In-situ imaging of advanced materials subjected to in-plane biaxial loading using X-ray micro-computed tomography
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Materials Science↗
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Oil-Pressure Based Apparatus for In-Situ High-Energy Synchrotron X-Ray Diffraction Studies During Biaxial Deformation
Background: Understanding biaxial loading response at the microstructural level is crucial in helping better design sheet manufacturing processes and calibrate/validate material deformation models. Objective: The objective of this work was to develop a low-cost testing apparatus to probe, with sufficient spatial resolution, the micro-mechanical response of a sheet material in-situ under biaxial loading conditions. Methods: The testing apparatus fabricated as a part of this study operates in a similar fashion to a standard bulge test and uses oil pressure to generate biaxial loading conditions. This biaxial testing apparatus was operated within a synchrotron beamline to characterize the mechanical response of a flash-processed steel sheet using in-situ high-energy X-ray diffraction (XRD) measurements. Further, the GSAS-II package was utilized to develop a workflow for the analysis of the large volume of diffraction data acquired. The workflow was then used to extract the peak position, width, and integrated intensity of the XRD peaks corresponding to the major body-centered cubic phase. Results: The equi-biaxial nature of the loading in the measured area was independently corroborated using experimental (XRD) and simulation (finite element analysis) methods. Furthermore, we discuss the evolution of elastic strain in the major body-centered cubic phase as a function of applied oil pressure and location on the steel sheet. Conclusions: A key advantage of the biaxial apparatus fabricated in this synchrotron study is demonstrated using the results obtained for the flash-processed steel sheet – i.e., mapping the lattice plane-dependent response to biaxial loading for a relatively large sample area in a spatially resolved manner.
36 MATERIALS SCIENCE↗
Effects of rejuvenation modes on the microstructures and mechanical properties of metallic glasses
This study systematically investigates the effects of three rejuvenation modes, namely biaxial loading, thermal pressure loading, and cryogenic thermal cycling, on the microstructures and mechanical properties of Cu 64 Zr 36 metallic glasses (MGs) using molecular dynamics (MD) simulations. The simulation results demonstrate that biaxial tension application during loading results in a rejuvenated glassy state with high strength. Specifically, we find that the yield stress, Young's modulus, and shear modulus of the rejuvenated glass obtained by biaxial tensile loading decreased by 2.8%, 2.1%, and 2.7%, respectively, compared to an as-cast MG reference. We also find that MGs achieve the greatest degree of rejuvenation, at the expense of strength, with the use of thermal pressure loading. Interestingly, the application of cryogenic thermal cycling results in a rejuvenated state with a lower strength drop compared to thermal pressure loading. Furthermore, analysis of the potential energy and medium-range-order (MRO) size indicates that the microstructures of MGs achieves a high-energy ordered glass state after thermal pressure loading, but a high-energy disordered glass state after biaxial tensile loading and cryogenic thermal cycling. Furthermore, these findings provide meaningful insights into the effect of rejuvenation modes on the microstructures and mechanical properties of MGs, as well as useful guidelines for designing MGs with high strength and superior plasticity for prospective applications in industry.
36 MATERIALS SCIENCE↗
Plasticity-mediated deformation instabilities in thin film-compliant substrate systems: direct three-dimensional simulations
Abstract Surface wrinkles driven by mechanical instability commonly form in thin-film structures attached to a compliant substrate. In this study, a recently developed computational approach is employed to simulate the formation and transformation of wrinkles involving plastic yielding of the thin film. The three-dimensional (3D) finite element models contain an embedded imperfection at the film-substrate interface, serving to trigger the bifurcation modes. Successful application of this technique to allow for film plasticity is demonstrated, including the evolution of 3D surface patterns and their correlation with the overall load–displacement response. The simulations reveal that plastic yielding transforms the surface instability patterns into more localized forms. Under uniaxial loading, the sinusoidal elastic wrinkles undergo the wrinkle-to-fold transition. With equi-biaxial loading, the initial square-checkerboard array turns into continuous tall ridges along the 45° directions. In both loading modes, the plasticity-induced instability patterns are only partially relieved upon unloading, leaving permanent features on the surface.
