Phase field simulations of elastic deformation-driven grain growth in 2D copper polycrystals

In this work, a phase field grain growth model coupled with a spectral stress calculation method is used to investigate the effect of applied elastic deformation on grain growth in 2D copper polycrystals with isotropic grain boundary properties. The applied deformation accelerates the grain growth compared to a relaxed polycrystal, though the effect of the deformation decreases rapidly with time. The softest grain orientations with respect to the applied deformation grow at the expense of other orientations, though they have higher elastic energy density. Due to a rapid decrease in the elastic energy stored in the system, the GB energy eventually dominates the growth leading to a linear change in the average grain area with time. Increasing the magnitude of the applied deformation accelerates the growth, while increasing the temperature accelerates the growth but decreases the effect of the applied deformation.     

Precise 3D crack growth simulations

The continuous growth of 3D cracks under cyclic loading conditions is considered within a discrete simulation procedure. It is performed within the framework of linear elastic fracture mechanics. An incremental procedure is applied to consider the non-linear behavior of crack growth within the simulation. In each increment the direction and magnitude of the crack propagation for each point along the crack front are needed to define the new crack front. Within the present context the crack deflection results from the maximum tangential stress criterion and the crack extension is obtained by the evaluation of a crack propagation rate. To simulate the crack propagation as exactly as possible the evolution of the stress field between two consecutive crack fronts is taken into account. The analysis of the changing stress field is utilized for optimization of the predicted crack fronts. The whole procedure is realized in terms of a predictor–corrector scheme. Numerical examples are presented to demonstrate the benefits of this concept.     

Effect of 3D grain structure representation in polycrystal simulations

Simulation results from finite element models using two types of 3D polycrystal geometric representations, one with a voxel representation and stair-stepped grain boundaries and the other with smooth grain boundaries, are compared. Both models start with a periodic grain structure representation, which is in the form of a regular, rectangular 3D array of points, where each point is assigned an orientation. The voxel representation is obtained by simply sampling the array of grid points on a coarser regular grid with a prescribed resolution and forming a voxel centered at each grid point, which is assigned the grain orientation from the sampled grid point. The voxel representation may be meshed directly by decomposing each voxel into finite elements. In the second case, a method is presented that extracts geometric topology information for a grain structure with smooth, flat grain boundaries from the discrete grain structure representation. From the geometric topology information, a finite element mesh is created. The two representations are then subjected to large strain deformations, and the simulation results and efficiencies are compared. The macroscopic behavior, overall texture evolution, and statistical distribution of stress and slip are found to be nearly identical for both models. However, noticeable differences are observed in the misorientation distribution within grains and the smoothness of the stress field. The voxel representation is found to be more efficient because of the uniform finite element mesh.     

3D full field study of drying shrinkage of foam concrete

Drying shrinkage (DS) of concrete is important. The graded and heterogeneous DS inside the concrete may lead to cracking and further deteriorate the mechanical and durability properties. To elaborate the drying gradient and deformation heterogeneity, the full field DS distributions of foam concrete have been studied using an expanded Digital Volume Correlation method, which has a high precision of 0.01 voxel (about 0.6 μm) in displacement. The effectiveness of DS in local sub-volume is verified from bulk shrinkage of the whole specimen. The DS gradient due to drying is clearly revealed, and DS heterogeneity in spatial domain and in frequency domain is identified. A full view of foam concrete's drying processes is built. At the middle drying stage, three different states exist simultaneously, especially a drying front arises with high drying shrinkage.     

3D physical modeling of anisotropic grain growth at high temperature in local strong magnetic force field

A new mechanism based on the effect of local magnetic forces on diffusing ions around a growing ferromagnetic precipitate is proposed. A 3D simulation based only on physical parameters is undertaken in which main assumption is of interface limited growth controlled by the effect of both curvature and local magnetic field distortion. Although usually neglected in magnetic field effect mechanisms, it is shown that these local magnetic forces acting on a single paramagnetic ion can change markedly affect the growth process and induce strong shape anisotropy.     

3D physical modeling of anisotropic grain growth at high temperature in local strong magnetic force field

Abstract

A new mechanism based on the effect of local magnetic forces on diffusing ions around a growing ferromagnetic precipitate is proposed. A 3D simulation based only on physical parameters is undertaken in which main assumption is of interface limited growth controlled by the effect of both curvature and local magnetic field distortion. Although usually neglected in magnetic field effect mechanisms, it is shown that these local magnetic forces acting on a single paramagnetic ion can change markedly affect the growth process and induce strong shape anisotropy.     

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.     

An optimized predictor–corrector scheme for fast 3D crack growth simulations

An optimized predictor–corrector scheme for the accelerated simulation of 3D fatigue crack growth is presented. Based on experimental evidence, it is assumed that the crack front shape ensures a constant energy release rate. Starting from a crack front satisfying this requirement a predictor step is performed. Usually, the new crack front does not fulfill the requirement of a constant energy release rate. Therefore, several corrector steps are needed. Within the new predictor–corrector scheme the history of crack growth is taken into account to reduce the number of corrector steps. The efficiency of the new scheme is shown on two numerical examples providing a speed up of a factor above three.     

