The aluminum (Al) alloy AW-7075 is recognized for its high yield strength, making it suitable to replace high strength steels, thereby contributing with lightweight strategies worldwide. However, due to its metallurgical properties it is considered not suitable for joining via fusion methods, exhibiting a wide melting range, proneness to cracking and low solubility of the alloying elements in the solidified Al matrix. To address this problem, a new resistance spot welding (RSW) procedure to properly join AW-7075 was developed in previous work. This procedure involved continuous upslope current profiles, larger electrode force, and copper-silver electrode caps, which were implemented to validate the application of RSW to join AW-7075. In this work, a parametric study was carried out to assess the impacts of these welding parameters on the weld quality. Optical microscopy was used to assess the weld quality, electron back-scattered diffraction (EBSD) for microstructural texture characterization, and scanning-electron microscopy (SEM) along with electrondiffraction spectroscopy (EDS) to identify the resulting phases in the grains and at the grain boundaries. Defect-free weld joints were repeatedly produced, process boundaries were validated, and improvement of the microstructure was verified, whereby finer and equiaxial grains (EG) were detected directly in the vicinities of the heat-affected zone (HAZ). Results show that slower upslope grades favor the formation of EG by changing the solidification mechanism from columnar (directional) to equiaxial (non-directional).

We introduce a method that combines neural operators, physics-informed machine learning, and standard numerical methods for solving PDEs. The proposed approach unifies aforementioned methods and we can parametrically solve partial differential equations in a data-free manner and provide accurate sensitivities. These capabilities enable gradient-based optimization without the typical sensitivity analysis costs, unlike adjoint methods that scale directly with the number of response functions. Our Finite Operator Learning (FOL) approach originally employs feed-forward neural networks to directly map the discrete design space to the discrete solution space, and can alternatively be combined with existing physics-informed neural operator techniques to recover continuous solution fields, while avoiding the need for automatic differentiation when formulating the loss terms. The discretized governing equations, as well as the design and solution spaces, can be derived from any well-established numerical techniques. In this work, we employ the Finite Element Method (FEM) to approximate fields and their spatial derivatives. Thanks to the finite-element formulation, Dirichlet boundary conditions are satisfied by construction, and Neumann boundary conditions are naturally included in the FE residual through the weak form. Subsequently, we conduct Sobolev training to minimize a multi-objective loss function, which includes the discretized weak form of the energy functional, boundary conditions violations, and the stationarity of the residuals with respect to the design variables. Our study focuses on the heat equation and the mechanical equilibrium problem. First, we primarily address the property distribution in heterogeneous materials, where Fourier-based parameterization is employed to significantly reduce the number of design variables. Second, we explore changes in the source term in such PDEs. Third, we investigate the solution under different boundary conditions. In the context of gradient-based optimization, we examine the tuning of the microstructure's heat transfer characteristics. Our technique also simplifies to an efficient matrix-free PDE solver that can compete with standard available solvers. This is demonstrated by solving a nonlinear thermal and mechanical PDE on a complex 3D geometry.

In injection molding processes of semi-crystalline polymers, different cooling rates occur at the mold walls and in the part center leading to an inhomogeneous melt solidification and the formation of locally different spherulitic microstructures. To determine their effect on the local thermo-elastic properties and their impact on the part warpage, a multi-scale simulation scheme is used here to investigate the injection molding of an alpha-iPP stepped plate. After modeling the melt flow during the injection phase, the residual packing pressure is determined in the cooling phases. Then, the formation of the spherulite microstructure is calculated over a plate section with an athermal nucleation model. Based on the predicted effective lamella properties, the radial spherulite model is extended here. It permits deriving more accurate and less anisotropic effective thermo-elastic properties. The local mechanical properties vary strongly in accordance with the local crystallization degree. A generalized plane strain model is used to predict the warpage and shrinkage of the plate section during the in-mold cooling phase and after ejection. Simulations with either constant, mean properties or local ones show clearly that crystallization-dependent properties predict more accurately the warpage and shrinkage behavior compared to constant properties over the plate section.

