Close cooperation of the department exists with the institute’s external scientific member R. Kirchheim on the fundamentals of the strength of heavily deformed Fe-C systems. This collaboration aims at a better understanding of the origin of deformation-induced alloying and the associated stabilization of sub-grain nanostructures via defectant effects, Fig. 3 [17,41-43]. Similarly, a close collaboration exists with the Max-Planck Fellow G. Eggeler on elementary dislocation creep processes in high temperature alloys, Fig. 4.
The department has five permanent scientific groups,
- Theory and Simulation (F. Roters)
- Microscopy and Diffraction (S. Zaefferer)
- Alloy Design and Thermomechanical Processing (D. Ponge)
- Biological Materials (H. Fabritius)
- Combinatorial Metallurgy and Processing (H. Springer)
and five additional non-permanent scientific groups that are financed by third-party funds,
- Atom Probe Tomography (P. Choi, funded by Leibniz award)
- Adaptive Structural Materials (C. Tasan and B Grabowski, funded by ERC advanced grant)
- Computational Mechanics of Polycrystals (P. Eisenlohr, funded by MPG-FhG program of Max-Planck-Society)
- Theory and Simulation of Complex Fluids (F. Varnik, funded by MMM-initiative of Max-Planck-Society)
- Intermetallic Materials (F. Stein, M. Palm; group will be merged into new department of G. Dehm)
Owing to their extramural funding the latter initiatives are temporary groups. The project of P. Eisenlohr on the Computational Mechanics of Polycrystals was jointly funded after two subsequent evaluation workshops (2005, 2008) by the Max-Planck-Society and the Fraunhofer-Society for 3+3 years, 2005-2011. The group of F. Varnik on the Theory and Simulation of Complex Fluids was funded by the Max-Planck-Multiscale Modeling Initiative for 4 years, 2005-2009. Now it is carried further jointly through third party funds of MPIE and institutional funds of ICAMS (Interdisciplinary Centre for Advanced Materials Simulation) at Ruhr-University Bochum, Germany. The Atom Probe Tomography group, headed by P. Choi, has been established in 2010. It is financed through Prof. Raabe's Leibniz Award (German Research Foundation, DFG). The group for Adaptive Structural Materials, headed jointly by C. Tasan and B. Grabowski, is funded by an ERC advanced grant that was awarded in 2012 to D. Raabe and J. Neugebauer. The group for Intermetallic Materials was originally part to the department of the late Prof. Frommeyer and is currently cooperating with us on high temperature materials, iron-aluminides, and Laves phases. Since October 2012 it is part of the new department of G. Dehm.
Research focus of permanent groups
The group develops mechanism-based crystal plasticity constitutive models that describe the relationship between microstructures and mechanical properties of crystalline materials . The approaches are based on mean field formulations that describe the evolution of lattice defect structure such as dislocations and twins under given mechanical or thermal loading boundary conditions. The predicted defect densities enter into kinetic structure-property relations that translate them into strength and deformation measures [44,45]. Owing to the crystalline anisotropy of metallic alloys the constitutive laws assume a tensorial form both in their elastic and plastic formulations, i.e. they predict the defect evolutions on all crystallographic shear and twinning systems under external loads and their internal interactions. The formulations are built on dislocation densities (different types depending on the exact model), and can include mechanical twinning as additional deformation carrier. Interactions among dislocations and of dislocations with twins and grain boundaries can be considered. The resulting sets of nonlinear internal-variable differential equations are solved using either the Finite Element Method (CPFEM) [16,19,25,26,29,32-34,47,48] or a Spectral Method (CPFFT) [49,50], Fig. 5.
Research Highlights 2010-2012 including main trends over the past 6 years
The most important highlight during the past years was the further development of a Spectral Crystal Plasticity (Fast Fourier) Method (CPFFT) together with R. Lebensohn from Los Alamos who spent a year in the group as Alexander von Humboldt Awardee [49,50]. This method was modified to enable the use of advanced non-linear constitutive models, such as described above, and equipped with a robust integration algorithm. Furthermore, a regrinding capability has been developed to ensure that the gradual micromechanical distortions do not impede convergence. The fundamental advantage of this approach is that FFTs can solve the underlying constitutive elasto-plastic equations under periodic boundary conditions about orders of magnitude faster than FEM solvers at much lower memory costs. Also CPFFT has the advantage that it can directly be applied to EBSD or other fixed-grid microstructure data sets circumventing the requirement to reconstruct complicated mesh geometries as it should be done for corresponding CPFEM simulations. The novel method is mature and currently successfully applied to full-field simulations of deformation heterogeneity in dual phase steels, porous alloys, and ice mechanics.
Another field of activity was the application of advanced CPFEM simulations to the prediction and better understanding of shear banding in crystalline materials . Shear bands are the most frequently observed yet least understood mesoscopic, collective plasticity mechanism. They play an essential role in strain hardening, strain localization, texture evolution, and damage initiation. We found that shear banding is strongly orientation dependent. For example Copper and Brass-R-oriented crystals (FCC lattice) show the largest tendency to form shear bands and build up an inhomogeneous texture inside the shear bands. Shear banding in these crystals can be understood in terms of a mesoscopic softening mechanism. The predicted local textures and the shear banding patterns agree well with experimental observations in low SFE FCC crystals [47,48].
