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By V. L., McCutchan

FORM of ore bodies, strength of wall rock, and quantity of water that must be handled differ so greatly in the various districts in which the Corporation operates that a variety of mining methods have to be employed. All are underground, however, with the exception of glory holes at Cerro de Pasco from which siliceous silver pacos ore is obtained. In general, the ors is in many relatively small bodies unsuitable for hulk mining, such as caving or top slicing. The strength of the rock and ore rarely permit open stopes, though shrinkage is successfully used on various veins with strong walls, particularly in, Casapalca. Horizontal cut and-fill and square-set stoping with careful filling are the principal methods employed, with the necessarily higher cost for supplies and labor offset as much as possible by care in the avoidance of dilution. The mines at both Morococha and Casapalca are notoriously wet, and even at Cerro de Pasco the quantity of water was enough to retard deep development until the perfection of electric pumps. In Morococha particularly, the extension of successive levels, first from adits of moderate length, then from shafts and heavy pumping installations on the 750 and 1000 levels, and finally by the 30,564-ft. Kingsmill tunnel, was one of the most difficult and long continued fights against water and resulting heavy ground that is recorded in mining history.

Jan 1, 1945

By Philip D. Anderson, Ralph Hultgren

Heat contents of extremely pure iron were measured over the range 300"to 1433"K, using a diphenyl ether calorimeter. Results from three samples containing widely differing impurities agreed with one another and with Previously reported results at higher temperatures (1184 ° to 1809°K) by Olette and Ferrier. From these data a table of heat contents of iron has been Prepared which is believed to be more accurate than those previously available. CP values have been derived which are consistent with these heat contents, with the best experimental Cp data, and with the thermodynamic conditions of equilibrium between bcc and fcc iron. The opinion is expressed that low-temperature extrapolations of presently known Cp values for y-Fe are not reliable. It would seem that the thermodynamic properties of iron, which is by far our most important metal, should have been well established long ago. This is not the case, however. As discussed by Olette and Ferrier,' there is objection to every earlier heat content measurement. While the best true Cp determinations agree well at temperatures below the Curie point, there is wide divergence at higher temperatures. Several investigators have examined available data and attempted to calculate thermodynamic functions for iron that are consistent with the two equilibrium temperatures of bcc and fcc iron. The two primary efforts were those of Austin' in 1930 and Darken and smith3 in 1948. The recommended values differ considerably; integration of Austin's Cp values leads to a heat content at 1100°K which is 300 cal per g-atom higher than the value recommended by Darken and Smith. The compilation of Fisher4 in 1949 was based on the selection of Austin. In 1956, Weiss and Tauer obtained yet another set of values by resolving Cp values into components due to dilation, lattice vibration, electronic excitation, and magnetism. The magnitude of contribution by each component and its dependence on temperature was estimated by semiempirical means. Their values are not self-consistent in that they do not form smooth curves when plotted vs temperature; moreover, their calculations cannot easily be repeated since they do not give the values of some of the parameters used. Clearly, experimental values for iron were in a most unsatisfactory state. The presently described measurements of the heat content of iron were therefore undertaken, covering temperatures as high as 1433°K. While the work was in progress, the high-temperature (1193" to 1789"K) heat content measurements of Olette and Ferrier' were published; in the region of temperature overlap the present results agree with Olette and Ferrier well within experimental accuracy. It is believed that the present results, combined with those of Olette and Ferrier, provide for the first time a reliable set of heat contents of iron from room temperature to the melting point. From these data, guided by available Cp measurements, it proved possible to derive Cp, entropy, and free energy function values for @-iron from room temperature to the melting point, and for y- iron in the temperature region of its stability. Exhaustive study led to the conclusion that extrapolations of y-iron functions to room temperature were not reliable enough to be useful; hence these have been omitted from the tables. EXPERIMENTAL Materials. Three samples of extremely high purity iron from different sources, containing widely different impurities, were measured. The first of these, designated "Chipman", was kindly supplied by Dr. K. K. Kelley of the U. S. Bureau of Mines from a lot which was made many years ago by Dr. John Chipman of the Massachusetts Institute of Technology. The second, designated6'Teddington", was supplied by the National Physical Laboratory, Teddington, England, from a lot zone-refined by them. The third sample, designated "Irsid", was supplied by the Institute de Recherches de la

