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By Wilbur Nelson

THE year 1924 showed even less drilling in Kentucky and Tennessee than the preceding year. The operators in this section, however, are anxious to resume development work and are only waiting for a higher market for crude oil before starting such a program. In Kentucky, during 1924, 1605 wells were completed, the combined initial daily production of these wells being 25,599 bbl. Of the total number of wells drilled 1176 were oil wells, 61 gas wells, and 368 were dry holes. The average initial production of the oil wells was 21.8 bbl. per well. In Tennessee, 28 wells having an initial daily production of 1199 bbl. were completed during 1924. Of these, 3 were oil wells, 6 were gas wells, and 19 were dry holes. The initial production of the three oil wells was 400 bbl. Of the total number of wells drilled in Kentucky in 1924, 73 per cent. came in as producing wells; and of those drilled in Tennessee, 10 ½ per cent. came in as producing wells and 20 per cent. as gas wells. In Tennessee, during 1924, wildcatting dropped off considerably and only about one-half as many wells were drilled as in the preceding year; in Kentucky, on the other hand, there was only a slight curtailment in drilling, there being 1943 wells drilled in 1923 as against 1605 in 1924.

Jan 3, 1925

The regular activities of the Institute are financed mainly by income derived from members' dues, from advertising in MINING AND METALLURGY, and from the sale of publications to the public. In addition, collateral activities and special projects are financed each year by means of income from endowed funds controlled and administered by the Institute. In the aggregate, the amount of these endowments totals more than $637,000. An active effort is being made to increase the endowment funds of the Institute through a standing committee, of which Henry Krumb is Chairman, and of which the other members are: George D. Barron, Cleveland E. Dodge, John V. N. Dorr, Howard N. Eavenson, D. C. tackling, Harvey S. Mudd, Wallace E. Pratt, Milnor Roberts, and Wilfred Sykes. This committee believes that there exists a tremendous opportunity for the Institute to be of evergrowing service to the public, to the mineral industries, and to the 'profession. It welcomes suggestions as to names of men of means who are vitally interested in the mineral industries, and to whom the opportunity to make a contribution or bequest might appeal favorably if presented in the proper light.

Jan 1, 1946

By B. Pitchumani, D. Venkateswarlu

INTRODUCTION The characteristics of feed and product of any size reduction operation are normally expressed as mean size, the size corresponding to 80 percent undersize or the percentage below a specified size or specific surface area. But the feed has a distribution of sizes and quite often it becomes essential to obtain a product of desired distribution. In such cases, size distribution of feed is related to product by matrix methods. The technique of matrix representation of crushing operation was proposed by Broadbent and Calcott (1 to 4). They divided the complete crushing mechanism of coal into breakage, selection and classifying functions for a closed-circuit system to establish relations between the feed and product distribution. Ellis, Ray and Venables (6) suggested an empirical method of determining the breakage matrix by combining the characteristic functions and proposed the following hypotheses: 1. The breakage of individual size fractions passing through the mill at a given rate is the same whether passed separately or as part of a mixed feed. 2. The breakage of a mixed feed may be estimated from the products of individual size fractions passed through the mill separately at a rate at which they would be crushed as part of the mixed feed. This method is stated to be applicable when there is no interaction between the individual sizes.

Jan 1, 1980

By Geo. W. Goetz

The following tables show the analyses of ores from nearly all of the mines which will produce over 10,000 tons of ore each during the season of 1890. There are many small mines now in the course of development, some of which may become large producers. Many of the mines produce several different grades of ore, but the analyses given in the tables are fair averages of ore such as the respective mines can deliver. Most of these analyses were obtained from the agents of the respective ores, and are averages of the season of 1889. One can state positively that over 75 per cent. of all the iron-ores of the Lake Superior district will average over 60 per cent. of metallic iron. During the past 34 years this region has produced about 48,137,421 tons of ore, the different districts contributing about as follows: Marquette District,. 29,754,057 Menominee " .10,415,859 Gogebic " . 6,622,194 Vermilion " . 2,342,991 Miscellaneous,. .. .. 2,320 In the year 1889, the product of all the districts was nearly '1,300,000 tons. The product of the entire region for the season of 1890 may exceed 9,000,000 tons. This large amount of ore is shipped to the lower lake ports, from Escanaba, Marquette, Two Harbors and Gladstone.

