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This paper presents a final report on "Stresses and Strains within the "Stable" North American Plate". The topics include: 1) Strain rates near the New Madrid seismic zone; 2) Signal Processing of intermediate term data; and 3) Transform fault stresses and strains. The paper also includes graphs of the stress and strain distributions.
An in-depth tutorial on the constitutive equations for elastic, anisotropic materials is presented. Basic concepts are introduced that are used to characterize materials, and notions about how anisotropic material deform are presented. Hooke s law and the Duhamel-Neuman law for isotropic materials are presented and discussed. Then, the most general form of Hooke s law for elastic anisotropic materials is presented and symmetry requirements are given. A similar presentation is also given for the generalized Duhamel-Neuman law for elastic, anisotropic materials that includes thermal effects. Transformation equations for stress and strains are presented and the most general form of the transformation equations for the constitutive matrices are given. Then, specialized transformation equations are presented for dextral rotations about the coordinate axes. Next, concepts of material symmetry are introduced and criteria for material symmetries are presented. Additionally, engineering constants of fully anisotropic, elastic materials are derived from first principles and the specialized to several cases of practical importance.
A new phase observed in a nominal Ni30Pt20Ti50 (at.%) high temperature shape memory alloy has been characterized using transmission electron microscopy and 3-D atom probe tomography. This phase forms homogeneously in the B2 austenite matrix by a nucleation and growth mechanism and results in a concomitant increase in the martensitic transformation temperature of the base alloy. Although the structure of this phase typically contains a high density of faults making characterization difficult, it appears to be trigonal (-3m point group) with a(sub o) approx. 1.28 nm and c(sub o) approx. 1.4 nm. Precipitation of this phase increases the microhardness of the alloy substantially over that of the solution treated and quenched single-phase material. The effect of precipitation strengthening on the work characteristics of the alloy has been explored through load-biased strain-temperature testing in the solution-treated condition and after aging at 500 C for times ranging from 1 to 256 hours. Work output was found to increase in the aged alloy as a result of an increase in transformation strain, but was not very sensitive to aging time. The amount of permanent deformation that occurred during thermal cycling under load was small but increased with increasing aging time and stress. Nevertheless, the dimensional stability of the alloy at short aging times (1-4 hours) was still very good making it a potentially useful material for high-temperature actuator applications.
A Ti(49.5)Ni25Pd25Sc(0.5) high-temperature shape memory alloy is thermomechanically processed to obtain enhanced shape-memory characteristics: in particular, dimensional stability upon repeated thermal cycles under constant loads. This is accomplished using severe plastic deformation via equal channel angular extrusion (ECAE) and post-processing annealing heat treatments. The results of the thermomechanical experiments reveal that the processed materials display enhanced shape memory response, exhibiting higher recoverable transformation and reduced irrecoverable strain levels upon thermal cycling compared with the unprocessed material. This improvement is attributed to the increased strength and resistance of the material against defect generation upon phase transformation as a result of the microstructural refinement due to the ECAE process, as supported by the electron microscopy observations.
In this analysis, a delamination between the belt and core sections is assumed to grow parallel to the belt direction in the tapered and uniform sections. These delaminations in each section are denoted by a and b respectively. The core section in the taper portion is modeled by two equivalent sublaminates. The stiffness properties are smeared to obtain effective cracked and uncracked stiffnesses which are designated A (u) and A (c). These stiffnesses change from one ply drop group to another with crack growth a by experiencing a sudden change at discrete locations. Therefore, A (u) and A (c) can be represented in three consecutive regions.
Two methods for determining stresses and internal forces in geometrically nonlinear structural analysis are presented. The simplified approach uses the mid-deformed structural position to evaluate strains when rigid body rotation is present. The important feature of this approach is that it can easily be used with a general-purpose finite-element computer program. The refined approach uses element intrinsic or corotational coordinates and a geometric transformation to determine element strains from joint displacements. Results are presented which demonstrate the capabilities of these potentially useful approaches for geometrically nonlinear structural analysis.
Presented here is a method of solving highly flexible curved beam undergoing huge static or quasi-static deformations. A geometrically exact beam theory based on the use of Jaumann stresses and strains and exact coordinate transformation is presented in terms of 17 first-order ordinary differential equations, and a multiple shooting method is used to solve the corresponding nonlinear two-point boundary value problems. The geometrically exact beam theory accounts far large rotations, large displacements, initial curvatures, extensionality, and transverse shear strains. Four examples are used to demonstrate this method, including a rotating clamped-free beam under the influence of gravity and centrifugal forces, an L-frame subjected to an in-plane tip load, a circular arch subjected to a concentrated load, and a clamped-hinged helical spring subjected to an axial displacement. Results show that the combination of the multiple shooting method and the geometrically exact beam theory works very well. Moreover, the obtained numerically exact solutions can be used to verify the accuracy of nonlinear finite element codes for nonlinear analysis of complex structures.
