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By H. H. Rachford, D. S. Howard

In the withdrawal of fluids from tilted aquifers it is of value to be able to predict pressure patterns during the course of the pressure decline. As an example of this, in the displacement of fluids from oil reservoirs being produced by water-drive, prediction of the reservoir pressure is an important factor in fixing production rate. The prediction of pressure patterns in the depletion of an inclined aquifer has conventionally been made by solving the well known flow equations for the pressure Patterns in a horizontal aquifer, and correcting these patterm for the pressure difference due to the hydrostatic head associated with the vertical distance between a point in the horizontal aquifer and the corresponding point in the tilted aquifer. Inasmuch as the equation describing flow in tilted strata is different from that for horizontal flow. there was question as to the validity of the simple corrective procedure current1y in use. To examine the magnitude of error made using this procedure, an inclined aquifer was chosen for which the error was expected to he large, and the equation for flow in this tilted stratum was solved numerically. The results of the conventional procedure of correcting the solution of the equation for horizontal flow was compared with the solution of the correct equation by studying the difference between predicted pressures by the two methods. Three forms of the hydrostatic head correction were studied. The results for all three forms of the head correction are similar. The error in the approximate solution is quite dependent on the position of the horizontal aquifer with respect to the inclined one. The error is greatest at the producing end ad increases with amount of fluid withdrawn. The magnitude of the errors is not large if a good choice is made for the position of the horizontal datum. The most satisfactory position for the datum in all cases is near or slightly about the mid-point of the inclined stratum. Use of the best approximate method studied with the best datum tested yielded predicted pressures in error no greater than 7 psi. INTRODUCTION The movement of water by expansion from an aquifer to displace fluids from a contiguous oil reservoir was first recognized over 20 years ago.9 Since that time much work has been done to relate this mechanism to reservoir behavior mathematically. The result of this effort on the part of many workers has led to an understanding of underground fluid movement which has enabled us to follow and predict the behavior of the water-drive reservoir. One reason that good progress has been made in the application of mathematics to the study of pressure patterns and water movements in aquifers has been that the differential equation which describes this process is of a relatively simple form. The equation for the isothermal, horizontal, viscous flow of water through homogeneous sandstone is identical with that for the diffusion of heat through homogeneous solids, and this equation and means of obtaining solutions for it with many types of boundary conditions have been studied extensively. That this work has been highly successful is clearly emphasized by the large number of solutions developed for problems of interest both by methods of formal mathemat-

Jan 1, 1957

By R. I. Jaffee, F. C. Holden, H. R. Ogden

Ti-Mn alloys were studied in order to determine the factors affecting the mechanical properties of &stabilized titanium alloys. The principal compositional factors have been found to be solid-solution strengthening, the martensitic transformation, and instability of the P phase. Structural factors, such as grain size and shape, were found to have more influence on ductility and toughness than on strength. THE alloys of titanium with the &stabilizing elements offer the chief hope for developing useful heat treatments. Conversely, the heat-treatment response possible with the p-stabilizing elements causes difficulties such as weld embrittlement and thermal instability during service at elevated temperature. Therefore, it is of considerable technical importance to understand the factors that govern the heat-treatment responses in these alloys, so as to be able to soften the alloys if they are embrittled by an adventitious heat treatment, to render them stable in service, or to harden them while maintaining adequate ductility and toughness. The Ti-Mn system is a good example with which to demonstrate the factors that govern strength and heat-treatment response in. a P-stabilized system. The region of the a-j3 transformation, after the work of Maykuth, Ogden, and Jaffee,' is shown in Fig. 1. The a solubilities are low. This means that, in the two-phase a-p field, partition of manganese between the two phases occurs practically only to the P phase. The solid-solution effects are therefore chiefly the result of solution in the ,8 phase. The eutectoid occurs at 20 pct Mn and 550°C, and proceeds very sluggishly. It can be ignored in heat treatments in hypo-eutectoid alloys, except for long-time storage at low temperatures below the eutectoid temperature. Even here, there is some question that diffusion proceeds far enough to involve eutectoid decomposition. Three compositional factors bear on the mechanical properties and structure of titanium a-P alloys. These are: 1—solid-solution strengthening, 2—mar-tensite transformation, and 3—P instability. Combined with the purely structural factors of grain size and shape, these govern the properties of the alloys. Perhaps the most important factor is solid-solution strengthening. The facts that manganese dissolves in a titanium to a maximum of only 0.5 pct and most of the manganese partitions to the p phase dominate the structure and properties of the a-/3 alloys. Because of the overwhelming preference of manganese for the ,3 phase, the P phase is harder and the a phase is softer. The relative amounts of both phases may be modified by heat treatment in the a-P field as application of the lever rule in the two-phase field clearly shows. A critical temperature in the Ti-Mn diagram is 800°C. This is the P transus temperature of the 6.4 pct Mn alloy, which has the lowest manganese content which will form all retained-P phase on quenching to room temperature. Any quench performed from below 800°C will produce a structure consisting of only a, a plus retained P, or retained p, for alloys of the compositions used in this work. For alloys containing less than 6.4 pct Mn, any quench from above 800°C will always result in structures

Jan 1, 1955

By B. J. Shaw, R. Kossowsky, W. C. Johnston

High purity (99,95) Ni-51 wt pct cr eutectic alloy was unidirectionalty solidified at rates of 0.1 to 8 in. per hr. The resulting material was characterized by large grains, approximately 0.5 mm in cross section and extending through almost the entire length of the specimen, parallel to the growth axis. The eutectic structure of specimens the growth at -1/3 The per hr consisted of a continuous nickel-rich phase and chrome -rich lamellae approximately 2 thick, spaced about apart. Specimens were tested in compression at temperatures ranging from —196 to 850"C over which range the 0.2 pet yield strength dp -creased from 160,000 p si to 35,000psi, respectively. Swaging to 40 pet reduction in area, followed by a 30-min anneal at 1000c to remove residual cold work, increased the 0.2 pet yield to 260,000 psi at -196°C, dropping to 35,000 psi at 850°C. The increase in strength was attributed to a residual cell structure. The strength of the alloy could be rationalized by the simple rule of mixtures if one assumed that additional strength is derived front a size effect characterized by is petch equation IN recent years there has been increasing interest in dispersion and second phase strengthening in materials needed for high-temperature applications. inm role of structure on the mechanical The of such alloys has been well established of such some extent accounted for theoretically. and to of how the strengthening mechanisms due to fibers and lamellae operate has been reduced to its fibers form by the fabrication of composites of strong rods unidirectionally aligned in a From work on tungsten-fiber-reinforced copper, for example, it was established that the "Rule of Mixtures" could explain the strengthening.12 " some what more sophisticated technique for introducing strong fibers into copper matrix was used by Hertzberg strong Kraft3 who unidirectionally solidified the copper-chromium eutectic. The use of unidirectionally fied eutectics has advantages in that there are no matrix-fiber wetting problems and fine fibers are automatically aligned and uniformly fiber However, one Is restricted to a specific volume fraction of the second phase. Nevertheless, even though the volume fraction is fixed, the rod or lamella thickness, , can be varied by controlling the freezing interface velocity. Alternatively, the grown material may be worked down by swaging or rolling. Embury and Fisher, " using this approach, drew down pear lite in iron and studied the mechanical properties iron and that the yield strength, oy, was properties.proportional They that d was the wire diameter. It could be inferred that was also proportional to but the work hardening had to be taken into consideration at the same time. By varying the growth rate of the cadmium-zinc lamellar eutectic, Shaw'1 showed that was proportional to without the introduction of work hardening and suggested that the lamellar interface itself contributed to the strengthening of the composite. In this investigation we have evaluated the mechanical properties of the unidirectionally solidified fec-bec eutectic Ni-Cr. This eutectic was selected because it presented the possibility was selected beca temperature, and high corrosion resistant alloy, and also represented a hard-soft phase combination with two completely different slip systems. Specimens were tested in compression and tension up to 850°C and a detailed study of the micro structure as a function of plastic strain and temperature was carried out by light and electron microscopy. It was shown that the composite strength tested in compression can be accounted for by the simple rule of mixtures if one allows for an additional term representing the effect of Intereprese EXPERIMENTAL PROCEDURE 1) Unidirectional Solidification. Fig. 1 is a schematic drawing of the apparatus used to produce 0.2 in. diam by 12 in. long alloy ingots. The crucible tube is alumina, containing the charge which has been is swaged, or machined to 0.195 in. diam. The lower end of the tube is immersed to 0 .195in in.d iam. The upper end is supported by a 10 mil nichrome wire which lowers the crucible mil nic hr the] wire at a prescribed rate. Surrounding the furnace is a graphite susceptor into which a control thermocouple is inserted. The furnace is insulated with fiberfrax and enclosed in a quartz tube. There is a sliding seal at the bottom around the crucible and one on the top so that an atmosphere may be used for the sample and suscep tor. The power for the furnace is supplied from a 10-kw, 450 kc generator. The skin depth (the skin depth at which the field falls to l/e of its value at the outer surface) for graphite (p = 10 (j-ohm-cm) is 0.1 in. at this fre-