Jan 1, 1962

By T. A. Rickard

MILLING is one of the metallurgical arts whereby the extraction of the largest possible proportion of the value in an ore is effected at the least possible expense. Stamp-milling* is that particular process in which a heavy body of iron is caused to fall upon the ore so as to disintegrate it and thereby induce a separation between what is valuable and what is worthless. The latter is usually less in specific gravity, and is therefore, by the further aid of water, removed from the former, which is then collected by the use of mercury. Several similes have been employed to describe this process. The stamp has been likened to a hammer of which the stem is the handle and the die the anvil. The ore upon which the stamp falls has been compared to a nut awaiting the descent of the hammer whose blow is to separate the valueless shell, the quartz, from the valuable kernel, the gold. When we begin to pursue our inquiries, however, we find that the analogy is just sufficiently true to emphasize the departures from it. The hammer falls, the anvil is fixed; so with the stamps and the mortar. The anvil is made of softer metal than the hammer; so also the die is often, and should be always, of steel or iron less hard and more tough than that of the shoe. The movement of the hammer and the drop of the stamp are both intermittent. In regard to their intermittent action, as in many other respects, stamp-mills arrange themselves under two types, which, though apparently contradictory, have both been evolved from a common original, and are united by a great variety of intermediate modifications. The slow speed and the high drop of the mills of Gilpin county Colorado, appear to have very little in common with the fast speed and short drop of those of the main gold belt of California; yet the practice of the one was largely derived from that of the other,

Jan 1, 1894

By Claus Goetzel

THE object of this investigation was to determine whether silver alloys could be used instead of the currently employed insert of high-expansion AVERAGE COEFFICIENT PER DE G. C. OVEN RANGE 20° To 200° C. Pure aluminum '31.6 X 10-6 Cast low-expansion Si-Cu-Ni-Al piston alloy 20.0 X 10-6 High-expansion austenitic Cu-Ni cast iron 19.3 X 10-6 Cast steel (0.25-0.35 C, 0.10-1.0 Mn) 12.6 X 10-6 Cast iron (3.15 total C, 2.16 Si) 12.8 X 10-6 Pure silver 18.9 X 10-6 austenitic ferronickel alloy, to reduce the wear of ring grooves in light metal pistons. A typical example of a piston containing a ferronickel insert is shown in Fig. 1. The high coefficient of expansion of silver made it worthy of consideration, while the small size of the insert would render it use feasible in Germany as an emergency in is- tire. The coefficients of linear expansion of several metals and alloys are as shown in the table above. Obviously the melting point of the insert must be high enough to prevent it from melting when the light alloy is cast around it. This imposes a lower limit of about 850° C. for the solidus of the silver alloy. Pure silver melts at about 961° C., so that the Fin. 1.-PISTON CONTAINING tolerable depression in the solidus is rather FERRONICKEL INSERT. small. To avoid deformation of the insert during use a Brinell hardness number of at least 60 appears necessary.

Jan 1, 1937

By W. C. Lacy

This article is a progress report of a program designed to quantitatively evaluate geological parameters to predict stable slope angles. The author feels that, although there does not appear to be any one technique or characteristics that will suffice as an index to the determination of stable slope angles, a combination of seismic methods as outlined here, detailed geological mapping and logging of core, and a better understanding of the angle of internal friction in rock types will permit accurate estimation. A mining engineer friend once remarked, "If we don't have pit slope failures, the slopes are too flat." Since economic justification of an open pit project is based upon ultimate pit slopes, we cannot wait until the pit is developed and slopes established by trial and error. Some combination of geological and/or geophysical techniques must be developed to permit accurate prediction of stable slope angles and to suggest modification of pit outlines to result in slopes enabling maximum economic yield. This presentation is a progress report of a program designed to quantitatively evaluate geological parameters to predict stable slope angles. The principle of the weakest link applies to any slope stability evaluation and necessitates detailed geological examination and recording of observations. Physical failure will occur along any surface where shearing stress exceeds shearing resistance. Rock conditions are seldom uniform even within a single cut or pit face, so stability conditions will vary. Consequently, both plan outline and ultimate slope limits must be tailored to the specific situation. Economic advantages to be gained by slight increases in slope angles in deep pits are well recognized and stimulate efforts to obtain maximum permissible slope angles. MECHANICS OF SLOPE FAILURE Excellent reviews on the nature of slope failure have been presented+2,6,8,11 For the purpose of this study, the writer considers failure to take place by one or more of three processes: 1) ravelling, 2) translation or slope failure, and 3) rotation or base failure (Fig. 1). The effects of increased pore water pressure in soils were recognized in 1923 by Terzaghi in his development of the concept of effective stress, and he has applied the same principle to jointed rocks designating water pressure as cleft-water pressure.8 Cleft-water pressure in a rock slope reduces normal pressure on the plane of failure, thus reducing shearing resistance and resulting in slope failure. In the following discussion it is assumed that adequate drainage is supplied to prevent any build-up of water pressure. This is the first step in any program to establish maximum slopes. Ravelling: Ravelling occurs in rocks with low cohesion and entails the free movement of individual fragments ranging from single rock falls to running ground. Removal of lateral support wherever slope angle exceeds the angle of repose of the rock parti-

