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This document reports the research performed to construct a model capable of predicting the damage development caused by out-of-plane static loading in laminated graphite/epoxy composite plates.
The state of the art and recent developments in the field of composite material damage mechanics are reviewed, with emphasis on damage accumulation. The kinetics of damage accumulation are considered with emphasis on the general accumulation of discrete local damage events such as single or multiple fiber fractures or microcrack formation. The issues addressed include: how to define strength in the presence of widely distributed damage, and how to combine mechanical representations in order to predict the damage tolerance and life of engineering components. It is shown that a damage mechanics approach can be related to the thermodynamics of the damage accumulation processes in composite laminates subjected to mechanical loading and environmental conditions over long periods of time.
Modern durability and damage tolerance predictions for composite material systems rely on accurate estimates of the local stress and material states for each of the constituents, as well as the manner in which the constituents interact. In this work, an number of approaches to estimating the stress states and interactions are developed. First, an elasticity solution is presented for the problem of a penny-shaped crack in an N-phase composite material system opened by a prescribed normal pressure. The stress state around such a crack is then used to estimate the stress concentrations due to adjacent fiber fractures in composite materials. The resulting stress concentrations are then used to estimate the tensile strength of the composite. The predicted results are compared with experimental values. In addition, a cumulative damage model for fatigue is presented. Modifications to the model are made to include the effects of variable amplitude loading. These modifications are based upon the use of remaining strength as a damage metric and the definition of an equivalent generalized time. The model is initially validated using results from the literature. Also, experimental data from APC-2 laminates and IM7/K3B laminates are used in the model. The use of such data for notched laminates requires the use of an effective hole size, which is calculated based upon strain distribution measurements. Measured remaining strengths after fatigue loading are compared with the predicted values for specimens fatigued at room temperature and 350 F (177 C).
The translaminate fracture behavior of carbon/epoxy structural laminates with through-penetration notches was investigated to develop a residual strength prediction methodology for composite structures. An experimental characterization of several composite materials systems revealed a fracture resistance behavior that was very similar to the R-curve behavior exhibited by ductile metals. Fractographic examinations led to the postulate that the damage growth resistance was primarily due to fractured fibers in the principal load-carrying plies being bridged by intact fibers of the adjacent plies. The load transfer associated with this bridging mechanism suggests that a progressive damage analysis methodology will be appropriate for predicting the residual strength of laminates with through-penetration notches. A progressive damage methodology developed by the authors was used to predict the initiation and growth of matrix cracks and fiber fracture. Most of the residual strength predictions for different panel widths, notch lengths, and material systems were within about 10% of the experimental failure loads.
The goal of damage mitigating control in reusable rocket engines is to achieve high performance with increased durability of mechanical structures such that functional lives of the critical components are increased. The major benefit is an increase in structural durability with no significant loss of performance. This report investigates the feasibility of damage mitigating control of reusable rocket engines. Phenomenological models of creep and thermo-mechanical fatigue damage have been formulated in the state-variable setting such that these models can be combined with the plant model of a reusable rocket engine, such as the Space Shuttle Main Engine (SSME), for synthesizing an optimal control policy. Specifically, a creep damage model of the main thrust chamber wall is analytically derived based on the theories of sandwich beam and viscoplasticity. This model characterizes progressive bulging-out and incremental thinning of the coolant channel ligament leading to its eventual failure by tensile rupture. The objective is to generate a closed form solution of the wall thin-out phenomenon in real time where the ligament geometry is continuously updated to account for the resulting deformation. The results are in agreement with those obtained from the finite element analyses and experimental observation for both Oxygen Free High Conductivity (OFHC) copper and a copper-zerconium-silver alloy called NARloy-Z. Due to its computational efficiency, this damage model is suitable for on-line applications of life prediction and damage mitigating control, and also permits parametric studies for off-line synthesis of damage mitigating control systems. The results are presented to demonstrate the potential of life extension of reusable rocket engines via damage mitigating control. The control system has also been simulated on a testbed to observe how the damage at different critical points can be traded off without any significant loss of engine performance. The research work reported here is built upon concepts derived from the disciplines of Controls, Thermo-fluids, Structures, and Materials. The concept of damage mitigation, as presented in this report, is not restricted to control of rocket engines. It can be applied to any system where structural durability is an important issue.
