4,310 research outputs found

    Effect of aspect ratio on transverse diffusive broadening: A lattice Boltzmann study

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    We study scaling laws characterizing the inter-diffusive zone between two miscible fluids flowing side by side in a Y-shape laminar micromixer using the lattice Boltzmann method. The lattice Boltzmann method solves the coupled 3D hydrodynamics and mass transfer equations and incorporates intrinsic features of 3D flows related to this problem. We observe the different power law regimes occurring at the center of the channel and close to the top/bottom wall. The extent of the inter-diffusive zone scales as square root of the axial distance at the center of the channel. At the top/bottom wall, we find an exponent 1/3 at early stages of mixing as observed in the experiments of Ismagilov and coworkers [Appl. Phys. Lett. 76, 2376 (2000)]. At a larger distance from the entrance, the scaling exponent close to the walls changes to 1/2 [J.-B. Salmon et al J. Appl. Phys. 101, 074902 (2007)]. Here, we focus on the effect of finite aspect ratio on diffusive broadening. Interestingly, we find the same scaling laws regardless of the channel's aspect ratio. However,the point at which the exponent 1/3 characterizing the broadening at the top/bottom wall reverts to the normal diffusive behavior downstream strongly depends on the aspect ratio. We propose an interpretation of this observation in terms of shear rate at the side walls. A criterion for the range of aspect ratios with non-negligible effect on diffusive broadening is also provided.Comment: 19 pages, 7 figure

    Ab-initio simulation and experimental validation of beta-titanium alloys

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    In this progress report we present a new approach to the ab-initio guided bottom up design of beta-Ti alloys for biomedical applications using a quantum mechanical simulation method in conjunction with experiments. Parameter-free density functional theory calculations are used to provide theoretical guidance in selecting and optimizing Ti-based alloys with respect to three constraints: (i) the use of non-toxic alloy elements; (ii) the stabilization of the body centered cubic beta phase at room temperature; (iii) the reduction of the elastic stiffness compared to existing Ti-based alloys. Following the theoretical predictions, the alloys of interest are cast and characterized with respect to their crystallographic structure, microstructure, texture, and elastic stiffness. Due to the complexity of the ab initio calculations, the simulations have been focused on a set of binary systems of Ti with two different high melting bcc metals, namely, Nb and Mo. Various levels of model approximations to describe mechanical and thermodynamic properties are tested and critically evaluated. The experiments are conducted both, on some of the binary alloys and on two more complex engineering alloy variants, namely, Ti-35wt.%Nb-7wt.%Zr-5wt.%Ta and a Ti-20wt.%Mo-7wt.%Zr-5wt.%Ta.Comment: 23 pages, progress report on ab initio alloy desig

    Microstructure Mechanics of Crystalline Materials - Introduction

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    Polykristallmechanik Grundlagen

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    Mikrostruktur: Gesamtheit aller Gitterfehler, die sich nicht im thermodynamischen Gleichgewicht befinden (Haasen). Pfad: Prozeßgeschichte; meßbar nicht durch Prozeßparameter, sondern durch mikrostrukturelle Zustandsparameter (i.d.R. keine Analogie zu thermodynamischen ZustandsgrĂ¶ĂŸen, Vorsicht bei Differentiation). Textur: Volumengewichtete Gesamtheit aller Kristallorientierungen in einer Probe. Materialeigenschaften: Makroskopische Reaktionen einer Probe auf makroskopische Anregungen. Konstitutive Gesetze: Quantitativ gefaßte Relationen zwischen makroskopischen Anregungen und makroskopischen Reaktionen (FeldgrĂ¶ĂŸen, z.B. Hooke, evtl. auf Basis der Mikrostruktur). Konstitution: Thermodynamik der Phasen Isotropie: RichtungsunabhĂ€ngigkeit (Tropos (gr.): Richtung) Anisotropie: RichtungsabhĂ€ngigkeit (Morphologie, Toplogie, Textur, etc.) Fließort: Gesamtheit aller SpannungszustĂ€nde, bei denen plastisches (zusĂ€tzlich zu elastischem) Fließen auftrit