Jan 1, 1891

By A. U. Seybolt

DURING the course of an investigation of hot corrosion of nickel-base superalloys (combination oxidation-sulfidation attack at high temperature), it was considered possible that sulfur might gain entrance to the alloy in part, at least, by diffusion through the scale. Cr203 is nearly always observed as a prominent component of the oxide scale, and hence some experiments were carried out to examine the tracer diffusion of sulfur through Cr203 at 1000° C in the upper temperature range experienced by jet engine blades and vanes. Some hot-pressed Cr203 discs of quite high density were available from an earlier investigation1 on the rate of crf3 migration through Cr203. The Cr203 was 99.3 pct pure and contained -0.06 pct Fe as the largest metallic impurity. Additional data is given in Ref. 1. In this earlier work it was found that the rate of cation diffusion was independent of the atmosphere of thermal equilibration when using nitrogen, argon, or air, and also that the electrical conductivity of the hot-pressed Cr203 compacts was likewise independent of atmosphere in this range, thus indicating that the de-

Jan 1, 1969

By Alan U. Seybolt

UNLIKE its sister elements, columbium (niobium) and tantalum, vanadium has not been available until recently in fabricated form. While Vanadium Corporation of America has offered the metal in fairly pure form for sale for many years in small lots for research purposes, this grade of vanadium has been brittle, probably because of a high oxygen content. Hence, when in 1950 the announcement1 was made that wrought vanadium was available as a commercial material, this represented a large step forward in the metallurgy of vanadium. While vanadium is generally regarded as a rare metal, data on its occurrence in the earth's crust show it to be as abundant as copper, zinc, and lead combined. Vanadium is widely distributed, but it does not seem to occur in massive deposits except in a few localities, principally in Colorado, Utah, and Arizona, where it is found in sandstone formations, and in Mina Ragra, Peru. Only in Colorado or Peru are ores mined solely for the vanadium content. Ores in the United States are principally carnotite and roscoelite; the former is of particular interest because of its uranium content. It is a uranium-potassium vanadate containing approximately 52 pct of UO2 and 18 pct of V2O5. Production in the United States during the war years averaged around 2000 tons a year, but dropped to 636 tons in 1946. In recent years, ferrovanadium has been selling for about $2.80 per pound of contained vanadium. This suggests that the price of the pure metal will never be as low as $2.80 per pound, but it could

Jan 1, 1953

By AIME

AS the Petroleum Division rounds off the first quarter century since its evolution from technical committee status, there steps to the long line of notable men who have presided over its activities a young man, currently of Tulsa, one Herbert F. Beardmore by name. For one year, as Chairman for 1946, the Division will be his oyster. hi; baby, his responsibility. "Herb" Beardmore was born at Columbus, Ohio, Feb. 6, 1904, and lived there until he was thirteen. Then his family moved to Oklahoma City, and later sent him to the University of Oklahoma, where he graduated in 1925 with a B.S. in engineering geology. His final year in college was the first year in which a petroleum engineering course was taught at the school. Since his course of study so closely paralleled that of a petroleum engineer, he has frequently been spoken of as the first petroleum engineering graduate from the University of Oklahoma. Out of college he went to work as an oil-field roustabout in the Ranger, Texas, field for Jake L. Hamon. This work consisted of all manual labor phases of cable-tool operation and beam-pumping of oil wells. He moved in 1926 to Bartlesville, to become a gas engineer for the Indian Territory Illuminating Oil Co., where he was employed in gas-well drilling, gas production, and transportation, mostly in Osage County, Oklahoma.

