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NASA NTRS1981

Computerized symbolic manipulation in nonlinear finite element analysis

The potential of using computerized symbolic manipulation in the development of nonlinear finite elements is discussed. Three tasks which can be efficiently performed using computerized symbolic manipulation are identified: (1) generation of algebraic expressions for the stiffness coefficients of nonlinear finite elements, (2) generation of FORTRAN source code for numerical evaluation of stiffness coefficients, and (3) checking the correctness of the FORTRAN statements for the arrays of coefficients. The symbolic and algebraic manipulation system MACSYMA is used in the present study. Two sample MACSYMA programs are presented for the development of the nonlinear stiffness coefficients of two-dimensional, shear-flexible, doubly-curved deep shell elements. The first program is for displacement models and the second program is for mixed models with discontinuous stress-resultant fields at interelement boundaries.

Noor, A. K.↗

NASA NTRS1999

Analysis of X-Ray Microradiographs of Al-Au Interface Quench Profile using Modeling of Solidification Including Double-Diffusion and Convection in the Melt

Experimental data on Al-0.8Au horizontal solidification of a 1 mm thick specimen in a BN crucible shows the effect of growth rate on the solidification interface shape. For translation rates below 0.5 micron/s the interface maintains a plain and flat shape. When the translation rate is 3 to 5 micron/s or more, the interface appearance changes to two planar zones, with the zone closer to the bottom having higher inclination. The interface shapes were measured by first quenching in place during growth. X-ray microscopy shows the interface shape within the quenched sample by viewing through the side of the specimen. In order to provide theoretical explanation of the phenomena, numerical modeling was undertaken using finite element code FIDAP. Double diffusion convection in Al-0.8Au melt and crystal-melt interface curvature during directional solidification was analyzed numerically. Actual thermophysical properties of Al-0.8Au including the binary Al-Au phase diagram were used. Although convection in the sample is weak, for the slower translation rate convection and diffusion is sufficient for the redistribution of initial compositional stratification caused by gravity. When translation rate is raised, neither convection nor diffusion can provide proper mixing so that solidification temperatures differ significantly near the bottom within the bulk of the sample. As a result, the solid-liquid interface appears to have two planar zones with different inclination.

Bune, Andris V.↗

DOE OSTI2020

Energy Release Rate Approximation for Small Surface Cracks in Three-Dimensional Domains Using the Topological Derivative

The topological derivative describes the variation of a response functional with respect to infinitesimal changes in topology, such as the introduction of an infinitesimal crack or hole. In this three-dimensional fracture mechanics work, we propose an approximation of the energy release rate field associated with a small surface crack of any boundary location, direction, and orientation combination using the topological derivative. Furthermore, this work builds on the work of Silva et al. (“Energy Release Rate Approximation for Small Surface-Breaking Cracks Using the Topological Derivative,” J. Mech. Phys. Solids 59(5), pp. 925–939), in which the authors proposed an approximation of the energy release rate field which was limited to two-dimensional domains. The proposed method is computationally advantageous because it only requires a single analysis. By contrast, current boundary element and finite element-based methods require an analysis for each crack length-location-direction-orientation combination. Furthermore, the proposed method is evaluated on the non-cracked domain, obviating the need for refined meshes in the crack tip region.

42 ENGINEERING↗

NASA NTRS1983

Advances and trends in structural and solid mechanics; Proceedings of the Symposium, Washington, DC, October 4-7, 1982

The mechanics of materials and material characterization are considered, taking into account micromechanics, the behavior of steel structures at elevated temperatures, and an anisotropic plasticity model for inelastic multiaxial cyclic deformation. Other topics explored are related to advances and trends in finite element technology, classical analytical techniques and their computer implementation, interactive computing and computational strategies for nonlinear problems, advances and trends in numerical analysis, database management systems and CAD/CAM, space structures and vehicle crashworthiness, beams, plates and fibrous composite structures, design-oriented analysis, artificial intelligence and optimization, contact problems, random waves, and lifetime prediction. Earthquake-resistant structures and other advanced structural applications are also discussed, giving attention to cumulative damage in steel structures subjected to earthquake ground motions, and a mixed domain analysis of nuclear containment structures using impulse functions.