Lightning is a major cause of damage in laminated composite aerospace structures during flight. Due to the dielectric nature of Carbon fiber reinforced polymers (CFRPs), the high energy induced by lightning strike transforms into extreme, localized surface temperature accompanied with a high-pressure shockwave resulting in extensive damage. It is crucial to develop a numerical tool capable of predicting the damage induced from a lightning strike to supplement extremely expensive lightning experiments. Delamination is one of the most significant failure modes resulting from a lightning strike. It can be extended well beyond the visible damage zone, and requires sophisticated techniques and equipment to detect. A popular technique used to model delamination is the cohesive zone approach. Since the loading induced from a lightning strike event is assumed to consist of extreme localized heating, the cohesive zone formulation should additionally account for temperature effects. However, the sensitivity to this dependency remains unknown. Therefore, the major focus point of this work is to investigate the importance of this dependency via defining various temperature dependency profiles for the cohesive zone properties, and analyzing the corresponding delamination area. Thus, a detailed numerical model consisting of multidirectional composite plies with temperature-dependent cohesive elements in between is subjected to lightning (excessive amount of heat and pressure) and delamination/damage expansion is studied under specified conditions.
NASA is developing graphite/epoxy filament-wound cases for solid rocket motors of the space shuttle. They are wet-wound with AS4W graphite fiber and HBRF-55A epoxy. The membrane region is about 1.4 inches thick. Two 30-inch-diameter by 12-inch-long cylinders were impacted every two inches of circumference with 1/2-inch radius impactors that were dropped from various heights. One cylinder was empty and the other was filled with inert propellant. Two-inch-wide test specimens were cut from the cylinders. Each was centered on an impact site. The specimens were x-rayed and loaded to failure in uniaxial tension. Rigid body mechanics and the Hertz law were used to predict impact force, local deformations, contact diameters, and contact pressures. The depth of impact damage was predicted using Love's solution for pressure applied on part of the boundary of a semi-infinite body. The predictions were reasonably good. The strengths of the impacted specimens were reduced by as much as 37 percent without visible surface damage. Even the radiographs did not reveal the nonvisible damage.
Impacters of various masses were dropped from various heights onto thick graphite/epoxy filament-wound cylinders. The cylinders represented filament-wound cases made for the booster motors of the Space Shuttle. Tups of various shapes were affixed to the impacters. Some of the cylinders were filled with inert propellant, and some were empty. The cylinders were impacted numerous times around the circumference and then cut into tension coupons, each containing an impact site. The size of the damage and the residual tension strength were measured. For hemispherical tups, strength was reduced as much as 30 percent by nonvisible damage. The damage consisted of matrix cracking and broken fibers. Analytical methods were used to predict the damage and residual tension strength. A factor of safety to account for nonvisible damage was determined. For corner and rod shaped tups, any damage that resulted in strength loss was readily visible.
The electric resistance of woven SiC fiber reinforced SiC matrix composites were measured under tensile loading conditions. The results show that the electrical resistance is closely related to damage and that real-time information about the damage state can be obtained through monitoring of the resistance. Such self-sensing capability provides the possibility of on-board/in-situ damage detection or inspection of a component during "down time". The correlation of damage with appropriate failure mechanism can then be applied to accurate life prediction for high-temperature ceramic matrix composites.
Windows in the International Space Station are subjected to on-going micrometeoroid and orbital debris damage (MMOD). The reliability of the windows is being ensured by monitoring of damage, life prediction, and measurement of the residual strength of man-made and natural hypervelocity impact damage. The residual strength of man-made craters and MMOD craters harvested from space shuttle windows were used to estimate strength as a function of damage dimensions and thereby derive design allowables for U.S. and Russian fused silicas used in the ISS. US and Russian silica exhibit similar mechanical properties. An effect of impact angle is apparent, with 0o impacts exhibiting the lowest strength for Russian quartz-derived silica. The crater morphology for fused silica consists of a central pit, crush zone, shallow rings and radial cracks dividing petaloids. Morphology of alkaline glass is different from than that of fused silica, with a more distinct pit and pulverized region, and bell and tail-like features below the pit.
A technique was developed to calculate the stress intensity factor for multiple interacting cracks. The analysis was verified through comparison with accepted methods of calculating stress intensity factors. The technique was incorporated into a fatigue crack growth prediction model and used to predict the fatigue crack growth life for multiple-site damage (MSD). The analysis was verified through comparison with experiments conducted on uniaxially loaded flat panels with multiple cracks. Configuration with nearly equal and unequal crack distribution were examined. The fatigue crack growth predictions agreed within 20 percent of the experimental lives for all crack configurations considered.
The effects of stresses induced by the lamination of off-axis plies to O-deg lamina on the development of damage during the fatigue loading of the O-deg plies are discussed. The transverse normal stresses in the plane of the laminae and the laminate created by the laminating constraints when an axial force is applied to the laminate are calculated in terms of a differential Poisson ratio between the ply in question in the unconstrained and constrained states, and significant differences in the constraint environments of an unnotched specimen joined to plies of 45 and 90 deg inclination are noted which correspond to an increase in longitudinal splitting in the 90 deg case and a marked decrease in longitudinal splitting in the 45 deg case. If a notch is present, shear and crack-opening damage is found to be very effectively suppressed in 45-deg laminates, and less so in the 90-deg case. It is pointed out that whereas the 45-deg laminate represents the least damage situation, it does not have the greatest notched strength. It is concluded that an understanding and prediction of damage development in laminates requires knowledge of the stress fields caused by the lamination constraints.
The equations of motion are developed for laminated composite beams with load-induced matrix cracking. The damage is accounted for by utilizing internal state variables. The net result of these variables on the field equations is the introduction of both enhanced damping, and degraded stiffness. Both quantities are history dependent and spatially variable, thus resulting in nonlinear equations of motion. It is explained briefly how these equations may be quasi-linearized for laminated polymeric composites under certain types of structural loading. The coupled heat conduction equation is developed, and it is shown that an enhanced Zener damping effect is produced by the introduction of microstructural damage. The resulting equations are utilized to demonstrate how damage dependent material properties may be obtained from dynamic experiments. Finaly, experimental results are compared to model predictions for several composite layups.
NASA and the European Space Agency (ESA) are currently planning the Mars Sample Return campaign, comprising missions whose combined objective is to bring the first samples of Mars material back to Earth for detailed study. At present, the NASA-ESA plan is to return samples to Earth using three missions to be launched over the next 5-10 years. The final component, the Earth Entry System (EES), is intended to bring the Mars samples back to the Earth, where it will land following safe entry through the Earth's atmosphere. There is a concern regarding the risk of biological contamination of the Earth’s biosphere from returned Martian samples if, for example, the structural integrity of the EES were compromised during its return mission due to a perforation of a critical surface resulting from a high-speed meteoroid impact. To assess the risks associated with such an event, NASA is developing equations that predict the damage that various EES elements will sustain as a result of such an impact, as well as equations that predict whether or not a particular system will sustain a critical failure following such an impact. In this paper, we review recent progress in the development of such equations for the EES forebody and the EES aftbody, the two elements of the EES that are most exposed to the meteoroid environment. Limitations of the BLEs are also discussed, which can also be used to further inform the next steps in the BLE development.
The first year included a study of the non-visible damage of composite overwrapped pressure vessels with B. Poe of the Materials Branch of Nasa-Langley. Early determinations showed a clear reduction in non-visible damage for thin COPVs when partially pressurized rather than unpressurized. Literature searches on Thicker-wall COPVs revealed surface damage but clearly visible. Analysis of current Analytic modeling indicated that that current COPV models lacked sufficient thickness corrections to predict impact damage. After a comprehensive study of available published data and numerous numerical studies based on observed data from Langley, the analytic framework for modeling the behavior was determined lacking and both Poe and Bogan suggested any short term (3yr) result for Jove would be overly ambitious and emphasis should be placed on transverse shear moduli studies. Transverse shear moduli determination is relevant to the study of fatigue, fracture and aging effects in composite structures. Based on the techniques developed by Daniel & Tsai, Bogan and Gates determined to verify the results for K3B and 8320. A detailed analytic and experimental plan was established and carried out that included variations in layup, width, thickness, and length. As well as loading rate variations to determine effects and relaxation moduli. The additional axial loads during the torsion testing were studied as was the placement of gages along the composite specimen. Of the proposed tasks, all of tasks I and 2 were completed with presentations given at Langley, SEM conferences and ASME/AIAA conferences. Sensitivity issues with the technique associated with the use of servohydraulic test systems for applying the torsional load to the composite specimen limited the torsion range for predictable and repeatable transverse shear properties. Bogan and Gates determined to diverge on research efforts with Gates continuing the experimental testing at Langley and Bogan modeling the apparent non-linear behavior at low torque & angles apparent from the tests.
Continuum Damage Mechanics (CDM) based progressive damage and failure analysis (PDFA) methods have demonstrated success in a variety of finite element analysis (FEA) implementations. However, the technical maturity of CDM codes has not yet been proven for the full design space of composite materials in aerospace applications. CDM-based approaches represent the presence of damage by changing the local material stiffness definitions and without updating the original mesh or element integration schemes. Without discretely representing cracks and their paths through the mesh, damage in models with CDM-based materials is often distributed in a region of partially damaged elements ahead of stress concentrations. Having a series of discrete matrix cracks represented by a softened region may affect predictions of damage propagation and, thus, structural failure. This issue can be mitigated by restricting matrix damage development to discrete, fiber-aligned rows of elements; hence CDM-based matrix cracks can be implemented to be more representative of discrete matrix cracks. This paper evaluates the effect of restricting CDM matrix crack development to discrete, fiber-aligned rows where the spacing of these rows is controlled by a user-defined crack spacing parameter. Initially, the effect of incrementally increasing matrix crack spacing in a unidirectional center notch coupon is evaluated. Then, the lessons learned from the center notch specimen are applied to open-hole compression finite element models. Results are compared to test data, and the limitations, successes, and potential of the matrix crack spacing approach are discussed.
Predictions of radiation damage for Low Earth Orbit (LEO) satellites now use semi-empirical models developed from prior satellite data. From these models it is clear that the low field strength of the South Atlantic Anomaly (SAA) controls where the maximum radiation damage occurs. One may make an estimate of future radiation damage to LEO spacecraft if one can predict the future of the SAA. Although reliable maps of the geomagnetic field strength and its secular change have only been made in the last few decades, certain geomagnetic observatories in South America and Africa have recorded the geomagnetic field for a much longer time. These observatories show that the present geomagnetic field change has persisted for more than 100 years. In spite of the fact that a few observatories have shown sudden changes in secular variation, those around the SAA have shown a stable secular variation. Assuming that this will continue for the next 50 to 100 years one can show that the SAA will expand to cover most of the South Atlantic Ocean and will become much weaker. This will greatly intensify the radiation hazard in LEO, put significant new limitations on radiation-hardened hardware, severely restrict the length of time that humans can remain in orbit, and materially change the configuration of the radiation belts.
The purpose was to characterize damage initiation and growth in notched titanium matrix composites at room temperature. Double edge notched or center open hole SCS-6/Ti-15-3 specimens containing 0 deg plies or containing both 0 and 90 deg plies were fatigued. The specimens were tested in the as-fabricated (ASF) and in heat-treated conditions. A local strain criterion using unnotched specimen fatigue data was successful in predicting fatigue damage initiation. The initiation stress level was accurately predicted for both a double edge notched unidirectional specimen and a cross-plied center hole specimen. The fatigue produced long multiple cracks growing from the notches. These fatigue cracks were only in the matrix material and did not break the fibers in their path. The combination of matrix cracking and fiber/matrix debonding appears to greatly reduce the stress concentration around the notches. The laminates that were heat treated showed a different crack growth pattern. In the ASF specimens, matrix cracks had a more tortuous path and showed considerable more crack branching. For the same specimen geometry and cyclic stress, the (0/90/0) laminate with a hole had far superior fatigue resistance than the matrix only specimen with a hole.