Triple Junction Distributions Research Articles

Evolution of Grain Boundary Character Distribution in B10 Alloy from Friction Stir Processing to Annealing Treatment.

In this study, the grain boundary character distribution (GBCD) of a B10 alloy was optimized, employing thermomechanical processing consisting of friction stirring processing (FSP) and annealing treatment. Using electron backscatter diffraction, the effects of rotational speed of FSP and annealing time on the evolution of GBCD were systematically investigated. The GBCD evolution was analyzed concerning various parameters, such as the fraction of low-Σ coincidence site lattice (CSL) boundaries, the average number of grains per twin-related domain (TRD), the length of longest chain (LLC), and the triple junction distribution. The experimental results revealed that the processing of a 1400 rpm rotational speed of FSP followed by annealing at 750 °C for 60 min resulted in the optimum grain boundary engineering (GBE) microstructure with the highest fraction of low-Σ CSL boundaries being 82.50% and a significantly fragmented random boundary network, as corroborated by the highest average number of grains per TRD (14.73) with the maximum LLC (2.14) as well as the highest J2/(1 - J3) value (12.76%). As the rotational speed of FSP increased from 600 rpm to 1400 rpm, the fraction of low-Σ CSL boundaries monotonously increased. The fraction of low-Σ CSL boundaries first increased and then decreased with an increase in annealing time. The key to achieving GBE lies in inhibiting the recrystallization phenomenon while stimulating abundant multiple twinning events through strain-induced boundary migration.

Influence of grain boundary energy anisotropy on the evolution of grain boundary network structure during 3D anisotropic grain growth

In this paper, we present the results of grain growth simulations in three-dimensions using an existing level set method. Most of the previous grain growth studies have been either isotropic or, if they are not isotropic, consider simplified models of anisotropy. We perform these simulations using three different grain boundary (GB) energy functions (a realistic 5D GB energy function, a Read–Shockley energy model that depends only on disorientation angle, and an isotropic GB energy model). We compare the results in terms of several statistical microstructural descriptors (crystallographic texture, GB character distribution, triple junction distribution (TJD), etc.). In addition to considering different energy models, we also compare the evolution of microstructures that have different initial crystallographic textures (fiber texture and random texture). We find that the morphological evolution of individual grains can be completely different depending on the GB energy function employed. However, we also find that certain spatially independent microstructural statistics (e.g. orientation distribution function, misorientation distribution function, and TJD) are similar at steady state for all of the tested GB energy functions.

Outstanding improvement in the CSL distribution in interstitial free (IF) steel via strain annealing route

In the last two decades, grain boundary engineering (GBE) study has neglected the high stacking fault energy BCC materials. Researchers have tried many single or multi-step strain recrystallization routes for improving the grain boundary character distribution (GBCD) in BCC materials, but the results have not been satisfactory. So, in this study, a single-step low deformation (5%, 10%) strain annealing route is employed for obtaining optimized GBCD and triple junction distribution (TJD) in interstitial free steel. This low deformation (5%) and low temperature (923 K) short annealing (10 min) treatment led to the evolution of 48.2% of Σ3, 54.3% of low Σ CSL boundaries, and 31.1% of special triple junctions (J2 and J3 type) in the microstructure. To the best of the authors' knowledge, these are the highest values reported for BCC material in literature. A good correlation is found between {111}〈110〉, {111}〈112〉 gamma fiber texture components and low deviation Σ3 boundaries. Moreover, a thorough analysis of average grain size, residual strain, GBCD, TJD, and grain orientation spread indicates that the regeneration mechanism (due to strain-induced boundary migration (SIBM)) is responsible for establishing a GBE microstructure in the thermomechanically processed sample (5%, 923 K, 10 min). The present work also explains the role of abnormal grain growth (AGG) on the deterioration of GBCD and TJD in the highly deformed (10%) samples.

New perspectives on twinning events during strain-induced grain boundary migration (SIBM) in iteratively processed 316L stainless steel

Characterization of microstructure and grain boundary character distribution (GBCD) during iterative thermo-mechanical processing (TMP) of 316L stainless steel were done using electron backscatter diffraction (EBSD). Results from EBSD scans were analyzed in terms of the fraction of special boundaries, their deviation from ideal misorientation, connectivity of random high-angle grain boundaries, and grain size. In order to understand the efficacy of the iterative processing route leading to a well-connected twin boundary network, additional analysis was done in terms of twin-related domain statistics and triple junction distribution. Results from these analyses show that initial iteration results in a microstructure with insufficient twin boundary density, and a poor twin boundary network. Although the next iteration leads to a small increase in twin statistics, it also does not significantly improve the statistics of favorable grain boundaries and their network. However, the fourth iteration of the processing results in a large improvement in both the population and distribution of favorable grain boundaries. All the subsequent iterations were found to result in microstructural deterioration in terms of both population and network of these grain boundaries. Based on the analysis, role of underlying mechanisms such as strain-induced grain boundary migration and static recrystallization in the effective optimization of GBCD was analyzed. The present research gives important insights into these mechanisms and their control during TMP in order to achieve an engineered microstructure.

