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Ultrafine-grained Fe-TiB 2 high-modulus nanocomposite steel with high strength and isotropic mechanical properties by laser powder bed fusion
Fe-TiB 2 metal matrix composite, also called high-modulus steels (HMSs), are of great interest for applications in fuel-efficient transportation infrastructure, aerospace, and wear industries due to their high specific stiffness and yield strength. However, conventional cast Fe-TiB 2 HMSs often contain coarse and sharp-edged TiB 2 particles which easily trigger premature cracking during loading. Here, we synthesized a Fe-TiB 2 nanocomposite HMS via laser powder bed fusion (LPBF) additive manufacturing of mixed micro-sized powders of Fe, Ti, and Fe 2 B. We investigated the microstructure formation and mechanical behavior of the Fe-TiB 2 HMS. We found that in situ chemical reaction of Ti and Fe 2 B enables the formation of TiB 2 particles at nanoscale during rapid solidification of LPBF. These nanoscale TiB 2 particles can serve as heterogeneous nucleation sites and promote the formation of ultrafine and equiaxed α-Fe grains with random crystallographic textures, which differ from many other additively manufactured (AM) metal alloys characteristic of strong crystallographic textures. As such, isotropic mechanical properties were achieved in the AM Fe-TiB 2 nanocomposite HMS with a high elastic modulus of ~ 240 GPa, an exceptional yield strength of ~ 1450 MPa, and a large plasticity of ~ 20% under compression. Quantitative analysis reveals that the high yield strength primarily originates from strengthening contributions of the ultrafine grains with an average grain size of ~450 nm, the nanoscale TiB 2 reinforcing particles of 20–180 nm, and a high density of printing-induced dislocations of the order of 10 15 m –2 . In situ synchrotron high-energy X-ray diffraction unveils the load partitioning from the softer α-Fe matrix to the stiffer and stronger TiB 2 nanoparticles, contributing to the sustained strain hardening during compression. Our work not only provides a general pathway for achieving high-performance metal matrix nanocomposites by in situ chemical reaction and precipitation of ceramic nanoparticles during additive manufacturing, but also offers mechanistic insights into the deformation mechanism of nanoparticle-reinforced HMS composites.
Statistical evaluation of microscale stress conditions leading to void nucleation in the weak shock regime
Here, we investigate the heterogeneity of the stress state driven by anisotropic deformation response at the single crystal level through five statistical volume element (SVE) calculations of polycrystalline BCC tantalum. This work focuses on grain boundaries as a prominent material defect type prone to void nucleation based upon experimental observations of predominantly intergranular void nucleation in this material. The SVEs are constructed to be statistically representative of larger volumes of material and are meshed such that mean and standard deviation of grain size and orientation information is reconstructed. The computational meshes feature hexahedral (brick) elements and smooth conformal grain boundaries where significant stress concentration is known to occur, a tail effect of interest in the extreme events process of dynamic ductile damage. An existing micromechanical crystallographic plasticity model shown to capture the single crystal behavior of BCC tantalum well is used to perform the polycrystal calculations. The model includes representation of the non-Schmid effect of non-planar screw dislocation kinetics in tantalum. A three-dimensional stress state time profile predicted by damage modeling of a flyer plate impact experiment is applied as boundary conditions to each SVE. Resulting grain boundary stress state statistics are strongly non-Gaussian. Significant structural evolution is observed within the compressive hold before unloading into tension in the stress profile. Strong angular dependence of grain boundary traction magnitude with shock direction is observed. Non-Schmid effects continue to suggest their influence on propensity of microstructural defect types to nucleate voids. A general void nucleation criterion is proposed using probability theory. The general framework is specified to polycrystalline BCC tantalum in the weak shock regime to include the SVE calculations and literature molecular dynamics calculations of grain boundary void nucleation strength. Probability density functions (PDFs) are used to describe the interaction between the local stress state heterogeneity and the distributed grain boundary void nucleation strength state. A causation entropy maximization procedure removes the requirement for ad hoc selection of a PDF functional form and provides a rigorous procedure for data-based PDF determination. The resulting physically informed PDF describes the spatial appearance frequency of nucleated voids as a function of applied macroscale pressure. Lower length scale physics are thus packaged in a precise and computationally efficient way to provide computational plasticity insight to macroscale dynamic ductile damage models.