The progress in these various fields of polycrystal mechanical modeling achieved by our group in terms of methods development and applications was recently published as an overview article in Acta Materialia  and is since its appearance the most downloaded publication of all papers published in this journal. The software developed during the last years was released to the public domain as Düsseldorf Advanced MAterials Simulation Kit (DAMASK) and can be downloaded from the internet: damask.mpie.de. It is already used by several research groups in Europe and the US.
Another growing field of interest are discrete dislocation dynamics (DDD) simulations [35,36]. These models are built on three assumptions. First, the distortions around lattice dislocations are treated as linear elastic fields and are solved piecewise (i.e. for a portion of the dislocation) via the Volterra equation and Hooke’s law. Second, all dislocation lines are decomposed into sequences of connected segments. Third, the dynamics of each segment is solved using a damped viscous form of the equation of motion considering long and short range elastic interactions among all dislocation segments via the Peach-Koehler equation plus external loads. The simulations using the massively parallel ParaDiS code of the Lawrence Livermore National Laboratory (USA)  are computationally highly demanding so that they run on the Blue Gene/P high performance computer of FZ Jülich on up to several thousand processors.
In this field we also aim twofold: First we improve the theoretical foundations of the approach further (e.g. by including dislocation climb) and second apply it to problems where the simulation of small sets of interacting dislocations provides insights into the underlying micromechanics.
Main projects pursued by discrete dislocation simulations are the strengthening effects of small angle grain boundaries [35,36], creep in Ni-based superalloys, and dislocation patterning.
The group pursues two main missions. The first one is the development of advanced microstructure characterization methods focussing during the past years on SEM- and FIB-SEM based approaches. Specific focus is placed on diffraction methods such as high angular and spatial resolution orientation microscopy (HR EBSD) in the SEM, electron channelling contrast imaging (ECCI), internal stress determination via SEM/EBSD, and 3D electron backscatter diffraction (3D EBSD, tomographic EBSD) [6,15,18-22,55-57].
The second main objective of the group lies in the application of these advanced characterization methods with the aim to understand and quantify with high crystallographic precision microstructure evolution phenomena associated with transformation and plasticity mechanisms and the proper characterization of the dislocations and interfaces involved. The metallurgical phenomena of interest are mainly in the fields of polycrystal crystal plasticity (mainly steels, Ni-alloys, and Mg-alloys), twinning and martensitic transformation (in steels with twinning or transformation induced plasticity (TWIP or TRIP)) as well as annealing phenomena.
The group operates several instruments. Among these is a Zeiss Crossbeam XB1560 FIB-SEM for 3D EBSD investigations, a JEOL JSM 6500 F SEM (both with field emission gun), and a Camscan 4 tungsten filament SEM. These instruments are equipped with EBSD analysis hardware and allow mounting micro-deformation machines for in-situ deformation testing. A heating stage is also available for conducting in situ transformation experiments. For ECCI a eucentric 5-axis goniometer stage has been custom-designed by Kleindiek nanotechnology. Transmission electron microscopy (TEM) is performed on a Phillips CM 20. This instrument is equipped with a large angle, high dynamics camera (Olympus) for image and diffraction pattern acquisition and the software TOCA for on-line crystallographic analysis. Furthermore, several XRD goniometers are available.
Research Highlights 2010-2012 including main trends over the past 6 years
Highlight activities of the group during the past two years were the development of a new approach to electron channelling contrast imaging (ECCI), named “controlled ECCI”, or cECCI [15,21,22], Fig. 6. This method improves the existing ECCI method in a way that it uses EBSD to determine the crystal orientation. Based on this the optimum sample alignment for obtaining good channelling contrast is calculated using the computer software TOCA . A dedicated eucentric goniometer stage is then used to move the sample into the calculated position for imaging of dislocations and other crystal defects in the SEM. The approach offers excellent opportunities for the efficient quantification of substructure features at a large field of view that were not accessible so far to SEM characterization, Fig. 7. It can be combined with EBSD maps so that we are now capable of conducting detailed microstructure quantification mappings of orientations together with its inherent dislocation substructure in the same experiment. Tedious and time consuming TEM investigations of dislocation structures that provide a small field of view thus may become obsolete in a number of cases.
A second focus of the group lies in the improved analysis of 3D EBSD data with respect to the characterisation of interface segments. As was shown in the last bi-annual reports it is in principle straight forward to extend the 2D EBSD (electron backscatter diffraction)-based orientation microscopy technique to a 3D technique by collecting sequential sets of 2D maps by serial sectioning, e.g. by mechanical or chemical polishing or sputtering with a focussed ion beam (FIB). 3D EBSD offers unique and novel features to characterize microstructures, in particular the full, 5-parameter grain boundary description but also, for example, the description of connectivity of phases, 3D morphology of crystals, or the determination of geometrically necessary dislocation (GND) densities [20,33]. The 3D EBSD data can be analysed in 2 approaches, either as volume pixels (voxels) or by rendering interfaces and boundaries. While the former method has been discussed in the past reports the interface segment reconstruction is currently the most important pending problem. In our current approach the grain boundary reconstruction consists of two sequential steps; namely, first, in identifying the boundary surface and subsequently translating this surface into a mesh of triangles. A well-known method for boundary reconstruction is the Marching Cubes (MC) algorithm which has been applied for boundary reconstruction from orientation voxels before. The standard MC algorithm suffers from several inherent ambiguities. These ambiguities can be solved by disassembling each cube into unambiguous tetrahedra, resulting in the so-called Marching Tetrahedra (MT) algorithm which leads to better results. Once grain boundaries are established as sets of triangles these boundaries have to be smoothed before any quantitative statements about spatial or crystallographic features of the boundaries can be made. Different smoothing algorithms have been developed and tested. Furthermore a number of algorithms have been developed to display and interpret the crystallographic nature of boundaries in the 5 parameter grain boundary space (3 parameters describing the misorientation and 2 the boundary normal) , Fig. 8.