36 MATERIALS SCIENCE↗
Step-loaded creep testing of Zircaloy-4 cladding at higher temperatures in the α-phase
A refined understanding of zirconium-based cladding thermomechanical performance during rapid transients is essential for enhancing the safety and operation of light-water reactors. Traditional models for zirconium alloys under accident conditions generally assume that creep dominates fuel cladding performance. Here, these historic models have largely remained unchanged and serve as the basis for safety criteria development. As the U.S. nuclear industry pursues higher burnup levels, the increased release of fission gases during transients raises the risk of cladding failure in the low-temperature hcp α-phase, making the fidelity of these models of greater importance. Creep testing was conducted from 550–700°C with 25–120 MPa applied hoop stresses to investigate Zircaloy-4 deformation at accident-relevant temperatures in the α-phase. Step-loading was employed to capture creep behavior across a wide stress range from a single sample. The stress-strain rate data at higher temperatures (650 and 700°C) were well-described by isotropic versions of the Erbacher and Kaddour models, while the lower temperature data (550 and 600°C) were underpredicted by both anisotropic and isotropic model variants. Greater strain rates during the initial loading step at 650 and 700°C were attributed to recrystallization and grain growth of sub-micron crystallites. Yet, texture analysis revealed the basal split texture remained after testing. These observations produced results suggesting Zircaloy-4 claddings experience higher creep rates across the α-phase than previously thought, possibly related to dynamic anisotropy due to temperature dependent activation of deformation mechanisms, effects of biaxial loading, and variation in material condition between the current testing used in previous model development.
36 MATERIALS SCIENCE↗
Multiaxial Plastic Deformation of Zircaloy-4 Nuclear Fuel Cladding Tubes
Here, this work is motivated by the desire to devise an internal pressure test that can mimic a displacement-controlled loading scenario and demonstrate how to apply the multiaxial stress and strain data from the test to develop an elastic/plastic constitutive model for a thin-walled tubular component. This is achieved by conducting simultaneous measurements of tangential and axial strain during the pressure test and integrating these strain measures into a feedback loop with the pressure controller. It is shown how data from such a test can be used to develop a large mechanical property data set relevant to biaxial loading conditions. The data obtained have high confidence evidenced by their low variability and alignment with other literature studies. Additionally, data from these internal pressure tests combined with full-tube axial tensile tests allow for the derivation of the Hill anisotropic yield function. The developed Hill yield function is validated by comparing the plastic strain ratios from the full-tube tension tests and by comparing the predicted yield stress in the tangential direction with measured values from ring tension tests in a previous study.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Mechanical failure of fresh nuclear grade iron–chromium–aluminum (FeCrAl) cladding under simulated hot zero power reactivity initiated accident conditions
The reactivity initiated accident (RIA) is a postulated accident in light water reactors initiated by a rapid increase in reactivity which causes an increase in fission rate and fuel temperature. One potential mode of fuel system failure during RIA is pellet cladding mechanical interaction (PCMI) due to the rapid thermal expansion of the fuel pellet. Simulated PCMI experiments were performed by rapidly pressurizing iron-chromium-aluminum (FeCrAl) cladding tube samples using a hydraulic modified burst test system, causing the specimens to burst under a biaxial loading path. Deformation and rupture of the specimens were tracked with a telecentric lens and high-speed camera system. Outer surface strains were calculated using digital image correlation (DIC) on speckle patterns painted on the specimens’ outer surfaces. Experiments were conducted at approximately 275 °C, representative of hot zero power RIA conditions. The failure hoop strain was DIC-calculated between approximately 1.8–3.4%, corresponding to quasi-static energy depositions of approximately 110–260 calories per gram UO 2 assuming initial pellet-cladding contact. These conditions are very similar to the proposed energy deposition limit of 150 calories per gram UO 2 for unirradiated zirconium-based cladding in US Nuclear Regulatory Commission (NRC) Draft Regulatory Guide 1327. A very small strain rate dependence was observed in the data, with the magnitude of the failure hoop strain decreasing slightly with increasing strain rate. This observed dependence may be relevant because the FeCrAl cladding strain rate will be approximately 20% higher than in zirconium-based cladding due to the harder neutron spectrum and resultant shorter neutron generation time.