Jan 1, 1963

By E. J. Eisenach, Edward Matsen

AT the present time the Climax Molybdenum Co. is the largest molybdenum producer in the world and the operator of the largest underground mine in North America. It has grown steadily and rapidly since its beginning in 1917. Only 250,000 lb of MoS2 were produced during the first year from 1917 to 1918 when the company was formed. Operations were suspended shortly thereafter because of the lack of a market and knowledge of the uses of molybdenum. During World War I it was used as a substitute for some rare metals and for minor chemical purposes. After 5 years of intensive research and sales promotion, Climax metallurgists succeeded in finding proper applications for the newly discovered metal and the mine was reopened in 1924. Demand for molybdenum increased gradually and in 1930, 3.5 million lb of MoS2 were produced. In the meantime, research work for additional uses of molybdenum continued until it had established itself as one of the most important alloying elements in producing high quality steels. After the start of World War 11, from January 1942 to October 1953, 43 million tons of molybdenum ore were mined and 484 million lb of MoS2 were produced. Climax mine is located in Colorado, 100 miles southwest of Denver and 12 miles northeast of Leadville on the Continental Divide of the Rocky Mountains. The principal mine workings range from 11,170 to 12,000 ft in elevation. Topographically, it lies in the base of a large cirque that is surrounded by Mt. Bartlett to the north, Clinton Peak and McNamee Peak to the east and Ceresco Ridge to the south. This cirque opens to the west and to the Ten Mile Valley.

Jan 3, 1954

By Paul Gemmill

Production was first recorded from the Pioche district in 1864, and it has continued to show an inherent ability to take on new life after periods of depression in the metal markets. Production from replacement leadsilver- zinc sulfide ore bodies in limestones of Cambrian age now accounts for several times the gross value of silver production from rich fissures in Lower Cambrian Quartzite. Aggregate production of some 6 million tons represents a gross value over $100-million. Future output is expected mostly to be from limestone replacement deposits of which the most productive are "channels" of ore up to several hundred feet wide and several thousand feet long with thicknesses from a few feet up to 50 feet. Such channels are restricted to the lowermost limestone bed of the district, about 250 feet above the basement quartzite. The "blotter-like" characteristic of this highly productive Jimesto~e bed in absorbing mineralization is believed to be, at least in part, due to lithology, including free carbon in the bed, which has created a unique set of conditions for delicately balanced mineralizing solutions that rejected any tendency to replace siliceous wall rock and were properly constituted for replacement of Limestone. All recognizable orogenic history is considered to be related to the Basin and Range faulting that created the mountain ranges. The faults developed after mid-Tertiary time and after widespread extrusives that are themselves involved in the faulting. Flat faults, formerly believed to be part of regional thrust faulting, are now interpreted as gravity slide faulting that can be shown to be large in magnitude and not simply local landslides. Large slide faults generally have concealed the great magnitude of mountain-bordering faults. Mineralization that accounts for ore is later than the faulting. Most faults are pre-mineral since they influence the shape of ore bodies, and some clearly have been offset by fault fissures containing ore. Post-mineral movement probably has been an important component of some large, initially pre-mineral faults. A single period of mineralization was begun by the introduction of large quantities of ironmanganese carbonate, and, in places, carbonate manganese with minor values in sulfides. Closely following the carbonate invasion, massive sulfides were brought in, usually replacing part of the carbonate body though in some places the massive sulfides replaced limestone that was not previously mineralized. Manganese mineralization is not a "halo" but leaks of manganese to higher formations and to the surface are the most significant exploration guides. The Pioche district is expected to be long lived with technological developments in ore treatment being important to the exploitation of low-grade manganiferous ores, while aggressive exploration is expected to find important quantities of bedded lead-silver-zinc ores of the massive sulfide type.