The algorithms used for interface characterization are part of a large software suite, Qube, which has been developed over the last two years mainly by P. Konijnenberg. It embeds under a user-friendly software interface powerful tools for 3D microstructure characterization. This includes, for example, the calculation of GND densities from the 3D orientation field curvature, the calculation of 3D orientation gradients, 3D rendering of interfaces and the quantitative calculation of grain and boundary textures (Microscopy and Diffraction Group).
A further recent focus of the group is placed on the development and use of EBSD-based methods for the measurement of local elastic (lattice) and plastic strain. In one approach, followed by T. Jaepel, a cross-correlation technique is used to measure the distribution of lattice strains inside of individual crystals of a polycrystal or in single crystal samples. The fact that this technique requires reference patterns of similar orientation limits this technique to special cases and does not allow determining absolute levels of internal stresses. A second approach, therefore, uses a reference pattern-free algorithm to measure absolute lattice strains. A third approach, finally, is followed by F. Ram, who developed the Kikuchi bandlet method to determine with highest accuracy the position of Kikuchi cones from EBSD patterns. These data can then be used to determine the geometrical pattern origin and the lattice distortion with high accuracy. The Kikuchi bandlet method can also be used to determine, from the Kikuchi band profile, the crystal defect density (i.e. the total dislocation density) in the electron beam interaction volume.
Related to the measurements of stress and strain are research initiatives which use in-situ deformation tests to observe strain hardening mechanisms in various materials. Besides local strain measurements with the above mentioned techniques these projects use ECCI and digital image correlation to quantify the local plastic strain. The project was so far mainly pursued by C. Tasan.
Finally, several research initiatives deal with the statistical representativeness of local property measurements. In a project on low alloyed TRIP steels the statistical representativeness of EBSD for phase and texture determination was studied and a new software tool for large area measurements developed . Another project, pursued so far by J. Zhang, deals with the analysis of nanoindentation for measurement of residual stresses. The results are interpreted in terms of dislocation structures that are observed using the cECCI technique, fig. 9.
Alloy Design and Thermomechanical Processing (D. Ponge)
In the past 6 years the group worked mainly on microstructure design and optimization of the mechanical properties of carbon-manganese steels via grain refinement by thermomechanical treatment [55,58-63]. Main examples were the design of advanced ultrastrong spring steels and bulk ultra-fine grain steels. More specific the main alloy systems addressed were ultra fine grained plain C-Mn steels and dual phase (DP) steels for light-weight automotive applications [55,58-63]. The microstructure-oriented optimization of microstructures and properties of novel complex engineering steels via thermomechanical treatment requires a detailed understanding of the relations between processing and microstructure evolution on the one hand and the relations between microstructures and mechanical properties on the other. This two-fold strategy is essential in this field as no direct link exists between processing and properties.
In addition to the development of optimal thermomechanical processes, in the past few years projects increasingly included mechanism-based alloy design strategies [1,15,21,22,64,65]. The reason is that alloy development offers an ideal addition to thermomechanical processing as it gives access to a larger variety of bulk phase transformations, precipitate strategies, and grain refinement mechanisms. The joint design of both, novel alloy variants in accord with thermodynamic and kinetic prediction tools and adequate thermomechanical processing hence describes the current research strategy of the group. In order to probe the composition phase space more efficiently the team closely interacts with the new group on combinatorial materials synthesis and processing (Combinatorial Metallurgy and Processing Group).
Research Highlights 2010-2012 including main trends over the past 6 years
During the past two years the group was mainly concerned with the development of a new alloy class, namely, Mn-based lean maraging-TRIP steels [1,37,38]. The concept is based on combining the TRIP effect with the maraging effect (TRIP: transformation-induced plasticity; maraging: martensite aging) (Alloy Design and Thermomechanical Processing Group). The Fe-Mn-based maraging-TRIP alloys combine different hardening mechanisms. The first one is the formation of strain-induced martensite (alloys with 0.01 wt.% C and 12 wt.% Mn have retained austenite fractions up to 15 vol.%) and exploits the same hardening principles as TRIP steels. The second effect is the strain hardening of the already transformed ductile, low carbon α’- and ɛ-martensite phases and of the remaining retained austenite. The third effect is the formation of nano-sized intermetallic precipitates in the martensite during heat treatment. These precipitates have high dispersion owing to the good nucleation conditions in the heavily strained martensite matrix in which they form. The fourth one is the formation of nanoscaled re-austenitization layers on the formerly segregation-decorated martensite grain boundaries during the maraging heat treatment. This combination of mechanisms leads to the surprising property that both strength and total elongation jointly increase upon martensite aging (e.g. 450°C, 48 hours) reaching an ultimate tensile strength of nearly 1.3 GPa at an elongation above 20% [37,38].
