A meshless grain element for micromechanical analysis with crystal plasticity

This study concerns the development of a 2‐D meshless grain element for elasto‐plastic deformation and intergranular damage initiation and propagation in polycrystalline fcc metals under static loading. The crystallographic material behaviour of the grains is represented by a rate‐independent single‐crystal plasticity model while including material orthotropy. The two slip planes are arbitrarily located with respect to the crystallographic axis of the grain. A non‐linear constitutive model known as the cohesive zone model is employed to represent the inelastic interaction between the grain boundaries, thus permitting grain boundary opening and sliding. The cohesive model describes the deformation characteristics of the grain boundaries through a non‐linear relation between the effective grain boundary tractions and displacements. Because of the presence of non‐linear material behaviour both inside the grain and along the cohesive grain boundaries, the method utilizes the principle of virtual work in conjunction with the meshless formulation in the derivation of the system of non‐linear incremental equilibrium equations. The solution is obtained via an incremental procedure based on the Taylor series expansion about the current equilibrium configuration. The fidelity of the present approach is verified by considering simple polycrystalline metals of only a few grains. Copyright © 2006 John Wiley & Sons, Ltd.     

Micromechanical modeling of cohesive thermoelastic steady-state and transient cracking in polycrystalline materials

In this paper, a micromechanical formulation is proposed for modeling thermoelastic intergranular and transgranular damage and microcracking evolution in brittle polycrystalline materials. The model is based on a multiregion boundary element approach combined with the dual boundary element formulation. Polycrystalline microstructures are created through a Voronoi tessellation algorithm. Each crystal has an elastic isotropic behavior, and multiphase aggregates have been considered. Damage evolution along (intergranular or transgranular) interfaces is modeled using thermomechanical cohesive laws, and upon failure, nonlinear frictional contact analysis is introduced to model separation, stick or slip. Steady-state and transient thermoelastic formulations have been modeled, and numerical simulations are presented, not only to demonstrate the validity but also to study the physical implications of the proposed formulation, in comparison with other numerical methods as well as experimental observations and literature results.     

Application of a new automatic lattice orientation measurement technique to polycrystalline aluminum

The power of a fully automatic system for measuring lattice orientation in the scanning electron microscope is demonstrated. The system couples automatic analysis of electron backscattering diffraction patterns with precise movement of a computer-controlled stage. Over 100 000 lattice orientations were measured on 40% channel-die compressed aluminum. The texture calculated from these measurements closely matched the expected rolling texture. The value of this technique for exploring the relationships between lattice orientation and morphology in polycrystalline microstructures is demonstrated by reconstructing grain boundary maps from the measurements and using color to visualize particular orientations. It is also shown that the average grain shape for a particular orientation can be recovered from the measurements using statistical measures of spatial orientation correlation.     

The Influence of the Boundary Conditions on Low‐Velocity Impact Composite Damage

Abstract: The objective of this work was to study the influence of the boundary conditions on low‐velocity impact behaviour of carbon‐epoxy composite plates. Experimental work and numerical analysis were performed on [0₄,90₄]_s laminates. The influence of different boundary conditions on the impacted plates was analysed considering rectangular and square plates. The X‐radiography was used as a non‐destructive technique to evaluate the internal damage caused by impact loading. A three‐dimensional numerical analysis was also performed considering progressive damage modelling. The model includes three‐dimensional solid elements and interface finite elements including a cohesive mixed‐mode damage model, which allows simulating delamination between different oriented layers. It was verified that plate’s boundary conditions have influence on the delaminated area. Good agreement between experimental and numerical analysis for shape, orientation and size of the delamination was obtained.     

A grain-scale study of spall in brittle materials

The evolution of spall for a brittle material is investigated under variance of anisotropy, grain boundary fracture energy, and loading. Because spall occurs in the interior of the specimen, fundamental studies of crack nucleation and growth are needed to better understand surface velocity measurements. Within a cohesive approach to fracture, we illustrate that for anisotropic materials, increases in the fracture energy cause a transition in crack nucleation from triple-points to entire grain boundary facets. Analysis of idealized flaws reveals that while crack initiation and acceleration are strong functions of the fracture energy, flaws soon reach speeds on the order of the Rayleigh wave speed. Finally, simulated surface velocities of spalled configurations are correlated with microstructural evolution. These fundamental studies of nucleation, growth, and spall attempt to link atomic separation to the macroscopic spall strength and provide a computational framework to examine the evolution of spall and the impact on the simulated surface velocity field.     

