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In crystal plasticity finite element (CPFE) simulations, accurately quantifying geometrically necessary dislocations (GNDs) is critical for capturing strain gradients in polycrystals. We compare different methods for quantifying GNDs, all of which originate from the Nye tensor, which is computed as the curl of the plastic deformation gradient. The projection technique directly decomposes the Nye tensor onto individual screw and edge dislocation components to compute GNDs. This approach requires converting a nine-component Nye tensor into densities for a larger number of dislocation systems, a fundamentally underdetermined (non-unique) process, which is resolved using L2 minimization. In contrast, when employing CPFE analysis, one could directly compute dislocation densities on each slip system using shear gradients. Projection and slip gradient methods are compared with respect to their prediction of GNDs with changing grain size, strain, and grain neighborhoods, including multigrain junctions. Although these techniques match analytical GND densities for single slip, single crystal deformation, and are consistent with anticipated overall GND trends, we find that the GND densities from projection techniques are significantly lower than those predicted from CPFE-based slip gradients in polycrystals. A suggested improvement of only using the active dislocation systems in the projection technique almost entirely resolved this mismatch.
The thermally anisotropic building envelope (TABE) is an active building envelope that redistributes thermal loads in response to weather conditions and building energy demand. Conductive layers throughout the TABE distribute low-grade heat among hydronic loops, altering heat flow direction and intensity. Finite element models of TABE roof and wall panels were developed and calibrated using field evaluation data. The calibration results showed that heat flux differences between the experimental data and finite element models averaged –0.42% and 3.57%, with a maximum mean square error of 1.78 and 3.96 for roof and wall panels, respectively. A reduction in heat flux from the environment to the building living space over the entire testing period (weeks in July/August) was found to be 85% for roof panels and 335% (load reversed) for wall panels. Finally, these results indicate TABE can effectively harness low-grade thermal energy sources to achieve high energy efficiency and promote demand-side management.
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The superior performance of niobium superconducting radio frequency (SRF) cavities is achieved through meticulous surface treatment, notably via chemical electropolishing, ensuring exceptionally smooth surfaces. While this technique has been extensively employed for cylindrically symmetric structures, addressing more intricate geometries poses significant challenges in achieving uniform polishing and controlled material removal, especially when moving away from retractable cathodes. This presents a multifaceted electrochemical, thermal, and fluid dynamics conundrum. A prime example is the 197 MHz radio frequency dipole (RFD) crabbing cavity proposed for the Electron Ion Collider (EIC) project, exemplifying such complex structures. Our groundbreaking work integrates the localized oxide thickness variation, considering its impact on current distribution and Joule heating, within the framework of multi-physics modeling using the COMSOL® simulation suite. This approach was applied to a comprehensive model of the RFD cavity, allowing us to investigate optimal external cooling water flow conditions necessary for achieving desirable outcomes. In conclusion, this illustrates the increasing utility of such multi-physics codes to greatly aid in designing solutions to challenging processing requirements for increasingly complex accelerator cavities.
The objective of this project is to validate low-fidelity models of 304L to 304L stainless steel partial-penetration laser welds for thin sheets. Low-fidelity means that the weld is represented by coarsely meshed element blocks. Here, the hexahedral element size is approx imately half the weld penetration depth. The material behavior of the block is represented by a J2 plasticity model with a Voce hardening function. The source of the data used in this work is an extensive experimental study conducted by Sharlotte Kramer (1528) and published in 2015. Figure 1 shows a cross-section of the weld of interest. The nominal thickness of the sheets is 0.063 in. while the target penetration depth of the weld is in the range of 0.028 to 0.032 in., extending about half the sheet thickness. Uniaxial tension tests provided data for calibration of base material and weld models. Results of two validation geometries were also provided. The principal validation geometry is shown in Fig. 2. It consists of a plate specimen with in-plane dimensions 6 in × 2.875 in loaded in tension. A circular plug with a 1.5 in. diameter was cut from the center of the plate and then welded in place. The details of the welding schedule are given. An important assumption is that the welds in the calibration and validation specimens have similar geometric and material properties as those in the validation tests. The task was to first calibrate models for the base material and the welds and then simulate the validation tests until the point of weld first failure.