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Crack Identification and Characterization in Deformed Nb3Sn Rutherford Cable Stacks Using Machine Learning
An investigation of instance segmentation of cracks in Nb3Sn 4-stack 40-strand Rutherford cables using machine learning is presented. Three samples were uniaxially and biaxially loaded before metallographic inspections were performed. The Mask R-CNN model was used in the Detectron2 framework with pre-trained weights but fine-tuned to detect and segment cracks. The model detected cracks with bounding box and mask average precisions (AP) of 42.8 and 27.9, respectively, and was used for instance segmentation of all cracks in the three samples. More cracks were found in the sample pre-loaded along the z-axis (i.e., along the cable length). Pre-loading along the x-axis (i.e., on the cables edges) reduced the number of cracks and changed the crack orientation distribution, away from being highly aligned with the y-axis (i.e., normal to the cables broad faces), i.e., the direction with the highest applied load. Fine-tuning of the Segment Anything Model (SAM) was also studied but performed poorly without human-provided prompts. However, the zero-shot capability of SAM showed high promises to accelerate the image annotation process for applications beyond this study.
Croteau, Jean-Francois↗
Investigating Various Failure Models on Commercial Silicon Carbide
Structures and components made from ceramic materials are often brittle and can fail by the unstable growth of existing flaws such as voids and cracks. There have been several failure criteria developed for ceramics, in the past and they are broadly categorized based on their dependency on crack geometry. The present work implements eight failure criteria using an open-source software package – srlife, which predicts the lifetime or failure probability of concentrated solar power (CSP) structural components. The present work also checks the viability of building a ceramic CSP receiver, by analyzing the reliability predictions from srlife for a SiC ceramic. The reliability predictions for a biaxial loading problem indicated the Shetty Mixed-Mode criterion gives the most conservative predictions. Whereas, in case of the CSP receiver, the predictions show that the co-planar strain energy criterion gives the most conservative predictions as it is agnostic towards the type of stress, and therefore, is not recommended to be used designing ceramic receivers.
Chaugule, Pawan (ORCID:0000000275706572)↗
Strain dependent electronic and optical responses of penta-BCN monolayer
We report here, structural, dynamic, and mechanical stability in pentagonal boron carbon nitride (p-BCN) monolayer, a new member of direct bandgap two-dimensional (2D) semiconductor. The identified visible range bandgap with excellent mechanical strength allows it to be a promising candidate material in optoelectronics, nanomechanics, and optomechanical sensors. By employing density functional theory (DFT), we reveal a unique geometrical reconstruction with rigidity in B–N and C–N bond lengths with applied strain. These quasi-sp 3 hybridized short and strong covalent bonding and unique geometry support the monolayer to possess extraordinary mechanical response. The desired bandgap is manipulated by loading the biaxial strain. Most importantly, our predictions on p-BCN show excellent optical response such as good static dielectric constant and refractive index, strong optical absorption (up to 1.08 x 10 5 cm -1 in VR and 7.01 x 10 cm -1 in UV) with small energy loss and reflectance both appearing in visible and ultraviolet regions (UV). The desired optical response along with the blue and red shift is demonstrated by tailoring with tensile and compressive strain. The predicted strong optical anisotropy provides it’s application in polarized photodetection.
