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10-th order of accuracy for numerical solution of 3-D elasticity equations for heterogeneous materials on unfitted Cartesian meshes

We have developed the Optimal Local Truncation Error Method (OLTEM) with 10-th order of accuracy on unfitted Cartesian meshes for a system of 3-D elasticity equations with smooth irregular interfaces. 5 x 5 x 5 = 125-point stencils (similar to those for quadratic finite elements) for elastic heterogeneous materials are used for OLTEM. There are no unknowns at the interface points between different materials; the structure of the global discrete equations is the same for homogeneous and heterogeneous materials. The calculation of unknown stencil coefficients is based on the minimization of the local truncation error of the stencil equations and yields the optimal 10-th order of accuracy for OLTEM on unfitted Cartesian meshes, i.e., the increase by 7 orders in accuracy compared to quadratic finite elements on conformal meshes. A new post-processing procedure provides the 9-th order of accuracy for stresses in the 3-D case. Similar to basic computations it uses OLTEM with the 125-point stencils, the interface conditions and the elasticity equations. It was shown that the use of the elasticity equations for post-processing improves the accuracy of 0.1% stresses by 6 orders compared to post-processing without the use of PDEs. At an accuracy of for stresses, OLTEM with the new post-processing procedure reduces the number of degrees of freedom by 360 - 8000 times compared to quadratic finite elements with similar stencils. OLTEM with the 125-point stencils yields even more accurate results than high-order finite elements with much wider stencils. OLTEM provides accurate numerical results for compressible and nearly incompressible materials.

elasticity equations

Stress computation in displacement methods for two-material elastic media

The method of best fit strain tensors is extended to compute the stresses satisfying the conditions of equilibrium, compatibility, and constitutive relationships. It is assumed that the deflections at the mesh points have already been computed with acceptable accuracy. Results of examples presented show better accuracy than the usual procedure, in which equilibrium conditions are not enforced. Special emphasis is placed here upon two-material elastic media.

Salama, M.

A survey of strength analysis methods for laminates with holes

The methods for predicting the strength of composite laminates with fastener holes are reviewed for the cases of unloaded as well as loaded holes. Three categories of methods are discussed: (1) the hole-boundary stress (HBS) methods which compare the peak stresses and the laminate strength; (2) the linear elastic fracture (LEFM) methods which assume cracks emanating from the hole and predict failure when the stress intensity factor for a crack equals the laminate fracture toughness; and (3) two different two-parameter (TP) methods: the average-stress (ASTP) method, which predicts failure when the average stress over a distance from the hole equals the laminate strength; and the point-stress (PSTP) Whitney-Nuismer (1974) approach, which predicts failure when the stress near the hole equals the material strength. The PSTP is relatively accurate and is by far the most widely used of all the prediction methods. However, for large ranges of variables and cases, the current strength predictions may not always be accurate.

Crews, J. H., Jr.

Ab initio Computations of the Electronic, Mechanical, and Thermal Properties of Ultra High Temperature Ceramics (UHTC) ZrB2 and HfB2

Refractory materials such as metallic borides, often considered as ultra high temperature ceramics (UHTC), are characterized by high melting point, high hardness, and good chemical inertness. These materials have many applications which require high temperature materials that can operate with no or limited oxidation. Ab initio, first principles methods are the most accurate modeling approaches available and represent a parameter free description of the material based on the quantum mechanical equations. Using these methods, many of the intrinsic properties of these material can be obtained. We performed ab initio calculations based on density functional theory for the UHTC materials ZrB2 and HfB2. Computational results are presented for structural information (lattice constants, bond lengths, etc), electronic structure (bonding motifs, densities of states, band structure, etc), thermal quantities (phonon spectra, phonon densities of states, specific heat), as well as information about point defects such as vacancy and antisite formation energies.

Lawson, John W.