Jan 1, 1946

By Jerome J. English, Gordon W. Powell

An experimental investigation and mathematical analysis of the thermal-dilation behavior of the titanium alloy Ti-7Al-3Cb have shown that the linear dimensional changes associated with the polymorphic transformation need not be isotropic. The absolute magnitude of the linear dimensional change, which may be either positiue or negative, associated with the cr-p transformation is dependent upon the relutzve volumes of different orientations of the transformation product. It is hypothesized that the dilation irregulati-ties that have been observed during the polymorphic transformation of pure, coarse-grained titanium and other titanium-base alloys can be explained in the same manner. When titanium is heated above about 165O°F, the hcp a structure transforms to bcc 0. Thermal-dilatioh measurements have shown that the transformation is accompanied by a decrease in length of 0.16 pct.' Such dilation behavior would be expected because the volume of the hcp unit cell is about 0.3 to 0.4 pct greater than that of the bcc unit cell. A recent investigation2 of the thermal-dilation behavior of an experimental a-p* titanium alloy, Ti- 7A1-3Cb, containing 0.06 wt pct 0 showed that its dilation behavior during the polymorphic transformation differed substantially from that reported for unalloyed titanium. The first time the alloy was cycled through the transformation, the dilation curve closely duplicated that of unalloyed titanium. However, upon repeated cycling through the transformation temperature range, both the magnitude and the sign of the dimensional change associated with the transformation were observed to vary with each cycle. This investigation was undertaken to obtain additional data on the dimensional changes associated with the polymorphic transformation in the Ti-7A1-3Cb alloy and to determine the cause of the dimensional irregularities. After testing, the specimens were examined metallo-graphically. In addition, Laue back-reflection patterns were obtained from selected sections taken perpendicular to the specimen axes to determine the a orientations present in these sections. White radiation from a tungsten target and a 0.1-mm-diam collimator were used to produce the diffraction patterns. RESULTS Dilation Curves. Three types of thermal-dilation curves were obtained when the a-8 titanium alloy was heated and cooled through the transformation temperature range. These three types of curves are illustrated in Fig. 1. The type I curve represents what is considered normal behavior, because the dilation change is what would be expected on the basis of the volumes of the unit cells of a and p. The Type I1 curve is the inverse of Type I. Normal behavior is characterized by an expansion on cooling through the transformation, whereas a contraction takes place in the Type 11 curve. With Type ni behavior, no clearly distinguishable length change occurs during the transformation. No other anomalies that might be indicative of other phase transformations were observed in the dilation curves at lower temperatures. Apparently, the cooling rate was low enough for equilibrium to be reached during the 0 to a transformation. Table I lists the types of dilation curves observed during the polymorphic transformation as a function of the direction of measurement and cycle number. The A1 value was determined by extrapolating the low-temperature (a + 5 pct p) and high-temperature (100 pct p) segments of the dilation curves to a common temperature and measuring the difference in the or-dinates at that temperature, see Fig. 1. The transformation occurs over a temperature range in this alloy, so the magnitude of A1 is not an absolute value but depends on the choice of temperature. A mean temperature, T,, within the transformation temperature range was selected for the measurement. T, on cooling occurred about 100°C lower than T, on heating. The first time each of the three dilation specimens was heated to above the temperature, that is, Cycle 2, normal Type I behavior was observed. In Cycle 3, two deviations from normal behavior occurred. First, during cooling of the longitudinal specimen, a substantially larger expansion, +0.21 pct, was measured as 0 transformed to a compared with +0.03 pct in Cycle 2. Second, the thickness specimen was observed to undergo a contraction instead of the anticipated expansion on cooling. Continued cycling of the three specimens from room temperature to 2500°F produced additional changes in the dilation behavior. These changes did not seem to be related to the fabrication direction of the alloy because the values of a1 for the longitudinal, transverse, and thickness specimens varied unpredictably in magnitude and sign. Furthermore, both the longitudinal and transverse specimens showed all three types of dilation curves at least once during the six cycles that they received. Fig. 2 is a sketch of the transverse specimen after

