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NASA NTRS1987

Power flow as a complement to statistical energy analysis and finite element analysis

Present methods of analysis of the structural response and the structure-borne transmission of vibrational energy use either finite element (FE) techniques or statistical energy analysis (SEA) methods. The FE methods are a very useful tool at low frequencies where the number of resonances involved in the analysis is rather small. On the other hand SEA methods can predict with acceptable accuracy the response and energy transmission between coupled structures at relatively high frequencies where the structural modal density is high and a statistical approach is the appropriate solution. In the mid-frequency range, a relatively large number of resonances exist which make finite element method too costly. On the other hand SEA methods can only predict an average level form. In this mid-frequency range a possible alternative is to use power flow techniques, where the input and flow of vibrational energy to excited and coupled structural components can be expressed in terms of input and transfer mobilities. This power flow technique can be extended from low to high frequencies and this can be integrated with established FE models at low frequencies and SEA models at high frequencies to form a verification of the method. This method of structural analysis using power flo and mobility methods, and its integration with SEA and FE analysis is applied to the case of two thin beams joined together at right angles.

Cuschieri, J. M.↗

NASA NTRS1993

Reliability based structural optimization - A simplified safety index approach

A probabilistic optimal design methodology for complex structures modelled with finite element methods is presented. The main emphasis is on developing probabilistic analysis tools suitable for optimization. An advanced second-moment method is employed to evaluate the failure probability of the performance function. The safety indices are interpolated using the information at mean and most probable failure point. The minimum weight design with an improved safety index limit is achieved by using the extended interior penalty method of optimization. Numerical examples covering beam and plate structures are presented to illustrate the design approach. The results obtained by using the proposed approach are compared with those obtained by using the existing probabilistic optimization techniques.

Reddy, Mahidhar V.↗

DOE OSTI2023

Multi-fidelity microstructure-induced uncertainty quantification by advanced Monte Carlo methods

Quantifying uncertainty associated with the microstructure variation of a material can be a computationally daunting task, especially when dealing with advanced constitutive models and fine mesh resolutions in the crystal plasticity finite element method (CPFEM). Numerous studies have been conducted regarding the sensitivity of material properties and performance to the mesh resolution and choice of constitutive model. However, a unified approach that accounts for various fidelity parameters, such as mesh resolutions, integration time-steps and constitutive models simultaneously is currently lacking. Further, this paper proposes a novel uncertainty quantification (UQ) approach for computing the properties and performance of homogenized materials using CPFEM, that exploits a hierarchy of approximations with different levels of fidelity. In particular, we illustrate how multi-level sampling methods, such as multi-level Monte Carlo (MLMC) and multi-index Monte Carlo (MIMC), can be applied to assess the impact of variations in the microstructure of polycrystalline materials on the predictions of homogenized materials properties. We show that by adaptively exploiting the fidelity hierarchy, we can significantly reduce the number of microstructures required to reach a certain prescribed accuracy. Finally, we show how our approach can be extended to a multi-fidelity framework, where we allow the underlying constitutive model to be chosen from either a phenomenological plasticity model or a dislocation-density-based model.

36 MATERIALS SCIENCE↗

NASA NTRS2010

Improved Creep Measurements for Ultra-High Temperature Materials

Our team has developed a novel approach to measuring creep at extremely high temperatures using electrostatic levitation (ESL). This method has been demonstrated on niobium up to 2300 C, while ESL has melted tungsten (3400 C). This method has been extended to lower temperatures and higher stresses and applied to new materials, including a niobium-based superalloy, MASC. High-precision machined spheres of the sample are levitated in the NASA MSFC ESL, a national user facility and heated with a laser. The samples are rotated with an induction motor at up to 30,000 revolutions per second. The rapid rotation loads the sample through centripetal acceleration, producing a shear stress of about 60 MPa at the center, causing the sample to deform. The deformation of the sample is captured on high-speed video, which is analyzed by machine-vision software from the University of Massachusetts. The deformations are compared to finite element models to determine the constitutive constants in the creep relation. Furthermore, the non-contact method exploits stress gradients within the sample to determine the stress exponent in a single test.