We have used the space based geodetic techniques of Satellite Laser Ranging (SLR) and VLBI to study strain along subduction and transform plate boundaries and have interpreted the results using a simple elastic dislocation model. Six stations located behind island arcs were analyzed as representative of subduction zones while 13 sites located on either side of the San Andreas fault were used for the transcurrent zones. The length deformation scale was then calculated for both tectonic margins by fitting the relative strain to an exponentially decreasing function of distance from the plate boundary. Results show that space-based data for the transcurrent boundary along the San Andreas fault help to define better the deformation length scale in the area while fitting nicely the elastic half-space earth model. For subduction type bonndaries the analysis indicates that there is no single scale length which uniquely describes the deformation. This is mainly due to the difference in subduction characteristics for the different areas.
This paper is a hardware description manual for the Dynamic Stability Instrumentation System that is used in specific NASA Langley wind tunnels. The instrumentation system performs either a synchronous demodulation or a fast Fourier transform on dynamic balance strain gage signals, and ultimately computes aerodynamic coefficients. The DSIS consists of a double rack of instruments, a remote motor-generator set, two special stings each with motor driven shafts, and specially designed balances. The major components in the instrumentation rack include a personal computer, digital signal processor microcomputers, computer-controlled signal conditioners, function generator, digital multimeter, and an optional fast Fourier transform analyzer.
Linear-variable differential transformer replaces conventional resistance strain gages to measure crack-mouth-opening displacement. LVDT is superior in tests under liquid hydrogen, where boiling of hydrogen on resistive is suited to broad temperature range and hostile environments such as nuclear reactors.
The paper is an operating manual for the Dynamic Stability Instrumentation System in specific NASA Langley wind tunnels. The instrumentation system performs either a synchronous demodulation or a Fast Fourier Transform on dynamic balance strain gage signals, and ultimately computes aerodynamic coefficients. The dynamic balance converts sting motor rotation into pitch or yaw plane or roll axis oscillation, with timing information provided by a shaft encoder. Additional instruments control model attitude and balance temperature and monitor sting vibrations. Other instruments perform self-calibration and diagnostics. Procedures for conducting calibrations and wind-off and wind-on tests are listed.
Calibration data of a wind tunnel sting balance was processed using a candidate math model search algorithm that recommends an optimized regression model for the data analysis. During the calibration the normal force and the moment at the balance moment center were selected as independent calibration variables. The sting balance itself had two moment gages. Therefore, after analyzing the connection between calibration loads and gage outputs, it was decided to choose the difference and the sum of the gage outputs as the two responses that best describe the behavior of the balance. The math model search algorithm was applied to these two responses. An optimized regression model was obtained for each response. Classical strain gage balance load transformations and the equations of the deflection of a cantilever beam under load are used to show that the search algorithm s two optimized regression models are supported by a theoretical analysis of the relationship between the applied calibration loads and the measured gage outputs. The analysis of the sting balance calibration data set is a rare example of a situation when terms of a regression model of a balance can directly be derived from first principles of physics. In addition, it is interesting to note that the search algorithm recommended the correct regression model term combinations using only a set of statistical quality metrics that were applied to the experimental data during the algorithm s term selection process.
Existing nondestructive evaluation (NDE) technologies are inherently limited by the physical response of the structural material being inspected and are therefore not generally effective at the identification of small discontinuities, making the detection of incipient damage extremely difficult. One innovative solution to this problem is to enhance or complement the NDE signature of structural materials to dramatically improve the ability of existing NDE tools to detect damage. To address this need, a multifunctional metallic material has been developed that can be used in structural applications. The material is processed to contain second phase sensory particles that significantly improve the NDE response, enhancing the ability of conventional NDE techniques to detect incipient damage both during and after flight. Ferromagnetic shape-memory alloys (FSMAs) are an ideal material for these sensory particles as they undergo a uniform and repeatable change in both magnetic properties and crystallographic structure (martensitic transformation) when subjected to strain and/or temperature changes which can be detected using conventional NDE techniques. In this study, the use of a ferromagnetic shape memory alloy (FSMA) as the sensory particles was investigated.
To eliminate the need to use finite-element modeling for structure shape predictions, a new method was invented. This method is to use the Displacement Transfer Functions to transform the measured surface strains into deflections for mapping out overall structural deformed shapes. The Displacement Transfer Functions are expressed in terms of rectilinearly distributed surface strains, and contain no material properties. This report is to apply the patented method to the shape predictions of non-symmetrically loaded slender curved structures with different curvatures up to a full circle. Because the measured surface strains are not available, finite-element analysis had to be used to analytically generate the surface strains. Previously formulated straight-beam Displacement Transfer Functions were modified by introducing the curvature-effect correction terms. Through single-point or dual-point collocations with finite-elementgenerated deflection curves, functional forms of the curvature-effect correction terms were empirically established. The resulting modified Displacement Transfer Functions can then provide quite accurate shape predictions. Also, the uniform straight-beam Displacement Transfer Function was applied to the shape predictions of a section-cut of a generic capsule (GC) outer curved sandwich wall. The resulting GC shape predictions are quite accurate in partial regions where the radius of curvature does not change sharply.
