Defect and Diffusion Forum Vol. 446

Abstract: The mechanical behaviour of materials is influenced by processing and thermomechanical exposure. In safety-sensitive industries there is a need to make predictions on the envelope of safe use beyond proven constitutive equations. Microstructural simulations, such as crystal plasticity modelling, can model features like grain size, morphology and texture. However, they are computationally demanding and it can be hard to translate measured microstructures into meaningful or representative statistical distributions. Surrogate models incorporate machine learning regression and statistical methods to emulate the response of a complex model. As they are much faster, they can model the response over a wide range of material parameters, permitting sensitivity analysis and uncertainty quantification. Preferred orientation (texture) can be challenging to incorporate into surrogate models as accurate representations can require a lot of parameters. In this study, reduced-order representations of crystallographic texture are presented to represent the bulk response of a polycrystal volume element. These representations are used as inputs to a gaussian process regression (GPR) model that is used to predict the macroscopic stress-strain response of a polycrystal for different crystallographic textures. The GPR acts as a surrogate model of the underlying crystal plasticity model and allows an inherent quantification of the model epistemic uncertainty and the uncertainty related to unobserved effects not captured by the texture parameterization. Incorporation of the surrogate model into finite element coding will be used as an application of the method.

Abstract: Noting that there is very little literature on the topic, a first analytical approach is proposed in this work for estimating the viscosity-like parameter of three-phase viscoplastic materials. In a first part, the conditions of application and the consequences of the three classical averaging equations involving the strain rates, the stresses and the power are reviewed for 2-phase mixtures and extended to three phases. The classical static and Taylor bounds as well as the heuristic Iso-strain rate assumption are analyzed. An extension of the Mori-Tanaka estimation to the three-phase case is then proposed for viscoplastic linear constituents. If the volume fraction of one of the phases (inclusions) is very low, in particular when its viscosity tends towards zero or infinity, fully analytical results are presented, which provides an extension of the classical dilute model.

Abstract: The critical resolved shear strength of pure metals is given by the Peierls-Nabarro equation; impurities or alloying elements will significantly increase . Additional strength is introduced by strain hardening (SH), the grain size effect (GSE), precipitates and particle dispersion. The combination of these mechanisms is generally described in an additive manner, which can be justified by the Taylor expansion of a multivariate function. This approach is highly empirical and involves extensive parameter fitting. The Kocks-Mecking model (KM) and discrete dislocation dynamics show that SH is mainly due to forest effects (latent hardening). Consequently, the main explanation for alloy strength must be sought in the resistance against dislocation percolation through a field of obstacles with different strengths, with the slip length limited by the grain diameter. This hypothesis is explored by reviving early graphical simulations to the percolation problem by introducing a grain boundary and variable obstacle strength in an efficient computer program. Such simulations and theoretical considerations demonstrate the limitations of the additive description of combined hardening. An alternative approximation is proposed, based on the statistical analysis of dislocation percolation, dislocation junctions and dislocation-grain boundary interaction.

Abstract: Vanadium alloys are highly promising as structural materials of fusion reactor blanket, owing to their excellent high-temperature strength, and good compatibility with liquid metal lithium, which functions as both a coolant and a fuel tritium breeder material. Chemical composition of V-4Cr-4Ti has been selected as the primary candidate after systematic investigations into its neutron irradiation properties. Since V and Cr do not produce long-lived radioactive isotopes emitting high-energy gamma rays even under intense neutron irradiation conditions, low-activation characteristics are primarily governed by Ti and detrimental high-activation impurities, such as Co, Cu, Fe, Mo, Nb, and Ni. Very early material recycling, such as remote recycling within ten years, and re-use even in the same fusion reactor is achievable through effective impurity removal and minimization of Ti concentration. This paper discusses the progress in and mechanisms of vanadium metal refining. Additionally, the present paper reviews recent results and current status of redesign efforts for the Cr and Ti concentration balance to identify a new high-Cr and low-Ti composition, maintaining various attractive properties of the V-4Cr-4Ti alloy.