Jan 1, 1970

By John V. Beall

When the mineral seekers came, they brought romance, excitement and, too often, transitory riches. It has been so for uncounted centuries. While the rich ore lasted, living was high and money flowed-mostly out of town. The whole creation was like a circus. The headframe went up like the center pole of the big top. The reduction works was an ingenious affair; an opportunity for self-expression by the mining engineer on the job. When the high grade gave out or the bottom dropped out of the market, the whole show folded. Machinery was scavenged for the next location. About all that was left were the raw footings, like giantsteps on the hillside; and the headframe above the silent diggings. Mostly, the people went away too. Arizona Territory was like that at the turn of the century. It can still happen. But, in copper, the age-old pattern has been disrupted. From Mineral Park in the northwest to Chino in the east and Cananea in the South, a growing number of companies have emerged-large, stable, productive. Southwest copper is truly a mighty industry, accounting for one fifth of world new copper production. In this period of scientific development, changes are fast, often dramatic. But even mining engineers, or possibly more so because they have an intimate knowledge of the industry, fail to appreciate the evolutionary changes that have shaped Southwest copper into what it is today.

Jan 10, 1965

By W. F. Hosford, E. W. Kelley

By testing polycrystalline specimens from textured plates which had Previously been used to provide materials for growing single crystals, it has been possible to relate the plastic anisotropy of textured materials to the deformation behavior of single crystals. The deformation studies have been conducted at room temperature on textured polycrystalline magnesium and binary Mg-Th and Mg-Li alloys. Variously oriented specimens of the textured materials were deformed in plane-strain compression and in uniaxial tension and compression. The stress-strain curves are similar in their general jorm of anisotropy and stress levels to those obtained on single crystals of the same alloys. The degree of anisotropy is lower, however, in the polycrystalline materials and correlates with the intensity of the basal texture. Yield loci for the textured materials appear reasonable in terms of the deformation mechanisms, and deviate sharply from the form predicted by the Hill analysis for aniso-tropic material. A N earlier study1 of single crystals has shown that magnesium and magnesium alloys with thorium and with lithium deform at room temperature primarily by basal slip, {10i2) twinning, and (1011) banding. The (10i1) banding mode is a combination of {10ll) twinning followed by (1012) twinning and basal slip within the doubly twinned material.2, 3 Magnesium with lithium can also deform by {1010)(1210) prism slip.1'4'5 Still other deformation modes have been reported for magnesium6-11 but these are considered to play a minor role in room-temperature deformation. In a polycrystalline material, plastic deformation must occur in the individual grains through the operation of one or more of the various deformation modes. Because the critical shear stress for basal slip is very low compared to the activation stresses for the other deformation modes,' basal slip accounts for much of the deformation in the polycrystalline aggregate. However, since there are only two mutually independent basal slip systems, and because five independent systems must be active for an arbitrary shape change in any material,'' modes other than basal slip must account for some of the strain. The deformation of textured magnesium, like that of other hcp metals, must be controlled by the same mechanisms observed in single crystals. In strongly textured material, the form of the anisotropy should be similar to that of single crystals, and the degree of anisotropy should depend on the intensity of the texture. EXPERIMENTAL PROCEDURE The anisotropy of deformation was investigated through the use of plane-strain compression tests, as well as uniaxial tension and compression tests. Materials. Test specimens were cut from the three textured plates of magnesium which had previously been used to provide material for single crystals.' These plates, furnished by Dow Chemical Co., had been reduced about 80 pct during the process of being hot-rolled to their final 1/4-in. thicknesses. The plates had the three respective compositions, pure magnesium, Mg-0.5 wt pct Th (0.49 pct Th by spectro-graphic analysis), and Mg-4 wt pct Li (3.84 pct Li by chemical analysis). Impurities other than iron were less than 0.0005 pct Al, 0.01 pct Ca, 0.001 pct Cu, 0.0006 pct Mn, 0.001 pct Ni, 0.003 pct Pb, 0.001 pct Si, 0.001 pct Sn, and 0.01 pct Zn. Iron was 0.001 pct in the pure magnesium, 0.002 pct in the Mg-0.5 pct Th, and 0.014 pct in the Mg-4 pct Li. The textures of the three plates were determined by X-ray diffraction utilizing only the reflection technique out to an angle of 50 deg from the sheet normal. The resulting basal pole figures are presented in Figs. 1, 3, and 5. Grain sizes in the plates were ASTM number 4 in the pure magnesium and number 7 in each of the alloys. Plane-Strain Compression Tests. Plane-strain compression specimens approximately $ in. thick by 4 in. wide by $ in. long were prepared for each of the three compositions. These specimens were prepared in a manner similar to that used for the single-crystal specimens of the earlier study.' All polycrystalline specimens were stress-relieved at 500°F for hr as the final step in their preparation for testing. The testing procedure was identical to that used for the single crystals, involving compression in a channel and using 2-mil Teflon film as a lubricant. The specimens were tested in six orientations of interest, these being the six combinations of the rolling, transverse, and thickness directions of the material serving as loading, extension, and constraint directions in the plane-strain compression test. Each of the six orientations was assigned a two-letter identifying code. These are combinations of the letters (thickness direction), R (rolling direction), and T (transverse direction) with the first letter signifying the loading direction and the second letter the extension direction. For example, ZR specimens were compressed in the thickness direction while extension was permitted to operate in the rolling direction of the textured material. To facilitate comparison of the present work with that of the single-crystal study1 the orientations used for single crystals are given in Table I along with the polycrystalline orientations that most nearly correspond. To insure reproducibility, at least three duplicate