Jan 1, 1968

By J. L. Gillson

The word "other" in paragraph 4, line 11, column 1, page 205, should read "over;" the correct version of reason 2, this paragraph, is: 'L. . . 2) to evaluate the usefulness of certain geo-chemical techniques, V. C. Kennedy and S. W. Hobbs of the USGS had already studied the distribution of copper, lead, and zinc in the soils (both in background areas and over veins) and in the water and plants, providing a criterion for measuring the magnitude and effect of soil contamination; ...9 On page 206, in the top left hand corner of Fig. 1 (in the area bounded by 47°35' and 116°10), the reference to Fig. 3 is incorrect. The area of Pine Creek, South Fork Coeur d'Alene River, and portion of Big Creek (the area which includes, from left to right, Kingston, Pinehurst, Smelterville, and Kellogg) should be identified as that of Fig. 2A. The headings for columns 1, 3, and 4, Tables I and 11, page 209, column 2, were reversed when the paper was printed. The corrected tables are:

Jan 1, 1961

Jan 1, 1969

By C. D. King

A QUARTER century ago this country was producing an extraordinary quantity of iron and steel, with a decisive influence on the outcome of the first World War. Today this country is again demonstrating its industrial capacity with telling results. If this lapse of time has confirmed the opinion that man learns little from experience with respect to human relationships, at least we can derive some consolation from the knowledge that in the same period we have made huge strides industrially, and particularly in the steel industry. The differences represented by 25 years are striking, and have resulted from a multitude of changes that have contributed to the present-day high state of our pig iron and steel manufacture.

Jan 1, 1944

BENEFICIATION AND CONCEN'TRATION; FROTH FLOTATION U.S. 4,069,144 - In the froth flotation beneficiation of phosphate rock using at least an acid flotation step and an amine flotation step, the crude ore is dried either during transport or storage or by air circulation immediately prior to classification, and the dried ore mixed with water and classified prior to flotation The preliminary drying substantially eliminates the usual problems with clay slimes G. C. Johnson and A. E. Schweizer, assigned to Mobil Oil Corp. Jan 17. 1978. 4 pp (209- 11) . Filed 1 1-19-75 (633,535).

Jan 1, 1979

By R. M. Asimow, J. J. Svitak

Tile crilical resoll,r,d shear stress, CRSS, for slip of slow1y cooled Ag-All single crystals was measured at 201K. Tlze importance of short-range order and Suzuki sogregalion was inrestigated by deter~rlining llze ciic.cl of quenching on the CRSS. Thr obserz.ed rfrtenching effects were generally small and indicate that short-range ordcr and Slczuki srgregation do no1 account for n significant portion of the solid-solution strengthening in this system. However, all alloys slzozcwi yield drops ulhich rilere heat- lreat nrenl-sensiline THERE have been a number of mechanisms proposed to explain alloy strengthening in the Ag-Au system. The effectiveness of some of the proposed mechanisms, especially those that depend on Suzuki segregation1" or on short-range order,2-6 SRO? should be strongly dependent on heat treatment. Since internal friction investigations in this system indicate that there is stress-induced order,' we must also consider the possibility of local atomic rearrangement or short-range ordering in the stress field of a dislocation. There is not complete agreement whether these mechanisms should be most effective in raising the flow stress, in causing yield drops. or some combination of these two effects. This work was undertaken to determine the effects in the Ag-Au system of mechanisms that depend on segregation or order by using known but drastically different cooling rates following a high-temperature treatment. By comparing the critical resolved shear stress, CRSS, for slip measured after a very slow cool and again after a fast cool (quench) of the same crystal, it is possible to determine the effect of cooling rate on CRSS* and on yield drops. The single-crystal CRSS was determined at several compositions because there has been no data published across the phase field since the publication of room-temperature flow stress by Sachs and Weerts.' EXPERIMENTAL PROCEDURE Starting with materials of 99.999 pct purity, single-crystal specimens of random orientation 1.25 mm square by 4 cm long were prepared with 0, 10, 14, 25, 30. 50, 70. 75. 80, 90. and 100 at. pct Au. Crystals were grown in an inert atmosphere using a modified Bridgman technique with a growth rate of 1.5 cm per hr in a gradient of 3°C per cm. To obtain a maximum practical degree of SRO, the crystals were cooled at a rate of 275'C per hr to about 310°C and then cooled at 6°C per hr to approximately 200°C. Specimens were tested in tension immersed in an alcohol bath at -72°C (201°K) at a strain rate > = 0.003 mm"1 to determine the CRSS (7). The activation volume of several crystals was determined from the flow stress increment (72 - T1) for a tenfold increase in strain rate. The total shear strain varied from 0.05 to 2.3 pct but was generally less than 0.4 pct. After testing, each crystal was then held at 500°C for 10 min, quenched into brine at -35°C and. after storage at -71°C for 1 day, retested in tension using a procedure identical to that of the first test. The quenching apparatus, see Fig. 1, was designed to enable accurate temperature control and rapid quenching while preventing specimen contamination and accidental deformation. Test data from a specimen with a fine thermocouple spot-welded to it indicated a cooling rate of 104C per sec. The relatively low heat-treatment temperature was chosen to minimize quenching defects caused by a large vacancy

