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NASA NTRS2015

Variable-Domain Displacement Transfer Functions for Converting Surface Strains into Deflections for Structural Deformed Shape Predictions

Variable-Domain Displacement Transfer Functions were formulated for shape predictions of complex wing structures, for which surface strain-sensing stations must be properly distributed to avoid jointed junctures, and must be increased in the high strain gradient region. Each embedded beam (depth-wise cross section of structure along a surface strain-sensing line) was discretized into small variable domains. Thus, the surface strain distribution can be described with a piecewise linear or a piecewise nonlinear function. Through discretization, the embedded beam curvature equation can be piece-wisely integrated to obtain the Variable-Domain Displacement Transfer Functions (for each embedded beam), which are expressed in terms of geometrical parameters of the embedded beam and the surface strains along the strain-sensing line. By inputting the surface strain data into the Displacement Transfer Functions, slopes and deflections along each embedded beam can be calculated for mapping out overall structural deformed shapes. A long tapered cantilever tubular beam was chosen for shape prediction analysis. The input surface strains were analytically generated from finite-element analysis. The shape prediction accuracies of the Variable- Domain Displacement Transfer Functions were then determined in light of the finite-element generated slopes and deflections, and were fofound to be comparable to the accuracies of the constant-domain Displacement Transfer Functions

displacement transfer functions↗

NASA NTRS1988

Compression creep of filamentary composites

Axial and transverse strain fields induced in composite laminates subjected to compressive creep loading were compared for several types of laminate layups. Unidirectional graphite/epoxy as well as multi-directional graphite/epoxy and graphite/PEEK layups were studied. Specimens with and without holes were tested. The specimens were subjected to compressive creep loading for a 10-hour period. In-plane displacements were measured using moire interferometry. A computer based data reduction scheme was developed which reduces the whole-field displacement fields obtained using moire to whole-field strain contour maps. Only slight viscoelastic response was observed in matrix-dominated laminates, except for one test in which catastrophic specimen failure occurred after a 16-hour period. In this case the specimen response was a complex combination of both viscoelastic and fracture mechanisms. No viscoelastic effects were observed for fiber-dominated laminates over the 10-hour creep time used. The experimental results for specimens with holes were compared with results obtained using a finite-element analysis. The comparison between experiment and theory was generally good. Overall strain distributions were very well predicted. The finite element analysis typically predicted slightly higher strain values at the edge of the hole, and slightly lower strain values at positions removed from the hole, than were observed experimentally. It is hypothesized that these discrepancies are due to nonlinear material behavior at the hole edge, which were not accounted for during the finite-element analysis.

Graesser, D. L.↗

NASA NTRS1972

Finite element analysis of large transient elastic-plastic deformations of simple structures, with application to the engine rotor fragment containment/deflection problem

Assumed-displacement versions of the finite-element method are developed to predict large-deformation elastic-plastic transient deformations of structures. Both the conventional and a new improved finite-element variational formulation are derived. These formulations are then developed in detail for straight-beam and curved-beam elements undergoing (1) Bernoulli-Euler-Kirchhoff or (2) Timoshenko deformation behavior, in one plane. For each of these categories, several types of assumed-displacement finite elements are developed, and transient response predictions are compared with available exact solutions for small-deflection, linear-elastic transient responses. The present finite-element predictions for large-deflection elastic-plastic transient responses are evaluated via several beam and ring examples for which experimental measurements of transient strains and large transient deformations and independent finite-difference predictions are available.

Wu, R. W.↗

DOE OSTI2020

Predicting metal–metal interactions. I. The influence of strain on nanoparticle and metal adlayer stabilities

Strain-engineering of bimetallic nanomaterials is an important design strategy for developing new catalysts. In this paper, we introduce an approach for including strain effects into a recently introduced, density functional theory (DFT)-based alloy stability model. The model predicts adsorption site stabilities in nanoparticles and connects these site stabilities with catalytic reactivity and selectivity. Strain-based dependencies will increase the model’s accuracy for nanoparticles affected by finite-size effects. In addition to the stability of small nanoparticles, strain also influences the heat of adsorption of epitaxially grown metal-on-metal adlayers. In this respect, we successfully benchmark the strain-including alloy stability model with previous experimentally determined trends in the heats of adsorption of Au and Cu adlayers on Pt (111). For these systems, our model predicts stronger bimetallic interactions in the first monolayer than monometallic interactions in the second monolayer. We explicitly quantify the interplay between destabilizing strain effects and the energy gained by forming new metal–metal bonds. While tensile strain in the first Cu monolayer significantly destabilizes the adsorption strength, compressive strain in the first Au monolayer has a minimal impact on the heat of adsorption. Hence, this study introduces and, by comparison with previous experiments, validates an efficient DFT-based approach for strain-engineering the stability, and, in turn, the catalytic performance, of active sites in bimetallic alloys with atomic level resolution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1981