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This report describes the methodology used for the safety basis analysis of the Building (Bldg.) 3525 casks and presents preliminary results for a selected geometry. The specific problem analyzed is a free fall load case onto an unyielding target at various orientations. The various orientations were analyzed to ensure that the packages were subjected to the orientation that causes the most damage. The analysis approach, material modeling, finite element modeling, and results for the selected case are presented, along with a brief discussion of conservatism and uncertainties. The results for the analyzed load cases show that through selected administrative controls, no breach of the container or loss of shielding will occur in the package.
Creep strength-enhanced ferritic (CSEF) steels such as Grade 91 (9Cr-1Mo-V) and Grade 92 (Fe-9Cr-2W-0.5Mo) steels are widely used in the fossil-fuel-fired and nuclear power plants. The weld integrity of these steels is crucial for power plants' safe and reliable operations. Due to harsh service conditions, the steel weld can become susceptible to environmental degradation. Field welding repair is used to restore the degraded weld’s performance where a controlled temper-bead welding technique is commonly used to temper the freshly formed martensite during welding. However, knowledge of weld repairability is limited and experimental trial and error optimization to achieve desired microstructure and joint properties is expensive and time-consuming. Many existing computational models, e.g., finite element models, are limited to solving heat conduction equation and ignoring convective heat transfer due to molten metal flow. These models can result in over-prediction of peak temperatures of weld pool and heat-affected zone (HAZ), which in turn can affect the accuracy of tempering prediction. Moreover, these finite element models require an input of the deposit profiles in advance and thus limits the usability of these models. Here, a molten pool-based, multi-pass multi-layer model has been developed based on computational fluid dynamics (CFD) approach with the Volume of Fluid (VOF) method. The model calculates the bead formation, thereby eliminating the need for pre-determined bead profiles required by finite element models. For computational efficiency, a coordinate system attached to the moving heat source is utilized. A subroutine is developed to convert the temperature profiles in the reference frame stationary to the heat source to that stationary to the workpiece. The converted thermal cycles are then imported into a microstructure model to compute the tempering kinetics and resultant hardness using a Johnson-Mehl-Avrami-Kolmogorov (JMAK), and modified Grange-Baughman parameter. The modeling approach is first developed and validated on single- and multi-pass deposition of stainless steel filler metal onto a SA-533 high strength steel substrate. The models are then applied to a multi-pass V-groove repair weld of Grade 91 steel plate as well as directed energy deposition of Grade 92 steel. Non-destructive characterization of microstructures was performed on Grade 91 and 92 steel welds. Two welding processes, cold metal transfer (CMT) and flux-cored arc welding (FCAW), were investigated for the Grade 91 steel weld samples. For the Grade 92 weld samples, three different heat inputs (low, medium, and high) of gas tungsten arc welding (GTAW) were utilized to replicate traditional field welding processes. The non-destructive evaluation (NDE) method used for this research was immersion ultrasonic testing (UT) using a micro-resolution ultrasonic imaging methodology specifically designed to operate in the through-transmission configuration operating at 20 MHz of frequency. The system used a focused ultrasonic beam spot size diameter between 250-300 μm, and a 6 μm laser vibrometer spot size for detection, to produce highly defined images with longitudinal and mode-converted shear waves. From the micro-resolution ultrasonic C-scan images, three microstructural regions, i.e., weld metal (WM), HAZ, and base metal (BM), were clearly identifiable. Various levels of ultrasonic amplitudes distributed over the three regions were correlated with electron beam backscattered diffraction (EBSD) images using grain size, grain boundaries, and dislocation densities. The results showed that areas with relatively higher ultrasonic amplitude levels were associated with smaller grains and higher dislocation densities, while areas with lower amplitude levels were associated with larger grains and lower dislocation densities. In addition, ultrasonic velocity data obtained across the three different weld microstructural regions of Grade 91 test samples were correlated with optical metallographic images and hardness measurements. The results showed distinctive decreases in ultrasonic velocity and hardness over the HAZ region, where weld failures often occur during service.