Noor, A. K.↗

NASA NTRSDate not supplied

Impact of Thermoplastic Composites: Testing and Modeling

Thermoplastic Composites (TPCs) are being increasingly considered for aerospace applications given their faster manufacturing cycles and lower cost. The NASA High-Rate Composite Aircraft Manufacturing (HiCAM) project aims to evaluate and mature thermoplastic manufacturing technologies to achieve a 4X – 6X increase in the production rate of Next Generation Single Aisle (NGSA) commercial aircraft. Within the purview of the NASA HiCAM project, this work investigates the response of thermoplastic composites under High Energy Dynamic Impact (HEDI) conditions. HEDI tests were conducted on panels fabricated with a carbon fiber reinforced low melt semi-crystalline resin TC1225 LMPAEK T700G (T700/LMPAEK) material system. A blunt metal projectile was chosen as the impactor which impacted the T700/LMPAEK panels over a range of impact velocities imparted by a gas gun test setup. As expected, lower velocity impacts caused the projectile to rebound, whereas higher velocity impacts resulted in the projectile penetrating the test panels. For the test cases in which the projectile rebounded, the predominant damage modes recorded with Ultrasonic (UT) scans included interlaminar delaminations which exhibited a “rotating fan” like structure when viewed in the through-thickness direction. Additionally, the dynamic deflection of the center point of the back face of the test panels and the velocity of the projectile was also measured during the test. Finite element models were developed to model a test case in which the projectile rebounded. These models were developed using LS-DYNA® wherein the primary objective was to evaluate the ability of the material model MAT299 to capture the dynamic response and damage modes in the T700/LMPAEK test panels. MAT299 is a Deformation Gradient Decomposition (DGD) based Continuum Damage Mechanics (CDM) material model. The interlaminar delaminations were modeled using the cohesive contact formulation available within LS-DYNA, wherein the mixed-mode fracture is captured via the Benzegaggh-Kenane (B-K) mode-dependent fracture energy interpolation law. The above-mentioned modeling methods have mostly been applied to thermoset composites and adapting them to TPCs involves addressing challenges associated with appropriately representing material behavior. Therefore, the proposed paper would discuss the systematic approach taken to adapt thermoset composites modeling practices for applications to TPCs, while appropriately addressing material behavior. The proposed paper would show that the predicted back face center point deflection correlated reasonably well with experimental data and the peak deflection was predicted to be within 5% of the experimental measurements. The projectile rebound velocity, while predicted to be higher than the experimental measurement, was within reasonable bounds. Additionally, it will be shown that the predicted delamination shapes were in reasonable agreement with experimental data.

Composite Materials↗

DOE OSTI2025

Evaluating the bond strength and fracture mechanisms of cold-sprayed zinc coating on AZ91 magnesium substrate via a combined experimental and computational approach

Magnesium (Mg) alloys are ideal candidates for automotive applications due to their high strength to weight ratio, castability, recyclability etc., however, they lack corrosion and oxidation resistance. Solid-state deposition techniques, such as cold spray, have been demonstrated to enhance their corrosion resistance as it relies on the severe plastic deformation of powder particles upon impact with the substrate to form a metallurgical bond with the substrate and within the coating. At cold sprayed interfaces, a heterogeneous microstructure is formed that includes some porosity, oxides and intermetallics which can significantly affect coating performance. Thus, establishing a direct correlation between the interface microstructure and its properties can aid in designing optimal cold spray parameters. In this study, we investigated the microstructure and mechanical properties of a zinc (Zn) coating deposited on a high pressure die cast (HPDC) AZ91 Mg substrate via high resolution scanning transmission electron microscopy, in situ micro-tensile testing, and finite element method (FEM) modeling. Micro-tensile pillars fabricated using the plasma focused ion beam (PFIB) successfully isolates the coating-substrate interface within the gauge length. The average bond strength of Zn-Mg interface was determined to be ∼140 MPa with failure occurring partially at the interface and mostly into the coatings. A detailed microstructural characterization revealed evidence of a strong metallurgical bonding at the Zn-Mg interface and formation of the C14 MgZn 2 laves phase interlayer resulting in a mixed mode of fracture during the micro-tensile experiments. FEM modeling reveals the stress distribution along the interfaces and suggests that a MgZn 2 layer thickness between 200–400 nm is optimum to increase the bond strength and minimize the triaxiality. Such a site-specific interfacial analysis with correlative computational modeling provides crucial insight into the overall performance of cold spray interfaces.