Development of a new software for adaptive crack growth simulations in 3D structures

A new software system called ADAPCRACK3D has been developed by the authors to predict fatigue crack growth in arbitrary 3D geometries under complex loading by the use of the finite element method. The main focus of ADAPCRACK3D is on the determination of 3D crack paths and surfaces as well as on the evaluation of components' lifetimes as a part of the damage tolerant assessment. Throughout the simulation of crack propagation an automatic adaptive mesh adaption is carried out in the vicinity of the crack front nodes. The fracture mechanical evaluation is based on a new criterion recently developed by the authors.     

Hybrid parallel multigrid preconditioner based on automatic mesh coarsening for 3D metal forming simulations

A parallel multigrid (MG) method is developed to reduce the large computational costs involved by the finite element simulation of highly viscous fluid flows, especially those resulting from metal forming applications, which are characterized by using a mixed velocity/pressure implicit formulation, unstructured meshes of tetrahedra, and frequent remeshings. The developed MG method follows a hybrid approach where the different levels of nonnested meshes are geometrically constructed by mesh coarsening, while the linear systems of the intermediate levels result from the Galerkin algebraic approach. A linear O(N) convergence rate is expected (with N being the number of unknowns), while keeping software parallel efficiency. These objectives lead to selecting unusual MG smoothers (iterative solvers) for the upper grid levels and to developing parallel mesh coarsening algorithms along with parallel transfer operators between the different levels of partitioned meshes. Within the utilized PETSc library, the developed MG method is employed as a preconditioner for the usual conjugate residual algorithm because of the symmetric undefinite matrix of the system to solve. It shows a convergence rate close to optimal, an excellent parallel efficiency, and the ability to handle the complex forming problems encountered in 3‐dimensional hot forging, which involve large material deformations and frequent remeshings.     

Nonintrusive coupling of 3D and 2D laminated composite models based on finite element 3D recovery

In order to simulate the mechanical behavior of large structures assembled from thin composite panels, we propose a coupling technique, which substitutes local 3D models for the global plate model in the critical zones where plate modeling is inadequate. The transition from 3D to 2D is based on stress and displacement distributions associated with Saint‐Venant problems, which are precalculated automatically for a simple 3D cell. The hybrid plate/3D model is obtained after convergence of a series of iterations between a global plate model of the structure and localized 3D models of the critical zones. This technique is nonintrusive because the global calculations can be carried out using commercial software. Evaluation tests show that convergence is fast and that the resulting hybrid model is very close to a full 3D model. Copyright © 2014 John Wiley & Sons, Ltd.     

Unification scheme for 3D surface reconstruction using physically based models

We propose a unification framework for three-dimensional shape reconstruction using physically based models. A variety of 3D shape reconstruction techniques have been developed in the past two decades, such as shape from stereopsis, from shading, from texture gradient, and from structured lighting. However, the lack of a general theory that unifies these shape reconstruction techniques into one framework hinders the effort of a synergistical image interpretation scheme using multiple sensors/information sources. Most shape-from-X techniques use an “observable” (e.g., the stereo disparity, intensity, or texture gradient) and a model, which is based on specific domain knowledge (e.g., the triangulation principle, reflectance function, or texture distortion equation) to predict the observable, in 3D shape reconstruction. We show that all these “observable–prediction-model” types of techniques can be incorporated into our framework of energy constraint on a flexible, deformable image frame. In our algorithm, if the observable does not confirm to the predictions obtained using the corresponding model, a large “error” potential results. The error potential gradient forces the flexible image frame to deform in space. The deformation brings the flexible image frame to “wrap” onto the surface of the imaged 3D object. Surface reconstruction is thus achieved through a “package wrapping” or a “shape deformation” process by minimizing the discrepancy in the observable and the model prediction. The dynamics of such a wrapping process are governed by the least action principle which is physically correct. A physically based model is essential in this general shape reconstruction framework because of its capability to recover the desired 3D shape, to provide an animation sequence of the reconstruction, and to include the regularization principle into the theory of surface reconstruction.     

Sintering and grain growth of 3 mol% yttria zirconia in a microwave field

A comparative study of the sintering and grain growth of 3 mol% yttria zirconia using conventional and microwave heating was performed. Extensive measurements of grain size were performed at various stages of densification, and following isothermal ageing at 1500 °C for 1, 5, 10 and 15 h. Microwave heating was found to enhance densification processes during constant rate heating. The grain size/density relationship for the microwave-sintered samples was shifted in the direction of increased density for density values less than 96% of the theoretical value when compared to conventionally heated samples. This suggests that there may be a difference in the predominant diffusion mechanisms operating during the initial and intermediate stages of sintering. Results of the ageing experiments showed that once densification was near completion, grain growth was accelerated in the microwave field, and exaggerated grain growth occurred.     