Hyers, Robert W.↗

NASA NTRS1988

Extension of vibrational power flow techniques to two-dimensional structures

In the analysis of the vibration response and structure-borne vibration transmission between elements of a complex structure, statistical energy analysis (SEA) or finite element analysis (FEA) are generally used. However, an alternative method is using vibrational power flow techniques which can be especially useful in the mid frequencies between the optimum frequency regimes for SEA and FEA. Power flow analysis has in general been used on 1-D beam-like structures or between structures with point joints. In this paper, the power flow technique is extended to 2-D plate-like structures joined along a common edge without frequency or spatial averaging the results, such that the resonant response of the structure is determined. The power flow results are compared to results obtained using FEA results at low frequencies and SEA at high frequencies. The agreement with FEA results is good but the power flow technique has an improved computational efficiency. Compared to the SEA results the power flow results show a closer representation of the actual response of the structure.

Cuschieri, Joseph M.↗

NASA NTRS2004

Coating Development for GRCop-84 Liners for Reusable Launch Vehicles Aided by Modeling Studies

The design of the next generation of reusable launch vehicles calls for using GRCop-84 copper alloy liners based on a composition invented at the NASA Glenn Research Center. Despite its considerable advantage over other copper alloys, it is expected that GRCop-84 will suffer from environmental degradation depending on the type of rocket fuels used and on thermomechanical fatigue. Applying protective coatings on GRCop-84 substrates can minimize or eliminate many of these problems and extend the operational life of the combustion liner. This could increase component reliability, shorten depot maintenance turnaround times, and lower operating costs. Therefore, Glenn is actively pursuing the development of advanced coatings technology for GRCop-84 liners. Technology is being developed in four major areas: (1) new metallic coating compositions, (2) application techniques, (3) test methods, and (4) life prediction design methodology using finite element analysis. The role of finite element analysis in guiding the coating effort is discussed in this report. Thermal analyses were performed at Glenn for different combinations of top- and bondcoat compositions to determine the temperature variation across the coated cross section with the thickness of the top coat. These calculations were conducted for simulated LH2/LO2 booster engine conditions assuming that the bond coat had a constant thickness of 50 m. The preceding graphs show the predicted temperatures at the outer surface of the top coat (hot wall), at the top-coat/bond-coat interface, at the bond-coat/GRCop-84 interface, and at the GRCop-84 cold wall as a function of top-coat thickness for Cu- 26(wt%)Cr top coat (top graph), Ni-17(wt%)Cr-6%Al-0.5%Y top coat and Cu-26%Cr bond coat, and NiAl top coat and Ni bond coat. In all cases, the temperature of the top coat at the hot wall increased with increasing top-coat thickness and with corresponding decreases in the temperatures at the two interfaces and the cold wall. These temperatures are not acutely sensitive to the thermal conductivity of the top coat when it exceeds 25 and 50 W/m/K for low and high heat flux engines. This observation is significant for two reasons. First, several different top-coat compositions can be evaluated as potential protective coatings without loss in the heat-transfer efficiency of the coated system. Second, materials with thermal conductivities less than the critical values of 25 or 50 W/m/K are more likely to act as thermal barrier coatings. The deposition of overlay coatings on GRCop-84 substrates results in the development of residual stresses. The presence of these residual stresses influences the probability of coating spallation, the thermal cycling life, and the fatigue properties of the coated substrate during use. Since it is important to understand how these stresses develop during the vacuum-plasma-spraying coating deposition process, the nature and magnitudes of the cool-down residual stresses were calculated and compared with experimentally determined values across the coated cross section of a disk specimen. The calculations were conducted assuming that the specimen cools down to room temperature from vacuum plasma-spraying temperatures of either 250 or 650 C. The effects of coating the substrate with and without grit blasting were also theoretically examined. The final graph compares the predicted and the experimental results for a GRCop-84 disk coated with about a 50- m-thick Ni bond coat and a 75- to 100- m NiAl top coat, where the curves for NASA-2 assume the presence of a prior residual stress generated by grit blasting under conditions similar to the experimental situation. The predicted cool-down in-plane stresses were compressive in both the NiAl top coat and the Ni bond coat. They were also compressive in the substrate to a depth of about 0.25 mm from the Ni/GRCop-84 interface when the vacuum-plasma-spraying temperature was low. However, using a higher plasma spraying temperaturs likely to leave the substrate under a small tensile stress to counter the compressive stresses in the bond and top coats because of the relaxation of residual stresses generated in the substrate during the grit blasting of its surface prior to spraying. These results suggest that the NiAl and Ni coatings are unlikely to spall after spraying as confirmed by the microstructural observations shown in the following photomicrograph of an as-sprayed specimen. Finally, it is noted that the calculated and experimental results are not in complete agreement, which indicates that both the experimental and modeling techniques need further refinement.

