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By E. C. Burke, W. R. Hibbard

G. B. Craig (University of Toronto, Toronto, O,nt., Canada)—The advent of pyramidal slip at room temperatures in a magnesium crystal (M2,) and the very low value reported for the critical shear stress are puzzling. Table I1 shows the calculated values (approximate) for sin x cos I in this specimen if all the (10l) planes are considered. If So is the shear stress resolved in the direction of glide, on the glide plane, and U, is the stress operative in yield point tests, then: S,, — 325 (0.169) 55gpersqmm (approximately) for 1101: S,, = 325 (0.465) = 151 gpersqmm (approximately) for (0001): S,, — 325 (0.101) - 32.8 gpersqmm (approximately) Thus, we see the pyramidal plane in which the minimum shearing component operated. Barrett"' stated: "Experiments have repeatedly shown that, when there are several crystallographically equivalent slip systems in a crystal, the one having the greatest resolved shear stress will become active. ..." It does not appear to me that the measurements given are conclusive proof that pyramidal slip operated. E. C. Burke and W. R. Hibbard, Jr. (authors' reply) —Although the low value for the critical resolved shear stress for pyramidal slip may be puzzling, there does not appear to be any basis for questioning the validity of the measurements. Under the influence of constraints, slip systems having decidedly lower shearing components may become operative, e.g., "cross-slip" or the "forced glide" in magnesium reported by Bakarian. Since we believe that pyramidal slip occurred in the specimen because basal slip was inhibited, it is not too surprising to find an operative plane with a lower shear stress. -7 C. S. Barrett: Structure of Metals U94jl p. 2J6. New York. McGraw-Hill Book Co.

Jan 1, 1953

Mr. Tays (communication to the Secretary): Mr. Wynne's criticism of my paper* brings forward a few points which are really important, and might properly have been considered in the original paper. By calling attention to them he has rendered me a service. It is quite true, as Mr. Wynne says, that, in the tests reported by me, the Bryan mill was always working at a relative disadvantage, and my comparison of the work of this mill with that of the stamp-battery should be interpreted, therefore, so much the more favorably to the mill. Of course, wire screens can be used to advantage on the Bryan mill, if they are not of smaller size than 30-mesh; but

Jan 1, 1902

ROBERT VAN ARSDALE NORRIS, who died at his home at Wilkes-Barre, Pa., on April 20, 1928, was born at Newark, N. J., on May 2, 1864, of parents who were direct descendants of such sterling New Eng-landers as Governor William Bradford, John Alden and Timothy Dwight. He went to the Collegiate School in New York and then to the Colum-bia School of Mines where he graduated with the class of 1885, having among class-mates A. S. Dwight, E. N. En-gelhardt, H. L. Hollis, G. B. Lee, Richard Moldenke, Wil-bur Sanders, Joseph Struth-ers, E. A. Wiltsee, and I. H. Woolson. His marked ability even among so many men of unusual ability caused him to be chosen as assistant to Pro- fessor Munroe in the summer school of mining and survey-ing immediately after gradua-tion, and he shortly after was also inspector of dredging operations on the Maurice River improvement work, Millville, N. J. The follow- ing year he worked in the chemical laboratory of Herman Behr in Brooklyn, and toward the end of 1886 he joined the staff of the Pennsylvania R. R. Coal Co. and the Susquehanna Coal Co. as assistant engineer. Six years later he was made principal assistant en- gineer and in 1900 he was made chief engineer of these companies. In 1904, he withdrew from them and estab- lished an office as a consulting engineer at Wilkes- Barre, later taking his son, Robert V., Jr., into partner- ship with him. They acted as consulting engineers for the coal department of the Delaware, Lackawanna & Western R. R. Co., the Lehigh Valley Coal Co., Coke Bros. & Go., Inc., the coal department of the Pennsyl- vania R. R. Co., the Wilkes-Barre & Hazelton R. R. Co., the Sterling Salt Co., and others, specializing in ex- amination and appraisal of coal properties, and also matters of Federal taxation.

