#### Dr. Rebecca Janisch

Micromechanical and Macroscopic Modelling at ICAMS

Ruhr-Universität Bochum

##### Contact

##### Hub

**Efficient Prediction of Grain Boundary Energies from Atomistic Simulations via Sequential Design**

Kroll, M. and Schmalofski, T. and Dette, H. and Janisch, R.*Advanced Theory and Simulations*5 (2022)view abstract 10.1002/adts.202100615 **Unravelling the lamellar size-dependent fracture behavior of fully lamellar intermetallic γ-TiAl**

Neogi, A. and Janisch, R.*Acta Materialia*227 (2022)Strengthening of metals by incorporating nano-scale coherent twin boundaries is one of the important breakthroughs of recent years in overcoming the strength-ductility trade-off. To this effect, also twin boundaries in nano-lamellar lightweight Ti-Al alloys promise a great potential, but their contribution to the deformation and fracture behavior needs to be better understood for designing optimal microstructures. To this end, we carry out linear elastic fracture mechanics informed large-scale atomistic simulations of fully lamellar microstructures consisting of the so-called ”true twin” boundaries in γ-TiAl. We find that nano-scale lamellae are not only effective in improving the fracture toughness and crack growth resistance, but also that the lamellar size controls the crack tip mechanisms. We identify a critical lamella thickness in the region between 1.64 and 3.04 nm, above which the crack tip events are primarily dislocation-based plasticity and the critical fracture initiation toughness exhibits an increasing trend with decreasing lamella size. Below the critical thickness, a decline in fracture toughness is observed and the crack tip propagation mechanisms are quasi-brittle in nature, i.e. the cleavage of atomic bonds at the crack tip is accompanied by plasticity events, such as twin-boundary migration and dislocation nucleation. A layer-wise analysis of the unstable stacking fault energy, the energy barrier for dislocation nucleation, that the critical thickness is of a similar value as the distance from the twin boundary at which bulk properties are restored. © 2022view abstract 10.1016/j.actamat.2022.117698 **Influence of temperature on void collapse in single crystal nickel under hydrostatic compression**

Prasad, M.R.G. and Neogi, A. and Vajragupta, N. and Janisch, R. and Hartmaier, A.*Materials*14 (2021)Employing atomistic simulations, we investigated the void collapse mechanisms in single crystal Ni during hydrostatic compression and explored how the atomistic mechanisms of void collapse are influenced by temperature. Our results suggest that the emission and associated mutual interactions of dislocation loops around the void is the primary mechanism of void collapse, irrespective of the temperature. The rate of void collapse is almost insensitive to the temperature, and the process is not thermally activated until a high temperature (1200-1500 K) is reached. Our simulations reveal that, at elevated temperatures, dislocation motion is assisted by vacancy diffusion and consequently the void is observed to collapse continuously without showing appreciable strain hardening around it. In contrast, at low and ambient temperatures (1 and 300 K), void collapse is delayed after an initial stage of closure due to significant strain hardening around the void. Furthermore, we observe that the dislocation network produced during void collapse remains the sample even after complete void collapse, as was observed in a recent experiment of nickel-base superalloy after hot isostatic pressing. © 2021 by the authors.view abstract 10.3390/ma14092369 **MD simulation study on defect evolution and doping efficiency of p-type doping of 3C-SiC by Al ion implantation with subsequent annealing**

Wu, J. and Xu, Z. and Liu, L. and Hartmaier, A. and Rommel, M. and Nordlund, K. and Wang, T. and Janisch, R. and Zhao, J.*Journal of Materials Chemistry C*9 (2021)We use molecular dynamics (MD) simulation with numerical characterisation and statistical analysis to study the mechanisms of damage evolution and p-type doping efficiency by aluminum (Al) ion implantation into 3C silicon carbide (SiC) with subsequent annealing. By incorporating the electronic stopping power for implantation, a more accurate description of the atomic-scale mechanisms of damage evolution and distribution in SiC can be obtained. The simulation results show a novel observation that the recrystallization process occurs in the region below the subsurface layer, and develops from amorphous-crystalline interface to the damage center region, which is a new insight into previously published studies. During surface recrystallization, significant compressive stress concentration occurs, and more structural phase transition atoms and dislocations formed at the damage-rich-crystalline interface. Another point of interest is that for low-dose implantation, more implantation-induced defects hamper the doping efficiency. Correspondingly, the correlation between lattice damage and doping efficiency becomes weaker as the implant dose increases under the same annealing conditions. Our simulation also predicts that annealing after high temperature (HT) implantation is more likely to lead to the formation of carbon vacancies (VC). © The Royal Society of Chemistry 2021.view abstract 10.1039/d0tc05374k **On the role of pre-existing defects in influencing hardness in nanoscale indentations — Insights from atomistic simulations**