Abstract In situ brazing is a powerful method for understanding dynamic material behavior during joining process, enabling real-time observation of melting, wetting, and interfacial reactions. The present study investigates the influence of aluminum alloy chemical composition on wetting behavior and interfacial phase formation during soldering with a Sn78Cu22 alloy. The experiments were performed inside a large-chamber scanning electron microscope (LC-SEM) to monitor heat-induced deformation, melting, melt propagation, elemental segregation, and solidification. Microstructural and compositional analyses were carried out using SEM/EDX and TEM, supported by thermodynamic calculations using Thermo-Calc. Despite the low melting point of Sn78Cu22, solder reactions could only be initiated at significantly higher temperatures, namely 466 °C for EN AC-42,100, 500 °C for EN AW-5083, and 600 °C for EN AW-3003, due to the presence of stable surface oxide films. The Si-rich EN AC-42,100 alloy exhibited early filler deformation and formation of Al–Cu and Cu–Sn intermetallic compounds, namely Cu6Sn5, Cu2Sn, while Sn wetting was limited by a Si diffusion barrier. In contrast, the EN AW-5083 and EN AW-3003 alloys showed delayed wetting caused by MgO and MgAl2O4 oxide layers, respectively. For EN AW-5083, Mg reacted with Sn to form Mg2Sn within the filler and at the interface, accompanied by Al–Cu formation. For EN AW-3003, Al–Cu interdiffusion led to the formation of Cu-rich Al4Cu9-type intermetallics with shallow Sn penetration. These results demonstrate that aluminum alloy chemistry critically governs wetting kinetics and interfacial reactions during soldering with Sn78Cu22.

The pursuit of lightweighting in critical industries necessitates advanced joining solutions for high-strength aluminum alloys like AW-7075. However, the inherent metallurgical characteristics of AW-7075 render it highly susceptible to hot cracking and detrimental microstructural defects during conventional fusion welding processes such as Resistance Spot Welding (RSW). Our previous work (Part 1 and Part 2 of this series) demonstrated that a novel RSW procedure, characterized by continuous upslope current profiles, significantly improves weld quality and promotes a beneficial shift from columnar to refined equiaxed grain structures within the fusion zone (FZ).The current work employs comprehensive Finite Element Method (FEM) simulations to provide a quantitative, mechanistic understanding of the underlying thermal phenomena governing this microstructural evolution. A robust multiphysics FEM model was employed and validated against experimental temperature profiles and weld nugget diameters. The model enabled the extraction and analysis of solidification parameters, including temperature gradient (G), solidification rate (R), cooling rate (GxR), and the morphological parameter (G/R), as functions of time and spatial position within the weld nugget.The simulations reveal that lower upslope grades effectively reduce the temperature difference between the FZ and the heat-affected zone (HAZ) and lead to significantly lower G/R ratios, promoting formation of fine, equiaxed grains. Additionally, higher cooling rates were associated with upslope welding current, resulting in finer grains in comparison with conventional RSW. These systematically explained the experimentally observed changes in Columnar-to-Equiaxed Transition (CET) and enhanced weld quality. This study provides fundamental, simulation-based insights into the manipulation of solidification conditions in RSW, paving the way for optimized process control and broader application of AW-7075 in high-performance structural designs.