Jan 5, 1928

By E. Buehler, E. Berry

HE magnetic properties of dilute palladium alloys are of fundamental interest.''' Neutron diffraction studies3 have indicated that a better understanding of the behavior of these alloys could be realized with the availability of high-purity single crystals of palladium. Crucible melts of 99.999 pct pure palladium were found inadequate for such research. In a successful effort to fill this need, floating zone refining of palladium was undertaken. In this note the results of the initial experiments are reported. Zoning was accomplished in an argon atmosphere using 450 kc rf generator for an energy source. Samples 5 to 6 mm in diam were suspended in a gastight quartz envelope which could be moved vertically through the rf coil. A nominal upward traverse rate of 1.5 mm per min was maintained during a pass. Close coupling was found to be essential for stable retention of the liquid in the zone. Single crystals averaging 3.5 cm in length were obtained. Laue photography showed them to be continuous single crystals without gross imperfections. Several criteria were used for evaluation of the purity of the zoned material: magnetic behavior, low-temperature specific heat and residual resistivity ratios. Table I shows the residual resistance ratios obtained for two samples, one subjected to a single pass, the other zoned four times. It is appilrent that palladium can be zone refined with the electrically active impurities being transported toward the tail end. A decrease in susceptibility for zone-melted specimens over any previously measured material from 1.5" to 80'~ has been obserted by H. J. Williams and R. C. Sherwood4 substantiating the residual resistance data. The specific heat measurements are currently being made3 and will be published at some later date. Discussions with J. H. Wernick and S. C. Abrahams are acknowledged. We also wish to thank G. F. Brennert for the residual resistance measure ments.

Jan 1, 1962

By Alan U. Seybolt

IN examination of some cold-rolled copper and cupronickel that contained a little columbium, it was discovered that these alloys were unusually resistant to annealing. This effect was sufficiently pronounced to warrant some investigation [ ] of the annealing characteristics of such compositions. EXPERIMENTAL PROCEDURE The alloys were made from cathode copper, electrolytic nickel, and a special copper-columbium hardener alloy furnished by the Electro Metallurgical Corporation. This hardener alloy contained 10 per cent columbium, with tantalum, aluminum and iron as major impurities. The melting was carried out in a clay-graphite crucible in a high-frequency induction furnace, under a charcoal or [ ] electrode carbon cover. No deoxidizing additions were made. The 7-lb. copper heats were poured into a steel mold, hot-rolled to ¼ -in. thickness, and annealed for ½ hr. at 760°C.; the cupronickels were annealed I hr. at 815°C. The material was then cold-rolled to a go per cent reduction in thickness and annealing tests were carried out on this 1/8-in. hard-rolled strip. A little silver was added to copper-columbium alloys 402 and 403 to find out

