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United Engineering Society WILLIAM L SAUNDERS,, President GEORGE H PEGRAM, 1st Vie-president ALFRED D FLINN, Secretary J V W REYNDERS, 2d Vice-president JACOB S LANGTHORN, Treasurer HENRY A LARDNER Assistant treasurer Finance Committee House Committee GEORGE H PEGRAM, Chairman ALFRED D FLINN, Chairman J 'VIPOND DAVIES FREDERICK F SHARPLESS BANCROFT GHERARDI . JOHN H DUNLAP WILLIAM L SAUNDERS CALVIN W RICE W F M GOSS, ex-officio F L HUTCHINSON

Jan 1, 1923

J. MURRAY RIDDELL, Chairman Guy N. BJORGE, Vice-chairman Alluvial Mining CLINTON BERNARD , H. R. NORSWORTHY BENERE H. GRANT O. B. PERRY

Jan 1, 1938

By John Tyssowski

IN 1925, Harry Howard Stout, then metallurgist for Phelps Dodge Corporation, while investigating the cleaning of cathode copper by various gases at elevated temper-atures below the melting point of the metal, observed in the laboratory that particles of pure copper heated in a closed tube filled with hydrogen seemingly "stuck together." By further investigation he found that there was actual crystal growth across the boundaries of the particles of pure metal; in other words, there was a complete new crystal realignment and growth throughout the newly formed copper mass. It was coalescence, not adhesion; the several parti-cles had become one unit. From this dis-covery has been developed the coalescence process, whereby copper of cathode purity is squirted out in semifabricated form from an extrusion press, by the appli-cation of about 30c0 tons pressure on a 10-in. piston. Stout decided that cathode copper pro-duced by electrolytic deposition was the logical source of the pure copper required for the coalescence process, but as there was no way of reducing the ordinary tough commercial cathodes to the small particles required he was confronted by a serious problem at the outset. Under his direction, this problem was solved by William H, Osborn and Harry Howard Stout, Jr. They developed the process and technique for producing cathode copper in brittle, friable form, and to them must be given the greater part of the credit for this phase of the development program as well as for that relating to the gas cleaning of the cathode particles.

