Polymer research
Stress-strain distribution in elastomers, and chemical and physical properties of prepolymers, rigid urethane foam, and thermoplastic rubbers for composite solid propellant binders
ELASTOMER↗
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The Pursuit of K: Reflections on the Current State-of-the-Art in Stress Intensity Factor Solutions for Practical Aerospace Applications
The elastic stress intensity factor (SIF, commonly denoted as K) is the foundation of practical fracture mechanics (FM) analysis for aircraft structures. This single parameter describes the first-order effects of stress magnitude and distribution as well as the geometry of both structure/component and crack. Hence, the calculation of K is often the most significant step in fatigue analysis based on FM. This presentation will provide several reflections on the current state-of-the-art in SIF solution methods used for practical aerospace applications, including a brief historical perspective, descriptions of some recent and ongoing advances, and comments on some remaining challenges. Newman and Raju made significant early contributions to practical structural analysis by developing closed-form SIF equations for surface and corner cracks in simplified geometries, often based on empirical fits of finite element (FE) solutions. Those solutions (and others like them) were sometimes revised as new analyses were conducted or limitations discovered. The foundational solutions have exhibited striking longevity, despite the relatively "coarse" FE models employed many decades ago. However, in recent years, the accumulation of different generations of solutions for the same nominal geometry has led to some confusion (which solution is correct?), and steady increases in computational capabilities have facilitated the discovery of inaccuracies in some (not all!) of the legacy solutions. Some examples of problems and solutions are presented and discussed, including the challenge of maintaining consistency with legacy design applications. As computational power has increased, the prospect of calculating large numbers of SIF solutions for specific complex geometries with advanced numerical methods has grown more attractive. Fawaz and Andersson, for example, have been generating literally millions of new SIF solutions for different combinations of multiple cracks under simplified loading schemes using p-version FE methods. These data are invaluable, but questions remain about their practical use, because the tabular databases of key results needed to support practical life analysis can occupy gigabytes of storage for only a few classes of geometries. The prospect of using such advanced numerical methods to calculate in real time only those K solutions actually needed to support a specific crack growth analysis is also tempting, but the stark reality is that the computational cost is still so high that the approach is not practical except for specific, critical application problems. Some thoughts are offered about alternative paradigms. Compounding approaches are some of the earliest building blocks of SIF development for more complex geometries. These approaches are especially attractive because of their very low computational cost and their conceptual robustness; they are, in some ways, an intriguing contrast and complement to the brute-force numerical methods. In recent years, researchers at NRC-Canada have published remarkable results showing how compounding approaches can be used to generate accurate solutions for very difficult problems. Examples are provided of some successes--and some limitations--using this approach. These closed-form, tabulated numerical, and compounding approaches have typically been used for simple remote loading with simple load paths to the crack. However, many significant cracks occur in complex stress gradient fields. This is a job for weight function (WF) methods, where the arbitrary stress distribution on the crack plane in the corresponding uncracked body (typically determined using FE methods) is used to determine K. Several significant recent advances in WF methods and solutions are highlighted here. Fueled by advanced 3D numerical methods, many new solutions have been generated for classic geometries such as surface and corner cracks with wide ranges of geometrical validity. A new WF formulation has also be developed for part-through cracks considering the arbitrary stress gradients in all directions in the crack plane (so-called bivariant solutions). Basic WF methods have recently been combined with analytical expressions for crack plane stresses to develop a large family of accurate SIF solutions for corner, surface, and through cracks at internal or external notches with very wide ranges of shapes, sizes, acuities, and offsets. Finally, WF solutions are much faster than FE or boundary element solutions, but can still be much slower than simple closed-form solutions, especially for bivariant solutions that can require 2D numerical integration. Novel pre-integration and dynamic tabular methods have been developed that substantially increase the speed of these advanced WF solutions. The practical utility of advanced SIF methods, including both WF and direct