Chauniyal, A. and Dehm, G. and Janisch, R.*Journal of the Mechanics and Physics of Solids*154 (2021)Using in-situ nanoindentation experiments it is possible to study the dislocation mechanisms which unfold under an indenter.Large-scale atomistic simulations of the same are possible due to similarities in length scale, provided that defects can be included in the simulation. Yet, nanoindentation simulations have so far been mostly undertaken on defect free samples, while studies with pre-existing defects are few. The latter show that the average hardness is not affected by the presence of pre-existing defects, which justifies the use of ideal crystals in such simulations. However, this observation is counter-intuitive, as indenter-defect interactions should lead to work hardening and manifest themselves in hardness calculations. Our simulations along with a new look at the evolution of dislocations under the indenter, show for the first time, that hardness in atomistic simulations is influenced by pre-existing defects in the sample. Utilizing a face-centred tetragonal TiAl bicrystal with misfit dislocations at the interface, to populate the sample with defects, we correlate the contact-pressure variations to defect-indenter interactions. We show that the measured contact-pressure is affected by the presence and nature of defects under the indenter. Dislocation pile ups lead to intermittent rise in contact pressure, while seamless growth leads to steady convergence. The sensitivity to detect such defect interactions depends upon indenter size while convergence to average hardness is a result of curvature accommodation near the surface. Our findings prove that pre-existing defects have a profound influence on calculated hardness in indentation simulations which also corroborates with experimental observations in the literature. © 2021 Elsevier Ltdview abstract 10.1016/j.jmps.2021.104511 **Twin-boundary assisted crack tip plasticity and toughening in lamellar γ-TiAl**

Neogi, A. and Janisch, R.*Acta Materialia*213 (2021)The internal twin-boundaries in lamellar γ-TiAl alloys, namely true-twin (TT), rotational boundary (RB), and pseudo-twin (PT), are known to be effective in strengthening the TiAl microstructures. Nevertheless, for designing microstructures with optimised mechanical properties, a better understanding of the role of these boundaries on fracture behavior is still required. To this end, we study how and to what degree crack advancement is affected by the local lattice orientation and atomic structure at the various twin boundaries. Molecular statics simulations were performed in conjunction with a linear elastic fracture mechanics based analysis, to understand the inter-lamellar and as well as trans-lamellar crack advancement at a TT, RB, and PT interface. The fracture toughness as well as the crack advancement mechanisms of the inter-lamellar cracks depend critically on the propagation direction. For instance, cracks along 〈112¯] in the TT, RB, and PT plane always emit dislocations at the crack tip, while the cracks along the opposite direction are brittle in nature. When it comes to trans-lamellar crack advancement, the crack tip shows significant plastic deformation and toughening for all interfaces. However, at a TT, a brittle crack is able to penetrate through the interface at a higher applied load, and propagates in the adjacent γ′ phase, while in the case of RB and PT, the crack tip is blunted and arrested at or near the boundary, resulting in dislocation emission and crack tip toughening. This suggests that a variation of the sequence of the different rotational boundaries could be a possibility to tune the crack tip plasticity and toughening in lamellar TiAl. © 2021 The Author(s)view abstract 10.1016/j.actamat.2021.116924 **Amorphization-governed elasto-plastic deformation under nanoindentation in cubic (3C) silicon carbide**

Zhao, L. and Alam, M. and Zhang, J. and Janisch, R. and Hartmaier, A.*Ceramics International*46 (2020)Amorphization plays an important role in ceramic deformation under mechanical loading. In the present work, we investigate the elasto-plastic deformation mechanisms of monocrystalline cubic silicon carbide (3C–SiC) in spherical nanoindentation by means of molecular dynamics simulations. The indentation-induced amorphization and its interactions with other deformation modes are emphasized. Initially, the suitable empirical potential capable of accurately characterizing the mechanical and defect properties of monocrystalline 3C–SiC, as well as the propensity of phase transformation from 3C–SiC to amorphous SiC, is rationally selected by benchmarking of different empirical potentials with experimental data and density functional theory calculations. Subsequently, the inhomogeneous elastic-plastic transitions during nanoindentation of monocrystalline 3C–SiC, as well as their dependence on crystallographic orientation, are investigated. Phase transformations including amorphization are analyzed using combined methods based on radial distribution function and bond angle distribution. Our simulation results demonstrate that before plasticity initiation-related “pop-in” event, each indented-monocrystalline 3C–SiC experiences a pure quasi-elastic deformation governed by the formation of amorphous structures. And this process of amorphization is fully reversible for small indentation depths. Further amorphization and dislocation nucleation jointly dominate the incipient plasticity in 3C–SiC nanoindentation. It is found that the indentation-induced defect zone composed of amorphous phase and dislocations is more pronounced in 3C–SiC(010) than that in the other two orientations of (110) and (111). © 2020 Elsevier Ltd and Techna Group S.r.l.view abstract 10.1016/j.ceramint.2020.02.009 **Anisotropic failure behavior of ordered intermetallic TiAl alloys under pure mode-I loading**