Raj, Sai V.↗

NASA NTRS2007

Topology Synthesis of Structures Using Parameter Relaxation and Geometric Refinement

Typically, structural topology optimization problems undergo relaxation of certain design parameters to allow the existence of intermediate variable optimum topologies. Relaxation permits the use of a variety of gradient-based search techniques and has been shown to guarantee the existence of optimal solutions and eliminate mesh dependencies. This Technical Publication (TP) will demonstrate the application of relaxation to a control point discretization of the design workspace for the structural topology optimization process. The control point parameterization with subdivision has been offered as an alternative to the traditional method of discretized finite element design domain. The principle of relaxation demonstrates the increased utility of the control point parameterization. One of the significant results of the relaxation process offered in this TP is that direct manufacturability of the optimized design will be maintained without the need for designer intervention or translation. In addition, it will be shown that relaxation of certain parameters may extend the range of problems that can be addressed; e.g., in permitting limited out-of-plane motion to be included in a path generation problem.

Hull, P. V.↗

NASA NTRS2007

Revisiting and Extending Interface Penalties for Multi-Domain Summation-by-Parts Operators

General interface coupling conditions are presented for multi-domain collocation methods, which satisfy the summation-by-parts (SBP) spatial discretization convention. The combined interior/interface operators are proven to be L2 stable, pointwise stable, and conservative, while maintaining the underlying accuracy of the interior SBP operator. The new interface conditions resemble (and were motivated by) those used in the discontinuous Galerkin finite element community, and maintain many of the same properties. Extensive validation studies are presented using two classes of high-order SBP operators: 1) central finite difference, and 2) Legendre spectral collocation.

Carpenter, Mark H.↗

NASA NTRS1987

Extension of vibrational power flow techniques to two-dimensional structures

In the analysis of the vibration response and structure-borne vibration transmission between elements of a complex structure, statistical energy analysis (SEA) or Finite Element Analysis (FEA) are generally used. However, an alternative method is using vibrational power flow techniques which can be especially useful in the mid- frequencies between the optimum frequency regimes for FEA and SEA. Power flow analysis has in general been used on one-dimensional beam-like structures or between structures with point joints. In this paper, the power flow technique is extended to two-dimensional plate like structures joined along a common edge without frequency or spatial averaging the results, such that the resonant response of the structure is determined. The power flow results are compared to results obtained using FEA at low frequencies and SEA at high frequencies. The agreement with FEA results is good but the power flow technique has an improved computational efficiency. Compared to the SEA results the power flow results show a closer representation of the actual response of the structure.

