TY - JOUR A1 - Rosenbusch, Sjard Mathis A1 - Diercks, Philipp A1 - Kindrachuk, Vitaliy A1 - Unger, Jörg F. T1 - Integrating custom constitutive models into FEniCSx: A versatile approach and case studies N2 - The development and integration of user-defined constitutive relationships into finite element (FE) tools using standardized interfaces play a pivotal role in advancing the capabilities of FE solvers for structural mechanics applications. While commercial FE solvers like Abaqus and Ansys have designed their interfaces to provide custom stresses, tangents, and updated history variables, the open-source solver FEniCSx remains efficient only when the constitutive update has an analytical representation. This restricts the application of FEniCSx for non-linear structural mechanics. Since FEniCSx has become a powerful and popular open-source tool for solving partial differential equations, particularly due to its automatic computation of Hessians, we aim to develop a generalized interface to enhance its capability for constitutive modeling. This approach will address complex constitutive equations that require iterative solutions at the quadrature point level. Specific implementation challenges, such as using return-mapping procedures, can then be managed commonly. The provided interface for custom constitutive models offers a versatile way to implement them in various languages, including C++, Python, Rust, and Fortran. Finally, with UMATs for viscoplastic models as an example, we demonstrate how existing user subroutines can be incorporated into the interface and utilized within the FEniCSx framework. KW - Finite element method KW - Constitutive models KW - FEniCSx KW - UMAT KW - Rust KW - Python KW - C++ PY - 2025 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-630439 DO - https://doi.org/10.1016/j.advengsoft.2025.103922 SN - 0965-9978 VL - 206 SP - 1 EP - 11 PB - Elsevier CY - Amsterdam AN - OPUS4-63043 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Haapalehto, Matias A1 - Pinomaa, Tatu A1 - Wang, Lei A1 - Laukkanen, Anssi T1 - An atomistic simulation study of rapid solidification kinetics and crystal defects in dilute Al–Cu alloys N2 - Rapid solidification kinetics of dilute Al–Cu alloys is simulated using a quantum mechanics based bondorder potential (BOP), in free solidification conditions, to determine kinetic and thermodynamic properties of solidification, as well as point defects and chemical ordering of the solidified structures. We measure the anisotropic kinetic coefficient, anisotropic solid–liquid interface energy, as well as solute trapping kinetics in terms of partition coefficient versus velocity and solute drag coefficient. Furthermore, solid–liquid interface free energy and its anisotropy are measured in equilibrium simulations, showing reasonably good agreement with previous studies. We also verified the self-consistency of the MD simulations, by comparing the interfacial temperature vs. velocity to that predicted by the continuous growth model. These solid–liquid interface properties are important for quantitative parametrization of larger scale solidification modeling techniques such as phase field models. We also investigated the point defect content, local chemical ordering, and local crystalline structures in the rapidly solidified samples. We found clustering of solute with vacancies, whereas copper atoms repelled each other in these dilute alloy simulations. In addition to vacancies, a large number of interstitials were found. In solidification velocities approaching the complete solute trapping regime, we found that the vacancies and interstitials formed in conjunction, i.e. as Frenkel pairs. Finally, in addition to FCC, we detected BCC and HCP phases, where the latter two were accompanied by an increase in local copper content. Understanding the formation of point defects and their relationship to chemical ordering is an important step towards controlling the formation of pre-precipitates and precipitates, which are an important strengthening mechanism for aluminum–copper alloys. KW - Rapid solidification KW - Aluminum–copper KW - MD PY - 2022 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-628722 DO - https://doi.org/10.1016/j.commatsci.2022.111356 SN - 0927-0256 VL - 209 SP - 1 EP - 13 PB - Elsevier CY - Amsterdam AN - OPUS4-62872 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Dub, S. A1 - Haftaoglu, Cetin A1 - Kindrachuk, Vitaliy T1 - Estimate of theoretical shear strength of C60 single crystal by nanoindentation N2 - The onset of plasticity in a single crystal C60 fullerite was investigated by nanoindentation on the (111) crystallographic plane. The transition from elastic to plastic deformation in a contact was observed as pop-in events on loading curves. The respective resolved shear stresses were computed for the octahedral slip systems ⟨011¯¯¯⟩{111}, supposing that their activation resulted in the onset of plasticity. A finite element analysis was applied, which reproduced the elastic loading until the first pop-in, using a realistic geometry of the Berkovich indenter blunt tip. The obtained estimate of the C60 theoretical shear strength was about 1/11 of the shear modulus on {111} planes. KW - Finite element analysis KW - Fullerite KW - Nanoindentation PY - 2021 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-523208 DO - https://doi.org/10.1007/s10853-021-05991-2 VL - 56 IS - 18 SP - 10905 EP - 10914 PB - Springer Nature AN - OPUS4-52320 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Kindrachuk, Vitaliy A1 - Klunker, Andre T1 - Phase field modeling of Hertzian cone cracks under spherica indentation N2 - A phase field model of brittle fracture has been developed to simulate the Hertzian crack induced by penetration of a rigid sphere to an isotropic linear-elastic half-space. The fracture formation is regarded as a diffusive field variable, which is zero for the intact material and unity if there is a crack. Crack growth is assumed to be driven by a strain invariant. The numerical implementation is performed with the finite element method and an implicit time integration scheme. The mechanical equilibrium and the phase field equations are solved in a staggered manner, sequentially updating the displacement field and the phase field variable. Numerical examples demonstrate the capability of the model to reproduce the nucleation and growth of the Hertzian cone crack. KW - Hertzian cracks KW - Phase field model KW - Contact mechanics PY - 2021 DO - https://doi.org/10.1007/s11223-021-00251-9 VL - 52 IS - 6 SP - 967 EP - 974 AN - OPUS4-52276 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Schilling, Markus A1 - Marschall, Niklas A1 - Niebergall, Ute A1 - Wachtendorf, Volker A1 - Böhning, Martin T1 - Characteristics of environmental stress cracking of PE-HD induced by biodiesel and diesel fuels N2 - In the context of the increasing effect of carbon dioxide emissions on the global climate biodiesel produced from renewable sources has emerged as a promising contender replacing fossil fuels, especially in long-range transport vehicles, using existing engines and infrastructure. High-density polyethylene is one of the prevailing materials for pipe and container applications for storage and transport of such fuels, both, from fossil and renewable resources. The contact with the respective fuels raises questions concerning material compatibility as biodiesel exhibits significant differences compared to conventional diesel fuel affecting its sorption and plasticization behavior in polyethylene. In this study, its behavior with respect to environmental stress cracking, considered one of the most frequent damage mechanisms leading to failure of polymer parts and packaging, was evaluated using the well-established Full Notch Creep Test. This approach allows for a detailed fracture surface analysis using imaging techniques, such as optical and laser scanning microscopy, as well as infrared spectroscopy. Comparing the environmental stress cracking behavior in standard surfactant solutions with that in biodiesel and diesel, respective crack propagation rates, showing different levels of acceleration, were determined and details of the underlying mechanisms could be revealed. Furthermore, the specific infrared absorption of the biodiesel’s ester functionality allows its semi-quantitative determination on the fracture surface of the tested specimens after failure. Thus, a preferred uptake of sorptive fluids in the fracture zone due to local morphological changes of the polyethylene could be directly evidenced by infrared spectroscopy. KW - Environmental stress cracking (ESC) KW - Full notch creep test (FNCT) KW - Confocal laser scanning microscopy (LSM) KW - Biodiesel KW - Diesel PY - 2024 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-608591 DO - https://doi.org/10.1016/j.polymertesting.2024.108547 SN - 0142-9418 VL - 138 SP - 1 EP - 16 PB - Elsevier Ltd. AN - OPUS4-60859 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Schilling, Markus A1 - Niebergall, Ute A1 - Marschall, Niklas A1 - Alig, I. A1 - Böhning, Martin T1 - A phenomenological criterion for an optical assessment of PE-HD fracture surfaces obtained from FNCT N2 - The full-notch creep test (FNCT) is a common test method to evaluate the environmental stress cracking (ESC) behavior of high-density polyethylene (PE-HD), e.g. for container materials. The test procedure as specified in ISO 16770 provides a comparative measure of the resistance against ESC using the time to failure of PE-HD specimens under constant mechanical load in a well-defined liquid test environment. Since the craze-crack damage mechanism underlying the ESC phenomenon is associated with brittle failure, the occurrence of a predominantly brittle fracture surface is a prerequisite to consider an FNCT measurement as representative for ESC, i.e. a time to failure dominated by craze-crack propagation. The craze-crack propagation continuously reduces the effective residual cross-sectional area of the specimen during the test, which results in a corresponding increase of the effective mechanical stress. Thus, a transition to ductile shear deformation is inevitable at later stages of the test, leading usually to a pronounced central ligament. Therefore, an optical evaluation of FNCT fracture surfaces concerning their brittleness is essential. An enhanced imaging analysis of FNCT fracture surfaces enables a detailed assessment of craze-crack Propagation during ESC. In this study, laser