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At least 325 records · Page 18

Theoretical study of stress concentrations at circular holes and inclusions in strain hardening materials.

Nonlinear boundary value problems of an infinite elastic-plastic plate with a circular hole subjected to pure tension and pure shear at infinity are solved by a method involving Fourier series and finite difference. On the basis of these solutions, the validity of Neuber's relationship between the stress and strain concentration factors for the plane stress problems is examined and a generalized Stowell formula for the stress concentration factor is proposed for problems in which the applied loading may be pure shear as well as pure tension and, furthermore, other stress states. By the same method of solution, the stress distributions around a rigid circular cylindrical inclusion embedded in an infinite rigid-plastic matrix subjected to uniform transverse pure shear and tension are obtained.

Huang, W. C.↗

Plasticity Tool for Predicting Shear Nonlinearity of Unidirectional Laminates Under Multiaxial Loading

This study implements a plasticity tool to predict the nonlinear shear behavior of unidirectional composite laminates under multiaxial loadings, with an intent to further develop the tool for use in composite progressive damage analysis. The steps for developing the plasticity tool include establishing a general quadratic yield function, deriving the incremental elasto-plastic stress-strain relations using the yield function with associated flow rule, and integrating the elasto-plastic stress-strain relations with a modified Euler method and a substepping scheme. Micromechanics analyses are performed to obtain normal and shear stress-strain curves that are used in determining the plasticity parameters of the yield function. By analyzing a micromechanics model, a virtual testing approach is used to replace costly experimental tests for obtaining stress-strain responses of composites under various loadings. The predicted elastic moduli and Poisson's ratios are in good agreement with experimental data. The substepping scheme for integrating the elasto-plastic stress-strain relations is suitable for working with displacement-based finite element codes. An illustration problem is solved to show that the plasticity tool can predict the nonlinear shear behavior for a unidirectional laminate subjected to multiaxial loadings.

Wang, John T.↗

Icing Formation Strains on Airfoil Skin

Aircraft icing has long presented a safety hazard to the aerospace industry. One problem inherent to aircraft icing is predicting the adhesive properties of the ice-aircraft interface; values commonly reported span multiple orders of magnitude, making shedding prediction and surface evaluation difficult. An effort has been undertaken at the NASA Glenn Research Center to understand the cause of the scatter in the data. Geometry dependencies, variation in testing procedures, and residual stresses in ice samples have previously been identified as significant contributors to the problem. Residual stresses were singled out for this study, which investigated the strains at the leading edge of a Common Research Model (CRM) wind tunnel model in the NASA Glenn Icing Research Tunnel. Sprays were conducted at a particle size median volumetric diameter (MVD) of 20 µm, with liquid water contents (LWC) spanning from 0.4 to 3.0 g/m3. Total temperatures were varied between 0 and -25 °C, and test section velocity between 51 and 118 m/s. The leading edge was instrumented with custom strain gages, resistance temperature detectors (RTDs), optical fibers, and a pressure mat. Results indicate Δ strains, which were the difference between recorded strains and those predicted from isotropic thermal expansion of aluminum, below -400 µε with consistent patterns of strain across a wide variety of tunnel conditions. Isotropic, linear elastic finite element analysis (FEA) was conducted by varying the temperature of simplified airfoil and ice geometries, producing similar strains to those observed in testing. This allowed induced stresses to be predicted. Predicted stresses were above the expected tensile strength for ice, and suggest a source for previously observed cracking in tunnel ice.

Ice Adhesion↗

A K-BKZ Formulation for Soft-Tissue Viscoelasticity

A viscoelastic model of the K-BKZ (Kaye 1962; Bernstein et al. 1963) type is developed for isotropic biological tissues, and applied to the fat pad of the human heel. To facilitate this pursuit, a class of elastic solids is introduced through a novel strain-energy function whose elements possess strong ellipticity, and therefore lead to stable material models. The standard fractional-order viscoelastic (FOV) solid is used to arrive at the overall elastic/viscoelastic structure of the model, while the elastic potential via the K-BKZ hypothesis is used to arrive at the tensorial structure of the model. Candidate sets of functions are proposed for the elastic and viscoelastic material functions present in the model, including a regularized fractional derivative that was determined to be the best. The Akaike information criterion (AIC) is advocated for performing multi-model inference, enabling an objective selection of the best material function from within a candidate set.