Jan 1, 1940

By D. G. Westlake

The electrical resistance of a series of V-H alloys (0 to 3.5 at. pct H) has been measured over the temperature range G° to 360°. Interstitial impurities made contributions to the residual resistivity, but not the ideal resistivity. The contribution of hydrogen in solid solution is expressed by Ap = 1.12 microhm-cm per at. pct H; but the contribution of precipitated hydride was negligible. A portion of the so1vu.s for the V-H phase diagram is presented. The solubility limit is given by In N (at. pct H) = (5.828 i 0.009) - (2933 i 44)/RT. Comparison of critical temperatures joy hydride precipitation and published critical temperatures for hydrogen embrittlement suggests the two are related. ThiS study was initiated as part of an investigation of the mechanism by which small concentrations of hydrogen embrittle the hydride-forming metals at low temperatures. It has already been shown that, in the case of hcp zirconium, a reduction in ductility accompanies the strengthening resulting from precipitation of a finely dispersed hydride phase.''' Our attempts to detect a similar precipitation of a second phase at low temperatures in V-H alloys by transmission electron microscopy have been thwarted because we have been unable to prepare thin foils that are representative of the bulk material with respect to hydrogen concentrati~n.~'~ The present investigation establishes the solvus of the V-H system at subambient temperatures. Subsequently, we hope to be able to determine whether the embrittlement temperature is related to the critical temperature for precipitation of the hydride in a given V-H alloy. veleckis5 has proposed a partial phase diagram for the V-H system based on extrapolations of the pressure-composition relations he measured at higher temperatures. Kofstad and wallace' conducted a similar study of single-phase alloys but did not attempt to establish the phase diagram. Zanowick and wallace' and ~aeland' have studied a portion of the phase diagram by X-ray diffraction, but they investigated no alloys in the hydrogen concentration range 0 to 3 at. pct, the range of interest to us. EXPERIMENTAL PROCEDURE The vanadium was obtained from the Bureau of Mines, Boulder City, Nev., in the form of electrolytic crystals. The analyses supplied with them listed 230 ppm by weight metallic impurities, 20 ppm C, 100 ppm N, and 290 ppm 0. The crystals were electron-beam-melted into an ingot that was rolled to 0.64 mm. Strips, 60 mm long and 4.2 mm wide, were cut from the sheet, and both rolled surfaces were ground on wet 600-grit Sic paper to produce specimens 0.4 mm thick. They were wrapped in molybdenum foil, vacuum-encapsulated in quartz, and annealed 4 hr at 1273°K. The specimens were annealed in a dynamic vacuum of 2X lo-' Torr for 30 min at 1073°K for dehydrogenation, and charged with the desired quantity of hydrogen by allowing reaction with hydrogen gas at 1073°K for 2 hr and cooling at 100°K per hr. Purified hydrogen was obtained by thermal decomposition of UH3. Sixteen specimens were studied: two contained no hydrogen and the others had hydrogen concentrations between 0.5 and 3.5 at. pct (hydrogen analyses were done by vacuum extraction at 1073°K). Electrical resistances were measured by the four-terminal-resistor method on an apparatus similar to the one described by Horak.~ The specimen holder was designed so that both current and potential leads made spring-loaded mechanical contact with the specimen. The potential leads were 30 mm apart, and the current leads were 55 mm apart. The current was 0.10000 amp. We used the following baths for the indicated temperature ranges: liquid nitrogen, 77°K; Freon 12, 120" to 230°K; Freon 11, 230" to 290°K; and ethanol, 290" to 340°K. Temperatures lower than 77°K were achieved by allowing the specimen to warm up after removal from liquid helium. Temperatures above 77°K were measured by a calibrated copper-constantan thermocouple (soldered to the specimen holder) and below 77°K by a calibrated carbon resistor. The temperature of the bath changed less than 0.l0K between duplicate measurements of the resistance. RESULTS AND DISCUSSION Typical plots of resistivity p vs temperature T are shown in Fig. 1. In the interest of clarity, only five curves are presented and the data points have been

Jan 1, 1968

By H. T. Morris

ONE of the chief concerns of the Bethlehem Steel Co. naturally is the proper functioning of its organization. This involves the training of a continuous supply of younger men to fill the vacancies caused not only by the inevitable departure of older men, but also by the growth of existing establishment, and by expansion in new directions. It does not oper-ate a student training course with a fixed time schedule or with definite periods of rotation through the differ-ent divisions. To state the case positively, the gradu-ate's training course must operate continuously from the beginning of his employment through a long term of years. No period of weeks or months nor pair of years suffice to bring him into contact with all the com-binations needed to qualify him for the larger destiny toward which we hope he is headed. Our first step in selecting a college man is to require that he have a degree. We thus approximate the assur-ance that at least four annual siftings have reduced the chance that a non-worker may find himself in a job where work is necessary. The next step is to try to ascertain facts, from the graduate and from others who have known him at his home and in 'his college, to indi-cate whether our opportunities offer him a career that will challenge his continuing interest, and hold him to tenacious effort against all happenings. We aim to avoid knowingly bringing into our organization a man who will not develop in it enough enthusiasm to keep him happily striving. Having made our selections, we assemble the gradu-ates into a probationary observation circuit. We-put ourselves under their observation by taking them in small groups, usually of two to four men, on a circuit of every part of the Bethlehem plant, in which every manufacturing principle of our steel business is ex-emplified. The probationers work at something from day to day, with their hands if it can be arranged; otherwise in questioning, examining, and note-taking. Their observations include talks with superintendents, foremen, and workmen, the conditions under which workmen labor, apparatus, machinery, methods, design and operation of plant.