X-ray beam method for displacement measurement in hostile environments

A new method of extensometry using an X-ray beam was devised, and the results of current testing reveal it to be highly feasible. This technique has been shown to provide a non-contacting system that is immune to problems associated with density variations in gaseous environments, that plague currently available optical methods. This advantage is a result of the non-refracting penetrating nature of X-rays. The method is based on X-ray-induced X-ray fluorescence of targets, which subsequently serve as fudicial markers. Some target materials have melting points over 1600 degrees C which will facilitate measurement at extremely high temperatures. A highly focused intense X-ray beam, which is produced using a Johansen 'bent crystal', is then scanned across the target, which responds by fluorescing X-rays when stimulated by the incident beam. This secondary radiation is monitored using a detector. By carefully measuring beam orientation, change in target edge position can be determined. Many variations on this basic theme are now possible such as two targets demarcating a gage length, or a beam shadowing method using opaque targets.

Jordan, Eric H.

A Special Investigation to Develop a General Method for Three-dimensional Photoelastic Stress Analysis

The method of strain measurement after annealing is reviewed and found to be satisfactory for the materials available in this country. A new general method is described for the photoelastic determination of the principal stresses at any point of a general body subjected to arbitrary load. The method has been applied to a sphere subjected to diametrical compressive loads. The results show possibilities of high accuracy.

Frocht, M M

X-Ray Moire Techniques For Measuring Strain

X-ray moire method provides for measurement of strains throughout relatively large regions and in locations invisible or inaccessible to measurement by other techniques. For example, used to measure strains between layers of material in rubber tires. Method exploits body of knowledge already developed for optical moire measurement of strains. Offers advantages over optical methods of measuring strains within depths of objects, in that x-ray imaging not restricted to optically transparent materials. Also offers advantages over strain-gauge method that gauge wires not needed and measurements not limited to discrete gauge points.

Madaras, Eric Irvine

A Framework for Performing Multiscale Stochastic Progressive Failure Analysis of Composite Structures

A framework is presented that enables coupled multiscale analysis of composite structures. The recently developed, free, Finite Element Analysis - Micromechanics Analysis Code (FEAMAC) software couples the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) with ABAQUS to perform micromechanics based FEA such that the nonlinear composite material response at each integration point is modeled at each increment by MAC/GMC. As a result, the stochastic nature of fiber breakage in composites can be simulated through incorporation of an appropriate damage and failure model that operates within MAC/GMC on the level of the fiber. Results are presented for the progressive failure analysis of a titanium matrix composite tensile specimen that illustrate the power and utility of the framework and address the techniques needed to model the statistical nature of the problem properly. In particular, it is shown that incorporating fiber strength randomness on multiple scales improves the quality of the simulation by enabling failure at locations other than those associated with structural level stress risers.

Bednarcyk, Brett A.

A Framework for Performing Multiscale Stochastic Progressive Failure Analysis of Composite Structures

A framework is presented that enables coupled multiscale analysis of composite structures. The recently developed, free, Finite Element Analysis-Micromechanics Analysis Code (FEAMAC) software couples the Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) with ABAQUS to perform micromechanics based FEA such that the nonlinear composite material response at each integration point is modeled at each increment by MAC/GMC. As a result, the stochastic nature of fiber breakage in composites can be simulated through incorporation of an appropriate damage and failure model that operates within MAC/GMC on the level of the fiber. Results are presented for the progressive failure analysis of a titanium matrix composite tensile specimen that illustrate the power and utility of the framework and address the techniques needed to model the statistical nature of the problem properly. In particular, it is shown that incorporating fiber strength randomness on multiple scales improves the quality of the simulation by enabling failure at locations other than those associated with structural level stress risers.

Bednarcyk, Brett A.

Integrating Manned Aircraft and UAVs for the Prediction, Tracking, and Eradication of Desert Locust Swarms