Specifically the occurrence of nano-scaled re-austenitization layers at the martensite grain boundaries seems to have a beneficial effect on the blunting of cracks rendering the martensite ductile. This effect could be realized in a second alloy class, namely, in a martensitic Fe–13.6 Cr–0.44 C (wt.%) martensite steel. After tempering the martensite was rendered into an ultra-high-strength ferritic stainless steel with excellent ductility. The nanoscale austenite reversion mechanism that occurred in this alloy 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 °C for 1 min produces a 2 GPa ultimate tensile strength (UTS) and 14% elongation while 30 min at 400 °C results in a UTS of 1.75 GPa with an elongation of 23% .
A third group of steels that is being addressed jointly by this group and the new group on combinatorial alloy design are weight-reduced austenitic or austenitic-ferritic steels. These are steels with up to 30wt.% Mn, up to 8 wt.% Al and up to 1.2 wt.% C which are sometimes also referred to as TRIPLEX steels owing to their two- or three phase composition. They are characterized by about 10% reduced specific weight and excellent stress-ductility profiles, Fig. 10. Depending on heat treatment and composition they can contain nanostructured kappa carbides .
Most biological materials with structural functions consist of an organic matrix of structural biopolymers like collagen and chitin, which is modified and reinforced with different proteins and in many cases also with biominerals. The most prominent examples like the bones of vertebrates, the exoskeletons of arthropods, and mollusk shells are known to possess optimized function-related physical properties (e.g., mechanical properties: stiffness-to-density ratio and fracture toughness). The origins of these properties, particularly the underlying structure/composition/property relations, are the research subject of this group [66-70].
In our work on mineralized chitin-based arthropod cuticle we found out that the specific design and properties at the nanoscale contribute significantly to their macroscopic properties. Evidently, the overall properties depend on the specific microstructure at all levels of hierarchy [8,71]. However, especially the properties at small length scales are experimentally hard, if not impossible, to access due to methodological constraints. Hence, multiscale modeling that can systematically describe and investigate materials properties from the atomistic scale up to the macroscopic level has become a major approach in the group in close cooperation with the department of J. Neugebauer to tackle the structure/property relations of biological organic/inorganic nanocomposites. The method has been applied to bone and crustacean cuticle [8,72,73]. In addition to modeling fully differentiated structural composites, the approach has also been applied to model the mechanical properties of individual constituents and explain the structure/property relations on increasingly complex structural hierarchy levels.
Research Highlights 2010-2012 including main trends over the past 6 years
The cuticle of Arthropoda is a continuous tissue that covers the entire body. In order to function as an exoskeleton, it has to form skeletal elements with physical properties that are adapted to specific functions which are very diverse, like providing mechanical stability in the shell of body segments, elasticity in arthrodial membranes, or wear resistance and friction reduction in joint structures and mandibles. The required properties for each skeletal element are adjusted by local modifications in structure and composition. The transitions between parts with different properties are brought about by structural interfaces, which are generated on different hierarchical levels. Employing our established experimental approaches, we investigate the nature of such interfaces in functionally differentiated cuticle parts such as mandibles of Crustacea species with different feeding habits and transitions between mineralized load-bearing cuticle and unmineralized arthrodial membranes. Since our theoretical multi-scale model can only predict the average elastic properties of cuticle, we developed a hierarchical model for the elasto-viscoplastic cuticle properties at large deformations using a Fast Fourier Transforms (FFT) approach that is able to describe the local development of stress and strain fields within the material, including those at the interfaces.
In addition to serving as exoskeleton, the cuticle of Arthropoda also plays an important role for the ecophysiology of the organisms by forming photonic crystals that generate colors through scattering of light by photonic band gap materials. We use the cuticle of various beetle species to both experimentally and theoretically investigate the structure and resulting optical properties of photonic crystals as found in the small scales covering the beetle Entimus imperialis. They consist of a diamond-structured cuticular network and air, where the structural parameters are optimized to produce the brightest colors possible by maximizing band gaps width. In some scales, this effect is turned into the opposite, transparency, through alteration of the refractive index contrast by substitution of the air with SiO2. In collaboration with the group of Prof. Zollfrank (TU Munich), this biological photonic crystal has been biomimetically transferred into identical silica replicas with tunable structural parameters. Based on these results, we started to combine experiments and theory to develop biomimetic photonic crystals with tailored optical and mechanical properties for potential mechanochromic applications.
Over the last years, we expanded our studies on structure/property relations in biological composites beyond mechanical properties with particular focus on multifunctional parts, property transitions and different and/or unusual property combinations with the aim to expand the knowledge necessary to develop corresponding synthetic materials.