numerical methods, is greatly enhanced if the FM life analysis can be directly and efficiently linked with digital models of the actual structure or component (e.g., FE models for stress analysis). Two recent advances of this type will be described. One approach directly interfaces the FM life analysis with the FE model of the uncracked component (including stress results). Through a powerful graphical user interface, simplified FM life models can be constructed (and visualized) directly on the component model, with the computer collecting the geometry and stress gradient information needed for the life calculation. An even more powerful paradigm uses expert logic to automatically build an optimum simple fracture model at any and every desired location in the component model, perform the life calculation, and even generate fatigue crack growth life contour maps, all with minimal user intervention. This paradigm has also been extended to the automatic calculation of fracture risk, considering uncertainty or variability in key input parameters such as initial crack size or location. Another new integrated approach links the engineering life analysis, the component model, and a 3D numerical fracture analysis built with the same component model to generate a table of SIF values at a specific location that can then be employed efficiently to perform the life calculation. Some attention must be given to verification and validation (V&V) issues and challenges: how good are these SIF solutions, how good is good enough, and does anyone believe the life answer? It is important to think critically about the different sources of error or uncertainty and to perform V&V in a hierarchal, building-block manner. Some accuracy issues for SIF solutions, for example, may actually involve independent material behavior issues, such as constraint loss effects for crack fronts near component surfaces, and can be a source of confusion. Recommendations are proposed for improved V&V approaches. This presentation will briefly but critically survey the range of issues and advances mentioned above, with a particular view towards assembling an integrated approach that combines different methods to create practical tools for real-world design and analysis problems. Examples will be selectively drawn from the recent literature, from recent enhancements in the NASGRO and DARWIN computer codes, and from previously unpublished research
CraigMcClung, R.↗
Photoelastic analysis of prebuckling deformations of cylindrical shells.
Prebuckling deformation and stress-strain distributions in clamped thin cylindrical shell subjected to axial load, determining effect of boundary supports
AXIAL LOAD↗
Uncertainties in obtaining high reliability from stress-strength models
There has been a recent interest in determining high statistical reliability in risk assessment of aircraft components. The potential consequences are identified of incorrectly assuming a particular statistical distribution for stress or strength data used in obtaining the high reliability values. The computation of the reliability is defined as the probability of the strength being greater than the stress over the range of stress values. This method is often referred to as the stress-strength model. A sensitivity analysis was performed involving a comparison of reliability results in order to evaluate the effects of assuming specific statistical distributions. Both known population distributions, and those that differed slightly from the known, were considered. Results showed substantial differences in reliability estimates even for almost nondetectable differences in the assumed distributions. These differences represent a potential problem in using the stress-strength model for high reliability computations, since in practice it is impossible to ever know the exact (population) distribution. An alternative reliability computation procedure is examined involving determination of a lower bound on the reliability values using extreme value distributions. This procedure reduces the possibility of obtaining nonconservative reliability estimates. Results indicated the method can provide conservative bounds when computing high reliability. An alternative reliability computation procedure is examined involving determination of a lower bound on the reliability values using extreme value distributions. This procedure reduces the possibility of obtaining nonconservative reliability estimates. Results indicated the method can provide conservative bounds when computing high reliability.
Neal, Donald M.↗
Stresses In And Near A Bend In A Thin-Walled Duct
Report describes computational study of distributions of stresses in and near 90 degrees bend in thin-walled duct subject to various applied loads. Purpose of study to help satisfy need for more accurate knowledge of local concentrations of stresses caused by loads: such knowledge makes possible to design light-weight ducts to survive reasonably foreseeable operating conditions with some degree of reliability. Also guides selection of locations for mounting strain gauges to measure local stresses for comparison with computed values, contributing to refinement of theoretical concepts and computational techniques.
