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NASA NTRS1996

Integrated Optical Interferometers with Micromachined Diaphragms for Pressure Sensing

Optical pressure sensors have been fabricated which use an integrated optical channel waveguide that is part of an interferometer to measure the pressure-induced strain in a micromachined silicon diaphragm. A silicon substrate is etched from the back of the wafer leaving a rectangular diaphragm. On the opposite side of the wafer, ring resonator and Mach-Zehnder interferometers are formed with optical channel waveguides made from a low pressure chemical vapor deposited film of silicon oxynitride. The interferometer's phase is altered by pressure-induced stress in a channel segment positioned over the long edge of the diaphragm. The phase change in the ring resonator is monitored using a link-insensitive swept frequency laser diode, while in the Mach-Zehnder it is determined using a broad band super luminescent diode with subsequent wavelength separation. The ring resonator was found to be highly temperature sensitive, while the Mach-Zehnder, which had a smaller optical path length difference, was proportionally less so. The quasi-TM mode was more sensitive to pressure, in accord with calculations. Waveguide and sensor theory, sensitivity calculations, a fabrication sequence, and experimental results are presented.

DeBrabander, Gregory N.↗

NASA NTRS1947

Elastic Properties in Tension and Shear of High Strength Nonferrous Metals and Stainless Steel - Effect of Previous Deformation and Heat Treatment

A resume is given of an investigation of the influence of plastic deformation and of annealing temperature on the tensile and shear elastic properties of high strength nonferrous metals and stainless steels in the form of rods and tubes. The data were obtained from earlier technical reports and notes, and from unpublished work in this investigation. There are also included data obtained from published and unpublished work performed on an independent investigation. The rod materials, namely, nickel, monel, inconel, copper, 13:2 Cr-Ni steel, and 18:8 Cr-Ni steel, were tested in tension; 18:8 Cr-Ni steel tubes were tested in shear, and nickel, monel, aluminum-monel, and Inconel tubes were tested in both tension and shear. There are first described experiments on the relationship between hysteresis and creep, as obtained with repeated cyclic stressing of annealed stainless steel specimens over a constant load range. These tests, which preceded the measurements of elastic properties, assisted in devising the loading time schedule used in such measurements. From corrected stress-set curves are derived the five proof stresses used as indices of elastic or yield strength. From corrected stress-strain curves are derived the secant modulus and its variation with stress. The relationship between the forms of the stress-set and stress-strain curves and the values of the properties derived is discussed. Curves of variation of proof stress and modulus with prior extension, as obtained with single rod specimens, consist in wavelike basic curves with superposed oscillations due to differences of rest interval and extension spacing; the effects of these differences are studied. Oscillations of proof stress and modulus are generally opposite in manner. The use of a series of tubular specimens corresponding to different amounts of prior extension of cold reduction gave curves almost devoid of oscillation since the effects of variation of rest interval and extension spacing were removed. Comparison is also obtained between the variation of the several properties, as measured in tension and in shear. The rise of proof stress with extension is studied, and the work-hardening rates of the various metals evaluated. The ratio between the tensile and shear proof stresses for the various annealed and cold-worked tubular metals is likewise calculated. The influence of annealing or tempering temperature on the proof stresses and moduli for the cold-worked metals and for air-hardened 13:2 Cr-Ni steel is investigated. An improvement of elastic strength generally is obtained, without important loss of yield strength, by annealing at suitable temperature. The variation of the proof stress and modulus of elasticity with plastic deformation or annealing temperature is explained in terms of the relative dominance of three important factors: namely, (a) internal stress, (b) lattice-expansion or work-hardening, and (c) crystal reorientation. Effective values of Poisson's ratio were computed from tensile and shear moduli obtained on tubular specimens. The variation of Poisson's ratio with plastic deformation and annealing temperature is explained in terms of the degree of anisotropy produced by changes of (a) internal stress and (b) crystal orientation.