Jan 1, 1969

By R. E. Smallman

R. E. Smallman (University of Birmingham, England)—Recently, Tedmon and Ferriss11 have determined the yield stress parameters oi and ky for tantalum by measuring the lower yield stress as a function of grain size 2d and fitting the results to a relationship of the form They report that although ky , which is taken to be a measure of the dislocation locking strength, is small (- 2 to 4 x 106 cgs units) a substantial yield drop is nevertheless observed in a normal tensile test. Niobium gives a similar result,12-14 as pointed out in the original work by Adams et a1.,12 and in order to check this apparent anomaly the yield-stress parameters of electron beam-melted niobium have recently been reanalyzed15 by the Luders strain technique. In this method the strain hardening part of the stress-strain curve is extrapolated to zero plastic strain; the intercept on the preyield portion of the curve is taken to give oi, whilst the difference between oi and the lower yield stress gives kyd-1/2. The results indicate that ky increases with increasing grain size and hence, a plot of vs d-112 yields an apparent ky, which is lower than the true value. A similar effect could account for the small ky found in the relatively pure tantalum used by Tedmon and Ferriss. The variation of ky with grain size shows that dislocations are more strongly locked in coarse-grained specimens than in fine-grained samples. In niobium, this may be attributed to the fact that the dislocation density in the fine-grained material is higher than that found in the coarse-grained samples which are given a sufficiently prolonged anneal to remove any residual substructure and, since the metal contains only a small amount of interstitual impurity, a variation in locking occurs. By contrast, application of both the grain size analysis and the Luders strain method to yield-stress data from commercially pure vanadium containing a large amount of interstitial impurity gives consistent values of oi and ky, with ky independent of grain size and temperature. Electron microscope observations show minor variations in dislocation density from grain size to grain size, but in any case in this material the dislocations are heavily locked with precipitate. On yielding new dislocations are generated and, as a consequence, the importance of any differences in dislocation density between the various specimens of different grain size is considerably reduced. It is perhaps significant that Adams and lannucci,16 working with a grade of tantalum containing a higher interstitial content than that used by Tedmon and Ferriss, prepared the specimens of different grain size by annealing in the temperature range 1500" to 2000° C to minimize any differences in dislocation structure, and found that ky had a value of 1.04 x 107 cgs units, independent of testing temperature. Such behavior is consistent with the dislocations being locked by carbide precipitates so that the generation of free dislocations is an athermal process. The recent work of Gilbert et al.17 also shows that in tantalum there is no significant variation of ky with grain size provided it contains 150 ppm of oxygen. In this case, however, the dislocations are not locked by precipitate and ky is temperature dependent. C. S. Tedmon and D. P. Ferriss (authors' reply)— We would like to thank Dr. Smallman for his interesting comments and discussion to our paper, "The Dependence of Yield Stress on Grain Size for Tantalum and a 10 pct W-90 pct Ta Alloy".18 It was suggested that perhaps the relatively small values obtained by us for ky of tantalum could be attributed to the same cause that accounts for the apparently small values of ky that result when it is determined by the Luders Strain technique. Since our values were obtained by plotting the lower yield stress vs the reciprocal of the square root of the grain size, it is not clear how this could be the case. The values of ky in this experiment have been calculated, using the Luders strain technique. With this method, values for ky on the order of 2 x 105 to 5 x lo6 cgs units were obtained. In spite of this rather large variation, the magnitudes are still small, and there appeared to be no good correlation between ky and the grain size or the yield stress, probably because of the difficulty in accurately extrapolating the work-hardening portion of the curve back to zero plastic strain. As was shown in the original data,18 there was little work hardening in any of the curves, at any temperature. In his discussion, Dr. Smallman also points out how ky has been observed to increase with increasing grain size, when determined by the Luders strain technique. There are at least two possible explanations for this. In the first case, if it is assumed that the bulk of the interstitial impurities are concentrated at the grain boundaries, then, of course, the available grain boundary area would decrease with increasing grain size, thus presenting less area for the interstitials, which would then presumably increase the concentration within the grains, thereby increasing the locking of the dislocations. In the second case, the increase in ky with increasing grain size would be attributed to the nature of the grain boundary itself. One of the several ways of deriving the Hall-Petch equation19 is based on the stress concentration arising from a pile-up of dislocations at the boundary. The ability of the stress concentration to unlock a source in a neighboring grain would depend on the strength of the grain boundary. As is well-known, the nature and struc-

Jan 1, 1963

By N. H. van Lingen

A laboratory stud], has been made to determine what factors affect the penetration rate of roller bits, diamond bits and drag bits in rock drilling with clay /water muds. The rather simple relations that exist when pressures in and around the borehole are equal become more conzplicated when under down-hole conditions the penetration rate is hampered by the existence of a pressure differential between the mud at the hole bottom and the pore liquid at cutting depth. Expressions that have been derived for both the penetration rate and the magnitude of the pressure differential in permeable rock together fully account for operating, rock, mud and bit variables. In impermeable rock a similar pressure differential is caused by the bit action itself. In all cases, the pressure difierential and the reduction in penetration rate increase with the effectiveness of the plastering at the bottom of the hole by mud particles. Where bits are employed whose action is largely that of crushing, however, the plastering may become even more effective owing to the addition of rock particles rubbed into the pores of the rock. With roller bits, a plastically hehaving layer may be formed, which causes a further reduction in penetration. In the case of bits whose action is chiefly scraping, moreover, penetration may be arrested by the bit's becoming balled-up. The various adverse effects are reduced by thorough scavenging of the hole bottom. This paper shows how with jet bits the efficiency of such scavenging may he improved by suitable choice of the position of the nozzles. INTRODUCTION The reduction in a bit's penetration rate with increasing depth of hole has been the subject of many investigations. Various investigators ',' have independently reached the conclusion that this reduction occurs not so much because the rock-breaking process becomes more difficult as it does because the lifting of the rock fragments is impaired by a fluid pressure differential holding the fragments down. When such a pressure differential can be avoided, as in air drilling and to a smaller extent in water drilling, penetration rates remain high. Although the range of applicability of these techniques is being extended, most oil wells still have to be drilled with mud. In this paper we present the results of laboratory experiments carried out to determine what factors govern the hold down effect encountered in mud drilling. In the course of this investigation, the well known importance of bottom scavenging came more and more into prominence. Not only may it reduce the magnitude of the hold-down forces, but also it appeared to be a means of preventing the accumulation of a plastic mass of cuttings and mud on the hole bottom and bit which may cause penetration to cease almost completely. So that the effects of fluid pressures may be more readily understood, the factors that govern penetration rate in the absence of these pressures will first be discussed. The effect of down-hole pressures will then be assessed for the case of permeable rock where fluid pressures are well defined, and it will be demonstrated how rock strengthening due to confining can be accounted for. Subsequently, fluid pressures in less-permeable rock will be examined; we will show that in impermeable rock it is the bit action that governs fluid-pressure distribution and hold-down. In the case of poor scavenging and/or high bit load. cutting cake manifests itself. The effect, like various others. appears to depend on the type of bit used. From the very beginning, therefore, we shall base our discussion on the three main types of bits used in rotary oil-well drilling— roller bits, diamond bits and drag bits. Since space is limited, it will be impossible to make more than a passing reference to many aspects of the problem. Moreover. certain relations that are not of primary irnportance to our argument will unavoidably have to be stated in a somewhat dogmatic fashion, and the experimental data on which these are based necessarily must be omitted. EQUIPMENT The drilling experiments were performed on three machines, of which one has been designed for the realistic simulation of down-hole pressure conditions. HIGH-PRESSURES MACHINE In this machine (diagramed in Fig. 1) the mud, pore and confining pressures can all be adjusted independently. The foil-covered rock sample contained in the inner pressure vessel is confined by oil that is pressurized by means of a hand pump. The pore space of the watersaturated sample is connected to an arrangement which keeps the pressure in the pore space constant regardless of the rate of filtrate flow through the sample.