Neogi, A. and Alam, M. and Hartmaier, A. and Janisch, R.*Modelling and Simulation in Materials Science and Engineering*28 (2020)Whether a metallic material fractures by brittle cleavage or by ductile rupture is primarily governed by the competition between cleavage and dislocation emission at the crack tip. The linear elastic fracture mechanics (LEFM) based criterion of Griffith, respectively the one for dislocation emission of Rice, are sufficiently reliable for determining the possible crack tip propagation mechanisms in isotropic crystalline metals. However, the applicability of these criteria is questionable when non-cubic, anisotropic solids are considered, as e.g. ordered intermetallic TiAl phases, where slip systems are limited and elastic anisotropy is pronounced. We study brittle versus ductile failure mechanisms in face-centered tetragonal TiAl and hexagonal Ti3Al using large-scale atomistic simulations and compare our findings to the predictions of LEFM-based criteria augmented by elastic anisotropy. We observe that the augmented Griffith and Rice criteria are reliable for determining the direction dependent crack tip mechanisms, if all the available dislocation slip systems are taken into account. Yet, atomistic simulations are necessary to understand crack blunting due to mixed mechanisms, or shear instabilities other than dislocation emission. The results of our systematic study can be used as basis for modifications of the Griffith/Rice criteria in order to incorporate such effects. © 2020 The Author(s). Published by IOP Publishing Ltd.view abstract 10.1088/1361-651X/aba738 **Hydrogen embrittlement at cleavage planes and grain boundaries in bcc iron—revisiting the first-principles cohesive zone model**

Guzmán, A.A. and Jeon, J. and Hartmaier, A. and Janisch, R.*Materials*13 (2020)Hydrogen embrittlement, which severely affects structural materials such as steel, comprises several mechanisms at the atomic level. One of them is hydrogen enhanced decohesion (HEDE), the phenomenon of H accumulation between cleavage planes, where it reduces the interplanar cohesion. Grain boundaries are expected to play a significant role for HEDE, since they act as trapping sites for hydrogen. To elucidate this mechanism, we present the results of first-principles studies of the H effect on the cohesive strength of α-Fe single crystal (001) and (111) cleavage planes, as well as on the Σ5(310)[001] and Σ3(112)[1¯10] symmetrical tilt grain boundaries. The calculated results show that, within the studied range of concentrations, the single crystal cleavage planes are much more sensitive to a change in H concentration than the grain boundaries. Since there are two main types of procedures to perform ab initio tensile tests, different in whether or not to allow the relaxation of atomic positions, which can affect the quantitative and qualitative results, these methods are revisited to determine their effect on the predicted cohesive strength of segregated interfaces. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.view abstract 10.3390/ma13245785 **Influence of lattice misfit on the deformation behaviour of α2/γ lamellae in TiAl alloys**

Chauniyal, A. and Janisch, R.*Materials Science and Engineering A*796 (2020)Interfaces play a significant role in the deformation behaviour of lamellar two-phase TiAl alloys and contribute to their increased strength. We study the deformation behaviour of α2/γ bilayers with either coherent or semicoherent interfaces, using atomistic simulations. We identify the nucleation sites for dislocations and decouple the effects of the microstructural parameters volume fraction and layer thickness on the yield stress and strain. Uniaxial tensile tests are carried out on bi-layer specimens with α2 and γ phases along directions parallel and perpendicular to the interface. Coherent α2∕γ bi-layers show residual stresses due to lattice mismatch which are linearly related to the volume fractions of the phases. These residual stresses, superimposed with tensile stresses during loading, lead to early yielding of the γ phase. In contrast, a semi-coherent interface leads to negligible residual stresses, but contains misfit dislocations which create localized stresses within the γ layer and thus contributes to dislocation nucleation. We show that along loading directions parallel to the interface, the layer thickness does not affect the deformation behaviour, irrespective of the type of interface, instead volume fraction is the governing parameter. When loading perpendicular to the interface, the absolute layer thickness does not affect the deformation behaviour of a bi-layer with a coherent interface, but determines the yield stress and strain in case of a semi coherent interface. © 2020 Elsevier B.V.view abstract 10.1016/j.msea.2020.140053 **Ab initio study of the combined effects of alloying elements and h on grain boundary cohesion in ferritic steels**