A finite element model with nonviscous damping

A constitutive law by which structural damping is modeled as a relationship between stress, strain, and strain rate in a material is used in conjunction with the finite element method to develop general integral expressions for viscous and nonviscous damping matrices. To solve the set of nonlinear equations resulting from the presence of nonviscous damping, a solution technique is developed by modifying the Newmark method to accommodate an iterative solution and treat the nonviscous damping as a pseudo-force. The technique is then checked for accuracy and convergence in single- and multi-degree-of-freedom problems, and is found to be accurate and efficient for initial-condition problems with small nonviscous damping.

Roussos, L. A.↗

NASA NTRS1986

Experimental study of a metal-matrix composite

A metal-matrix specimen was investigated using moire interferometry with 2400 lines/m (60,960 l/in.). The specimen was a 6-ply (0/ + or - 45)s boron-aluminum tensile coupon with a central slot. The unequal deformations in fibers and matrix were evident. Special attention was given to a plastic slip zone in the matrix. Normal and shear strains were calculated in the slip zone; the shear-strain concentration factor rose dramatically with the onset of plastic slip and continued to rise gradually with load to 95 percent of the failure load. The precipitous change from maximum tensile strain in one fiber to zero tensile strain in the neighboring fiber was accommodated by the very high shear strains of the matrix in the slip zone. Experimental considerations are discussed: shear strains are independent of rigid-body rotations; simplified strain calculations are justified; averaging across the narrow slip region and the influence of finite thickness of the specimen grating contribute to underestimation of peak strains.

Post, D.↗

DOE OSTI2025

Shear Band Formation in Thin-Film Multilayer Columns Under Compressive Loading: A Mechanistic Study

Micro-pillar compression is a popular experimental technique used for characterizing the mechanical behavior of nano- and micro-laminates. The compressive stress–strain response of the column-shaped thin-film composite can be measured, and the deformation and damage features can be revealed by post-test cross-section microscopy. The development of plastic instability in the form of localized strain concentration (shear bands), leading to eventual failure, is frequently observed. In the present study, a computational approach is used to illustrate the commonality of shear band formation from a continuum standpoint. Systematic finite element analyses are conducted, showing that the strain field tends to become localized once plastic yielding commences. Distinct shear offsets of the layered structure can be revealed from the numerical model, which is similar to those observed in experiments. The actual appearance of shear bands depends on the materials’ constitutive behavior and precise geometries. Post-yield strain hardening reduces the propensity of shear band formation, while strain softening enhances it. Imperfections such as the undulated layer geometry, as well as the frictional characteristics between the specimen and test apparatus, can also influence the shear band morphology and overall stress–strain response.

finite element modeling↗

NASA NTRS1998

Gel stretch method: a new method to measure constitutive properties of cardiac muscle cells

Diastolic dysfunction is an important cause of congestive heart failure; however, the basic mechanisms causing diastolic congestive heart failure are not fully understood, especially the role of the cardiac muscle cell, or cardiocyte, in this process. Before the role of the cardiocyte in this pathophysiology can be defined, methods for measuring cardiocyte constitutive properties must be developed and validated. Thus this study was designed to evaluate a new method to characterize cardiocyte constitutive properties, the gel stretch method. Cardiocytes were isolated enzymatically from normal feline hearts and embedded in a 2% agarose gel containing HEPES-Krebs buffer and laminin. This gel was cast in a shape that allowed it to be placed in a stretching device. The ends of the gel were held between a movable roller and fixed plates that acted as mandibles. Distance between the right and left mandibles was increased using a stepper motor system. The force applied to the gel was measured by a force transducer. The resultant cardiocyte strain was determined by imaging the cells with a microscope, capturing the images with a CCD camera, and measuring cardiocyte and sarcomere length changes. Cardiocyte stress was characterized with a finite-element method. These measurements of cardiocyte stress and strain were used to determine cardiocyte stiffness. Two variables affecting cardiocyte stiffness were measured, the passive elastic spring and viscous damping. The passive spring was assessed by increasing the force on the gel at 1 g/min, modeling the resultant stress vs. strain relationship as an exponential [sigma = A/k(ekepsilon - 1)]. In normal cardiocytes, A = 23.0 kN/m2 and k = 16. Viscous damping was assessed by examining the loop area between the stress vs. strain relationship during 1 g/min increases and decreases in force. Normal cardiocytes had a finite loop area = 1.39 kN/m2, indicating the presence of viscous damping. Thus the gel stretch method provided accurate measurements of cardiocyte constitutive properties. These measurements have allowed the first quantitative assessment of passive elastic spring properties and viscous damping in normal mammalian cardiocytes.

