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A small-deflection theory that takes into account deformations due to transverse shear is presented for the elastic-behavior analysis of orthotropic plates of constant cylindrical curvature, with consideration of buckling included. The theory is applicable primarily to sandwich construction. (author)
The linear elastic response is determined for an internally pressurized, long circular cylindrical shell stiffened on the inside by a regular arrangement of identical stringers and identical rings. Periodicity of this configuration permits the analysis of a portion of the shell wall centered over a generic stringer-ring joint; i.e., a unit cell model. The stiffeners are modeled as discrete beams, and the stringer is assumed to have a symmetrical cross section and the ring an asymmetrical section. Asymmetery causes out-of-plane bending and torsion of the ring. Displacements are assumed as truncated double Fourier series plus simple terms in the axial coordinate to account for the closed and pressure vessel effect (a non-periodic effect). The interacting line loads between the stiffeners and the inside shell wall are Lagrange multipliers in the formulation, and they are also assumed as truncated Fourier series. Displacement continuity constraints between the stiffeners and shell along the contact lines are satisfied point-wise. Equilibrium is imposed by the principle of virtual work. A composite material crown panel from the fuselage of a large transport aircraft is the numerical example. The distributions of the interacting line loads, and the out-of-plane bending moment and torque in the ring, are strongly dependent on modeling the deformations due to transverse shear and cross-sectional warping of the ring in torsion. This paper contains the results from the semiannual report on research on 'Pressure Pillowing of an Orthogonally Stiffened Cylindrical Shell'. The results of the new work are illustrated in the included appendix.
Flight experiments on NASA Langley's B737-100 (TSRV) airplane have been conducted to document flow characteristics in order to further the understanding of high-lift flow physics, and to correlate and validate computational predictions and wind-tunnel measurements. The project is a cooperative effort involving NASA, industry, and universities. In addition to focusing on in-flight measurements, the project includes extensive application of various computational techniques, and correlation of flight data with computational results and wind-tunnel measurements. Results obtained in the most recent phase of flight experiments are analyzed and presented in this paper. In-flight measurements include surface pressure distributions, measured using flush pressure taps and pressure belts on the slats, main element, and flap elements; surface shear stresses, measured using Preston tubes; off-surface velocity distributions, measured using shear-layer rakes; aeroelastic deformations of the flap elements, measured using an optical positioning system; and boundary-layer transition phenomena, measured using hot-film anemometers and an infrared imaging system. The analysis in this paper primarily focuses on changes in the boundary-layer state that occurred on the slats, main element, and fore flap as a result of changes in flap setting and/or flight condition. Following a detailed description of the experiment, the boundary-layer state phenomenon will be discussed based on data measured during these recent flight experiments.
A higher-order bending theory is derived for laminated composite and sandwich beams thus extending the recent {1,2}-order theory to include third-order axial effect without introducing additional kinematic variables. The present theory is of order {3,2} and includes both transverse shear and transverse normal deformations. A closed-form solution to the cylindrical bending problem is derived and compared with the corresponding exact elasticity solution. The numerical comparisons are focused on the most challenging material systems and beam aspect ratios which include moderate-to-thick unsymmetric composite and sandwich laminates. Advantages and limitations of the theory are discussed.
A numerical simulation of Hurricane Bob (1991) is conducted using the Penn State University-National Center for Atmospheric Research mesoscale model MM5 with a horizontal grid spacing of 1.3 Km on the finest nested mesh The model produces a realistic hurricane that intensifies slowly during the period of fine-scale simulation. Time-averaged results reveal the effects of storm motion. vertical shear, beta gyres and deformation forcing on the structure of radial inflow, vertical motion, and precipitation. Instantaneous model fields show that radial inflow in the eyewall is very intense near the surface but transitions to strong low-level outflow near the top of the boundary layer. The low-level structure is modulated by a wavenumber 2 disturbance that rotates around the eyewall at half the speed of the maximum tangential winds and is consistent with a vortex Rossby edge wave. The statistical distribution of vertical velocity in the eyewall indicates that the eyewall is composed of a small number of intense updrafts that account for the majority of the upward mass flux rather than a more gradual and symmetric eyewall circulation, consistent with the concept of hot towers. Tongues of high equivalent potential temperature, Theta(sub e), are seen along the inner edge of the eyewall updraft and within the low-level outflow. This air originates from outside of the eyewall with the highest theta(sub e) air coming from the layer closest to the surface after penetrating closest to the center. Occasionally, high Theta(sub e), air within the eye is drawn into the eyewall updrafts. The high Theta(sub e), air rising within the eyewall is shown to be associated with positive eyewall buoyancy with sufficient convective available potential energy along its path to produce relatively strong convective updrafts. Although the requirements for conditional symmetric instability are met within the eyewall and the air parcel trajectories follow slanted paths, the radial displacement of air parcels in the low-level outflow moves the air parcel sufficiently far away from the upper- warm core that the air becomes unstable to vertical displacements. Hence, convective instability rather than symmetric instability accounts for the stronger updrafts in the eyewall.