Subramanyam, A.P.A. and Guzmán, A.A. and Vincent, S. and Hartmaier, A. and Janisch, R.*Metals*9 (2019)Hydrogen enhanced decohesion is expected to play a major role in ferritic steels, especially at grain boundaries. Here, we address the effects of some common alloying elements C, V, Cr, and Mn on the H segregation behaviour and the decohesion mechanism at a Σ5(310)[001] 36.9° grain boundary in bcc Fe using spin polarized density functional theory calculations. We find that V, Cr, and Mn enhance grain boundary cohesion. Furthermore, all elements have an influence on the segregation energies of the interstitial elements as well as on these elements’ impact on grain boundary cohesion. V slightly promotes segregation of the cohesion enhancing element C. However, none of the elements increase the cohesion enhancing effect of C and reduce the detrimental effect of H on interfacial cohesion at the same time. At an interface which is co-segregated with C, H, and a substitutional element, C and H show only weak interaction, and the highest work of separation is obtained when the substitute is Mn. © 2019 by the authors. Licensee MDPI, Basel, Switzerland.view abstract 10.3390/met9030291 **Partitioning of interstitial segregants during decohesion: A DFT case study of the ∑3 symmetric tilt grain boundary in ferritic steel**

Huang, X. and Janisch, R.*Materials*12 (2019)The effect of hydrogen atoms at grain boundaries in metals is usually detrimental to the cohesion of the interface. This effect can be quantified in terms of the strengthening energy, which is obtained following the thermodynamic model of Rice and Wang. A critical component of this model is the bonding or solution energy of the atoms to the free surfaces that are created during decohesion. At a grain boundary in a multicomponent system, it is not immediately clear how the different species would partition and distribute on the cleaved free surfaces. In this work, it is demonstrated that the choice of partitioning pattern has a significant effect on the predicted influence of H and C on grain boundary cohesion. To this end, the ∑3(112)[110] symmetric tilt grain boundary in bcc Fe with different contents of interstitial C and H was studied, taking into account all possible distributions of the elements, as well as surface diffusion effects. H as a single element has a negative influence on grain boundary cohesion, independent of the details of the H distribution. C, on the other hand, can act both ways, enhancing or reducing the cohesion of the interface. The effect of mixed H and C compositions depends on the partition pattern. However, the general trend is that the number of detrimental cases increases with increasing H content. A decomposition of the strengthening energy into chemical and mechanical contributions shows that the elastic contribution dominates at high C contents, while the chemical contribution sets the trend for high H contents. © 2019 by the authors.view abstract 10.3390/ma12182971 **Fracture ab initio: A force-based scaling law for atomistically informed continuum models**

Möller, J.J. and Bitzek, E. and Janisch, R. and Ul Hassan, H. and Hartmaier, A.*Journal of Materials Research*33 (2018)In fracture mechanics, established methods exist to model the stability of a crack tip or the kinetics of crack growth on both the atomic and the macroscopic scale. However, approaches to bridge the two scales still face the challenge in terms of directly converting the atomic forces at which bonds break into meaningful continuum mechanical failure stresses. Here we use two atomistic methods to investigate cleavage fracture of brittle materials: (i) we analyze the forces in front of a sharp crack and (ii) we study the bond breaking process during rigid body separation of half crystals without elastic relaxation. The comparison demonstrates the ability of the latter scheme, which is often used in ab initio density functional theory calculations, to model the bonding situation at a crack tip. Furthermore, we confirm the applicability of linear elastic fracture mechanics in the nanometer range close to crack tips in brittle materials. Based on these observations, a fracture mechanics model is developed to scale the critical atomic forces for bond breaking into relevant continuum mechanical quantities in the form of an atomistically informed scale-sensitive traction separation law. Such failure criteria can then be applied to describe fracture processes on larger length scales, e.g., in cohesive zone models or extended finite element models. Copyright © Materials Research Society 2018 This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (.view abstract 10.1557/jmr.2018.384 **Efficient sampling in materials simulation - Exploring the parameter space of grain boundaries**