Jan 1, 1967

By K. Winterton

The effect of a near-saturation unidirectional magnetic field was to decrease slightly the endurance life in Armco iron in the annealed condition. This is expected since the energy-absorbing mechanism associated with domain wall movemenfs is inhibited bv the strong field. THE factors determining failure under dynamic loading are not yet clearly recognized. One of the properties of a metal which might be thought to influence fatigue life is its damping capacity. Foppl1 conducted an alternating torsion test at a frequency of 700 cpm continuously for a period of 3 years, without the test piece breaking or showing any sign of deterioration after 1100 Million cycles of stress; the rate of dissipation of energy was sufficient to maintain the test piece at about 100°C above the ambient temperature. cazaud2 concludes from this, and others follow him, that ('the capacity for dissipation in the form of heat by internal damping is unlimited" and that therefore "damping is not directly related with fracture by fatigue." Future work may necessitate qualification of this rather uncompromising view. It is shown later that in all

Jan 1, 1960

By James L. Calver

Fuller’s earth is an inexact term applied to certain clays that have a marked ability to adsorb coloring materials from animal, vegetable, and mineral oils. Many clays have this adsorbing power to a slight or very limited degree, and certain other clays, chiefly bentonites, as well as minerals such as bauxite, can be made highly adsorbent by activation with acids or alkalies, but the term fuller's earth is generally reserved for clays that are naturally highly adsorptive. In most fuller's earths and practically all activable clays montmorillonite is a dominant mineral. No definite clay mineral or group is implied in the name fuller's earth, and the distinction between fuller's earth and other clays that have more or less bleaching power is not sharply drawn. The name as generally used has no genetic or mineralogical significance. The fuller's earth produced in the Florida-Georgia district contains the clay mineral attapulgite. This mineral name was first used in 1930 by DeLapparent to apply to a hydrous aluminum magnesium silicate found in the fuller's earth from Attapulgus, Ga., and Quincy, Fla. An essential component of its structure, determined by Bradley in 1940, is that the silica chains of the molecule are arranged similarly to those of the amphibole minerals. The fibrous nature of the lath-like crystals of attapulgite is apparent under magnifications reached by the electron microscope. The ideal formula, [(OH,), (OH), Mg, Si, 0,-4H,O], contains no aluminum, but there is considerable replacement of the magnesium by aluminum. In the classification of clay minerals, attapulgite is associated with sepiolite and polygorskite rather than with mont-morillonite.

Apr 1, 1956

By Olav Idelgeland

FROM indirect evidence point defects have been believed to influence the fatigue behavior of metals and alloys.1,2 Measurements of changes in resistivity made after cyclicstressing at low temperatures indicate that a very high density of defects is present, part of which may be removed by room-temperature annealing.3'4 These results are consistent with the generation of a high number of point defects at low temperatures. Corresponding measurements made after room-temperature stressing did not show any recovery effects.3 This was attributed to a stabilization of the dislocation network after a few thousand cycles without generation of vacancies. In this laboratory resistance measurements of copper single crystals, shaped as normal fatigue specimens ,5 have been made with a Kelvin double bridge at room temperature during and after cyclic stressing at 80 cps by comparing with a dummy at a close and constant temperature. Temperature differences were measured to ±0.025°C with fine thermocouples taped onto the gage lengths. Potential leads were tin-soldered into small holes in the gage length to give stable values. Corrections for differences in temperature and changes in mean length of the specimen were made according to the formula:

Jan 1, 1968

By Cresap P. Watson

ABOUT the time this magazine reaches its readers, Cresap P. Watson will celebrate his 53d birthday. If he spends that birthday at his West Los Angeles home, he won't be far, as distance is measured today, from Santa Barbara, where he was born on July 8, 1895. He is truly a member of a petroleum family; one brother, N. O. Watson, managed Royal Dutch Shell interests in Venezuela for years and is now general manager of the Caribbean Petroleum Co. at. Maracaibo; another brother, Rex, is vice-president of the Drilling and Exploration Co., while brother-in-law Ben Belt is an executive of Gulf Oil. His own life has centered in the petroleum industry since his first job in 1913 as camp cashier for a Mexican oil field at Tampico. Down on the isthmus of Tehuantepec he advanced to tool dresser and' production foreman for the company. The first World War interrupted his Mexican experience by transforming him into an artillery officer in France. Once the Army ceased to demand his services¬by then it was 1919-he returned to the task of furthering his professional career as agent for the Amerada Petroleum Corp. By 1927 he had reached the position in which he could be called an executive in the petroleum industry, having organized and become president of the Federal Royalties Co. His activities in local and national legislation affecting the petroleum industry increased as has his advocacy of the development of oil and gas fields under sound engineering and conservation principles through unitization or other co-operative forms of operation. Considerable amounts of his time go to the promotion of industry public relations.

Jan 1, 1948

The International Mining Convention held in Nelson, B; C., May 17 , to 19, was attended by nearly 500 delegates, of whom about 100 were from Spokane, 150 from the Slocan district, and the others from different points in Canada and the United States. Arrangements were in charge of the Nelson, Slocan and Eastern British Columbia Mining Men's Club, under the direction of Secretary Fred A. Starkey, assisted by the City of Nelson, Associated Boards of Trade of Eastern British Columbia and Nelson Board of Trade. The Columbia Section of the American Institute of Mining Engineers; cooperating with the Western Branch of the Canadian Mining Institute, provided the technical program, under the management of Secretary E. Jacobs, of Victoria, and Secretary L. K. Armstrong, of Spokane. Three technical sessions were held, at which the following were read: Difficulties of the Electrolytic Zinc Process, by Thomas French. Sketch of the Geology and Ore Deposits of Nelson and Kootenay Region, by Arthur Lake's. Advantages of Local Organization of National Societies, by W. H. Linney. Review of Kootenay Mining, by Bruce White. Milling of Partially Oxidized Ores, by S. S. Fowler.

Jan 7, 1917

L. C. GRATON, Cambridge, Mass.-I should like to ask the authors if they attempted to draw any analogies with the manganese deposits at Franklin Furnace, N. J., and whether there are. any traces of zinc in these Brazilian-deposits. J. T. SINGEWALD, JR.-We did not think of them at all as analogous to the Franklin Furnace deposits and there is no appreciable percentage of zinc present. If these ores do contain zinc it could be there 'only as a fraction of a per cent. F. LYNWOOD GARRISON, Philadelphia, Pa. (communication to the Secretary *).-There is no disputing the fact that the manganese ore ,supply situation in this country demands serious consideration and is a matter of fundamental public concern. We are consuming this material at a steadily accelerating rate and there is no hope for a proportionate increase in the domestic supply. In the year 1916, this country imported 560,000 tons and produced only 27,000 tons from our own territory In 1915, the local production was 9,709 tons, which on its face shows the American output to have tripled during the past year. Those of us who are familiar with the

Jan 4, 1917

By R. W. Smith, R. W. M. Lai, J. Leja

J. Leja (Professor, Dept. of Mineral Engineering, U.B.C. Vancouver, Canada) — I would like to offer some comments on the behavior of contact angle with time, treated in this paper. The authors should be congratulated for a clear exposition of these uncommon departures in the correlation between flotation and contact angle, in systems of importance to industrial practice. Some nine years ago Professor J. H. Schulman (presently at Columbia University, New York) and I reported on a similar study conducted at the Ernest Oppenheimer Laboratory, Cambridge, England.' The systems used by us had, how- ever, no direct practical application at that time, as mercury in solutions of xanthates was tested with a variety of alkyl-aryl polyoxyethylene frothers which were then new to flotation practice. Further, the paper dealt with findings contrary to the then widely held belief that the contact angle established in collector-solution is unaffected by the addition of a frother. Correlation with flotation, or lack thereof, was not sought, though we did suggest that in many cases the selectivity of frothers might be influenced by the dynamic contact angles. We also stated (on p. 243,

