterization of grain-boundary configuration and fracture surface roughness by fractal geometry and creep-rupture properties of metallic materials

Grain-boundary configuration in heat-treated specimens and fracture surface roughness in creep-ruptured specimens of several kinds of metallic material were quantitatively evaluated on the basis of fractal geometry. Correlations between the fractal dimension of grain boundary, that of fracture surface profile, the creep-rupture properties and the fracture mechanisms of the alloys are discussed. In heat-resistant alloys, the fractal dimension of a nominally serrated grain boundary was always larger than that of a straight grain boundary in the same alloy. The relative importance of the ruggedness of grain boundaries was estimated by the fractal dimension difference between these two grain boundaries. There was a quantitative relationship between the increase of the fractal dimension of the grain boundary and the improvement of rupture ductility and rupture strength owing to grain-boundary serration in the alloy. A similar correlation was also found between the increase in the fractal dimension of the fracture surface profile and the improvement of the creep-rupture properties, since in some cases the fractal dimension of the fracture surface profile was correlated with that of the grain boundary. Both grain boundary and fracture surface profile were assumed to exhibit a fractal nature between one grain boundary length (upper bound) and an interatomic spacing (lower bound). In carbon steels with ferrite-pearlite structure, according to the increase in pearlite volume fraction, the rupture ductility decreased and the fracture mechanism changed from transgranular fracture in pure iron and low-carbon steels to intergranular fracture at ferrite-pearlite grain boundaries in medium-carbon steels, and further to intergranular fracture at pearlite grain boundaries in high-carbon steels. The correspondence between the fractal dimension of the grain boundary and that of the fracture surface was confirmed in ruptured specimens of ferrite-pearlite steels when the grain boundary was the fracture path.

Fracture toughness and brittle-ductile transition controlled by grain boundary character distribution (GBCD) in polycrystals

The structural dependence of intergranular fracture processes in bicrystals and polycrystals of metals and alloys is first reviewed. It is shown that even in polycrystals, grain boundary structure plays a significant role in controlling the fracture properties of the material. Next, we evaluate quantitatively the effect of different types, frequencies and configurations of grain boundaries, so-called the grain boundary character distribution (GBCD), on the toughness of a three-dimensional (3D) polycrystals. The results show that the toughness of a polycrystals increases monotonically with increasing overall fraction of fracture-resistant low-energy boundaries in the material. A brittle-ductile transition, corresponding to a change of fracture mode from predominantly intergranular with low toughness to predominantly transgranular with high toughness, is observed when the overall fraction of low-energy boundaries reaches a critical value. For a 3D polycrystals with a non-random GBCD such that the fraction of low-energy boundaries on the inclined boundary facets is maximised, a smaller critical overall fraction of low-energy boundaries is needed to bring about the brittle-ductile transition. Similar effect is also found if the grains are made elongated and aligned with the stress axis. The results are discussed in relation to the concept of grain boundary design for strong and tough polycrystals proposed by one of the present authors (T.W.).

FIRST-PRINCIPLES CALCULATIONS OF THE ELECTRONIC STRUCTURE OF GRAIN BOUNDARIES

FIRST-PRINCIPLES CALCULATIONS OF THE ELECTRONIC STRUCTURE OF GRAIN BOUNDARIES

Effects of grain-boundary configuration on the high-temperature creep strength of cobalt-base L-605 alloys

The effects of grain-boundary configuration on the high-temperature creep strength are investigated using commercial cobalt-base L-605 alloys with low carbon content in the temperature range 816 to 1038° C (1500 to 1900° F). Serrated grain boundaries are formed principally by the precipitation of tungsten-rich b c c phase (the same as α2 phase found in Ni-20Cr-20W alloys) on grain boundaries by a relatively simple heat treatment in these alloys. The creep rupture properties are improved by strengthening of grain boundaries by the precipitation of tungsten-rich bcc (α2) phase. The specimens with serrated grain boundaries have longer rupture lives and higher ductility than those with normal straight grain boundaries under low stress and high-temperature creep conditions, while the rupture lives and the creep ductility of both specimens are almost the same under high stresses below 927° C. The matrix of the alloys is strengthened by the precipitation of carbides at temperatures below 927° C and by the precipitation of tungsten-rich α2 phase at 1038° C during creep. It is found that there is an orientation relationship between tungsten-rich a2 phase particles andβ-Co matrix, such that (0 1 1)α2 ¶ (1 1 1)β-Co and [1\(\overline 1 \) 1]α2 ¶ [1\(\overline 1 \) 0]β-Co. The fracture surface of specimens with serrated grain boundaries is a ductile grain-boundary fracture surface, while typical grain-boundary facets prevailed in specimens with straight grain boundaries.