Dette, H. and Gösmann, J. and Greiff, C. and Janisch, R.*Acta Materialia*125 (2017)In the framework of materials design there is the demand for extensive databases of specific materials properties. In this work we suggest an improved strategy for creating future databases, especially for extrinsic properties that depend on several material parameters. As an example we choose the energy of grain boundaries as a function of their geometric degrees of freedom. The construction of many existing databases of grain boundary energies in face-centred and body centred cubic metals relied on the a-priori knowledge of the location of important cusps and maxima in the five-dimensional energy landscape, and on an as-densely-as-possible sampling strategy. We introduce two methods to improve the current state of the art. Based on an existing energy model the location and number of the energy minima along which the hierarchical sampling takes place is predicted from existing data points without any a-priori knowledge, using a predictor function. Furthermore we show that in many cases it is more efficient to use a sequential sampling in a “design of experiment” scheme, rather than sampling all observations homogeneously in one batch. This sequential design exhibits a smaller error than the simultaneous one, and thus can provide the same accuracy with fewer data points. The new strategy should be particularly beneficial in the exploration of grain boundary energies in new alloys and/or non-cubic structures. © 2016 Acta Materialia Inc.view abstract 10.1016/j.actamat.2016.11.044 **The shear instability energy: A new parameter for materials design?**

Kanani, M. and Hartmaier, A. and Janisch, R.*Modelling and Simulation in Materials Science and Engineering*25 (2017)Reliable and predictive relationships between fundamental microstructural material properties and observable macroscopic mechanical behaviour are needed for the successful design of new materials. In this study we establish a link between physical properties that are defined on the atomic level and the deformation mechanisms of slip planes and interfaces that govern the mechanical behaviour of a metallic material. To accomplish this, the shear instability energy Γ is introduced, which can be determined via quantum mechanical ab initio calculations or other atomistic methods. The concept is based on a multilayer generalised stacking fault energy calculation and can be applied to distinguish the different shear deformation mechanisms occurring at TiAl interfaces during finite-temperature molecular dynamics simulations. We use the new parameter Γ to construct a deformation mechanism map for different interfaces occurring in this intermetallic. Furthermore, Γ can be used to convert the results of ab initio density functional theory calculations into those obtained with an embedded atom method type potential for TiAl. We propose to include this new physical parameter into material databases to apply it for the design of materials and microstructures, which so far mainly relies on single-crystal values for the unstable and stable stacking fault energy. © 2017 IOP Publishing Ltd.view abstract 10.1088/1361-651X/aa865a **First-principles study of carbon segregation in bcc iron symmetrical tilt grain boundaries**

Wang, J. and Janisch, R. and Madsen, G.K.H. and Drautz, R.*Acta Materialia*115 (2016)Segregation of light elements can profoundly affect the energies and cohesive properties of grain boundaries. First-principles calculations have been performed to determine the carbon solution energies and cohesive properties of three different grain boundaries in presence of carbon. It is demonstrated that the most stable segregation sites possess the greatest coordination number and maximum Fe-C nearest neighbor distance. Thereby a geometric criterion for predicting the segregation sites is suggested. Open grain boundary structures are shown to be more attractive to C atoms than the compact grain boundary structure, vacancies and dislocations, and C segregation at open grain boundaries decreases the grain boundary energy. The theoretical fracture strength of grain boundaries increases with C concentration and tend to similar values for certain areal concentrations irrespective of the grain boundary structures. This implies that the maximum fracture strength of a grain boundary depends on the maximum C areal concentration it can accommodate. © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.view abstract 10.1016/j.actamat.2016.04.058 **Stacking fault based analysis of shear mechanisms at interfaces in lamellar TiAl alloys**

Kanani, M. and Hartmaier, A. and Janisch, R.*Acta Materialia*106 (2016)The interfaces in lamellar TiAl alloys have a strong influence on the strength and deformability of the microstructure. It is widely accepted that their number and spacing can be used to tune these properties. However, the results of molecular dynamics simulations of sliding at γ/γ interfaces in lamellar TiAl alloys presented here suggest that important factors, namely the sequence of different interface types as well as the orientation of in-plane directions with respect to the loading axis, have to be included into meso-scale models. Simulations of bicrystal shear show significant differences in the deformation behavior of the different interfaces, as well as pronounced in-plane anisotropy of the shear strength of the individual interfaces. The critical stresses derived from bicrystal shear simulations are of the same order of magnitude as the one for nucleation and motion of twins in a γ-single crystal, showing that these mechanisms are competitive. In total four different deformation mechanisms, interface migration, twin nucleation and migration, dislocation nucleation, and rigid grain boundary sliding are observed. Their occurrence can be understood based on a multilayer generalized stacking fault energy analysis. This link between physical properties, geometry and deformation mechanism can provide guidelines for future alloy development. © 2016 Published by Elsevier Ltd on behalf of Acta Materialia Inc.view abstract 10.1016/j.actamat.2015.11.047 **The role of silicon, vacancies, and strain in carbon distribution in low temperature bainite**

