Effects of grain boundary- and triple junction-character on intergranular fatigue crack nucleation in polycrystalline aluminum

The effects of grain boundary- and triple junction-character on intergranular fatigue crack nucleation were studied in coarse-grained polycrystalline aluminum specimens whose grain boundary microstructures were analyzed by SEM-EBSD/OIM technique. Fatigue crack nucleation occurred mainly along grain boundaries and depended strongly on both the grain boundary character and grain boundary configuration with respect to the persistent slip bands. However, it was little dependent on the geometrical arrangements between the grain boundary plane and the stress axis. Particularly, random boundaries become preferential sites for fatigue crack nucleation. The fatigue cracks were also observed at CSL boundaries when the grain-boundary trace on the specimen surface was parallel to persistent slip bands. On the other hand, no intergranular fatigue cracks were observed at low-angle boundaries. The fatigue cracks were observed at triple junctions as well as grain boundaries. Their nucleation considerably occurred at triple junctions where random boundaries were interconnected. The grain boundary engineering for improvement in fatigue property was discussed on the basis of the results of the structure-dependent intergranular and triple junction fatigue crack nucleation.     

Grain boundary engineering and the role of the interfacial plane

Abstract

Grain boundary engineering (GBE) involves the use of microstructural design to improve bulk material properties and enhance resistance to intergranular degradation. More specifically, the patented GBE procedure involves the design and control of fcc metallic microstructures using thermomechanical treatments and grain boundary characterisation based on the coincidence site lattice model. The phenomenon of multiple twinning is used to create a ‘twin limited’ microstructure, i.e. a microstructure composed entirely of special grain boundaries and triple junctions that is highly resistant to intergranular degradation. However, the theory behind GBE is not fully developed and therefore further study of the interfacial geometry, including the grain boundary plane and its role in GBE, is required to improve understanding of multiple twinning with the ultimate aim of improving the bulk and intergranular properties of metallic materials. An introduction to GBE is presented, including a number of cases where grain boundary design has improved the properties of fcc alloys for industrial applications. The theoretical characterisation of grain boundaries, including interfacial structure and geometry, is reviewed, highlighting the problems associated with microstructural characterisation based on limited knowledge of the grain boundary geometry. The importance of the grain boundary network is discussed: the grain boundary and triple junction character distributions are known to have a significant influence on bulk properties. Finally, the role of the interfacial plane is considered. It is concluded that although GBE has produced significant results, its theoretical basis and the ultimate creation of twin limited microstructures require further development.     

Universal features of grain boundary networks in FCC materials

Grain boundary character distributions and triple junction distributions have been determined for 70 experimental microstructures, comprising aluminum-, copper-, austenitic iron- and nickel-based alloys in a wide variety of processed states. In these FCC metals, the fraction of coincidence site lattice (CSL) boundaries ranges from about 12% (as for a random Mackenzie distribution) to values as high as 75%. Despite wide variations in composition, processing, and grain size, we find that the grain boundary character distribution and triple junction distributions of these materials have striking similarities, and can be described by just a few parameters. This universality arises due to the highly non-random laws that govern the assembly of the grain boundary network, and due to the kinematic limitation that CSL boundaries arise primarily through twinning.     

Statistics and probabilistic modeling of simulated intergranular cracks

Using Monte Carlo simulation, the statistical properties of intergranular crack trajectories in polycrystalline materials are estimated. The polycrystalline microstructures are two dimensional and are modeled by a Poisson–Voronoi tessellation for the grain geometry and a uniform orientation distribution function for the crystallographic orientation. A heuristic is introduced for determining the path of crack propagation when the crack tip arrives at a grain boundary triple junction. This heuristic applies a combination of two criteria for determining the direction of crack propagation, the maximum circumferential stress criterion, and a criterion in which the crack is assumed to propagate in the direction with the least material resistance. The resistance of grain boundaries is assumed to be related to the crystallographic misorientation at the grain boundary. The trajectories of microcracks can be treated as a random process, and simulation results indicate that the crack process exhibits linear variance growth, the rate of which is related to the importance attached to the circumferential stress and the material resistance in determining the direction of propagation. The rate of variance growth is shown to vary with the average grain diameter, so that microcracks in polycrystals with small grain size will exhibit less spatial uncertainty. The statistics and distributions of the increments of the crack process are also given. Through a small change made to the normalization applied to non-dimensionalize the statistics, the results are extended to polycrystals that have spatially varying grain size. Finally, a probabilistic model is proposed that is able to produce synthetic crack trajectories that replicate the important statistical properties of the simulated cracks. Such a model may prove useful in studies of the transition from micro to macrocracking.     