36 MATERIALS SCIENCE↗
A generalizable machine learning-assisted fast Fourier transform algorithm to simulate the large strain phenomena in polycrystalline materials
Machine learning methods have shown initial promise in constitutive modeling for single crystals or homogenized polycrystals, delivering notable computational efficiency. However, existing machine learning-based constitutive models often lack generalizability, limiting their application across diverse boundary value problems. This study introduces a thermodynamics-informed artificial neural network model to accelerate rate-tangent crystal plasticity fast Fourier transform simulations for cross-scale deformation behaviors of polycrystals under complex loading. Our model integrates microstructural variability and local interactions effectively. To address local effects in each grain, we employ K-means clustering to group Gauss points within the microstructure into clusters assumed to be in similar mechanical states. This approach, based on self-clustering analysis, extends model scope from macroscopic stress response to the granular level, capturing mechanical responses and orientation evolution across grains. This reduces the number of nonlinear problems to solve, with cluster responses propagated throughout each group. The thermodynamics-based artificial neural network-extracted features are further processed using local material state clusters to account for history-dependent deformation and evolving microstructures. Additionally, representative volume element simulations with rate-tangent crystal plasticity fast Fourier transform provide reliable datasets for model training. The proposed model demonstrates high efficiency, accuracy, self-consistency, and enhanced generalizability in predicting strain–stress responses and orientation evolution at both individual grain and aggregate scales under complex loading conditions, such as biaxial tension and arbitrary loading scenarios.
36 MATERIALS SCIENCE↗
Fracture toughness evaluations for spent nuclear fuel dry storage canister welds and spent nuclear fuel clad-pellet structures
Integrity of spent nuclear fuel (SNF) interim storage canisters is very important to the safety of the back-end nuclear fuel cycle. Stress corrosion cracking (SCC) potential of interim storage canister has been considered as a high priority. Because no post-weld heat treatment was required for forming these canisters, the high tensile residual stress existed within these canister welds. This can change the fracture resistance capacity significantly as well as increase SCC potential. Due to relative thin shell thickness of a canister weldment, the spiral notch torsion test (SNTT) method was used to estimate the canister weldment fracture toughness. SNTT was developed to measure the intrinsic fracture toughness of structural materials using small specimens. The SNTT method has been applied to a wide variety of structural materials, such as low-alloy steels, stainless steel, aluminum alloy, ceramics, concrete, and composites. The SNTT system operates by applying pure torsion to cylindrical specimens with a notch line that spirals around the specimen at a 45° pitch. In order to carry out pure torsion load mode, biaxial tension/torsion tester was developed accordingly to perform SNTT protocol. Moreover, applying fracture mechanics approach to SNF system reliability investigation is warranted due to the inherent flaws and hydride structures existed in a SNF system after nuclear reactor operation. However, none of the existing fracture toughness data deal with fuel cladding specific geometry or spent fuel material conditions, such as cladding structure with the pellet-inserts and the associated pellet clad mechanical interactions induced mixed-mode damage mechanisms. Thus, the development of an intrinsic fracture mechanics approach that is suitable for SNF materials is needed. Furthermore, due to thin wall and small dimension of clad tubing structure, the SNTT method was used to estimate the clad tubing structure fracture toughness. Fracture testing were performed on the received stainless steel canister weldment, most SNTT weld samples fracture initiation sites are at heat-affected zone (HAZ) regions. The estimated fracture toughness J Q ’ for the baseline SS304 steel is at 283 kJ/m². The estimated JQ’ for the SS304/308 weld and baseline metals are 148 kJ/m 2 and 459 kJ/m 2 , respectively. Out of cell fracture testing for spent fuel structure were carried out on the surrogate rods made of Zr-4 clad and alumina inserts, the estimated fracture toughness values for baseline Zr-4 cladding with alumina-pellet inserts are: (1) For SNTT samples with a short or medium crack length, between 5.4-mm and 8-mm, the estimate J IQ upon fracture initiation for the baseline Zr-4 cladding is at 50 kJ/m 2 with 2-sigma uncertainty of 3.26 kJ/m 2 , and the associated K IQ is at 67.46 MPa$\sqrt{m}$; and (2) For SNTT samples with a long crack length, around 13-mm, the crack initialization is deviated from that of the Mode-I tensile fracture and appears to be a mixed-mode fracture of Mode I - tensile stress and Mode III - out of plane shear stress; the estimated J MQ is at 18.9 kJ/m 2 , the associated K MQ is at 41.4 MPa$\sqrt{m}$.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Deformation and Delamination of Dynamically Bulging Bilayered Films
