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NASA NTRS2013

Estimating the Collapse Pressure of an Inflatable Aerodynamic Decelerator

The collapse pressure of an inflatable membrane is the minimum differential pressure which will sustain a specific desired shape under an applied load. In this paper, we present a method for estimating the collapse pressure of a tension-cone inflatable aerodynamic decelerator (IAD) that is subject to a static aerodynamic load. The IAD surface is modeled as an elastic membrane. For a given aerodynamic load and sufficiently high torus differential pressure, the IAD assumes a stable axisymmetric equilibrium shape. When the torus pressure is reduced sufficiently, the symmetric equilibrium state becomes unstable and we define this instance to be the critical pressure Pcr. In this paper, we will compare our predicted critical torus pressure with the corresponding observed torus collapse pressure (OTCP) for fifteen tests that were conducted by the third author and his collaborators at the NASA Glenn Research Center 10x10 Supersonic Wind Tunnel in April 2008. One of the difficulties with these types of comparisons is establishing the instance of torus collapse and determining the OTCP from quantities measured during the experiment. In many cases, torus collapse is gradual and the OTCP is not well-defined. However, in eight of the fifteen wind tunnel tests where the OTCP is well-defined, we find that the average of the relative differences (Pcr - OTCP/Pcr) was 8.9%. For completeness, we will also discuss the seven tests where the observed torus collapse pressure is not well-defined.

Baginski, Frank E.↗

NASA NTRS2013

Qualification of UHF Antenna for Extreme Martian Thermal Environments

The purpose of this development was to validate the use of the external Rover Ultra High Frequency (RUHF) antenna for space under extreme thermal environments to be encountered during the surface operations of the Mars Science Laboratory (MSL) mission. The antenna must survive all ground operations plus the nominal 670 Martian sol mission that includes summer and winter seasons of the Mars thermal environment.The qualification effort was to verify that the RUHF antenna design and its bonding and packaging processes are adequate to survive the harsh environmental conditions. The RUHF is a quadrifilar helix antenna mounted on the MSL Curiosity rover deck. The main components of the RUHF antenna are the helix structure, feed cables, and hybrid coupler, and the high-power termination load. In the case of MSL rover externally mounted hardware, not only are the expected thermal cycle depths severe, but there are temperature offsets between the Mars summer and winter seasons. The total number of temperature cycles needed to be split into two regimes of summer cycles and winter cycles. The qualification test was designed to demonstrate a survival life of three times more than all expected ground testing, plus a nominal 670 Martian sol missions. Baseline RF tests and a visual inspection were performed prior to the start of the qualification test. Functional RF tests were performed intermittently during chamber breaks over the course of the qualification test. For the RF return loss measurements, the antenna was tested in a controlled environment outside the thermal chamber with a vector network analyzer that was calibrated over the antenna s operational frequency range. A total of 2,010 thermal cycles were performed. Visual inspection showed a dulling of the solder material. This change will not affect the performance of the antenna. No other changes were observed. RF tests were performed on the RUHF helix antenna, hybrid, and load after the 2,010 qualification cycles test. The RF performance of the RUHF antenna, hybrid, and load were almost identical before and after the complete test. Therefore, the developed design of RUHF is qualified for a long-duration MSL mission. The RUHF antenna has not been used for long-duration missions such as MSL in the past. The state-of-the-art technology of the RUHF antenna is used to develop the antennas for MSL mission survivability. This developmental test data provides the confidence in using this RUHF antenna for future NASA missions to Mars.

Ramesham, Rajeshuni↗

NASA NTRS2016

X-ray Micro-Tomography of Ablative Heat Shield Materials

X-ray micro-tomography is a non-destructive characterization technique that allows imaging of materials structures with voxel sizes in the micrometer range. This level of resolution makes the technique very attractive for imaging porous ablators used in hypersonic entry systems. Besides providing a high fidelity description of the material architecture, micro-tomography enables computations of bulk material properties and simulations of micro-scale phenomena. This presentation provides an overview of a collaborative effort between NASA Ames Research Center and Lawrence Berkeley National Laboratory, aimed at developing micro-tomography experiments and simulations for porous ablative materials. Measurements are carried using x-rays from the Advanced Light Source at Berkeley Lab on different classes of ablative materials used in NASA entry systems. Challenges, strengths and limitations of the technique for imaging materials such as lightweight carbon-phenolic systems and woven textiles are discussed. Computational tools developed to perform numerical simulations based on micro-tomography are described. These enable computations of material properties such as permeability, thermal and radiative conductivity, tortuosity and other parameters that are used in ablator response models. Finally, we present the design of environmental cells that enable imaging materials under simulated operational conditions, such as high temperature, mechanical loads and oxidizing atmospheres.Keywords: Micro-tomography, Porous media, Ablation