Ab initio study of tungsten-based alloys under fusion power-plant conditions
Tungsten (W) is considered a leading candidate for structural and functional materials in future fusion energy devices. The most attractive properties of tungsten for magnetic and inertial fusion energy reactors are its high melting point, high thermal conductivity, low sputtering yield, and low long-term disposal radioactive footprint. However, tungsten also presents a very low fracture toughness, primarily associated with intergranular failure and bulk plasticity, limiting its applications. In recent years, several families of tungsten-based alloys have been explored to overcome the aforementioned limitations of pure tungsten. These include tungsten-based high-entropy alloys (W-HEAs) and tungsten-based Self-passivating Metal Alloys with Reduced Thermo-oxidation or “SMART alloys” (W-SAs). Given their proximity to the plasma, it is crucial to understand how the exposure of these candidate plasma-facing materials (PFMs) to the neutron fluxes expected in fusion reactors impacts their material behavior over time. In this work, we present a computational approach that combines inventory codes and first-principles DFT electronic structure calculations to understand the behavior of transmuting tungsten-based PFMs. In particular, we calculate the changes in the chemical composition, production uncertainties, the elastic and ductility properties, and the density of states for five tungsten-based PFMs when exposed to EU-DEMO fusion first wall conditions for ten years.
In-situ 4D visualization and analysis of temperature-driven creep in an oil shale propped fracture
Here, the proppant embedment due to creep in shales is a known issue affecting the useable lifetime of wells in unconventional oil and gas recovery. One of the factors influencing creep is the presence of organics, whose properties can be very sensitive to temperature. In this work we investigated for the first time the role of temperature-induced creep increase in proppant embedment in an organics-rich Green River oil shale sample via in-situ synchrotron X-ray micro-computed tomography. We observed that temperatures as low as 75 °C already induce fast creep, with a fracture aperture closing rate of 13 μm/h and a loss of fracture conductivity rate of 8.7%/h, due only to proppant embedment, in the measured interval at the first heating stage. Local displacement data analysis provided evidence for markedly plastic deformation around the proppant-shale contacts, in contrast with the brittle proppant embedment observed on more cemented and less organics-rich shales at room temperature. The results highlight how the problem of temperature-dependent mechanical behavior might be more important than previously thought, in shales with a high content in organics, and that in-situ micro-imaging techniques can play a key role in understanding the underlying mechanisms, contributing to solve creep-related problems associated with hydraulic fracturing in complex scenarios.
Identification of contamination in the pulse-compression chamber of the OMEGA EP Laser System originating from clean room garments
The contamination of optical components with microscopic particles strongly impacts their ability to handle high-power or high-intensity laser pulses via an array of mechanisms. This work explores the nature and origin of a subset of contamination particles found inside the pulse-compression chamber of the OMEGA EP Laser System. Using Raman microscopy accompanied by other analytical methods, it was shown that sodium nitrate constitutes a significant fraction of the particles that possess diameters on the order of a few micrometers. Further investigation aiming to reveal the origin of these particles suggests that these sodium nitrate particles are deposited via shedding from the reusable clean room garments worn in the Laser Bay and compression chamber. Raman microscopy also revealed various plastic particles such as polystyrene, polyethylene, and poly(diallyl isophthalate).