Jan 1, 1941

By E. O. Wagner, V. F. Parry, W. S. Landers

Development work has shown that the yield of primary tar from coal is proportional to the heat in the volatile matter of the coal and that the yield of tar from noncoking coals may vary from 10 to 45 gal per ton on the ash-free and moisture-free basis. Pilot plant operations have proved that 100 to 135 pct of the bench-scale carbonization-assay yield of tar can be obtained. FOLLOWING investigations by the Denver Bureau of Mines on drying fine coal in the entrained state,'. ' Texas Power & Light Co. employed the fluidized technique to upgrade Texas lignite for use in power plants. Because of the rapidly rising cost of natural gas in Texas the company agreed to cooperate with the Bureau of Mines in studying further the upgrading of lignite by low-temperature carbonization, since potential value of the tar would help offset the cost of fuel. Considerable interest was aroused, therefore, when Aluminum Co. of America decided to use dried lignite in its 240,000-kw power plant at Rockdale, Texas, operated by Texas Power & Light. Carbonization of coal before burning in a power plant is not new. Plants in Germany have been operated for many years on carbonized brown coal and lignite briquets produced in large integrated plants. Large-scale experiments in carbonizing pulverized coal with hot flue gases were made 30 years ago at Milwaukee," and many inventors have proposed other processes. In the U. S., technical and economic problems have prevented successful operation of large plants on carbonized coal. but new techniques of handling solids in fluidized beds may overcome these difficulties, particularly if the higher volatile noncoking coals are used. Any bituminous material will decompose when heated to about 900°F to yield primary tar, gas, and char. The quantity of tar obtained from various coals depends on their rank and volatile content and to some extent on rate and method of heating. The liquid products derived from thermal decomposition of peat, brown coal. lignites, oil shale, and noncoking bituminous coals can be easily liberated by rapidly heating these materials in a fluidized bed at about 500°C (932°F). Since it takes only a few minutes to heat small particles of fuel to carbonizing temperature in a fluidized bed, processing plants can be built to handle up to 50 tph at relatively low cost. The pioneering development work being conducted at Rockdale, Texas, by Alcoa and Texas Power & Light will solve many engineering problems of such operations. The Bureau of Mines at Denver has studied the carbonizing properties of several hundred coals by small scale assay at 500°C, deriving a simple correlation between the potential yield of tar and the proximate analysis. This correlation, shown in Fig. 1, compares the heat in the volatile matter of the coal with the potential yield of primary tar. The yield of primary tar varies from 12 to 50 gal per ton of pure coal." About the same amount of heat is needed to * MAF equals moisture-and-ash-free basis. distil any dry coal at 500°C, and the time required to carbonize a given particle size is about the same for any coal. It is therefore obvious that coals rich in volatile matter will show the greatest profits when processed. Texas lignites are rich in volatile matter, which contributes some 5700 Btu per lb of MAF coal, and the potential primary tar and oil yield from this lignite averages 12 pct by weight or 27 gal per ton from the pure lignite. Texas lignites are considerably richer in potential tar than lignites of North Dakota and Montana. During 1950 the Bureau of Mines conducted many experiments on carbonizing fine dry coal in the entrained state, publishing a report4 n major features of pilot and commercial-size units required to carry out the process. Additional experimental work has been done at Denver and the pilot plant has been improved, particularly the facilities for studying removal of fine dusts from tar vapors and gases at high temperatures by electrostatic precipitation. A number of materials have been carbonized, including sawdust, peat, brown coal, Brazilian oil shale, lignites, and the lower rank bituminous coals having noncoking properties. Straight coking coals cannot

Jan 1, 1957

ALABAMA Anniston.-Carrington, F. G. Auburn.-Brown, R. L. Battelle.-Green, G. G. Bessemer.-Abbott, C. E. Dobbs, G. G. Ferguson, V. Birmingham.-Adams, J. H. Aldrich, T. H. Aldrich, T. H., Jr. Allen, A. W. Bonnyman, J. Bowron, J. Bush, M. W. Crawford, G. G. Crockard, F. H. Ellis, E. E. Fairbairn, C. T. Gallacher, J. Geismer, H. S.

Jan 1, 1917

By AIME AIME

THE Charleston Section of the A. I. M. E. held a joint meeting with the National Coal Association and the American Society of Mechanical Engineers on May 6 and 7, at which 94 members and guests were registered. Mechanical operation of coal mines was the subject discussed. First on the program was a paper entitled "Rock Dusting in the Coal Mines of West Virginia," by R. M. Lambie, chief of the Department of Mines, and Gordon MacVean. It appears in full in the current issue of MINING AND METALLURGY, p. 290. J. E. Jones of the Old Ben Coal Corp. opened this discussion by describing the method of rock dusting employed in the mines of that company, giving many interesting details, incidentally referring to the use of rock dust in fighting mine fires. He described one case where a number of troughs was brought to within 150 ft. of the fire, and rock dust had been thrown in its direction. After each trough had been thrown the party advanced a few feet, where another trough was discharged. About 10 ft. were gained on each advance, until the party found they had advanced completely over the fire.