tomography↗

NASA NTRS2017

Nuclear Rocket Ceramic Metal Fuel Fabrication Using Tungsten Powder Coating and Spark Plasma Sintering

Nuclear thermal propulsion is an enabling technology for crewed Mars missions. An investigation was conducted to evaluate spark plasma sintering (SPS) as a method to produce tungsten-depleted uranium dioxide (W-dUO2) fuel material when employing fuel particles that were tungsten powder coated. Ceramic metal fuel wafers were produced from a blend of W-60vol% dUO2 powder that was sintered via SPS. The maximum sintering temperatures were varied from 1,600 to 1,850 C while applying a 50-MPa axial load. Wafers exhibited high density (>95% of theoretical) and a uniform microstructure (fuel particles uniformly dispersed throughout tungsten matrix).

Barnes, M. W.↗

NASA NTRS2017

Design, Manufacture and Test of Cryotank Components

On the composite cryotank technology development (CCTD) project, the Boeing Company built two cryotanks as a means of advancing technology and manufacturing readiness levels (TRL and MRL) and lowering the risk of fabricating full-scale fuel containment vessels.1 CCTD focused on upper stage extended duration applications where long term storage of propellants is required. The project involved the design, analysis, fabrication, and test of manufacturing demonstration units (MDU), a 2.4 m (precursor) and a 5.5 m composite cryotank. Key design features included one-piece wall construction to minimize overall weight (eliminating the need for a bellyband joint), 3-dimensionally (3D) reinforced y-joint material to alleviate stress concentrations at the tank to skirt interface and a purge-able ﬂuted core skirt to carry high axial launch loads. The tanks were made with OoA curing pre-impregnated (prepreg) carbon/epoxy (C/E) slit-tape tow (STT) that contained thin micro-crack resistant plies in the tank wall center to impede permeation. The tanks were fabricated at Boeing's Seattle-based Advanced Development Center (ADC) using RAFP and multipiece break-down tooling. The tooling was designed and built by Janicki Industries (JI) at Sedro Woolley, Washington. Tank assemblage consisted of co-bonded dome covers, one-piece ﬂuted core skirts and mechanical fastened cover/sump. Ultrasonic inspection was performed after every cure or bond and a structural health monitoring system (SHMS) was installed to identify potential impact damage events (in-process and/or during transportation). The tanks were low temperature tested at NASA's George C. Marshall Space Flight Center (MSFC) in Huntsville, Alabama. The testing, which consisted of a sequence of ﬁll/drain pressure and thermal cycles using LH2, was successfully concluded in 2012 on the 2.4 m tank and in 2014 on the 5.5 m tank. Structural, thermal, and permeation performance data was obtained. 2 Critical design features and manufacturing advancements, which helped to validate 25% weight and 30% cost reduction projections, were matured. These advancements will help to guide future composite tank integration activities on next generation long duration aircraft and space launch vehicles. Because CCTD addressed innovative design features, heavy lift size scale-up, multipiece captured tooling, new generation automated material placement (AMP) equipment and OoA materials, this chapter should be of interest to educators, students and manufacturers of composite hardware and ﬂight vehicles.