Sampath, S. and Rementeria, R. and Huang, X. and Poplawsky, J.D. and Garcia-Mateo, C. and Caballero, F.G. and Janisch, R.*Journal of Alloys and Compounds*673 (2016)We investigated the phenomenon of carbon supersaturation and carbon clustering in bainitic ferrite with atom probe tomography (APT) and ab-initio density functional theory (DFT) calculations. The experimental results show a homogeneous distribution of silicon in the microstructure, which contains both ferrite and retained austenite. This distribution is mimicked well by the computational approach. In addition, an accumulation of C in certain regions of the bainitic ferrite with C concentrations up to 13 at % is observed. Based on the DFT results, these clusters are explained as strained, tetragonal regions in the ferritic bainite, in which the solution enthalpy of C can reach large, negative values. It seems that Si itself only has a minor influence on this phenomenon. © 2016 Elsevier B.V.view abstract 10.1016/j.jallcom.2016.02.151 **Interplanar potential for tension-shear coupling at grain boundaries derived from ab initio calculations**

Pang, X.Y. and Janisch, R. and Hartmaier, A.*Modelling and Simulation in Materials Science and Engineering*24 (2015)Based on ab initio density functional theory (DFT) calculations we derive an analytical expression for the interplanar potential of grain boundaries and single crystals as a function of coupled tensile and shear displacements. This energy function captures even details of the grain boundary behaviour, such as the tension-softening of the shear instability of aluminium grain boundaries, with good accuracy. The good agreement between the analytical model and the DFT calculations is achieved by introducing two new characteristic parameters, namely the position of the generalised unstable stacking fault with respect to the stable stacking fault, and the ratio of stable and unstable generalised stacking fault energies. One of the potentials' parameters also serves as a criterion to judge if a grain boundary deforms via crack propagation or dislocation nucleation. We suggest this potential function for application in continuum models, where constitutive relationships for grain boundaries need to be derived from a sound physical model. © 2016 IOP Publishing Ltd.view abstract 10.1088/0965-0393/24/1/015007 **Coupled atomistic-continuum study of the effects of C atoms at α-Fe dislocation cores**

Chockalingam, K. and Janisch, R. and Hartmaier, A.*Modelling and Simulation in Materials Science and Engineering*22 (2014)The influence of carbon at dislocation cores in α-Fe is studied to determine the Peierls stress, i.e. the critical stress required to move the dislocation at 0 K. The effect of carbon on both edge and screw dislocations is investigated. A coupled molecular statics (MS) and extended finite element method (XFEM) is employed for this study, where the dislocation core is modeled atomistically. The results on pure Fe are found to be in good agreement with a fully atomistic study. The coupled approach captures the right core behavior and significantly reduces the size of the atomistic region, while describing the behavior of a single dislocation in an infinite anisotropic elastic medium. Furthermore, mechanical boundary conditions can be applied consistently. It was found that the influence of carbon on edge dislocations is much stronger than that on screw dislocations, and that carbon causes a directionally dependent Peierls stress in the case of a screw dislocation. Even though the increase of the Peierls stress is much more pronounced for edge dislocations, the total value does not reach the level of the Peierls stress for screw dislocations, either with or without carbon at the core. Hence, we conclude that the motion of screw dislocations remains the rate limiting factor for plastic deformation of α-Fe. © 2014 IOP Publishing Ltd.view abstract 10.1088/0965-0393/22/7/075007 **Hydrogen embrittlement of a carbon segregated σ5 (310) [001] symmetrical tilt grain boundary in α-Fe**

Tahir, A.M. and Janisch, R. and Hartmaier, A.*Materials Science and Engineering A*612 (2014)The physical and mechanical properties of a σ5 (310) [001] symmetrical tilt grain boundary (STGB) in body centred cubic (bcc) Fe are investigated by means of ab initio calculations with respect to the effect of a varying number of C and H atoms at the grain boundary. The obtained results show that with increasing number of C atoms the grain boundary energy is lowered, and the segregation energy remains negative up to a full coverage of the grain boundary with C. Thus, in a bcc Fe-C system with a sufficient amount of interstitial C, the C segregated state should be considered as the ground state of this interface. Ab initio uni-axial tensile tests of the grain boundary reveal that the work of separation as well as the theoretical strength of the σ5 (310) [001] STGB increases significantly with increasing C content. The improved cohesion due to C is mainly a chemical effect, but the mechanical contribution is also cohesion enhancing. The presence of hydrogen changes the cohesion enhancing mechanical contribution of C to an embrittling contribution, and also reduces the beneficial chemical contribution to the cohesion. When hydrogen is present together with C at the grain boundary, the reduction in strength amounts to almost 20% for the co-segregated case and to more than 25% if C is completely replaced by H. Compared to the strength of the STGB in pure iron, however, the influence of H is negligible. Hence, H embrittlement can only be understood in the three component Fe-C-H system. © 2014 Elsevier B.V.view abstract 10.1016/j.msea.2014.06.071 **Interface properties in lamellar TiAl microstructures from density functional theory**