EBSD characterization of pure and K-doped tungsten fibers annealed at different temperatures

Electron Backscatter Diffraction was used to investigate the grain boundary character and triple junction distributions as well as the microtexture on drawn pure and potassium doped (60–75 ppm) tungsten wires. With an approximate diameter of 150 μm, pure W wires were annealed at 1300, 1600 and 1900 °C, whereas K-doped material was annealed at 1300, 1600 and 2100 °C. The annealing was performed under hydrogen atmosphere for 30 min. Both longitudinal and transversal sections were analyzed to assess anisotropic features. Up to 1600 °C, all conditions presented a strong <110> fiber texture parallel to the drawing axis. With increasing annealing temperature, the pure W material developed a more heterogeneous fiber texture while for the K-doped material, it remained homogeneous. Orientation correlation function (OCF) analysis suggested sub-grain coarsening as the recrystallization mechanism while grain boundary density and grain boundary character distribution exhibited anisotropic behavior, as well as the triple junction distribution network. On the other hand, the coincidence site lattices (CSL) distribution did not present any anisotropy and followed the empirical law of the inverse cubic root of Σ-value. For all conditions, the most abundant CSL boundaries were Σ3, Σ9, Σ11, Σ17b, Σ19a, Σ27a and Σ33a. Based on the statistics of the triple junction types and their resistance to intergranular cracking, it was revealed that increasing the annealing temperature might play a role in crack deflection since the resistance to intergranular crack growth is increased in the transversal section and reduced in the longitudinal section. This anisotropic behavior is preserved up to a higher annealing temperature in the K-doped material.

On the significance of misorientation axes of CSL boundaries in triple junctions in cubic materials

Understanding the interactions of Σ3n boundaries and the triple junction character is important in the context of grain boundary engineering in cubic materials. In a triple junction, when two boundaries are Σ3 and Σ9, the third boundary is either a Σ3 or a Σ27 as per the Σ-combination rule. In the present work, the role of the misorientation axis of the interacting Σ boundaries on the character of the third boundary is systematically studied. The calculated probabilities of occurrences of Σ3, Σ9 and Σ27 boundaries are correlated with the experimental triple junction distributions in Ni and Ni based superalloys.

The effect of grain boundary structure on sensitization behavior in a nickel-based superalloy

The present work discusses the evolution of grain boundary structure during thermomechanical processing and its effect on sensitization behavior in a nickel-based superalloy. Alloy 600 was deformed to varied degrees of strain (4–25%) using hot rolling followed by annealing at 1000 °C for 10 min followed by water quenching. Structure of the grain boundary was analyzed with reference to various parameters, such as grain boundary character distribution, twin-related domains, misorientation, and triple junction distribution. Each thermomechanically processed sample was heat-treated at 650 °C for 24 h before studying its sensitization behavior. The effect of structure of the grain boundary on sensitization was assessed through double loop electrochemical potentiokinetic reactivation test and measured in terms of degree of sensitization (DOS). DOS was found to be in a direct relation with the fraction of random high-angle grain boundaries and their connectivity, while it was inversely related to the fraction of low-Σ coincidence site lattice boundaries and special triple junctions. Residual strain and the fraction of low-angle grain boundaries were found to be weakly related to DOS. We show that a simple parameter can be used to predict the combined effect of all these factors on sensitization behavior.