Grain microstructure evolution and grain boundary junction engineering

Abstract

The grain microstructure evolution in the course of two dimensional (2D) grain growth is considered in greater detail, taking into account the influence of grain boundary triple junctions. It is shown that there are two limiting regimes of grain growth in polycrystals: the first one is associated with the situation when the kinetics of grain growth are controlled by the motion of grain boundaries, while the second one is defined by the motion of grain boundary triple junctions, i.e. when the mobility of triple junctions determines the kinetics of grain growth. A generalised theory of 2D grain growth including a limited triple junction mobility is presented. The theoretical predictions are compared with results of computer simulations by a virtual vertex model. We introduce a new branch of grain boundary engineering, namely, grain boundary junction engineering that utilises junction properties for microstructure control.     

Characterisation of interfaces in nanocrystalline palladium

Structures of grain boundaries and triple line junctions in nanocrystalline materials are of interest owing to large fractions of atoms in nanocrystalline materials being at these interfacial positions. Grain boundary and triple line junction structures in nanocrystalline palladium have been studied using high-resolution transmission electron microscopy (HRTEM). The main micro structural features observed include the varying atomic structures of grain boundaries and the presence of disordered regions at triple line junctions. Also, there is variation in lattice parameters in different nanocrystalline grains. Geometric phase analysis is used to quantify atomic displacements within nanocrystalline grains. Displacement fields thus detected indicate links to the interface structures.     

Multi-length scale modeling of chemical vapor deposition of titanium nitride coatings

Chemical Vapor Deposition (CVD) of TiN coatings has been analyzed at three different length scales: (a) At chemical reactor length scale, by solving the appropriate reactive-gas, fluid-dynamics, heat-transfer boundary value problem; (b) At the atomic scale, by applying a kinetic Monte Carlo method to model the deposition process in a stochastic manner and (c) At the coating-grain scale, by employing an improved van der Drift-type model to simulate the evolution of surface morphology, grain size distribution, evolution of the morphological and crystallographic texture, etc. in polycrystalline TiN coatings. It has shown that by combining the three modeling schemes, one can establish a direct link between the processes parameters and the microstructure (and thus the properties) of as CVD-grown TiN coatings. This, in turn, enables optimization of both the coating deposition process, and the microstructure and properties of CVD-grown coatings.     

Micromechanical modeling of intrinsic and specimen size effects in microforming

Size effect is a crucial phenomenon in the microforming processes of metallic alloys involving only limited amount of grains. At this scale intrinsic size effect arises due to the size of the grains and the specimen/statistical size effect occurs due to the number of grains where the properties of individual grains become decisive on the mechanical behavior of the material. This paper deals with the micromechanical modeling of the size dependent plastic response of polycrystalline metallic materials at micron scale through a strain gradient crystal plasticity framework. The model is implemented into a Finite Element software as a coupled implicit user element subroutine where the plastic slip and displacement fields are taken as global variables. Uniaxial tensile tests are conducted for microstructures having different number of grains with random orientations in plane strain setting. The influence of the grain size and number on both local and macroscopic behavior of the material is investigated. The attention is focussed on the effect of the grain boundary conditions, deformation rate and the grain size on the mechanical behavior of micron sized specimens. The model is intrinsically capable of capturing both experimentally observed phenomena thanks to the incorporated internal length scale and the crystallographic orientation definition of each grain.     

On the design of controlled tricrystal specimens for the systematic investigation of static grain boundary triple junction properties

We consider the optimal design of tricrystal specimens for use in experimental studies of static triple junction properties. Important considerations in this regard are the stability and reproducibility of the tricrystal structure, and we develop a straightforward criterion for the selection of particular grain boundary misorientations and interfacial planes that meet these needs. A small set of particular cases is proposed to provide representative, reproducible and therefore comparable bases for the experimental study of triple junction properties.     