Vectorized 3D microstructure for finite element simulations

Microstructure based forming models using statistically representative microstructural input provide the most accurate predictions for early localization and failure during complex forming operations. However, the sheer size and complexity of the three dimensional (3D) microstructural data from real materials makes it hard to implement that data in current finite element models. In this report, a technique to create a vectorized 3D microstructure suitable for input into finite element codes is developed and applied to represent the distribution of particles of different phases found in continuous cast (CC) AA5754 sheets, which tend to have heterogeneous particle distributions with particles of several phases in different shapes and sizes (from 0.2 μm to 10 μm) and distributed at random, in stringers and along the “centerline”. The technique consists of a 3D reconstruction of the true microstructure by performing serial sections and conversion of the 3D raster image to the vector image. A 3D mesh is generated automatically using Unigraphics and Hypermesh from real particle field measurements, which can be imported to any FE code. The vectorized microstructure is validated by comparison with the reconstructed images of particle distribution data.     

Modeling transgranular crack growth in random 3D grain structures under cyclic loading

A probabilistic method to predict the crack formation in polycrystalline materials with a random microstructure under cyclic loading is developed. In particular, transgranular crack growth in 3D grain structures generated randomly by the Voronoï process is considered. The potential crack extension planes in the individual grains are dependent on the different grain orientations and the crystal structure of the considered material. Under cyclic loading fatigue cracks initiate and propagate along the slip planes of the crystal structure. For this reason, an energy-based criterion is used in order to describe the successive material damage under cyclic loading which is completely projected into the crack extension planes and finally causes the crack propagation. Subsequently, the computation of the crack path in a number of randomly generated grain structure models provides a raw data base in order to determine probability distributions of the number of cycles up to a pre-defined crack depth. As an input for many fracture mechanics evaluation concepts which are based on an assumed incipient crack depth, the number of cycles and the corresponding scatter band width up to a postulated incipient crack depth is of great interest.     

基于时延优化的三维成像声呐视野展宽方法研究

针对平面阵,研究并探讨了一种近场聚焦波束形成中时延参数的优化方法,以扩大三维成像声呐的有效视野范围。该方法是在方位角和俯仰角重新定义时,将精确的近场时延表达式按泰勒公式展开,取前三项,并对每一项进行加权。然后,通过求三个加权系数的偏导,再令其等于0,得出最优加权系数,此时优化的时延表达式与精确的近场时延表达式的误差最小,即优化的时延表达式更接近于精确的时延表达式,能够有效地用于扩大成像声呐的有效视野。最后,通过计算机仿真验证了该方法的有效性。     

Applications of high‐resolution schemes based on normalized variable formulation for 3D indoor airflow simulations

Computational fluid dynamics (CFD) has been used in a routine manner for the design of indoor environments. The quality of these CFD studies varies from poor to excellent, and only in year 2003 Sørensen and Nielsen recommend a detailed guideline on imposing quality control in the CFD‐related works for indoor airflow simulations. One of these recommendations is to use monotone high‐resolution (HR) schemes that apply flux limiters to ensure solution boundedness while preserving the high‐order accuracy of the differencing schemes. In this paper, based on the γ‐formulations derived from the normalized variable formulation, four recently developed HR schemes, GAMMA, CUBISTA, AVLSMART and HOAB, are applied to several indoor airflow problems such as (1) Smith–Hutton problem (dead‐end channel); (2) forced convection problem (horizontal/oblique inflow) in a parallelepiped room; (3) mixing ventilation problem focusing on the prediction of local mean age of air; (4) flow in a two‐room chamber with internal partition and (5) displacement ventilation in a mockup office. Based on the flow results, the aspects of accuracy and robustness of these HR schemes are addressed for appropriate selection of an ‘ideal’ differencing scheme to improve the quality of 3D indoor CFD calculations. Copyright © 2007 John Wiley & Sons, Ltd.     

A medial axis based method for irregular grain shape representation in DEM simulations

This paper describes a novel method for representing arbitrary grain shapes in discrete element method (DEM) simulations. The method takes advantage of the efficient sphere contact treatment in DEM and approximates the overall grain shape by combining a number of overlapping spheres. The method is based on the medial axis transformation, which defines the set of spheres needed for total grain reconstruction. This number of spheres is then further diminished by selecting only a subset of reconstructing spheres and opting for a grain approximation rather than a full grain reconstruction. The effects of the grain approximating parameters on the key geometrical features of the grains and the overall mechanical response of the granular medium are monitored by an extensive sensitivity analysis. The results of DEM quasi-static oedometric compression on a granular sample of approximated grains exhibit a high level of accuracy even for a small number of spheres.