Preliminary description of a new creep-fatigue design method that reduces over conservatism and simplifies the high temperature design process
The report provides the initial description of a new creep-fatigue design method for structural components in high temperature nuclear service. The new method is based on an integrated elastic-perfectly plastic (EPP) analysis and Simplified Model Test (SMT) approach that reduces over conservatism, improves the treatment of elastic follow up, and simplifies the design procedure, when compared with the current creep-fatigue design methods in ASME Boiler and Pressure Vessel Code. Developing the design charts for the EPP-SMT design method requires extrapolating SMT test data as a function of hold time and follow up factor. The report develops the preliminary design charts for Alloy 617 at temperatures between 800°C and 950°C by combining two extrapolation approaches developed in a previous work. The report also presents a comparative analysis between the EPP-SMT design method and the current ASME creep-fatigue design methods by evaluating design life of two sample geometries under different loading conditions. Results from the comparative analysis verify the EPP-SMT design charts but suggest the requirement of additional test data in the low strain range regime for improving the extrapolation procedure that will further reduce the over conservatism in the creep-fatigue damage evaluation. The report also concludes that the EPP-SMT design procedure can account for effect of primary load on creep-fatigue life by using a fixed, bounding value of follow up in constructing the design charts. The conclusions to this report describe the future work required to complete this new design method so it can be codified through a nuclear Code Case.
Nuclear Materials Packaging, Transportation, and Systems Analysis Group Software Quality Assurance Plan: ANSYS Mechanical Finite Element Analysis Software Version 2023R1
ANSYS Inc. develops and markets engineering simulation software and services used in the aerospace, automotive, manufacturing, electronics, biomedical, energy, defense, and many other industries. ANSYS is dedicated to engineering simulation and is the world’s leading software provider. ANSYS was founded in 1970 and is headquartered in Canonsburg, Pennsylvania. ANSYS provides an engineering analysis tool combining structural, thermal, computational fluid dynamics, acoustic, and electromagnetic simulation capabilities. ANSYS has two main programs, which use the same solvers: (1) Mechanical APDL (ANSYS Design Parametric Language), a Fortran-based coding platform, and (2) ANSYS Workbench, which uses a graphical user interface to aid in finite element analysis implementation. This plan covers both APDL and Workbench. The ANSYS computer program is a large-scale, multipurpose finite element program that can be used to solve several classes of engineering analyses. The analysis capabilities of ANSYS include the ability to solve static and dynamic structural analyses, steady-state and transient heat transfer problems, mode-frequency and buckling eigenvalue problems, static or time-varying magnetic analyses, and various types of field and coupled-field applications. The program contains many special features that allow nonlinearities or secondary effects such as plasticity, large strain, hyperelasticity, creep, swelling, large deflections, contact, stress stiffening, temperature dependency, material anisotropy, and radiation to be included in the solution. As ANSYS has been developed, other special capabilities such as substructuring, submodeling, random vibration, kinetostatics, kinetodynamics, free convection fluid analysis, acoustics, magnetics, piezoelectrics, coupled-field analysis, and design optimization have been added to the program. These capabilities contribute further to making ANSYS a multipurpose analysis tool for varied engineering disciplines. The ANSYS program has been in commercial use for over 50 years and has been used extensively in the aerospace, automotive, construction, electronic, energy services, manufacturing, nuclear, plastics, oil, and steel industries. Additionally, many consulting firms and hundreds of universities have used ANSYS for analysis, research, and educational purposes. ANSYS is recognized worldwide as one of the most widely used and capable programs of its type. Ansys design analysis software is the first created within a quality system with ISO 9001 certification, the internationally accepted quality standard. Product development, testing, maintenance and support processes also meet the United States Nuclear Regulatory Commission's quality requirements, as they have for nearly four decades. The Quality Assurance Service Agreement is suitable for the customers working in the nuclear industry who need to meet specific federal regulations including 10CRF50 Appendix B and provisions of 10CFR21. ANSYS has retained its original International Organization for Standardization (ISO) 9001 accreditation certificate since1995-05-04, It’s current certificate is valid until 2027-05-29.
