Harwood
Engineering Company, Inc.
Harwood
Engineering Company, Inc.
If spheres of the same material and of equal radii are brought into
contact under pressure, their interface is plane and, when loaded within
the elastic limit, the pressure distribution at the interface can be represented
by a hemispherical surface (4)3. When loaded to destruction,
they rupture in a predictable way. This predictability is the basis of
a testing procedure recommended by the AFBMA4 for quality control.
A stack of three spheres is crushed between the platens of a press as shown
in Figure 2. Usually, the middle sphere shatters
first. The load required to rupture spheres of the same material and hardness,
but of various diameters, is related: F=KD2, where F is the
load required to rupture; K is a constant depending on the material, its
condition, and the units used; and D is the diameter of the spheres. It
is difficult to harden large spheres as effectively as small ones. This
fact is reflected in smaller values of K for larger sizes. The steel most
commonly used in ball bearings is SAE 52100 hardened to 61 to 67 Rockwell
"C." The AFBMA recommends the minimum acceptable crushing loads shown in
Table 1, and correlated therewith are the corresponding values of K.
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For the spheres to be useful as anvils, it is not only necessary to grind anvil faces, but also to take means to prevent the spheres from rotating under load and to register them on parallel press platens so that the anvil faces will meet properly. Two methods have been used. The first uses a massive support of relatively soft materials, e.g., steel bar stock, Figure 3, in which the spheres are provided with spherical seats. A hole slightly smaller than the diameter of the sphere is initially bored in the face of the steel block to a depth of about two-thirds of the radius of the sphere. The sphere is then pressed into place. In this way, and autofrettaged support is provided. Note that the spheres have been slightly flatted, as at a, so that the final embossment into their seats will key them against rotation. It is possible that the spheres might resist rotation sufficiently without the flats if they were held in position by suitable cement, epoxy, for instance. The anvil faces are then ground parallel with the bases of the supports. The other method, Figure 4, simply provides flatted bases on the spheres parallel to the anvil faces but larger in diameter by a factor of 2½ to 3.
Crushing loads of the anvil-faced spheres have been measured by simply loading pairs of them to destruction. For selected sphere diameters, various diameters of anvil face were used. It was found that the load-carrying capacity of a given sphere increased linearly with the diameter of the anvil face. The data illustrated in Figure 5 was for SAE 52100 hardened steel spheres as they were produced commercially for use in ball bearings. The fracture pattern, Figure 6, was interesting in that the fragments would include a conical piece, the base of which had been the anvil flat. Rupture in the shear along the slant height of the cone allowed it to wedge itself into the sphere which apparently broke in tension from internal pressure along radial paths to form three or four segments. The fragmentation and the energy released at rupture make it very apparent that anvil devices should be shielded to protect personnel. Since the yield strength and tensile strength of steel at the hardness used in these spheres are nearly the same, it follows that the yielding and the rupture loads of the anvils must be nearly the same.
A virtue of the spherical anvil is that it is relatively inexpensive and, therefore, more expendable. Spheres are available commercially in a fairly wide variety of materials and sizes. The commonly used SAE 52100 steel is limited in usefulness by its low draw temperature and by relatively poor hardenability, making the larger sizes softer than the smaller. Spheres are available in many maraging, stainless, and tool steels and in other alloys which have better high-temperature properties. Spheres made of glass, sintered sapphire, ceramics, stellite, and various carbides are also available. The glass anvils make it possible to study larger samples and to photograph pressure phenomena in much the same way that Van Valkenburg (5), Weir (6), and their associates have been doing with diamond anvils, although at less pressure. Some manufacturers will make spheres of useful materials in relatively small quantities.