Atomistic to continuum modeling of solidification microstructures

We summarize recent advances in modeling of solidification microstructures using computational methods that bridge atomistic to continuum scales. We first discuss progress in atomistic modeling of equilibrium and non-equilibrium solid–liquid interface properties influencing microstructure formation, as well as interface coalescence phenomena influencing the late stages of solidification. The latter is relevant in the context of hot tearing reviewed in the article by M. Rappaz in this issue. We then discuss progress to model microstructures on a continuum scale using phase-field methods. We focus on selected examples in which modeling of 3D cellular and dendritic microstructures has been directly linked to experimental observations. Finally, we discuss a recently introduced coarse-grained dendritic needle network approach to simulate the formation of well-developed dendritic microstructures. This approach reliably bridges the well-separated scales traditionally simulated by phase-field and grain structure models, hence opening new avenues for quantitative modeling of complex intra- and inter-grain dynamical interactions on a grain scale.     

Comparative study of two phase-field models for grain growth

There exist different phase-field models for the simulation of grain growth in polycrystalline structures. In this paper, the model formulation, application and simulation results are compared for two of these approaches. First, we derive relations between the parameters in both models that represent the same set of grain boundary energies and mobilities. Then, simulation results obtained with both models, using equivalent model parameters, are compared for grain structures in 2D and 3D. The evolution of the individual grains, grain boundaries and triple junction angles is followed in detail. Moreover, the simulation results obtained with both approaches are compared using analytical theories and previous simulation results as benchmarks. We find that both models give essentially the same results, except for differences in the structure near small shrinking grains which are most often locally and temporary for large grain structures.     

Explicit Backscattering Coefficient for Ultrasonic Wave Propagating in Hexagonal Polycrystals with Fiber Texture

Hexagonal polycrystalline materials such as titanium, zirconium and magnesium are common in engineering structures like car bodies and airplane engines. These components are usually specially designed in microstructure level to guarantee desired mechanical properties, so microstructure characterization is of great importance to the optimization of manufacturing processes. Compared with traditional destructive characterization methods like scanning electron microscopy (SEM), the ultrasonic approach is nondestructive and cost-effective. Although some progress has been made in ultrasonic microstructure characterization of polycrystal aggregates of hexagonal grains, some factors like macro texture and grain size distribution associated with realistic microstructures were not accounted for yet. Targeting one common texture component for hexagonal polycrystalline materials, {0001} basal fiber texture, this paper derived the explicit backscattering coefficient for aggregates of ellipsoidal grains through one texture parameter and obtained an analytical backscattering coefficient for microstructures with various grain size distributions. In this study, the basal fiber texture was quantified by the 1D Gaussian orientation distribution function (ODF), which merely includes one texture parameter, and its relationship with generalized spherical harmonics ODF was also addressed. Moreover, explicit expressions for effective elastic moduli and elastic constant covariances were derived. Furthermore, some computational examples were given to demonstrate the impacts of texture, frequency, grain geometry and grain size distribution on backscattering behavior. The theoretical results in this study will greatly benefit the later ultrasonic microstructure characterization of hexagonal polycrystalline materials.     

Phase field modeling of grain growth: effect of boundary thickness,triple junctions,misorientation, and anisotropy

Phase-field models based on multiple order parameters are used extensively to study grain growth in polycrystalline materials. However, if simulations are to be carried out using experimentally obtained microstructures as the initial condition, and the resultant microstructures are to be carefully compared with those obtained from experiments, then the parameters used in the numerical simulations need to be benchmarked with analytical solutions. Furthermore, the models themselves need to be modified to incorporate the dependence of grain boundary energy on misorientation across the boundary as well as the anisotropy in the boundary energy for any given misorientation that stems from the planes of different grains that make up the boundary. In this article, we address both these issues and present some preliminary results from our 2D and 3D simulations.     

Long-range topological correlations of real polycrystalline grains in two dimensions

The topological and geometric properties of real polycrystalline grains in two dimensions are investigated on the basis of a large dataset (14,810 grains). The distribution of grain edges, the grain topology–size relationship and the short- and long-range topological correlations between neighboring grains are characterized quantitatively. The results show a strong short-range topological correlation between a center grain and its first nearest neighbors, and a trivial long-range topological correlation beyond the first nearest neighbors (on average). Both the short- and long-range relations are well described by a generalized Aboav–Weaire law reported recently. Meanwhile, it is the perimeter law, rather than the Lewis law, that describes appropriately the relationship between the topology and geometry of metallurgical grains.     