Application of symbolic and algebraic manipulation software in solving applied mechanics problems
As its name implies, symbolic and algebraic manipulation is an operational tool which not only can retain symbols throughout computations but also can express results in terms of symbols. This report starts with a history of symbolic and algebraic manipulators and a review of the literatures. With the help of selected examples, the capabilities of symbolic and algebraic manipulators are demonstrated. These applications to problems of applied mechanics are then presented. They are the application of automatic formulation to applied mechanics problems, application to a materially nonlinear problem (rigid-plastic ring compression) by finite element method (FEM) and application to plate problems by FEM. The advantages and difficulties, contributions, education, and perspectives of symbolic and algebraic manipulation are discussed. It is well known that there exist some fundamental difficulties in symbolic and algebraic manipulation, such as internal swelling and mathematical limitation. A remedy for these difficulties is proposed, and the three applications mentioned are solved successfully. For example, the closed from solution of stiffness matrix of four-node isoparametrical quadrilateral element for 2-D elasticity problem was not available before. Due to the work presented, the automatic construction of it becomes feasible. In addition, a new advantage of the application of symbolic and algebraic manipulation found is believed to be crucial in improving the efficiency of program execution in the future. This will substantially shorten the response time of a system. It is very significant for certain systems, such as missile and high speed aircraft systems, in which time plays an important role.
2024 Second Half Semi Annual Report: Modeling plasticity-mediated flow in metals with pressurized cavities
The objective is to better predict the bulk-scale mechanical behavior of porous metals that have over pressurized cavities (e.g., irradiated metals with helium bubbles) by quantifying the complex coupling among cavity aspects (e.g., size distribution, inhomogeneous overpressure values, spatial arrangement) and metal properties (e.g., rate-dependency, crystallographic lattice). This requires up-scaling local mechanical fields from the single crystal scale and will be accomplished using a homogenization approach that combines full-field numerical simulations, analytical formalisms, and physics-informed machine learning to produce symbolically-defined constitutive equations (e.g., gauge functions). These equations will satisfy the objective because they enable computationally efficient predictions that approach the accuracy of computationally expensive full-field numerical simulations, abide by theoretical requirements (e.g., conservation of energy, work conjugacy), and retain the transparency of analytical models.
An anisotropic viscoplasticity model for shale based on layered microstructure homogenization
Viscoplastic deformation of shale is frequently observed in many subsurface applications. Many studies have suggested that this viscoplastic behavior is anisotropic—specifically, transversely isotropic—and closely linked to the layered composite structure at the microscale. In this work, we develop a two-scale constitutive model for shale in which anisotropic viscoplastic behavior naturally emerges from semianalytical homogenization of a bilayer microstructure. The microstructure is modeled as a composite of soft layers, representing a ductile matrix formed by clay and organics, and hard layers, corresponding to a brittle matrix composed of stiff minerals. This layered microstructure renders the macroscopic behavior anisotropic, even when the individual layers are modeled with isotropic constitutive laws. Using a common correlation between clay and organic content and magnitude of creep, we apply a viscoplastic modified Cam-Clay plasticity model to the soft layers, while treating the hard layers as a linear elastic material to minimize the number of calibration parameters. We then describe the implementation of the proposed model in a standard material update subroutine. The model is validated with laboratory creep data on samples from three gas shale formations. We also demonstrate the computational behavior of the proposed model through simulation of time-dependent borehole closure in a shale formation with different bedding plane directions.
