No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
Advanced numerical method for generation of three-dimensional particles and its application in microstructure-based simulation of fatigue behavior
Abstract
The topology of representative elementary volumes (REV) generated to model materials microstructure is getting more and more complex. This paper presents advanced mesh generation methods used to improve the description of 3D microstructural particles. The goal is to adapt easily the shape of the elements at the interface between the isotropic matrix and embedded inclusions. Two methods are described in this work to generate inclusions: an analytical method based on statistical experimental data and a reconstruction approach, based on tomographic imaging. Sensitivity analyses on meshing parameters are performed to obtain efficient data in order to reconstruct the most representative volume and to perform subsequent accurate numerical computations. As an example of calculations, fatigue tests are chosen to validate the proposed approach.
... The ICME (Integrated Computational Materials Engineering) methods permit to circumvent some difficulties induced by microstructural inhomogeneities such as the non-isotropic distribution of inclusions and their influence on the mechanical anisotropy as exhaustively discussed by Horstemeyer (2012) and pragmatically studied by Milesi et al. (2010) and Milesi et al. (2011) for specific fatigue problems. Standard polycrystalline models can be used to predict texture evolutions of zinc and titanium as briefly discussed by Funderberger et al. (1997) and more precisely by Philippe et al. (1994a,b) or their effect on mechanical behavior, e.g. the ViscoPlastic Self-Consistent model (VPSC) (Lebensohn and Tomé, 1993). ...
The mechanical behavior of zinc has been studied and linked to the formability of sheets. An anisotropic elastic–viscoplastic behavior law has been developed to take into account the anisotropy of the material. Anisotropy is induced by crystallographic and morphological textures, and possibly by the spatial distribution of intermetallics. The temperature dependence is introduced through a Zener–Hollomon type term. The resulting anisotropic formability of sheets implies a new approach by adapting the forming limit diagram with a stress based criterion. This approach is confronted and validated by considering the industrial forming of a head clip.
Hot tearing is a major defect arising during solidification of aluminium alloys. This defect is associated with the inability of liquid to feed areas where voids have started to appear, not allowing to heal small defects before they grow bigger. To understand hot tearing, it is mandatory to develop a good knowledge of the semi-solid mechanical behaviour. It is thus very useful to carry out X-ray microtomographies experiments and mechanical simulations on representative elementary volumes. In this work, we couple the both approaches by initialising a finite element simulation with the help of microtomography data obtained during an isothermal tensile testing of an aluminium-copper alloy in the mushy state. This innovative approach gives a direct access to the experimental reality and allows comparisons of numerical and experimental evolutions of the sample. We explain in a first time how to get the numerical representation thanks to a marching cubes algorithm and the immersed volume method. Then, we present our numerical model for which we solve the Stokes equations in a monolithic way. Once the velocity computed in all the solid, liquid and gaseous phases, we use a level set method in a Eulerian formalism to obtain the morphological evolution of our numerical sample. Despite the model simplicity, numerical and experimental results show a reasonable agreement concerning the air propagation inside the sample.
Dual phase (DP) steels were modeled using 2D and 3D representative volume elements (RVE). Both the 2D and 3D models were generated using the Monte-Carlo-Potts method to represent the realistic microstructural details. In the 2D model, a balance between computational efficiency and required accuracy in truly representing heterogeneous microstructure was achieved. In the 3D model, a stochastic template was used to generate a model with high spatial fidelity. The 2D model proved to be efficient for characterization of the mechanical properties of a DP steel where the effect of phase distribution, morphology and strain partitioning was studied. In contrast, the current 3D modeling technique was inefficient and impractical due to significant time cost. It is shown that the newly proposed 2D model generation technique is versatile and sufficiently accurate to capture mechanical properties of steels with heterogeneous microstructure.