Jan 1, 1926

By D. R. Irving

Prior to this time, ample supplies of high grade mineral fillers, such as clay, have been available close to consuming centers. Now depletion of these accessible deposits, coupled with other factors such as increasing demand due to population expansion and standard of living rise, has made development of upgrading techniques attractive to producers. Various investigations being carried out by the U.S. Bureau of Mines are described. Factors making the development of improved methods for upgrading clays attractive to producers include: depletion of accessible deposits of high-grade clays, rising transportation and labor costs, more exacting specifications, and increased demand resulting from an expanding population and a constantly rising standard of living. Industry recognizes the need for upgrading presently unusable materials and has cooperated with the U.S. Bureau of Mines by providing samples from submarginal deposits and by evaluating the products that USBM upgrades. Following are some examples of recent clay beneficiation work by the Bureau. FIRE CLAY BENEFICIATION At the Rolla Metallurgical Center, Rolla, Mo., the Bureau is conducting research to develop technically and economically feasible mineral-dressing methods to remove quartz, pyrite, and other impurities from submarginal fire clays. The research has been spurred by the growing shortage of high-grade bur-ley, flint, and plastic clays in the Missouri fire-clay district resulting from increased consumption and the low rate of discovery of new deposits of adequate quality. There apparently is ample tonnage of submarginal flint and plastic clays to maintain the industry for many years if such material can be upgraded to commercial quality. Samples have been submitted to USBM by several major producers of refractories, including A. P. Green Fire Brick Co.; Harbison-Walker Refractories Co.; Mexico Refractories Div., Kaiser Aluminum and Chemical Corp.; and Wellsville Fire Brick Co. Research on some samples has been completed and still is in progress on others. The Bureau has found that specimens containing quartz or pyrite in grains coarser than the accompanying clay generally can be upgraded either with a gravity table or hydraulic cyclone. The improvement in quality is notable not only in chemical analysis but in an increase in pyrometric cone equivalent (PCE) of one or more cones. As an example, consider the results attained on a sandy flint—a fine-grained mixture of kaolin and halloysite with quartz and minor quantities of iron and manganese oxides. Chemical analysis was: 35.4 pct alumina (A12O3) and 47.8 pct silica (SiO2). The sample contained 9.2 pct free silica as quartz. The PCE was 33. The sample was crushed to -10-mesh, blunged with water, and then stage-ground to -48-mesh. The ground sample was tabled to yield a clay fraction containing 37.6 pct A12O3, and 45.3 pct SiO2 of which 2.4 pct was free silica. The PCE was 34. Recovery of alumina by this process was 73.6 pct. Concentration of the same clay in the hydraulic cyclone was even more effective in respect to quartz removal. The clay fraction analyzed 38.6 pct A12O3, 45.0 pct SiO2 of which 0.5 pct was free silica as quartz, and had a PCE of 34. Recovery of alumina was 71.9 pct. The hydraulic cyclone was also effective in reducing the pyrite content of a plastic clay which likewise was a mixture of kaolin and halloysite, plus some pyrite, quartz, and carbonaceous material. It analyzed 30.6 pct Al2O3, 52.3 pct SiO2, 2.3 pct Fe2O3, and 0.76 pct S. The sample was blunged and screened through 10-mesh to remove some coarse pyrite, then ground to -65-mesh and cycloned to remove most of the remainder. The final product recovered 81.8 pct of the alumina at a grade of 32.3 pct A12O3, 50.9 pct SiO2, 1.4 pct Fe2O3, and 0.1 pct S. The PCE was 32-1/2, compared with a PCE of 31-1/2 for the crude clay. The fine beneficiated clays, of course, must be pelletized and dried or fired to meet commercial acceptance. This operation has already been solved by industry. Little progress has been made on two remaining problems. One is that of fine-grained impurities, not separable by table or cyclone. Flotation is being investigated to solve this. Although fine pyrite is readily rejected, a satisfactory quartz-clay separation has not been attained. The second problem, a stubborn one, is that of alkali. Samples containing as much as 5 pct potas-

Jan 1, 1961

By Alan U. Seybolt

In examination of some cold-rolled copper and cupronickel that contained a little columbium, it was discovered that these alloys were unusually resistant to annealing. This effect was suficiently pronounced to warrant some investigation of the annealing characteristics of such compositions. Experimental Procedure The alloys were made from cathode copper, electrolytic nickel, and a special copper-columbium hardener alloy furnished by the Electro Metallurgical Corporation. This hardener alloy contained 10 per cent columbium, with tantalum, aluminum and iron as major impurities. The melting was carried out in a clay-graphite crucible in a high-frequency induction furnace! under a charcoal or electrode carbon cover. No deoxidizing additions were made. The 7-lb. copper heats were poured into a steel mold, hot-rolled to 1/4-in. thickness, and annealed for 56 hr. at 760°C.; the cupronickels were annealed I hr. at 815°C. The material was then cold-rolled to a 50 per cent reduction in thickness and annealing tests were carried out on this 1/8-in. hard-rolled strip. A little silver was added to copper-columbium alloys 402 and 403 to find out