Modelling of microstructural features in Y-Ba-Cu-O superconductors

Abstract We have investigated characteristics of four important microstructural features, namely, grain boundaries (small-and large-angle), twins, stacking faults and cracks in high-Tc YBa2Cu3O7-x superconducting oxides using transmission electron microscopy techniques. A detailed analysis of these microstructural features is carried out to understand their effect on the superconducting properties, mechanical properties and their environmental sensitivity. An atomic model of the small-angle and large-angle grain boundaries in these superconducting oxides is provided using a geometric description. Some important differences between the grain-boundary structure of the superconducting oxides and that of metals have been identified. The environmental sensitivity of the superconducting oxide is explained in terms of the atomic structure of dislocations associated with the grain-boundary configurations. The strain energy associated with the twinned regions and oriented domains is determined using discrete dislo...

HREM STUDIES OF THE SUPERCONDUCTING PHASE Tl2Ba2Ca2Cu3Ox

The superconducting phase Tl 2 Ba 2 Ca 2 Cu 3 O x (Tl2223) has been identified in high-T c superconducting ceramics with nominal composition of Tl 2 Ba 2 Ca 2 Cu 3. The configurations of grains and grain boundaries have also been observed directly by high resolution electron microscopy [HREM]. The small angle grain boundaries are mixed with both translation and orientation characteristics. The boundary regions are nearly parallel to (100) to (010) in crystal state, While in amorphous state, they are nearly parallel to (001). There also exists large angle grain boundaries in TlBaCaCuO superconductor.

Creep rupture strength and grain-boundary sliding in austenitic 21 Cr-4Ni-9Mn steels with serrated grain boundaries

The effect of grain-boundary strengthening on the creep-rupture strength by modification of the grain-boundary configuration is studied using austenitic 21 Cr-4Ni-9Mn steel in the temperature range from 600 to 1000° C in air. Grain-boundary sliding is also examined on a steel with serrated grain boundaries during creep at 700° C. The improvement of creep-rupture strength by the strengthening of grain boundaries is observed at high temperatures above 600° C. The 1000 h rupture strength of steels with serrated grain boundaries is considerably higher than that of steels with straight grain boundaries, especially at 700 and 800° C. The strengthening by serrated grain boundaries is effective in retarding both the crack initiation and the crack propagation at 700° C, while it does not improve the life to crack initiation at 900° C. Grain-boundary sliding is considerably inhibited by the strengthening of grain boundaries at 700° C. The amount of it in steels with serrated grain boundaries is less than about one-third of that of steels with straight grain boundaries at the same creep strain. The stress dependence of grain-boundary sliding rate in the steady-state regime is also examined from the steels with these two types of grain-boundary configuration.

Effects of grain-boundary configuration on the creep rupture strength and grain-boundary sliding in austenitic heat-resisting steel.

The effect of grain-boundary configurations on the creep rupture strength was investigated using austenitic 21Cr-4Ni-9Mn (21-4N) steel in the temperature from 600 to 1000°C. The grain-boundary sliding was also examined on specimens crept at 700°C. Further, discussions were made on the relation between the amount of grain-boundary sliding and the initiation of grain-boundary cracks.The creep rupture strength was improved by serrated grain boundaries at temperatures above 600°C. The specimens with serrated grain boundaries had longer rupture lives than those with normal straight grain boundaries even at high temperatures around 1000°C.It was experimentally confirmed that both the life to crack initiation and the life of crack propagation increased by the serrated grain boundary at temperatures around 700°C, and that only the resistance to crack growth of the steel was improved by the strengthening at high temperatures above 900°C.The average amount of grain-boundary sliding in specimens during creep at 700°C was reduced by serrated grain boundary to about one-third or one fourth of that of the specimen with straight grain-boundary configuration. A good agreement was found between the experimental results on the critical amount of grain-boundary sliding for crack initiation and those predicted by the theory of triple point cracking.

Geometrical models for grain boundary structures in L2 0 and L1 2 ordered alloys—on the twist boundaries

The geometrically possible configurations of twist-type boundaries in AB L2 0 and A 3B L1 2 ordered alloys were analyzed, based on the consideration for symmetry in lattice and geometric degrees of freedom in the grain boundary. The degree of freedom regarding to “relative translation” yielded two configurations of types T and PT. The degree of freedom regarding “position of grain boundary”, which relates to atomic composition in the grain boundary region, yielded four configurations of types α, β, γ and δ. The defects of pair bondings were usually recognized in the grain boundary region and were characterized into three kinds of faults, depending on the appearance of these defects, i.e. SF, APB and SF + APB faults. The fault (excess) energies attributed to these defects were evaluated in each configuration of grain boundaries. With the energetics in this evaluation, a few characteristics in grain boundaries of ordered alloys were discussed. Also, the results of this analysis were compared with results obtained in grain boundaries of tilt-type and of pure metals.

Atomic Resolution Studies of Tilt Grain Boundaries in NiO

AbstractThe atomic structures of a number of <001> high-angle tilt grain boundaries in NiO have been studied by high-resolution electron microscopy (HREM). Crystal 1inity is always maintained right up to the grain boundary (GB). Grain boundary planes bounded by a (100)-plane are preferred, however symmetrical facets are also found at each misorientation. A tendency to match atomic planes across the GB is not only observed in symmetrical, but also in asymmetrical GBs. Structural units can be clearly recognized in symmetrical GBs. Contrast differences suggest that a multiplicity of structural units exists for some GB configurations. Frequently symmetric GBs also show deviations from mirror symmetry. Multislice simultations indicate that the image contrast associated with HREM GB images is not particularly sensitive to GB relaxation.