By John Chipman

Published data on the equilibria of carbon in binary Fe-C austenite with H2-CH4 and CO2-CO gas mixtures are used to obtain the constants of an equation repre -senting the activity coefficient of carbon throughout the stable austenite range of temperatutre mid compositiotl. Calculated values for the solubility of graphite are found to be in agreement with the best-published direct observations. Its heat of solution is 10,680 calper g-atom. The free energy of formation of cementite is culculated from the equilibrium compositions of austenite and of gas. Its entropy and heat of formation are also obtained. BASIC knowledge of the high-temperature properties and treatment of steels is contained in the Fe-C diagram and its extensions for the effects of alloying elements. The application of thermodynamics to the Fe-C system, with addition of alloying elements, can serve to simplify and systematize this knowledge. The points of beginning are the binary fee solution, austenite, concerning which our information is reasonably complete, and the binary carbide, cementite. Further studies must include the other phases of the binary system, a and liquid, and for these an accurate knowledge of the ? phase boundaries is essential. These studies should provide a firm base for systematic study of the effects of alloying elements on all phases of the system, their transformations, and precipitation phenomena. With the aid of the simplifying thermodynamic concepts of activity coefficients and interaction parameters it is to be hoped that the results of these studies will be amenable to computer solution thus making the information on multicomponent systems more readily available than would be possible in multidimensional diagrams. Studies of the thermodynamic properties of austenite have utilized equilibrium measurements on the reactions:

Jan 1, 1968

HIGH-GRADE manganese ore, from which manganese is obtained commercially, is not found in large quantities in any major steel-producing nation in the free world. The U. S. is a "have not" nation with respect to deposits of directly mineable high-grade manganese ore. Known resources of 48 pct Mn or better grade ore amount to less than 200,000 tons. In 1950 the U. S. steel industry consumed 1.8 million short tons of metallurgical grade manganese ore that contained about 800,000 tons of manganese. About 16 pct of the manganese content was lost in processing, so that about 650,000 tons, or 13 pounds per ton of steel actually entered into steel production. Under present practices use expands directly with steel output, and by 1975 the demand in both the U. S. and the rest of the free world is expected to be roughly 60 pet greater than in 1950. In peacetime about 80 pet of manganese consumption goes into steel production; high-manganese steel, dry cells, and chemicals account for the remainder. The manganese supply problem centers around high-grade ore for ferromanganese production. Use of ores containing less than 35 pet Mn sharply increase the costs of making ferromanganese. Use of ferro-manganese of grade below 70 pet in turn requires changes in steelmaking that increase steel cost. Under normal conditions the present small domestic production cannot be expected to increase. Major resources in the U. S. consist of 12 low-grade deposits. The cost of mining and treating these ores to extract a product as good as that yielded by imported ores is at least twice and in some cases more than four times the 1951 price of foreign ores delivered to the U. S. However, as long as trade relations and overseas shipping are not interrupted, deposits in India, Africa, and Brazil can meet steadily increasing demand at approximately present costs. Cost considerations indicate that the U. S. should continue to rely upon overseas sources for its peace-time supply, and that this situation is satisfactory. But, this does not take into account the question of how the U. S. will be able to meet its needs in war. Position of the Rest of the Free World In 1950, free world steel producers outside the United States, with a steel output of 70 million ingot tons, consumed about 1.3 million tons of metallurgical-grade ore. Their manganese ore demand, expected to increase directly with steel production, will by 1975 be about 2.3 million tons. Russia possesses over half the known manganese ore reserves of the world and is producing twice the tonnage of any other country. It supplied more than a third of the U. S. manganese requirements up to 1938 and again in 1948, but by 1950 Soviet manganese exports to the free world had virtually ceased. The free world's supply of manganese now comes mainly from India and Africa. Somewhat over 10 pet of U. S. imports came from Brazil and Cuba. Security Considerations In the event of war the U. S. might be substantially cut off from 90 pet of present sources. Reduction in manganese specifications might cut consumption by over 10 pet without seriously affecting steel quality. By elimination of losses in the production of ferromanganese savings as high as 10 pet might be possible. But, wartime manganese requirements cannot be met through conservation alone. To meet possible future emergencies the U. S. should continue its comprehensive security program for manganese, including stockpiling and research on the economic use of low-grade ore, domestic ores, the recovery of manganese from slag and the reduction of manganese requirements in steel production. If this work, including additional pilot plant operation is pursued vigorously, it should be possible in an emergency to get an adequate supply of manganese from domestic sources. The national stockpile then can be looked upon as a source of supply during the period of at least 2 years required to reach full-scale production from low-grade resources. Ferromanganese Smelting In comparison with smelting of pig iron, ferro-manganese smelting is a very wasteful process. Under present ferromanganese blast-furnace smelting practice, about 8 pet of the manganese in the furnace charge is lost to the slag, and roughly the same amount is lost to the stack gases; the total loss approaches 15 pct. Present practice is a compromise between excessive slag loss and excessive stack loss. In fact, it may be seriously questioned whether conventional blast furnace design is suitable for manganese smelting. U. S. Resources The known manganese deposits of the U. S. contain a total of 3500 million long tons of raw material and 75 million long tons of metallic manganese. More than 98 pct of this contained metal is in 12 large low-grade deposits of which the most important are those at Chamberlain, S. Dak; Cuyuna, Minn.; Aroostook County, Maine; and Artillery Peak, Ariz. Reserves of high-grade ore (48 pct Mn) amount to less than 200,000 tons. About 20 million tons of ore average over 15 pct Mn, and when grade is decreased to 10 pct Mn reserves amount to about 100 million long tons. If cut-off grade is decreased to 5 pet Mn, resources amount to 800 million long tons. Many of these low-grade ores may be beneficiated by flotation or other concentration methods. Pyrometallurgical Methods For smelting ferromanganese, it is essential to have an ore containing at least 50 pct manganese, with an Mn:Fe ratio of about 8:1. Direct smelting of 20 pct Mn concentrates is not promising. The only method that offers any promise involves two-step smelting.

Jan 1, 1952

By M. S. Azun

M.S. Azun I have many objections to the content of the author's paper. Before discussing it, however, I would like to repeat the property of semivariogram function. Second order stationary properties of regionalized variables (ReV's) such as semivariogram function ?(h) are perfectly known in geostatistics. Also, the kriging equations in the language of mathematical statistics using second order stationary properties are well understood. However, the way to use the sample (estimated) semivariogram function in any one of the kriging procedures is vague. The sample semivariogram function is given as follows: [1 N-hy*(h) = 2(N h) i21 {Xi-Xi+h}Z, h=0, 1, N-1] where N is the total number of samples, Xi is the sample value at the i - th location, X i+h is the sample value at the i +h - th location, and h is the distance among the samples. An estimation variance of sample semivariogram function of first lag is smaller than that of higher order lag. The theoretical semivariogram function reaches the variance of samples asymptotically. But this is not easily observable because of the larger variation involved in the estimate of semivariogram function. In general, an estimation procedure is done for h = 0, 1, 2,…., up to the greatest integer less than N/2, even though sample semivariogram function can be computable through N-1. After estimating semivariogram function, the critical question of how to model sample semivariogram function arises. As seen in the above equation, sample semivariogram function is discrete and can be smoothed by the model being selected. Therefore, modeling of sample semivariogram function is the most important step in geostatistics. It not only smoothes a discrete function but also affects the results of the kriging procedure. When the only aim is to model the semivariogram function, which is the basic point of the author's paper, one can employ any fitting techniques, such as curve fitting, or any ar¬bitrary functions, which are called submodels in the paper. The term "arbitrary function" is used rather than "submodel" because there is no basic understanding of developing them. The author suggests that the sum of those submodels can also be used for the modeling of sample semivariogram function. The combination of any arbitrary functions brings many problems instead of giving an insight of the domain structure considered. The author used two arbitrary functions and the nugget effect in response to sample semivariogram function (Fig. 10). For the same example, he stated that the parameters involved in the mixed arbitrary function model can be accepted when the discrepancy between sample semivariogram function and the model is small visually. For verifying the fitting behavior of any selected model, one should not be contented with the visual satisfactory. Some statistical measure such as goodness of fit has to be used. The author's practice is no more than an exercise in curve fitting without any fundamental understanding or conceptualization of the underlying physical mechanism. Furthermore, the selection of any model is not an easy task if the purpose is the search for the "best" response to the observed second order properties of ReV's. I suggest that the Markovian model (Azun, 1983), on the basis of a theoretical understanding of underlying mechanism, which gives more information about the occurrence of regionalized variables, is used to respond all properties of ReV's. There are a lot of problems for modeling of onedimensional sample semivariogram function. Thus, it is not appropriate to go to higher order dimensional sample semivariogram function modeling. In the meantime, I would recommend that one can connect the values of standardized sample semivariogram function rather than simple values of semivariogram function in the two-dimensional estimation. The standardized values can be computed in dividing the semivariogram function value by the number of sample pairs involved in each lag regardless of the directions. In conclusion, geostatistics is an interdisciplinary area in mining that uses the principles of mathematical statistics. Thus, it should not violate any probabilistic and statistical rules. When Matheron was developing the theory of geostatistical study in the early years of geostatistics, many mining people had a reservation accepting the geostatistical tools. However, this does not mean that we, the geostatisticians, might try to convince those people using some "strange" tools or rules as some authors implied (Baafi and Kim, 1984). Instead, we have to develop and explain the geostatistical tools staying only in the framework of statistical concepts and properties. ? References Azun, M.S., 1983, "Stochastic Process Modeling of Spatially Distributed Geostatistical Data," Columbia University, Ph.D. Thesis. Baafi, E.Y., and Kim, Y.C., 1984, "Discussion - Comparison of Different Ore Reserve Estimation Methods Using Conditional Simulation," Mining Engineering, Vol. 36, No. 3, p. 280. Reply by J.M. Rendu The interactive method proposed by Rendu allows practitioners to develop semivariogram models that take into account not only the numerical information obtained by sampling, but also highly significant additional information that often cannot be quantified. The geology of the deposit - including hypotheses concerning its genesis, sampling methods, assaying methods, and mathematical methods used to calculate the semivariograms - all have an influence on the numerical results obtained and on how these results should be interpreted. If all the information concerning the spatial distribution of values in a mineral deposit was contained in the sample values, it could be argued that statistical techniques alone would produce optimum models. However, this is rarely, if ever, the case. Methods that allow the user to take into account his experience and his geologic understanding of the deposit should not be rejected for the sake of theoretical statistical purity. ?