Bond strength↗

DOE OSTI2023

Computationally Efficient Control Co-Design Optimization Framework with Mixed-Fidelity Fluid and Structure Analysis: OpenTurbineCoDe (OTCD) - ARPA-E ATLANTIS Phase I Project (Final Technical Report)

The goal of the Department of Energy (DOE) Advanced Research Projects Agency-Energy (ARPA-E) Aerodynamic Turbines Lighter and Afloat with Nautical Technologies and Integrated Servo-control (ATLANTIS) Program is to develop new technologies for floating offshore wind turbines, or wind farms, using the discipline of control co-design (CCD.) In this context, our goal is to develop a computationally efficient optimization framework for design of floating offshore wind turbines. Our specific aim is to utilize high-fidelity structural, aerodynamic, aero-structural tools, and to derive control-oriented reduced- or low-order models directly from the high-fidelity tools. We proposed a mixed-fidelity modeling approach which means that we are also using low- and mid-fidelity tools when necessary. This research is conducted by a multidisciplinary team consisting of Rutgers University, University of Michigan, Brigham Young University, and the National Renewable Energy Laboratory (NREL). The computational framework, called OpenTurbineCoDe, is designed to integrate, where possible, traditional structural, aerodynamic, aeroelastic models (e.g., OpenFAST) and advanced control algorithms with higher fidelity simulation tools including Reynolds-averaged Navier–Stokes (RANS) solvers, and three-dimensional structural finite element solvers. All the high-fidelity tools used in this research provide numerically exact gradients to facilitate both efficient optimization and local linearization for control implementation.

17 WIND ENERGY↗

NASA NTRS1985

Delamination and debonding of materials

The general topics consist of stress analysis, mechanical behavior, and fractography/NDI of composite laminates. Papers are presented on a dynamic hybrid finite-element analysis for interfacial cracks in composites, energy release rate during delamination crack growth in composite laminates, matrix deformation and fracture in graphite-reinforced epoxies, and the role of delamination and damage development on the strength of thick notched laminates. In addition, consideration is given to a new ply model for interlaminar stress analysis, a fracture mechanics approach for designing adhesively bonded joints, the analysis of local delaminations and their influence on composite laminate behavior, and moisture and temperature effects on the mixed-mode delamination fracture of unidirectional graphite/epoxy.

Johnson, W. S.↗

NASA NTRS1999

A Viscoelastic Hybrid Shell Finite Element

An elastic large displacement thick-shell hybrid finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at he element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses in included in the mixed variational functional. Nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to numerically simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.

Johnson, Arthur↗

DOE OSTI2023

Three-pion effects in $K^0-\bar{K}^0$ mixing

The rate of mixing between a neutral kaon and an anti-kaon ($K^0$-$\bar{K}^0$) is given, in part, by a long-range matrix element, defined with two insertions of the weak Hamiltonian separated by physical, Minkowski time evolution. For physical quark masses, the kaon mass lies above the two- and three-pion thresholds and, as a result, this long-range matrix element receives contributions from intermediate on-shell $2\pi$ and $3\pi$ states. These contributions cannot easily be captured in a finite Euclidean spacetime, meaning that such matrix elements are not directly accessible via lattice QCD. In this talk, we present a strategy for combining quantities that can be extracted in numerical lattice QCD calculations in order to reproduce the physical, infinite-volume long-range amplitude for $K^0-\bar{K}^0$. The key novelty relative to published work is that we fully include the effects of three-particle states that were previously neglected. The strategy is built on existing formalism for long-range matrix elements with two-particle intermediate states, together with the relativistic-field-theory finite-volume formalism for extracting three-hadron weak decays.

Jackura, Andrew↗

NASA NTRS1987

Interlaminar shear fracture toughness and fatigue thresholds for composite materials

Static and cyclic end notched flexure tests were conducted on a graphite epoxy, a glass epoxy, and graphite thermoplastic to determine their interlaminar shear fracture toughness and fatigue thresholds for delamination in terms of limiting values of the mode II strain energy release rate, G-II, for delamination growth. The influence of precracking and data reduction schemes are discussed. Finite element analysis indicated that the beam theory calculation for G-II with the transverse shear contribution included was reasonably accurate over the entire range of crack lengths. Cyclic loading significantly reduced the critical G-II for delamination. A threshold value of the maximum cyclic G-II below which no delamination occurred after one million cycles was identified for each material. Also, residual static toughness tests were conducted on glass epoxy specimens that had undergone one million cycles without delamination. A linear mixed-mode delamination criteria was used to characterize the static toughness of several composite materials; however, a total G threshold criterion appears to characterize the fatigue delamination durability of composite materials with a wide range of static toughness.