Grain boundary network evolution in Inconel 718 from selective laser melting to heat treatment

Inconel 718 fabricated by selective laser melting (SLM) was used to investigate the evolution of grain boundary (GB) network structures from as-SLM to heat-treated (HT) samples. Using electron backscatter diffraction (EBSD) data and percolation theory based cluster analysis, GB character distribution and GB network topological metrics were computed at different build locations and directions. The microstructures of the as-SLM samples reveal large spatial heterogeneity in grain morphology and are dominated by general GBs (i.e., ∑> 29), which form one connected cluster spanning across the whole GB network. Heat-treatment homogenizes the microstructure and leads to the formation of annealing twins as a result of recrystallization, which dramatically increases the number of special boundaries (mainly twin ∑3 and twin-related ∑9, ∑27 boundaries with ~ 60% in boundary length fraction). However, these special boundaries have not yet fully connected/merged to form a percolated path throughout the GB network. The triple junction distributions of the HT sample are dominated by J1-type that consists of one special and two general boundaries, further confirming the interweaving GB network made of the general and special boundary clusters. In addition, the implication of applying GB engineering to the SLMed parts is discussed based on the comparison of GB network structures between the SLMed alloys and the conventionally GB engineered metals and alloys.

A critical evaluation on efficacy of recrystallization vs. strain induced boundary migration in achieving grain boundary engineered microstructure in a Ni-base superalloy

A critical evaluation of recrystallization vs. strain induced boundary migration (SIBM) as the mechanism responsible behind the grain boundary engineering (GBE) in alloy 617 is made. Towards this hot deformation processing (in the temperature range of 1173–1473 K and strain rates of 0.001–10 s−1) as well as GBE-type iterative processing is performed on solution-annealed specimen. GBE-quantifying parameters such as Σ3n fraction, triple junction distribution, twin-related grain size ratio, twin-related domain (TRD) parameters and fractal dimension have been utilized to quantify the extent of GBE in the processed microstructures. Occurrence of dynamic recrystallization (DRX) during hot deformation processing does not induce notable multiple twinning leading to a microstructure analogous to that of solution-annealed condition even after complete DRX. Following GBE-type iterative processing, GBE microstructure has only been achieved when prolific multiple twinning occurred due to activation of SIBM leading to a high fraction of Σ3n boundaries (∼79%) with most of the twins being part of the grain boundary network. Consequently, an increasing proportion of J2 and J3 triple junctions with a concomitant increase in both the average number of grains per TRD and twin-related grain size ratio are achieved. However, occurrence of static recrystallization during GBE-type processing has led to smaller TRD size and copious random boundaries connectivity as confirmed by fractal analysis thus clearly suggesting that SIBM, not recrystallization catalyzes the profusion of Σ3n boundaries. As GBE relies on the multiple twinning mechanisms promoted via SIBM, recrystallization needs to be circumvented for successful attainment of GBE microstructure.

Grain boundary character modification employing thermo-mechanical processing in type 304L stainless steel

Grain boundary engineering (GBE) approach has been employed to modify the boundaries character of a type 304L stainless steel through thermo-mechanical processing (TMP) route, which combined a low level of cold deformation (5, 10 and 15%) followed by annealing at 1173K and 1273K for 1hour. Employing Electron Back Scatter Diffraction based Orientation Imaging Microscopy, the fraction and distribution of low ∑ CSL boundaries (∑≤ 29) and its effect on random high-angle grain boundaries connectivity and triple junction distribution of as-received (AR) and GBE specimens were evaluated. It was possible to increase the fraction of low ∑ CSL boundaries up to 75% following GBE treatment (as compared to 50% in AR specimen). The GBE specimens also contained maximum number of percolation resistant triple junctions which could render better resistance against percolation related phenomena.

Reliability of twin-dependent triple junction distributions measured from a section plane

Numerous studies indicate polycrystalline triple junctions are independent microstructural features with distinct properties from their constituent grain boundaries. Despite the influence of triple junctions on material properties, it is impractical to characterize triple junctions on a large scale using current three-dimensional methods. This work demonstrates the ability to characterize twin-dependent triple junction distributions from a section plane by adopting a grain boundary plane stereology. The technique is validated through simulated distributions and simulated electron back-scatter diffraction (EBSD) data. Measures of validation and convergence are adopted to demonstrate the quantitative reliability of the technique as well as the convergence behavior of twin-dependent triple junction distributions. This technique expands the characterization power of EBSD and prepares the way for characterizing general triple junction distributions from a section plane.

Measuring twin dependent triple junctions from a single section plane

Given that polycrystalline triple junctions are significant contributors to material properties, they are frequently becoming the focus of emerging research. Despite this interest, the tools to quickly and quantitatively analyze triple junction textures remain severely limited. To enable characterization of triple junctions on a large scale, the parameters, space, and conventions of twin dependent triple junction distributions have been developed. In addition, by adopting grain boundary stereological techniques, triple junction distributions have been generated from a single section plane for triple junctions containing a coherent twin boundary. This methodology has been validated using simulated microstructures and, with further experimental development, will provide insight into actual triple junction structures. This technique also establishes the foundation for a generalized non-twin dependent approach in the future.