Solids Under Extreme Shear: Friction‐Mediated Subsurface Structural Transformations

Tribological contacts consume a significant amount of the world's primary energy due to friction and wear in different products from nanoelectromechanical systems to bearings, gears, and engines. The energy is largely dissipated in the material underneath the two surfaces sliding against each other. This subsurface material is thereby exposed to extreme amounts of shear deformation and often forms layered subsurface microstructures with reduced grain size. Herein, the elementary mechanisms for the formation of subsurface microstructures are elucidated by systematic model experiments and discrete dislocation dynamics simulations in dry frictional contacts. The simulations show how pre‐existing dislocations transform into prismatic dislocation structures under tribological loading. The stress field under a moving spherical contact and the crystallographic orientation are crucial for the formation of these prismatic structures. Experimentally, a localized dislocation structure at a depth of ≈100–150 nm is found already after the first loading pass. This dislocation structure is shown to be connected to the inhomogeneous stress field under the moving contact. The subsequent microstructural transformations and the mechanical properties of the surface layer are determined by this structure. These results hold promise at guiding material selection and alloy development for tribological loading, yielding materials tailored for specific tribological scenarios.     

Multiphase-field modelling of concurrent grain growth and coarsening in complex multicomponent systems

Phase-field modelling of microstructural evolution in polycrystalline systems with phase-associated grains has largely been confined to continuum-field models. In this study, a multiphase-field approach,with a provision for introducing grain boundary and interphase diffusion, is extended to analyse concurrent grain growth and coarsening in multicomponent polycrystalline microstructures with chemically-distinct grains. The effect of the number of phases and components on the kinetics of evolution is investigated by considering binary and ternary systems of duplex and triplex microstructures, along with a single phase system. It is realised that the mere increase in the number of phases minimises the rate of concurrent grain growth and coarsening. However, the effect of components is substantially dependent on the respective kinetic coefficients. This work unravels that the disparity in the influence of phases and components is primarily due to the corresponding change introduced in the transformation mechanism.While the raise in number of phases convolutes the diffusion paths, the increase in number of component effects the rate of evolution through the interdiffusion, which introduces interdependency in the diffusing chemical-species. Additionally, the role of phase-fractions on the transformation rate of triplex microstructure is studied, and correspondingly, the interplay of interface-and diffusion-governed evolution is elucidated. A representative evolution of three-dimensional triplex microstructure with equal phase-fraction is comparatively analysed with the evolution of corresponding two-dimensional setup.     

The role of grain boundary sliding and reinforcement morphology on the creep deformation behaviour of discontinuously reinforced composites

In this study, the role of grain boundary sliding behaviour on the creep deformation characteristics of discontinuously reinforced composites is investigated numerically together with the other influencing parameters: reinforcement aspect ratio, grain size and interfacial behaviour between the reinforcement and the matrix. The results obtained for the composites are compared with results obtained for a polycrystalline matrix material having identical grain size and morphology. The results indicate that, with sliding grain boundaries, the stress enhancement factor for the composites is much higher than the one observed for the matrix material and its value increases with increasing reinforcement aspect ratio, reduction in the matrix grain size and sliding interfacial behaviour between the reinforcement and the matrix. In the composites, the contribution of the grain boundary sliding to overall steady state creep rates occurs in a larger stress range in comparison to the matrix material. Experimentally observed higher creep exponent values or stress dependent creep exponent values for the composites could not be explained solely by the mechanism of grain boundary sliding. However, experimentally observed large scale triple point grain boundary cavitation in the composites could occur due to large grain rotations resulting from grain boundary sliding.     

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.     