X-ray computer tomography (CT) is fast becoming an accepted tool within the materials science community for the acquisition of 3D images. Here the authors review the current state of the art as CT transforms from a qualitative diagnostic tool to a quantitative one. Our review considers first the image acquisition process, including the use of iterative reconstruction strategies suited to specific segmentation tasks and emerging methods that provide more insight (e.g. fast and high resolution imaging, crystallite (grain) imaging) than conventional attenuation based tomography. Methods and shortcomings of CT are examined for the quantification of 3D volumetric data to extract key topological parameters such as phase fractions, phase contiguity, and damage levels as well as density variations. As a non-destructive technique, CT is an ideal means of following structural development over time via time lapse sequences of 3D images (sometimes called 3D movies or 4D imaging). This includes information needed to optimise manufacturing processes, for example sintering or solidification, or to highlight the proclivity of specific degradation processes under service conditions, such as intergranular corrosion or fatigue crack growth. Besides the repeated application of static 3D image quantification to track such changes, digital volume correlation (DVC) and particle tracking (PT) methods are enabling the mapping of deformation in 3D over time. Finally the use of CT images is considered as the starting point for numerical modelling based on realistic microstructures, for example to predict flow through porous materials, the crystalline deformation of polycrystalline aggregates or the mechanical properties of composite materials. © 2014 Institute of Materials, Minerals and Mining and ASM International.
This paper presents an anisotropic h-adaptation approach to compute Rayleigh-Taylor instabilities (RTI). The aim of this study is to analyse the impact of anisotropic mesh adaptation on the development of the instabilities and the rate of mixing of the fluids. Actually, the RTI has no exact solution, therefore a geometric a posteriori error estimate is well suited. Furthermore, for such simulation, a mesh adaptation algorithm based on a transient fixed point problem has been designed in order to control the error in space and in time.
Numerical modelling of fatigue behavior for anisotropic structures has become critical for design applications. This is particularly true for forged components due to the intrinsic anisotropy of the material resulting from the process. The aim of this study is to relate the microstructure features to the process scale, i.e. the engineering scale. Anisotropy is induced by the forming process and the most relevant feature which results from forging, is the preferential orientation of structur-al defects and grains in the direction of the deformation. Grain flow is modelled using a fiber tensor at the level of the rep-resentative elementary volume. It can then be used to improve and refine the Papadopoulos fatigue criterion by taking into account fatigue limits for each direction of anisotropy. In practice, it is very tedious to determine precisely these fatigue limits and impossible to experimentally obtain all of them for each direction of uniaxial loading. To circumvent this diffi-culty, we simulate the problem at the microstructure scale by considering fiber tensor as the result of the inclusion and grain orientation. Microstructures are then precisely modelled using DIGIMICRO software. A representative elementary volume with several inclusions is meshed and high cycle fatigue simulation is performed.
A major problem arising in finite element analysis of welding is the long computer times required for a complete three-dimensional analysis. In this study, an adaptative strategy for coupled thermometallurgical analysis of welding is proposed and applied in order to provide accurate results in a minimum computer time. The anisotropic adaptation procedure is controlled by a directional error estimator based on local interpolation error and recovery of the second derivatives of different fields involved in the finite element calculation. The methodology is applied to the simulation of a gas–tungsten-arc fusion line processed on a steel plate. The temperature field and the phase distributions during the welding process are analyzed by the FEM method showing the benefits of dynamic mesh adaptation. A significant increase in accuracy is obtained with a reduced computational effort. Copyright © 2007 John Wiley & Sons, Ltd.
Forged components exhibit good mechanical strength, particularly in terms of high cycle fatigue properties. This is due to the specific microstructure resulting from large plastic deformation as in a forging process. The goal of this study is to account for critical phenomena such as the anisotropy of the fatigue resistance in order to perform high cycle fatigue simulations on industrial forged components. Standard high cycle fatigue criteria usually give good results for isotropic behaviors but are not suitable for components with anisotropic features. The aim is to represent explicitly this anisotropy at a lower scale compared to the process scale and determined local coefficients needed to simulate a real case. We developed a multi-scale approach by considering the statistical morphology and mechanical characteristics of the microstructure to represent explicitly each element. From stochastic experimental data, realistic microstructures were reconstructed in order to perform high cycle fatigue simulations on it with different orientations. The meshing was improved by a local refinement of each interface and simulations were performed on each representative elementary volume. The local mechanical anisotropy is taken into account through the distribution of particles. Fatigue parameters identified at the microscale can then be used at the macroscale on the forged component. The linkage of these data and the process scale is the fiber vector and the deformation state, used to calculate global mechanical anisotropy. Numerical results reveal an expected behavior compared to experimental tendencies. We proved numerically the dependence of the anisotropy direction and the deformation state on the endurance limit evolution.