Jan 7, 1928

By C. V. Millikan

THE year 1930 in the petroleum industry has been characterized by the establishment of large potential production of crude oil. This has resulted in closer cooperation between companies by proration and unit operation agreements in order to afford an equitable outlet to all, and to prevent a flood of oil being forced on the market with attendant tremendous material and economic waste. Drilling wells in proved areas and wildcat wells are fewer than in the past several years. Restricted production and low prices have caused greater effort to increase producing and recovery efficiencies. Increased refinery efficiencies have amplified the effect of overproduction. Pipe line departments have been especially busy. New oil lines have reached more refineries by new and shorter routes. Establishing greater gas reserves by new fields has justified new gas lines to industrial centers, and has brought this fuel to thousands of new domestic consumers. Two long gasoline lines, a new venture in pipe lines, are being built to obtain a lower cost of transportation and less loss between the refineries and their distribution centers. The chairmen of the various divisions have discussed the developments of their respective branches more fully in the following reviews.

Jan 1, 1931

THE distinction btween price reduction as a re-sult of lowering of production cost and price re-duction through unrestricted competition cannot be made too clear, because they are often interwoven in actual experience. Take the whole population of a town whose principal industry is shoe manufacturing as a concrete example. If the manufacturer is able to cut his price per pair in half because he has found out how to make a pair at half the cost, he will com-monly let a number of his men go, because reduction in production cost usually results from substituting cheap mechanical energy for expensive human energy. These people will normally find other employment. The workmen who remain employed usually earn more in dollars than they did before, and in spending it give employment where there was less before. Mining companies that initiate considerable enter-prises in foreign lands where the economic level is low, and where most of the people are busily but in-efficiently engaged in raising enough food to support themselves and their families, often find themselves confronted with an acute labor problem. If any con-siderable number of workers leave the land to work in and about the mines, those left on the land cannot raise enough food to keep them all unless they are taught better methods of agriculture and provided with equipment that will enable them to produce more with less expenditure of effort. Add to this the fact that managers commonly find that the "natives," as our British cousins designate them, usually need more food and a better balanced diet than they have been accustomed to in order to show anything above the lowest order of efficiency in industrial work,. and it is clear that to make a new industry possible in what may be termed an economic province involves increas-ing the productivity, not only of those who are em-ployed in it, but of the whole social group. It has already been pointed out that the employ-ment of large numbers of men in automobile manu-facture is only possible because the others have in-creased their productivity enough to turn out every-thing else that is needed without the help of the auto-mobile workers.

Jan 7, 1928

By J. Gurland

THE microstructure of sintered carbides consists of particles of metal carbides, such as WC and TiC, embedded in a metallic binder which is usually a cobalt—or nickel-rich solid solution. One of the important factors influencing the strength of the alloys is the degree of dispersion of the carbide particles in the binder matrix. While it is generally accepted

Jan 1, 1960

By K. A. Natarajan, I. Iwasaki

The meaning and the utility of redox potential (Eh) measurements in sulfide flotation systems are examined. Since some preliminary plant Eh and laboratory flotation data were available, experiments were made to establish the pH range at which a platinum electrode might be used for such measurements without much difficulty in aerated systems. Triangular wave voltammetry was used to study the surface conditions of the electrode immersed in pyrrhotite suspensions at different pH. The measured Eh both at the plant and the laboratory is interpreted in terms of the experimental water-oxygen line.

Jan 1, 1974

By F. M. Jardine

I1944 the cry was for higher production more tons, more metal. New plants were built, capacity of old plants was increased and millmen all over the country were treating tonnages far above normal, sacrificing recoveries to vet that extra metal from extra tons. The list of "critical minerals," at first long, has been scratched until there remains, not a list, but only an item or two. Stocks of all metals and minerals, with possibly one or two exceptions, are now entirely adequate and numerous plants have curtailed or suspended operation.

Jan 1, 1945

By AIME AIME

WITHOUT frills, but with an admirable program of technical papers and discussion, many opportunities for social contact, and all New York for a playground, the 142d Meeting of the Institute will make the Engineering Societies Building a lively place from Feb. 20 to 23. Prices are down, even in New York. Come and forget the depression listening to the stories of old friends. Hear at first hand what is going on in your professional world. The fare is varied, of wide appeal. The program on the opposite page has been arranged carefully to minimize conflicts between the subjects in which you are interested. If it is not possible to come for all four days, check over the sessions that are most important to you. No changes in the scheduling are likely.