Min, J. B.↗
Optical and Scanning Electron Microscopy of the Materials International Space Station Experiment (MISSE) Spacecraft Silicone Experiment
Under a microscope, atomic oxygen (AO) exposed silicone surfaces are crazed and seen as "islands" separated by numerous crack lines, much analogous to mud-tile cracks. This research characterized and compared the degree of AO degradation of silicones by analyzing optical microscope images of samples exposed to low Earth orbit (LEO) AO as part of the Spacecraft Silicone Experiment. The Spacecraft Silicone Experiment consisted of eight DC 93-500 silicone samples exposed to eight different AO fluence levels (ranged from 1.46 to 8.43 10(exp 21) atoms/sq cm) during two different Materials International Space Station Experiment (MISSE) missions. Image analysis software was used to analyze images taken using a digital camera. To describe the morphological degradation of each AO exposed flight sample, three different parameters were selected and estimated: (1) average area of islands was determined and found to be in the 1000 to 3100 sq mm range; (2) total length of crack lines per unit area of the sample surface were determined and found to be in the range of 27 to 59 mm of crack length per sq mm of sample surface; and (3) the fraction of sample surface area that is occupied by crack lines was determined and found to be in the 25 to 56 percent range. In addition, average crack width can be estimated from crack length and crack area measurements and was calculated to be about 10 mm. Among the parameters studied, the fraction of sample surface area that is occupied by crack lines is believed to be most useful in characterizing the degree of silicone conversion to silicates by AO because its value steadily increases with increasing fluence over the entire fluence range. A series of SEM images from the eight samples exposed to different AO fluences suggest a complex sequence of surface stress due to surface shrinkage and crack formation, followed by re-distribution of stress and shrinking rate on the sample surface. Energy dispersive spectra (EDS) indicated that upon AO exposure, carbon content on the surface decreased relatively quickly at the beginning, to 32 percent of the pristine value for the least exposed sample in this set of experiments (1.46 10(exp 21) atoms/sq cm), but then decreased slowly, to 22 percent of the pristine value for the most exposed sample in this set of experiment (8.43 10(exp 21) atoms/sq cm). The oxygen content appears to increase at a slower rate. The least and most AO exposed samples were, respectively, 52 and 150 percent above the pristine values. The silicone samples with the greater AO exposure (7.75 10(exp 21) atoms/sq cm and higher) appear to have a surface layer which contains SiO2 with perhaps small amounts of unreacted silicone, CO and CO2 sealed inside.
Hung, Ching-cheh↗
Using Hyperspectral Imagery to Identify Turfgrass Stresses
The use of a form of remote sensing to aid in the management of large turfgrass fields (e.g. golf courses) has been proposed. A turfgrass field of interest would be surveyed in sunlight by use of an airborne hyperspectral imaging system, then the raw observational data would be preprocessed into hyperspectral reflectance image data. These data would be further processed to identify turfgrass stresses, to determine the spatial distributions of those stresses, and to generate maps showing the spatial distributions. Until now, chemicals and water have often been applied, variously, (1) indiscriminately to an entire turfgrass field without regard to localization of specific stresses or (2) to visible and possibly localized signs of stress for example, browning, damage from traffic, or conspicuous growth of weeds. Indiscriminate application is uneconomical and environmentally unsound; the amounts of water and chemicals consumed could be insufficient in some areas and excessive in most areas, and excess chemicals can leak into the environment. In cases in which developing stresses do not show visible signs at first, it could be more economical and effective to take corrective action before visible signs appear. By enabling early identification of specific stresses and their locations, the proposed method would provide guidance for planning more effective, more economical, and more environmentally sound turfgrass-management practices, including application of chemicals and water, aeration, and mowing. The underlying concept of using hyperspectral imagery to generate stress maps as guides to efficient management of vegetation in large fields is not new; it has been applied in the growth of crops to be harvested. What is new here is the effort to develop an algorithm that processes hyperspectral reflectance data into spectral indices specific to stresses in turfgrass. The development effort has included a study in which small turfgrass plots that were, variously, healthy or subjected to a variety of controlled stresses were observed by use of a hand-held spectroradiometer. The spectroradiometer readings in the wavelength range from 350 to 1,000 nm were processed to extract hyperspectral reflectance data, which, in turn, were analyzed to find correlations with the controlled stresses. Several indices were found to be correlated with drought stress and to be potentially useful for identifying drought stress before visible symptoms appear.