Desert locusts (Schistocerca gregaria) present an acute threat to the agriculture of certain regions, capable of annihilating vast expanses of farmland and destabilizing food security. In this paper, an aviation-based framework concept is introduced that integrates both manned aircraft and Unmanned Aerial Vehicles (UAVs) to preemptively forecast, localize, and eliminate locust swarms efficiently. The framework begins by leveraging predictive modeling methods to refine search areas and pinpoint high-value Points of Interest (POIs) where locust swarms are most likely to materialize. From there, the proposed two-step model uses optical, infrared, and hyperspectral sensors onboard manned aircraft to conduct long-range surveying of probable swarm locations. Upon detection of a swarm, UAVs equipped with sophisticated sensors, including pheromone detectors, thermal and optical imaging systems, are deployed directly from the aircraft to carry out targeted biopesticide applications. This approach, which capitalizes on the combined strengths of both vehicles, provides the rapid response and large-scale intervention necessary to control locust outbreaks. By targeting locust swarms during their most destructive phase, this paper aims to disrupt the locust life cycle and mitigate their severe agricultural impact, offering a scalable and sustainable solution for food security in afflicted regions.

locust monitoring systems

Considerations to achieve directionality for gamma ray lasers

A method of alignment of nuclei for a gamma ray laser and a means of achieving preferential emission of radiation along the crystal axis are studied. Atomic alignment was achieved by materials researchers who made composite structures composed of needle-like single crystals all with the same orientation and all pointing in the same direction contained in a matrix of cobalt or nickel. The proposed method of preferential emission of radiation along the aligned needles is to have a symmetric field gradient at the nucleus and a sequence of excited levels of spin and parity 2(+) and 0(+). The proposed scheme reduces the density of excited states required for lasing and reduces the linewidth due to inhomogenous broadening. Mossbauer absorption experiments intended to test these ideas are outlined.

Jha, S.

Microstructural Influence on Deformation and Fatigue Life of Composites Using the Generalized Method of Cells

A fully coupled deformation and damage approach to modeling the response of composite materials and composite laminates is presented. It is based on the semi-­‐analytical generalized method of cells (GMC) micromechanics model as well as its higher fidelity counterpart, HFGMC, both of which provide closed-form constitutive equations for composite materials as well as the micro scale stress and strain fields in the composite phases. The provided constitutive equations allow GMC and HFGMC to function within a higher scale structural analysis (e.g., finite element analysis or lamination theory) to represent a composite material point, while the availability of the micro fields allow the incorporation of lower scale sub­‐models to represent local phenomena in the fiber and matrix. Further, GMC's formulation performs averaging when applying certain governing equations such that some degree of microscale field accuracy is surrendered in favor of extreme computational efficiency, rendering the method quite attractive as the centerpiece in a integrated computational material engineering (ICME) structural analysis; whereas HFGMC retains this microscale field accuracy, but at the price of significantly slower computational speed. Herein, the sensitivity of deformation and the fatigue life of graphite/epoxy PMC composites, with both ordered and disordered microstructures, has been investigated using this coupled deformation and damage micromechanics based approach. The local effects of fiber breakage and fatigue damage are included as sub‐models that operate on the microscale for the individual composite phases. For analysis of laminates, classical lamination theory is employed as the global or structural scale model, while GMC/HFGMC is embedded to operate on the microscale to simulate the behavior of the composite material within each laminate layer. A key outcome of this study is the statistical influence of microstructure and micromechanics idealization (GMC or HFGMC) on the overall accuracy of unidirectional and laminated composite deformation and fatigue response.

Microscale Models

Radiant Heating of Ampoule contents

Ampoule charge heating system exploits spectral properties of blackbody radiation and ampoule material transparency to heat charge to high temperature. Cooling gas prevents softening of outside wall of ampoule. Use of proposed method may be limited by tendency of silica (or any other viteous material) to devitrify on prolonged exposure to temperatures near softening point.

Holland, L. R.

Multimodal Defect Imaging of Pure Tungsten Components Fabricated via Electron Beam Powder Bed Fusion