Kanani, M. and Hartmaier, A. and Janisch, R.*Intermetallics*54 (2014)The deformability and strength of lamellar two-phase (γ and α2) TiAl alloys strongly depends on the mechanical properties of the different interfaces in such microstructures. We carried out ab-initio density functional theory calculations of interface energy and strength for all known interface variants as well as the corresponding single crystal slip/cleavage planes to obtain a comprehensive database of key mechanical quantities. This data collection can be used for meso-scale simulations of deformation and fracture in TiAl. In spite of the different atomic configurations of the lamellar interfaces and the single crystal planes, the calculated values for the tensile strength are in the same range and can be considered as equal in a meso-scale model. Analysis of generalized stacking fault energy surfaces showed that the shear strength is directional dependent, however, the [112̄] direction is an invariant easy gliding direction in all investigated systems. The probability of different dislocation dissociation reactions as part of a shear deformation mechanism are discussed as well. © 2014 Elsevier Ltd. All rights reserved.view abstract 10.1016/j.intermet.2014.06.001 **Ab initio calculation of traction separation laws for a grain boundary in molybdenum with segregated C impurites**

Tahir, A.M. and Janisch, R. and Hartmaier, A.*Modelling and Simulation in Materials Science and Engineering*21 (2013)We have determined the influence of carbon on mechanical properties such as grain boundary energy, work of separation (WoS) and fracture strength of the Σ5(3 1 0)[0 0 1] symmetrical tilt grain boundary (STGB) in molybdenum with ab initio methods. From our ab initio results, we derived traction-separation laws that can be used in continuum simulations of fracture employing cohesive zones. Our results show that with an increasing number of C atoms at the grain boundary, the energy of the grain boundary is lowered, indicating a strong driving force for segregation. Uni-axial tensile tests of the grain boundary reveal that there is only a small effect of segregated C atoms on the cohesive energy or WoS of the grain boundary, while the strength of the Σ5(3 1 0)[0 0 1] STGB increases by almost 30% for a complete monolayer of C. This increase in strength is accompanied by an increase in grain boundary stiffness and a decrease of the interface excess volume. The characteristic parameters are combined in the concentration-dependent traction-separation laws. A study of the scaling behaviour of the different investigated systems shows that the energy-displacement curves can be well described by the universal binding energy relationship even for different C concentrations. These findings open the way for significant simplification of the calculation of ab initio traction separation laws for grain boundaries with and without impurities. © 2013 IOP Publishing Ltd.view abstract 10.1088/0965-0393/21/7/075005 **Ab initio prediction of the critical thickness of a precipitate**

Sampath, S. and Janisch, R.*Journal of Physics Condensed Matter*25 (2013)Segregation and precipitation of second phases in metals and metallic alloys is an important phenomenon that has a strong influence on the mechanical properties of the material. Models exist that describe the growth of coherent, semi-coherent and incoherent precipitates. One important parameter of these models is the energy of the interface between matrix and precipitate. In this work we apply ab initio density functional theory calculations to obtain this parameter and to understand how it depends on chemical composition and mechanical strain at the interface. Our example is a metastable Mo-C phase, the body-centred tetragonal structure, which exists as a semi-coherent precipitate in body-centred cubic molybdenum. The interface of this precipitate is supposed to change from coherent to semi-coherent during the growth of the precipitate. We predict the critical thickness of the precipitate by calculating the different contributions to a semi-coherent interface energy by means of ab initio density functional theory calculations. The parameters in our model include the elastic strain energy stored in the precipitate, as well as a misfit dislocation energy that depends on the dislocation core width and the dislocation spacing. Our predicted critical thickness agrees well with experimental observations. © 2013 IOP Publishing Ltd.view abstract 10.1088/0953-8984/25/35/355005 **The mechanical shear behavior of Al single crystals and grain boundaries**