Jan 1, 1986

By J. J. Jonas, G. Gagnon

SHG zinc was extruded in the temperature range 110" to 350°C and the strain rate range 0.05 to 5 sec-1 The strain rate/flow stress/temperature results were analyzed using a power sinh stress relationship. When temperature changes due to the heat of deformation and to heat losses are neglected, the exponent of the sinh function of the stress is 5.6, and the apparent activation energy of deformation is 28 kcal per mole. When these changes are taken into account, the exponent decreases to 4.7 and the activation energy to 23 + 2 kcal per mole. The corrected stress exponent and activation energy are in very good agreement with published values obtained from creep experiments, and suggest that the hot extrusion of zinc is controlled by a mechanism involving self-diffusion. When the extrusion and creep data are compared using a Zener-Hollomon parameter and either a sinh or an exponential stress term, an appreciable offset is observed, which may be due to the difference in impurity content. For a given set of extrusion conditions the ram speed, maximum pressure, and initial temperature can also be correlated using a Zener-Hollomon parameter and a sinh pressure term. THE deformation of metals at temperatures over about one-half the absolute melting temperature has been extensively studied at creep strain rates. By contrast, relatively little work has been carried out on the behavior of metals at hot working strain rates. Most of the latter investigations have been performed using simulative methods, such as hot torsion and hot compression, in which the friction conditions and temperature rise during deformation may differ appreciably from those existing under industrial conditions. Recently, however, Wong and Jonas1 used a scaled-down industrial process to determine the stress and temperature dependence of the strain rate during the extrusion of aluminum. In such tests, the effects of friction and adiabatic heating are closer to those produced in industrial operations. Also, with regard to the testing of materials of limited ductility such as zinc, hot compression and hot torsion do not permit the attainment of true strains as large as the deformations usually applied commercially. The present study was undertaken to investigate the extrusion behavior of Special High Grade (SHG) zinc. The detailed objectives were: 1) to establish the stress and temperature dependence of the strain rate with and without a consideration of adiabatic heating, 2) to study the pressure and temperature dependence of the ram speed, and 3) to investigate the microstruc- tural changes occurring during the deformation. The last aspect of the investigation will be covered in a separate paper. The treatment described below differs from that of Wong and Jonas in that the adiabatic temperature rise during deformation is taken into account, and the calculation of the mean equivalent strain rate is based on the redundant as well as on the homogeneous work. EXPERIMENTAL PROCEDURE Rods from two shipments of continuously cast SHG zinc* were used in the investigation. The composition *Supplied by courtesy of Cominco Ltd. range of the impurities present, as given by the supplier, was: Pb: 0.0013 to 0.0023 pct, Fe: 0.001 pct max Cd: 0.0001 to 0.0006 pct, Cu: 0.0002 to 0.0005 pct, Ti: 0.0001 pct max; thus, by balance, zinc valued from 99.9963 to 99.9966 pct. The as-received rods were machined into billets having a nominal diameter of 1.56 in. and a nominal length of 1½ in.; longer billets up to 4 in. in length, were also used to investigate special aspects. The as-machined rods were annealed at 400°C for 24 hr and slowly cooled. This treatment produced a columnar grain structure, with a grain size of about $ by 2½ cm which was appreciably larger than the as-cast one. A 150-ton, direct extrusion, vertical press was used. Ram displacement and force were recorded continuously against time. A constant flow control valve permitted the maintenance of a range of preselected ram speeds up to in. per sec. The selected speed was held constant, irrespective of the required force, as long as the load developed was below the maximum available. Strain gages were used to determine the force; the gages were calibrated before and after each testing period with a 200,000-lb capacity load cell. Further details of the experimental equipment can be found in Ref. 2. The billets were preheated for 90 min in the extrusion container, which was well insulated so as to minimize temperature gradients. This period was sufficient for the billet to reach a uniform temperature at all temperatures between 110" and 350°C. A square-shoulder die having a 0.290-in. diam central hole was used. The extrusion ratio was 30 to 1. This is equivalent to a reduction in area of 96.7 pct, an elongation of 2900 pct, and a true strain of 3.4. The ram speed was varied over two orders of magnitude from 0.0027 to 0.26 in. per sec. The ram was water-cooled during most of the tests, although some experiments were conducted with a preheated, uncooled ram. All extrusions were run without lubricant, which resulted in conditions of sticking friction. EXPERIMENTAL RESULTS Stress Dependence of the Strain Rate Neglecting Adiabatic Heating. The maximum force required to extrude is given in Table 1 for each of the five initial

Jan 1, 1970

By J. J. Brown

Wilkes-Barre Meeting, Julie, runs., THE ore-hearth was the earliest type of furnace used in smelting Mississippi Valley lead-ores, which are very pure, and low in silver-content. The first smelters made no attempts to recover lead from the smoke; and since about 15 per cent. of the lead -in the charge escaped in this manner, early practice with the hearth was decidedly wasteful. At most of the large smelting-plants blast-furnaces with auxiliary roasters were substituted for the hearths long ago. But, upon the introduction of the Lewis and Bartlett bag-process for collecting fume, the ore-hearth was used by companies engaged in the manufacture -of pigments, simply on account of the large percentage of fume made by it. In fact, the extraction of lead was kept down by the use of hot blast and other devices. During recent years, however, several smelting companies have realized that the preliminary roasting of galena for the blast-furnace is not economical, and have, therefore, replaced the roasting-furnace with a modification. of the old Scotch hearth, in which a large percentage of the lead in a charge is recovered directly as pig-lead, while the remainder passes partly into fume and partly into slag low enough in sulphur to be charged into the blast-furnace without further treatment. The results obtained have proved so satisfactory, both As to recovery and operating-expense, that one eminent metallurgist has predicted the universal use of the ore-hearth on non-argentiferous ores. The-ore-hearth, thus employed as an adjunct to a blast-furnace plant, is rather a desulphurizer than a smelting-furnace proper,-the chief object being to make a blue slag suitable for the cupola-furnace. Hence, no special care is taken to obtain from it a large lead-extraction. * Head of Department of Ore Dressing and Metallurgy, Oklahoma School of Mines and Metallurgy, Wilburton, Okla.