Hutto, Kendall↗
Models of recurrent strike-slip earthquake cycles and the state of crustal stress
Numerical models of the strike-slip earthquake cycle, assuming a viscoelastic asthenosphere coupling model, are examined. The time-dependent simulations incorporate a stress-driven fault, which leads to tectonic stress fields and earthquake recurrence histories that are mutually consistent. Single-fault simulations with constant far-field plate motion lead to a nearly periodic earthquake cycle and a distinctive spatial distribution of crustal shear stress. The predicted stress distribution includes a local minimum in stress at depths less than typical seismogenic depths. The width of this stress 'trough' depends on the magnitude of crustal stress relative to asthenospheric drag stresses. The models further predict a local near-fault stress maximum at greater depths, sustained by the cyclic transfer of strain from the elastic crust to the ductile asthenosphere. Models incorporating both low-stress and high-stress fault strength assumptions are examined, under Newtonian and non-Newtonian rheology assumptions. Model results suggest a preference for low-stress (a shear stress level of about 10 MPa) fault models, in agreement with previous estimates based on heat flow measurements and other stress indicators.
Lyzenga, Gregory A.↗
Stress studies in EFG
A computer code which can account for plastic deformation effects on stress generated in silicon sheet grown at high speeds is fully operative. Stress and strain rate distributions are presented for two different sheet temperature profiles. The calculations show that residual stress levels are very sensitive to details of the cooling profile in a sheet with creep. Experimental work has been started in several areas to improve understanding of ribbon temperature profiles and stress distributions associated with a 10 cm wide ribbon cartridge system.
Source record↗
Shallow Lunar Seismic Activity and the Current Stress State of the Moon
A vast, global network of more than 3200 lobate thrust fault scarps has been revealed in high resolution Lunar Reconnaissance Orbiter Camera (LROC) images. The fault scarps very young, less than 50 Ma, based on their small scale and crisp appearance, crosscutting relations with small-diameter impact craters, and rates of infilling of associated small, shallow graben and may be actively forming today. The population of young thrust fault scarps provides a window into the recent stress state of the Moon and offers insight into the origin of global lunar stresses. The distribution of orientations of the fault scarps is non-random, inconsistent with isotropic stresses from late-stage global contraction as the sole source of stress Modeling shows that tidal stresses contribute significantly to the current stress state of the lunar crust. Tidal stresses (orbital recession and diurnal tides) superimposed on stresses from global contraction result in non-isotropic compressional stress and thrust faults consistent with lobate scarp orientations. Stresses due to orbital recession do not change with orbital position, thus it is with the addition of diurnal stresses that peak stresses are reached. At apogee, diurnal and recession stresses are most compressive near the tidal axis, while at perigee they are most compressive 90 degrees away from the tidal axis. Coseismic slip events on currently active thrust faults are expected to be triggered when peak stresses are reached. Analysis of the timing of the 28 the shallow moonquakes recorded by the Apollo seismic network shows that 19 indeed occur when the Moon is closer to apogee, while only 9 shallow events occur when the Moon is closer to perigee. Here we show the results of relocating the shallow moonquake using an algorithm designed for sparse networks to better constrain their epicentral locations in order to compare them with stress models. The model for the current stress state of the Moon is refined by investigating the contribution of polar wander.
siesmology↗
Shallow Lunar Seismic Activity and the Current Stress State of the Moon
A vast, global network of more than 3200 lobate thrust fault scarps has been revealed in high resolution Lunar Reconnaissance Orbiter Camera (LROC) images. The fault scarps are very young, less than 50 Ma, based on their small scale and crisp appearance, crosscutting relations with small-diameter impact craters, and rates of infilling of associated small, shallow graben and may be actively forming today. The population of young thrust fault scarps provides a window into the recent stress state of the Moon and offers insight into the origin of global lunar stresses. The distribution of orientations of the fault scarps is non-random, inconsistent with isotropic stresses from late-stage global contraction as the sole source of stress. Modeling shows that tidal stresses contribute significantly to the current stress state of the lunar crust. Tidal stresses (orbital recession and diurnal tides) superimposed on stresses from global contraction result in non-isotropic compressional stress and may produce thrust faults consistent with lobate scarp orientations. At any particular point on the lunar surface, peak compressive stress will be reached at a certain time in the diurnal cycle. Coseismic slip events on currently active thrust faults are expected to be triggered when peak stresses are reached. Analysis of the timing of the 28 the shallow moonquakes recorded by the Apollo seismic network shows that 19 indeed occur when the Moon is closer to apogee, while only 9 shallow events occur when the Moon is closer to perigee. Here we report efforts to refine the model for the current stress state of the Moon by investigating the contribution of polar wander. Progress on relocating the epicentral locations of the shallow moonquakes using an algorithm designed for sparse networks is also reported.