A new refined theory for laminated-composite and sandwich beams that contains the kinematics of the Timoshenko Beam Theory as a proper baseline subset is presented. This variationally consistent theory is derived from the virtual work principle and employs a novel piecewise linear zigzag function that provides a more realistic representation of the deformation states of transverse shear flexible beams than other similar theories. This new zigzag function is unique in that it vanishes at the top and bottom bounding surfaces of a beam. The formulation does not enforce continuity of the transverse shear stress across the beam s cross-section, yet is robust. Two major shortcomings that are inherent in the previous zigzag theories, shear-force inconsistency and difficulties in simulating clamped boundary conditions, and that have greatly limited the utility of these previous theories are discussed in detail. An approach that has successfully resolved these shortcomings is presented herein. This new theory can be readily extended to plate and shell structures, and should be useful for obtaining accurate estimates of structural response of laminated composites.
Little is known about the microstructural behavior of magnetite during hypervelocity impact events, even though it is a widespread accessory mineral and important magnetic carrier in terrestrial and extraterrestrial rocks. We report systematic electron backscatter diffraction crystallographic analysis of shock features in magnetite, from a transect across the 52-km diameter ~380 Ma Siljan impact structure in Sweden. Magnetite grains in granitoid samples contain brittle fracturing, crystal-plasticity, and lamellar twins. Deformation twins along {111} with shear direction of <112> are consistent with spinel-law twins. Inferred bulk shock pressures for investigated samples, as constrained by planar deformation features (PDFs) in quartz and shock twins in zircon, range from 0–20 GPa; onset of shock-induced twinning in magnetite is observed at >5 GPa. These results highlight the utility of magnetite to record shock deformation in rocks that experience shock pressures >5 GPa, which may be useful in quartz-poor samples. Despite significant hydrothermal alteration, and variable transformation of host magnetite to hematite, shock effects are preserved, demonstrating that magnetite is a reliable mineral for preserving shock deformation over geologic time.
The viability as an efficient aircraft material of advanced textile composites is currently being addressed in the NASA Advanced Composites Technology (ACT) Program. One of the expected milestones of the program is to develop standard test methods for these complex material systems. Current test methods for laminated composites may not be optimum for textile composites, since the architecture of the textile induces nonuniform deformation characteristics on the scale of the smallest repeating unit of the architecture. The smallest repeating unit, also called the unit cell, is often larger than the strain gages used for testing of tape composites. As a result, extending laminated composite test practices to textiles can often lead to pronounced scatter in material property measurements. It has been speculated that the fiber architectures produce significant surface strain nonuniformities, however, the magnitudes were not well understood. Moire interferometry, characterized by full-field information, high displacement sensitivity, and high spatial resolution, is well suited to document the surface strain on textile composites. Studies at the NASA Langley Research Center on a variety of textile architectures including 2-D braids and 3-D weaves, has evidenced the merits of using moire interferometry to guide in test method development for textile composites. Moire was used to support tensile testing by validating instrumentation practices and documenting damage mechanisms. It was used to validate shear test methods by mapping the full-field deformation of shear specimens. Moire was used to validate open hole tension experiments to determine the strain concentration and compare then to numeric predictions. It was used for through-the-thickness tensile strength test method development, to verify capabilities for testing of both 2-D and 3-D material systems. For all of these examples, moire interferometry provided vision so that test methods could be developed with less speculation and more documentation.