Freed, Alan D.↗

Nonlinearity and Strain-Rate Dependence in the Deformation Response of Polymer Matrix Composites Modeled

There has been no accurate procedure for modeling the high-speed impact of composite materials, but such an analytical capability will be required in designing reliable lightweight engine-containment systems. The majority of the models in use assume a linear elastic material response that does not vary with strain rate. However, for containment systems, polymer matrix composites incorporating ductile polymers are likely to be used. For such a material, the deformation response is likely to be nonlinear and to vary with strain rate. An analytical model has been developed at the NASA Glenn Research Center at Lewis Field that incorporates both of these features. A set of constitutive equations that was originally developed to analyze the viscoplastic deformation of metals (Ramaswamy-Stouffer equations) was modified to simulate the nonlinear, rate-dependent deformation of polymers. Specifically, the effects of hydrostatic stresses on the inelastic response, which can be significant in polymers, were accounted for by a modification of the definition of the effective stress. The constitutive equations were then incorporated into a composite micromechanics model based on the mechanics of materials theory. This theory predicts the deformation response of a composite material from the properties and behavior of the individual constituents. In this manner, the nonlinear, rate-dependent deformation response of a polymer matrix composite can be predicted.

Goldberg, Robert K.↗

On the role of constant-stress surfaces in the problem of minimizing elastic stress concentration

Cases involving antiplane shear deformation, axisymmetric torsion, and plane strain theory, with surfaces of constant stress magnitude optimal in terms of minimizing stress, are investigated. Results for the plane theory refer to exterior doubly connected domains. Stresses generated by torsion of an elastic solid lying within a radially convex region of revolution with plane ends, body force absent, and lateral surface traction-free, are examined. The unknown portion of the boundary of such domains may involve a hole, fillet, or notch.

Wheeler, L.↗

The Extensional Rheology of Non-Newtonian Materials

The evolution of the transient extensional stresses in dilute and semi-dilute viscoelastic polymer solutions are measured with a filament stretching rheometer of a design similar to that first introduced by Sridhar, et al. The solutions are polystyrene-based (PS) Boger fluids that are stretched at constant strain rates ranging from 0.6 less than or equal to epsilon(0) less than or equal to 4s(exp -1) and to Hencky strains of epsilon greater than 4. The test fluids all strain harden and Trouton ratios exceeding 1000 are obtained at high strains. The experimental data strain hardens at lower strain levels than predicted by bead-spring FENE models. In addition to measuring the transient tensile stress growth, we also monitor the decay of the tensile viscoelastic stress difference in the fluid column following cessation of uniaxial elongation as a function of the total imposed Hencky strain and the strain rate. The extensional stresses initially decay very rapidly upon cessation of uniaxial elongation followed by a slower viscoelastic relaxation, and deviate significantly from FENE relaxation predictions. The relaxation at long times t is greater than or equal to 5 s, is compromised by gravitational draining leading to non-uniform filament profiles. For the most elastic fluids, partial decohension of the fluid filament from the endplates of the rheometer is observed in tests conducted at high strain rates. This elastic instability is initiated near the rigid endplate fixtures of the device and it results in the progressive breakup of the fluid column into individual threads or 'fibrils' with a regular azimuthal spacing. These fibrils elongate and bifurcate as the fluid sample is elongated further. Flow visualization experiments using a modified stretching device show that the instability develops as a consequence of an axisymmetry-breaking meniscus instability in the nonhomogeneous region of highly deformed fluid near the rigid endplate.