Non-NASA Center↗

NASA NTRS1987

Nonlinear heat transfer and structural analyses of SSME turbine blades

Three-dimensional nonlinear finite-element heat transfer and structural analyses were performed for the first stage high-pressure fuel turbopump blade of the space shuttle main engine (SSME). Directionally solidified (DS) MAR-M 246 material properties were considered for the analyses. Analytical conditions were based on a typical test stand engine cycle. Blade temperature and stress-strain histories were calculated using MARC finite-element computer code. The study was undertaken to assess the structural response of an SSME turbine blade and to gain greater understanding of blade damage mechanisms, convective cooling effects, and the thermal-mechanical effects.

Abdul-Aziz, A.↗

NASA NTRS1991

Detailed analysis and test correlation of a stiffened composite wing panel

Nonlinear finite element analysis techniques are evaluated by applying them to a realistic aircraft structural component. A wing panel from the V-22 tiltrotor aircraft is chosen because it is a typical modern aircraft structural component for which there is experimental data for comparison of results. From blueprints and drawings supplied by the Bell Helicopter Textron Corporation, a very detailed finite element model containing 2284 9-node Assumed Natural-Coordinate Strain (ANS) elements was generated. A novel solution strategy which accounts for geometric nonlinearity through the use of corotating element reference frames and nonlinear strain displacements relations is used to analyze this detailed model. Results from linear analyses using the same finite element model are presented in order to illustrate the advantages and costs of the nonlinear analysis as compared with the more traditional linear analysis. Strain predictions from both the linear and nonlinear stress analyses are shown to compare well with experimental data up through the Design Ultimate Load (DUL) of the panel. However, due to the extreme nonlinear response of the panel, the linear analysis was not accurate at loads above the DUL. The nonlinear analysis more accurately predicted the strain at high values of applied load, and even predicted complicated nonlinear response characteristics, such as load reversals, at the observed failure load of the test panel. In order to understand the failure mechanism of the panel, buckling and first ply failure analyses were performed. The buckling load was 17 percent above the observed failure load while first ply failure analyses indicated significant material damage at and below the observed failure load.

Davis, D. Dale, Jr.↗

NASA NTRS1993

Accuracy of the Generalized Self-Consistent Method in Modelling the Elastic Behaviour of Periodic Composites

Local stress and strain fields in the unit cell of an infinite, two-dimensional, periodic fibrous lattice have been determined by an integral equation approach. The effect of the fibres is assimilated to an infinite two-dimensional array of fictitious body forces in the matrix constituent phase of the unit cell. By subtracting a volume averaged strain polarization term from the integral equation we effectively embed a finite number of unit cells in a homogenized medium in which the overall stress and strain correspond to the volume averaged stress and strain of the constrained unit cell. This paper demonstrates that the zeroth term in the governing integral equation expansion, which embeds one unit cell in the homogenized medium, corresponds to the generalized self-consistent approximation. By comparing the zeroth term approximation with higher order approximations to the integral equation summation, both the accuracy of the generalized self-consistent composite model and the rate of convergence of the integral summation can be assessed. Two example composites are studied. For a tungsten/copper elastic fibrous composite the generalized self-consistent model is shown to provide accurate, effective, elastic moduli and local field representations. The local elastic transverse stress field within the representative volume element of the generalized self-consistent method is shown to be in error by much larger amounts for a composite with periodically distributed voids, but homogenization leads to a cancelling of errors, and the effective transverse Young's modulus of the voided composite is shown to be in error by only 23% at a void volume fraction of 75%.