退火过程中晶粒生长的二维计算机模拟

由于多晶体材料中晶粒取向不同,对晶粒的生长产生影响．本文以蒙特卡罗（ＭｏｎｔｅＣａｒｌｏ）方法为基础,通过对Ｐｏｔｔｓ算法的改进,建立快速的Ｐｏｔｔｓ算法,实现了对多晶材料在退火中晶粒生长过程的结构演化的计算机模拟和统计分析．与以前的模拟过程相比,计算量减少,逼真度较高．生长指数的模拟值约为１／３,与正常晶粒拓朴演化和理论分析的生长动力学相符合．     

多晶材料晶粒生长的Monte Carlo计算机模拟方法 Ⅰ 模拟正常晶粒生长

多晶固体材料的显微结构的演化与诸多因素密切相关,是一复杂的过程。运用适当的计算机方法进行模拟,完成对晶粒生长的完全预测,具有重要意义,且可为材料研究提供新的重要的依据。近年来,一些材料科学研究者运用蒙特卡罗（ＭｏｎｔｅＣａｒｌｏ）方法模拟二维晶粒生长,已取得了较大进展。本文对他们在模拟正常晶粒生长方面采用的基本方法进行综述。关于模拟异常晶粒生长的情况将在下一篇文章中介绍。     

Revealing Nanoscale Chemical Heterogeneities in Polycrystalline Mo‐BiVO4 Thin Films

The activity of polycrystalline thin film photoelectrodes is impacted by local variations of the material properties due to the exposure of different crystal facets and the presence of grain/domain boundaries. Here a multi‐modal approach is applied to correlate nanoscale heterogeneities in chemical composition and electronic structure with nanoscale morphology in polycrystalline Mo‐BiVO₄. By using scanning transmission X‐ray microscopy, the characteristic structure of polycrystalline film is used to disentangle the different X‐ray absorption spectra corresponding to grain centers and grain boundaries. Comparing both spectra reveals phase segregation of V₂O₅ at grain boundaries of Mo‐BiVO₄ thin films, which is further supported by X‐ray photoelectron spectroscopy and many‐body density functional theory calculations. Theoretical calculations also enable to predict the X‐ray absorption spectral fingerprint of polarons in Mo‐BiVO₄. After photo‐electrochemical operation, the degraded Mo‐BiVO₄ films show similar grain center and grain boundary spectra indicating V₂O₅ dissolution in the course of the reaction. Overall, these findings provide valuable insights into the degradation mechanism and the impact of material heterogeneities on the material performance and stability of polycrystalline photoelectrodes.     

Mechanistic model for grain size and temperature dependence of flow stress in 316L austenitic stainless steel

Abstract

During plastic deformation of a polycrystalline material, both the grain interior and the grain boundary regions exhibit distinctly different dislocation behaviours at a given strain and temperature. Studying the variation of experimental flow stress with temperature, it seems that the flow stress of a fine grained polycrystalline material is mainly controlled by dislocation dynamics at and in the vicinity of grain boundaries. At low temperatures in a polycrystalline material, the dislocations are piled up at grain boundaries and the density of dislocations increases significantly in the grain boundary region, while at high temperatures the annihilation of dislocations take place at and in the vicinity of the grain boundaries during deformation. Therefore, the flow stress behaviour of a polycrystalline material can be understood in terms of the process of accumulation and annihilation of dislocations at and in the vicinity of grain boundaries at a given strain and temperature.     

Transparent Polycrystalline Alumina Ceramic with Sub‐Micrometre Microstructure by Means of Electrophoretic Deposition

The optical quality attainable in coarse‐grained polycrystalline alumina is severely limited by grain‐boundary scattering, which is inherent to non‐cubic materials. The optical properties of sub‐micrometre polycrystalline alumina are of growing interest triggered by the fact that a decrease in the grain sizes of the final sintered material yields an improvement in the optical quality while the scattering mechanism changes as the grain size becomes comparable with the wavelength of light. To achieve transparent alumina ceramics with a fine‐grained microstructure, however, porosity and other defects must be avoided. This necessitates the optimization of processing and sintering procedures. Electrophoretic deposition (EPD) is a colloidal process in which ceramic bodies are directly shaped from a stable suspension by application of an electric field. Electrophoretic deposition enables the formation of homogeneous, uniform green microstructures with high density, which can be sintered to transparency. It is a simple and precise technique to synthesize not only monoliths, but also composites with complex geometries [1]. Alumina green bodies were deposited from stabilized aqueous suspensions with and without doping. Green alumina compacts were evaluated based on their pore size distribution and density. Densification behaviour was characterized by dilatometric studies conducted at constant heating rate. Samples were sintered at different temperatures with subsequent post‐densification by hot isostatic pressing. Transparency was evaluated by means of spectroscopic measurements. The measured in‐line transmission of the samples at 645 nm was more than 50 % and that is 58 % of the value of sapphire. The influence of dopings on transparency was investigated. The mechanical properties of the samples were tested.     