The group was opened in 2010 and has since then seen very rapid growth in terms of topics and personnel. Atom Probe Tomography (APT) is a characterization technique enabling spatially resolved chemical analyses of materials at sub-nanometer resolution (in-plane: ≈0.2 nm; in-depth: ≈0.1 nm) [1,9,11,14,17,41-43]. The instrument (Imago Scientific Instruments, LEAP 3000X HR) is equipped with a local electrode, a wide-angle reflectron, a high-speed delay line detector system as well as an ultrafast laser with a pulse width of 10 ps and wavelength of 510 nm. Such an instrument design has numerous advantages over conventional atom probes, particularly regarding the analysis of alloys with complex chemical composition. The local electrode enhances the electric field at the specimen and allows fast pulsing (max. 200 kHz) at low voltage. A high-speed delay line detector system provides fast data acquisition rates of up to 2 Mio ions/min. Due to the proximity between specimen and detector, the field of view can be as large as 200 nm. As a result, large volumes, which can contain up to several hundred millions of atoms, can be probed within a few hours. The wide-angle reflectron substantially enhances the mass resolution of this instrument. Complex multi-component systems can therefore be analyzed at high compositional accuracy. Furthermore, impurity concentrations as low as few tens of ppm can be detected. The ultra-fast laser extends the applicability of this technique to materials having low electrical conductivity such as semiconductors and ceramics [10,11].
The research objectives of the group are in two fields. The first one is the near-atomic scale analysis of interface-related phenomena, such as segregation, partitioning and associated local thermodynamic and kinetic phenomena, for instance phase transformations at grain boundaries [1,14]. Owing to the capability of instrument to probe samples with small electrical conductive in Laser excitation mode, increasingly also interfaces and quantum well structures of functional polycrystalline materials are studied.
The second aim of the group lies in comparing atom probe tomography observations quantitatively with theoretical predictions. For this purpose we use ThermoCalc and Dictra approaches as well as ab initio predictions in conjunction with kinetic Monte Carlo methods. While the former set of statistical simulations are mainly conducted in close collaboration with G. Inden and the group of D. Ponge (Alloy Design and Thermomechanical Processing) the latter calculations are done in the department of J. Neugebauer in the group of T. Hickel (Computational Phase Studies).
Research Highlights 2010-2012 including main trends over the past 3 years
The group studies both, functional and structural materials. Examples are thin-film solar cells (based on Cu(In,Ga)Se2 and CdTe) and light-emitting diodes (based on III-V semiconductors) , as well as Al- and Cr-Nitride multilayer hardcoatings. Regarding metallic alloys essential research topics are the formation of nanoscaled re-austenitization films on martensite grain boundaries in Fe-Cr-C and Fe-Mn steels; interfaces in Ni-based superalloys, Fig. 11 ; the stabilization of ferrite nanograins in mechanically alloyed and heavily deformed pearlite by massive carbon decoration of the grain boundaries [41-43]; the formation of Cu-based nano-precipitates in Fe-Si-Cu soft magnetic steels; partially crystalline soft magnetic metallic glasses; and nano-structured carbides in weight reduced Fe-Mn-Al-C steels, Fig. 12. The group is currently financed through the remaining funds of Prof. Raabe's Leibniz Award (German Research Foundation, DFG).
The group was founded in 2005 as the first joint research group between the Max-Planck-Society and the Fraunhofer-Society (Fraunhofer-Institut für Werkstoffmechanik IWM, Freiburg). Funding was jointly provided by the Max-Planck and Fraunhofer-Societies. The group develops theoretical approaches for the mechanics and damage initiation of textured polycrystalline matter with the aim to promote its use for industrial applications such as encountered in the fields of metal forming and microstructure mechanics.
Research Highlights 2010-2012 including main trends over the past 6 years
In the past years the group has pursued the following goals in collaboration with the group for Theory and Simulation (F. Roters) [16,50,74,75]: The first direction was the development of an advanced homogenization schemes [77,78]. This model calculates the stress for a group of interacting crystals under an external given boundary condition considering internal relaxations among the abutting crystals. Such approaches allow polycrystal simulations at a scale above the full-field crystal plasticity finite element schemes. A novel approach, referred to as Relaxed Grain Cluster model (RGC), was developed and successfully applied to steels. This method does not only improve existing homogenization schemes for polycrystal mechanics but it can also be used as a homogenization method for multiphase polycrystalline materials, such as for instance for TRIP steels.
The second aim of the group was the development of advanced constitutive models that describe the individual deformation behaviour inside the crystals. Of particular interest was the development of constitutive models that include deformation twinning and its interaction with dislocation slip . Also, an improved mean-field dislocation flux model is being developed that communicates dislocation streams and balances reaction as well as annihilation rates among neighboring field integration points according to the local boundary conditions. This flux formulation naturally accounts for the build up of geometrically necessary dislocations and the associated local stress peaks.
The third area of interest is the role of heterogeneous deformation on damage nucleation at grain boundaries in single phase metals . This work is done in close cooperation between our department (P. Eisenlohr) and T.R. Bieler and M.A. Crimp from Michigan State University in East Lansing, USA, and Professor D.E. Mason from Albion College in Albion, USA. The project aims to understand which mechanical criteria determine where and why cracks or voids form in a strained polycrystal particularly at grain boundaries. This project is jointly funded by the US and German research foundations, NSF and DFG.