Jan 1, 1942

By Alan U. Seybolt

In examination of some cold-rolled copper and cupronickel that contained a little columbium, it was discovered that these alloys were unusually resistant to annealing. This effect was suficiently pronounced to warrant some investigation of the annealing characteristics of such compositions. Experimental Procedure The alloys were made from cathode copper, electrolytic nickel, and a special copper-columbium hardener alloy furnished by the Electro Metallurgical Corporation. This hardener alloy contained 10 per cent columbium, with tantalum, aluminum and iron as major impurities. The melting was carried out in a clay-graphite crucible in a high-frequency induction furnace! under a charcoal or electrode carbon cover. No deoxidizing additions were made. The 7-lb. copper heats were poured into a steel mold, hot-rolled to 1/4-in. thickness, and annealed for 56 hr. at 760°C.; the cupronickels were annealed I hr. at 815°C. The material was then cold-rolled to a 50 per cent reduction in thickness and annealing tests were carried out on this 1/8-in. hard-rolled strip. A little silver was added to copper-columbium alloys 402 and 403 to find out

Jan 1, 1942

By John B. Hastings

Ten miles from Hartsel, near Antelope springs, in Park county, Colorado, there is a large area of unconsolidated lake-beds, which are interesting because at least a part of the lacustrine sands contains in the aggregate an immense amount of gold. During 1906, one of the arms of this dessicated lake was fairly well prospected with shafts and cuts by an Eastern company to test its value, as favorable amounts of gold had in some instances been found upon it. The claims of the company contain about 5,000 acres of the beds; bat this is only a small portion of them, a south branch from a main body, which is at least 7 miles in diameter, with other and very wide lateral gulches, paralleling the one herein described on the east and west. A certain amount of digging and sampling was done in the outside areas; but the result was evidently unsatisfactory, since the work was discontinued. This section of Colorado has not been studied geologically, and the age of the ancient lake is unknown. It is probably Quaternary. I spent two weeks on the ground, in September

Jan 1, 1909

By F. Valton

In the number of the Engineering and Mining Journal for April 7th, 1877, Mr. W. P. Ward, of Cartersville, Georgia, explains in a very interesting manner, the results he obtained in the manufacture of ferromanganese in the blast furnace. These results may be summed up as follows : Production in the blast furnace of an alloy containing 67.2 per cent. manganese and 3 per cent. of carbon at most, with a utilization of the manganese amounting to 58 per cent. With the exception of the indicated proportion of' carbon, which should be almost doubled to express the true state of facts, we would have had no observations to make on Mr. Ward's paper had he taken into account the results obtained in the same line in other centres of production. Before 1870, spiegel with 8 or 10 per cent. manganese only was known among blast-furnace products. In a journey to Sweden, in 1871,I ascertained that the Schysshyttan works manufactured regolarly a spiegel with 18 per cent. manganese. Later, at the Vienna Exhibition, in 1873, the Sava and Jauerburg works, in Carniola, presented to the jury a ferromanganese, obtained in the blast fur-

Jan 1, 1879

E. O?C. Acker Jinzoc Adachi Truman H. Aldrich Walter H. Aldridge Anson W. Allen John H. Allen William R. Appleby W. Lawrence Austin W. S. Ayres David Baker John Henry Banks Henry C. Banon Alonzo F. Bardwell Wm de L. Benedict Robert Bentley Andrew A Blair Walter M. Brodie Elwin F. Brown Fredrick Burbidge H.H. Burden Charles Butters