Cuschieri, J. M.↗

NASA NTRS1987

Power flow analysis of an L-shaped plate structure

In the analysis of the vibration response and structure-borne vibration transmission between elements of a complex structure, statistical energy analysis (SEA) or finite element analysis (FEA) are generally used. However, an alternative method is using vibrational power flow techniques which can be especially useful in the mid frequencies between the optimum frequency regimes for FEA and SEA. Power flow analysis has in general been used on one-dimensional beam-like structures or between structures with point joints. In this paper, the power flow technique is extended to two-dimensional plate like structures joined along a common edge without frequency or spatial averaging the results, such that the resonant response of the structure is determined. The power flow results are compared to results obtained using FEA at low frequencies and SEA at high frequencies. The agreement with FEA results is good but the power flow technique has an improved computational efficiency. Compared to the SEA results the power flow results show a closer representation of the actual response of the structure.

Cuschieri, J. M.↗

DOE OSTI2019

Combined crystal plasticity and grain boundary modeling of creep in ferritic-martensitic steels: II. The effect of stress and temperature on engineering and microstructural properties

This paper describes a series of physically-based crystal plasticity finite element method (CPFEM) simulations of long-term creep and creep rupture of Grade 91 steel. It is Part 2 of a two part series of papers. Part 1 describes the simulation framework; this part focuses on specific simulations and on how the predicted long-term creep properties of Grade 91 compare to the assumptions used in current high temperature design practices. This work extends the model developed in Part 1 to look at creep properties at different temperatures, principal stresses, and multiaxial stress states. The simulations show that empirically extrapolating creep rupture stresses from short-term experimental data may substantially over predict the actual long-term creep properties of Grade 91. Additionally, the CPFEM calculations predict a transition from notch strengthening creep behavior for high values of maximum principal stress and moderate notch severity to notch weakening behavior for low principal stresses and more severe notches. The latter regime better categorizes conditions in engineering components designed for long term elevated temperature use, which implies Grade 91 may be a notch weakening material in actual service. This would have a significant impact on high temperature design practices, though confirmatory test data on long-life, low stress notched specimens is difficult to obtain. Finally, one advantage of the physically-based modeling approach adopted here is that the simulation results also elucidate the microstructural mechanisms causing the macroscopic trends in engineering properties predicted by the simulations. This paper shows that the detailed micromechanical mechanisms predicted by the CPFEM simulations can be abstracted with a simple micromechanical model that can be used to both explain the detailed results and make improved predictions of engineering properties from experimental data.

36 MATERIALS SCIENCE↗

DOE OSTI2016

Uncertainty Quantification and Comparison of Weld Residual Stress Measurements and Predictions.

In pressurized water reactors, the prevention, detection, and repair of cracks within dissimilar metal welds is essential to ensure proper plant functionality and safety. Weld residual stresses, which are difficult to model and cannot be directly measured, contribute to the formation and growth of cracks due to primary water stress corrosion cracking. Additionally, the uncertainty in weld residual stress measurements and modeling predictions is not well understood, further complicating the prediction of crack evolution. The purpose of this document is to develop methodology to quantify the uncertainty associated with weld residual stress that can be applied to modeling predictions and experimental measurements. Ultimately, the results can be used to assess the current state of uncertainty and to build confidence in both modeling and experimental procedures. The methodology consists of statistically modeling the variation in the weld residual stress profiles using functional data analysis techniques. Uncertainty is quantified using statistical bounds (e.g. confidence and tolerance bounds) constructed with a semi-parametric bootstrap procedure. Such bounds describe the range in which quantities of interest, such as means, are expected to lie as evidenced by the data. The methodology is extended to provide direct comparisons between experimental measurements and modeling predictions by constructing statistical confidence bounds for the average difference between the two quantities. The statistical bounds on the average difference can be used to assess the level of agreement between measurements and predictions. The methodology is applied to experimental measurements of residual stress obtained using two strain relief measurement methods and predictions from seven finite element models developed by different organizations during a round robin study.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS2015