May 1, 1911

By C. F. Weinaug, P. M. Blair

Many difference equations used to approximate reservoir flow problems treat the phase pressures implicitly but not the mobility-density coefficients. Such difference equations are neither wholly explicit nor implicit, but might be described as mixed. Mixed equations are relatively easy to apply. But the associated time truncation error is relatively large, and when used to solve problems characterized by high flow rates, these equations may be unstable for practical size time steps. This paper outlines the development of a completely implicit difference analogue for reservoir simulation, along with a Newtonian iterative method for solving the resulting nonlinear set of algebraic equations that arise at each time step. While this implicit equation requires two to three times more work than does the mixed equation, it is shown to markedly decrease the time truncation error and to yield a stable solution for much larger time steps than does the mixed equation. INTRODUCTION Calculation of multiphase, multidimensional flow in porous media is generally accomplished by numerical methods that involve approximating systems of partial differential equations by systems of partial difference equations. The early development of difference equation techniques was directed toward the solution of linear differential systems. However, the equations of multiphase fluid flow through porous media are highly nonlinear in that mobility and density often are strong functions of pressure and saturation. Thus, solution of the flow problems by difference equations involves solving sets of algebraic equations whose coefficients change from step to step of the calculations. Current practice is to evaluate most coefficients at the beginning of a time step and then to apply difference methods well suited for solving linear problems. At least two major difficulties arise from the use of this practice. First, evaluation of coefficients at the old time level and evaluation of pressures at the new time level results in larger time truncation errors near displacement fronts than if all quantities in the distance derivative were evaluated at the same time level. Second, evaluation of mobility coefficients at old time levels results in an unstable difference equation in regions of high flow rate. The first of these difficulties often results in optimistic recovery behind the displacement front, and the second requires the use of small time steps or special techniques in solving coning problems1 or problems of gas percolation.2 Evaluation of all quantities in the distance differences at the new time level results in a completely implicit difference system. Such a difference system has a lower time truncation error than equations in which mobilities are evaluated at the old level and pressures evaluated at the new level. The algebraic equations resulting from the fully implicit difference equation are, in this case, nonlinear and require some iterative method for their solution. This paper develops fully implicit difference equations for two-phase flow in porous media, describes their solution by Newtonian iteration, and gives examples of problems more easily solved by the new method than by previous methods. EVOLUTION OF DIFFERENCE EQUATIONS FOR NONLINEAR PROCESSES The completely implicit difference equation used in these calculations results from evolution beginning with explicit difference equations, proceeding through what we will call "mixed" equations, and arriving now at a completely implicit equation. Let us illustrate the evolution by considering different analogs of the nonlinear equation

Jan 1, 1970

By Robert Schorr

A Discussion of the Paper by Robert Schorr, read at the Atlantic City meeting, February, 1904. (Washington Meeting, May, 1905.) E. T. DUMBLE, Houston, Texas (communication to the Secretary*) :-In addition to the list of publications mentioned by Mr. Schorr and those by Prof. Hofman, I call attention to the following references : Studi sulle Lignite, by Capacci. Turin (1890). (An excellent work.) Report of Brown Coal Industry in Germany. J. Cosmo Newberry. Department of Mines, Victoria (1892). Second Report of the Royal Commission. on Coal Supply. Vol. II. London (1904). Peat Fuel: Its Manufacture and Use. Report of the Bureau of Mines of Ontario, 1903. Mr. Schorr says : " Brown coal and peat are briquetted as a rule without binder," but this statement is entirely true only so far as raw peat is concerned, and it is but partly true of brown coal. With regard to raw peat, briquetting without bond is carried on successfully both in Europe and America, and the development of the industry in Canada is fully described in the Bureau of Mines report for 1903, mentioned above. While there is still room for improvement in the efficiency of some of the arrangements for drying the peat previous to briquetting, a very satisfactory fuel is made at a price which enables it to compete with coal. During the late strike in the anthracite regions of Pennsylvania, the manufacture of peat: briquettes received a considerable impetus, and possibly the attention directed to it on this account may result in a. considerable increase in the output. In Canada. the peat when it is first excavated from the ground

Mar 1, 1905

By B. C. Raynes

IN the early part of 1952, under the auspices of the U. S. Atomic Energy Commission, Horizons Inc. undertook an investigation dealing with the preparation of high purity thorium metal in order to develop an economically competitive production process for this metal based on a recovery of the metal by a fused salt electrolysis, since a survey of the literature of thorium chemistry indicated that electrolytic methods had not received much attention, despite the consideration that electrochemical production methods often offer attractive commercial potentialities. Thorium metal has been prepared by methods which fall into four general categories: 1) reduction of halides or double halides; 2) reduction of the oxide; 3) thermal decomposition of halides; and 4) electrolytic methods. Some of the important results obtained by various investigators since about 1900 in recorded attempts to prepare pure thorium metal are summarized in Table I. A bibliography of pertinent literature is included in this paper. Thorium is strongly electropositive and possesses a great affinity for oxygen and nitrogen. As a result the prospects for the production of high purity thorium from aqueous media or oxygen bearing compounds are remote. The most promising and profitable area of investigation for production of thorium metal lies in fused salt electrolysis. Thorium has been produced previously by this technique from halide salts in fused alkali chloride eutectic mixtures. Until recently, however, the lack of known large uses for thorium has inhibited the investigation of these methods. The basic problem in an investigation into fused salt production methods for thorium is to develop a suitable fused salt system for the economic preparation of thorium. The first portion of the work in these laboratories was a small scale investigation of the electrolysis of potassium thorium fluoride, KThF5, under a variety of conditions. High purity thorium was prepared in this manner, but the process did not appear to offer the simplest and most attractive continuous commercial operation. The work reported here relates to an all-chloride system employing thorium chloride as the cell feed. ThCL4 was produced as an anhydrous material stabilized in molten sodium chloride. This product, further diluted in NaCl, was subjected to electrolysis. The electrolytic process has been studied in cells capable of holding up to 50 lb total salt charge. Ductile, pure thorium metal has been reproducibly obtained in this operation. Considerable experimentation was carried out in the preparation of ThCL as a cell feed free from moisture, oxides, and other impurities. Thorium was cathodically deposited as a coarsely crystalline powder interspersed with residual bath salts. Aqueous procedures for separating and recovering the metal were developed. The thorium metal powder obtained has been evaluated with respect to its hardness, chemical purity, and certain other physical properties. Preparation of ThC1,—Thorium chloride, and the chlorides of some other metals (aluminum, beryllium, tantalum, zirconium, etc.) cannot be obtained from aqueous solution by direct heating and evaporation. Evaporation and heating of a solution of thorium chloride yields a hydrated salt or partially hydrated salt, and finally Tho,. Anhydrous thorium chloride is obtained by forming a hydrated ammonium chloride complex salt in acidified water solution, dehydrating this compound, and finally decomposing the double salt and subliming the ammonium chloride component. Various methods for the preparation of anhydrous thorium chloride, in accordance with this concept, were investigated as indicated in Table I1 from hydrated thorium chloride (ThCl, . 3H2O), and from thorium oxycarbonate (ThOCO,). In the method found most satisfactory for this work, thorium oxycarbonate was dissolved in an excess of concentrated HC1 to give a clear yellow solution. At least 2 mol NH,Cl were added to the solution per mol of contained thorium. Ammonium thorium chloride hydrate was crystallized from solution by cooling and saturation with HC1. The resultant complex, (NH,Cl),ThCl;xH,O, was dehydrated by evaporation at 130° to 150°C and thoroughly dried at about 250°C. The dried ammanium thorium chloride was then mixed with sodium chloride in proportions to form NaThCL or to produce a ThCL4-NaCl mixture with a given thorium content. The ammonium chloride was sublimed off at temperatures above 500°C in an inert atmosphere furnace to give an anhydrous chloride source electrolyte, essentially free of Tho, and of NKC1.