Spiegelberg, Stephen H.↗

Development of a simplified procedure for cyclic structural analysis

Development was extended of a simplified inelastic analysis computer program (ANSYMP) for predicting the stress-strain history at the critical location of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a plasticity hardening model. Creep effects can be calculated on the basis of stress relaxation at constant strain, creep at constant stress, or a combination of stress relaxation and creep accumulation. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, dwell times at various points in the cycles, different materials, and kinematic hardening. Good agreement was found between these analytical results and nonlinear finite-element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite-element analysis.

Kaufman, A.↗

Ultrasonic characterization of the nonlinear elastic properties of unidirectional graphite/epoxy composites

The theoretical treatment of linear and nonlinear elasticity in a unidirectionally fiber reinforced composite as well as measurements for a unidirectional graphite/epoxy composite (T300/5208) are presented. Linear elastic properties were measured by both ultrasonic and strain gage measurements. The nonlinear properties were determined by measuring changes in ultrasonic natural phase velocity with a pulsed phase locked loop interferometer as a function of stress and temperature. These measurements provide the basis for further investigations into the relationship between nonlinear elastic properties and other important properties such as strength and fiber-matrix interfacial stength in graphite/epoxy composites.

Prosser, William H.↗

Ultrasonic characterization of the nonlinear elastic properties of unidirectional graphite/epoxy composites

The theoretical treatment of linear and nonlinear elasticity in a unidirectionally fiber reinforced composite as well as measurements for a unidirectional graphite/epoxy composite (T300/5208) are presented. Linear elastic properties were measured by both ultrasonic and strain gage measurements. The nonlinear properties were determined by measuring changes in ultrasonic natural phase velocity with a pulsed phase locked loop interferometer as a function of stress and temperature. These measurements provide the basis for further investigations into the relationship between nonlinear elastic properties and other important properties such as strength and fiber-matrix interfacial strength in graphite/epoxy composites.

Prosser, William H.↗

Computing Fault Displacements from Surface Deformations

Simplex is a computer program that calculates locations and displacements of subterranean faults from data on Earth-surface deformations. The calculation involves inversion of a forward model (given a point source representing a fault, a forward model calculates the surface deformations) for displacements, and strains caused by a fault located in isotropic, elastic half-space. The inversion involves the use of nonlinear, multiparameter estimation techniques. The input surface-deformation data can be in multiple formats, with absolute or differential positioning. The input data can be derived from multiple sources, including interferometric synthetic-aperture radar, the Global Positioning System, and strain meters. Parameters can be constrained or free. Estimates can be calculated for single or multiple faults. Estimates of parameters are accompanied by reports of their covariances and uncertainties. Simplex has been tested extensively against forward models and against other means of inverting geodetic data and seismic observations. This work

Lyzenga, Gregory↗

Three-dimensional elastic-plastic finite-element analysis of fatigue crack propagation

Fatigue cracks are a major problem in designing structures subjected to cyclic loading. Cracks frequently occur in structures such as aircraft and spacecraft. The inspection intervals of many aircraft structures are based on crack-propagation lives. Therefore, improved prediction of propagation lives under flight-load conditions (variable-amplitude loading) are needed to provide more realistic design criteria for these structures. The main thrust was to develop a three-dimensional, nonlinear, elastic-plastic, finite element program capable of extending a crack and changing boundary conditions for the model under consideration. The finite-element model is composed of 8-noded (linear-strain) isoparametric elements. In the analysis, the material is assumed to be elastic-perfectly plastic. The cycle stress-strain curve for the material is shown Zienkiewicz's initial-stress method, von Mises's yield criterion, and Drucker's normality condition under small-strain assumptions are used to account for plasticity. The three-dimensional analysis is capable of extending the crack and changing boundary conditions under cyclic loading.