Pang, X. and Ahmed, N. and Janisch, R. and Hartmaier, A.*Journal of Applied Physics*112 (2012)To investigate the mechanical shear properties of interfaces in metals, we have determined the γ-surfaces of different special tilt and twist grain boundaries in aluminum by means of ab initio calculations. From the γ-surfaces, we obtained minimum energy paths and barriers, as well as the theoretical shear strength. For the [110] tilt grain boundaries, there is a pronounced easy-sliding direction along the tilt axis. The theoretical shear strength scales with the height of the slip barrier and exhibits a relation with the misorientation angle: the closer the angle to 90°, the higher the shear stress. There is no simple relationship with the periodicity of the grain boundary, i.e., the Σ value or the grain boundary energy. © 2012 American Institute of Physics.view abstract 10.1063/1.4736525 **Simulation of fracture in heterogeneous elastic materials with cohesive zone models**

Prechtel, M. and Ronda, P.L. and Janisch, R. and Hartmaier, A. and Leugering, G. and Steinmann, P. and Stingl, M.*International Journal of Fracture*168 (2011)In brittle composite materials, failure mechanisms like debonding of the matrix-fiber interface or fiber breakage can result in crack deflection and hence in the improvement of the damage tolerance. More generally it is known that high values of fracture energy dissipation lead to toughening of the material. Our aim is to investigate the influence of material parameters and geometrical aspects of fibers on the fracture energy as well as the crack growth for given load scenarios. Concerning simulations of crack growth the cohesive element method in combination with the Discontinuous Galerkin method provides a framework to model the fracture considering strength, stiffness and failure energy in an integrated manner. Cohesive parameters are directly determined by DFT supercell calculations. We perform studies with prescribed crack paths as well as free crack path simulations. In both cases computational results reveal that fracture energy depends on both the material parameters but also the geometry of the fibers. In particular it is shown that the dissipated energy can be increased by appropriate choices of cohesive parameters of the interface and geometrical aspects of the fiber. In conclusion, our results can help to guide the manufacturing process of materials with a high fracture toughness. © 2010 Springer Science+Business Media B.V.view abstract 10.1007/s10704-010-9552-z **Solubility of carbon in α-iron under volumetric strain and close to the Σ5(3 1 0)[0 0 1] grain boundary: Comparison of DFT and empirical potential methods**

Hristova, E. and Janisch, R. and Drautz, R. and Hartmaier, A.*Computational Materials Science*50 (2011)The solubility of carbon in α-Fe as a function of lattice strain and in the vicinity of the ∑5(310)[001] symmetrical tilt grain boundary is calculated with ab initio methods based on density-functional theory (DFT). The results are compared to four different empirical potentials: the embedded-atom method (EAM) potentials of Lau et al. [1], Ruda et al. [2] and Hepburn et al. [3], and the modified embedded-atom method (MEAM) potential of Lee [4]. The results confirm that the solubility of carbon in body-centered-cubic (bcc) Fe increases under local volume expansion and provide quantitative data for the excess enthalpy to be used in thermodynamic databases. According to our study the excess enthalpy obtained from DFT is more strain-sensitive than the ones obtained from the tested empirical potentials. The comparison of the applied methods furthermore reveals that among the empirical potentials the MEAM is most appropriate to describe the solubility of C in bcc Fe under strain. The differences between the four empirical potentials stem from different parameterizations of the EAM potentials and, in the case of the MEAM, from the altogether different formalism that also includes angular dependent terms in the binding energy. © 2010 Elsevier B.V. All rights reserved.view abstract 10.1016/j.commatsci.2010.11.006 **Ab initio tensile tests of Al bulk crystals and grain boundaries: Universality of mechanical behavior**

Janisch, R. and Ahmed, N. and Hartmaier, A.*Physical Review B - Condensed Matter and Materials Physics*81 (2010)We have performed ab initio tensile tests of bulk Al along different tensile axes, as well as perpendicular to different grain boundaries to determine mechanical properties such as interface energy, work of separation, and theoretical strength. We show that all the different investigated geometries exhibit energy-displacement curves that can be brought into coincidence in the spirit of the well known universal binding energy relationship curve. This simplifies significantly the calculation of ab initio tensile strengths for the whole parameter space of grain boundaries. © 2010 The American Physical Society.view abstract 10.1103/PhysRevB.81.184108

#### Ziel2: ICAMS Start-up Funding (concluded)

#### ab initio calculations

#### density functional theory

#### dislocations

#### electronic structure

#### grain boundaries

#### interfaces

#### mechanical properties

#### molecular dynamics

#### single crystals