Obrien, T. Kevin↗

NASA NTRS1989

Interlaminar shear fracture toughness and fatigue thresholds for composite materials

O'Brien, T. Kevin↗

DOE OSTI2022

Experiments and modelling of adhesive failure initiation of an epoxy underfill: a study of electronic packaging survivability

Epoxy underfills can be implemented in electronic packaging to enhance solder joint reliability of surface mounted components. However, it is important for an engineer to have a failure criterion that can be used for failure predictions and redesign of electronic assemblies. For this study, data from epoxy bond failure in mock electronic part assemblies were correlated to finite element analyses to predict adhesive failure initiation. Experiments were performed to determine failure loads for various loading locations and nonlinear viscoelastic analyses were performed for the same loading locations to determine a maximum principal strain failure parameter. Predictions showed that a maximum principal strain failure parameter defined from one test could be used as an indicator of adhesive failure of an epoxy bond undergoing other modes of loading. Failure initiation predictions matched experimental data using a maximum principal strain failure parameter for an epoxy bond undergoing mixed modes of loading for both unfilled and alumina oxide filled 828DEA epoxy. Such experimental setup is deemed appropriate for future epoxy testing.

42 ENGINEERING↗

DOE OSTI2022

Simulation and Reynolds-averaged Navier-Stokes modeling of a three-component Rayleigh-Taylor mixing problem with thermonuclear burn

Rayleigh-Taylor mixing in the presence of a third component with intermediate density is investigated through three-dimensional large-eddy simulation (LES) with a high-order compact finite-difference code. Two configurations are considered: (1) a symmetric configuration in which the Atwood number between the heavy and intermediate components matches the Atwood number between the intermediate and light components and (2) an asymmetric configuration in which the Atwood number between the heavy and intermediate components is an order of magnitude greater than the Atwood number between the intermediate and light components. Mass fraction covariances are extracted, and proposed Reynolds-averaged Navier-Stokes (RANS) closures for density-specific-volume and density-mass-fraction covariances are evaluated in an a priori fashion. Additionally, a multicomponent extension of the k - Φ - L - a - V RANS model [Morgan, Phys. Rev. E 104, 015107 (2021)] is presented which includes model equations for the upper-triangular elements of the mass fraction covariance matrix. This model, referred to as the k - Φ - L - a - C model, is compared against results from LES and against other RANS models. Profiles of average mass fraction, mass-fraction covariance, and density-specific-volume covariance obtained with the k - Φ - L - a - C model are found to agree well with LES data. Finally, the impact of three-component turbulent mixing on average reaction rate is investigated in both premixed and nonpremixed cases by heating the mixing layer and allowing it to undergo thermonuclear (TN) burn. A closure model for average reaction rate is proposed for use with the k - Φ - L - a - C model, and when this model is applied, improved agreement is obtained between LES and RANS in total TN neutron production.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Role of Intersections in Fracture Connectivity

Networks of intersecting fractures often provide the flow paths through subsurface reservoirs. Assessing network connectivity is challenging because fracture intersections compose a vanishingly small fraction of the network void volume. In this paper, motivated by 3D X-ray imaging of the simplest element of fracture network, that is, two orthogonal fractures, we perform a percolation and finite-size scaling analysis to study the connectivity provided by fracture intersections. The conditions when an intersection enhances connectivity across a sample depend on spatial correlations in the fracture aperture distributions, on the stress state, and on the direction of flow. Here we consider three flow directions: (a) across intersections, (b) parallel to intersections and (c) around corners. For (a), intersections provide minimal enhancement of connectivity because they contribute little additional void area. For (b), intersections increase the probability of a connected path near threshold by enabling 3D connected pathways that are not possible in parallel fractures. Flow around corners, (c), is fundamentally the result of the intersection connecting two fractures in series and spatial correlations are broken around corners, suppressing the connectivity relative to (a). When the connected fractures are stressed equally, a joint percolation threshold emerges that continues to have scale invariance. However, when the fractures are stressed unequally, the system has mixed percolation without clearly defined percolation thresholds. In all cases, percolation probabilities are found to be scale dependent which has important consequences for the connectivity of larger fracture networks composed of the fundamental element studied here.