This paper proposes to use the metric properties of the distance function between two bodies in contact (or gap function) in simulations involving contact problems. First, the normal vectors, which are involved in the formulation of the contact condition, are defined through the gradient of this distance function. This definition avoids to deal with the numerical penetration parameter, which is generally introduced otherwise. Furthermore, it allows the contact problem to be extended in a simple way to an Eulerian formulation. Second, this paper investigates two mesh adaptation strategies based on the properties of the distance function. The first strategy consists in building a size map according to the values of this function, in order to refine locally the mesh, and consequently to improve the description of the contact surface. The second strategy consists in adapting locally the mesh to the geometry of the contact surface. This anisotropic adaptation is performed by constructing a metric map that allows the mesh size to be imposed in the direction of the distance function gradient. A lot of elements are saved when compared with the isotropic case. Throughout this paper, many numerical simulations are presented in the context of the forging process: the deformable material is pressed between two rigid tools. Furthermore, the algorithm used to calculate the signed distance to a surface mesh is detailed in appendix of this paper. Copyright © 2008 John Wiley & Sons, Ltd.
Mesoscale analysis is a promising discipline for concrete mix design and damage prediction. Besides many other aspects, its success crucially depends on accurate modeling of the mesoscale geometry and efficient numerical analysis of high resolution, to both of which this article contributes. Mesoscale models of concrete include aggregates, cement stone and, optionally, interfacial transition zones. The present paper establishes transparent formulas for consistent numerical generation of aggregate sizes. Fast separation checks are applied to place ellipsoidal and in particular arbitrary shaped particles. The multigrid method enables efficient computation of very large heterogeneous mesoscale models. This is exemplified by linear finite element analysis of two-dimensional models. Corresponding results are confirmed by experiments and analytical models from literature. The influence of concrete mix parameters on effective elastic properties is studied.
In this paper we present a 3D tetrahedral, unstructured and anisotropic mesh generator that is not based on the Delaunay, frontal or octree method. Instead, it proceeds by local optimizations and uses an anisotropic shape criterion to fit a metric field.Then, we introduce a new 3D metric field that tightens the mesh around interfaces when the calculation domain is divided in several subdomains, and a 3D metric field that places enough elements through each subdomain thickness, without introducing too many nodes in the other directions.Finally, we show some applications for material forming geometries.
A convolution-backprojection formula is deduced for direct reconstruction of a three-dimensional density function from a set of two-dimensional projections. The formula is approximate but has useful properties, including errors that are relatively small in many practical instances and a form that leads to convenient computation. It reduces to the standard fan-beam formula in the plane that is perpendicular to the axis of rotation and contains the point source. The algorithm is applied to a mathematical phantom as an example of its performance.
The paper describes a robust finite element model of interface motion in media with multiple domains and junctions, as is the case in polycrystalline materials. The adopted level set framework describes each domain (grain) with a single level set function, while avoiding the creation of overlap or vacuum between these domains. The finite element mesh provides information on stored energies, calculated from a previous deformation step. Nucleation and growth of new grains are modelled by inserting additional level set functions around chosen nodes of the mesh. The kinetics and topological evolutions induced by primary recrystallization are discussed from simple test cases to more complex configurations and compared with the Johnson-Mehl-Avrami-Kolmogorov theory.
This work is currently under development within the framework of an American‐European project (Digimat Project). The paper details the development of some numerical tools dedicated to the digital representation of metallic materials structures, to the finite element
modelling of the polycrystalline microstructure deformation under large strains and to the subsequent recrystallization. The level set method used for the description of the microstructure interfaces is shown to represent a common base to all these developments.