Jan 1, 1942

By P. Bolsaitis, L. Skolnick

A model of metallic solutions is postulated which explains the energy of formation of alloys on the basis of changes in electron density around solute and solvent atoms and changes in pairwise interactions between atoms. The model is based on the Wigner-Seitz cell model of metals, with the electronegativities of the metals as the parameter for the electron-attracting power of the constituent atoms. In contrast to models based on the description of cohesive energy in terms of pairwise interactions only, which require an empirical, adjustable correction parameter to the Berthe-lot relations in order to predict negative energies of formation, the electron cell model accounts for both negative and positive energies on the basis of parameters of the pure components. Calculated heats of mixing based on published parameters of the pure metals are found to compare favorably to experimental values, despite the absence of any adjustable parameters in the model. THE formulation of an "exact" quantum mechanical model for the energy of cohesion of metals reduces ultimately to the many-body problem and for a complete solution would require the knowledge of wave functions and energy levels of all the particles in the system. The case of alloys is further complicated by the fact that the potential fields around the constituent atoms are different and the matching of boundary conditions in terms of the resulting wave functions is still an unresolved mathematical problem. It appears that in spite of the numerous investigations that have led to an elucidation of many properties of the metallic state, the formulation of the Hume-Rothery rules in 1931 marks the lone accomplishment toward simple, qualitative prediction of the energy of formation of alloys. More recently Friedel'' and Arafa have utilized the modern concepts of the electronic structure in metals in combination with the Hume-Rothery rules to arrive at quantitative estimates of the energy of formation of alloys with low solute contents. The relative success of the Hume-Rothery rules and Friedel's and Arafa's studies encouraged broaching the subject of formulation of a model based on realistic physical parameters and of conceptual and mathematical simplicity that could be applied to alloys regardless of concentration. On the basis of the free-electron theory, the cohesive energy of pure metals can be expressed as a function of "valence" (number of free electrons per atom), lattice parameter (or density), and the ioniza-tion energy. In addition to the electronic contributions to cohesion, one has to consider the pairwise exchange interaction energy between neighboring ion cores and the contribution from van der Waals forces. The energy changes upon alloying are viewed as resulting primarily from a redistribution of electron densities around the ions (a simplification of the more basic concept of a change of the wave functions of the electrons in the presence of a perturbing potential field). In addition there is a change in the pairwise interactions between neighboring ions which is usually the only factor taken into account in commonly used adaptations of the quasichemical theory. The electronegativities of the metals forming the alloy are used as the measure of the electron-attracting power of the ions in the alloy and the difference in electronegativities as the driving force for changes in electron energy on alloying. The interplay of pairwise interactions and electronic forces results in positive or negative energies of formation of alloys. Results obtained for systems to which the free electron model is best applicable are in good agreement with experimental values. 1) COHESIVE ENERGY OF METALS IN TERMS OF THE ELECTRON CELL MODEL The simplest physical model of a metal is that of a lattice of positive charges immersed in a sea of uniform, negative charge distribution represented by the

Jan 1, 1969

E. O?C. Acker Jinzoc Adachi Truman H. Aldrich Walter H. Aldridge Anson W. Allen John H. Allen William R. Appleby W. Lawrence Austin W. S. Ayres David Baker John Henry Banks Henry C. Banon Alonzo F. Bardwell Wm de L. Benedict Robert Bentley Andrew A Blair Walter M. Brodie Elwin F. Brown Fredrick Burbidge H.H. Burden Charles Butters

Jan 1, 1941

By D. L., Hayes

THE concentration of zinc ore in Wisconsin is a comparatively simple process, although it presents problems that must be overcome in an efficient manner in such a way that installation and operating costs are low. As the ore deposits are small, the first cost of the concentrating plant must be low; while the low margin of profit makes it necessary to have the minimum operating costs. The original mills were copied from those of the Joplin district, as most of them were built and operated by Joplin millmen. These served the purpose well; they made a clean concentrate, which was the chief requirement at that time, as most 'of the mines were' considerably 'richer than the average at the present time, and wages and supplies were also considerably lower. ' The apparatus used at present has changed very little in principle. . The grizzly opening has gradually been increased to 12 in. and sometimes no grizzly 'is used. The crusher, gradually grew in size, the largest crusher has -an opening of about 24 by 13 in. and a 7/8-in. throw on the. eccentric shaft.