In this work, we introduce implicit Finite Operator Learning (iFOL) for the continuous and parametric solution of partial differential equations (PDEs) on arbitrary geometries. We propose a physics-informed encoder-decoder network to establish the mapping between continuous parameter and solution spaces. The decoder constructs the parametric solution field by leveraging an implicit neural field network conditioned on a latent or feature code. Instance-specific codes are derived through a PDE encoding process based on the second-order meta-learning technique. In training and inference, a physics-informed loss function is minimized during the PDE encoding and decoding. iFOL expresses the loss function in an energy or weighted residual form and evaluates it using discrete residuals derived from standard numerical PDE methods. This approach results in the backpropagation of discrete residuals during both training and inference. iFOL features several key properties: (1) its unique loss formulation eliminates the need for the conventional encode-process-decode pipeline previously used in operator learning with conditional neural fields for PDEs; (2) it not only provides accurate parametric and continuous fields but also delivers solution-to-parameter gradients without requiring additional loss terms or sensitivity analysis; (3) it can effectively capture sharp discontinuities in the solution; and (4) it removes constraints on the geometry and mesh, making it applicable to arbitrary geometries and spatial sampling (zero-shot super-resolution capability). We critically assess these features and analyze the network's ability to generalize to unseen samples across both stationary and transient PDEs. The overall performance of the proposed method is promising, demonstrating its applicability to a range of challenging problems in computational mechanics.

The transition from primary to secondary aluminium production offers substantial environmental benefits but introduces challenges related to impurity-induced changes in microstructure and final materials performance in mechanical integrity and corrosion resistance. This study investigates the influence of most common Fe, Mn, and Cu impurities on the formation of intermetallic phases in AlSi7Mg0.3 alloys using a combined CALPHAD and machine learning framework. High-throughput Scheil solidification simulations were conducted on 4999 alloy compositions using Thermo-Calc, and the resulting data were used to train and validate a Random Forest regression model. The model exhibited robust predictive performance (R2 = 0.98, NRMSE = 0.07, NMAE = 0.05) and was employed to compute phase fractions for over 20 million alloy compositions within the defined impurity space. SHAP-based feature analysis revealed interactions, direct as well as indirect, between impurity elements and key phases, highlighting the opposing roles of Fe and Mn in stabilizing β-Al5FeSi (AL9FE2SI2) and Al15SI2M4. And the resulting impurity-phase maps provide quantitative, thermodynamics-based decision support for impurity management and manganese optimization in recycled aluminium alloys.

This work extends finite element–guided physics–informed operator learning to multiphysics problems with coupled partial differential equations (PDEs) and systematically evaluates its performance across several representative problem settings. The extended formulation for multiphysics problems learns solution operators with a weighted residual formulation based on the finite element method, enabling predictions on discretizations different from the training resolution without relying on labeled simulation data. It is implemented in Folax, a JAX–based operator–learning platform, and is evaluated on nonlinear thermo–mechanical and chemo–mechanical problems. Two– and three–dimensional representative volume elements with varying heterogeneous microstructures, and an application–oriented industrial casting example with a fixed irregular geometry and parametrically varying boundary conditions are investigated as the example problems. We investigate the potential of several neural operators combined with the finite element–guided approach, including Fourier neural operators (FNOs), deep operator networks (DeepONets), and an adapted implicit finite operator learning (iFOL) approach based on conditional neural fields. The results demonstrate that FNOs yield highly accurate solution operators on regular domains, where the global features can be efficiently learned in the spectral domain, and iFOL offers efficient parametric operator learning capabilities on the complex irregular casting geometry considered in this study. Furthermore, additional studies identify trade–offs among training strategies and network decomposition schemes in terms of prediction accuracy and computational efficiency. Overall, the results clarify the capabilities and limitations of finite element–guided operator learning for coupled multiphysics problems and provide practical insights into the selection of neural operator architectures and training strategies.

The effect of metallic impuritiesImpurities on mechanical and corrosive properties of aluminum alloysAluminum alloy are well documented. It is attributed to the microstructural changes in the alloy. Especially precipitationPrecipitation of electrochemically active or brittle intermetallicIntermetallic particles is problematic for the final component’s integrity. In this work, a workflow is proposed to predict the microstructureMicrostructure of AlSi7Mg0.3 cast alloy, depending on the Fe and Cu impurityImpurities content and the corresponding corrosion and mechanical propertiesMechanical properties via a cascade of different simulationSimulation methods.