A fluid-structure interaction method, based on a eulerian monolithic approach is introduced in order to study distributive and dispersive aspects of mixing within a multiscale approach of the processes. A first example investigates macroscopic flow resolution for the whole process including moving tools, then the dispersion of a single agglomerate is studied within a microscopic approach, and finally one shows a full macroscopic simulation coupled through a kinetic theory for dispersive mixing. Nous présentons une méthode d'interaction fluide-structure basée sur une approche monolithique eulérienne permettant d'étudier à différentes échelles les procédés de mélange sous leur aspect dispersif et distributif. Une première approche macroscopique traitant de la résolution mécanique dans le procédé, où interviennent des outils tournants, est présentée, puis une approche microscopique modélisant la dispersion d'un agglomérat, et enfin une approche couplée via une théorie cinétique.
Durant le procédé de forgeage, la pièce subit des déformations complexes et importantes. Ainsi, la microstructure finale n'est pas homogène, et le comportement macroscopique du matériau change selon la direction de sollicitation. Ce phénomène, directement lié au procédé mécanique de mise en forme constitue, l'anisotropie du comportement de la pièce forgée. Le but de cette étude est de relier cette anisotropie à des calculs de fatigue à grand nombre de cycles. Pour des pièces suffisamment isotropes (des pièces coulées par exemple), les critères classiques sont de bons prédicteurs, mais leur utilisation pour des pièces forgées n'est pas recommandée. Ainsi, pour tenir compte de cet effet, l'anisotropie est représentée à une échelle d'étude plus petite que celle du procédé : l'échelle mésoscopique c'est à dire l'échelle du grain. A partir des données statistiques obtenues sur la pièce réelle, nous pouvons reconstruire un volume élémentaire digital et lui faire subir des déformations et des analyses en fatigue dans toutes les directions. Ceci afin de déterminer les coefficients locaux dont nous avons besoin pour revenir sur la simulation de la mise en forme et des propriétés induites en fatigue de la pièce forgée. Il s'agit donc d'une étude multi-échelles reliant l'échelle de la microstructure à celle de l'ingénieur. Par ce biais, l'anisotropie mécanique locale est prise en compte à travers des paramètres locaux qui dépendent de l'orientation de la microstructure mais aussi du taux de déformation. Les liens avec la pièce industrielle sont un vecteur fibrage (qui donne l'anisotropie induite par le procédé de forgeage) et un taux de déformation locale subie. Ainsi, les résultats peuvent être utilisées dans l'optique d'optimiser la préforme du composant pour optimiser sa tenue en fatigue.
The Alkali-Silica Reaction (ASR) induces aggregates swelling leading to irreversible degradation of concrete structures. Modelling damage and cracks in a 3D concrete structure submitted to ASR is hence of prime importance in civil engineering. FEMCAM (Finite Element Model for Concrete Analysis Method) software has been developed within this framework to model 3D numerical concrete. In this thesis, we have developed a mesoscale approach where concrete is considered as a heterogeneous material with two main phases: the mortar paste and aggregates. An elastic damage law has been successfully implemented to take into account the mortar paste behavior. The non local Mazars model with an implicit formulation is hence used to deal with damage. This model requires determining elastic and damage parameters. In this way, an experimental campaign has been carried out at the Civil Engineering Department of the Ecole des Mines de Douai to identify concrete material parameters. These experimental results have been compared with numerical ones through the inverse analysis modulus RheOConcrete. Applications on concrete (compression tests, three point bending tests and
This paper presents CIMLIB with its two main characteristics: an Object
Oriented Program and a fully parallel code. CIMLIB aims at providing a
set of components that can be organized to build numerical simulation of
a certain process. We describe two components: one treats the complex
task of parallel remeshing, the other puts the focus on the Finite
Element modeling. In a second part, we present some parallel
performances and an example of a very large simulation (over a mesh of
25 millions nodes) that begins with the mesh generation and ends up
writing results files, all done using 88 processors.
In this paper the mechanisms of a composite material are treated in terms of a numerical model which simulates in finite elements terms the two major phases: inclusions and the matrix binding them, with a mechanically weak interface. Analysis of laboratory specimens loaded to failure have lent substantial support to the theoretical model used to describe and predict with reasonable certainty the global mechanical behaviour of composites and in particular the complex failure process. The simulation explains the incompatibility of the two phases for variations in water content and temperature, accounting for the possible degradation due to these effects. Although the model presented is, in its character, two dimensional, it can effectively described the cracking behaviour of concretes. The computational power made available through the advent of more sophisticated data-processing equipmennt components makes it imperative for the model to be extended to its third dimension. It has been shown that numerical concrete is a powerful research tool which allows us to study properties and processes hitherto inaccessible.