structure↗
3D Finite Element Analysis of Particle-Reinforced Aluminum
Deformation in particle-reinforced aluminum has been simulated using three distinct types of finite element model: a three-dimensional repeating unit cell, a three-dimensional multi-particle model, and two-dimensional multi-particle models. The repeating unit cell model represents a fictitious periodic cubic array of particles. The 3D multi-particle (3D-MP) model represents randomly placed and oriented particles. The 2D generalized plane strain multi-particle models were obtained from planar sections through the 3D-MP model. These models were used to study the tensile macroscopic stress-strain response and the associated stress and strain distributions in an elastoplastic matrix. The results indicate that the 2D model having a particle area fraction equal to the particle representative volume fraction of the 3D models predicted the same macroscopic stress-strain response as the 3D models. However, there are fluctuations in the particle area fraction in a representative volume element. As expected, predictions from 2D models having different particle area fractions do not agree with predictions from 3D models. More importantly, it was found that the microscopic stress and strain distributions from the 2D models do not agree with those from the 3D-MP model. Specifically, the plastic strain distribution predicted by the 2D model is banded along lines inclined at 45 deg from the loading axis while the 3D model prediction is not. Additionally, the triaxial stress and maximum principal stress distributions predicted by 2D and 3D models do not agree. Thus, it appears necessary to use a multi-particle 3D model to accurately predict material responses that depend on local effects, such as strain-to-failure, fracture toughness, and fatigue life.
Shen, H.↗
Shear-stress, eddy-viscosity, and mixing- length distributions in hypersonic turbulent boundary layers
Shear-stress, eddy-viscosity, and mixing-length distributions in hypersonic turbulent boundary layers using assumption of local similarity
Bushnell, D. M.↗
Stress intensity and flaw-shape variations in surface flaws
Flaw shapes and stress intensity distributions for a variety of technologically important surface-flaw problems using the frozen-stress method are described. Limitations of the method are noted. Results are used to illustrate effects peculiar to three-dimensional cracked-body problems.
Smith, C. W.↗
A Study of the Development of Steady and Periodic Unsteady Turbulent Wakes Through Curved Channels at Positive, Zero, and Negative Streamwise Pressure Gradients, Part 1
The turbomachinery wake flow development is largely influenced by streamline curvature and streamwise pressure gradient. The objective of this investigation is to study the development of the wake under the influence of streamline curvature and streamwise pressure gradient. The experimental investigation is carried out in two phases. The first phase involves the study of the wake behind a stationary circular cylinder (steady wake) in curved channels at positive, zero, and negative streamwise pressure gradients. The mean velocity and Reynolds stress components are measured using a X-hot-film probe. The measured quantities obtained in probe coordinates are transformed to a curvilinear coordinate system along the wake centerline and are presented in similarity coordinates. The results of the steady wakes suggest strong asymmetry in velocity and Reynolds stress components. However, the velocity defect profiles in similarity coordinates are almost symmetrical and follow the same distribution as the zero pressure gradient straight wake. The results of Reynolds stress distributions show higher values on the inner side of the wake than the outer side. Other quantities, including the decay of maximum velocity defect, growth of wake width, and wake integral parameters, are also presented for the three different pressure gradient cases of steady wake. The decay rate of velocity defect is fastest for the negative streamwise pressure gradient case and slowest for the positive pressure gradient case. Conversely, the growth of the wake width is fastest for the positive streamwise pressure gradient case and slowest for the negative streamwise pressure gradient. The second phase studies the development of periodic unsteady wakes generated by the circular cylinders of the rotating wake generator in a curved channel at zero streamwise pressure gradient. Instantaneous velocity components of the periodic unsteady wakes, measured with a stationary X-hot-film probe, are analyzed by the phase averaging techniques. The temporal distribution of velocity and Reynolds stress components obtained in a stationary frame of reference are transformed to a spatial distribution in a relative frame of reference. Profiles of phase-averaged velocity and Reynolds stress distributions in the relative frame of reference and similarity coordinates are presented. The velocity defect and Reynolds stress distributions agree with the results of the wake development behind a stationary cylinder in the curved channel at zero streamwise pressure gradient. The phase-averaged third-order correlations, presented in the relative frame of reference and similarity coordinates, show pronounced asymmetric features.