On the improvement of high-temperature low-cycle fatigue property by grain-boundary reaction precipitates.

The effect of grain-boundary reaction (GBR) on high-temperature low-cycle fatigue life was investigated for austenitic 21-4N heat-resisting steel at 973K. The grain-boundary was considerably serrated by GBR during aging. The high-temperature fatigue life was remarkably improved by the occurrence of GBR for fast-fast and slow-slow symmetrical triangular strain wave shapes. The fatigue life was not changed by GBR for the asymmetrical triangular wave shape. The longest fatigue life was observed on the specimen with GBR nodule was internally cracked by cyclic deformation. The improvement of fatigue life by a small amount of GBR was resulted from the retardation of brittle intergranular fracture by the serrated grain-boundary configuration.

Configuration of grain boundaries

AbstractIn the present paper a model of the configuration of grain boundaries from a general point of view in the framework of the CSL concept has been developed. Rotations and rotations with translations were taken under consideration. The main result is the determination of the coincidence conditions for symmetrical and asymmetrical grain boundary facets between two and three grains. The facet angles of grain boundaries in any crystal surface are determined.

Equilibrium Shapes for Grain Boundaries and Surfaces with Anisotropic Surface Tension Functions

ABSTRACTThe geometric configuration of grain boundaries and surfaces seems to play a significant role in phase transformations and surface phenomena. Determining the equilibrium configurations of such boundaries for a given surface tension function γ is additionally an interesting mathematical problem; it reduces in the case of isotropic surface tension to the minimal surface problem. A framework is given here for determining such configurations in the other extreme case, where the equilibrium shape of a crystal of fixed volume (the Wulff shape) is a polyhedron. Some results obtained within this framework are outlined.

Consideration of lattice translations in computer studies of grain-boundary coincidence

The proposal that boundaries between crystals related by a high-density coincidence misorientation will not contain shared atom sites is examined. The rigid lattice translations which reputedly destroy boundary coincidence in computer-simulated minimum-energy grain-boundary configurations are compared with the set of special displacements which conserve the pattern of coincidence sites. The lattice of all such displacements has been termed the ``DSC lattice''. It is shown that most of the computed translations cited as evidence in support of the proposal are very nearly DSC lattice vectors, and hence shared atoms are still present in the boundaries, in most cases, after the translations. Therefore, little justification for discarding the concept of atom sharing in grain-boundary structures is provided by the computer calculations performed thus far. The importance of considering the properties of the DSC lattice in computer modeling of coincidence boundaries, both in setting up the computer program and in evaluating its results, is clearly indicated.

On the role of grain-boundary migration during the creep of zinc

Constant engineering strain-rate tensile tests have been carried out in the temperature range 20 to 150‡C on high purity Zn, Zn-0.14 at. % Cu (alloy C) and Zn-0.16 at. % Al (alloy A) alloys. Measurements of angular distribution of orientations of grain boundaries have been used to study grain-boundary migration during deformation. Significant cavitation, with increasing propensity at higher test temperatures, occurred in the two alloys but not in pure Zn. A striking feature of the observations in pure Zn and alloy C, as the test temperature was raised, was the formation and subsequent decay of a diamond pattern of uncavitated grain boundaries, a majority of which were preferentially aligned at ∼ 45‡ to the stress axis. By comparison the changes in the angular distribution of grain boundaries was least marked in alloy A. Cavitation was observed in alloy C to maintain grain boundaries in the 45‡ orientation. At the test temperature of 150‡C alloy C, which was prone to the formation of diamond grain-boundary configuration, developed much larger volume fraction of cavities than alloy A. These results are discussed in terms of the different distribution coefficients of Cu and Al in Zn, the different rates of grain-boundary migration in pure Zn and the two alloys and the differences in the substructural features (cells) formed during high-temperature deformation.

Diffusional Viscosity of a Polycrystalline Solid

According to a suggestion of Nabarro, any crystal can change its shape by self-diffusion in such way as to yield to an applied shearing stress, and this can cause the macroscopic behavior of a polycrystalline solid to be like that of a viscous fluid. It is possible that this phenomenon is the predominant cause of creep at very high temperatures and very low stresses, though not under more usual conditions. The theory underlying it is developed quantitatively, and calculations of rate of creep, or equivalently of effective viscosity, are given for aggregates of quasi-spherical grains and for wires composed of cylindrical grains. Allowance is made for the effect of tangential stress relaxation at the grain boundaries. It is suggested that mosaic boundaries and boundaries between grains of nearly the same orientation may be unable to serve as sources or sinks of the diffusion currents, in which case the creep rate will depend only on the configuration of grain boundaries having a sizable orientation difference. Numerical comparison of the theory with experiments on the high temperature creep of wires favors this view, but is not entirely satisfactory. Suggestions for further experiments are made.