Jan 1, 1958

By L. E. Tanner

A study was made of the transformation kinetics of the commercial titanium-base alloys, Ti-2.5Al-16V and Ti-4A1-3Mo-1V, using two different heat treatment cycles: 1) step-quenching to aging temperatures from a ß solution anneal and 2) water-quenching from an a+ß solution anneal followed by reheating to aging temperatures. Metallographic examination and hardness testing provided the major portion of the data, while electrical resistivity, dynamic elastic modulus, and X-ray diffraction techniques were also used to obtain critical or confirnzatory data. TTT diagrams were constructed from these results. The sheet alloys, Ti-2.5Al-16V and Ti-4Al-3Mo-lV, are of current interest to the Department of Defense. As an aid to the planning of their respective heat treatments, a program was carried out to determine the transformation kinetics of these alloys using ß and a + ß reference states. This paper presents the TTT diagrams constructed from data obtained by metallographic examination and hardness testing, as well as by X-ray diffraction, electrical resistivity, and dynamic elastic modulus determinations. EXPERIMENTAL PROCEDURE Materials—Sheets of the alloys were obtained from the producers in the "mill anneal'' condition and were tested prior to shipment to assure their meeting mill specifications. Chemical analyses were also supplied and are presented in Table I. Heat Treatment—The majority of the data presented in this study were obtained from hardness testing and metallographic examination. Sample coupons were cut from the alloy sheets and heat treated on a mass scale. The annealing cycles were operated in the following manner: 1) The ß solution anneals were carried out in a horizontal tube furnace with the bare samples protected by a dynamic helium atmosphere. Following this treatment, the samples were quickly transferred to lead, solder, or oil-bath furnaces for aging. After prescribed times at the various reaction temperatures they were water-quenched. 2) The second cycle simulated commercial practice, which requires the alloys be quenched to room temperature following the a + ß sotution anneal. This anneal was carried out in a muffle furnace with a dynamic helium atmosphere. The specimens were then reheated from room temperature to the reaction temperatures in lead, solder, or oil-bath furnaces, followed by water-quenching after prescribed times at these temperatures. Information concerning the critical temperatures of the alloys was obtained from the literature and solution treatments were based on these values. A summary of the solution annealing treatments is found in Tables II and 111. The aging temperatures for the (a - ß alloys ranged in 50°C intervals from 200°C (392oF) to approximately 50°C below the ß/a + ß transus in the first cycle and approximately 50°C below the a + ß solution temperature in the second. The transformations in these alloys were known to be rather rapid, and thus aging times started at 0.5 min and went to a maximum of 7000 min. Hardness Testing and Metallographic Preparation— Heat-treated samples were sheared and mounted in Bakelite with their cut edges exposed. After a flat surface was ground, the hardness was determined in Vpn on an Armstrong-Vickers machine utilizing a 20-kg load. Three to four impressions were made on each specimen. After this procedure, the hardness impressions were removed and the edge surfaces of the specimens were prepared for metallographic examination in the usual manner. The etchant was 20 pct HF and 20 pct HNO3 in glycerine. Electrical Resistivity—It has been shown that the isothermal reactions in titanium-base alloys can be followed by measuring the changes in e1etrical resistivity attending these transformations. As mentioned earlier, the reaction kinetics of a-ß alloys are rather rapid; thus, it would be expected that resistivity data obtained from these alloys would be more significant if measurements were made continuously at the respective aging temperatures. To accomplish this end a special apparatus, based on the current-potential principle, was assembled. Its design was derived from earlier devices constructed by Colner and zmeska1 4 and Levinson.5 The set-up provided for the heat treatment zof machined specimens (approximately 2 x l0-4in. in cross section by 3 in. in length) and the determination of their relative

Jan 1, 1962

By W. D. Robertson, E. Scala

Electrical resistivity of a number of pure liquid metals and alloys has been measured as a function of temperature and composition. The data show a close correspondence between the liquid and solid states with respect to thermal, structural, and compositional relationships. STUDY of diffuse scattering of X-rays by liquid metals1 has demonstrated that some degree of order persists above the melting point and that the atomic constitution of liquids is more analogous to the solid state than to a gas. Consideration of the change in various thermodynamic properties that accompanies transformation from solid to liquid leads to the same general conclusion.² evertheless, specific knowledge of the constitution of the liquid state is limited when compared with that of the solid and gaseous states owing, in part, to the difficulty of interpreting the X-ray data and in part to the indirect character of deductions based on thermodynamic data. Of the structure-sensitive physical properties, electrical resistivity of liquid metals is perhaps the most easily interpretable, particularly when comparison is made with the solid state. According to the available data, most of which was obtained prior to 1914, cubic metals exhibit a normal linear and positive temperature dependence in the liquid state and the data have been accepted without question. The divalent metals, zinc and cadmium, are apparently exceptional in that resistivity is not linear with temperature and it passes through a minimum. Mercury also exhibits a nonlinear temperature dependence but the slope is always positive. Important comparisons with magnesium could not be made at the time the following work was undertaken because the necessary experimental data were not available. Data on liquid solutions are very limited and are largely from a single source."-" Based on Bornemann's work, Norbury7 pointed out that the resistivity of liquid copper alloys appeared to be dependent on the valence of the solute and that the increase due to the solute was of the same order as in the solid state. However, large extrapolations were involved and no quantitative relationship was developed. Therefore, before proceeding with additional deductions regarding the resistivity of liquid metals and interpretation in terms of structure, it appeared necessary to verify and extend the previous work with particular emphasis on divalent metals and the effect of alloying elements of different valence in dilute liquid solutions. The present work includes: 1—A determination of the resistivity of high purity liquid magnesium, tin, indium, copper, zinc, and cadmium as a function of temperature. 2—The effect of 1 atom pct of copper, cadmium, aluminum, tin, antimony, and

Jan 1, 1954

By J. Sibakin, R. D. Hindson

In order to devise a practicable soaking pit schedule for use at The Steel Co. of Canada Ltd.'s Hamilton Works, soaking pit heating temperatures, sooking times, pit capacity, and safe maximum mill drafts were correlated with fluctuations in the current or load of the bloom mill driving motor. Other variables such as total delays in the pit, rolling schedules, mill delays, and track times were also investigated. IN order to show an easily applied and accurate means of establishing soaking pit heating temperatures, soaking times, pit capacity, and safe maximum mill drafts, these various factors are correlated herein with fluctuations in the current or load of the bloom mill driving motor. Rolling practices have a considerable influence on the production capacity of a blooming mill. The maximum values of the torque, in particular, are of importance, since even instantaneous current peaks lead to the tripping of the motor by the overload relay and result in loss of mill time. The establishment of safe maximum drafts and accelerations for ingots of different sizes and of a soaking pit practice which would ensure a consistent and satisfactory plasticity of the metal is of considerable importance for increasing the efficiency of both the blooming mill and the soaking pits. The Bloom Mill Dept. of the Hamilton Works, The Steel Co. of Canada Ltd., is equipped with one 44 in. mill driven by a 7000 hp motor with the setting of the overload relay at 22.0 ka. The speed of rotation of the motor is regulated after the Ward-Leonard system. There are three basic speeds of 9.5, 28, and 47 rpm and a further possibility of increasing the speed by weakening the field. This last possibility is hardly ever used during practical operations. The rolling program of the blooming mill is varied, both in the size of the ingots to be handled and in the steel grades. The total tonnage handled by the mill is about 2,000,000 ingot tons per year. At the time of the investigation, the Bloom Mill Dept. was equipped with 22 soaking pits (6 regenerative, 14 bottom-fired, and 2 one-way top-fired pits) with a total bottom area of 2770 sq ft. The pits are fired with a blast furnace-coke oven gas mixture having a calorific value of 155 Btu per cu ft. The foregoing figures show that the production program was such as to impose the necessity of a most efficient usage of the available equipment. For this purpose, the operations of the 44 in. mill and of the soaking pits were investigated, and the results of the investigation were used as a basis for a revised soaking pit schedule and drafting practice. The plasticity of an ingot of a certain chemical composition when being rolled is determined mainly by the following factors: I—the ingot size, both thickness and width; 2—the length of the gas soak; and 3—the surface temperature. The first two factors determine the uniformity of the temperature distribution over the cross-section of an ingot. The third factor introduces the level of the heating of an ingot. The torque produced by an ingot being rolled is determined by the area of the metal displaced, its plasticity, and acceleration values. On the other hand, with shunt motors the torque is determined by the current. This can be assumed to be correct with only a small degree of error for compound motors with a relatively small effect of the series windings as long as the velocity is not regulated by weakening the field. Since the spread is relatively unimportant when compared to the width of an ingot and since it is also reduced several times during rolling by edging passes, the draft alone and not the area of the metal displaced may be taken into consideration with ingots of a similar size. It is therefore possible to determine the main features of the heating and drafting of an ingot by measuring the current and acceleration of the mill motor. After the acceleration has been taken into account, the amount of current will be an indication of how the motor responds to a heating and/or drafting practice and these practices can be adjusted in order to get the desired result. As peak currents are more likely when heavier ingots are rolled, the rolling of plate and slab ingots was investigated. Conditions prevailing when smaller ingots are rolled can be deduced from the results obtained on heavier ingots. All measurements were made when plain carbon grades under 0.15 pct C were rolled. The motor current, the voltage across the armature, and the rpm were recorded simultaneously on synchronized charts, Fig. 1, which moved with the speed of 6 in. per min. Each draft was recorded by a special observer. The rpm curve made it possible to establish the acceleration at any given moment. For purposes of correlation, the maximum current during a pass and the corresponding acceleration were used. The charts made it possible to establish the position of the roller's lever at any given moment as well as the total time of a pass. The slab ingots were divided into three groups (28x35, 28x45, and 27Mx53 in. ingots) and each group was investigated separately. Since they account for most of the current peaks, only flat passes were used for purposes of correlation, a total of 1373 having been investigated.