We propose a Newton-based scheme, initialized by neural operator predictions, to accelerate the parametric solution of nonlinear problems in computational solid mechanics. First, a physics informed conditional neural field is trained to approximate the nonlinear parametric solutionof the governing equations. This establishes a continuous mapping between the parameter and solution spaces, which can then be evaluated for a given parameter at any spatial resolution. Second, since the neural approximation may not be exact, it is subsequently refined using a Newton-based correction initialized by the neural output. To evaluate the effectiveness of this hybrid approach, we compare three solution strategies: (i) the standard Newton-Raphson solver used in NFEM, which is robust and accurate but computationally demanding; (ii) physics-informed neural operators, which provide rapid inference but may lose accuracy outside the training distribution and resolution; and (iii) the neural-initialized Newton (NiN) strategy, which combines the efficiency of neural operators with the robustness of NFEM. The results demonstrate that the proposed hybrid approach reduces computational cost while preserving accuracy, highlighting its potential to accelerate large-scale nonlinear simulations.

The MaterialDigital initiative represents a major driver toward the digitalization of material science. Next to providing a prototypical infrastructure required for building a shared data space and working on semantic interoperability of data, a core focus area of the Platform MaterialDigital (PMD) is the utilization of workflows to encapsulate data processing and simulation steps in accordance with findable, accessible, interoperable, and reusable principles. In collaboration with the funded projects of the initiative, the workflow working group strives to establish shared standards, enhancing the interoperability and reusability of scientific data processing steps. Central to this effort is the Workflow Store, a pivotal tool for disseminating workflows with the community, facilitating the exchange and replication of scientific methodologies. This article discusses the inherent challenges of adapting workflow concepts, providing the perspective on developing and using workflows in the respective domain of the various funded projects. Additionally, it introduces the Workflow Store's role within the initiative and outlines a future roadmap for the PMD workflow group, aiming to further refine and expand the role of scientific workflows as a means to advance digital transformation and foster collaborative research within material science.

In injection molding processes of semi-crystalline polymers, inhomogeneous solidification of the melt occurs resulting in complex warpage of the final part. They present a strongly different cooling behavior at mold walls and in their center. Thus, locally different spherulite microstructures are formed in the component leading to residual stresses formed during the injection molding process. To determine the effect of these inhomogeneities on the local thermo-elastic and thermal properties, the injection molding of an isotactic polypropylene (alpha-iPP) stepped plate is investigated. The previously developed multiscale simulation scheme has been extended to address thermo-elastic homogenization of semi-crystalline polymers. A new Representative Volume Element (RVE) of the cross-hatched crystalline-amorphous alpha-iPP lamella is introduced at the nanoscale, leading to a stiffer and less anisotropic effective lamella behavior. Besides, a relationship between the local crystallization degree and the cooling rate is derived, based on DSC and Flash-DSC measurements. Corresponding to the local crystallization degree, a specific RVE either with or without secondary branches is designed. In this way, the effect of locally different crystallization degrees on the effective thermo-elastic and thermal properties of the effective semi-crystalline alpha-iPP lamella is first determined at the nanoscale. The predicted values for the effective elastic Young's and shear moduli are smaller at mold walls and stiffer in the core area of the part than the corresponding modules, predicted with a constant, mean crystallization degree xi over the plate thickness; whereas the mean effective thermal expansion alpha m decreases continuously with the crystallization degree xi over the half plate section.

Fast prediction of microstructural responses based on realistic material topology is vital for linking process, structure, and properties. This work presents a digital framework for metallic materials using microscale features. We explore deep learning for two primary goals: (1) segmenting experimental images to extract microstructural topology, translated into spatial property distributions; and (2) learning mappings from digital microstructures to mechanical fields using physics-informed operator learning. Loss functions are formulated using discretized weak or strong forms, and boundary conditions-Dirichlet and periodic-are embedded in the network. Input space is reduced to focus on key features of 2D and 3D materials, and generalization to varying loads and input topologies are demonstrated. Compared to FEM and FFT solvers, our models yield errors under 1–5% for averaged quantities and are over 1000× faster during 3D inference.