Hybrid molecular dynamics–finite element simulations of the elastic behavior of polycrystalline graphene

In this paper, we develop an efficient multiscale molecular dynamics (MD)–finite element (FE) modeling scheme capable of determining the elastic and fracture properties of polycrystalline graphene. The local elastic properties of a grain boundary (GB) connecting two adjacent graphene grains, with different lattice orientations, were first determined using MD simulations. In a two-dimensional medium, randomly distributed grains connected with GBs were then created using the Voronoi tessellation method. The constructed Voronoi diagrams were used to create FE models of the polycrystalline graphene, where the GBs were represented by interphase regions with their local properties determined using MD. The grains were modeled as pristine graphene and the accuracy of the polycrystalline FE model was validated with MD simulations of a geometrically identical polycrystalline graphene. The results reveal good agreement between MD and FE simulations. They further show that the elastic and fracture properties of polycrystalline graphene are greatly influenced by the grain size and the misorientation angle. They also indicate that the predicted elastic properties are in agreement with earlier reported experimental and MD results. We believe that this newly proposed multiscale scheme could be easily integrated into current design software to model graphene based nano- and micro-devices.     

A boundary cohesive grain element formulation for modelling intergranular microfracture in polycrystalline brittle materials

In this paper, a cohesive grain boundary integral formulation is proposed, for simulating intergranular microfracture evolution in polycrystalline brittle materials. Artificially generated polycrystalline microstructures are discretized using the proposed anisotropic boundary element method, considering the random location, morphology and material orientation of each grain. Each grain is assumed as a single crystal with general elastic orthotropic mechanical behaviour. Crack initiation and propagation along the grain boundaries interfaces are modelled using a linear cohesive law, considering mixed mode failure conditions. Furthermore, a non‐linear frictional contact analysis is performed over cracked grain interfaces to encounter cases where crack surfaces come into contact, slide or separate. The effect of randomly located pre‐existing flaws on the overall behaviour and microcracking evolution of a polycrystalline material is also investigated for different Weibull moduli. The stochastic effects of each grain morphology‐orientation, internal friction and randomly distributed pre‐existing flaws, under different loading conditions, are studied probabilistically by simulating various randomly generated microstructures. Copyright © 2006 John Wiley & Sons, Ltd.     

Non—uniform Stress Field and Stress Concentration Induced by Grain Boundary and Triple Junction of Tricrystal

The stress characteristics in the anisotropic bicrystal and tricrystal specimens were analyzed using the anisotropic elastic model, orthotropic Hill‘s model and rate-dependent crystallographic model. The finite element analysis results show that non-uniform stresses are induced by the grain boundary. For bicrystal specimens in different crystallographic orientations, there exist stress concentrations and high stress gradients nearby the boundaries. The activation and slipping of the slip systems are dependent on the crystallographic orientations of the grains and also on the relative crystallographic orientations of the two adjoining grains. For the tricrystal specimens, there is not always any stress concentrations in the triple junction, and the concentration degree depends on the relative crystallographic orientations of the three grains. Different from the bicrystal specimens, there may be or no stress concentration in the vicinity of grain boundaries for the tricrystal specimens, which depends on the relative crystallographic orientations of the three grains. The stress concentration near to the grain boundaries and triple junction can be high enough for the local plastic deformation, damage and voiding or cracking even when the whole specimen is still under the elastic state.It can be further concluded that homogeneous assumption for polycrystalline materials is not suitable to study the detailed meso- or micro-mechanisms for damaging and fracturing.     

An energy analysis of triple junction crack nucleation due to the wedging action of grain boundary dislocations

A physical model of wedge crack formation at triple junctions in polycrystalline materials is analyzed in this paper. The origin of the crack formation is the sliding of grain boundaries meeting at triple junctions. Based on the dislocation model of grain boundaries, the sliding is attributed to the gliding of grain boundary dislocations (GBDs). Consequently, the resulting crack formation can be analyzed theoretically in terms of the energetics of the piling up of interacting GBDs. The model permits the determination of crack stability or instability as well as the length of the stable crack. Results are obtained in this paper for polycrystalline ice and aluminium.     

Challenges to marrying atomic and continuum modeling of materials

As the engineering and characterization of bulk materials has progressed down to the nanometer scale, atomic-level modeling has moved from the realm of chemistry and physics to become an important tool for mechanical and materials engineers. However, connecting even the largest atomic simulations currently carried out in three dimensions to full engineering scales is a major challenge. The purpose of this brief article is to comment on these challenges and on the future of approaches that marry atomic and continuum modeling with the goal of increasing the spatial domain accessible to molecular modeling of the mechanical properties of materials.