The Parameters and Fundamental Zones of Twin-Dependent Triple Junction Distributions

Given the increasing awareness of their influence to material properties, polycrystalline triple junctions are becoming a focal point of substantial research. Despite increasing interest in triple junctions, there is a deficiency in experimental methods for fully characterizing junctions on a large scale. This work provides the necessary foundation for experimentally generating fully characterized twin-dependent triple junction distributions from a section plane. This paper establishes the necessary parameters, space, and conventions of twin-dependent triple junction distributions. A simulated twin-dependent triple junction distribution is developed within a single fundamental zone within the distribution space using discrete equal and non-equal volume cells. A novel method of plotting distribution values and a technique for correcting inherent distribution sampling biases are presented. This work not only establishes necessary foundational work but also prepares the way for a non-twin-dependent approach in the future.

The Application of Grain Boundary Engineering to a Nickel Base Superalloy for 973 K (700 °C) USC Power Plants

The microstructure of a Ni-base superalloy Inconel740H designed for the ultra-supercritical coal-fired power plants has been enhanced via grain boundary engineering. Single-step thermomechanical processing treatments were carried out to optimize the grain boundary character distribution (GBCD) and assessed based on the fraction of low-Σ (Σ ≤ 29) coincidence site lattice (CSL) boundaries, f csl, as well as on the interrupted high-angle grain boundary (HAGB) network. Solution-annealed samples were compressed by 3, 6, 10, and 15 pct at room temperature followed by annealing at 1373 K (1100 °C) for between 5 and 40 minutes. For samples deformed to strains of values of less than 10 pct, deformation-induced grain boundary migration occurs and high values of f csl, with large cluster sizes, are obtained. For samples deformed to strains larger than 10 pct, static recrystallization dominates, resulting in decreased value of f csl. The highest f csl value (≈80 pct) was obtained in the sample annealed at 1373 K (1100 °C) for 20 minutes after 6 pct cold deformation, in which the HAGB network was substantially interrupted. The triple junction distributions of samples before and after GBE were also studied. The introduction of large amounts of CSLBs after thermomechanical-processing treatment increased both fractions of J2 and J3 type junctions (triple junctions containing 2 or 3 CSL boundaries), therefore leading to a significant increase in the resistant triple junction fraction, defined as f J2 /(1 − f J3 ). In addition, the thermal stability of the GBCD-optimized microstructure was confirmed to be stable at 1023 K (750 °C) for 500 hours without significant decrease in f csl.

The uncorrelated triple junction distribution function: Towards grain boundary network design

Triple junctions are recognized as important microstructural features in the context of grain boundary network topology and grain boundary sensitive materials properties. In spite of this prominence, mathematical tools for quantifying distributions of misorientations around triple junctions have been limited to special cases. Here we derive a general formula for the uncorrelated triple junction distribution function (TJDF) for materials of arbitrary texture. Additionally, we provide the mathematical link between TJDF and the orientation distribution function, which should facilitate the use of materials design paradigms on the grain boundary network.

Coarsening kinetics of topologically highly correlated grain boundary networks

We apply phase-field simulations in two dimensions to study the thermal coarsening of grain boundary (GB) networks with high fractions of twin and twin-variant boundaries, which for example are seen in grain-boundary-engineered FCC materials. Two types of grain boundary networks with similar starting special boundary fractions but different topological features were considered as initial conditions for the grain growth simulations. A lattice Monte Carlo method creates polycrystalline microstructures (Reed and Kumar (RK)), which exhibit hierarchical organization of random and special coincidence site lattice boundaries. The other type of microstructures (randomly distributed (RD)) contains random distributions of special boundaries subject only to crystallographic constraints. Under the assumption that random boundaries have larger energy and much higher mobility than special boundaries, simulations show that increasing the initial special boundary fraction in both microstructures slows down grain growth. However, the two starting microstructures exhibit very different behavior in the evolution of GB character and triple junction (TJ) distributions. The RD networks coarsened more slowly than the RK networks with comparable initial fractions of special boundaries. The observed trend in the evolution of the RK microstructures is explained by an extended von Neumann-Mullins analysis. This study demonstrates that the special boundary fraction is not a sufficient indicator of the coarsening behavior of twinned GB networks; the network topology must also be considered to correctly predict the grain growth kinetics.