Jan 1, 1970

By Walter Bradley

MINING by hydraulic process of the important gold-bearing gravels of the Sacramento Valley in the basins of the Yuba, Bear and American rivers began in 1853, and continued at an ever-increasing rate for 30 years. In its most active days it reached an annual production of $15,000,000, and averaged $10,000,000 per year over the 30 years. During that period no provisions were made to prevent the debris from being dis-charged into the water courses, and ultimately large quantities of silt, sand and gravel were washed down to the lower valleys; filling channels, causing overflow of agricultural lands and difficulty in maintaining navigable depths in the Sacramento River. Agitation and suits filed because of these damages finally resulted in the injunction decision of Judge L. B. Sawyer,1 in the U.S. Circuit Court, Jan. 23, 1884, which closed down practically all hydraulic mining operations not having means to restrain their debris. In 1893 (approved March 1, 1893), Congress passed the act introduced by Representative Anthony Caminetti, of California, creating the California Debris Com-mission, composed of three officers assigned from the Engineer Corps of the U.S. Army, and since that time it has been legal and possible within the drainage systems of Sacramento and San Joaquin rivers to conduct hydraulic mining of gold-bearing gravels behind dams built under this commission's permit and supervision. In the watersheds of the Trinity and Klamath rivers, which flow directly to the Pacific Ocean and do not affect navigation or agriculture, operating permits from the California Debris Commission are not required. There is a measure of restriction there, however,. through what is known as the Trinity and Klamath River Fish and Game Dis-trict. Chap. 215, Stat. 1931, in order to secure relatively clear water for the fishing season, provides that between July 15 and October 15 each year there must not be discharged into these rivers debris that will cause a turbidity greater than a content of 50 parts per million in the

Jan 1, 1936

By George H. K. Schenck

Diminishing returns in management's fight to lower manufacturing expenses have added luster to savings that can be achieved in delivered costs through creative management of the distribution function. This is especially true for companies engaged in the production of bulk commodities, for which transport costs may represent 25 to 50% or more of total delivered price, A. E. Cascino, vice president of International Minerals and Chemical Corporation, recently gave an example of why top management in his firm is concerned with distribution: "The price of a ton of phosphate rock, f.o.b. mine, is about $7. The cost of warehousing, freight, and handling frequently totals an additional $11 . . . . If one of our competitors . . . discovers a way in which he can cut his distribution costs by $3, we're dead! Even if we wanted to offset our competitor's more efficient means of shipping with reduced f.o.b. price for our product-we don't have that much profit margin . . . ." In a special report on the revolution now occurring in transportation of goods, Business Week stated in its September 24 issue: "Moving and storing goods on their way from mine and mill through various sub-assemblies to their final markets costs anywhere from $50 billion to $75 billion a year- $100 billion if paperwork costs are included.