Jan 1, 1933

By R. M. Schuller, J. J. Suloway, W. F. Childers, R. A. Griffin, S. J. Russell

Seven solid wastes from coal conversion processes were characterized chemically and mineralogically. The wastes included three Lurgi gasification ashes, two liquefaction residues (SRC and H-coal), a fly ash, and a water-quenched slag. Leachates generated from the solid wastes at various pH levels over the range 2.5 to 11.0 were analyzed for over 40 constituents. Results of the leachate analyses demonstrate the wide variation in constituent solubility for the solid wastes. To help assess the environmental impact of the disposal of these wastes, the leachates were also employed in soil attenuation studies and acute 96-hr static bioassays using young fathead minnows.

Jan 1, 1981

I-Mine Ventilation A. C. CALLEN, Chairman E. A. HGLBROOK, Vice-chairman H. I. SMITH, Secretary CLARENCE E. ABBOTT ALFRED W. HESSE FRANK H. PBOBERT GAM BRIGHT G. R. JACKSON GEORGE S. RICE THOMAS H. CLAGETT JAMES F. MCCARTHY E. J. RISTEDT . OSCAR A. GLASSER W. B. PLANK GERALD F. SHERMAN Coal Mining M. D. COOPER, Chairman HOWARD N. EAVENSON JOHN A. GARCIA THOMAS D. THOMAS CHARLES ENZIAN JAMES W. PAUL C. M. YOUNG JOHN J. RUTLEDGE

Jan 1, 1929

[ARIZONA Established July 10, 1915 ROBERT W. HUGHES, Chairman CHARLES R. KUZELL, First Vice-Chairman GILBERT C. DAVIS, Second Vice-Chairman W. CLARK MASON, Secretary-Treasurer Inspiration Cons. Copper Co., Inspiration, Ariz. LYLE BARKER ROBERT HIGH T. G. CHAPMAN P. D. I. HONEYMAN GEORGE M. COLVOCORESSES WALTER C. LAWSON EDWIN H. CRABTREE, JR. W. H. LOERPABEL WALTER I. GARMS ALBERT MENDELSOHN WESLEY P. Goss CARL E. MILLS H. C. HENRIE JOSEPH A. WILLCOX C. F. WILLIS]

Jan 1, 1946

By Frances H. Clark

IN wartime, the fabrication and use of metals assumes increased importance, for a modern war of sizable proportions cannot be undertaken with- out a vast supply of this material. Light alloys of aluminum and magnesium, which were comparatively unknown in the last war, will play an important role in this one. Due to research on a vast scale in the interim of years, industry is today well equipped to fabricate metals on an enormous scale. Research for the past year has been most productive and a comprehensive survey in the space of this article would be impossible. It is hoped that the stressing of a few items here and there out of a great quantity of able work will indicate in a small way the advances made within recent times. Specific references to the literature will be omitted at the Editor's re- quest but some authors of papers that I have found of special interest are mentioned.