McCarville, Douglas A.↗

NASA NTRS2018

Experimental Investigation of Heat Pipe Startup Under Reflux Mode

In the absence of body forces such as gravity, a heat pipe will start as soon as its evaporator temperature reaches the saturation temperature. If the heat pipe operates under a reflux mode in ground testing, the liquid puddle will fill the entire cross sectional area of the evaporator. Under this condition, the heat pipe may not start when the evaporator temperature reaches the saturation temperature. Instead, a superheat is required in order for the liquid to vaporize through nucleate boiling. The amount of superheat depends on several factors such as the roughness of the heat pipe internal surface and the gravity head. This paper describes an experimental investigation of the effect of gravity pressure head on the startup of a heat pipe under reflux mode. In this study, a heat pipe with internal axial grooves was placed in a vertical position with different tilt angles relative to the horizontal plane. Heat was applied to the evaporator at the bottom and cooling was provided to the condenser at the top. The liquid-flooded evaporator was divided into seven segments along the axial direction, and an electrical heater was attached to each evaporator segment. Heat was applied to individual heaters in various combinations and sequences. Other test variables included the condenser sink temperature and tilt angle. Test results show that as long as an individual evaporator segment was flooded with liquid initially, a superheat was required to vaporize the liquid in that segment. The amount of superheat required for liquid vaporization was a function of gravity pressure head imposed on that evaporator segment and the initial temperature of the heat pipe. The most efficient and effective way to start the heat pipe was to apply a heat load with a high heat flux to the lowest segment of the evaporator.

Thermal Control Systems↗

NASA NTRS2019

Effect of 3D Roughness Patch on Instability Amplification in a Supersonic Boundary Layer

Surface roughness is known to have a substantial impact on the aerothermodynamic loading of high-speed vehicles, particularly via its influence on the laminar-turbulent transition process within the boundary layer. Numerical simulations are performed to investigate the effects of a distributed region of densely packed, sinusoidal shape roughness elements on a Mach 3.5 flat plate boundary layer for flow conditions corresponding to the planned conditions of an upcoming experiment in the Mach 3.5 Supersonic Low Disturbance Tunnel at the NASA Langley Research Center. Analysis of convective instabilities in the wake of the roughness patch was reported in a previous paper and the current work extends that analysis to instability amplification across the length of the roughness patch. Quasi-parallel stability analysis of the modified boundary layer flow over the patch indicates two dominant families of unstable disturbances, namely, a group of high frequency modes that amplify in localized regions along the roughness patch and another group of low frequency modes that have smaller peak amplification rates but amplify steadily both above the roughness patch and in the wake region behind it. The results suggest that the amplification factors associated with the high-frequency modes are sufficiently low, at least for the roughness patches considered in this paper, so that these modes are unlikely to have a major influence on the transition process. The amplification of the low-frequency modes within the region of the roughness patch is further quantified via direct numerical simulations. Results confirm the strongly destabilizing influence of the roughness patch on the first mode instabilities, yielding an N-factor increment of ΔN ≈ 3.6 for a roughness patch length of eight wavelengths.

Laminar turbulent transition↗

NASA NTRS2014

TPSAS-NF1676L-18913-DND

Composite materials and structures are enabling technology for modern aerospace vehicles. Numerical-control manufacturing, including automated fiber placement (AFP), is widely used to fabricate these components. However, weight and performance requirements for the next generation of aerospace vehicles will push the state-of-art even further, and require development of more advanced materials, manufacturing, and structures technologies that are both affordable and efficient. The Integrated Structural Assembly of Advanced Composites (ISAAC) system is intended to address much of NASA?s critical research needs in advanced composites. The baseline ISAAC system, combining a commercial robot with multiple redundant degrees of freedom, a tool changer interface, and a special-purpose AFP end effector, enables precise and accurate additive manufacturing of composite structures, as well as development of advanced tow-steered structures with tailored load paths. The highly capable baseline system can quickly change end effectors, thus enabling further research for composites manufacturing. This extended system is similar to a high-speed machining center, where interchangeable cutters are used for different operations during metal structures fabrication. This capability enables future development, integration and assessment of new advanced manufacturing technologies, such as in-situ curing and NDE, and through-thickness reinforcements to reduce delaminations. End effectors with these advanced capabilities may be purchased, developed internally or with industry or academia, and then integrated onto the existing robotic platform to perform advanced manufacturing operations and develop new techniques and processes. Technologies, techniques and processes developed using this research-oriented system could then be transitioned to the broader composites industry.