METALS - ELASTICITY↗

NASA NTRS2014

A Technique for Mapping Characteristic Lengths to Preserve Energy Dissipated via Strain Softening in a Multiscale Analysis

It is often advantageous to account for the microstructure of the material directly using multiscale modeling. For computational tractability, an idealized repeating unit cell (RUC) is used to capture all of the pertinent features of the microstructure. Typically, the RUC is dimensionless and depends only on the relative volume fractions of the different phases in the material. This works well for non-linear and inelastic behavior exhibiting a positive-definite constitutive response. Although, once the material exhibits strain softening, or localization, a mesh objective failure theories, such as smeared fracture theories, nodal and element enrichment theories (XFEM), cohesive elements or virtual crack closure technique (VCCT), can be utilized at the microscale, but the dimensions of the RUC must then be defined. One major challenge in multiscale progressive damage modeling is relating the characteristic lengths across the scales in order to preserve the energy that is dissipated via localization at the microscale. If there is no effort to relate the size of the macroscale element to the microscale RUC, then the energy that is dissipated will remain mesh dependent at the macroscale, even if it is regularized at the microscale. Here, a technique for mapping characteristic lengths across the scales is proposed. The RUC will be modeled using the generalized method of cells (GMC) micromechanics theory, and local failure in the matrix constituent subcells will be modeled using the crack band theory. The subcell characteristic lengths used in the crack band calculations will be mapped to the macroscale finite element in order to regularize the local energy in a manner consistent with the global length scale. Examples will be provided with and without the regularization, and they will be compared to a baseline case where the size and shape of the element and RUC are coincident (ensuring energy is preserved across the scales).

softening↗

NASA NTRS1995

Structural design using equilibrium programming formulations

Solutions to increasingly larger structural optimization problems are desired. However, computational resources are strained to meet this need. New methods will be required to solve increasingly larger problems. The present approaches to solving large-scale problems involve approximations for the constraints of structural optimization problems and/or decomposition of the problem into multiple subproblems that can be solved in parallel. An area of game theory, equilibrium programming (also known as noncooperative game theory), can be used to unify these existing approaches from a theoretical point of view (considering the existence and optimality of solutions), and be used as a framework for the development of new methods for solving large-scale optimization problems. Equilibrium programming theory is described, and existing design techniques such as fully stressed design and constraint approximations are shown to fit within its framework. Two new structural design formulations are also derived. The first new formulation is another approximation technique which is a general updating scheme for the sensitivity derivatives of design constraints. The second new formulation uses a substructure-based decomposition of the structure for analysis and sensitivity calculations. Significant computational benefits of the new formulations compared with a conventional method are demonstrated.

Scotti, Stephen J.↗

NASA NTRS1995

Validation of Long Bone Mechanical Properties from Densitometry

The objective of this study was to assess whether cross-sectional areal properties, calculated from densitometry, correlate to the true flexural properties. Right and left male embalmed tibiae were used in the study. Prior to scanning, the proximal end of each tibia was potted in a fixture with registration pins, flushed thoroughly with water under pressure to remove trapped air, and then placed in a constant thickness water bath attached to a precision indexer. Two sets of three scans of the entire tibia were taken with an Hologic QDR 1000/W densitometer at rotations of 0, 45, and 90 degrees about the tibia long axis. An aluminum step phantom and a bone step phantom, machined from bovine cortical bone, were also in the bath and scanned separately. Pixel attenuation data from the two sets of scans were averaged to reduce noise. Pixel data from the high energy beam were then converted to equivalent thicknesses using calibration equations. Cross-sectional areal properties (centroid, principal area moments and principal angle) along the length were computed from the three registered scans using methods developed in our laboratory. Flexural rigidities. Four strain gages were bonded around the circumference of each of 5 cross-sections encompassing the entire diaphysis. A known transverse load was then applied to the distal end and the bone was rotated 360 degrees in eight increments of 45 degrees each. Strains from the eight orientations were analyzed along with the known applied bending moments at each section to compute section centroids, curvatures, principal flexural rigidities and principal angle. Reference axes between the two methods were maintained within +/- 0.5 degrees using an electronic inclinometer. Principal angles (flexural - areal) differed by -2.0 +/- 4.0 degrees, and 1.0 +/- 2.5 degrees for the right and left tibia, respectively. Section principal flexural rigidities were highly correlated to principal areal moments (right: r(sup 2)= 0.997; left: r(sup 2)= 0.978) indicating a nearly constant effective flexural modulus. Right and left tibia exhibited a very high degree of symmetry when comparing either flexural or areal properties. To our knowledge this is the first study to validate the use of densitometry (DXA) to predict three dimensional structural properties of long bones. Our initial results support the conclusion that bone mineral and its distribution are the primary determinants of flexural modulus and rigidity.