The group for the simulation of complex fluids is rooted both at the ICAMS at Ruhr-University Bochum and at MPIE. Its field is the study of the structural and mechanical properties of complex multiphase and colloidal fluids [79-85]. Typically, fluids can be deformed already when being exposed to weak forces such as in the case of shear melting. This effect often goes along with a drop in shear viscosity upon increasing shear rate. This phenomenon is referred to as shear thinning. The relation between the stress and deformation for a complex fluid is often non-linear. There is a wide field of applications of complex fluid mechanics, for instance in polymer processing, metallurgical processing [86,87], and biology [81,82]. As a modeling method we mainly use the lattice Boltzmann method (LBM) and multiphase variants thereof [62-68]. LBM is well suited for the numerical calculation of fluid flow, heat, and solute transport. Unlike Navier-Stokes solvers, the LBM mimics flows as collections of pseudo-particles that are represented by a velocity distribution function. These fluid portions reside and interact on the nodes of a grid. System dynamics emerge by the repeated application of local rules for the motion, collision, and re-distribution of the fluid particles. The method is an ideal approach for mesoscale and scale-bridging simulations owing to its computational efficiency and versatility in terms of constitutive description of its pseudo-particles. Also it can be efficiently cast into parallel codes. In particular, LBM exhibits good numerical stability for simulating complex fluids, such as multi-phase and multi-component flow phenomena under complicated boundary conditions. Since LBM describes fluid motion at the level of the distribution functions, it can be naturally coupled with related simulation techniques such as cellular automata or phase field models [86,87].
Research Highlights 2010-2012 including main trends over the past 6 years
The group investigates problems in micro-fluidics such as inhomogeneous diffusive broadening, droplet and contact dynamics on chemically and topographically patterned substrates as well as flow between topographically rough walls. On the nano-scale, on the other hand, the group focuses on the effects of thermal fluctuations on droplet dynamics. Furthermore, the group has also developed efficient parallel LBM variants that are recently particularly used for the study of blood flow mechanics [64,68]. These studies have proved very fruitful with a number of interesting observations as well as theoretical predictions, the latter being verified by independent computer simulations. To name just a few examples, we mention the observation of instantaneous droplet motion on a gradient of texture, and the discovery of new types of wetting states in the case of small droplets with a size comparable to the roughness scale .
The group for Intermetallic Materials was initially part to the department of the late Prof. Frommeyer and is currently closely cooperating with us on high temperature materials and iron-aluminides. Since October 2012 it is part of the new department of G. Dehm.
Key interdisciplinary research fields of the department
The groups introduced above represent the main competence centers of the department. Our mission, however, aims beyond these fields, i.e. we additionally pursue a number of joint grand challenges tackling of which requires efficient bundling of these skills. Some cross-disciplinary and cross-departmental topics are described in the research highlight section. Here, we introduce some main inter-disciplinary research fields where the different groups team up and conduct long-term fundamental research. In the past years three main areas prevailed, namely:
I) Designing intrinsically nanostructured metallic alloys
II) Advanced characterization of complex materials
III) Predictive and quantitative multiscale models
In the following we give a concise introduction into our respective approaches:
I New materials: Mechanism-oriented design of intrinsically nanostructured metallic alloys
The design of advanced high strength and damage tolerant metallic alloys for energy, mobility, safety, health and infrastructure applications forms the engineering and manufacturing backbone of our modern society. Examples are creep-resistant steels and Ni-alloys  in power plants and plane turbines; ultrahigh strength steels [1,14,21,39,44], Ti-, and Mg-alloys for light-weight mobility and aerospace design [2,3]; metallic glasses for low-loss functional components; or biomedical Ti-implant alloys in aging societies .
Since the Bronze Age the design of novel metallic alloys was based on trial and error approaches, owing to the complexity of the physical and chemical mechanisms involved and the engineering boundary conditions imposed during synthesis and manufacturing. This traditional method has two shortcomings. First, current alloy design is not based on systematic design rules but on metallurgical experience alone. This renders the development of novel alloys inefficient. Second, the increase in strength via traditional hardening mechanisms such as solute solution, increase in dislocation density, or second phase precipitates, albeit leading to a high strength level, always causes a dramatic decrease in ductility, i.e., making the material brittle and much more susceptible for failure.
The joint research field of designing new metallic alloys aims at solving this inverse strength-ductility problem: The recent achievements in ab initio modeling and atomic scale characterization methods presented above and in some of the highlight papers open a fundamentally new pathway to the systematic and knowledge-based design of next generation metallic alloys. The objective is to use these methods to identify and utilize strengthening mechanisms that enable us to overcome the inverse relationship between strength and ductility. The key idea to better reconcile high strength and high ductility is to incorporate second phases into bulk alloys that are close or even beyond their mechanical and thermodynamic stability limit. While this sounds at a first glance counterintuitive – in the end we aim at materials with superior mechanical stability – the well-controlled inclusion of topologically confined phases with reduced stability provides a method to stimulate finely dispersed deformation-driven displacive transformations. Optimizing the degree of instability, dispersion, and volume mismatch associated with transformations allows one to tailor compliant microstructures that reduce damage initiation. The novelty of the approach is that the transformation occurs only in regions with high local stress concentrations and, hence, acts as spatially localized self-organized repair mechanisms against localization softening and premature internal damage owing to its associated strain hardening and compressive stresses. This new principle of designing higher mechanical stability of metallic alloys by including instable phases carries the potential to deviate from the inverse strength-ductility principle that currently sets a limit to advanced engineering alloys.
The cornerstones for this systematic alloy design approach are a better understanding of the thermodynamics and kinetics of instable phases; the bulk combinatorial lean synthesis, processing, and probing of corresponding alloy classes; and the discovery of the governing strain hardening mechanisms and their interactions.