This letter describes a level set framework for the numerical modelling of primary static recrystallization in a polycrystalline material. The topological evolution of the grain structure is simulated in two and three dimensions, based on a kinetic law relating the velocity of the boundary to the thermodynamic driving force. The adopted finite element approach is described, discussed and tested from simple to more complex configurations. The possibility to accurately describe nucleation and growth is illustrated in three dimensions.
Directional, anisotropic features like layers in the solution of partial differential equations can be resolved favorably by using anisotropic finite element meshes. An adaptive algorithm for such meshes includes the ingredients Error estimation and Information extraction/Mesh refinement. Related articles on a posteriori error estimation on anisotropic meshes revealed that reliable error estimation requires an anisotropic mesh that is aligned with the anisotropic solution. To obtain anisotropic meshes the so-called Hessian strategy is used, which provides information such as the stretching direction and stretching ratio of the anisotropic elements. This article combines the analysis of anisotropic information extraction/mesh refinement and error estimation (for several estimators). It shows that the Hessian strategy leads to well-aligned anisotropic meshes and, consequently, reliable error estimation. The underlying heuristic assumptions are given in a stringent yet general form. Numerical examples strengthen the exposition. Hence the analysis provides further insight into a particular aspect of anisotropic error estimation. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 625–648, 2002; DOI 10.1002/num.10023
The indentation load-displacement behavior of six materials tested with a Berkovich indenter has been carefully documented to establish an improved method for determining hardness and elastic modulus from indentation load-displacement data. The materials included fused silica, soda–lime glass, and single crystals of aluminum, tungsten, quartz, and sapphire. It is shown that the load–displacement curves during unloading in these materials are not linear, even in the initial stages, thereby suggesting that the flat punch approximation used so often in the analysis of unloading data is not entirely adequate. An analysis technique is presented that accounts for the curvature in the unloading data and provides a physically justifiable procedure for determining the depth which should be used in conjunction with the indenter shape function to establish the contact area at peak load. The hardnesses and elastic moduli of the six materials are computed using the analysis procedure and compared with values determined by independent means to assess the accuracy of the method. The results show that with good technique, moduli can be measured to within 5%.
This work aims at improving the calculation of stress fields around non-metallic inclusions in high strength bearing steels. A new methodology is proposed, based on: (i) the determination of 3D morphologies of inclusions by X-ray micro-tomography imaging; (ii) the characterization of the mechanical properties of the inclusion by nano-indentation, and (iii) finite element (FE) calculations of the stress concentration induced by the inclusions. The methodology is applied to a calcium aluminate inclusion with cavities, located in a Hertzian stress field. The stress concentration appears to be strongly dependent on the orientation of the inclusion-cavity considered. The stress concentration fields obtained from realistic 3D shapes are compared to those obtained from simplified shapes of inclusions.
Concrete is a composite material with a variety of inhomogeneities. Its composite behavior may be studied analytically using the mesoscopic approach which treats the concrete as a three-phase system consisting of coarse aggregate, mortar matrix with fine aggregate dissolved in it, and interfacial zones between the coarse aggregate and the mortar matrix. For such mesoscopic study, it is first necessary to generate a random aggregate structure in which the shape, size and distribution of the aggregate particles resemble real concrete in the statistical sense. Then, if the composite structure is to be analyzed by the finite element method, a mesh for each of the three phases needs to be generated. In this paper, a procedure for generating random aggregate structures for rounded and angular aggregates based on the Monte Carlo random sampling principle is proposed and a method of mesh generation using the advancing front approach is developed. These are combined with a nonlinear finite element method for mesoscopic study of concrete whose methodology and results will be presented in part II of the paper.