Impedance Eduction in Sound Fields With Peripherally Varying Liners and Flow

A two-dimensional impedance eduction theory is extended to three-dimensional sound fields and peripherally varying duct liners. The approach is to first measure the acoustic pressure field at a series of flush-mounted wall microphones located around the periphery of the flow duct. The numerical solution for the acoustic pressure field at these microphones is also obtained by solving the three-dimensional convected Helmholtz equation using the finite element method. A quadratic objective function based on the difference between the measured and finite element solution is constructed and the unknown impedance function is obtained by minimizing this objective function. Impedance spectra educed for two uniform-structure liners (a wire-mesh and a conventional liner) and a hard-soft-hard peripherally varying liner (for which the soft segment is that of the conventional liner) are presented. Results are presented at three mean flow Mach numbers and fourteen sound source frequencies. The impedance spectra of the uniform-structure liners are also computed using a two-dimensional impedance eduction theory. The primary conclusions of the study are: 1) when measured data is used with the uniform-structure liners, the three-dimensional theory reproduces the same impedance spectra as the two-dimensional theory except for frequencies corresponding to very low or very high liner attenuation; and 2) good agreement between the educed impedance spectra of the uniform structure conventional liner and the soft segment of the peripherally varying liner is obtained.

Watson, W. R.↗

DOE OSTI2018

High-Temperature Sapphire Pressure Sensors for Harsh Environments

The project aimed to develop and characterize an optical pressure sensor capable of withstanding high temperatures, up to 1000 °C. Survivability in harsh environments was enabled using sapphire for both the substrate and the optical fibers, therefore mitigating thermal expansion mismatch. Such material cannot be machined through conventional microfabrication techniques, and unique additive and subtractive methods had to be studied and implemented. Subtractive methods included laser-machining the sapphire substrate using a picosecond laser machining tool. At first, the parameters of importance were theoretically and experimentally evaluated such that the fluence, the pulse spacing, and the number of passes were found to strongly influence the laser ablation process. A simulation tool was designed to predict the final pattern when inputting a set of parameters and a profile. This model was complemented with laser ablation material physics models and Bayesian uncertainty analysis for one dimensional and three dimensional ablation processes. An additive process called thermocompression bonding was studied in order to seal the diaphragm substrate to the back cavity. At first, bonding strength using this technique was examined using the chevron-notch method that allow to determine the fracture toughness of this bond. This parameter is independent of the geometry used and therefore can be extended to other geometries used in actual sensor bonding. A theoretical and experimental study of internal damage caused by the laser micromachining of the sapphire material was carried out. The research identified enhanced strength and fracture toughness along laser ablated surfaces. This was determined using bend bar specimens and Vicker’s microindentations. Softening of the plasticity behavior (as indicated by nanoindentation experiments) was also investigated using finite deformation plasticity modeling via a contact mechanics finite element simulation. Good correlations between experiments and the model were achieved to determine material parameters that can be used in future MEMS based sensor design and modeling to minimize sensor failure loads. The enhanced strength and fracture toughness was determined to be due to compressive residual stress near laser ablated surfaces. This was confirmed through x-ray spectra taken along different crystal structure planes in combination and Bayesian uncertainty analysis. The Bayesian analysis inferred the entire residual strain tensor (six components) and the residual stress tensor. The results illustrated compressive in-plane stress was the most likely cause of enhanced strength and toughness after laser machining. Due to major equipment failures, a parallel route for fabricating the sensor was taken, using commercially available sapphire removal method (subtractive) and ceramic adhesive bonding (additive). The fully-packaged sensor utilized laser micromachining for the sapphire substrate fabrication and was comprised only of high-temperature-compatible materials. Calibration tests of the sensor in both room-temperature and high-temperature plane-wave tubes showed good linearity and consistent frequency response, in the tested frequency range. The sensor also showed good thermal stability in tests up to 300 °C, proving the fiber-optic lever and its packaging process to be a promising approach for high-temperature measurements. The calibration from 23 °C to 300 °C gave a raw sensitivity of 3.9 × 10 -7 V/Pa and a normalized sensitivity of 9.8 × 10 -8 Pa -1 which were consistent within the temperature range. The sensor had a resonance at 16.3 kHz and a flat band (±3 dB) up to 10.3 kHz. The noise floor of the sensor at 1 kHz was 316 nV/Hz 1/2 , resulting in a MDP of 0.8 Pa. Previously, diaphragm delamination due to CTE mismatch was found at 500 °C, causing packaging failure. Unfortunately high temperature validation in hot jet environment could not be made in time. In the future, it is suggested that the two sapphire substrates be bonded by thermal compression bonding with an intermediate platinum layer instead of using an alumina-based adhesive, and therefore achieve higher temperature capacity up to 1000 °C.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2024