Whalen, R.↗

NASA NTRS1998

Development of In-Fiber Reflective Bragg Gratings as Shear Stress Monitors in Aerodynamic Facilities

Bragg gratings centered at nominal wavelengths of 1290 nm and 1300 run were inscribed in a 9/125 microns germano-silicate optical fiber, using continuous wave frequency doubled Ar+ laser radiation at 244 nm. Such gratings have been used extensively as temperature and strain monitors in smart structures. They have, however, never been used for measuring aerodynamic shear stresses. As a test of their sensitivity as shear stress monitors, a Bragg fiber attached to a metal plate was subjected to laminar flows in a glass pipe. An easily measurable large flow-induced wavelength shift (Delta Lambda(sub B)) was observed in the Bragg reflected wavelength. Thereafter, the grating was calibrated by making one time, simultaneous measurements of Delta Lambda(sub B) and the coefficient of skin friction (C(sub f)) with a skin friction balance, as a function of flow rates in a subsonic wind tunnel. Onset of fan-induced transition in the tunnel flow provided a unique flow rate for correlating Delta Lambda(sub B) and (C(sub f) values needed for computing effective modulus of rigidity (N(sub eff)) of the fiber attached to the metal plate. This value Of N(sub eff) is expected to remain constant throughout the elastic stress range expected during the Bragg grating aerodynamic tests. It has been used for calculating the value of Cf at various tunnel speeds, on the basis of measured values of Bragg wavelength shifts at those speeds.

Parmar, Devendra S.↗

NASA NTRS2003

Strain-Gauge Measurement of Weight of Fluid in a Tank

A method of determining the amount of fluid in a tank is based on measurement of strains induced in tank supports by the weight of the fluid. Unlike most prior methods, this method is nonintrusive: there is no need to insert instrumentation in the tank and, hence, no need to run wires, cables, or tubes through the tank wall. Also unlike most prior methods, this method is applicable even if the fluid in the tank is at supercritical pressure and temperature, because it does not depend on the presence of a liquid/gas interface (as in liquid-level-measuring methods). The strain gauges used in this method are of two types: foil and fiber-optic. Four foil gauges and one or more fiber-optic gauges are mounted on each of the tank-supporting legs. An additional fiber-optic gauge is mounted on an object, made of the same material as that of the tank-supporting legs, that is not subjected to any mechanical load. The reading obtained by the additional fiber-optic gauge is used to compensate for apparent strains caused by changes in temperature. The signals from the foil and fiber-optic gauges are conditioned, then digitized for input to a computer. As the tank is filled or emptied, the deformation in each leg increases or decreases, respectively. Measured deformations of all legs are added to obtain a composite deformation indicative of the change in weight of the tank plus fluid. An initial calibration is performed by recording data at two points (usually, empty and full) for which the mass or weight of fluid is known. It is assumed that the deformations are elastic, so that the line passing through the two points can be used as a calibration curve of mass (or weight) of fluid versus deformation. At the time of reporting the information for this article, a set of foil gauges had been tested on the supports of a 500-gallon (1,900-liter) tank. The gauges were found to be capable of measuring the deformations (up to 22 microstrain) that occurred during filling and emptying the tank. The fluid masses calculated from the gauge readings were found to be accurate within 4.5 percent. It has been estimated that once the fiber-optic gauges are put into operation, it should be possible to determine fluid masses with 3 percent or less. It may be possible to increase accuracy further by increasing the signal-to-noise ratio through the use of more deformable tank supporting legs.