Jan 1, 1968

By Werner Goldsmith, Akihiko Kumano

An experimental investigation was conducted to study the response of soft, porous rock, green shale, under dry and liquid-filled conditions to normal impact of hemispherically-tipped cylindrical steel projectiles with diameter and mass of 6.35 mm and 31 g, respectively. Disk-shaped green shale specimens with nominal thickness and diameter of 32 mm and 127 mm, respectively, were tested in the initial projectile velocity range of 18 to 42 m/s. For the liquid-filled tests, the green shale specimens were saturated with kerosene. A total of eight impact tests were conducted. Information on the extent and pattern of the damage in the rock and velocity histories of the projectiles were collected. It was found that while the penetration depth was quadratically related to the initial projectile kinetic energy for the dry case, the penetration depth for the liquid-filled case was directly proportional to the initial projectile kinetic energy. The results of the impact tests under dry and liquid-filled conditions conformed well to a linearly viscous model and a Coulomb frictional model, respectively. The major deformation processes in the dry specimens were found to be compaction and equivolumnial distortion of the material. In the liquid-filled case, however, formation of cracks and equivolumnial distortion with less material compaction were observed. Furthermore, craters were formed as a result of the crack formation in the liquid-filled specimens.

Jan 1, 1982

By James H. Courtright, Kenyon Richard

TOQUEPALA is a porphyry copper deposit in which mineralization is localized by a large breccia pipe formed in close genetic relation to intrusive rocks. The deposit is in southern Peru, 55 airline miles north of the small city of Tacna and the same distance inland from the port of 110. Quellaveco and Cuajone, geologically similar deposits, lie 12 and 19 miles north of Toquepala. Chuquicamata is 400 miles to the south. The deposit is high on the southwestern slope about 20 miles from the crest of the Cordillera Occidental of the Andes Chain. It lies in a mountainous desert where the steep southwesterly slope of the Andes is dissected by a succession of rapidly downcutting, deep canyons. Local topography is moderately rugged with a dendritic drainage pattern and an elevation of 8000 to 14,000 ft. Volcanic peaks along the crest of the Cordillera rise over 19,000 ft. Local precipitation, including a little snow, amounts to about 10 in. during January and February, but general runoff in the region is slight. Throughout southern Peru the springs and streams are widely separated. Crude canals irrigate small farms on terraced slopes along the streams and provide sparse subsistence to the semi-nomadic inhabitants. During the past decade, engineering and geological explorations of the region, as well as the mineral deposits themselves, have required construction of a network of several hundred miles of roads. Before this, roads extended only a few miles inland. Many areas still can be reached only by trail. Toquepala was briefly described in 19th century geographical literature as a copper deposit, and it received desultory attention from Chilean prospectors early in the present century. It was first recognized as a mineralized zone of possible real importance by geologist O.C. Schmedeman during an exploration trip for Cerro de Paso Copper Corp. in 1937. The discovery was late as compared to earlier recognition of Chuquicamata, Potrerillos, and Braden of Chile and Cerro Verde of southern Peru. This was due partly to the region's difficult accessibility but principally to the obscure character of the outcrop evidence of copper. From 1938 until 1942 Cerro de Pasco Copper Corp. partially explored the deposit by adits and diamond drillholes. This campaign was supplied by a 60-mule pack train continuously shuttling over a 30-mile trail. Northern Peru Mining & Smelting Co., a wholly owned subsidiary of American Smelting & Refining Co., undertook regional engineering stud- ies in 1945 and drill exploration in 1949. According to published data1 the deposit contains 400 million tons of open pit ore averaging a little over 1 pct Cu. It is currently undergoing large-scale development by Southern Peru Copper Corp., which is owned by American Smelting & Refining, Phelps Dodge, Cerro de Pasco, and Newmont Mining. Summary of Geology: The deposit is situated in a terrane composed of Mesozoic(?) and Tertiary volcanic rocks intruded by dioritic apophyses of the Andean Batholith. These formations are exposed in a northwesterly trending belt about 15 miles wide. Along the northeast they are unconformably overlain by Plio-Pleistocene pyroclastic rocks, which occupy much of the crest of the Andes, and along the southwest they are covered by the Moquegua formation of Pliocene(?) age. The mineralized area, oblong in shape and about 2 miles long, has been a locus of intense igneous activity. Several small intrusive bodies having irregular forms occur within and adjacent to a centrally located, large breccia pipe. The mushroom-shaped orebody consists of a flat-lying enriched zone of predominant chalcocite with a stem-like extension of hypogene chalcopyrite ore in depth within and around the pipe. This breccia pipe is relatively large and has been formed by repeated episodes of brecciation. Small satellitic pipes occur at random within a 2-mile radius of this central pipe. These too were individual sourceways of mineralization, although not always of ore grade. Within and around the zone of breccia pipes and mineralization there are a few faults and veins, but these are discontinuous random structures of minor significance. There are no regional or local systems of faults or other planar structures recognized which could account either for the mechanical development of the breccia pipes or for their localization as a group or as individuals. Hydrothermal alteration is pervasive in the zone of mineralization. Clay minerals appear to be abundant in places, but their percentages are undetermined. Quartz and sericite are the principal alteration products, and in many instances original rock textures are obliterated. The principal sulfides, hypogene pyrite and chalcopyrite and supergene chalcocite, occur mainly as vug fillings in the breccia and as small discrete grains scattered through all the altered rocks. Sulfide veinlets are relatively scarce. Sulfides are more abundant and alteration is more intense in certain rock units, such as the diorite and most of the breccias. Although the Toquepala mineral deposit is similar in most respects to the porphyry copper deposits of southwestern U. S., it most closely resembles the Braden deposit of Chile, as described by Lindgren