The utilization of additive manufacturing (AM) techniques for refractory materials in high-temperature environments has significantly expanded because of the ability to fabricate geometrically complex components. Electron beam powder bed fusion (EB-PBF), which provides lower residual stress, a cleaner vacuum environment, and better efficiency for high melting point, is one of the best-suited AM methods to produce advanced refractory components. However, the property variation attributed to the heterogeneous microstructure and process-induced defects has hindered the widespread adoption of EB-PBF-produced material like tungsten. While numerous in-situ monitoring and defect detection methods have been demonstrated for EB-PBF, a workflow that compares and evaluates process-induced abnormalities from different imaging perspectives is still limited. This study examines a feature-embedded tungsten component manufactured via the EB-PBF process to demonstrate the defect detection capabilities of a multimodal defect imaging workflow. The predefined and process-induced defects are evaluated by harnessing various imaging techniques, including in-situ electron imaging, layerwise near-infrared (NIR) imaging, post-build high-energy x-ray computed tomography (CT), and conventional destructive metallography. The results highlight the strengths and limitations of distinctive defect imaging techniques concerning specific defect types, sizes, and conditions. It was found that electron imaging can provide more abnormal detection capabilities while maintaining a higher measuring accuracy, against the conventional metallography in this case study, compared with NIR and CT imaging techniques.

36 MATERIALS SCIENCE

Regolith-Derived Heat Shield for Planetary Body Entry and Descent System with In Situ Fabrication

In this paper we will discuss a new mass-efficient and innovative way of protecting high-mass spacecraft during planetary Entry, Descent & Landing (EDL). Heat shields fabricated in situ can provide a thermal-protection system (TPS) for spacecraft that routinely enter a planetary atmosphere. By fabricating the heat shield with space resources from regolith materials available on moons and asteroids, it is possible to avoid launching the heat-shield mass from Earth. Three regolith processing and manufacturing methods will be discussed: 1) oxygen & metal extraction ISRU processes produce glassy melts enriched in alumina and titania, processed to obtain variable density, high melting point and heat-resistance; 2) compression and sintering of the regolith yield low density materials; 3) in-situ derived high-temperature polymers are created to bind regolith particles together, with a lower energy budget.

Hogue, Michael D.

Photoelastic techniques for the complete determination of stresses in composite structures

Three new methods are proposed for determining the individual values of the principal stresses or strains in an orthotropic birefringent model using transmission photoelastic analysis. One of the methods is an extension of the oblique incidence technique in which the model (or the light beam) is rotated about one of the material symmetry axes. In another method, transmission and reflection photoelastic responses are combined, while in the third method small circular holes are drilled at points of interest and the isochromatic fringe order is measured at selected points on the hole boundary. The three methods are applied to an orthotropic disc under diametral compression and results are compared with strain gage data.

Prabhakaran, R.

Micromechanics-Based Structural Analysis (FEAMAC) and Multiscale Visualization within Abaqus/CAE Environment

A unified framework is presented that enables coupled multiscale analysis of composite structures and associated graphical pre- and postprocessing within the Abaqus/CAE environment. The recently developed, free, Finite Element Analysis--Micromechanics Analysis Code (FEAMAC) software couples NASA's Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) with Abaqus/Standard and Abaqus/Explicit to perform micromechanics based FEA such that the nonlinear composite material response at each integration point is modeled at each increment by MAC/GMC. The Graphical User Interfaces (FEAMAC-Pre and FEAMAC-Post), developed through collaboration between SIMULIA Erie and the NASA Glenn Research Center, enable users to employ a new FEAMAC module within Abaqus/CAE that provides access to the composite microscale. FEA IAC-Pre is used to define and store constituent material properties, set-up and store composite repeating unit cells, and assign composite materials as sections with all data being stored within the CAE database. Likewise FEAMAC-Post enables multiscale field quantity visualization (contour plots, X-Y plots), with point and click access to the microscale i.e., fiber and matrix fields).

Arnold, Steven M.

Method of determining load in anisotropic non-crystalline materials using energy flux deviation

An ultrasonic wave is applied to an anisotropic sample material in an initial direction and the intensity of the ultrasonic wave is measured on an opposite surface of the sample material by two adjacent receiving points located in an array of receiving points. A ratio is determined between the measured intensities of two adjacent receiving points, the ratio being indicative of an angle of flux deviation from the initial direction caused by an unknown applied load. This determined ratio is then compared to a plurality of ratios of a similarly tested, similar anisotropic reference material under a plurality of respective, known load conditions, whereby the load applied to the particular anisotropic sample material is determined. A related method is disclosed for determining the fiber orientation from known loads and a determined flux shift.

Prosser, William H.