Walker, Kevin P.↗

NASA NTRS1982

On finite deformation elasto-plasticity

Lee (1969) has proposed a theory based on the decomposition of the total deformation gradient to an elastic and plastic part, and from it has concluded that the additive decomposition of the strain rates holds only approximately. Lubarda and Lee (1981) have declared that Lee's 'exact finite-deformation kinematics shows the almost universal assumption that the total velocity strain or rate of deformation is the sum of elastic and plastic rates to be in error'. Hence questions are raised regarding the validity of essentially all finite deformation elasto-plasticity theories. The present investigation is concerned with these questions. It is shown that the additive decomposition of the strain rates follows from all common finite elasto-plasticity concepts. Lee's theory is examined, and it is shown that this theory also leads to an additive strain rate decomposition, and therefore, his conclusion stems from misinterpretation. It is found that the elastic and the plastic strain rates considered by Lee do not correspond to the same configuration. They are, therefore, not compatible measures.

Nemat-Nasser, S.↗

DOE OSTI2022

High strain-rate compression behavior of polymeric rod and plate Kelvin lattice structures

The compressive high strain-rate behavior of polymeric Kelvin lattice structures with rod-based or plate-based unit cells was investigated through experimental techniques and finite element simulations. Polymeric lattice structures with 5x5x5 unit cell geometries were manufactured on the millimeter scale using vat polymerization additive manufacturing and tested at low (0.001/s) and high (1000/s) strain-rates. High strain-rate experiments were performed and validated for a viscoelastic split-Hopkinson (Kolsky) pressure bar system (SHPB) coupled with high-speed imaging and digital image correlation (DIC). Experimental results at both low and high strain-rates show the formation of a localized deformation band which was more prevalent in low relative density specimens and low strain-rate experiments. Strain-rate effects of lattice specimens strongly correlate with effects of the base polymer material; both bulk polymer and lattice specimen demonstrated strain-rate hardening, strain-rate stiffening, and decreased fracture strain under dynamic loading. Results show mechanical failure properties and energy absorption depended strongly on the relative density of the lattice specimen and exhibited distinct scaling between relative density and geometry type (rod, plate) and loading rate. High relative density plate-lattices demonstrated inferior mechanical properties to rod-lattices; however, there exists a critical relative density for a given mechanical property (17%- 28%) below which plate-lattices outperform rod-lattices of similar mass. As a result, high strain-rate explicit finite element simulations were performed and showed good agreement with the mechanical failure trends and deformation modes observed in the experiments.

36 MATERIALS SCIENCE↗

NASA NTRS1992

Structural analysis of an NDE-inspected carbon-carbon component

In this research, it is demonstrated that the integration of nondestructive evaluation with the finite element method (a quantitative NDE/FEM approach) can be used for analysis and behavior prediction of advanced materials, such as fiber composites, after processing and during in-service testing. First, stress, strain, and energy data were calculated by the finite element method for square plates with a 10 percent difference in the material properties between specified segments, i.e., between the center and the outside section or between two halves of the plate. This demonstrated the efficiency of the method in predicting variations in the structural behavior based on small material property differences. Then, finite element analyses and actual axial compression tests were performed on a Space Shuttle brake stator made from woven carbon-carbon composites. The material properties used in the numerical modeling of the stator were previously characterized at a large number of points on the component by quantitative NDE-procedures, i.e., ultrasonics and radiography. The results from the experimental compressive loading tests were used to verify the NDE/FEM results. Good agreement was found for most parameters.

Striz, A. G.↗

NASA NTRS1991

An Evaluation of the Iosipescu Specimen for Composite Materials Shear Property Measurement