Regarding the first aspect, the use of novel theoretical tools such as ab initio simulations (department of J. Neugebauer) in conjunction with established thermodynamic and kinetic simulation tools such as ThermoCalc and Dictra, combined ab initio and Thermocalc predictions in conjunction with local experimental analysis are conducted to discover composition and processing niches where phase instability can be exploited to lead to stronger and yet more ductile mechanical response. The second method, namely the combinatorial manufacturing of corresponding bulk specimens is described in a separate highlight article (### reference to Springer - new group). The third aspect, i.e. the understanding of new strain hardening effects requires the use of careful high resolution and at the same time wide field of view characterization methods such as the quantitative electron channelling contrast imaging, TEM, and atom probe tomography. Regarding the interplay of the thermodynamics of instable phases and the strain hardening effects that may result from local transformations we observed that it is vital to design the phase stability and hence the strain hardening as a sequence of gradually activated mechanisms that do not occur at the beginning of loading but gradually at later deformation stages, i.e. during ongoing loading at higher deformations.
Examples for successful new alloy design directions resulting from this strategy are maraging TRIP steels, TWIP– and TRIPLEX steels, Ti- and Fe-based GUM alloys, and ductile Mg.
A further essential detail pertaining to this strategy is the observation that the nanostructuring of such instable second phases leads in many cases to a profound increase in ductility without loss in strength. Examples are novel superplastic steels ; ultra-fine grained dual phase and C-Mn steels [55,58-63]; ultrastrong maraging-TRIP steels that are rendered ductile by the stabilization of retained austenite, formation of new instable re-austenitization layers on the former martensite lath grain boundaries, and intermetallic nano-precipitates, Figs. 13,14 [1,14]; nanotwin formation in Fe-Mn-C TWIP steels [15,21]; amorphous steels containing nanocrystalline second phases; weight-reduced Fe-Mn-Al-C steels containing nano-sized kappa carbides, Fig. 12 ; and nanostructured pearlite [41-43], Fig. 15. Regarding the latter material we currently hold the record of the world’s strongest bulk structural alloy having a yield strength of about 6.3 GPa .
II New insights: Advanced characterization of complex materials
The second field of long term developments is the development of a hierarchy of characterization methods that matches the hierarchy inherent in complex metallic micro- and nanostructures. This means that we require adequate structure and composition mapping at all scales that matter for understanding and quantifying the lattice defect populations that lead to the desired mechanical properties addressed above.
Mesoscopic characterization of the chemical and microstructural homogeneity of cast, formed, and heat treated samples can be conducted by using optical and scanning electron microscopy (SEM) in conjunction with EDX (energy dispersive x-ray spectrometry) and high resolution EBSD (electron back scatter diffraction). As suited SEM for this purpose we usually use a JEOL JSM-6500F field emission scanning electron microscope (FE-SEM) operated at 15 kV. The EBSD scans can be carried out in large areas or at high resolution down to a step size of 40 nm for the determination of phase patterning. When the 3D topology of the second phases is of high relevance 3D EBSD can also be used. This device consists of a dual beam set-up where we use fully automated serial sectioning and EBSD scanning cycles to reconstruct the microstructures in full 3D (Microscopy and Diffraction Group).
Strain-hardening phenomena in crystalline metallic act essentially through the reduction of the dislocation mean free path, for instance, through smaller grain sizes (UFG), mechanical twins (TWIP), cell walls, or phase transformations (TRIP). All these additional interfaces act as obstacles to dislocation glide. Mechanical twins in TWIP steels are extremely thin, and hence are generally studied by transmission electron microscopy (TEM). However, TEM is limited when it comes to the quantitative microstructural characterization of highly heterogeneous microstructures, such as encountered in deformed TWIP steels. Another microscopy technique for characterizing deformed microstructures is electron channeling contrast imaging (ECCI). ECCI is a scanning electron microscopy (SEM) technique that makes use of the fact that the backscattered electron intensity is strongly dependent on the orientation of the crystal lattice planes with respect to the incident electron beam due to the electron channeling mechanism [15,21,22]. Slight local distortions in the crystal lattice due to dislocations cause a modulation of the backscattered electron intensity, allowing the defect to be imaged. For quantitative characterization of dislocation structures (e.g. Burgers vector analysis) and to image these structures with optimal contrast, it is required to conduct ECCI under well-controlled diffraction conditions as dislocation imaging is obtained by orienting the crystal matrix exactly into Bragg condition for a selected set of diffracting lattice planes. To date the only method that was utilized for performing ECCI of dislocations under controlled diffraction conditions is based on electron channeling patterns (ECPs). The drawback of this technique is the requirement of a large final aperture to allow the beam to cover a large angular regime, leading to very low spatial resolution which is almost two orders of magnitude above the resolution of EBSD. This shortcoming reduces its application to the imaging of dislocation structures in lightly deformed metals. This also explains the limited number of works on the use of ECCI for imaging dislocation structures. In the past years we have developed a novel set-up for the ECCI technique under controlled diffraction conditions where the crystal orientation is obtained by means of EBSD. This set-up provides an efficient and fast means to perform ECCI of dislocations under controlled diffraction conditions with enhanced dislocation and interface contrast [15,21,22].