The rheological properties of mantle rocks are strongly dependent on their crystallographic preferred orientation (CPO). Olivine CPO, defined by the orientation of seismically fast [100] axes parallel to flow direction, is also thought to be a dominant contributor to seismic anisotropy in the Earth's upper mantle. However, the amount of deformation needed to overprint a new CPO on a pre-existing fabric and the impact of the inherited CPOs on the transient microstructure evolution, remain unknown. This study employs a full-field numerical approach (VPFFT-ELLE) to explore the dynamic recrystallization and microstructural evolution of olivine polycrystalline aggregates under complex deformation conditions. We test four combinations of successive pure shear and simple shear boundary conditions. Findings indicate that inherited CPOs influence subsequent deformation in a manner dependent on the kinematic relationship between successive stages. In all cases, a minor strain increment (ε ∼0.3–0.6) is sufficient to erase the previous microstructure and CPO. However, when deformation conditions change dramatically (e.g., stretching direction changes orthogonally), the intensity of the new CPO developed is significantly lower and strain distribution are specially altered. During a transient strain stage, pre-existing microstructures undergo extensive reworking, especially when deformation conditions are changed dramatically, such as switching from simple shear to a pure shear condition with a parallel shortening direction relative to the stretching direction. We estimate the significance of these results in interpreting observations of seismic velocity anisotropy, concluding that P-wave seismic anisotropy is significantly and positively correlated with the evolution of olivine CPO with deformation history. This research underscores the transient nature of microstructural rearrangement in olivine aggregates and the necessity for caution in interpreting seismic anisotropy in regions with complex deformation histories, as inherited CPOs can influence current fabric development and induce deviation to the present deformation conditions.
The objective of this project is to enable deliberate development of cost-effective, hydrogen resistant alloys by establishing detailed relationships specific to the effects of alloy composition, short-range order (SRO), and microsegregation in the presence of hydrogen on the transition between homogeneous deformation and localized plasticity in shear bands. In collaboration with the International Institute for Carbon-Neutral Energy Research, I2CNER, at Kyushu University in Japan, we conceptualized, designed, and manufactured four austenitic alloys that maintain corrosion resistance and ensure lower cost relative to baseline commercial alloys. The mechanical properties and deformation modes of the novel alloys (KU alloys) were assessed in the presence of hydrogen (H). Correlations between composition and performance revealed that two of the KU alloys are suitable replacements for 316 steel, while another is a viable replacement for 304 steel at room temperature. We found that, in the presence of other austenite stabilizing elements namely Mn and N, replacing Ni with Cu does not lead to martensite formation as has been previously reported.1–3 Furthermore, we found that the addition of Cu leads to an earlier onset of multiple slip resulting in an relative earlier onset of a higher work hardening rate (WHR). Greater understanding of the relationships between alloy composition and SRO required the development of a novel advanced electron diffraction methodology to characterize SRO in complex FCC alloys. This innovative approach, which combines fluctuation and correlation analyses of diffuse-scattering signals, successfully differentiated between SRO and long-range ordering (LRO). Further investigations into annealed austenitic stainless steels could provide insights into manipulating SRO and its effects on material properties. Atomistic simulations provided understanding of SRO behavior that was difficult to capture experimentally. This project created the first spin cluster expansion model that is able to capture and describe SRO effects in Fe-Ni-Cr FCC alloys, accounting for the non-negligible effects of magnetism. An automated computational workflow was established to provide reliable predictions of SRO in Fe-Ni-Cr austenitic alloys, both with and without the presence of H atoms. Analysis of the propensity for SRO in Fe-Ni-Cr alloys revealed that H tends to cluster with specific, well-defined SRO domains. The computational framework is general purpose and can be extended to realistic stainless steels across diverse composition ranges. With confidence that SRO is possible in austenitic stainless steels, we developed a discrete dislocation finite element code to understand the interaction of dislocations with SRO in the presence of H. By incorporating H effects on the dislocation emission and SRO stress field we show that the critical stress for the dislocation pileup to breakthrough the SRO domain decreases in the presence of H, which directly contributes localized deformation at the macroscale. Through the simulation of a uniaxial tension test, we demonstrated that H-induced weakening of SRO stress field and H-enhanced dislocation emission can lead to the onset of shear localization at lower macroscopic strains. As a whole, this project identified three novel alloys that show improvements in performance and cost efficiency for H-facing applications by studying correlations between alloy chemistry and deformation behavior. We also made significant advancements to experimental and computational methodologies necessary to study the chemistry and distribution of SRO across a range of alloys, which in turn allowed us to demonstrate how deformation mechanisms change due to the contributions of SRO in austenitic alloys in the presence of H. The combined advancements in fundamental understanding with novel alloy development in this project has increased the viability of next generation H-technologies for the broader public through accessible low-cost alloys and accelerated development towards future H-infrastructure.