Control of grain boundary microstructures in molybdenum polycrystals by thermomechanical processing of single crystals

The formation of grain structures and grain boundary microstructures in polycrystalline molybdenum, produced by thermomechanical processing from cylindrical single crystals with different initial surface normal orientations of ⟨110⟩, ⟨111⟩ and ⟨112⟩, were investigated with the objective of controlling grain boundary microstructures. The polycrystalline specimens displayed different microstructures depending on the initial orientation of the single crystal and the deformed microstructure. The recrystallized microstructure was composed of some oriented-grain clusters, in which grains possessing a similar orientation were assembled. The frequency of low-angle boundaries was very high in the oriented-grain clusters. A close relationship also existed between the grain boundary character distribution (GBCD) and the triple junction distribution. Grain boundary microstructures were compared of bcc molybdenum and fcc polycrystalline materials with reference to path-dependent percolation resistance.

Correlated grain-boundary distributions in two-dimensional networks

In polycrystals, there are spatial correlations in grain-boundary species, even in the absence of correlations in the grain orientations, due to the need for crystallographic consistency among misorientations. Although this consistency requirement substantially influences the connectivity of grain-boundary networks, the nature of the resulting correlations are generally only appreciated in an empirical sense. Here a rigorous treatment of this problem is presented for a model two-dimensional polycrystal with uncorrelated grain orientations or, equivalently, a cross section through a three-dimensional polycrystal in which each grain shares a common crystallographic direction normal to the plane of the network. The distribution of misorientations theta, boundary inclinations phi and the joint distribution of misorientations about a triple junction are derived for arbitrary crystal symmetry and orientation distribution functions of the grains. From these, general analytical solutions for the fraction of low-angle boundaries and the triple-junction distributions within the same subset of systems are found. The results agree with existing analysis of a few specific cases in the literature but present a significant generalization.

Determination of Percolation Threshold for Random Boundary Network on the Basis of EBSD/OIM Observations

Grain boundary engineering through the control of grain boundary character distribution (GBCD) has been extensively employed as a powerful tool for achieving enhanced properties and for development of high performance both structural and functional polycrystalline materials. Many efforts were made firstly to increase the frequency of low-energy CSL boundaries of polycrystalline materials in grain boundary engineering. However, the connectivity of grain boundaries can be an important microstructural parameter governing bulk properties of polycrystalline materials as well as the GBCD. In the present work, the connectivity of random grain boundaries was quantitatively evaluated using both the triple junction distribution and random boundary cluster length on the basis of SEM-EBSD/OIM observations, and then these evaluated parameters were linked to intergranular corrosion of SUS304 stainless steel. We have found that the length of the maximum random boundary cluster drastically decrease with increasing CSL boundaries in the fraction ranging 60 – 80% CSL boundaries, which leads to percolation threshold occurring at approximately 70±5% CSL boundary fraction (at 30±5% random boundary fraction). The experimentally observed percolation threshold is much higher than theoretically obtained one based on randomly assembled network (at 35% resistant bonds for a 2D hexagonal lattice). In addition, the fraction of resistant triple junctions is found to increase with increasing the the CSL boundary fraction. An increase in the frequency of resistant triple junctions can enhance intergranular corrosion resistance of polycrystalline austenitic stainless steel even if the GBCD is the same.

Three dimensional observations and modelling of intergranular stress corrosion cracking in austenitic stainless steel

Stress corrosion cracking is a life-limiting factor in many components of nuclear power plant in which failure of structural components presents a substantial hazard to both safety and economic performance. Uncertainties in the kinetics of short crack behaviour can have a strong influence on lifetime prediction, and arise due both to the complexity of the underlying mechanisms and to the difficulties of making experimental observations. This paper reports on an on-going research programme into the dynamics and morphology of intergranular stress corrosion cracking in austenitic stainless steels in simulated light water environments, which makes use of recent advances in high resolution X-ray microtomography. In particular in situ, three dimensional X-ray tomographic images of intergranular stress corrosion crack nucleation and growth in sensitised austenitic stainless steel provide evidence for the development of crack bridging ligaments, caused by the resistance of non-sensitised special grain boundaries. In parallel a simple grain bridging model, introduced to quantify the effect of crack bridging on crack development, has been assessed for thermo-mechanically processed microstructures via statically loaded room temperature simulant solution tests and as well as high temperature/pressure autoclave studies. Thermo-mechanical treatments have been used to modify the grain size, grain boundary character and triple junction distributions, with a consequent effect on crack behaviour. Preliminary three-dimensional finite element models of intergranular crack propagation have been developed, with the aim of investigating the development of crack bridging and its effects on crack propagation and crack coalescence.