To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of the finite element method with physics-informed neural networks and concept of neural operators. This approach generalizes and enhances each method, learning the parametric solution for mechanical problems without relying on data from other resources (e.g. other numerical solvers). We propose directly utilizing the available discretized weak form in finite element packages to construct the loss functions algebraically, thereby demonstrating the ability to find solutions even in the presence of sharp discontinuities. Our focus is on micromechanics as an example, where knowledge of deformation and stress fields for a given heterogeneous microstructure is crucial for further design applications. The primary parameter under investigation is the Young's modulus distribution within the heterogeneous solid system. Our investigations reveal that physics-based training yields higher accuracy compared to purely data-driven approaches for unseen microstructures. Additionally, we offer two methods to directly improve the process of obtaining high-resolution solutions, avoiding the need to use basic interpolation techniques. First is based on an autoencoder approach to enhance the efficiency for calculation on high resolution grid point. Next, Fourier-based parametrization is utilized to address complex 2D and 3D problems in micromechanics. The latter idea aims to represent complex microstructures efficiently using Fourier coefficients. Comparisons with other well-known operator learning algorithms, further emphasize the advantages of the newly proposed method.

For many high-performance alloys originally developed for the casting route, hot cracking is a serious problem in the Laser Powder Bed Fusion (PBF-LB/M) process and limits the use of e.g. high-gamma ' nickel-based alloys such as CM247LC in additive manufacturing. In this work, we investigate the relationship between PBF-LB/M processing parameters and the solidification path, i.e. phase formation and microsegregation, and its potential impact on hot cracking for the high-gamma ' alloy CM247LC. We combined experimental microstructural analysis using scanning and transmission electron microscopy, atom probe tomography and diffraction techniques with multiphase-field simulations on mu m scale. Process simulations at mesoscale of the melt pool provide the link between the process conditions and the thermal boundary conditions for the microstructural simulations. The study confirms the appearance of carbides, borides and gamma '-precipitates in the as-solidified microstructure. The quantity and particle size of these phases as observed in the experimental samples, are in qualitative agreement with the simulation results. Therefore, the simulations can be used to elucidate and quantify the differences in the solidification path for different thermal process conditions. Although the comparison of samples processed with high energy density (cooling rate 65,000 K/s) with those processed with low energy density (cooling rate: 570,000 K/s) show large differences in the crack density observed in the experiments, the microstructural differences and the phase formation at the dendritic scale do not show any remarkable qualitative or quantitative differences. The correlation between processing conditions, microstructure evolution and crack formation is critically discussed and differences to the current understanding presented in existing literature are identified.

In this work, a numerical approach is applied to study the impact of local cooling conditions on the hot tearing in an aluminium-copper alloy with iron, magnesium and silicon as impurities. At first, CALPHAD-coupled multicomponent and multiphase-field simulations were performed to elucidate the effect of cooling conditions on solidification morphology in the final, critical stage of solidification. Then, the evolution of the melt flow permeability is derived from the simulated three-dimensional microstructures and discussed in the context of the Rappaz-Drezet-Gremaud criterion for hot tearing susceptibility. With increasing cooling rates, the microstructure becomes finer and the resulting permeability first increases and then saturates within the investigated range. It is shown that the Rappaz-Drezet-Gremaud hot-tearing criterion in combination with microstructure simulations responds to different cooling conditions in contrast to a Scheil-Gulliver based model or an evaluation of the average Kou-index. The impact of cooling rate on the solidification morphology of an aluminum-copper alloy and the hot tearing susceptibility is studied utilizing microstructure simulations. The 3D solidification evolution of the alloy under different cooling rates is simulated using a multicomponent multiphase-field model. Morphologic parameters are evaluated and employed to study the hot tearing tendency.image