To predict effective thermal conductivities and permeabilities of open-cell foams, produced by a SlipReactionFoamSintering (SRFS)-process, a multiscale approach based on the homogenization method is applied. This formulation allows to calculate effective aerothermal properties by solving either special thermal or Stokes flow problems on a unit cell. Starting from a detailed foam description by tomographic images, 3D microstructure models of the SlipReaction (SR)-foam are generated by combining spectral analyses with a specific mesh generation. Effective thermal conductivities of an Inconel foam sample are predicted with different FE discretizations by the homogenization procedure and compared with the experimental results, measured by the transient plane source technique. Effective Darcy permeabilities are evaluated in the foam center and compared with experimental pressure drop measurements. Moreover, permeability predictions of the unit cells with extremal porosity allow to measure the permeability scatter of the Inconel SR-foam sample.
This paper deals with the data scatter occurring in uniaxial and multiaxial high cycle fatigue. The weakest link concept together with a critical plane damage model based on a microplasticity analysis are combined to describe the distributions of the fatigue limit and of the fatigue life under different loadings. Tension, torsion and combined proportional tension and torsion load conditions are analysed. The application of the Weibull approach is possible under any multiaxial loading by defining a relevant equivalent stress. This probabilistic approach is applied only on the specimen surface to reflect the fatigue damage mechanisms that lead generally to crack initiation on the free surface.The model predictions are compared to some fatigue data from tests on a mild steel C36. This material is first submitted to simple reversed tension and torsion and two reference SN curves are drawn. The scatter around the fatigue limits is estimated from these curves. Some tests under combined proportional tension and torsion loading modes with two different stress amplitude ratios are then conducted.A normalised SN curve can be derived from the probabilistic model and all the possible sinusoidal synchronous multiaxial load conditions can be represented and compared on the same graph giving some information about the cumulative failure probability. All the experimental results under the different loadings are gathered on this curve and it appears that all the points lie in a band from 10 to 90% cumulative failure probabilities.
The mechanical equations for large deformations occurring in metal forming processes are recalled. The finite element approaches for viscoplastic or for elastic viscoplastic materials are presented briefly. Different forms of the virtual work equation for viscoplastic or elastoplastic materials, in dynamic or quasi-static processes, are reviewed. The finite element discretisation is summarised and different time integration schemes are analysed, using a compact symbolic notation. The problem of meshing, remeshing and ALE formulation is mentioned and the space-time finite element method is briefly compared with the more classical approaches.
A new three-dimensional quadratic interface finite element is developed. The element is made up by two 6-noded triangular surfaces which initially lie together and connect the faces of adjacent quadratic tetrahedra, the only elements supported by automatic meshing algorithms. The element is introduced within the framework of implicit analysis and large displacements, and can include any traction–separation law at the interface. It is aimed at simulating damage by particle fracture and interface decohesion in composites by the numerical simulation in three-dimensions of a representative volume element which reproduces the microstructure. The element was validated by comparison with previous results of sphere–matrix decohesion obtained in two-dimensional, axisymmetric conditions. In addition, a new control technique is presented to obtain the whole load–displacement curve at a reasonable computational cost when progressive damage throughout the model (due to the simultaneous development of multiple cracks) leads to severe numerical instabilities. The potential of the new element and the control technique were checked in simulations including sphere fracture in composites made up of random distribution of elastic spheres within an elasto-plastic matrix.
The effect of the reinforcement spatial distribution on the mechanical behavior was investigated in model metal-matrix composites. Homogeneous microstructures were made up of a random dispersion of spheres. The inhomogeneous ones were idealized as an isotropic random dispersion of spherical regions—which represent the clusters—with the spherical reinforcements concentrated around the cluster center. The uniaxial tensile stress-strain curve was obtained by finite element analysis of three-dimensional multiparticle cubic unit cells, which stood as representative volume elements of each material, with periodic boundary conditions. The numerical simulations showed that the influence of reinforcement clustering on the macroscopic composite behavior was weak, but the average maximum principal stress in the spheres—and its standard deviation—were appreciably higher in the inhomogeneous materials than in the homogeneous ones (up to 12 and 60%, respectively). The fraction of broken spheres as a function of the applied strain were computed from experimental values of the Weibull parameters for the strength of the spheres, and the local stress computed in the simulations. It was found that the presence of clustering greatly increased (by a factor between 3 and 6) the fraction of broken spheres, leading to a major reduction of the composite flow stress and ductility.