Jan 1, 1940

By C. S. Finney, John Mitchell

The growing popularity in the United States of the vertical-flue even was emphasized when in 1905 the United States Steel Corp. chose the Koppers oven as the type which best suited their requirements. Heinrich Koppers was born on November 23. 1872. at a small farm in Walbeck near Geldern on the lower Rhine. When young Koppers was eight years old, however the family moved away from the farm to the industrial city of Bochum in the Ruhr. Here Koppers attended public school and subsequently served an apprenticeship to a tinsmith before taking a job as a lathe operator with a local steel company. He had ambitions to be much more than a machinist, however, and used his week-ends and evenings to improve his theoretical background by taking courses at a vocational-training school in Bochum. After winning the highest honor the school could bestow (the silver Staats-medaille), Koppers went on to continue his education at the Rheinisch-Westfalische Hüttenschule in Duisberg. One of his teachers there, Fritz Wüst who later became a professor at the Technische Hochschule at Aachen, recognizing Koppers' unusual abilities, predicted for him a great future. In 1894 Heinrich Koppers joined the firm of Dr. C. Otto and Co. in Dahlhausen, and in 1899 while superintendent of the Mathias Stinnes mine he built his first battery of ovens for Hugo Stinnes, the German industrialist. Two years later he started his own organization, and in 1902 he made Essen his headquarters. It was to Essen that a group of engineers from the United States Steel Corp. went in 1906 with an invitation to Koppers to design and supervise the construction of four batteries of ovens at the Joliet works of the Illinois Steel Co. Each battery was to consist of 70 ovens. Arriving in the United States in 1907, Koppers established a branch of his firm in Joliet, and construction began. The first battery was fired on July 27, 1908. Rugged and simple, these ovens incorporated basic design features which were to make the Koppers oven and its future modifications the choice of a very large segment of the by-product coking industry of America. The 280 ovens at Joliet were 35 ft long, 8 ¾ ft in height, and tapered from 21 to 17 in. The total daily capacity of the four batteries was 2240 tons of coke. The ovens were of the new cross-regenerative type; that is, instead of longitudinal regenerators serving an entire battery, as in the older Koppers ovens, cross regenerators for each separate oven were employed. Fuel gas was supplied from the side of the battery through ducts in the brickwork known as gun flues, which reached to the center of the battery under the vertical heating-flues. Removable, ceramic gas-nozzles fitted at the top of each gun flue helped to insure good control over the distribution of the fuel gas, and uniform heating conditions were also promoted by regulating the air supply to, and the suction in, each heating flue. A different refractory w& used for each battery. One was built of American silica brick, one of American quartzite, and two of imported German quartzite. The installation at Joliet proved to be very successful, and in 1911, 490 additional' Koppers ovens were built for the Illinois Steel Co. at the great new steelworks at Gary, Ind. By 1912 the H. Koppers Co. had established its headquarters in Chicago and was rapidly extending its business to include construction for such iron and steel companies as the Woodward Iron Co. at Woodward, Ma. (80 ovens in 1912); the Tennessee Coal, Iron and Rail- road Co. at Fairfield, Ala. (280 ovens in 1912); the Inland Steel Co. at Indiana Harbor, Ind. (86 ovens during 1913 and 1914) ; and the Republic Iron and Steel Co. at Youngstown, Ohio (68 ovens in 1913). In 1914 a group of men in Pittsburgh bought a major shareholding in the H. Koppers Co., and moved the headquarters of the organization from Chicago to their own city. Under its new management the company was highly successful in obtaining a large share of the contracts for by-product installations built during World War I. In 1917 the remaining German interests in the company were

Jan 1, 1961

By H. K. Work, H. B. Emerick

IN the past year the steel industry underwent an abrupt conversion from a war tempo to a highly competitive peacetime schedule. It is still too early to gain a comprehensive picture as to which of the measures in production metallurgy, that made the war effort so successful, will remain in the postwar production of steel, but many of them undoubtedly will fill an important place after the war. Considerable speculation has developed regarding the disposition of the war-born production facilities of the steel industry. These include new open-hearth and electric furnaces, as well as vast numbers of auxiliary, supplementary, and balancing units that increased and speeded up production beyond the normal capacities of existing melting furnaces and finishing mills. Although these facilities were installed primarily to help meet war requirements, consideration was also given, in planning, to their possible peacetime use. The new equipment is generally modern and efficient, and it seems reasonable to suppose that strategically located units will gradually be absorbed by various steel companies to supplement their own facilities, or to replace in kind, obsolete and inefficient equipment now ready to be scrapped. Some, however,

