D.H. Lammlein PhD Dissertation - Vanderbilt University

curvature. These geometries are used extensively in aerospace vehicles, in nautical
vessels, and in pressure vessels. In this work, friction stir welding is applied to the joining
of two small diameter, thin-walled, hollow hemispheres. This geometry presents a case of
practical significance with both a high degree of curvature (relative to the dimensions of
the tool and work material) and dual curvature. FSW of small diameter hemispheres is
not present in the literature, although a collaboration led by Lawrence Livermore
National Lab has joined pairs of aluminum alloy hemispherical forgings of approximately
40” diameter by FSW [2]. In the work presented here, the radius of curvature is an order
of magnitude smaller and the surface curvature is correspondingly greater.
The sphere has less surface area than that of any equivalent geometric volume.
The hollow sphere can withstand both external and internal pressures (as a spherical
pressure vessel) more efficiently than any other geometry, and consequently fuel tanks,
gas storage vessels, pneumatic reservoirs, and submarine vessels often utilize this shape.
Metal spheres are additionally used as precision bearings in mass properties test
equipment and aerospace attitude control system testing equipment [3,4].
The applications of spherical pressure vessels are manifold and pervasive. They
are found in industrial applications (oil refineries, petrochemical plants [5], nuclear
power plants, communication satellites [6], and propane tanks), space vehicles
(propellant tanks [6], oxygen tanks, and water tanks), underwater applications (submarine
vehicles, flotation elements, tanks, and buoys), and military applications (UAV's,
projectiles, torpedoes, ships, aircraft, and nosecones [8]). Spherical pressure vessels are
commonly made of steel, titanium, aluminum, inconel, fiber reinforced polymer (e.g.
carbon fiber reinforced polymer [9] or kevlar reinforced polymer), or some combination
of these materials. Ceramics and glass are also used for applications subject to external
compression [10].
In the case of metals, the geometry does not permit a single forged, cast, or
machined piece of material and the sections must be joined together by some secondary
means. In the case of steel, sections are welded together by conventional means or joined
by fastener and gasket [11,12,13]. Fastener and gasket joining can be used in applications
where weight and size are not a consideration, as fasteners and flanges add considerable
weight and bulk to the vessel. Despite its high cost, titanium is used heavily in aerospace
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