Figueroa, Jorge↗

NASA NTRS1998

Analysis and Testing of Plates with Piezoelectric Sensors and Actuators

Piezoelectric material inherently possesses coupling between electrostatics and structural dynamics. Utilizing linear piezoelectric theory results in an intrinsically coupled pair of piezoelectric constitutive equations. One equation describes the direct piezoelectric effect where strains produce an electric field and the other describes the converse effect where an applied electrical field produces strain. The purpose of this study is to compare finite element analysis and experiments of a thin plate with bonded piezoelectric material. Since an isotropic plate in combination with a thin piezoelectric layer constitutes a special case of a laminated composite, the classical laminated plate theory is used in the formulation to accommodated generic laminated composite panels with multiple bonded and embedded piezoelectric layers. Additionally, the von Karman large deflection plate theory is incorporated. The formulation results in laminate constitutive equations that are amiable to the inclusion of the piezoelectric constitutive equations yielding in a fully electro-mechanically coupled composite laminate. Using the finite element formulation, the governing differential equations of motion of a composite laminate with embedded piezoelectric layers are derived. The finite element model not only considers structural degrees of freedom (d.o.f.) but an additional electrical d.o.f. for each piezoelectric layer. Comparison between experiment and numerical prediction is performed by first treating the piezoelectric as a sensor and then again treating it as an actuator. To assess the piezoelectric layer as a sensor, various uniformly distributed pressure loads were simulated in the analysis and the corresponding generated voltages were calculated using both linear and nonlinear finite element analyses. Experiments were carried out by applying the same uniformly distributed loads and measuring the resulting generated voltages and corresponding maximum plate deflections. It is found that a highly nonlinear relationship exists between maximum deflection and voltage versus pressure loading. In order to assess comparisons of predicted and measured piezoelectric actuation, sinusoidal excitation voltages are simulated/applied and maximum deflections are calculated/measured. The maximum deflection as a function of time was determined using the linear finite elements analysis. Good correlation between prediction and measurement was achieved in all cases.

Bevan, Jeffrey S.↗

NASA NTRS1992

Mechanism of delayed intracranial hypertension after cerebroventricular infusions in conscious rats

Prior studies showed that cerebroventricular infusions of artificial cerebrospinal fluid, 8 microliter/min for 10 min, followed by a 10 min rest and a 24 h infusion of 0.5 microliters/min, raised cerebrospinal fluid pressure (CSFp) of conscious, unrestrained rats after about 2 h. Here, we report that the 10 min infusion alone evoked a delayed, prolonged rise in CSFp. Pressure during the infusion itself rose and recovered quickly, as is usually reported. Pressure/volume tests, used to calculate resistance to outflow (Ro) and compliance (C), revealed that infusions increased Ro and decreased C, after a delay (P less than 0.05). The rise in CSFp after infusion was blocked by pretreatment with acetazolamide + ouabain (P less than 0.05), but the delayed changes in Ro and C were unaffected. We suggest that the 10 min infusion of a sterile, balanced salt solution has a primary effect that increases Ro; as CSF synthesis continues, C is exhausted and the delayed rise in CSFp ensues. This non-traumatic method of raising CSFp may be a useful method to study intracranial fluid dynamics.

NASA Center ARC↗

NASA NTRS1945

The Elastic Constants for Wrought Aluminum Alloys

There are several constants which have been devised as numerical representations of the behavior of metals under the action of loadings which stress the metal within the range of elastic action. Some of these constants, such as Young's modulus of elasticity in tension and compression, shearing modulus of elasticity, and Poisson's ratio, are regularly used in engineering calculations. Precise tests and experience indicate that these elastic constants are practically unaffected by many of the factors which influence the other mechanical properties of materials and that a few careful determinations under properly controlled conditions are more useful and reliable than many determinations made under less favorable conditions. It is the purpose of this paper to outline the methods employed by the Aluminum Research Laboratories for the determination of some of these elastic constants, to list the values that have been determined for some of the wrought aluminum alloys, and to indicate the variations in the values that may be expected for some of the commercial products of these alloys.

ALUMINUM ALLOYS, WROUGHT-ELASTICITY↗

NASA NTRS1993

Wrinkle ridges, reverse faulting, and the depth penetration of lithospheric stress in lunae planum, Mars

Tectonic features on a planetary surface are commonly used as constraints on models to determine the state of stress at the time the features formed. Quantitative global stress models applied to understand the formation of the Tharsis province on Mars constrained by observed tectonics have calculated stresses at the surface of a thin elastic shell and have neglected the role of vertical structure in influencing the predicted pattern of surface deformation. Wrinkle ridges in the Lunae Planum region of Mars form a conentric pattern of regularly spaced features in the eastern and southeastern part of Tharsis; they are formed due to compressional stresses related to the response of the Martian lithosphere to the Tharsis bulge. As observed in the exposures of valley walls in areas such as the Kasei Valles, the surface plains unit is underlain by an unconsolidated impact-generated megaregolith that grades with depth into structurally competent lithospheric basement. The ridges have alternatively been hypothesized to reflect deformation restricted to the surface plains unit ('thin skinned deformation') and deformation that includes the surface unit, megaregolith and basement lithosphere ('thick skinned deformation'). We have adopted a finite element approach to quantify the nature of deformation associated with the development of wrinkle ridges in a vertically stratified elastic lithosphere. We used the program TECTON, which contains a slippery node capability that allowed us to explicitly take into account the presence of reverse faults believed to be associated with the ridges. In this study we focused on the strain field in the vicinity of a single ridge when slip occurs along the fault. We considered two initial model geometries. In the first, the reverse fault was assumed to be in the surface plains unit, and in the second the initial fault was located in lithospheric basement, immediately beneath the weak megaregolith. We are interested in the conditions underwhich strain in the surface layer and basement either penetrates or fails to penetrate through the megaregolith. We thus address the conditions required for an initial basement fault to propagate through the megaregolith to the surface, as well as the effect of the megareolith on the strain tensor in the vicinity of a fault that nucleates in the surface plains unit.

