5.5 Materialmodellierung
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Zn coatings are typically applied to steels in the liquid state. During spot welding, this coating is also presumed to remelt, and the subsequent embrittlement of the welded steel is therefore commonly associated with the presence of liquid Zn. However, whether the liquid phase itself, and hence temperatures above the Zn melting point, are necessary for the embrittlement phenomenon has so far remained unclear.
In a series of thermodynamic investigations [1-4], we show that a Zn-segregation transition in BCC-Fe grain boundaries occurs over a broad temperature range, associated with a magnetic miscibility gap in the Fe-Zn system, and can play a central role in the embrittlement. Although this range includes the melting temperature of Zn, the segregation transition can occur fully in the solid state. The resulting nanoscale, high-concentration Zn patches at grain boundaries are shown to constitute viable nucleation sites for a Zn-rich liquid phase and/or a Γ precipitate. More importantly, the work of separation is found to decrease drastically already before any phase change takes place.
The present results indicate that Zn-induced embrittlement in steels cannot be viewed solely as a liquid-metal embrittlement phenomenon. Instead, it should be understood more generally as a segregation-mediated grain-boundary instability, in which interfacial thermodynamics, local chemical transitions, and decohesion are the primary events, while liquid or intermetallic phase formation may follow as secondary consequences. This perspective opens a route toward a more unified thermodynamic description of Zn-induced liquid and solid metal embrittlement in steels.
By evaluating the long-wavelength limit of Khachaturyan’s microelasticity theory, we show that it recovers the Kamachali–Wang continuum formulation for multi-component solid solutions [Scripta Mater 206 (2022) 114226]. A corresponding expression for the elastic energy of multi-component solid solutions under cubic anisotropy is also obtained and discussed in comparison with the isotropic case. The framework is demonstrated on the Fe–Mn–Ni–Co–Cu alloy system to perform phase stability analysis at 873 K, including spinodal and binodal part of the phase diagram. The resulting cubic-anisotropic (incoherent) phase diagrams show that the spinodal promotion is reduced compared to the isotropic case, consistent with the derivations. The limit transition is examined using a Gaussian window function, which allows the definition of a critical coarse-graining length above which the continuum description becomes valid. This study provides a rigorous microscopic foundation for continuum multi-component elastic energy formulations, with broad computational implications in thermodynamic and phase-field modeling of chemically complex alloys and microstructures.
Radiation-induced segregation (RIS) and phase change phenomena have traditionally been framed as a transport-centric problem, and for good reason: it is fundamentally non-equilibrium diffusion governed by irradiation-generated point defects and their coupling to solute fluxes, which drive the redistribution of alloying elements toward or away from microstructural defects. Yet, this emphasis on transport aspects has created an asymmetry: The thermodynamic counterpart of the problem, namely the local free-energy landscape of the receiving defect, remains under-formalized: In most RIS frameworks, the governing description is closed through coupled transport equations for solutes and irradiation-generated point defects, augmented by source, recombination, and sink terms. Accordingly, the microstructural defects typically enters through sink strength, capture-efficiency, geometry, or boundary conditions, whereas their thermodynamic identity is represented in simplified form. Even where segregation energetics are included, they are often projected onto bulk thermodynamic factors or effective interfacial properties, rather than being based on a sink-specific free-energy landscape. In this Opinion Paper, I argue that a more complete understanding of RIS can emerge when sink-specific thermodynamic landscapes and their interaction with non-equilibrium fluxes are taken explicitly into account.
Liquid-metal embrittlement (LME) in galvanized advanced high-strength steels (AHSS) poses a major challenge during resistance spot welding, yet the mechanisms governing crack initiation remain incompletely understood. In this work, the early stages of LME are investigated through interrupted welding experiments, high-resolution electron microscopy, and CALPHAD-integrated phase-field modeling. The results reveal rapid Zn diffusion along grain boundaries and the formation of nanoscale Fe–Zn intermetallic Γ phases within milliseconds of welding, prior to crack formation. Crack initiation is found to preferentially occur at evolving α/Γ interfaces, while segregation-driven interfacial phase separation promotes grain-boundary destabilization. Thermodynamic grain-boundary phase diagram calculations further identify a Fe–Zn miscibility gap that drives segregation transitions and favors Γ-phase formation below the classical ductility trough temperature. The combined experimental and modeling results provide new insight into the nanoscale origins of LME and establish a framework for mitigating embrittlement through alloy and grain-boundary engineering.
Liquid-metal embrittlement (LME) in galvanized advanced high-strength steels (AHSS) represents a critical challenge during resistance spot welding, yet the early stages of crack initiation remain poorly understood. In this work, the time-dependent evolution of grain-boundary microstructures during interrupted welding is investigated using high-resolution electron microscopy and thermodynamic modeling. The results reveal rapid Zn diffusion along grain boundaries, followed by the formation of nanoscale Γ-phase (Fe3Zn10) intermetallics within milliseconds of welding. Crack initiation is found to occur preferentially at evolving α/Γ interfaces, while Zn segregation and grain-boundary density reduction promote interfacial instability and phase separation. Density-based grain-boundary phase diagram calculations further indicate the presence of a Fe–Zn miscibility gap that drives segregation transitions and intermetallic formation below the classical ductility trough temperature. These findings provide new insight into the nanoscale mechanisms governing the onset of LME in steels and establish a framework for alloy- and grain-boundary-engineering strategies to mitigate embrittlement.