Jan 1, 1946

Some Things We Don't Know about the Creep of Metals. By H. W. Gillett (T.P. 1087) Reduction of Iron Ores under Pressure by Hydrogen. By Michael Tenenbaum and T. L. Joseph (T.P. loll, with discussion) Induction Furnaces for Rotating Liquid Crucibles. By E. P. Barrett, W. F. Hol- bRook and C. E. Wood (T.P. 986, with discussion) Mechanism of Solidification and Segregation in a Low-carbon Rimming-steel Ingot,. By Anson Hayes and John Chipman (T.P. 988, with discussion) Solidification of Rimming-steel Ingots. By A. HultGRen and G. PhRagmen. (Contribution 112) Dendritic Structure of Some Alloy Steels. By Daniel .I. Martin and James L. Martin (T.P. 1066, with discussion) Occlusion and Evolution of Hydrogen by Pure Iron. By George A. Moore and Donald P. Smith (T.P. 1065, with discussion) Structure of Iron after Con~pression. Hy Charles S. Barrett (T.P. 977, with discussion) Structure of Iron after Drawing, Swaging, and Elongating in Tension. Ry Charles S. Barrett and L. H. LevensoN (T.P. 1038, with discussion) Magnetic Torque Studies of the Texture of Cold-rolled and of Recrystallized Iron-silicon Alloys. By Leo P. TaraSovJ(T.P. 1012, with discussion) Influence of Atmosphere and Pressure on Structure of Iron-carbon-silicon Alloys. By Alfred Boyles (T.P. 1046) Kinetics of the Decomposition of Austenite at Constant Temperature. By J. H. Austin and R. L. Rickett (T.P. 964, with discussion) Reaction Kinctics in Processes of Nucleation and Growth. By William A. Johnson and Robert F. Mehl (T.P. 1089, with discussion) Phase Changes in 3.5 Per Cent Nickel Steel in the Acl Region. By I. N. Bavarine (T.P. 1031, with discussion) Chromium in Structural Steel. By Walter Crafts (T.P. 1055) Surface Allotropic Transformation in Stainless Steel Induced by Polishing. By J. T. BuHwell and J. WUlff (T.P. 1032, with discussion) Nature of :Passivity in Stainless Steels and Other Alloys, I and 11. Ry H. H. Uhlig and John WUlff (T.P. 1050, with discussion) Thermal Expansion of Nickel-iron Alloys (Nickel from 30 to 70 Per Cent). Ry J. M. Lohr and Charles H. Hopkins (T.P. 987, with discussion) Low-temperature Transformation in Iron-nickel-cobalt Alloys. By L. L. Wy~Ian (T.P. 1013, with discussion) Fracture of Steels at Elevated Temperatures after Prolonged Loading. By R. H. Thielemann and E. R. Parker (T.P. 1034, with discussion)

Jan 1, 1939

Some Things We Don't Know about the Creep of Metals. By H. W. Gillett (T.P. 1087) Reduction of Iron Ores under Pressure by Hydrogen. By Michael Tenenbaum and T. L. Joseph (T.P. loll, with discussion) Induction Furnaces for Rotating Liquid Crucibles. By E. P. Barrett, W. F. Hol- bRook and C. E. Wood (T.P. 986, with discussion) Mechanism of Solidification and Segregation in a Low-carbon Rimming-steel Ingot,. By Anson Hayes and John Chipman (T.P. 988, with discussion) Solidification of Rimming-steel Ingots. By A. HultGRen and G. PhRagmen. (Contribution 112) Dendritic Structure of Some Alloy Steels. By Daniel .I. Martin and James L. Martin (T.P. 1066, with discussion) Occlusion and Evolution of Hydrogen by Pure Iron. By George A. Moore and Donald P. Smith (T.P. 1065, with discussion) Structure of Iron after Con~pression. Hy Charles S. Barrett (T.P. 977, with discussion) Structure of Iron after Drawing, Swaging, and Elongating in Tension. Ry Charles S. Barrett and L. H. LevensoN (T.P. 1038, with discussion) Magnetic Torque Studies of the Texture of Cold-rolled and of Recrystallized Iron-silicon Alloys. By Leo P. TaraSovJ(T.P. 1012, with discussion) Influence of Atmosphere and Pressure on Structure of Iron-carbon-silicon Alloys. By Alfred Boyles (T.P. 1046) Kinetics of the Decomposition of Austenite at Constant Temperature. By J. H. Austin and R. L. Rickett (T.P. 964, with discussion) Reaction Kinctics in Processes of Nucleation and Growth. By William A. Johnson and Robert F. Mehl (T.P. 1089, with discussion) Phase Changes in 3.5 Per Cent Nickel Steel in the Acl Region. By I. N. Bavarine (T.P. 1031, with discussion) Chromium in Structural Steel. By Walter Crafts (T.P. 1055) Surface Allotropic Transformation in Stainless Steel Induced by Polishing. By J. T. BuHwell and J. WUlff (T.P. 1032, with discussion) Nature of :Passivity in Stainless Steels and Other Alloys, I and 11. Ry H. H. Uhlig and John WUlff (T.P. 1050, with discussion) Thermal Expansion of Nickel-iron Alloys (Nickel from 30 to 70 Per Cent). Ry J. M. Lohr and Charles H. Hopkins (T.P. 987, with discussion) Low-temperature Transformation in Iron-nickel-cobalt Alloys. By L. L. Wy~Ian (T.P. 1013, with discussion) Fracture of Steels at Elevated Temperatures after Prolonged Loading. By R. H. Thielemann and E. R. Parker (T.P. 1034, with discussion)