Water-induced surface ordering facilitating the microcutting of ductile metals
Metal cutting is a crucial process in modern manufacturing. Enhancing the machinability of metals can significantly improve their production efficiency and surface integrity. Coating surface-active media (SAM) on the free surface of the metals before cutting is an easy method to improve machinability, which usually pertains to the category of the renowned Rehbinder effect. However, the existing SAM is usually hazardous and complex materials. Besides, the effect of SAM on the local structure of the metal surface remains unclear. In this study, water is employed as a simple yet often overlooked SAM in the microcutting of copper. Using water as SAM also allows the employment of X-ray absorption fine structure spectroscopy (XAFS) to study the local structure of copper with and without water coating. Results show that water coating on the free surface of copper can significantly reduce the cutting force and chip thickness, and improve the surface finish. Interestingly, removing the water coating enables the recovery of the cutting force, demonstrating a reversible effect. Based on the XAFS results and molecular dynamics simulation, a water-induced surface ordering mechanism is proposed to explain the findings from the microcutting experiments. This mechanism suggests that water molecules can induce surface ordering in copper, resulting in reduced surface energy and fracture toughness of copper, thus enhancing machinability. In conclusion, this work provides valuable insights into the comprehension of the Rehbinder effect and shows that picometer-scale modifications of the surface atom arrangement can considerably alter the deformation mode of metals, paving the way for the development of new manufacturing processes.
Size effect in stainless steel thin wires under tension
Miniaturization of modern devices drives the exploration into how materials behave in small dimensions. However, the mechanical behaviors of micro-scale specimens under varied loading conditions are still challenging to characterize and predict. In this work, specimen size-dependent weakening effect was experimentally revealed in 316L stainless steel thin wires under tension with wire diameter decreasing from 200 μm down to 61 μm. The underlying mechanisms were primarily associated with surface grain softening and strain localization, which were largely dependent on the number of grains across wire diameter. Through an analog composite model with surface and interior grains that follows the Hall-Petch relation, the extent of surface grain softening was found to coincide with the flow stress reduction due to lack of boundary strengthening. Further using elasto-plastic self-consistent polycrystal modeling, the stress-strain behaviors of interior and surface grains were well described in analogy to those of bulk materials with similar-size grains and extremely large grains, respectively. Subsequently, the analog composite model well simulated the specimen size-dependent weakening effect under tension. This article provided more insights into the size effect exploration and proposed a practical model for describing size-dependent mechanical behaviors of small-scale materials to be applied to miniaturized devices.
Abnormal Grain Growth in M-252 and S-816 Alloys
An experimental investigation was carried out on air- and vacuum-melted M-252 and S-816 alloys to find conditions of heating and hot-working which resulted in abnormal grain growth. The experiments were mainly limited to normal conditions of heating for hot-working and heat treatment and normal temperatures of solution treatment were used to allow grain growth after susceptibility to abnormal grain growth was developed by various experimental conditions. Results indicated that small reductions of essentially strain-free metal were the basic cause of such grain growth.
Gasification of Coal and Biomass: The Route to Net-Negative-Carbon Power and Hydrogen
One promising process that is a candidate for meeting the goals of the US Department of Energy’s 21st Century Power Plant initiative is to gasify a mixture of coal and biomass to yield a syngas, which can have CO2 removed and then be used to produce hydrogen as well as an off-gas that can be used to flexibly produce power. This concept would overall be carbon net-negative and readily meet the 21st Century Power Plant initiative targets of smaller scale MW generation, high ramp rates and turndown, feedstock flexibility, and high efficiency—at a reasonable cost. Moreover, adding the large-scale production of “ultra-green” hydrogen yields a system tailored for the coming hydrogen economy, providing long-term energy storage and an attractive co-product for sale. The objective of the work being led by the Electric Power Research Institute, Inc. (EPRI), with support by Bechtel Corporation (Bechtel), Gas Technology Institute (GTI), Hamilton Mauer International, Inc. (HMI), Nebraska Public Power District (NPPD), NexantECA, Inc. (Nexant), and Wärtsilä, is to perform a front-end design and engineering (FEED) study on an oxygen-blown gasification system coupled with water-gas shift, pre-combustion CO2 capture, and pressure-swing adsorption working off a coal/biomass mix to yield high-purity hydrogen and a fuel off-gas that can generate power. Several designs are being considered that will be capable of producing 50 MW net from a flexible generator, over 8500 kg/hr of hydrogen, and net-negative CO2 emissions, at an efficiency of 50% net HHV. The plant would be hosted at an NPPD site, where opportunities for enhanced oil recovery and sequestration have been