We employ finite element simulations to study the dynamic bulging of films under shock tube conditions and compare these responses with quasi-static bulging. Both scenarios subject the film to time-varying pressure. Two film types are considered: uniform material films and bilayers with a relatively soft interior layer and a hard exterior layer. The interface between the materials in the bilayer cases is modeled as a cohesive zone that follows a bilinear normal traction-separation cohesive law. Additionally, bilayer films with preexisting cracks in the interior layer are analyzed. Parametric studies are also conducted to explore the effects of loading rate and specimen size. The mechanical response of all materials is assumed to be strain-rate independent, focusing solely on the inertial effects in the response of the films under dynamic loading, and the absence of such effects under quasi-static loading. The results indicate that quasi-static bulging exhibits a predictable plate bending like deformation. In contrast, depending on the loading rate and specimen size, dynamic bulging can give rise to elastic waves, and a sequence of deformation processes including initial uniform acceleration, followed by bending-like deformation, and finally through-thickness biaxial stretching. Dynamic loading also leads to larger bulge formation and greater deformation than quasi-static loading. A key finding is the role of preexisting cracks in driving delamination under dynamic loading, which is absent in quasi-static loading. This work enhances our understanding of dynamic bulging and motivates further research on characterizing delamination in layered films using dynamic bulge tests.
36 MATERIALS SCIENCE↗
Energy based fracture initiation criterion for strain-crystallizing rubber-like materials with pre-existing cracks
Fracture prediction is indispensable for polymers, like rubbers, which have a broad range of applications mainly due to their high extensibility. The phenomenon known as strain-induced crystallization further contributes to the fracture toughness of certain rubbers. Here in this study, a criterion based on internal bond energy, incorporating the effects of crystallization, is proposed to predict fracture initiation in rubber-like materials with pre-existing cracks. First, a multi-scale mechanical model is developed for characterizing the behavior of rubber when subjected to both uniaxial and biaxial deformation states. At the microscale, both the amorphous and crystalline chain segments are modeled as elastic in order to consider the energy contribution by the molecular bond distortions. This internal energy is considered along with the entropic and crystalline free energy for each chain. In the chain model, the effects of loading condition and the relative orientation of a chain on its crystallinity are taken into account. At the macroscopic scale, an existing crystallinity distribution function is adapted and a mixed finite element formulation with an augmented Lagrangian multiplier is utilized to impose the incompressibility constraint. A non-affine maximal advance path constraint based homogenization model is utilized for bridging the two scales. Its potential to account for anisotropy in the stretched network compels the model to be preferable due to its physical significance, for the purpose of fracture modeling. The rigidity of the crystallites is accounted for by proposing a crystallite distortion energy in addition to the critical bond dissociation energy, for fracture initiation to occur. The model is validated by comparison with existing experimental results for both crystallizing and non-crystallizing rubbers. In addition to its potential to predict the material behavior when subjected to uniaxial and biaxial loading, the capability of the model to quantitatively estimate the effect of crystallization on fracture initiation is also verified.
36 MATERIALS SCIENCE↗
A novel framework for elastoplastic behaviour of anisotropic solids
A general framework for developing nonlinear hyperelastic/plastic constitutive laws for anisotropic solids experiencing large strains and strain rates has been developed. The proposed framework does not rely on the “a priori” known strain energy function, but instead introduces a physical decomposition of the material element into seven physically independent stress bearing mechanisms, each of which has a constitutive law in terms of internal moments described by a scalar function of a single variable. Furthermore, the model has been encoded into a combined finite-discrete element method and tested against static geomechanical test data. The numerical validation experiments show the model can reproduce plastic anisotropic behavior in both biaxial and uniaxial loading of a geomaterial.