Investigating the effects of grain boundary energy anisotropy and second-phase particles on grain growth using a phase-field model

A phase-field model was used to investigate the simultaneous effects of grain boundary energy anisotropy and the presence of second-phase particles on grain growth in polycrystalline materials. The system of grains with anisotropic grain boundary energies was constructed by considering models of low and high misorientation angles between adjacent grains. Systems without particles reached a steady state grain growth rate, and this rate decreased by including the grain boundary energy anisotropy. In addition, the presence of particles significantly altered the microstructures during grain growth. This study showed that for systems including particles, the critical average grain size to stop grain growth depends not only on the volume fraction and size of particles, but also on the grain boundary energy anisotropy.     

An approach for simulating microstructures of polycrystalline materials

In this paper, an approach is identified using concepts in molecular dynamics (MD) and discrete element method (DEM) to generate the microstructure of polycrystalline materials. Using the proposed methods, different types of particles with different grain size and volume fraction in the real material, can be easily generated. It is assumed that the particles can be randomly packed together into a simulation region, by defining artificial interaction forces among them. Such forces may be either adopted from Van der Waals potential energy, or Hooke pair and gravity forces. The proposed method has proved to be fast due to the fact that the algorithm has been implemented on graphical processing units (GPU). Utilizing the Voronoi tessellation method, the set of the generated discrete grains have been altered to space-filling, adjoining polyhedrons with respect to the real geometry. Moreover, as an advantage, the boundary and the interface region of the microstructures were modeled.     

Comparison of experimental results and finite element simulation of strain localization scheme under cyclic loading

The plastic behaviour of FCC materials is studied under cyclic tensile–compression loading at room temperature. The material is an oxygen-free high conductivity copper. The purpose of the work is to model the onset of plasticity, then the cycle by cycle evolution of the localized strain, at grain scale and at mesoscopic scale.A polycrystalline aggregate taking into account the material microstructure is developped to perform finite element simulations corresponding to the experiments. Finite element calculations are carried out on this mesh, using a constitutive law which takes into account the crystallographic orientation of each grain. An analysis of the localisation scheme is performed at different steps of the cyclic loading.     

Cohesive zone representation and junction partitioning for crystal plasticity analyses

A novel scheme is presented for incorporating finite thickness cohesive interfaces in virtual grain structures for crystal plasticity finite element (CPFE) analyses of intergranular crack initiation and propagation. A Voronoi tessellation model is used to define the virtual grain structure, with automatically generated nonzero thickness cohesive zones (CZs) representing the grain boundaries and multiple junctions. An efficient grain boundary offsetting algorithm is presented, and issues related to automatically partitioning multiple junctions are discussed. Two feasible junction partitioning schemes are presented, the second of which has the advantage of partitioning junctions using uniform quadrilateral elements and naturally defining their normal and tangential directions. For the second scheme, a rule‐based method is presented that carries out the preliminary meshing of CZ junctions, including data representation, edge event processing, and cut and trim operations. A virtual grain structure modelling system, VGRAIN, is introduced to implement the proposed CZ junction partitioning method and directly generate meshed virtual grain structures with CZ grain boundaries for CPFE studies. To demonstrate the proposed junction partitioning and CZ representation schemes, two finite strain CPFE simulations are presented for plane strain uniaxial tension and three‐point bending, demonstrating large‐scale crack initiation and propagation under shear and opening modes. Copyright © 2012 John Wiley & Sons, Ltd.     

M_5B_3 Boride at the Grain Boundary of a Nickel-based Superalloy

The grain boundary microstructures of a heat-treated Ni-based cast superalloy IN792 were investigated. The results show that M_5B_3 boride precipitates at the grain boundary. A special orientation relationship between M_5B_3 phase and the matrix at one side of the grain boundary is found. At the same time, two M_5B_3 borides with different orientations could co-exist in a single M_5B_3 particle as an intergrowth besides existing alone, thus forming orientation relationship between the two M_5B_3 phases and matrix. This phenomenon could be attributed to the special orientation relationship between M_5B_3 phase and the matrix.