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

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

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

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 für 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 Düsseldorf 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

Von Rittern und Rächern - Metalle für Krieg und Frieden

Die Entstehung des Schwertes; Von Balmung und Excalibur - Helden und ihre Schwerter; Justitia und die Waff der Scharfrichter; Männer in Metall - Die Ritter; Waffen aus Damaszener Stahl

Polykristallmechanik Grundlagen

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 Zustandsgrößen, 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 (Feldgrößen, z.B. Hooke, evtl. auf Basis der Mikrostruktur). Konstitution: Thermodynamik der Phasen Isotropie: Richtungsunabhängigkeit (Tropos (gr.): Richtung) Anisotropie: Richtungsabhängigkeit (Morphologie, Toplogie, Textur, etc.) Fließort: Gesamtheit aller Spannungszustände, bei denen plastisches (zusätzlich zu elastischem) Fließen auftrit

Nanoscale austenite reversion through partitioning, segregation, and kinetic freezing: Example of a ductile 2 GPa Fe-Cr-C steel

Austenite reversion during tempering of a Fe-13.6Cr-0.44C (wt.%) martensite results in an ultrahigh strength ferritic stainless steel with excellent ductility. The austenite reversion mechanism is coupled to the kinetic freezing of carbon during low-temperature partitioning at the interfaces between martensite and retained austenite and to carbon segregation at martensite-martensite grain boundaries. An advantage of austenite reversion is its scalability, i.e., changing tempering time and temperature tailors the desired strength-ductility profiles (e.g. tempering at 400{\deg}C for 1 min. produces a 2 GPa ultimate tensile strength (UTS) and 14% elongation while 30 min. at 400{\deg}C results in a UTS of ~ 1.75 GPa with an elongation of 23%). The austenite reversion process, carbide precipitation, and carbon segregation have been characterized by XRD, EBSD, TEM, and atom probe tomography (APT) in order to develop the structure-property relationships that control the material's strength and ductility.Comment: in press Acta Materialia 201

Kristallmechanik in Vielkristallen - Crystal Mechanics in Polycrystals

Bei der plastischen Verformung von Polykristallen ändern die Kristallite zumeist ihre Orientierung. Auch bei homogener gradientenfreier äußerer Krafteinwirkung kommt es aufgrund des anisotropen Verhaltens des Materials und aufgrund von Reibung zumeist zu Orientierungsänderungen und Kornfragmentierungen. Heterogenitäten bezüglich Spannung, Dehnung und kristallographischer Orientierung auf Kornebene sind die Folge. Neben dem grundlegenden Erkenntnisgewinn bei der Untersuchung lokaler Kornmechanik ist die Aufklärung des Auftretens und die Systematik solcher Heterogenitäten aus verschiedenen Gründen von Interesse: Erstens, strukturelle und funktionelle Bauelemente werden zunehmend miniaturisiert. Mit der Verkleinerung solcher metallischen Bauteile verringert sich das homogenisierende Zusammenwirken mehrerer Kristalle und somit die Möglichkeit zur gezielten Einstellung einer texturbedingten Quasi–Isotropie. Bei kleinen Abmessungen wird der einkristalline Anisotropieeinfluss dominant und somit auch Gradienten innerhalb einzelner Kristallite. Zweitens, in Bauteilen sehr geringer Abmessungen zumindest in einer Richtung, wie beispielsweise Drähte und dünne Folien, können solche Heterogenitäten zu Schädigungsoder Versagensursachen werden. Drittens, die Quantifizierung der elastisch-plastischen Kornwechselwirkung bei der Polykristallverformung ist ein wichtiger Baustein zur Verbesserung und Verifizierung von kristallplastischen Homogenisierungstheorien. Solche Theorien dienen zur statistischen Vorhersage der plastischen Anisotropie (Fließort-Theorie) und von Verformungstexturen nach der Taylor-Bishop-Hill-Theorie. Viertens, mikromechanische Untersuchungsmethoden, wie die Nano-Härteprüfung, werden zunehmend zur Charakterisierung von mikromechanischer Effekte verwendet. Solche Untersuchungsverfahren werden allerdings derzeit in der Regel ohne Berücksichtigung der Kristallkinematik des betroffenen Korns durchgeführt. Die Orientierungsabhängigkeit dieser Messung bleibt dabei unberücksichtigt. Allein der kinematische Anteil an der Einzelkristallhärte kann aber durchaus einen Faktor zwei ausmachen (z.B. durch Variation des Taylorfaktors) und verdient daher nähere Berücksichtigung. Ähnliche Argumente gelten für alle Werkstoffprüfungen, bei denen Mikrostrukturelemente in einer ähnlichen Größenordnung wie die Probenabmessungen vorliegen. Fünftens, Bereiche lokaler Heterogenitäten bezüglich Spannung und Dehnung sind stets auch Gebiete hoher Keimdichte bei homogenen und heterogenen Phasenumwandlungen

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

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

Heterogeneous shear in hard sphere glasses

There is growing evidence that the flow of driven amorphous solids is not homogeneous, even if the macroscopic stress is constant across the system. Via event driven molecular dynamics simulations of a hard sphere glass, we provide the first direct evidence for a correlation between the fluctuations of the local volume-fraction and the fluctuations of the local shear rate. Higher shear rates do preferentially occur at regions of lower density and vice versa. The temporal behavior of fluctuations is governed by a characteristic time scale, which, when measured in units of strain, is independent of shear rate in the investigated range. Interestingly, the correlation volume is also roughly constant for the same range of shear rates. A possible connection between these two observations is discussed.Comment: 5 pages, 4 figures, accepted at Phys. Rev. Let