58 GEOSCIENCES↗
Identification Uncertainty in Inverse Material Model Parameter Determination: A Sensitivity‐Based Decision Process for Load Path Selection
This research proposes a sensitivity-based framework for selecting the optimal prescribed loading path for a biaxial cruciform specimen. Optimality here is determined by the direction and magnitude of the prescribed displacement that minimizes the influence of random noise on the material model parameter identification. Using simulated experimental data based on finite element simulation, in this work, we identify the material model parameters of a Ludwik hardening model and plane stress implementation of the Hill-48 yield criterion using finite element model updating (FEMU). Our analysis reveals that the identification (or estimator) uncertainty of model parameters depends on the displacement boundary conditions (i.e., loading sequence) and the ground-truth value of the individual parameters. Optimal experimental design (OED) criteria based on the Fisher information matrix were investigated to mitigate indecision in the choice of optimal load path when the identification uncertainty of different material model parameters optimized at different load paths. The determinant of the Fisher information matrix was chosen here as the more useful metric due to its ability to capture uncertainty of the most influential material model parameters. The proposed framework demonstrates potential for real-time automated load step selection using scalar criteria derived prior to mechanical loading. The framework can be generalized to other geometries, boundary conditions and material models, allowing this procedure to be utilized for different experimental configurations and materials.
Fayad, Samuel S. [University of Illinois at Urbana↗
Advancements in Constitutive Model Calibration: Leveraging the Power of Full‐Field DIC Measurements and In Situ Load Path Selection for Reliable Parameter Inference
Accurate material characterization and model calibration are essential for computationally supported high-consequence engineering decisions. Historically, characterization and calibration methods (1) use simplified test specimen geometries and global data, (2) cannot guarantee that sufficient characterization data are collected for a specific model of interest, (3) use deterministic methods that provide best-fit parameter values with no uncertainty quantification, and (4) are sequential, inflexible, and time-consuming. This work brings together several recent advancements into an improved workflow called interlaced characterization and calibration (ICC) that advances the state-of-the-art in constitutive model calibration. The ICC paradigm (1) employs tools to efficiently use full-field data to calibrate high-fidelity material models, (2) aligns the data needed with the data collected by adopting an optimal experimental design protocol, (3) quantifies parameter uncertainty through Bayesian inference and (4) incorporates these advancements into a quasi real-time feedback loop. The ICC framework is demonstrated here on the calibration of a material model using simulated full-field data for an aluminium cruciform specimen being deformed biaxially. The cruciform is actively driven through the myopically preferred load path using Bayesian optimal experimental design, which selects load steps that yield the maximum expected information gain (EIG). Principal component analysis (PCA) is performed on the model predictions of full-field displacements, and fast surrogate models are built to approximate the input-output relationships of the expensive finite element model. Furthermore, the tools developed and demonstrated here show that high-fidelity constitutive models can be efficiently and reliably calibrated with quantified uncertainty, thus supporting credible decision-making and potentially increasing the agility of solid mechanics modelling by enabling utilization of computational simulations at earlier stages of the design cycle.
Bayesian optimal experimental design↗
Detection of thin film phase transformations at high-pressure and high-temperature in a diamond anvil cell
Abstract Quantifying how grain size and/or deviatoric stress impact (Mg,Fe) 2 SiO 4 phase stability is critical for advancing our understanding of subduction processes and deep-focus earthquakes. Here, we demonstrate that well-resolved X-ray diffraction patterns can be obtained on nano-grained thin films within laser-heated diamond anvil cells (DACs) at hydrostatic pressures up to 24 GPa and temperatures up to 2300 K. Combined with well-established literature processes for tuning thin film grain size, biaxial stress, and substrate identity, these results suggest that DAC-loaded thin films can be useful for determining how grain size, deviatoric stress, and/or the coexistence of other phases influence high-pressure phase stability. As such, this novel DAC-loaded thin film approach may find use in a variety of earth science, planetary science, solid-state physics, and materials science applications.
Environmental Sciences & Ecology↗