A detailed evaluation of the suitability of the Iosipescu specimen tested in the modified Wyoming fixture is presented. An experimental investigation using conventional strain gage instrumentation and moire interferometry is performed. A finite element analysis of the Iosipescu shear test for unidirectional and cross-ply composites is used to assess the uniformity of the shear stress field in the vicinity of the notch, and demonstrate the effect of the nonuniform stress field upon the strain gage measurements used for the determination of composite shear moduli. From the test results for graphite-epoxy laminates, it is shown that the proximity of the load introduction point to the test section greatly influences the individual gage readings for certain fiber orientations but the effect upon shear modulus measurement is relatively unimportant. A numerical study of the load contact effect shows the sensitivity of some fiber configurations to the specimen/fixture contact mechanism and may account for the variations in the measured shear moduli. A comparison of the strain gage readings from one surface of a specimen with corresponding data from moire interferometry on the opposite face documented an extreme sensitivity of some fiber orientations to eccentric loading which induced twisting and yielded spurious shear stress-strain curves. In the numerical analysis, it is shown that the Iosipescu specimens for different fiber orientations have to be modeled differently in order to closely approximate the true loading conditions. Correction factors are needed to allow for the nonuniformity of the strain field and the use of the average shear stress in the shear modulus evaluation. The correction factors, which are determined for the region occupied by the strain gage rosette, are found to be dependent upon the material orthotropic ratio and the finite element models. Based upon the experimental and numerical results, recommendations for improving the reliability and accuracy of the shear modulus values are made, and the implications for shear strength measurement discussed. Further application of the Iosipescu shear test to woven fabric composites is presented. The limitations of the traditional strain gage instrumentation on the satin weave and high tow plain weave fabrics is discussed. Test results of a epoxy based aluminum particulate composite is also presented. A modification of the Iosipescu specimen is proposed and investigated experimentally and numerically. It is shown that the proposed new specimen design provides a more uniform shear stress field in the test section and greatly reduces the normal and shear stress concentrations in the vicinity of the notches. While the fabrication and the material cost of the proposed specimen is tremendously reduced, it is shown the accuracy of the shear modulus measurement is not sacrificed.

Ho, Henjen↗

NASA NTRS2002

Automation Tools for Finite Element Analysis of Adhesively Bonded Joints

This article presents two new automation creation tools that obtain stresses and strains (Shear and peel) in adhesively bonded joints. For a given adhesively bonded joint Finite Element model, in which the adhesive is characterised using springs, these automation tools read the corresponding input and output files, use the spring forces and deformations to obtain the adhesive stresses and strains, sort the stresses and strains in descending order, and generate plot files for 3D visualisation of the stress and strain fields. Grids (nodes) and elements can be numbered in any order that is convenient for the user. Using the automation tools, trade-off studies, which are needed for design of adhesively bonded joints, can be performed very quickly.

Tahmasebi, Farhad↗

NASA NTRS1982

Evaluation of an improved finite-element thermal stress calculation technique

A procedure for generating accurate thermal stresses with coarse finite element grids (Ojalvo's method) is described. The procedure is based on the observation that for linear thermoelastic problems, the thermal stresses may be envisioned as being composed of two contributions; the first due to the strains in the structure which depend on the integral of the temperature distribution over the finite element and the second due to the local variation of the temperature in the element. The first contribution can be accurately predicted with a coarse finite-element mesh. The resulting strain distribution can then be combined via the constitutive relations with detailed temperatures from a separate thermal analysis. The result is accurate thermal stresses from coarse finite element structural models even where the temperature distributions have sharp variations. The range of applicability of the method for various classes of thermostructural problems such as in-plane or bending type problems and the effect of the nature of the temperature distribution and edge constraints are addressed. Ojalvo's method is used in conjunction with the SPAR finite element program. Results are obtained for rods, membranes, a box beam and a stiffened panel.

Camarda, C. J.↗

DOE OSTI2024

Phase-Field Model Incorporating Large Inelastic Strain with Application to the Oxidation of High-Temperature Coating Systems

Structural metallic and ceramic materials at high temperatures often suffer from creep, fatigue and oxidation, which typically involves local large inelastic strain. The large strain is usually approached by Lagrangian-description-based finite deformation theory. Here we develop an efficient, Eulerian-description-based, Incremental Realization of Inelastic Deformation (IRID) algorithm to deal with large inelastic strain with small elastic strain. We apply this algorithm to simulate high temperature oxidation with severe volume expansion using a phase-field approach. The oxidation and deformation of bond coat can lead to spallation and failure of the thermal barrier coatings (TBC) and environmental barrier coatings (EBC), which is a critical concern in design of these coatings. We simulate the growth of thermally grown oxide (TGO) in these coating systems, with phase transformations and microstructure evolution incorporated. The simulation results are compared with relevant experimental reports in the literature.

Cheng, Tianle↗