A serial sectioning process has been developed to visualize and model the behavior of SiC particle reinforced aluminum composite using a reconstructed 3D microstructure. Two-dimensional microstructures were acquired and used to develop 3D solids for visualization and finite-element modeling (FEM). Visualization and modeling of the 3D composite microstructure aided in the understanding of microstructure morphology and provided the means to make the connection between material structure and performance. The approach used here is a improvement over 3D unit cell modeling that uses simplified approximations of the microstructure. The Young's modulus of the composite predicted by the 3D microstructure model correlated very well with experimental results. Furthermore, the 3D microstructure model prediction was more accurate than 3D unit cell model prediction. The serial sectioning process coupled with finite element modeling is a powerful tool for understanding and accurately predicting the influence of microstructural characteristics on the behavior of materials.
Modeling and prediction of the overall elastic–plastic response and local damage mechanisms in composite materials, in particular particle-reinforced composites, is a very complex problem. This is because microstructural aspects of the composite, such as particle size, shape, and distribution, play important roles in deformation behavior. Analytical models and numerical models that simplify the microstructure of the composite do not account for the microstructural factors that influence the mechanical behavior of the material. In this paper we describe a serial sectioning process, followed by finite element method (FEM) simulation, to reproduce, visualize, and model the three-dimensional (3D) microstructure of particle-reinforced metal matrix composites. The 3D microstructure-based FEM accurately represents the alignment, aspect ratio, and distribution of the particles. Comparison with single-particle and multiparticle models of simple shape (spherical and ellipsoidal) shows that the 3D microstructure-based approach is more accurate in simulating and understanding macroscopic and microscopic material behavior.
The concept of the representative volume element (RVE) is analysed in the present paper. For elastic materials the RVE exists and one can determine the size of the RVE. However, for other applications, such as the case of softening materials, the RVE may not exist. In the present work the RVE has been investigated for different stages of the material response, including pre- and post-peak loading regimes. Results were based on a statistical analysis of numerical experiments, where tests have been performed on a random heterogeneous material.
A new algorithm called Mersenne Twister (MT) is proposed for generating uniform pseudorandom numbers. For a particular choice of parameters, the algorithm provides a super astronomical period of 2 ¹⁹⁹³⁷ −1 and 623-dimensional equidistribution up to 32-bit accuracy, while using a working area of only 624 words. This is a new variant of the previously proposed generators, TGFSR, modified so as to admit a Mersenne-prime period. The characteristic polynomial has many terms. The distribution up to v bits accuracy for 1 ≤ v ≤ 32 is also shown to be good. An algorithm is also given that checks the primitivity of the characteristic polynomial of MT with computational complexity O(p ² ) where p is the degree of the polynomial.
We implemented this generator in portable C-code. It passed several stringent statistical tests, including diehard. Its speed is comparable to other modern generators. Its merits are due to the efficient algorithms that are unique to polynomial calculations over the two-element field.
In this new edition of the successful book Level Set Methods, Professor
Sethian incorporates the most recent advances in Fast Marching Methods,
many of which appear here for the first time. Continuing the expository
style of the first edition, this introductory volume presents cutting
edge algorithms in these groundbreaking techniques and provides the
reader with a wealth of application areas for further study. Fresh
applications to computer-aided design and optimal control are explored
and studies of computer vision, fluid mechanics, geometry, and
semiconductor manufacture have been revised and updated. The text
includes over thirty new chapters. It will be an invaluable reference
for researchers and students.
Thèse no 788 sc. techn. EPF Lausanne.