scanning microscopy (LSM) was employed to evaluate whether FNCT fracture surfaces are representative with respect to craze-crack propagation and ESC. Based on LSM height data, a phenomenological criterion is proposed to assess the validity of distinct FNCT measurements. This criterion is supposed to facilitate a quick evaluation of FNCT results in practical routine testing. Its applicability is verified on a sample basis for seven different commercial PE-HD container materials. KW - Environmental stress cracking (ESC) KW - Full notch creep test (FNCT) KW - Laser scanning microscopy (LSM) KW - Fracture surfaces KW - Optical criterion of brittleness PY - 2021 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-521012 DO - https://doi.org/10.1016/j.polymertesting.2020.107002 VL - 94 SP - 107002 PB - Elsevier Ltd. CY - Amsterdam AN - OPUS4-52101 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Schilling, Markus A1 - Marschall, Niklas A1 - Niebergall, Ute A1 - Böhning, Martin T1 - Modernizing FNCT data handling in polymer labs: Towards efficient management N2 - A streamlined Python-based workflow for transforming Full-Notch Creep Test (FNCT) data into organized, machine-actionable formats is presented. The workflow automates the conversion of raw FNCT data from classic CSV and Excel files into structured outputs that facilitate future semantic integration. Emphasizing practical data handling, the approach includes automation scripts for efficient data extraction, transformation, and storage, which culminate in well-ordered files. This transformation paves the way for potential semantic data integration and facilitates access for users with varying levels of digital experience to enhanced data management in polymer research and testing. KW - PE-HD KW - Full-Notch Creep Test (FNCT) KW - Environmental Stress Cracking (ESC) KW - Data Interoperability KW - FAIR Data KW - Semantic Data PY - 2025 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-637826 DO - https://doi.org/10.1016/j.commatsci.2025.114085 SN - 0927-0256 VL - 259 SP - 1 EP - 5 PB - Elsevier B.V. AN - OPUS4-63782 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Schilling, Markus A1 - Niebergall, Ute A1 - Marschall, Niklas A1 - Meinel, Dietmar A1 - Böhning, Martin T1 - Relation of craze to crack length during slow crack growth phenomena in high‐density polyethylene N2 - The craze‐crack mechanism occurring in high‐density polyethylene (HDPE) causing slow crack growth and environmental stress cracking is investigated in detail with respect to the relation of crack length and the related craze zone. This is essential for the understanding of the resulting features of the formed fracture surface and their interpretation in the context of the transition from crack propagation to ductile shear deformation. It turns out that an already formed craze zone does not inevitably result in formation of a propagating crack, but could also undergo ductile failure. For the examination, the full notch creep test (FNCT) was employed with a subsequent advanced fracture surface analysis that was performed using various imaging techniques: light microscopy, laser scanning microscopy, scanning electron microscopy, and X‐ray micro computed tomography scan. FNCT specimens were progressively damaged for increasing durations under standard test conditions applying Arkopal, the standard surfactant solution, and biodiesel as test media were used to analyze the stepwise growth of cracks and crazes. From considerations based on well‐established fracture mechanics approaches, a theoretical correlation between the length of the actual crack and the length of the preceding craze zone was established that could be evidenced and affirmed by FNCT fracture surface analysis. Moreover, the yield strength of a HDPE material exposed to a certain medium as detected by a classic tensile test was found to be the crucial value of true stress to induce the transition from crack propagation due to the craze‐crack mechanism to shear deformation during FNCT measurements. Highlights - Progress of crack formation in high‐density polyethylene is analyzed by different imaging techniques - Determined growth rates depend on distinction between craze zone and crack - The ratio of the present crack to the anteceding craze zone is validated theoretically - The transition from crack propagation to ductile shear deformation is identified - An already formed craze zone may still fail by ductile mechanisms KW - Craze-crack mechanism KW - Environmental stress cracking (ESC) KW - Full notch creep test (FNCT) KW - Laser scanning microscopy (LSM) KW - Slow crack growth (SCG) KW - X-ray computed tomography (CT) PY - 2024 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-601831 DO - https://doi.org/10.1002/pen.26698 SN - 1548-2634 VL - 64 IS - 6 SP - 2387 EP - 2403 PB - Wiley AN - OPUS4-60183 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Stargardt, Patrick A1 - Bresch, Sophie A1 - Falkenberg, Rainer A1 - Mieller, Björn T1 - Effect of Reaction Layers on Internal Stresses in Co‐Fired Multilayers of Calcium Manganate and Calcium Cobaltite N2 - A widespread recovery of waste heat requires a cost‐effective production of thermoelectric generators. Thermoelectric oxides are