Jan 1, 1921

By G. Sachs, A. W. Dana, C. C. Chow

A great number of the investigations on the plastic flow of metals have been concerned with the establishment of a "universal" stress-strain relation. In such a relation some stress function when plotted against a strain function should yield identical curves for the various stress states. In the first investigation of this type, Ludwik and Scheu1 plotted the maximum shearing stress as a function of the maximum principal strain. Later Ros and Eichinger2 introduced two universal stress-strain relations, the one relating the maximum shearing stress to the maximum shearing strain, and the other relating a stress invariant, suggested by von Mises and Haigh, to the corresponding strain invariant. (In more recent investigations the stress and strain invariants are frequently supplemented with some factor to render their meaning more lucid.) A further suggestion which has not attracted appreciable attention is that by Baranski³ who used stress and strain deviators. The most common means of experimentation to determine the relation between stress and strain consists in subjecting thin walled tubes to combined internal pressure and axial tension.4a,4b,4c This method allows the study of plastic flow under stresses which are variable in two directions. However, the plastic flow which can be obtained in this manner is comparatively small, being limited by either tension failure or instability. For copper,'. only the relation between maximum shearing stress and maximum shearing strain yielded good agreement. On the other hand, tests on a stee14b and on an aluminum alloy4c. resulted in systematic deviations if any of the discussed universal stress-strain relations were used. It would seem, therefore, that the agreement mentioned above for copper is only incidental and explained by its high rate of strain hardening compared to that of other metals. Much larger strains than experienced in the tube tests can be obtained by subjecting a thin membrane of a ductile metal, which is restrained at its periphery, to a uniform hydraulic pressure. The thin sheet forms a deep bulge before it fails. The stresses and strains in such a bulge increase with increasing distance from the edge of the clamping "die," the maximum stresses and strains occurring at the pole (crown) of the bulge. While the stress and strain states are determined by the contour of the bulge, the absolute magnitude of the stresses and strains depends upon the hydraulic pressure. The bulge contour is in turn correlated with the geometry of the die opening. The deformation and fracture characteristics of circular bulges, that is, bulges formed with circular clamping dies, have been the subject of numerous experimental and analytical investi-gations.5,6,7 It has been shown that plastically deformed circular bulges develop large and comparatively uniform strains before failure by instability"6b,6c,6d and closely assume a spherical shape.6d Also the distribution of strains across the contour of the bulge is dependent on the metal being investigated and is correlated with, but cannot be predicted from, the metal's stress-strain characteristics. On the other hand, oblong or elliptical bulges, that is, bulges formed with elliptical clamping dies, are not as susceptible to analytical analysis and have not been investigated to the extent that circular bulges have. The few available data6c,7c indicate that stress states are obtained at the poles of the bulges, varying between plane strain and balanced biaxial tension, depending upon the geometry of the die opening. In this paper, the strain state and curvatures exhibited by three bulge shapes, a circular and two elliptical bulges, Fig 1, are analyzed experimentally using methods described in previous publications.6a,6c An attempt is made to derive the stress-strain relations for these bulges, which represent strain states in which the ratio of the two positive principal strains varied between 1.0 and 0.35. In addition, tension tests yielded data for a value of —0.5 for this strain ratio. Such an analysis should indicate the applicability of the various laws correlating stress with strain to the stress and strain states occurring in bulged shapes. Definitions and Nomenclature The definitions of the major stress and strain quantities used in this paper are as follows: s1, s2, s3 = principal normal stresses Sl > s2 > S3 t = shear stress e = conventional (unit) strain e = In (1 + e) El, E2, E3 = principal natural strains 7 = shear strain The maximum shear stress: , _ S1 — S3 lmax = 2 Frequently, the flow stress, s1 — s3 = 2lmax rather than the maximum shear stress is used.

Jan 1, 1950

ALABAMA Altoona -Cain, J Anniston -Cowie, L K Heimrod, A A White, H E Bessemer-Abbott, C C Ball, E M Mitchell, F R Thompson, N E Birmingham -Adler, T E Aldrich T H Aldrich, T H, Jr Blackburn, A R Bush, 117 W Clark, G H Cowin, P G Crane, W R Crawford, G G Crockard, F H Darnelspn, G E Davis, C B

Jan 1, 1923

[*E. O'C. Acker '86 Jinzoc Adachl '88 T. H. Aldrich '96 *Truman H. Aldrich '78 Walter H. Aldridge '89 *Anson W. Allen '87 John H. Allen '84 *Thomas Andrews '94 *William R. Analeby '90]

Jan 1, 1946