Reinforcement distributions play an important role in various aspects of the processing and final mechanical behaviour of particulate metal matrix composites (PMMCs). Methods for quantifying spatial distribution in such materials are, however, poorly developed, particularly in relation to the range of particle size, shape and orientation that may be present in any one system. The present work investigates via computer simulations the influences of particle morphology, homogeneity and inhomogeneity on spatial distribution measurements obtained by finite-body tessellation. Distribution inhomogeneity was simulated both by the segregation of particles away from specified regions within a microstructure and by generating point density peaks at random locations within a microstructure. Both isotropic and anisotropic inhomogeneous distributions were considered to simulate distribution patterns in PMMCs before and after mechanical working. It was found that the coefficient of variation of the mean near-neighbour distance (COV(dmean)), derived from particle interfaces using finite-body tessellation, was essentially independent of particle shape, size distribution, orientation and area fraction in homogeneous (random) distributions, but showed great sensitivity to inhomogeneity. Increased values of COV(dmean) were seen for both forms of inhomogeneous distributions considered here, with little influence of particle morphology. The COV(dmean) was also seen to be sensitive to anisotropic clustering, the presence of which was identified via nearest-neighbour angles and cell orientations. Although generally formulated for PMMCs, the present results may be generalized to other systems containing low aspect ratio finite bodies of low to moderate area fraction.
Surface texture and coatings, Significance of Tests and Properties of Concrete and Concrete Aggregates, ASTM STP 169
- B Mather
B. Mather, Shape, Surface texture and coatings, Significance of Tests and Properties of Concrete and Concrete Aggregates, ASTM STP 169, American Society of Testing Materials, 1955.
- C Gruau
- T Coupez
C. Gruau, T. Coupez, Comput. Methods Appl. Mech. Eng. 194 (2005) 4951–
4976.
- M Milesi
- Y Chastel
- M Bernacki
- R E Logé
- P O Bouchard
M. Milesi, Y. Chastel, M. Bernacki, R.E. Logé, P.O. Bouchard, Comput. Methods
Mater. Sci. 7 (2007) 383–388.
- M Matsumoto
- T Nishimura
M. Matsumoto, T. Nishimura, ACM Trans. Modell. Comput. Simul. 8 (1998) 3–
30.
- I M Gitman
- H Askes
- L J Sluys
I.M. Gitman, H. Askes, L.J. Sluys, Eng. Fract. Mech. 74 (2006) 2518–2534.
- K D Van
- B Griveau
- O Message
K.D. Van, B. Griveau, O. Message, Mech. Eng. Publ. EGF 3 (1989) 479–496.
- N Chawla
- R S Sidhu
- V V Ganesh
N. Chawla, R.S. Sidhu, V.V. Ganesh, Acta Mater. 54 (2006) 1541–1548.
- M Hamide
- E Massoni
- M Bellet
M. Hamide, E. Massoni, M. Bellet, Int. J. Numer. Methods Eng. 73 (2008) 624–
641.
Fatigue limit of metals under multiaxial stress conditions: the microscopic approach, Technical Note No. I.93
- I V Papadopoulos
I.V. Papadopoulos, Fatigue limit of metals under multiaxial stress conditions:
the microscopic approach, Technical Note No. I.93.101, Commission of the
European Communities, Joint Research Centre.
- M Bernacki
- Y Chastel
- T Coupez
- R E Logé
M. Bernacki, Y. Chastel, T. Coupez, R.E. Logé, Scr. Mater. 58 (12) (2008) 1129–
1132.
- J L Chenot
- F Bay
- J Mater
J.L. Chenot, F. Bay, J. Mater. Process. Technol. 80-81 (1998) 8–15.
- M Milesi
- Y Chastel
- E Hachem
- M Bernacki
- R E Logé
- P Bouchard
M. Milesi, Y. Chastel, E. Hachem, M. Bernacki, R.E. Logé, P. Bouchard, Steel Res.
Int. 81 (9) (2010) 1442–1445.
Surface texture and coatings, Significance of Tests and Properties of Concrete and Concrete Aggregates
- B Mather
- Shape
B. Mather, Shape, Surface texture and coatings, Significance of Tests and
Properties of Concrete and Concrete Aggregates, ASTM STP 169, American
Society of Testing Materials, 1955.
- M Bernacki
- H Resk
- T Coupez
- R E Logé
M. Bernacki, H. Resk, T. Coupez, R.E. Logé, Modell. Simul. Mater. Sci. Eng. 17 (6)
(2009) 064006.