The formation and growth of Al2O3 scales on (beta)-NiAl were studied using electron microscopy and other analytical techniques to gain an understanding of the oxidation properties of (beta)-NiAl and of alumina-forming alloys, in general. The transient and mature stages of oxidation were studied as well as the transformation stage during which the oxide scale transforms from metastable Al2O3 phases to the thermodynamically stable alpha-Al2O3 phase. The transient oxidation stages were studied at 800 deg C and for short times at 1100C. At 800C, the scales consist predominantly of delta-Al2O3 which forms by cation vacancy ordering in the defective spinel lattice of gamma-Al2O3. At 1100C, a fast-growth morphology of theta-Al2O3 forms as a surface layer over delta-Al2O3. For both oxidation temperatures, the scales are often epitaxially oriented with respect to the metal. The transient scales grow by outward cation diffusion as evidenced by surface growth morphologies. The transformation to alpha-Al2O3 occurs within 1 hour at 1100C by a nucleation and radial growth process. The large volume decrease associated with the transformation results in a highly strained alpha-Al2O3 microstructure. A change in scale growth mechanism from outward cation to inward anion diffusion allows transient surface morphologies to be smoothed by surface diffusion. The mature stage of oxidation involves the growth of an alpha-Al2O3 scale having the lacey morphology formed as a result of the gamma yields alpha transformation. Growth of the scale occurs by counterdiffusion along grain boundaries resulting in ridges formed by impingement of alpha-Al2O3 nuclei during the transformation stage. Also scale growth occurs by inward oxygen diffusion through healed cracks; the cracks result from transformation stresses. The measured growth rates of scales having the lacey morphology are an order of magnitude less than fine-grained alpha-Al2O3 scales. Metal orientations were found to have a large effect on oxide morpholoies during all stages of oxidation.
Shape memory alloys (SMAs) can produce large strains when deformed (e.g., up to 8%). Heating results in a phase transformation and associated recovery of all the accumulated strain. This strain recovery can occur against large forces, resulting in their use as actuators. Thus an SMA element can integrate both sensory and actuation functions, by inherently sensing a change in temperature and actuating by undergoing a shape change as a result of a temperature-induced phase transformation. Two aspects of our work on cryogenic SMAs are addressed here. First - a shape memory alloy based cryogenic thermal conduction switch for operation between dewars of liquid methane and liquid oxygen in a common bulkhead arrangement is discussed. Such a switch integrates the sensor element and the actuator element and can be used to create a variable thermal sink to other cryogenic tanks for liquefaction, densification, and zero boil-off systems for advanced spaceport applications. Second - fabrication via arc-melting and subsequent materials testing of SMAs with cryogenic transformation temperatures for use in the aforementioned switch is discussed.
Finite-element-model-trained artificial neural networks can be used to process efficiently the characteristic patterns or mode shapes from electronic holograms of vibrating blades. The models used for routine design may not yet be sufficiently accurate for this application. This document discusses the creation of characteristic patterns; compares model generated and experimental characteristic patterns; and discusses the neural networks that transform the characteristic patterns into strain or damage information. The current potential to adapt electronic holography to spin rigs, wind tunnels and engines provides an incentive to have accurate finite element models lor training neural networks.
The use of graphite-composites as primary structure is essential for the development of a cost effective single-stage-to-orbit reusable launch vehicle (RLV). A full-scale segment of a graphite-composite intertank was designed and fabricated by an industry team and tested at NASA Langley Research Center as a part of the RLV technology development program. The intertank test component was approximately 3.0 m long by 6.7 m wide and included slightly less than a 90deg section of a cylindrical intertank. The test article was fabricated using graphite-bismaelimide composite material and consisted of a hat-stiffened skin with five ring frames. The stiffeners were secondarily bonded to the panel skin and the ring frames were mechanically attached. The test article was loaded to failure with a uniform compression load applied by 21 individually controlled hydraulic actuators. Resistance strain gages, linear variable differential transformers and video cameras were used to measure and record the test results. A linear f d t e element analysis of the test article and test fixture was performed. The test results verified the structural integrity cf the intertank test article up to the design limit load. However, the test article failed in general skin buckling between the ring frames at a load 1.08 times design limit load. This load was considerably lower than the expected failure load. The cause of premature failure is being investigated. Good correlation of the test and analysis results was obtained for loads up to the design limit load.