R-Adaptivity to Enable Compression of Elementary Computations in Extreme-Scale Finite Element Simulators

Modern computing systems are capable of exascale calculations, which are revolutionizing the development and application of high-fidelity numerical models in computational science and engineering. While these systems continue to grow in processing power, the available system memory has not increased commensurately, and electrical power consumption continues to grow. A predominant approach to limit the memory usage in large-scale applications is to exploit the abundant processing power and continually recompute many low-level simulation quantities, rather than storing them. However, this approach can adversely impact the throughput of the simulation and diminish the benefits of modern computing architectures. We present three novel contributions to reduce the memory burden while maintaining, and sometimes improving, performance in simulations based on finite element discretizations. The first contribution develops dictionary-based data compression schemes that detect and exploit the structure of the discretization, due to redundancies across the finite element mesh. While these schemes are shown to reduce memory requirements by more than 99% on meshes with large numbers of identical mesh cells, there are applications where this structure does not exist. The second contribution leverages a recently developed augmented Lagrangian optimization algorithm to enable r-adaptivity for meshes with the goal of enhancing the redundancies in the mesh. The third contribution extends these methods to patch-based linear solvers and preconditioners by compressing local matrices. Numerical results demonstrate the effectiveness of the proposed methods to detect, enhance and exploit mesh structure on a suite of examples inspired by large-scale applications.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1988

Composite interlaminar fracture toughness - Three-dimensional finite-element modeling for mixed mode I, II, and fracture

A computational method/procedure is described which can be used to simulate individual and mixed mode interlaminar fracture progression in fiber composite laminates. Different combinations of Modes 1, 2, and 3 fracture are simulated by varying the crack location through the specimen thickness and by selecting appropriate unsymmetric laminate configurations. The contribution of each fracture mode to strain energy release rate is determined by the local crack closure methods while the mixed mode is determined by global variables. The strain energy release rates are plotted versus extending crack length, where slow crack growth, stable crack growth, and rapid crack growth regions are easily identified. Graphical results are presented to illustrate the effectiveness and versatility of the computational simulation for: (1) evaluating mixed-mode interlaminar fracture, (2) for identifying respective dominant parameters, and (3) for selecting possible simple test methods.

Murthy, Pappu L. N.↗

NASA NTRS1986

Composite interlaminar fracture toughness: Three-dimensional finite element modeling for mixed mode 1, 2 and 3 fracture

Murthy, P. L. N.↗

DOE OSTI2015

The Mechanical Properties of Energetically Deposited Non-Crystalline Carbon Thin Films

The mechanical behaviour of carbon films prepared with a variety of densities and microstructures was investigated using nanoindentation. Deposition energies between 25 and 600 eV and temperatures in the range 25-600 °C were used. Films prepared at low temperatures and moderate energy were amorphous with a high density. Finite element methods were used to model the stress fields, reproduce the indentation behaviour and evaluate elastic properties. Young s moduli up to 670 GPa and a low Poisson s ratio of ~ 0.17 were found, comparable to polycrystalline cubic boron nitride, one of the hardest materials known. Films with the same density did not always show the same behaviour, emphasising the role of microstructure in determining mechanical response. Extended graphite- like regions within the films grown at high energy and high temperature observed in transmission electron microscopy caused plastic deformation and failure to recover after a complete indentation cycle. At low deposition energies, the graphite-like regions were smaller in size causing plastic deformation but with complete recovery after indentation.

36 MATERIALS SCIENCE↗