Zuber, M. T.↗

NASA NTRS1990

Effects of zero gravity on myofibril content and isomyosin distribution in rodent skeletal muscle

The purpose of this experiment was to investigate the effects of 12.5 days of zero gravity (0 g) exposure (Cosmos 1887 Biosputnik) on the enzymatic properties, protein content, and isomyosin distribution of the myofibril fraction of the slow-twitch vastus intermedius (VI) and the fast-twitch vastus lateralis (VL) muscles of adult male rats. Measurements were obtained on three experimental groups (n = 5 each group) designated as flight group (FG), vivarium control (VC), and synchronous control (SC). Body weight of the FG was significantly lower than that of the two control groups (P less than 0.05). Compared with the two control groups, VI weight was lower by 23% (P less than 0.10), whereas no such pattern was apparent for the VL muscle. Myofibril yields (mg protein/g muscle) in the VI were 35% lower in the FG than in controls (P less than 0.05), whereas no such pattern was apparent for the VL muscle. When myofibril yields were expressed on a muscle basis (mg/g x muscle weight), the loss of myofibril protein was more exaggerated and suggests that myofibril protein degradation is an early event in the muscle atrophy response to 0 g. Analysis of myosin isoforms indicated that slow myosin (Sm) was the primary isoform lost in the calculated degradation of total myosin. No evidence of loss of the fast isomyosins was apparent for either muscle following spaceflight. Myofibril ATPase activity of the VI was increased in the FG compared with controls, which is consistent with the observation of preferential Sm degradation. These data suggest that muscles containing a high percentage of slow-twitch fibers undergo greater degrees of myofibril protein degradation than muscles containing predominantly fast-twitch fibers in response to a relatively short period of 0 g exposure, and the primary target appears to be the Sm molecule.

NASA Program Flight↗

NASA NTRS2000

Independent controls for neocortical neuron production and histogenetic cell death

We estimated the proportion of cells eliminated by histogenetic cell death during the first 2 postnatal weeks in areas 1, 3 and 40 of the mouse parietal neocortex. For each layer and for the subcortical white matter in each neocortical area, the number of dying cells per mm(2) was calculated and the proportionate cell death for each day of the 2-week interval was estimated. The data show that cell death proceeds essentially uniformly across the neocortical areas and layers and that it does not follow either the spatiotemporal gradient of cell cycle progression in the pseudostratified ventricular epithelium of the cerebral wall, the source of neocortical neurons, or the 'inside-out' neocortical neuronogenetic sequence. Therefore, we infer that the control mechanisms of neocortical histogenetic cell death are independent of mechanisms controlling neuronogenesis or neuronal migration but may be associated with the ingrowth, expansion and a system-wide matching of neuronal connectivity. Copyright 2000 S. Karger AG, Basel.

NASA Discipline Cell Biology↗

NASA NTRS2009

Use of Raman Spectroscopy and Delta Volume Growth from Void Collapse to Assess Overwrap Stress Gradients Compromising the Reliability of Large Kevlar/Epoxy COPVs