Riecker (7), using apparatus supplied by Harwood Engineering, has been using spherical anvils in his studies of the shearing strength of minerals and elements at elevated temperature and pressure, and at various shear rates. This apparatus, Figure 3, lent itself because of the shape of the spherical anvils and their support blocks, to the use of a high-frequency heating loop, b, surrounding the anvils at the level of the specimen, c. The high-frequency heating technique allows very fast and localized heating. Riecker has made approximately 2000 runs (8), reaching 60 kbar at 1000° C and over 100 kbar with metals and with strain rates from 10-4 to 10-1. In the course of this, he has experimented with many different kinds of anvil materials. At the present time, he has generally settled for three of these, his choice for a given experiment being dependent upon the temperature planned for a particular run and the nature of the sample. These materials are:
A special application of spherical anvils is shown in an apparatus, Figure 7, designed to use ultrasonic techniques (9, 10) to measure the effect of pressure on Young's modulus and Poisson's ratio. The anvils, a, and annular closures, b, are carefully flatted so that a pressure seal is effected surrounding the unsupported area of the anvil base. The oscillator plates, c, are held against the base of the anvils by springs and the electrical leads are brought out through the bore of the closures. The specimen, d, is loaded between the anvils and is surrounded at the same time by arbitrarily chosen environmental pressure, hydrostatic. The press not only has to supply the axial load to the specimen, but must also resist the thrust of the environmental pressure against the closures and overcome the friction of the packings in the moving closure, e.
In this apparatus, one anvil is used as a load cell. Strain gages, f, mounted longitudinally on an anvil register compressive strains, while in the transverse direction, they show tension strains. Two tension and two compression gages wired together to form a bridge make a very practical load cell. The use of a full bridge essentially eliminates errors due to eccentric loading. Electrical leads from the bridge are brought through the bottom closure in a routine way.
The range of pressure of this equipment is appreciably extended by the use of high environmental pressure. Griggs (11) and Balsley (12) in experiments to about 12 kbar reported remarkable increases in the compressive strengths of polycrystalline limestone and marble and moderate increase for calcite single crystals. Bridgman (13) in extensive experiments encompassing such brittle materials as tungsten carbide, quartz, sapphire, and Pyrex glass, as well as many varieties of steel and other metals, found, with the possible singe exception of cast iron, that both tensile and compressive strength, as well as ductility increased with environmental pressure. He applied this effect in extending his compressibility measurements from 50 to 100 kbar (14) by enclosing a miniature piston and cylinder of carboloy within the tapered cylinder of his 30-kbar apparatus in which the pressure was developed by piston stroke to the level of 25 to 30 kbar. In the present case, fluid at a maximum of 14 kbar from a separate compressor is introduced laterally through a port in the vessel wall. While the present apparatus was designed for uniaxial loading of solid specimens to 7½ tons (the press jack is rated at 500 tons), with super-imposed environmental pressure, it could readily be adapted for compressibility measurements on specimens much larger than those used by Bridgman, for instance, rock samples, which should be above a minimum size in order to be of significance.
A much simpler device wherein the sample is under pressure is provided
lateral support is illustrated in Figure 8. This
strongly resembles the well-known "belt" or "girdle" (15), with
the distinction that the anvils are spheres, shown here spherically supported.
The authors have not yet had occasion to exploit this device.
Thick-walled spherical vessels, subjected to internal and external pressures, develop stress patterns not unlike those of thick-walled cylinders loaded in the same way, except that the equations involve third- rather than second-order functions, due to Lamé (17).
The equations are, respectively, for tangential stress at the inner
surface, with internal pressure (4)5
where st is the tangential stress,
r is the pressure, and w
is the ratio of the outer to the inner radius. the advantages of the sphere
are obvious.
There are other advantages to the use of the hemispherical configuration. It lends itself to scale-up more than other similar devices, because less motion is required of the piston for a given change in volume. For instance, comparing the strokes required to compress equal volumes to the same pressure in cylindrical and hemispherical cavities, it will be found that the stroke is three halves greater in the first case.
It appears that there is a field where this type of apparatus is of advantage, indicated by considerations of expense, pressure range, and size of the sample.