Goglia, G. L.↗

Elevated temperature axial and torsional fatigue behavior of Haynes 188

The results of high-temperature axial and torsional low-cycle fatigue experiments performed on Haynes 188, a wrought cobalt-base superalloy, are reported. Fatigue tests were performed at 760 C in air on thin-walled tubular specimens at various ranges under strain control. Data are also presented for coefficient of thermal expansion, elastic modulus, and shear modulus at various temperatures from room to 1000 C, and monotonic and cyclic stress-strain curves in tension and in shear at 760 C. The data set is used to evaluate several multiaxial fatigue life models (most were originally developed for room temperature multiaxial life prediction) including von Mises equivalent strain range (ASME boiler and pressure vessel code), Manson-Halford, Modified Multiaxiality Factor (proposed here), Modified Smith-Watson-Topper, and Fatemi-Socie-Kurath. At von Mises equivalent strain ranges (the torsional strain range divided by the square root of 3, taking the Poisson's ratio to be 0.5), torsionally strained specimens lasted, on average, factors of 2 to 3 times longer than axially strained specimens. The Modified Multiaxiality Factor approach shows promise as a useful method of estimating torsional fatigue life from axial fatigue data at high temperatures. Several difficulties arose with the specimen geometry and extensometry used in these experiments. Cracking at extensometer probe indentations was a problem at smaller strain ranges. Also, as the largest axial and torsional strain range fatigue tests neared completion, a small amount of specimen buckling was observed.

Bonacuse, Peter J.↗

Simplified cyclic structural analyses of SSME turbine blades

Anisotropic high-temperature alloys are used to meet the safety and durability requirements of turbine blades for high-pressure turbopumps in reusable space propulsion systems. The applicability to anisotropic components of a simplified inelastic structural analysis procedure developed at the NASA Lewis Research Center is assessed. The procedure uses as input the history of the total strain at the critical crack initiation location computed from elastic finite-element analyses. Cyclic heat transfer and structural analyses are performed for the first stage high-pressure fuel turbopump blade of the space shuttle main engine. The blade alloy is directionally solidified MAR-M 246 (nickel base). The analyses are based on a typical test stand engine cycle. Stress-strain histories for the airfoil critical location are computed using both the MARC nonlinear finite-element computer code and the simplified procedure. Additional cases are analyzed in which the material yield strength is arbitrarily reduced to increase the plastic strains and, therefore, the severity of the problem. Good agreement is shown between the predicted stress-strain solutions from the two methods. The simplified analysis uses about 0.02 percent (5 percent with the required elastic finite-element analyses) of the CPU time used by the nonlinear finite element analysis.

Kaufman, A.↗

Effect of Ex Vivo Ionizing Radiation on Static and Fatigue Properties of Mouse Vertebral Bodies