Jan 1, 1959

By W. L. Mamme, G. Y. Chin

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain was analyzed by Taylor and by Bishop and Hill in terms of a minimum (internal) and a maximum (external) work criterion, respectively. These two criteria have now been generalized to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (noncrystallographic) pencil glide. The generalized treatment also takes into account the possibility of a Bauschinger effect and of unequal hardening among the shear systems, which were considered in the Bishop and Hill work. Optimization techniques of linear and nonlinear programming are shown to be applicable for the numerical calculation of the minimum or maximum work. In the case of crystallographic shear, the constraint functions are linear and hence the optimal work is obtained as the saddle value of the lagrangian function Wi(y) e minimum and W,(u) + (a) for the maximum, where Wi is the (internal) work, We is the (external) work, Y is the crystallographic shear strain, u is the applied stress, and and are constraints. It is shown that the Lagrangians are functionally the same and the saddle value of one problem is identical to the saddle value of the other, proving that the two analyses are completely equivalent. In the case of pencil glide, although the constraint functions are nonlinear and neither convex nor concave, the equivalence of the optimal values to the saddle value of the Lagrangian (which is again identical for both problems) is still valid. WHEN a crystal deforms plastically by crystallographic shear, five independent shears are generally required to accommodate five independent strain components specifying the deformation. Assuming slip as the only shear mechanism, Taylor1 in 1938 analyzed the deformation in terms of a minimum work criterion. He hypothesized that of all combinations of five slip systems which are capable of accommodating the deformation, the active combination is that one for which the internal work C is a minimum, where 1 TI is the critical resolved shear stress for slip on the 1-th slip system and is the corresponding simple shear. By further assuming equal 72 for all equivalent slip systems and no Bauschinger effect, Taylor re- duced the minimum work problem to one of minimum and applied the analysis to the case of axisym- Metric flow by {111}(110) slip in fcc crystals. However, he did not consider the question of whether the resolved shear stress has in fact attained the critical value for slip on the newly found active systems without exceeding it on the inactive systems. In 1951 Bishop and ill' put forth the maximum work analysis in which slip is again assumed as the only deformation mechanism. In this analysis, the work o1 done in a given strain ij by a stress ujj not violating the yield condition is maximized. In addition, the analysis takes into account the possibility that the critical resolved shear stress for slip may not be equal among the slip systems and that the slip behavior may exhibit the Bauschinger effect. As with Taylor, a single set of slip systems—{111)(110) — was analyzed numerically. It thus appears that the Bishop and Hill treatment is on a more sound physical basis than the Taylor treatment. However, Bishop and Hill showed that where there is equal hardening among all slip systems and when there is no Bauschinger effect, Eq. [11 ] of Ref. 2, as assumed by Taylor, the results of their maximum work analysis are the same as those of Taylor's minimum work analysis. Hence at least under those conditions there is an implication that the Taylor analysis does lead to a critical resolved shear stress for slip on the predicted active systems without violating the yield condition on the inactive systems. Recently, the Taylor analysis was applied for numerical solutions of the axisymmetric flow problem, for slip on {110}(111), {112}(111). {123)(111) systems as well as a mixture of all three sets of svstems."1 Computational techniques based on the optimization theories of linear and nonlinear programming4 were employed in these solutions. The same techniques were employed in the solutions of an axisymmetric flow problem of deformation by slip on (111) (110) systems and twinning on (111)(112) systems5 which had been considered theoretically from a modified Taylor approach. The utilization of these techniques has led to the realization that the solutions of Taylor's minimum work problem imply the solutions of Bishop and Hill's maximum work problem. The two problems turn out to be dual problems in the well known sense of mathematical programming. It is thus the purpose of this paper to first generalize the minimum and maximum work analyses to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (non-crystallographic) pencil glide, as well as the possibility of a Bauschinger effect and of unequal hardening