Composite Overwrapped Pressure Vessels (COPVs) are frequently used for storing pressurized gases aboard spacecraft and aircraft when weight saving is desirable compared to all-metal versions. Failure mechanisms in fibrous COPVs and variability in lifetime can be very different from their metallic counterparts; in the former, catastrophic stress-rupture can occur with virtually no warning, whereas in latter, a leak before burst design philosophy can be implemented. Qualification and certification typically requires only one burst test on a production sample (possibly after several pressure cycles) and the vessel need only meet a design burst strength (the maximum operating pressure divided by a knockdown factor). Typically there is no requirement to assess variability in burst strength or lifetime, much less determine production and materials processing parameters important to control of such variability. Characterizing such variability and its source is crucial to models for calculating required reliability over a given lifetime (e.g. R = 0.9999 for 15 years). In this paper we present a case study of how lack of control of certain process parameters in COPV manufacturing can result in variations among vessels and between production runs that can greatly increase uncertainty and reduce reliability. The vessels considered are 40-inch ( NASA Glenn Research center, Cleveland, OH, 44135 29,500 in3 ) spherical COPVs with a 0.74 in. thick Kevlar49/epoxy overwrap and with a titanium liner of which 34 were originally produced. Two burst tests were eventually performed that unexpectedly differed by almost 5%, and were 10% lower than anticipated from burst tests on 26-inch sister vessels similar in every detail. A major observation from measurements made during proof testing (autofrettage) of the 40-inch vessels was that permanent volume growth from liner yielding varied by a factor of more than two (150 in3 to 360 in3 ), which suggests large differences in the residual stress gradient through their overwraps. This resulted in large uncertainty in true fiber stress ratio (fiber stress at operating pressure divided by fiber stress at burst) which governs lifetime. The vessels were originally designed with tight safety margins, so it became crucial to develop a non-destructive evaluation (NDE) technique to directly measure the overwrap residual stress state of each vessel, and to identify those vessels at highest risk of having poor reliability. This paper describes a Raman Spectroscopy technique for measuring certain patterns of fluctuation in fiber elastic strains over the outside vessel surface (where all but one wrap is exposed at certain locations) that are shown to directly correlate to increased fiber stress ratios and reduced reliability.

Kezirian, Michael T.↗

NASA NTRS2012

Ultra-Compact Motor Controller

This invention is an electronically commutated brushless motor controller that incorporates Hall-array sensing in a small, 42-gram package that provides 4096 absolute counts per motor revolution position sensing. The unit is the size of a miniature hockey puck, and is a 44-pin male connector that provides many I/O channels, including CANbus, RS-232 communications, general-purpose analog and digital I/O (GPIO), analog and digital Hall inputs, DC power input (18-90 VDC, 0-l0 A), three-phase motor outputs, and a strain gauge amplifier. This controller replaces air cooling with conduction cooling via a high-thermal-conductivity epoxy casting. A secondary advantage of the relatively good heat conductivity that comes with ultra-small size is that temperature differences within the controller become smaller, so that it is easier to measure the hottest temperature in the controller with fewer temperature sensors, or even one temperature sensor. Another size-sensitive design feature is in the approach to electrical noise immunity. At a very small size, where conduction paths are much shorter than in conventional designs, the ground becomes essentially isopotential, and so certain (space-consuming) electrical noise control components become unnecessary, which helps make small size possible. One winding-current sensor, applied to all of the windings in fast sequence, is smaller and wastes less power than the two or more sensors conventionally used to sense and control winding currents. An unexpected benefit of using only one current sensor is that it actually improves the precision of current control by using the "same" sensors to read each of the three phases. Folding the encoder directly into the controller electronics eliminates a great deal of redundant electronics, packaging, connectors, and hook-up wiring. The reduction of wires and connectors subtracts substantial bulk and eliminates their role in behaving as EMI (electro-magnetic interference) antennas. A shared knowledge by each motor controller of the state of all the motors in the system at 500 Hz also allows parallel processing of higher-level kinematic matrix calculations.

Townsend, William T.↗

NASA NTRS1993

An engineering model of woven composites based on micromechanics

Composites with three-dimensional woven architectures exhibit large strains to failure when compared to composites made up of the same materials but not with three-dimensional interlocking tows. The fracture mechanics of such three-dimensional architectures is a subject requiring substantial investigation and experimental testing. Classical fracture mechanics concepts (for instance, an isolated defect in a homogeneous body) will not be applicable to the woven fracture test specimen. The use of an isolated singularity to characterize an entire specimen is inadequate when the density of defects is considerable and the material is heterogeneous. Modelling of such a complex system requires a great deal of insight and consideration as well as prudent choices of model sizes to make numerical schemes feasible. The purpose of this manuscript is to review our recently acquired knowledge of damage accumulation in woven composites and to describe a practicable model of the macroscopic behavior in these and other complex composite architectures based on such knowledge. In this manuscript, discussion will be limited to uniaxial compressive loading; considerations of general loading (monotonic and cyclic) will appear in a subsequent manuscript. Our modelling efforts may be briefly described as follows: the composite is subdivided into microstructural elements (microelements) in which the micromechanical modelling is either understood rigorously or can be represented adequately by statistical parameters. There can be microstructural elements for many different types of composite components, such as the various types of warp and weft and matrix for three-dimensional woven composites. The physical dimensions of microelements are made as large as possible while the response within the element can still be represented by a single micromechatlical calculation. The various elements are linked together(sometimes by associating distinct corners and edges, sometimes by superposition) in a pattern which resembles a particular weave architecture. The model can then be loaded in any manner and the linear and nonlinear elastic responses of representative weaves can be calculated. After the elastic regime, the fracture response is determined by monitoring the damage accumulation.

