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

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Parallel 3-d simulations for porous media models in soil mechanics

 Numerical simulations in 3-d for porous media models in soil mechanics are a difficult task for the engineering modelling as well as for the numerical realization. Here, we present a general numerical scheme for the simulation of two-phase models in combination with an abstract material model via the stress response with a specialized parallel saddle point solver. Therefore, we give a brief introduction into the theoretical background of the Theory of Porous Media and constitute a two-phase model consisting of a porous solid skeleton saturated by a viscous pore-fluid. The material behaviour of the skeleton is assumed to be elasto-viscoplastic. The governing equations are transfered to a weak formulation suitable for the application of the finite element method. Introducing an abstract formulation in terms of the stress response, we define a clear interface between the assembling process and the parallel solver modules. We demonstrate the efficiency of this approach by challenging numerical experiments realized on the Linux Cluster in Chemnitz. Received 15 February 2002 / Accepted 12 April 2002     

Boolean-based operation on overlapping CL paths for 3D models

A 3D model can be machined in sections by dividing with cutting slices vertical to the z-axis. This paper introduces a Boolean-based algorithm for planar profiles, which is a frequent implementation for overlapping elimination in CL paths generation. In the proposed algorithm, the profiles can be convex or concave, with or without islands. It is available for general planar profiles on contouring and pocketing machining. This algorithm searches for all intervals split by intersections of complicate planar profiles directly and transforms 2D transversal intersection problems into 1D interval identifications. It uses a simple but efficient odd-even determination based on interval-linked sets by tracking the intersections along the governing profile. Depending on the operation of Boolean union, intersection, and difference between two profiles, the solutions can be obtained under the same manipulation procedures. This proposed algorithm can be easily adapted to Boolean operations between regions composed of general closed profiles and be implemented on computerised CAD/CAM systems. Examples with various multiple profiles are demonstrated.     

Flow field analysis of a 3D wing with flap based on N-S solution

Summary A N-S solution of a 3D wing with flap deflection is presented. The complex flow around this kind of configuration is effectively solved by using a combination of patched grid and domain decomposition techniques. An internal coupling condition satisfying the conservation of flux is used in the domain decomposition method. The spatial flux terms are discretized by using central difference scheme and the time integration is performed by using explicit scheme in the flow solver. Based on this N-S solution the separated flow field is analyzed. The main flap flow features, such as the side-edge region flow pattern and 3D-leading edge separated flow pattern, are shown and discussed in detail.     

3D modelling of ferrite and austenite grain coarsening using real-valued cellular automata based on transition function

A new extended technique for 3D modelling of normal grain growth in low carbon steels is presented in this paper. This technique is based on real-valued cellular automata with the use of a local transition function that allows it to be applied to materials with both fcc and bcc lattices with the grain growth being easily simulated in ferrite as well as in austenite cases. The simulated data were calibrated with four sets of experimental data for isothermal grain coarsening in austenite, alpha- and delta-ferrites. The obtained results cogently demonstrate that there is a good agreement between simulated and experimental data across a wide range of temperatures. The new model developed in this paper, allows for the identification of two different mechanisms of grain growth in austenite. It is also shown in this paper that the newly presented approach can be used to extract additional parameters from the grain growth process, such as grain boundary velocity, mobility and driving force, which are hardly accessible even via real-time experiments.     

Module partition for 3D CAD assembly models: a hierarchical clustering method based on component dependencies

Reusing previous CAD assembly models directly in new product development is almost impossible in One-of-a-Kind Production (OKP) in which customer requirements vary from one to another. As such, modularisation of CAD assembly models is required to facilitate modular design for OKP. However, to the authors’ best knowledge, there has been no research carried out on modularisation of CAD assembly models so far. To bridge this gap and make the best use of existing CAD models, this paper proposes a novel module partition approach, to group existing CAD assembly models into modules based on component dependencies. In this approach, an extraction algorithm was developed to extract assembly information from a given assembly model directly, by using automated programmable interfaces of CAD software tools. The extracted information is processed to generate the component design structure matrix (DSM) representing hierarchical relations and dependency strengths between components. Four popular hierarchical clustering methods were used to work with the component DSM to produce results of module partition. A case study was carried out to illustrate the proposed methods and demonstrate their feasibility. It enables OKP companies to respond rapidly to changing customer requirements and develop customised products in a short period.     

Noise reduction using mean shift algorithm for estimating 3D shape

Abstract

The technique to estimate the three-dimensional (3D) geometry of an object from a sequence of images obtained at different focus settings is called shape from focus (SFF). In SFF, the measure of focus — sharpness — is the crucial part for final 3D shape estimation. However, it is difficult to compute accurate and precise focus value because of the noise presence during the image acquisition by imaging system. Various noise filters can be employed to tackle this problem, but they also remove the sharpness information in addition to the noise. In this paper, we propose a method based on mean shift algorithm to remove noise introduced by the imaging process while minimising loss of edges. We test the algorithm in the presence of Gaussian noise and impulse noise. Experimental results show that the proposed algorithm based on the mean shift algorithm provides better results than the traditional focus measures in the presence of the above mentioned two types of noise.