The geologic history of Martian meteorite Allan Hills (ALH) 84001 is more complex than previously recognized, with evidence for four or five crater-forming impacts onto Mars. This history of repeated deformation and shock metamorphism appears to weaken some arguments that have been offered for and against the hypothesis of ancient Martian life in ALH 84001. Allan Hills 84001 formed originally from basaltic magma. Its first impact event (I1) is inferred from the deformation (D1) that produced the granular-textured bands ("crush zones") that transect the original igneous fabric. Deformation D1 is characterized by intense shear and may represent excavation or rebound flow of rock beneath a large impact crater. An intense thermal metamorphism followed D1 and may be related to it. The next impact (I2) produced fractures, (Fr2) in which carbonate "pancakes" were deposited and produced feldspathic glass from some of the igneous feldspars and silica. After I2, carbonate pancakes and globules were deposited in Fr2 fractures and replaced feldspathic glass and possibly crystalline silicates. Next, feldspars, feldspathic glass, and possibly some carbonates were mobilized and melted in the third impact (I3). Microfaulting, intense fracturing, and shear are also associated with 13. In the fourth impact (I4), the rock was fractured and deformed without significant heating, which permitted remnant magnetization directions to vary across fracture surfaces. Finally, ALH 84001 was ejected from Mars in event I5, which could be identical to I4. This history of multiple impacts is consistent with the photogeology of the Martian highlands and may help resolve some apparent contradictions among recent results on ALH 84001. For example, the submicron rounded magnetite grains in the carbonate globules could be contemporaneous with carbonate deposition, whereas the elongate magnetite grains, epitaxial on carbonates, could be ascribed to vapor-phase deposition during I3.
Recent tectonic models have resulted in conflicting descriptions of how the late Precambrian sutures of the Arabian-Nubian shield extend into northeast Africa. The Hamisana shear zone in northeastern Sudan is critical to this discussion because it truncates and disrupts two sutures, the Allaqi-Heiani and the Onib-Sol Hamed. Analysis of field structural data, Thematic Mapper imagery, and Rb-Sr and U-Pb geochronology suggests that the Allaqi-Heiani suture is the western extension of the Onib-Sol Hamed suture and that both make up the exposed parts of a far-traveled, polydeformed ophiolitic nappe complex. Subsequent deformation localized in the Hamisana shear zone disrupted this nappe and displaced the suture between 660 and 550 Ma during regional deformation associated with the Najd fault system. These results indicate that at least one suture extends westward into the interior of northern Africa.
High-entropy alloys (HEAs) fabricated by powder metallurgy are considered to exhibit extremely-great potential application values in the field for high-speed impact deformation due to their uniform microstructures and compositions. The mechanical behavior of a powder-metallurgy-fabricated (PM) CoCrFeMnNi HEA was investigated at room temperature with strain rates ranging from 1200 s -1 to 2800 s -1 . It was found that the serration behavior and shear localization of the alloy under dynamic conditions occurred. Results also indicated that the serrated flow took place in the PM CoCrFeMnNi HEA during mechanical deformation at high strain rates (>1000 s -1 ) and became more pronounced as the strain rate increased. Furthermore, it was determined that the yield-strength values of the PM CoCrFeMnNi HEA were sensitive to strain rates, where the values increased from 500 MPa to 700 MPa when the strain rates increased from 1200 s -1 to 2800 s -1 . Shear bands with a width of about 20 μm were generated in the PM CoCrFeMnNi HEA after the shear stress reached a maximum value of 635 MPa, which corresponded to a nominal strain of about 8.71. Nanotwins and ultrafine-equiaxed grains with a diameter of about 150 nm also developed at the core of the shear band during deformation. The results revealed that the strength of the shear band was much higher than that of the matrix grain. Nanotwins in the shear band were composed of a single face-centered-cubic (FCC) structure with the twin plane of ($\bar{1}$1$\bar1$), which could be formed via a rotational dynamic recrystallization (RDR).
Soft gels, formed via the self-assembly of particulate materials, exhibit intricate multiscale structures that provide them with flexibility and resilience when subjected to external stresses. Here, this work combines particle simulations and topological data analysis (TDA) to characterize the complex multiscale structure of soft gels. Our TDA analysis focuses on the use of the Euler characteristic, which is an interpretable and computationally scalable topological descriptor that is combined with filtration operations to obtain information on the geometric (local) and topological (global) structure of soft gels. We reduce the topological information obtained with TDA using principal component analysis (PCA) and show that this provides an informative low-dimensional representation of the gel structure. We use the proposed computational framework to investigate the influence of gel preparation (e.g., quench rate, volume fraction) on soft gel structure and to explore dynamic deformations that emerge under oscillatory shear in various response regimes (linear, nonlinear, and flow). Our analysis provides evidence of the existence of hierarchical structures in soft gels, which are not easily identifiable otherwise. Moreover, our analysis reveals direct correlations between topological changes of the gel structure under deformation and mechanical phenomena distinctive of gel materials, such as stiffening and yielding. In summary, we show that TDA facilitates the mathematical representation, quantification, and analysis of soft gel structures, extending traditional network analysis methods to capture both local and global organization.