Welding processes used in the production of pressure vessels impart residual stresses in the manufactured component. Computational modeling is critical to predicting these residual stress fields and understanding how they interact with notches and flaws to impact pressure vessel durability. Here, in this work, we present a finite element model for a resistance forge weld and validate it using laboratory measurements. Extensive microstructural changes, near-melt temperatures, and large localized deformations along the weld interface pose significant challenges to Lagrangian finite element modeling. The proposed modeling approach overcomes these roadblocks in order to provide a high-fidelity simulation that can predict the residual stress state in the manufactured pressure vessel; a rich microstructural constitutive model accounts for material recrystallization dynamics, a frictional-to-tied contact model is coordinated with the constitutive model to represent interfacial bonding, and adaptive remeshing is employed to alleviate severe mesh distortion. An interrupted-weld approach is applied to the simulation to facilitate comparison to displacement measures. Several techniques are employed for residual stress measurement in order to validate the finite element model: neutron diffraction, the contour method, and the slitting method. Model-measurement comparisons are supplemented with detailed simulations that reflect the configurations of the residual-stress measurement processes themselves. The model results show general agreement with experimental measurements, and we observe some similarities in the features around the weld region. Factors that contribute to model-measurement differences are identified. Finally, we conclude with some discussion of the model development and residual stress measurement strategies, including how to best leverage the efforts put forth here for other weld problems.
Accurate identification of material parameters is crucial for predictive modeling in computational mechanics. Here, the two primary approaches in the experimental mechanics community for calibration from full-field digital image correlation data are known as finite element model updating (FEMU) and the virtual fields method (VFM). In VFM, the objective function is a squared mismatch between internal and external virtual work or power. In FEMU, the objective function quantifies the weighted mismatch between model predictions and corresponding experimentally measured quantities of interest. It is minimized by iteratively updating the parameters of an FE model. While FEMU is seen as more flexible, VFM is commonly used instead of FEMU due to its considerably greater computational expense. However, comparisons between the two methods usually involve approximations of gradients or sensitivities with finite difference schemes, thereby making direct assessments difficult. Hence, in this study, we compare VFM and FEMU in the context of numerically-exact sensitivities obtained through local sensitivity analyses and the application of automatic differentiation software. To this end, we conduct a series of test cases to assess both methods under practical challenges using a finite strain elastoplasticity model.
The multielectron reduction of CO 2 to liquid fuels could be a path to scalable energy storage, but reaching this goal requires major advances in catalysis and systems engineering. Cascade catalysis, which couples sequential reactions without isolating intermediates, has emerged as a promising route to enhance selectivity and efficiency in CO 2 reduction (CO 2 R). In this review, we examine how finite-element-based simulations of continuum model [finite element method (FEM)] approaches are being used to analyze and guide CO 2 R cascade systems. We first outline the fundamentals of cascade catalysis and recent advances in catalytic materials (metallic, molecular, and hybrid architectures). We then focus on FEM developments at the electrode and device scales, emphasizing how these models capture transport phenomena, local microenvironments, and geometry-dependent effects. To clarify design principles, we present case studies of cascade electrodes organized in systems without and with integrated semiconductors. We further emphasize the integration of FEM with multiscale frameworks (density functional theory, molecular dynamics, kinetic Monte Carlo) and its role in bridging atomic-level insights with device-level performance. Finally, we identify current limitations and future prospects, including improved boundary conditions, coupling with operando experiments, and machine learning-accelerated model development. Together, these insights provide design principles for next-generation CO 2 R cascade systems for efficient solar fuel production.
Heat transfer in phase change materials (PCMs) is complex because the melting and freezing fronts change as functions of stored or released heat. In prior attempts to optimize heat exchangers (HXs) in one or two dimensions, complex geometry has often been used to maximize the melt and freeze front area. This complex geometry is difficult and hence expensive to construct. This paper proposes a multiple-scale 3D finite element modeling approach to design fin-tube HXs for low-cost latent thermal energy storage applications. Further, the optimal fin and tube designs were determined at three scales (unit-scale, medium-scale, and large-scale) by modeling the melt and freeze front in three dimensions and using measured bulk thermal properties. The finite element model was validated by comparing it with the experimental data for a referenced design of a similar type. The results indicate that commercially available organic PCMs with low conductivity (<0.3 W/m·K) can have charge and discharge times appropriate for building thermal energy storage (i.e., 4–5 h) with fin-tube HX designs at costs <$26/kWh, even when the temperature difference (5.56°C) between the heat transfer fluid and the PCM phase change temperature is small. However, as the HX increases in length, the temperature reduction along the tube limits some larger-scale designs.