Abstract: Microstructural evolution during D.C. casting and subsequent homogenization of non-heat-treatable aluminium alloys involves complex phenomena, including micro-segregation of alloying elements and intermetallic phase selection during solidification as well as phase transformations of both primary (constituents - intergranular) and secondary (dispersoids - intragranular) intermetallic phases. In this study, we simulated the microstructural evolution of AA3003 using a CALPHAD-based modelling framework implemented in ThermoCalc®. The framework integrates a Scheil-Gulliver solidification model coupled with a 1-D micro-segregation alleviation and diffusional phase transformation model (DICTRA®) and a Kampmann-Wagner Numerical (KWN) model for dispersoid precipitation (TC-PRISMA®). According to this approach, the development of a robust computational methodology is aimed at accurately predicting the influence of homogenization cycles on dispersoid precipitation, which in turn affects recrystallization behaviour via the well-known Smith-Zener drag phenomenon. Additionally, these CALPHAD-based simulations facilitate the assessment of impurity content effects on dispersoid precipitation, considering the increasing use of scrap in the fabrication of non-heat-treatable aluminium alloys. Furthermore, they provide precise estimates of Smith-Zener pinning forces as inputs for downstream mesoscale full-field process models, contributing to a holistic through-process modelling approach.

Abstract: This research work focuses on the atomic study of hexagonal titanium (Ti) in order to estimate the relative accuracy of DFT (Density Functional Theory) and Molecular Statics (MS) approaches to better understand the interactions between solute atoms and twins. Four twins (2 tensile twins and 2 compressive twins) were modeled and then doped with the following elements: hydrogen, oxygen, nitrogen, aluminum and vanadium (H, O, N, Al, V). The formation energies of the twins as well as the segregation energies of the solute atoms were calculated to better predict the concentration heterogeneities of these elements in the material and their possible influence on local mechanical properties.

Abstract: Magnesium-based bulk metallic glasses (BMGs) present fabrication challenges due to their low glass-forming ability and high critical cooling rate. Copper mold casting, with its high thermal conductivity, is the most viable method for producing Mg-based BMGs, though amorphous diameters typically remain under 10 mm, limiting practical applications. This study uses FLOW-3D CAST simulations to analyze heat transfer and solidification behavior in two copper mold designs. The simulations evaluate flow uniformity, thermal dissipation, and cooling rate distribution, aiming to correlate cooling rate with achievable BMG diameter. The results provide design guidance for casting larger amorphous Mg components.

Abstract: This study presents a new mathematical model for determining the specific growth rate of biomass in biotechnological production processes, which aims to optimize the production of biotechnological products such as the advanced material polyhydroxyalkanoates. The specific growth rate is classified by the FDA as a critical process parameter that affects product quality and quantity, but is difficult for laboratory personnel to determine. Therefore, a simple and robust method for real-time monitoring and control is crucial. According to the current state of the art, the established Luedeking-Piret model for determining the specific growth rate requires the determination of the biomass as an absolute value to initialize the model and to determine two further model parameters. However, determining the biomass is time-consuming and error-prone. The new relative model replaces this value with the relative change in biomass, which can be easily recorded using standard laboratory methods such as optical density measurement. This eliminates the need for time-consuming and resource-intensive preliminary work. Despite this simplification, simulation tests have shown that the new model delivers identical results to the established model. It represents an independent, precise alternative and offers advantages in terms of handling. The results underline the model's potential to make bioprocesses more sustainable and efficient. Especially in research, material consumption, laboratory time and costs can be reduced compared to the established model. Future experiments will further investigate the performance of the new approach compared to the established model.

Abstract: This work investigates the influence of initial residual stresses after additive manufacturing, specifically directed energy deposition, in 5xxx aluminum alloys on the fatigue crack propagation behavior. For this purpose, initial plane stress states (compressive as well as tensile) are introduced along the crack path on a C(T)50 specimen via eigenstrains, mimicking possible residual stress states after both directed energy deposition and possible post-processing. The evolution of the stress intensity factor difference is determined and used to calculate the crack propagation rate via Walker’s equation. The stress state of the vicinity of the crack tip dictates the crack behavior: Compressive stresses perpendicular to the crack path exhibit crack closure, resulting in slower propagation rates. Finally, the influence of a more local distribution of the residual stresses on the fatigue crack propagation is investigated, highlighting the importance of the position of compressive stresses relative to the crack tip for effective crack growth retardation.