Thermo-physical data of the semi-solid region in directionally solidified materials are difficult to obtain by experiments, but at the same time of high importance for the prediction of casting defects like freckles, hot-tears, or micro-porosity, and further provide input for mesoscopic or macroscopic models. This paper shows how data like phase fractions, compositions, enthalpies, densities, as well as the melt permeability can be obtained for the whole range between liquidus and solidus temperature, and how an integral alloy-specific freckle risk can be assessed by performing 3D-phase-field simulations of a representative volume of the mushy zone. A phase-field model has been set up, and simulations have been done for the multicomponent Ni-base superalloys CMSX-4, SC2000, MAR-M247, and an MTU-test alloy using the software MICRESS® with online-coupling to thermodynamic and mobility databases. Furthermore, a numerical prediction of the primary dendrite arm spacing (PDAS) is provided by systematic variation of the simulation domain size using different methods based on the dendrite tip temperature and the diffusion fields in the liquid phase. The results are discussed against analytical relations.

We propose a novel finite element-based physics-informed operator learning framework that allows for predicting spatiotemporal dynamics governed by partial differential equations (PDEs). The Galerkin discretized weak formulation is employed to incorporate physics into the loss function, termed finite operator learning (FOL), along with the implicit Euler time integration scheme for temporal discretization. A transient thermal conduction problem is considered to benchmark the performance, where FOL takes a temperature field at the current time step as input and predicts a temperature field at the next time step. Upon training, the network successfully predicts the temperature evolution over time for any initial temperature field at high accuracy compared to the solution by the finite element method (FEM) even with a heterogeneous thermal conductivity and arbitrary geometry. The advantages of FOL can be summarized as follows: First, the training is performed in an unsupervised manner, avoiding the need for large data prepared from costly simulations or experiments. Instead, random temperature patterns generated by the Gaussian random process and the Fourier series, combined with constant temperature fields, are used as training data to cover possible temperature cases. Additionally, shape functions and backward difference approximation are exploited for the domain discretization, resulting in a purely algebraic equation. This enhances training efficiency, as one avoids time-consuming automatic differentiation in optimizing weights and biases while accepting possible discretization errors. Finally, thanks to the interpolation power of FEM, any arbitrary geometry with heterogeneous microstructure can be handled with FOL, which is crucial to addressing various engineering application scenarios.

We present a method that employs physics-informed deep learning techniques for parametrically solving partial differential equations. The focus is on the steady-state heat equations within heterogeneous solids exhibiting significant phase contrast. Similar equations manifest in diverse applications like chemical diffusion, electrostatics, and Darcy flow. The neural network aims to establish the link between the complex thermal conductivity profiles and temperature distributions, as well as heat flux components within the microstructure, under fixed boundary conditions. A distinctive aspect is our independence from classical solvers like finite element methods for data. A noteworthy contribution lies in our novel approach to defining the loss function, based on the discretized weak form of the governing equation. This not only reduces the required order of derivatives but also eliminates the need for automatic differentiation in the construction of loss terms, accepting potential numerical errors from the chosen discretization method. As a result, the loss function in this work is an algebraic equation that significantly enhances training efficiency. We benchmark our methodology against the standard finite element method, demonstrating accurate yet faster predictions using the trained neural network for temperature and flux profiles. We also show higher accuracy by using the proposed method compared to purely data-driven approaches for unforeseen scenarios.

To improve understanding of the material behavior of additive-produced components, this paper focuses on the development of a numerical model that reproduces a Wire Arc Additive Manufacturing (WAAM) process, with particular attention given to the evolution of the microstructure. In this study, a finite element model in Simufact Welding software is developed, that replicates a real wire arc welding process of building a multilayer straight wall. Microscopy analysis of the weld wall cut in the middle of its length gave information about the expected microstructure morphology at different levels of the build wall. The whole experimental setup is reproduced in the software Simufact Welding. Simulation results in the form of temperature-time and temperature gradient-time history are then used as superimposed thermal conditions to simulate the microstructure evolution at different areas of the welded part by using MICRESS software.