Shear Assisted Processing and Extrusion (ShAPE), a severe plastic deformation technique that is fast and scalable, was used to produce thin-wall tubing from alloy 6082 (Al-0.8Mg-0.9Si-0.7Mn) with in-situ solutionization during processing quickly followed by quenching. Quench medium and input material heat treatment were varied and natural aging behavior (T1 heat treatment) was evaluated using tensile testing. As-cast input material was found to have higher strength early in post-ShAPE natural aging and homogenized input material was found to have strengthening during natural aging. Compared to air quenching, water quenching gave greater strength both early in and after natural aging. These observations along with microscopy suggest that: 1. air quenching was too slow; 2. as-cast material was not fully solutionized but plastic deformation broke up the coarse intermetallic particles, which provided strengthening; and 3. homogenized material was solutionized well, which led to good natural aging behavior.
Stressing and rupture of a locked zone adjacent to a creeping fault segment was studied with special reference to strength heterogeneity depthwise and along-strike. The resulting precursory temporal and spatial variations of surface strain rate profiles were compared to geodetic measurements on the San Andreas fault in central California. Crustal deformation in great California earthquake cycles was also studied with special reference to the temporal decay of strain rate observed since the 1957 and 1906 great earthquakes, and comtemporary surface strain rate and velocity profiles at several locations along the San Andreas. The effect of viscoelastic response in the deep aseismic shear zone on the surface deformation behavior was examined. Work was begun on a fundamental reformulation of the crustal deformation problem focusing on the crustal deformation process affected by deep aseismic slip as the slip zone progresses toward an instability and as deep seismic slip continues postseismically, the 3-D nature of the problem due to geometry and material heterogeneity, and the time-dependent source coming from the lithosphere/astenospheric coupling process.
A study was conducted on the effects of internal hydrogen and microstructure on the deformation and fracture of a single crystal nickel-base superalloy. In particular, room temperature plane strain fracture toughness and tensile tests were performed on hydrogen-free and hydrogen charged samples of PWA 1480. The role of microstructure was incorporated by varying the levels of porosity and eutectic gamma/gamma prime through hot isostatic pressing and heat treatment. The room temperature behavior of PWA 1480 was unusual because precipitate shearing was not the primary deformation mechanism at all strains. At strains over 1 percent, dislocations were trapped in the gamma matrix and an attempt was made to relate this behavior to compositional differences between PWA 1480 and other superalloys. Another unique feature of the tensile behavior was cleavage of the eutectic gamma/gamma prime, which is believed to initiate the failure process. Fracture occurred on (111) planes and is likely a result of shear localization along these planes. Elimination of the eutectic gamma/gamma prime greatly improved the tensile ductility, but pososity had no effect on tensile properties. Large quantities of hydrogen (1.74 at. percent) were gas-phase charged into the material, but surprisingly this was not a function of the amount of porosity or eutectic gamma/gamma prime present. Desorption experiments suggest that the vast majority of hydrogen is at reversible lattice trapping sites. This large, uniform concentration of hydrogen dramatically reduced the tensile strain to failure, but only slightly affected the reduction in area. Available hydrogen embrittlement models were examined in light of these results and it was found that the hydrogen enhanced localized plasticity model can explain much of the tensile behavior. K(IC) fracture toughness tests were conducted, but it was necessary to also perform J(IC) tests to provide valid data.
It is shown that the creep deformation resistance of a variety of metals is reduced by repeated reversed deformation at temperatures above 0.4 Tm, where Tm is the absolute melting temperature of each metal. The reduction of creep deformation resistance due to stress reversals is most prominent at approximately 0.5 Tm where the average creep rate may increase by as much as a factor of twenty due to 50-100 stress reversals. Metallographic studies show that the observed acceleration of creep at high temperatures is in part due to the enhancement of grain boundary sliding as a result of gradual grain boundary migration toward planes of maximum shear stress during reversed creep deformation.