Jan 1, 1970

By Robert Bakish

VARIOUS aspects of structure-sensitive corrosion of single crystals and polycrystalline aggregates of Cu,Au have been presented in papers by the author, in association with W. D. Robertson. Prompted by some observations in the course of these studies, a new approach to the problem was undertaken. Results of these new experiments are reported here. Thin slices, less than 2 mm thick, were prepared from single crystals 3.5 mm in diam grown by the Bridgman technique. The crystals were homogen- ized for 300 hr at 850°C. Crystals with no deformation, crystals deformed in tension to the yield point, and crystals deformed 20 pct in excess of the yield point were used. Crystals of several different orientations were studied. Slices were immersed for one month in 2 pct aqueous solution of FeCl3 and, subsequent to this immersion, were subjected to bending. Immersion and bending were carried out at room temperature. The size and geometry of the crystals did not permit accurate data on the loads involved. A most unexpected result was obtained in the process of bending these slices of Cu3Au crystals normal to the (110) plane. Completely brittle be-

Jan 1, 1958

By Robert Maddin, Neng-Kuan Chen

THE (001) planes have been reported as the cleavage planes in body-centered cubic metals such as alpha-iron and tungsten.' However, in molybdenum, which is also body-centered cubic, experimental X-ray evidence indicating a similar cleavage plane still seems lacking. Tsien and Chow" observed microscopically in the extension at around 1000°C of molybdenum single crystalline wires 0.25 mm in diam that the fracture plane seemed to be parallel to the operative slip plane, which appeared to be (110) at that temperature. Zapffe' pointed out from fractographic study of polycrystalline molybdenum that "although the transgranular pattern is characteristically non-crystallographic, patterns occasionally reveal {100} cleavage." This has been generally assumed to be the case at ordinary temperatures. In the present experiments, a single crystal of Fansteel molybdenum, Vs in. diam x 2 in. long, prepared by the methods described by Chen, Maddin, and Pond" was fractured at room temperature by bending. The fracture surface appeared to be quite similar to the cleavage surface of zinc and was crys-tallographic. A back-reflection Laue photogram was made using 35 kv copper white radiation; the X-ray

Jan 1, 1952