Carter, W. C.↗

NASA NTRS2006

Ice Mass Fluctuations and Earthquake Hazard

In south central Alaska, tectonic strain rates are high in a region that includes large glaciers undergoing ice wastage over the last 100-150 years [Sauber et al., 2000; Sauber and Molnia, 2004]. In this study we focus on the region referred to as the Yakataga segment of the Pacific-North American plate boundary zone in Alaska. In this region, the Bering and Malaspina glacier ablation zones have average ice elevation decreases from 1-3 meters/year (see summary and references in Molnia, 2005). The elastic response of the solid Earth to this ice mass decrease alone would cause several mm/yr of horizontal motion and uplift rates of up to 10-12 mm/yr. In this same region observed horizontal rates of tectonic deformation range from 10 to 40 mm/yr to the north-northwest and the predicted tectonic uplift rates range from -2 mm/year near the Gulf of Alaska coast to 12mm/year further inland [Savage and Lisowski, 1988; Ma et al, 1990; Sauber et al., 1997, 2000, 2004; Elliot et al., 2005]. The large ice mass changes associated with glacial wastage and surges perturb the tectonic rate of deformation at a variety of temporal and spatial scales. The associated incremental stress change may enhance or inhibit earthquake occurrence. We report recent (seasonal to decadal) ice elevation changes derived from data from NASA's ICESat satellite laser altimeter combined with earlier DEM's as a reference surface to illustrate the characteristics of short-term ice elevation changes [Sauber et al., 2005, Muskett et al., 2005]. Since we are interested in evaluating the effect of ice changes on faulting potential, we calculated the predicted surface displacement changes and incremental stresses over a specified time interval and calculated the change in the fault stability margin using the approach given by Wu and Hasegawa [1996]. Additionally, we explored the possibility that these ice mass fluctuations altered the seismic rate of background seismicity. Although we primarily focus on evaluating the influence of ice mass changes since the end of the little Ice Age, the study is partially motivated by paleoseismic evidence from Yakataga and Kodiak regions which suggests that earlier glacier retreat may be associated with large earthquakes [Sauber et al., 2000; Carver et al., 2003].

Sauber, J.↗

NASA NTRS1991

The surface and through crack problems in layered orthotropic plates

An analytical method is developed for a relatively accurate calculation of Stress Intensity Factors in a laminated orthotropic plate containing a through or part-through crack. The laminated plate is assumed to be under bending or membrane loading and the mode 1 problem is considered. First three transverse shear deformation plate theories (Mindlin's displacement based first-order theory, Reissner's stress-based first-order theory, and a simple-higher order theory due to Reddy) are reviewed and examined for homogeneous, laminated and heterogeneous orthotropic plates. Based on a general linear laminated plate theory, a method by which the stress intensity factors can be obtained in orthotropic laminated and heterogeneous plates with a through crack is developed. Examples are given for both symmetrically and unsymmetrically laminated plates and the effects of various material properties on the stress intensity factors are studied. In order to implement the line-spring model which is used later to study the surface crack problem, the corresponding plane elasticity problem of a two-bonded orthotropic plated containing a crack perpendicular to the interface is also considered. Three different crack profiles: an internal crack, an edge crack, and a crack terminating at the interface are considered. The effect of the different material combinations, geometries, and material orthotropy on the stress intensity factors and on the power of stress singularity for a crack terminating at the interface is fully examined. The Line Spring model of Rice and Levy is used for the part-through crack problem. The surface crack is assumed to lie in one of the two-layered laminated orthotropic plates due to the limitation of the available plane strain results. All problems considered are of the mixed boundary value type and are reduced to Cauchy type of singular integral equations which are then solved numerically.

Erdogan, Fazil↗