    The Role of Texture and Elastic-Plastic Anisotropy in Metal Forming Simulations

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    Metals mostly occur in polycrystalline form where each grain has a different crystallographic orientation, shape, and volume fraction. The distribution of the grain orientations is referred to as crystallographic texture. The discrete nature of crystallographic slip along certain lattice directions on preferred crystallographic planes entails an anisotropic plastic response of such samples under mechanical loads. While the elastic-plastic deformation of single crystals and bicrystals can nowadays be well predicted, plasticity of polycrystalline matter is less well understood. This is essentially due to the intricate interaction of the grains during co-deformation. This interaction leads to strong in-grain and grainto- grain heterogeneity in terms of strain, stress, and crystal orientation. Modern metal forming and crash simulations are usually based on the finite element method. Aims of such simulations are typically the prediction of the material shape, failure, and mechanical properties during deformation. Further goals lie in the computer assisted lay-out of manufacturing tools used for intricate processing steps. Any such simulation requires that the material under investigation is specified in terms of its respective constitutive behavior. Modern finite element simulations typically use three sets of material input data, covering hardening, forming limits, and anisotropy. The current research report issued by the Max-Planck-Institut fĂŒr Eisenforschung is about the latter aspect placing particular attention on the physical nature of anisotropy. The report reviews different empirical and physically based concepts for the integration of the elastic-plastic anisotropy into metal forming finite Raabe, Texture and Anisotropy in Metal Forming Simulations Raabe, edoc Server, Max-Planck-Society - 3 - MPI DĂŒsseldorf element simulations. Particular pronunciation is placed on the discussion of the crystallographic anisotropy of polycrystalline material rather than on aspects associated with topological or morphological microstructure anisotropy. The reviewed anisotropy concepts are empirical yield surface approximations, yield surface formulations based on crystallographic homogenization theory, combinations of finite element and homogenization approaches, the crystal plasticity finite element method, and the recently introduced texture component crystal plasticity finite element method. The report presents the basic physical approaches behind the different methods and discusses engineering aspects such as scalability, flexibility, and texture update in the course of a forming simulation. Published overviews on this topic can be found in Raabe, Klose, Engl, Imlau, F. Friedel, Roters: Advanced Engineering Materials 4 (2002) 169-180, Raabe, Zhao, Mao: Acta Materialia 50 (2002) 4379–4394, and Raabe, Roters: International Journal of Plasticity 20 (2004) p. 339-36

    A 3D probabilistic cellular automaton for the simulation of recrystallization and grain growth phenomena

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    This MPG progress report presents applications of a 3D stochastic cellular automaton model for the spatial, kinetic, and crystallographic simulation of mesoscale transformation phenomena that involve non-conserved structural field variables and the motion of sharp interfaces, such as encountered in the fields of recrystallization and grain growth. The automaton is discrete in time, physical space, and orientation space. It is defined on a 3D cubic lattice considering the first, second, and third neighbor shell. The local transformation rule that acts on each lattice site consists of a probabilistic analog of the linearized symmetric Turnbull rate equation for grain boundary segment motion. All possible switches of cells are simultaneously considered using a weighted stochastic sampling integration scheme. The required input parameters are the mobility data for the grain boundaries, the local crystallographic texture, and a local stored energy measure as a function of space

    Some Critical Thoughts on Computational Materials Science

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    1. A Model is a Model is a Model is a Model The title of this report is of course meant to provoke. Why? Because there always exists a menace of confusing models with reality. Does anyone now refer to “first principles simulations”? This point is well taken. However, practically all of the current predictions in this domain are based on simulating electron dynamics using local density functional theory. These simulations, though providing a deep insight into materials ground states, are not exact but approximate solutions of the Schrödinger equation, which - not to forget - is a model itself [1]. Does someone now refer to “finite element simulations”? This point is also well taken. However, also in this case one has to admit that approximate solutions to large sets of non-linear differential equations formulated for a (non-existing) continuum under idealized boundary conditions is what it is: a model of nature but not reality. But us let calm down and render the discussion a bit more serious: current methods of ground state calculations are definitely among the cutting-edge disciplines in computational materials science and the community has learnt much from it during the last years. Similar aspects apply for some continuum-based finite element simulations. After all this report is meant to attract readers into this exciting field and not to repulse them. And for this reason I feel obliged to first make a point in underscoring that any interpretation of a research result obtained by computer simulation should be accompanied by scrutinizing the model ingredients and boundary conditions of that calculation in the same critical way as an experimentalist would check his experimental set-up
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