Jan 1, 1956

By A. K. Mukherjee, J. E. Dorn, J. D. Mole

Investigations were carried out on the effect of polyslip on the strain hardening of aluminum single crystals. The orientations investigated were those lor which the tensile axis was in the [001], [111], [112], and [012] directions plus another for which the Schmid angles for {111}(110) slip were 1 deg. The experimental data were analyzed on a model based on the intersection of dislocations with particular emphasis on the effect of polyslip on the activation volume for inter-section. It is shown that the rate of strain hardening inreases for those orientations wherein attractive dislocation intersections occur and that those orientations which produce the greater number of such intersections exhibit the greater strain hardening. Good correlation of the data is obtained with the concept that attractive junctions, as proposed by Saada, Play an important role in accounting for the rate of strain hardening. EXISTING concepts on the nature and cause of strain hardening in fcc metals have been deduced principally from experiments on the deformation of single crystals under single slip. The effect of crystal orientation on the shapes of the stress-strain curves for single slip have been summarized by seegerl and more recently by Clarebrough and Hargreaves.2 Tensile specimens whose axes fall near the center of the [001]-[011] line of the standard triangle of the stereographic projection exhibit the longest range of easy glide (Stage I) and the lowest rates of linear hardening (Stage 11) whereas specimens whose axes lie near fie [001]-[111] line of the standard triangle have limited or no easy-glide range and exhibit somewhat higher linear strain-hardening rates. Specimens whose axes lie near the [001] or the [ill] poles do not exhibit easy glide and have the highest rates of linear hardening. Kocks3 has shown that the highest rates of linear hardening Occur under Polyslip when the tensile axis coincides with the [111] or the [ 001] pole. Since the rate of strain hardening is sensitive to specimen orientation and the incidence of polyslip, these relationships might help to discriminate between various dislocation models for strain hardening in fcc metals. Previous attempts to analyze the effect of orientation on strain hardening,1"3 however, did not provide a unique answer to this problem. Consequently the present investigation was undertaken wherein additional data, particularly that for the effect of polyslip on the activation volume for intersection, was also determined in order to provide more complete information on the details of strain hardening. Whereas analyses of these data reveal that several recommended models for strain hardening are at variance with the facts, good correlation of the data is obtained with the concept that attractive junctions4 play an important role in accounting for the rate of strain hardening. I) EXPERIMENTAL APPROACH seegerl demonstrated that slip in fcc crystals at low temperatures is dependent on thermally activated intersection of glide dislocations with forest dislocations. This has been confirmed by tests on single crystals of aluminum by Mitra, Osborne and Dorn5 and on polycrystalline aluminum by Mitra and Darn.' Thus in accord with Seeger's theory, the shear strain rate, ?, below a critical temperature, T, is where .V is the number of points of contact per unit volume between forest dislocations and glide dislocations, A is the area swept out per successful intersection, b is the Burgers vector, v is the frequency of vibration of the segment of the glide dislocation undertaking intersection, U is the activation energy for intersection, k is Boltzmann's constant, and T is the absolute temperature. For aluminum, which has an extremely high staeking-fault energy, the constriction energy is negligibly small and therefore the activation energy decreases practically linearly with the stress according to as will be recomfirmed later, where Uo is jog energy at the absolute zero, G and Go are the shear moduli at the test temperature T and O°K, respectively, L is the spacing of the forest dislocations, t is the applied shear stress for slip, and tGo is the stress field that must be surmounted athermally.

Jan 1, 1965

By D. Walton

The effect of small solute additions of Cu on the activation energies for creep A1 single crystals were determined over the range from 78° to 850° K. Below 240°K and above 800°K activation energies were unchanged. Between 240°K and 400°K strain aging causes the creep rate to become vanishingly small and the flow stress was independent of the temperature. Between 500° and 50°K the activation energy was increased to 41,000 cal per mole. NUMEROUS investigationsL have shown that solid solution alloying invariably increases the flow stress. A typical example is documented in Fig. 1. Such increases in flow stress can arise from two general effects: Alloying can increase the long-range stress fields through which dislocations must move by causing appropriate clustering; modification of dislocation densities, and so forth. Alloying can also modify the short-range stress fields that determine the activation energies for thermally stimulated migration of dislocations, such as occurs in some solute atom pinning processes, and so forth. Actually both long- and short-range stress-field effects can occur simultaneously. It was the purpose of this investigation to evaluate the effect of alloying on the short-range stress fields by determining the effect of alloying on the activation energies for creep. The resulting observations also shed some light on the effect of long-range stress fields on dislocation processes. EXPERIMENTAL TECHNIQUE Single-crystal bars (6 in. long 3/8 in. wide and l/4 in. thick) of dilute solutions of Cu in A1 were seeded, so as to provide extensive single slip, with the pole of the tensile axis located in the standard stereographic projection as shown in Fig. 2. Each crystal was grown under an argon atmosphere in a graphite mold containing a large reservoir of molten alloy for the purpose of obtaining rather uniform composition of Cu along the length of the bar. The nominal compositions of the alloys which were produced from 99.99 pct Cu and high-purity A1 containing 0.001 pct Fe and 0.001 pct Si, are given in Table I. Strains, measured by linear variable transformers attached by quartz rods to a 3 in. gage section were sensitive to and the stresses were ap- plied by direct loading of the specimen. Temperatures were determined by thermocouples attached to the gage section of the specimens. Below 400°K the apparent activation energies for creep, Q, were determined by the effect of small, rapid changes in temperature of about + 10°K from T1 to T2 on the corresponding creep rates ?1 and ?2 during primary creep according to where R is the gas constant.' Above 400°K, Q was evaluated from Eq. [1] for the secondary creep rate using temperature changes of about ±20K. A typical set of results is shown in Fig. 3. RESULTS AND DISCUSSION The previously obtained effect of temperature on the apparent activation energy for creep of single crystals of high-purity A12 is shown by the broken curve of Fig. 4. The datum points on the same graph illustrate the effect of dilute a solid solution alloying with Cu on the activation energy between 600" and 750°K. Each plotted point is the average of not less than five independent test values between 600° and 750°K and not less than three at other tempera-

Jan 1, 1962