investigated and the need for low-carbon power and hydrogen is imminent. The principal biomass to be used is corn stover—prevalent in Nebraska where the plant will be located—mixed with Powder River Basin (PRB) coal, necessitating a gasifier that can use this feedstock and be flexible to allow other types. Waste plastics will also be reviewed for use. Two oxygen-blown gasifiers have been identified as candidates that have done testing with biomass including corn stover: the GTI gasifier—a high-pressure, fluidized-bed type—and HMI’s, a lower pressure moving-bed type. Both have relative advantages that were investigated in the Phase I design study, with a resultant down select of one system for which the FEED will be performed in Phase II. The technical tasks for the project are: • Design Development: Completion of design activities necessary to provide inputs for the FEED study. Multiple design cases will be assessed with the selection of the optimal one for the FEED. • Investment Case Preparation: Development of the draft investment case for the proposed process with business cases performed for the proposed host site and two other locations. • Host Site Selection: Evaluation of the two potential host sites within NPPD’s portfolio to select the preferred candidate based on technical, economic, and environmental considerations. • Environmental Information Volume (EIV) Development: Completion of the EIV for the host site. • FEED Study: Completion of a FEED study based on the design selected in Phase I. A Greenhouse Gas Life Cycle Analysis will also be performed for the process. • Update Investment Case: Finalization of the investment case based on findings from the FEED. The advantages of the proposed project are significant. Having an engaged U.S. power utility willing to provide a host site that will produce energy from coal plus a deep and experienced team is critical; the process meets all the goals of DOE’s 21st Century Power Plant initiative at an estimated total plant cost of ~$880M and a production cost of hydrogen of ~$2/kg-H2 while producing net-negative carbon power. If developed, this process has real commercial potential in the United States—supported by EPRI’s initial review of the considerable interest from selected U.S. utilities—and elsewhere around the globe. The process has fewer environmental hurdles compared to other concepts, lowering regulatory and protest risks—providing a pathway to preserving the viability of a critical indigenous energy source by transforming its use to match a changing world. This presentation outlines the motivation for the effort, summarizes project plans, work completed to date, results of the Phase I effort and, and detailed work scope for the remainder of the project in the Phase II FEED effort.
Elucidating the mechanical and thermal response of nanotwinned Ni alloys
Transformative advances in nanoscale materials synthesis, characterization and modeling are enabling the synthesis of materials with unprecedent properties and greater understanding of the nanoscale mechanisms that underpin these properties. Nanotwinned Cu alloys have received considerable attention due to their impressive balance of strength and ductility, but they have limited microstructural stability. Recent instantiation of nanotwins in sputter deposited Ni-Mo-W, and several commercial Ni-based superalloys, point to the potential development of a new class of high temperature materials with a very beneficial suite of mechanical and physical properties. The experimental study described in this report was undertaken to elucidate the nanoscale origins of the thermal and mechanical behavior of nanotwinned Ni alloys. Micropillar compression experiments have shown nanotwinned Ni 85 Mo 15-x W x alloys to possess unusually high strengths above 3.5GPa and enhanced microstructural stability. The strength of these nanotwinned alloys is determined by the abrupt formation of shear bands. This study focused on identifying the nanoscale trigger, or triggers, for shear banding in nanotwinned materials using in situ experiments and atomic-scale postmortem analysis. Contrasting and comparing the mechanical response and postmortem nanostructures of “Mo-rich” and “W-rich” nanotwinned specimens elucidated the importance of the lateral motion of easy glide defects that results in erasure of twins and local coarsening of the nanotwinned microstructure. This twin coarsening was then associated with very localized plasticity, strain softening, and shear band formation. The difference between alloys was further studied by considering the role of various material factors: stacking fault energy, coherent twin boundary spacing and flatness, grain size, and the interactions of solute atoms with twin and grain boundaries. The effect of alloy composition and sputtering power and temperature were also investigated and used to control twin spacing and geometry. Combined with atomic-scale simulations, these experiments insights should allow us to identify strategies for achieving concomitant ultrahigh strength and ductility in nanotwinned Ni alloys. In parallel but synergistic studies, our work was buoyed by collaborative state-of-the-art nanoscale orientation and strain mapping at the DOE National Center for Electron Microscopy (NCEM). For example, novel 4D-STEM techniques were used to acquire nanoscale strain maps. The extremely fine twin spacing limited our measurements of atomic-scale thermal expansion within twins, but recent results from NCEM suggest that it will soon be possible to conduct such measurements and to unravel the origins of the novel thermal expansion characteristics of nanotwinned Ni alloys.