To model material ductile failure and crack propagation, cohesive zone elements can be embedded along potential fracture paths in a finite element simulation. When damage criteria are met, elements in the mesh decohere, simulating the formation and propagation of a crack. In this paper, we present a novel computational algorithm based on finite deformation theory, essential to modeling crack initiation and growth in solids undergoing large deformations. This new algorithm was formulated within a Lagrangian frame of reference to extend previous cohesive zone algorithms to include modeling crack growth in finite deformation contexts. The local coordinate system, necessary for defining an embedded cohesive zone, is constructed based upon the current configuration and is updated within the nonlinear iteration process, thereby resulting in the convergence of the solution for a growing crack in a large deformation quasi-static setting. The model’s accuracy was demonstrated by comparing finite element model simulation results with the analytic case of a constant surface separation, as shown in the verification examples. The power and efficacy of the algorithm to capture large deformations during crack growth were then demonstrated with a double cantilever beam example case. It indicates that the model can be applied to a variety of physical circumstances for predicting crack initiation and growth with delamination and fracture.
Impedance Matched Multi-Axis Tests (IMMATs) can replicate in-service vibration induced stress more accurately than single axis shaker table tests as they can better match a part’s operational boundary conditions and excite it in multiple degrees of freedom simultaneously. Here, the shakers used in IMMATs are less powerful than shaker tables, so shaker force limits can be exceeded during tests if they are not placed adequately for the desired environment. The ability to predict shaker voltage and force before performing a test is, therefore, helpful in selecting shaker locations so that their limits are not exceeded. In this study, electrodynamic shakers were modeled as discrete electromechanical systems, and the shaker parameters were chosen to match experimentally obtained acceleration/voltage frequency response functions (FRFs). These models were coupled to a finite element model of the device under test (DUT) via dynamic substructuring, and the substructured model was demonstrated to accurately predict shaker voltage as well as the error in reproducing the environment at multiple accelerometer locations. A simple method called the FRF Multiplication method, in which the FRF of the substructured system is approximated as the product of two separate FRFs of the shaker and DUT respectively, was proposed and applied to the same system, yielding similar voltage and error predictions to those obtained using substructuring. Simple case studies were presented to explore the applicability of the proposed method, and it was demonstrated to have similar accuracy to the substructuring method in a range of cases. Additionally, we showed that while it was not possible to derive a unique model of the shakers from acceleration/voltage FRFs alone, the models that could be obtained were sufficient to predict test error almost perfectly and shaker voltage with less than 40 percent error.
A deep convolutional neural network (DCNN) was used for microstructure reconstruction using artificial intelligence (MR-AI) by predicting local average fiber orientation distributions (FOD) in a 3D prepreg platelet molded composite (PPMC) pin bracket. To train the MR-AI model, surface strain fields from residual stresses simulated in PPMC plates were used as the input to the DCNN. A training dataset included PPMC plates with various degrees of global fiber alignment, based on the information obtained from high-fidelity flow simulation of a pin bracket. Further, the MR-AI model was then deployed to analyze FOD in the 3D pin bracket by conducting thermo-elastic residual stress analysis. Initially, the MR-AI model was established entirely on the synthetic simulation data. Then, a μCT scan of a physically molded pin bracket was used to create a finite element model that provided data for additional validation of the DCNN model. For the μCT scan finite element pin bracket the MR-AI model predicted the distribution of fiber orientation tensor components with MAE of 0.10 indicating a global prediction error of 10%. For the flow simulated pin bracket, the MR-AI model predicted the distribution of fiber orientation tensor components with a global prediction error of 11%. The MR-AI model showed the ability to predict regions of varying alignment in the base and flange of the pin bracket. The proposed MR-AI methodology allows for rapid prediction of FOD in geometrically complex parts and offers a promising path to detecting unique fiber orientation states in molded components.