Rob Martin↗

NASA NTRS2021

Reliability and Safety Assessment of Urban Air Mobility Concept Vehicles

The following work was commissioned by the National Aeronautics and Space Administration (NASA) to guide industry and future regulation related to urban air mobility (UAM). Prior studies compared the relative safety of NASA concept vehicles, Figure ES1, designed for UAM and provided recommendations for industry research, aircraft architectural improvements, and regulatory updates. After the prior study completed, the European Aviation Safety Agency (EASA) released regulatory guidance in the form of a special condition (SC), SC-VTOL-01, for multirotors with distributed propulsion and flight controls (DPFC). The objective of the current work was to develop DPFC architectures that will comply with SC-VTOL-01. Vehicle designs, DPFC architectures, and stability & control (S&C) models were developed to find limitations and trends to guide industry. To guide this task, NASA developed quad, hex, and an octorotor to better define vehicle attributes and trade space. Aircraft for study included electric, hybrid-electric, and turboshaft powerplants and collective and RPM control schemes. Assessments are in terms of the safety level achieved, and/or aircraft component/features needed to meet SC-VTOL-01. The most challenging criteria being the catastrophic failure rate, ≤10-9 catastrophic failures per flight hour, and that no single failures may result in a catastrophic event. A disciplined process was followed, similar to that in Aerospace Recommended Practice (ARP) 4761. A preliminary system safety assessment (PSSA) leveraged prior work as a basis of creating failure rate budgets for system design teams. System designs were updated and iterated upon, working with reliability and safety subject matter experts to develop SC-VTOL-01 compliant designs. Design changes were reflected in updated PSSAs for initial verification of compliance. The DPFC architecture was broken into four system design teams, the (1) flight control system (FCS), (2) drive and power system, (3) thermal management system (TMS), and (4) electrical power and distribution system. The FCS including elements necessary to control the aircraft, drive and power including elements necessary to generate and transmit shaft power, the TMS including elements necessary to maintain temperature limits in all operating environments, and electrical pow-er and distribution including equipment necessary to store and transmit electrical energy. Results found that all aircraft evaluated may have paths to comply with SC-VTOL-01, Figure ES2. However, S&C models showed large power transients that must be addressed and PSSA results show that future work is needed in single load path structures, high voltage power storage and distribution, and in motor/rotor overspeed protection.

Boeing↗

NASA NTRS2021

Microsphere Plutonium-238 Oxide Fuel to Revolutionize New Radioisotope Power Systems and Heat Sources for Planetary Exploration

Microsphere 238PuO2 fuels have potential to provide performance and safety enhancements for future radioisotope heat and power systems (RPS) as well as enable more flexible and compact RPS designs. Improvements in RPS specific power and more flexible geometries were recently investigated by JPL and PNNL as part of a study on cryobot devices for exploring Ocean Worlds. Missions to penetrate ice and explore oceans, such as on Europa, will require RPS with high specific power within the vehicle to provide both heat and power. Such missions will be mass-constrained, and the energy required to penetrate the ice is highly dependent on cryobot size. Therefore, compact RPS geometries are needed to maximize heat and power while minimizing 238Pu inventory. Microsphere-based heat sources are an attractive way to obtain flexible geometries and high volumetric power loadings because they can fill a region of any size and shape provided fuel temperatures are kept below a threshold and launch/re-entry safety are not compromised. The sol-gel technique to produce 238PuO2 microsphere particles for heat sources has the benefit of preventing dust generation, as opposed to the current 238PuO2 powder/pellet processing method, reducing hazards in the fuel fabrication line. Microspheres can also be individually coated to enhance thermal conductivity, and/or reduce the likelihood of 238PuO2 fuel dispersal in an accident. Although PNNL has produced 238PuO2 microspheres using the sol-gel method, the application of coatings and their integrity over time has yet to be investigated. Continued R&D could demonstrate the feasibility of advanced, microspherebased heat sources and provide baseline data for planning future missions requiring new RPS with different heat source configurations.

Fleurial, Jean-Pierre↗

NASA NTRS2022

Investigating Particle-Particle Electrostatic Effects on Charged Lunar Dust Transport via Discrete Element Modeling