predestined for use at high temperatures. For manufacturing reasons, a multilayer generator design will be easily scalable and cost‐effective. To evaluate the potential of ceramic multilayer technology for that purpose, a multilayer of the promising thermoelectric oxides calcium cobaltite (Ca3Co4O9), calcium manganate (CMO, CaMnO3), and glass–ceramic insulation layers is fabricated. Cracks and reaction layers at the interfaces are observed in the microstructure. The compositions of these reaction layers are identified by energy‐dispersive X‐ray spectroscopy and X‐ray diffraction. Mechanical and thermal properties of all layers are compiled from literature or determined by purposeful sample preparation and testing. Based on this data set, the internal stresses in the multilayer after co‐firing are calculated numerically. It is shown that tensile stresses in the range of 50 MPa occur in the CMO layers. The reaction layers have only a minor influence on the level of these residual stresses. Herein, it is proven that the material system is basically suitable for multilayer generator production, but that the co‐firing process and the layer structure must be adapted to improve densification and reduce the tensile stresses in the CMO. KW - Ceramic multilayers KW - Co-firings KW - Internal stresses PY - 2024 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-601626 DO - https://doi.org/10.1002/pssa.202300956 SP - 1 EP - 9 PB - Wiley VHC-Verlag AN - OPUS4-60162 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Ikeda, Yuki A1 - Ni, H.C. A1 - Chakraborty, A. A1 - Ghassemi-Armaki, H. A1 - Zuo, J.M. A1 - Darvishi Kamachali, Reza A1 - Maaß, Robert T1 - Segregation-induced grain-boundary precipitation during early stages of liquid-metal embrittlement of an advanced high-strength steel N2 - Liquid-metal embrittlement (LME) of galvanized (Zn-coated) advanced high-strength steels is a long-known problem in materials science. Here we reveal the initial microstructural processes underneath the Zn-coating that lead to LME-microcrack initiation in the steel substrate. We track the microstructural evolution during the first tens of milliseconds and find pronounced signatures of Fe-Zn intermetallic precipitation in both ferrite grain boundaries and at internal ferrite-oxide phase boundaries. In concert with novel CALPHAD-integrated density-based thermodynamic modelling, we demonstrate that Zn-rich intermetallic phase-nucleation can occur at markedly low processing temperatures due to a segregation transition. We show that a small Znenrichment caused by Zn bulk-diffusion during the initial temperature rise in a joining process is sufficient to induce the segregation transition and subsequent nucleation of Fe-Zn intermetallic grain-boundary phases, which the experiments link to crack initiation sites. These findings direct focus onto LME-controlling microstructural and thermodynamic phenomena at temperatures below the ductility trough and the austenite formation temperature. KW - Resistance spot welding KW - Liquid-metal embrittlement KW - Steels KW - Grain boundaries PY - 2023 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-581067 DO - https://doi.org/10.1016/j.actamat.2023.119243 VL - 259 SP - 1 EP - 12 PB - Elsevier Ltd AN - OPUS4-58106 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Ikeda, Yuki A1 - Wallis, Theophilus A1 - Maaß, Robert A1 - Darvishi Kamachali, Reza T1 - Thermodynamics of grain boundary segregation transition and their relevance for liquid metal embrittlement in Fe-Zn system N2 - Grain boundaries (GBs) are common sites of failure in polycrystalline materials. Recently, a massive Zn segregation transition at Fe GBs was discovered and shown to act as a potent precursor of liquid metal embrittlement (LME) in the Fe-Zn system (Kamachali et al., Scripta Materialia 238 (2024) 115758). In this study, we elaborate on how temperature, GB type and the chemo-structurally coupled phase decomposition at the GB impact this segregation transition. CALPHAD and atomistic simulation data were utilized as inputs to conduct quantitative density-based thermodynamic modeling and phase-field simulations across various GBs, alloy compositions, and temperatures. We reveal that once the segregation transition becomes possible, the GB structural variation stabilizes spinodally formed Zn-rich phases within the GB region, with a higher tendency in disordered GBs. GB phase diagrams were constructed to identify and analyze the range of critical temperatures and alloy compositions associated with the segregation transition. The phase diagrams reveal that the miscibility gap for more disordered GB expands and, although the segregation transition is inevitable and occurs for all GBs, the barrier to triggering it is lower for more disordered GBs. Based on our thermodynamic analyses, potential processing modifications and GB engineering strategies for mitigating segregation-induced LME are thoroughly discussed. KW - Thermodynamics KW - Phase-Field Modelling KW - Steels PY - 2025 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-634145 DO - https://doi.org/10.1016/j.actamat.2025.121134 SN - 1359-6454 VL - 296 SP - 1 EP - 11 PB - Elsevier BV AN - OPUS4-63414 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -