All engineering components and structures contain geometrical discontinuities – threaded connections, windows in aircraft fuselages, keyways in shaft, teeth of gear wheels, etc. The size and shape of these features are important since they determine the strength of the artifact. Conventionally, the strength of components or structures containing defects is assessed by evaluating the stress concentration caused by the discontinuity features. However, such a conventional approach would give erroneous answers if the geometrical discontinuity features have very sharp radii. To illustrate this point, consider the following four cases:
The thickness of each plate is the same. The forces required to break the four samples can be arranged in the following order:
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The three fracture modes.
There are three ways of applying a force to enable a crack to propagate:
• Mode I crack - Opening mode (a tensile stress normal to the plane of the crack)
• Mode II crack - Sliding mode (a shear stress acting parallel to the plane of the crack and perpendicular to the crack front)
• Mode III crack - Tearing mode (a shear stress acting parallel to the plane of the crack and parallel to the crack front)
We must note that the expression for KI in Eq (2.1) will be different for geometries other than the center cracked plate, as discussed in the article on stress intensity. Consequently, it is necessary to introduce a dimensionless correction factor, Y, in order to characterise the geometry. We thus have:
(2.4)
where Y is a function of the crack length and width of sheet given by:
(2.5)
for a sheet of finite width W containing a through-thickness crack of length 2a, or
(2.6)
for a sheet of finite width W containing a through-thickness edge crack of length a
Nanotechnology for Defence
Research into nanotechnology devices for aeronautics applications should investigate bonding of dissimilar materials, material properties, and scaling. Industry would greatly benefit from any technology that improved the ability to bond dissimilar materials. Microelectromechanical systems (MEMS) research is investigating the ability to create strong bonds between (1) silicon and silicon and (2) silicon and other materials, and the committee is hopeful that nanotechnology research might someday lead to material bonding methodologies for critical aviation applications. Nanotechnology may lead to the development of new structural materials with high strength-to-weight ratios and fracture toughness, durable coatings, greater resistance to corrosion, self-healing, and multifunctional characteristics. For example, structural materials might have embedded sensors and actuators; custom-designed properties, such as electrical conductivity, mechanical strength, magnetic behavior, and optical properties; or improved damping properties. Multimode damping could lead to the elimination of swash plates in helicopter rotors, which would be a major design breakthrough, and greatly reduced fatigue failure in turbofan blade applications. Self-healing materials (e.g., materials embedded with small particles of liquid that would be released and fill in cracks to prevent them from propagating) may allow flying aircraft closer to their fatigue limits, but generally the benefits of self-healing are likely to be greatly exceeded by the benefits of increased strength and reduced weight. The properties that nanomaterials demonstrate at nanoscales do not necessarily predict the properties of macroscale materials that incorporate nanomaterials. For example, nano-microtubes have heat-transfer rates comparable to that of diamonds, but more research is needed to assess the ability of nanotubes to increase the heat transfer capabilities of structural materials. Also, segments of some nanotechnology fibers are on the order of 30 times stronger than glass fibers.
Rolled homogeneous armour, or RHA, is a theoretical basic type of steel plate, used as a baseline to compare the effectiveness of military vehicle armour. This can be used to protect the vehicles from spalls or blasts. Through the end of World War II, the type of armour for almost all tanks and other armoured vehicles was sheets of steel. Increasing the protection on a vehicle meant adding thicker sheets of steel, increasing the vehicle's weight and reducing its mobility. Since then, other forms of armour, incorporating empty spaces and materials such as ceramics or depleted uranium in addition to steel, have been developed. Made ineffective by modern weapons using high-impact or high-temperature cutting jets, RHA itself is obsolete due to advances in vehicle armor. The more recent term RHAe (Rolled Homogeneous Armour equivalency) is used when giving a rough estimate of either the penetrative capability of a projectile or the protective capability of a type of armour which may or may not be steel.
There are many recent advances in making RHA steel stronger and lighter in weight. There came many substitutes and still much of research is going on in this field. Carbon nanotubes (CNTs) are allotropes of carbon. A single-walled carbon nanotube (SWNT) is a one-atom thick sheet of graphite (called graphene) rolled up into a seamless cylinder with diameter on the order of a nanometer. This results in a nanostructure where the length-to-diameter ratio exceeds 1,000,000. Such cylindrical carbon molecules have novel properties that make them potentially useful in many applications in nanotechnology, electronics, optics and other fields of materials science. They exhibit extraordinary strength and unique electrical properties, and are efficient conductors of heat. Inorganic nanotubes have also been synthesized. Nanocomposites are materials that are created by introducing nanoparticulates (often referred to as filler) into a macroscopic sample material (often referred to as the matrix). This is part of the growing field of nanotechnology. After adding nanoparticulates to the matrix material, the resulting nanocomposite may exhibit drastically enhanced properties. For example, adding carbon nanotubes tends to drastically add to the electrical and thermal conductivity. Other kinds of nanoparticulates may result in enhanced optical properties, dielectric properties or mechanical properties such as stiffness and strength. In general, the nanosubstance is dispersed into the matrix during processing. The percentage by weight (called mass fraction) of the nanoparticulates introduced is able to remain very low (on the order of 0.5% to 5%) due to the incredibly high surface area to volume ratio of nanoparticulates. Much research is going into developing more efficient combinations of matrix and filler materials and into better controlling the production process.
Conclusion
The potential posed by nanoscience and technology is enormous, but how, when, and the extent to which this potential will be realized are impossible to predict, and the specifics of predictions become more uncertain the farther they are extended into the future (NRC, 002d). It is especially difficult to determine how the application of nanotechnology may improve top-level characteristics such as overall aircraft performance or the safety of the air transportation system. To date, nanotechnology has been very successful in some devices, but not in devices large enough and robust enough to be directly applicable to commercial aviation. Major advances in the application of nanotechnology are likely to depend upon the ability to integrate nanotechnology fibers and features in intelligent ways to create macroscale materials with specific desired properties. Fracture mechanics as a subject for critical study has barely been around for a century and thus is relatively new. Ultimately, the success of Fracture mechanics and nanotechnology rests upon the development of successful commercial products.
References
Fracture Mechanics, fundamentals and applications, by Anderson T.L, CRC Press
Ganesh Thiagarajan, Jimmy K. Hsia and Yonggang Huang (2003).“Finite Element Implementation of Virtual Internal Bond Model for Crack Behavior Simulation.” Engineering Fracture Mechanics, In Press..
www.wikipedia.org
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