NASA surface exploration missions have always seen negative effects of dust including the Apollo missions. The astronaut-witnessed unusual behavior of the dust particles that surround the vehicle after engine cutoff has the potential to have more of an influence on surface systems dust loading than the high velocity lunar rocket plume ejecta in the landing process. The levitation and transport of the fine components of regolith on lunar surface has been linked to electrostatic effects and electric field, but so far there is no accurate model considering the inter-particle electrostatic interactions, especially when the particles are charged by rocket plume or other mechanical interactions due to exploration activities. This study is proposed to investigate the dynamics of charged lunar regolith with a discrete element method (DEM) approach focusing on the inter-particle interactions and contact charge transfer. The grain dynamics is coupled with mechanical and electrical particle interactions, and both short- and long-range interactions between spherical particles are incorporated. A tribo-charging model based on instantaneous collisions between particles is adopted and validated by comparing the simulation results to existing experimental data. Sensitivity analysis is conducted to quantify the effects of initial charge, tribo-charging, and E-field on transport of lunar dust based on JSC-1 simulants with a radius of 50 lm. DEM simulations are also conducted in a near realistic lunar environment with the estimations of initial conditions that shows the difference in position and velocity distributions between charged particles and uncharged particles. The results indicate that the charged dust particles have higher dispersion of position and velocity by several orders of magnitude due to electrostatic effects. This provides a potential explanation for the phenomena of the approximately 30 s dust lofting following Apollo Lunar Module landing.

Lunar dust↗

NASA NTRSDate not supplied

Acoustic Testing of the Joby Aviation Propeller in the National Full-Scale Aerodynamics Complex 40- by 80-Foot Wind Tunnel

The advanced air mobility sector has progressed in recent years with electric vertical take-Off and landing vehicles at the forefront. In response, the NASA Advanced Air Mobility Project has initiated the Advanced Air Mobility National Campaign to partner with industry to progress this emerging market. This resulted in NASA’s Revolutionary Vertical Lift Technology project to participate to progress research efforts for software tool validation for these advanced air mobility vehicle configurations. Noise has been identified as one of the main obstacles to succeeding in this emerging market for community acceptance. To further understand electric vertical take-Off and landing vehicle noise, an isolated Joby Aviation S4 propeller was tested in the National Full-Scale Aerodynamics Complex 40- by 80-Foot Wind Tunnel to aid in providing high quality performance, loads, and acoustic data. Details of test hardware and setup are described with a focus on acoustics, which includes facility, test model, microphone locations, and data acquisition system details. Additionally, the data processing techniques and completed test matrix for acoustic points are provided. To aid in identifying potential acoustic reflections, an acoustic reflection test was performed prior to the start of the test and highlighted the presence of reflections at every microphone location. Acoustic results are provided for various flight regimes for sweeps of blade pitch, RPM, flow angle, and wind speed. These results show an optimum RPM for a specific thrust level for noise, and further reductions in RPM can increase noise levels. This dataset will be used to evaluate and improve computational tools.

Aviation Propeller↗

NASA NTRSDate not supplied

In-Situ Heat Rejection to the Martian Atmosphere

In order to provide in-situ heat rejection to the thin Martian atmosphere, approaches relying on forced convection and buoyancy flow are conceptualized. A convective radiator concept utilizing a fan to draw local atmosphere through an expanded metal foam heat exchanger panel is developed. To provide a pumped fluid loop interface, flow tubes are embedded in the heat exchanger panel and heat is transferred from the tubes to the foam via conduction and subsequently convectively to the environment. To forgo the use of a specialized high throughput fan, a concept utilizing a buoyant chimney tower to draw atmospheric flow through a low pressure drop heat exchanger is also considered. Both concepts may best align with moderate- to high-temperature heat loads that provide a significant delta temperature relative to the ambient atmosphere temperature. While eliminating dust accumulation on radiator surfaces, some type of serviceable filtration or screening may be required to prevent accumulation of dust inside the expanded metal foam heat exchanger for both concepts.

Heat Rejection↗

NASA NTRS1989

Structural analysis of a thermal insulation retainer assembly

In January 1989 an accident occurred in the National Transonic Facility wind tunnel at NASA Langley Research Center that was believed to be caused by the failure of a thermal insulation retainer. A structural analysis of this retainer assembly was performed in order to understand the possible failure mechanisms. Two loading conditions are important and were considered in the analysis. The first is the centrifugal force due to the fact that this retainer is located on the fan drive shaft. The second loading is a differential temperature between the retainer assembly and the underlying shaft. Geometrically nonlinear analysis is required to predict the stiffness of this component and to account for varying contact regions between various components in the assembly. High, local stresses develop in the band part of the assembly near discontinuities under both the centrifugal and thermal loadings. The presence of an aluminum ring during a portion of the part's operating life was found to increase the stresses in other regions of the band. Under the centrifugal load, high bending stresses develop near the intersection of the band with joints in the assembly. These high bending stresses are believed to be the most likely cause for failure of the assembly.