For a variety of medical and scientific reasons, human bones can be exposed to a wide range of ionizing radiation levels. In vivo radiation therapy (0.05 kGy) is used in cancer treatment, and ex vivo irradiation (25-35 kGy) is used to sterilize bone allografts. Ionizing radiation in these applications has been shown to increase risk of fracture, decrease bone quality and degrade collagen integrity. Past studies have investigated the deleterious effects of radiation on cortical or trabecular bone specimens individually, but to date no studies have examined whole bones containing both cortical and trabecular tissue. Furthermore, a clear relationship between the dose and the mechanical and biochemical response of bone's extracellular matrix has yet to be established for doses ranging from cancer therapy to allograft sterilization (0.05-35 kGy). To gain insight into these issues, we conducted an ex vivo radiation study to investigate non-cellular (i.e. matrix) effects of ionizing radiation dose on vertebral whole bone mechanical properties, over a range of radiation doses (0.05-35 kGy), with a focus on any radiation-induced changes in collagen. With underlying mechanisms of action in mind, we hypothesized that any induced reductions in mechanical properties would be associated with changes in collagen integrity. METHODS: 20-week old female mice were euthanized and the lumbar spine was dissected using IACUC approved protocols. The lumbar vertebrae (L1- S1) were extracted from the spine via cuts through adjacent intervertebral discs, and the endplates, posterior processes, surrounding musculature, and soft tissues were removed (approx. 1.5mm diameter, approx. 2mm height). Specimens were randomly assigned to one of five groups for ex vivo radiation exposure: x-ray irradiation at 0.05, 1, 17, or 35 kGy, or a 0 kGy control. Following irradiation, the vertebrae were imaged using microcomputed tomography (micro-CT) and then subjected to either monotonic compressive loading to failure or uniform cyclic compressive loading. During cyclic testing, samples were loaded in force control to a force level that corresponded to a strain of 0.46%, as determined in advance by a linearly elastic micro-CT-based finite element analysis for each specimen. Tests were stopped at imminent fracture, defined as a rapid increase in strain. The main outcome for the monotonic test was the strength (maximum force); for cyclic testing it was the fatigue life (log of the number of cycles of loading at imminent failure). A fluorometric assay was used on the S1 vertebrae to measure the number of non-enzymatic collagen crosslinks[4]. A one-way ANOVA was performed on mechanical properties and collagen crosslinks; means were compared with controls using Dunnett's method, with a Tukey-Kramer post-hoc analysis when significance was found (p < or = 0.05). RESULTS: Compared to the unirradiated control group, the concentration of non-enzymatic collagen crosslinks was significantly increased for all irradiated groups (p < 0.0001), and being higher by at least 50% (Figure 1a). By contrast, the radiation effects on the collagen were only evident at the higher doses. For irradiation exposures of 17 kGy or more, strength decreased substantially as the radiation level was increased, but no effect was evident below 17 kGy (Figure 1b). There was no significant change in the stiffness or maximum displacement for any radiation dose (p>0.05). The finite element analysis prescribed force level for cyclic loading exceeded the measured (monotonic) strength of the 17 and 35 kGy irradiated groups (mean +/- SD, 20.6 +/- 5.6 N; 13.2 +/- 3.7 N, respectively) and therefore these groups were eliminated from the fatigue study. The fatigue life for the 0.05 and 1 kGy groups were similar to each other and were not statistically significantly different from the control group (Figure 1c).

radiation↗

Viscoplasticity based on overstress with a differential growth law for the equilibrium stress

Two coupled, nonlinear differential equations are proposed for the modeling of the elastic and rate (time) dependent inelastic behavior of structural metals in the absence of recovery and aging. The structure of the model is close to the unified theories but contains essential differences. It is shown that the model reproduces almost elastic regions upon initial loading and in the unloading regions of the hysteresis loop. Under loading, unloading and reloading in strain control the model simulated the experimentally observed sharp transition from nearly elastic to inelastic behavior. When a formulation akin to existing unified theories is adopted the almost elastic regions reduce the points and the transition upon reloading is very gradual. For different formulations the behavior under sudden in(de)creases of the strain rate by two orders of magnitude is simulated by numerical experiments and differences are noted. The model represents cyclically neutral behavior and contains three constants and two positive, decreasing functions. The determination of constants and functions from monotonic loading with strain rate changes and relaxation periods is described.

Krempl, E.↗

Viscoplasticity based on overstress with a differential growth law for the equilibrium stress

Two coupled, nonlinear differential equations are proposed for the modeling of the elastic and rate (time) dependent inelastic behavior of structural metals in the absence of recovery and aging. The structure of the model is close to the unified theories but contains essential differences. It is shown that the model reproduces almost elastic regions upon initial loading and in the unloading regions of the hysteresis loop. Under loading, unloading and reloading in strain control the model simulated the experimentally observed sharp transition from nearly elastic to inelastic behavior. When a formulation akin to existing unified theories is adopted the almost elastic regions reduce the points and the transition upon reloading is very gradual. For different formulations the behavior under sudden in(de)creases of the strain rate by two orders of magnitude is simulated by numerical experiments and differences are noted. The model represents cyclically neutral behavior and contains three constants and two positive, decreasing functions. The determination of constants and functions from monotonic loading with strain rate changes and relaxation periods is described.

Krempl, E.↗