The ongoing digitalization trend has fostered a significant shift in polymer science and engineering towards increased utilization of digital methods. The integration and reuse of data across materials synthesis, production, characterization, and modeling leads to enhanced innovation. Recognizing the importance of FAIR data principles, OntoFNCT is introduced as an ontology specifically tailored to represent data from full notch creep tests (FNCT) in the interoperable RDF format. FNCT is a method for assessing polymer material behavior under defined stress and environmental conditions. OntoFNCT is aligned with the corresponding ISO 16770 standard and enriches FNCT data with Semantic technologies (ST). Using OntoFNCT, data exchange among stakeholders is facilitated while enhancing speed, precision, and reliability in material evaluation and quality control processes. The integration with higher-level ontologies promotes interoperability and reusability of FNCT data across diverse sources. Additionally, an automated Python-based analysis workflow tailored to FAIR RDF graph data obtained through SPARQL queries was developed to determine FNCT characteristic values. Its usability was successfully demonstrated through its application to real FNCT datasets with correct automated RDF conversion for all test records without data loss and reduced manual analysis time by approximately 60% compared to traditional spreadsheet-based evaluation.
Chemically complex materials (CCMats) including high-entropy alloys, oxides, and related multi-principal element systems offer a paradigm shift in materials design by leveraging chemical diversity to simultaneously optimize functional, structural, and sustainability criteria. The vastness of the compositional and structural space in CCMats propels the field into an expanding exploratory state. To reconcile functional and structural performance across this immense parameter space remains an open challenge. This Perspective evaluates the opportunities and challenges associated with harnessing chemical complexity across a broad spectrum of applications, such as hydrogen storage, ionic conductors, catalysis, magnetics, dielectrics, semiconductors, optical materials, and multifunctional structural systems. It is delineated how three central design strategies: targeted substitution (SUB), defect engineering (DEF), and diversity management (DIV) enable the reconciliation of high functional performance with long-term structural stability and environmental responsibility.
Advances in computational thermodynamics, microstructure simulations, machine learning, and multimodal characterization are accelerating the exploration and optimization of CCMats, while robust data infrastructures and automated synthesis workflows are emerging as essential tools for navigating their complex compositional space. By fostering cross-disciplinary knowledge transfer and embracing data-driven design, CCMats are poised to deliver next-generation materials solutions that address urgent technological, energy, and
environmental demands.
Although titanium offers an optimal combination of strength, low weight, and toughness for various applications, it suffers from a drawback: loss of ductility upon exposure to hydrogen. In this work, we couple CALPHAD-integrated density-based thermodynamic modelling of hydrogen segregation with an experimentally calibrated fracture model to investigate its on crack propagation in titanium. Here we propose to model the crack propagation path as a quasi-interface with slightly opened structure and reduced atomic density, enabling interstitial hydrogen segregation. The atomic density is then directly linked with the damage parameter. We found that hydrogen segregation in titanium undergoes a significant transition such that above a threshold of only few atomic percent hydrogen in the solid solution, the interfacial hydrogen concentration exceeds 20 at.%. Integrating this information into our fracture model, the material damage evolution could be explained by a segregation-affected Griffith crack energy, resulting in material decohesion. We found that the segregation transition and subsequent embrittlement effects are critically sensitive to the temperature in the system. The present results suggest a mechanism underlying the sudden loss of fracture toughness during crack propagation, in relation to the ductile-to-brittle transition observed in titanium alloys exposed to hydrogen. The proposed CALPHAD-integrated chemo-mechanical framework can be further generalised for studying more complex failure mechanisms in various materials.
The density-based phase-field model for grain boundary (GB) thermodynamics and kinetics has offered a broad range of applications in alloy and microstructure design. Originally, this model is based on a potential energy terms that is connected to the cohesive energy of a given substance. A more rigorous approach, however, is a full consideration of an interatomic potential over the possible range of distance and therefore density. In Manuscript I of this series, we developed and thoroughly analyzed the coarse-graining of atomistic GB structures. In this work (Manuscript II), we complete the coupling between atomic and mesoscale modeling of GBs by incorporating the full interatomic potentials into the density-based free energy functional. Using GB energies calculated from atomistic simulations, the coarse-graining approach and the atomistic-integrated density-based Gibbs free energy, we effectively evaluate the density gradient energy coefficient. We found that coupling the density-based model with atomistic potentials reveal physically-sound trends in the GB equilibrium properties. A universal equation was derived to describe the potential energy contribution to the GB energy and the gradient energy coefficient for BCC-Fe and -Mo GBs, similar to the universal equation for GB excess free volume presented in Manuscript I. The proposed approach provides a mesoscale density-based model rooted in atomic-scale characteristics for reliable predictions of GB properties.
The longstanding gap between atomistic and mesoscale simulations partly lies in the absence of a direct, physically grounded connection between atomic structure and mesoscale fields. In this work, we present a robust coarse-graining approach to systematically investigate the connection between phase-field and atomistic simulations of grain boundaries (GBs). The atomistic structures of 408 GBs in BCC-Fe and -Mo were studies to compute and analyze a continuous atomic density field. We discover a fundamental relationship between the GB density---defined as the average atomic density at the GB plane---and the GB excess free volume, an integral property of the boundary. An almost perfect linear correlation between the GB atomic density and GB excess free volume is identified. We also show that the width of BCC GBs, when scaled by the lattice constant, approaches a universal constant value. The relationships among GB density, width, and energy are systematically examined for various GB planes, and the GB energy--density correlations are classified with respect to GB types. It turns out that the atomic planes forming the GB strongly influence both the GB density and excess volume. The current results establish a dependable framework to bridge across scales, enabling density-based phase-field modeling of GBs with atomistic fidelity and enhancing the predictive reliability of mesoscale simulations.