Schobeiri, M. T.↗
Elasto-viscoplastic fast Fourier transform modeling framework for assessing microstructural effects on stress intensity factors characterizing fracture toughness
A large-strain elasto-viscoplastic fast Fourier transform (LS-EVPFFT) model with non-periodic (NP) velocity-based boundary conditions is adapted to simulate the sensitivity of stress intensity factors on microstructure for 304L stainless steel. The material was characterized via electron backscattered diffraction (EBSD) serial-sectioning to obtain a measured 3-D microstructural cell to perform simulations. The NP-LS-EVPFFT model, including the simulation setup and boundary conditions, was verified using a crystal plasticity finite element (CPFE) model. To this end, the generation of meshes of notched specimens was developed, which involved creating Python scripts for mesh “cutting” in Abaqus, and Sculpt scripts in Cubit for meshing of the measured microstructural cell processed with DREAM.3D. The complexity of the mesh preparation highlighted the advantages of the FFT-based model, which circumvents the mesh generation process. Given the efficiency of the FFT-based model, statistical distribution of stress intensity factors in function of crystal orientation at the crack tip, grain structure, and crystallographic texture surrounding the crack tip were predicted. Further, the distributions reveal about 10% variation of stress intensity factors with microstructure with the most significant sensitivity found to be the crystal orientation at the crack tip. The methodology developed in this work is discussed as a practical simulation tool for predicting the sensitivity of stress intensity factors on microstructural variability in metallic materials.
36 MATERIALS SCIENCE↗
Coupled elastic response of open section laminated composite beams subject to generalized beam loading
A generalized beam theory for arbitrary open section laminated composite beams subjected to generalized beam loading is developed using a strength of materials approach. At present, the theory is limited to statistically determinate beams. Solution of the general system of equations yields strain and curvature distributions as functions of the axial coordinate x and the contour coordinate s. Average stresses on a given cross section or ply stresses in a local coordinate system are determined using these distributions. Data obtained for thin-walled open section composite beams reveal that elastic coupling occurs among curvatures, shearing strains, and axial strain, depending on the laminate stiffness parameters. Laminate ply layup does not affect the location of the shear center in the thin-wall approximation, but may have a significant impact for thicker walled open sections. The average axial stress distribution is found to be distinctly different from the isotropic distribution, but the average shear stress distribution is the same as that in the isotropic case.
Zvarick, Albert G.↗
A crack problem with four distinct harmonic functions
The problem of an elastic solid containing a semi-infinite plane crack subjected to concentrated shears parallel to the edge of the crack is considered. A closed form solution using four distinct harmonic functions (none of which can be taken arbitrarily) is found to satisfy the finite displacement and inverse square root stress singularity at the edge of the crack. Explicit expressions in terms of elementary functions are given for the distribution of stress and displacement in the solid. These are obtained by employing Fourier and Kontorovich-Lebedev integral transforms and certain singular solutions of Laplace equations in three dimensions. The variations of the intensity of the local stress field along the crack border are shown graphically. An example is presented, which is in contrast with the conclusion established in the literature that one of the four Papkovich-Neuber functions in three-dimensional elasticity may be arbitrarily set to zero.
Sih, G. C.↗