Jan 1, 1939

By D. R. de Fontaine

By computing the values of the resolved shear stress for a great many orientations of the tensile axis on all 12 (111) <110> slip systems, Taylor and Elam&apos; were able to map out a stereogram of slip systems, given here, Fig. 1, in Diehl&apos;s notation (see, for example Hauser and Jackson&apos;). The purpose of the present note is to derive such a stereogram by mathematical reasoning and to give a simple method of defining the system with highest resolved shear stress for any direction of the tensile axis, thereby eliminating tedious computation of the Schmid factor. Let the tensile axis, of direction cosines [xyz], make the angles 0 and relative to the slip plane normal [HKL] and the slip direction [hkl] respectively. Fig. 2 shows a simple cubic cell whose edges define a Cartesian coordinate system. Let A be a unit vector of origin 0 supported by the tensile axis. Its end point [xyz] then lies on a sphere of unit radius, on the positive hemisphere of which the planes z = 0, x = y, y = z limit the so called primitive triangle of a standard [loo] stereographic projection. For any point of this triangle, the following hold: 0«2 «y *sx « 1 [l] Now, for given [xpz], the most highly stressed system will be the one for which the following expression of the Schmid factor has the largest possible value: (HKL) belonging to the form (111) and [hkl] to the form <110>, the denominator on the right hand side of Eq. [2] is equal to 1.fi.a. The unknowns H, ... h, . . . can now be determined by correctly distributing +1 and -1 to H, K, L, and +1, -1,O to h,k, 1 giving the numerator of Eq. [2] its greatest positive value (the angles 0 and cpare chosen acute) subject to the condition: Hh+Kk+Ll = 0 [3] since the slip direction must lie in the slip plane. Condition [3] can be satisfied only by having one of its terms vanish and the other two equal to +1 and -1. Taking the case of the tensile axis lying in the primitive triangle, x2y, z and therefore Hh will be chosen equal to +1 with H = h = +1 in order to retain a maximum of + signs. There remain two alternatives: either 1 = 0 or k = 0. 1) take 2 = 0 Then Kk = -1 and the numerator of [2] becomes: Retaining a maximum of + signs gives L = k = +1 and becomes: 2) take k = 0 Then L1 = -1and, likewise, the numerator of [2] becomes: xz - z2 + xy + yz [5] But the difference [5] - [4] can be written: (y - z)(x+y +z) [6] positive or zero by virtue of [I]. If [6] is positive (y > z), then the largest possible value for the numerator of [2] for any xyz inside the primitive triangle is given by [5], i.e., for: That is to say, the active slip system corresponding to an orientat:~on of the tensile axis inside the primitive triangle is:

Jan 1, 1962