Jan 1, 1967

By Howard N. Eavenson

DURING the past year, as in the preceding ones, prices continued to fall, production to decrease, and more mines were closed. Much attention is being given by the industry to suggested plans for betterment of its position, and if the scheme recently brought out for consolidation of sales agencies into district agencies is loyally carried out, it cannot but help to improve conditions. The progress in the anthracite industry is shown in the report of its chairman, E. H. Suender; changes in coal preparation are outlined in the report of J. B. Morrow, chairman of Committee on Coal Preparation, while increased mechanization of the western mines is described by Eugene McAuliffe, chairman of the Committee on Machine and Strip Mining. In spite of the depression, interest in the Coal Division has been increasing, its meetings have been well attended, and its committees are active and have been doing excellent work.

Jan 1, 1932

By R. P. Smith, L. S. Darken

FOR a high-purity iron-carbon alloy, the phases existing at equilibrium at temperatures slightly above the temperature of the metastable eutectoid are austenite and cementite (hyper-eutectoid) or austenite and ferrite (hypo-eutectoid) and those below the eutectoid temperature (carbdn content > 0.02 pct) are ferrite and cementite. Such an alloy, held in a carefully controlled and measured temperature gradient (about 1 cm per deg) which includes the eutectoid temperature, then quenched and examined metallographicall.y, provides a precise measure of the eutectoid temperature. The samples were hollow cylinders approximately 1.3 cm OD, 0.63 cm ID, and 2.5 cm long, which had been carburized to the desired carbon content at 1000°C with an appropriate hydrogen-methane mixture. In order to cool the samples to room temperature with a minimum change of carbon content and absence of cracks they were quenched in a Cerro Bend bath at 480°C, followed by a water quench to room temperature. Three cylinders were suspended in the furnace1 in a purified helium atmosphere, by a closed end, thin wall, silica tube which also served as a thermocouple well. The top and bottom cylinders served only as a means of making the temperature gradient along the center cylinder more uniform. The temperature was determined with a platinum-platinrhodium thermel calibrated by comparison with a thermel certified (* 0.5OC) by the National Bureau of Standards. After holding in the temperature gradient for 24 to 72 hr the samples were quenched in Cerro Bend at 480°C, followed by

Jan 1, 1960

By E. W. Davis

THIS nation has been depending upon the Lake Superior iron ranges for most of its iron ore requirements for over half a century. Furthermore, it can continue to draw the major portion of its ore requirements from the same source for another century or more, but to accomplish this, great changes must take place in the present ore mining industry. Preliminary preparations for these changes are now underway and in the next few years decisions of far-reaching importance must be made. But to understand the situation, it is first necessary to know something of the nature and occurrence of the Lake Superior iron formation. So far as is known, the merchantable grades of iron ore remaining in the various Lake Superior ranges are as shown in Table 1, which shows that

Jan 1, 1947

By J. Spotts McDowell

Ackowledgments........................... 5 Introduction............................. 5 The Silica Minerals. Stability Relations......................... 6 Optical Properties........................ 9 Density.............................. 10 Melting Points....;..................... 10 Thermal Expansion..................,..... 10 Solubilities............................ 12 Identification of Cristobalite and Tridymite.............. 12. The Silica Refractories. Raw Materia1........................... 13 American Deposits....................... 13 Properties Determining Usability................ 15 Expansion on Heating..................... 16 Texture........................... 17 Silica Brick............................ 17 Manufacture........................... 18 Properties of Silica Brick .................... 19 Analysis ......................... 19 Density......................... 19 Porosity......................... 20 Strength....................... 21 Melting Point....................... 22 Specific Heat....................... 22 Thermal Conductivity................... 23 Expansion........................ 24 Effect of Rapid Temperature Change.........:... 26 Constitution......................... 26

Jan 1, 1918

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

Organization Place Date 1919 American Chemical Society Philadelphia, Pa. Sept. 2-6 National Assn. of Stationary Engineers Huntington, W. Va. Sept. 8 American Peat Society Minneapolis, Minn. Sept. 22-24 American Iron, Steel Electrical Engineers St. Louis, Mo. Sept. 22-26 American Institute of Min. and Met. Engineers. Chicago, Ill. Sept. 22-27 American Steel Treaters&apos; Society, First Annual Convention Chicago Ill. Sept. 22-27 National Exposition of Chemical Industries.... Chicago, Ill. Sept. 22-27 National Safety Council Cleveland, O. Sept. 29-Oct. 2

Jan 8, 1919