Path-Integrated X-Ray Images for Multi-Surface Digital Image Correlation (PI-DIC)
X-ray imaging offers unique possibilities for Digital Image Correlation (DIC), opening the door for full-field deformation measurements of a test article in complex environments where optical DIC suffers severe biases or is impossible. While X-ray DIC has been performed in the past with standard DIC codes designed for optical images, the path-integrated nature of X-ray images places constraints on the experimental setup, predominantly that only a single surface of interest moves/deforms. These requirements are difficult to realize for many practical situations and limit the amount of information that can be garnered in a single test. Other X-ray based diagnostics such as Digital Volume Correlation (DVC) and Projection DVC (P-DVC) overcome these obstacles, but DVC is limited to quasi-static tests, and both DVC and P-DVC necessitate high-resolution computed tomography (CT) scan(s) and often require a potentially invasive pattern throughout the volume of the specimen. Here this work presents a novel approach to measure time-resolved displacements and strains on multiple surfaces from a single series of 2D, path-integrated (PI) X-ray images, called PI-DIC. The principle of optical flow or conservation of intensity—the foundation of DIC—was reframed for path-integrated images, for an exemplar setup comprised of two plates moving and deforming independently. Synthetic images were generated for rigid translations, rigid rotations, and uniform stretches, where each plate underwent a unique motion/deformation. Experimental specimens were fabricated (either an aluminum plate with tantalum features or a plastic plate with steel features) and the two specimens were independently translated. PI-DIC was successfully demonstrated with the synthetic images and validated with the experimental images. Prescribed displacements were recovered for each plate from the single set of path-integrated, deformed images. Errors were approximately 0.02 px for the synthetic images with 1.5% image noise, and 0.05 px for the experimental images. These results provide the foundation for PI-DIC to measure motion and deformation of multiple, independent surfaces with subpixel accuracy from a single series of path-integrated X-ray images.
A modular methodology for time-domain stochastic seismic wave propagation
Presented here is a modular methodology for time-domain stochastic seismic wave propagation analysis. Presented methodology is designed to analyse uncertain seismic motions as an input, propagating through uncertain material. Traditional approach for uncertain wave propagation relies on models that include deep bedrock, local soil site, and their random process and random field information. Such models can become quite large and computationally intractable. The modular approach proposed herein features two step approach that allows separate consideration of the deep bedrock and local site along with corresponding random field information. In this work, the first step considers an auxiliary stochastic motions problem in the bedrock. Stochastic local site response can then be simulated in a reduced domain within certain depth from the surface. Application of uncertain seismic motions at depth, for local uncertain site response is done using stochastic effective forces developed through the Domain Reduction Method. By using Hermite polynomial chaos expansion to represent the non-Gaussian random field of material parameters and non-stationary random process of seismic motion, the proposed modular methodology is formulated using intrusive stochastic Galerkin approach, as seen in the Stochastic Elastic–Plastic Finite Element Method (SEPFEM). Developed modular methodology is illustrated using a 1-D stochastic seismic wave propagation analysis with three cases, and simulation results are also verified with results from conventional approach.