Greene, William H.↗

NASA NTRS1995

Load measurement system with load cell lock-out mechanism

In the frame work of the project Shuttle Plume Impingement Flight Experiment (SPIFEX), a Load Measurement System was developed and fabricated to measure the impingement force of Shuttle Reaction Control System (RCS) jets. The Load Measurement System is a force sensing system that measures any combination of normal and shear forces up to 40 N (9 lbf) in the normal direction and 22 N (5 lbf) in the shear direction with an accuracy of +/- 0.04 N (+/- 0.01 lbf) Since high resolution is required for the force measurement, the Load Measurement System is built with highly sensitive load cells. To protect these fragile load cells in the non-operational mode from being damaged due to flight loads such as launch and landing loads of the Shuttle vehicle, a motor driven device known as the Load Cell Lock-Out Mechanism was built. This Lock-Out Mechanism isolates the load cells from flight loads and re-engages the load cells for the force measurement experiment once in space. With this highly effective protection system, the SPIFEX load measurement experiment was successfully conducted on STS-44 in September 1994 with all load cells operating properly and reading impingement forces as expected.

Le, Thang↗

NASA NTRS1979

A split sphere 60,000 ton press

A split sphere press which can have a total force of 60,000 tons applied to its exterior by a 0.55 GPa hydrostatic pressure vessel is described. The inner anvils are made of tungsten carbide and show considerable plastic deformation under load. Much greater pressures, in the 100 GPa range, are possible if diamond tipped anvils are used. Because of the uniformly loaded multi-anvil arrangement, the diamond tips can be maintained under a high degree of compressive load and therefore prevent fracture which may occur in a conventional opposed anvil arrangement. Press operation on CdS, ZnSe, ZnS, GaP, and BP samples is described, and their resistance versus external pressure on the sphere are plotted.

Wanagel, J.↗

NASA NTRS1988

Development in helicopter tail boom strake applications in the US

The use of a strake or spoiler on a helicopter tail boom to beneficially change helicopter tail boom air loads was suggested in the United States in 1975. The anticipated benefits were a change of tail boom loads to reduce required tail rotor thrust and power and improve directional control. High tail boom air loads experienced by the YAH-64 and described in 1978 led to a wind tunnel investigation of the usefullness of strakes in altering such loads on the AH-64, UH-60, and UH-1 helicopters. The wind tunnel tests of 2-D cross sections of the tail boom of each demonstrated that a strake or strakes would be effective. Several limited test programs with the U.S. Army's OH-58A, AH-64, and UH-60A were conducted which showed the effects of strakes were modest for those helicopters. The most recent flight test program, with a Bell 204B, disclosed that for the 204B the tail boom strake or strakes would provide more than a modest improvement in directional control and reduction in tail rotor power.

Wilson, John C.↗

NASA NTRS1991

Detailed analysis and test correlation of a stiffened composite wing panel

Nonlinear finite element analysis techniques are evaluated by applying them to a realistic aircraft structural component. A wing panel from the V-22 tiltrotor aircraft is chosen because it is a typical modern aircraft structural component for which there is experimental data for comparison of results. From blueprints and drawings supplied by the Bell Helicopter Textron Corporation, a very detailed finite element model containing 2284 9-node Assumed Natural-Coordinate Strain (ANS) elements was generated. A novel solution strategy which accounts for geometric nonlinearity through the use of corotating element reference frames and nonlinear strain displacements relations is used to analyze this detailed model. Results from linear analyses using the same finite element model are presented in order to illustrate the advantages and costs of the nonlinear analysis as compared with the more traditional linear analysis. Strain predictions from both the linear and nonlinear stress analyses are shown to compare well with experimental data up through the Design Ultimate Load (DUL) of the panel. However, due to the extreme nonlinear response of the panel, the linear analysis was not accurate at loads above the DUL. The nonlinear analysis more accurately predicted the strain at high values of applied load, and even predicted complicated nonlinear response characteristics, such as load reversals, at the observed failure load of the test panel. In order to understand the failure mechanism of the panel, buckling and first ply failure analyses were performed. The buckling load was 17 percent above the observed failure load while first ply failure analyses indicated significant material damage at and below the observed failure load.

Davis, D. Dale, Jr.↗