When higher resolutions are required for nanostructure analysis, transmission electron microscopy (TEM) is applied. For TEM sample preparation the material is usually first thinned to a thickness below 100 µm by mechanical polishing. Standard 3-mm TEM discs are then punched and electropolished into TEM thin foils using a Struers Tenupol twin-jet electropolishing device. The electrolyte consisted of 5% perchloric acid (HClO4) in 95% ethanol cooled to −30°C. Alternatively FIB thinning is possible too using our FEI nanolab dual beam system. The thinned specimens can then be investigated in the field emission transmission electron microscope JEOL JEM 2200 FS operated at 200 kV. The analysis are usually carried out in scanning TEM mode (STEM) using a bright field (BF) detector.
For yet higher resolution, specifically regarding the local chemical composition, nanostructure characterization via atom probe tomography (APT) is conducted. APT characterization is highly suited to study and understand nanostructural changes in non-equilibrium alloys such as addressed by our group [1,9]. Its results can be compared to ab initio or conventional thermodynamic predictions regarding chemical phase composition or partitioning. APT characterization is carried out using a state-of-the-art local electrode atom probe. This instrument provides three-dimensional elemental maps in real space with a maximum field of view of 200 nm. Both, structural and spatially resolved chemical analyses can be realized with sub-nanometer resolution. Special features of the installed instrument are a wide-angle reflectron, which enable high mass resolution (and therefore the analysis of multi-component alloys and detection of low elemental concentrations) and an ultrafast laser, which allows for the analysis of non- and semi-conducting materials. By applying high-resolution electron microscopy as a complementary technique, we are capable of identifying not only the thermodynamic and compositional but also the structural information at near atomic resolution, Fig. 16.
III New predictions: Multiscale models for quantitative simulations
For the alloy design strategy outlined above the prediction of accurate phase diagrams and of non-equilibrium phase transformations is a key element. While equilibrium data for stable phases is straightforward to measure and thus commonly available with high precision it is principally impossible to synthesize unstable bulk phases. Deducing their thermodynamic or mechanical properties is therefore only indirectly possible by e.g. epitaxially stabilizing such phases on suitable surface substrates (restricted to thin films only) or by extrapolating from the stable regime into the unstable one. In both cases the practical applicability is limited, often requires complex and expensive experimental setups, and provides large and often hard to estimate error bars. Ab initio calculations as a basis for searching unstable phases such as conducted on the department of J. Neugebauer is hence the basis and starting point for corresponding multiscale simulations of corresponding strain hardening phenomena that are based on non-equilibrium transformations (e.g. in TRIP, TWIP or GUM steels) [1,3].
To overcome the gap between the scale that is accessible to corresponding ab initio calculations predicting for instance phase stability, these data must enter into mechanism-based strain hardening models at the lattice defect scale. Examples are the use of ab initio calculated stacking fault energy values in a Fe-Mn steel that enter as an activation barrier into the cross slip term of a dislocation rate model or into the activation stress of a mechanical twinning event. Such multiscale approaches are often not restricted to bridging length scales but equally important to bridge time scales or sampling high dimensional configuration spaces.
Important examples from the past 6 years where such hierarchical scale-bridging concepts were realized in cooperation projects between our department and that of J. Neugebauer were the prediction of elastic constants of polycrystals by combining single crystal ab initio calculated elastic tensors with homogenization concepts developed in theoretical mechanics; the brittle-to-ductile transition behavior of MgLi alloys over the entire composition range; the activation of mechanical twinning in TWIP steels as a function of chemical composition and stress levels; the prediction of B2 and Heusler-type nano-particles in maraging steels (Alloy Design and Thermomechanical Processing Group), and Ti-based instable BCC and related Gum alloys which are characterized by large plastic yet hardening-free deformations (Adaptive Structural Materials Group). Further details about some of the developed multiscale concepts were part of the last bi-annual report.
Spirit and Outreach
Projects within our group and also among the departments are pursued in an interdisciplinary and team-oriented spirit. Scientists in our department come from such different backgrounds as metallurgy, physics, materials science, mechanical engineering, informatics, chemistry, and biology. Projects are conducted in an atmosphere of mutual inspiration, respect, communication, and cooperation. Paramount to the success of our work is the close exchange among theorists and experimentalists and an open minded attitude among the different disciplines.
The working atmosphere was during the past years dominated by an international flair bringing together young scientists and visiting scholars from Argentina, Australia, Bangladesh, Belgium, Brazil, Bulgaria, Colombia, China, Egypt, France, Germany, India, Indonesia, Iran, Japan, Jordan, Korea, Mexico, Nigeria, Romania, Russia, Sweden, Spain, Ukraine, Poland, The Netherlands, Turkey, UK, Ukraine, USA, and Venezuela. Our international orientation is also reflected by our extramural cooperation partners, namely, Prof. Schneider, Prof. Bleck, Prof. Mayer, Prof. Friedrich, and Prof. Gottstein (RWTH Aachen, Germany), Prof. Rollett and Prof. Rohrer (Carnegie Mellon University, USA), Prof. Lebensohn (Los Alamos, USA), Prof. Radovitzky (MIT, USA), Prof. Mao (University of Science and Technology Beijing, China), Prof. Sandim (University of Lorena, Brazil), Prof. Bieler and Prof. Crimp (Michigan State University, USA), Prof. Mason (Albion College, USA), Prof. Hono and Prof. Adachi (National Institute for Materials Science, Japan), and Prof. Kobayashi (Tohoku University, Japan).