02 PETROLEUM↗

NASA NTRS2000

Testing and Analysis of Composite Skin/Stringer Debonding Under Multi-Axial Loading

A consistent step-wise approach is presented to investigate the damage mechanism in composite bonded skin/stringer constructions under uniaxial and biaxial (in-plane/out-of-plane) loading conditions. The approach uses experiments to detect the failure mechanism, computational stress analysis to determine the location of first matrix cracking and computational fracture mechanics to investigate the potential for delamination growth. In a first step, tests were performed on specimens, which consisted of a tapered composite flange, representing a stringer or frame, bonded onto a composite skin. Tests were performed under monotonic loading conditions in tension, three-point bending, and combined tension/bending to evaluate the debonding mechanisms between the skin and the bonded stringer. For combined tension/bending testing, a unique servohydraulic load frame was used that was capable of applying both in-plane tension and out-of-plane bending loads simultaneously. Specimen edges were examined on the microscope to document the damage occurrence and to identify typical damage patterns. For all three load cases, observed failure initiated in the flange, near the flange tip, causing the flange to almost fully debond from skin. In a second step, a two dimensional plane-strain finite element model was developed to analyze the different test cases using a geometrically nonlinear solution. For all three loading conditions, computed principal stresses exceeded the transverse strength of the material in those areas of the flange where the matrix cracks had developed during the tests. In a third step, delaminations of various lengths were simulated in two locations where delaminations were observed during the tests. The analyses showed that at the loads corresponding to matrix ply crack initiation computed strain energy release rates exceeded the values obtained from a mixed mode failure criterion in one location, Hence. Unstable delamination propagation is likely to occur as observed in the experiments.

Krueger, Ronald↗

NASA NTRS2000

Testing and Analysis of Composite Skin/Stringer Debonding under Multi-Axial Loading

A consistent step-wise approach is presented to investigate the damage mechanism in composite bonded skin/stringer constructions under uniaxial and biaxial (in-plane/out-of-plane) loading conditions. The approach uses experiments to detect the failure mechanism, computational stress analysis to determine the location of first matrix cracking and computational fracture mechanics to investigate the potential for delamination growth. In a first step, tests were performed on specimens, which consisted of a tapered composite flange, representing a stringer or frame, bonded onto a composite skin. Tests were performed under monotonic loading conditions in tension, three-point bending, and combined tension/bending to evaluate the debonding mechanisms between the skin and the bonded stringer. For combined tension/bending testing, a unique servohydraulic load frame was used that was capable of applying both in-plane tension and out-of-plane bending loads simultaneously. Specimen edges were examined on the microscope to document the damage occurrence and to identify typical damage patterns. For all three load cases, observed failure initiated in the flange, near the flange tip, causing the flange to almost fully debond from the skin. In a second step, a two-dimensional plane-strain finite element model was developed to analyze the different test cases using a geometrically nonlinear solution. For all three loading conditions, computed principal stresses exceeded the transverse strength of the material in those areas of the flange where the matrix cracks had developed during the tests. In a third step, delaminations of various lengths were simulated in two locations where delaminations were observed during the tests. The analyses showed that at the loads corresponding to matrix ply crack initiation computed strain energy release rates exceeded the values obtained from a mixed mode failure criterion in one location. Hence, unstable delamination propagation is likely to occur as observed in the experiments.

Krueger, Ronald↗

DOE OSTI2025

Development, validation, and verification of multi-pass thermo-mechanical welding simulations using the open-source MOOSE framework: NeT TG4 benchmark weldment

This study develops and validates a sequentially coupled thermo-mechanical welding simulation for the three-pass 316L stainless steel NeT TG4 benchmark weldment using the open-source Multiphysics Object-Oriented Simulation Environment (MOOSE) and the Nuclear Engineering Material model Library (NEML). A diffused ellipsoidal heat source was calibrated against thermocouple data and weld macrographs to accurately model the fusion zone geometry and transient thermal fields. Material hardening is represented using the Lemaitre-Chaboche mixed isotropic-kinematic hardening model, while four annealing models - no annealing, single-stage at 1050 °C and 1300 °C, and two-stage at 800 °C/1300 °C - were implemented to assess the impact of annealing models on the accuracy of the predicted welding-induced plasticity, distortions, and residual stresses. The predictions were validated against experimental measurements and benchmarked against results from commercial software, demonstrating that thermo-mechanical MOOSE welding simulations achieve comparable accuracy with enhanced computational efficiency. This work highlights the potential of using open-source finite element frameworks like MOOSE for advanced manufacturing simulations.

Ji, Wendy [Australian Nuclear Science and Technolo↗