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By Shiro Ban-ya, John Chipman

The effects of many alloying eletnents on the acticity coefficient of sulfur in liquid iron have-been studied by the equilibriutn in the reaction Sfin Fe) + Hz = HzS at 1550°C'. Results are expressed in terms of a concentration variable for a nonmetallic or for a substitutional metallic solute. Activity coefficient of sulfur, defined as increased by B, Al, C, Si, Ge, Sn, P, As, Sb, Mo, W, Co, and PI. It is decreased by Cu,Au, Ti. Zr, V, h'b, Ta, Cr, ,23n, and Ni. Irulues oj. the interaction coejficient 0i = 6 In are labulated. The same interactions are expressed also in terms of atom fraction and of weight percent. The thermodynamic properties of sulfur in liquid iron have been fairly well established. Our recent paper1 reported new determinations of activity coefficient up an atom fraction of 0.12 and equations based on a careful review of all published data. The effects of alloying elements on the activity of sulfur have been studied by several investigators,2"11 especially by Morris and Williams for silicon,' by Morris and Buehl for carbon,~ and by Sherman and Chipman for manganese. phosphorus, and al~minum.~ However, the effects of some important alloying elements remain to be determined. The purpose of this investigation was to determine the effects of many alloying elements on the activity of sulfur in Fe-S-j ternary systems. EXPERIMENTAL METHOD This study was based on experimental determination of equilibrium in the reaction at 1550°C: The same apparatus and procedure as described in our previous paper have been retained, and the same corrections were applied for dissociation of H2S. The alumina crucibles used in the experiments consisted of four separate compartments. In a given experimental run. kach of three alumina crucibles held four different samples of about 3 g each which reached equilibrium in the same gas atmosphere and temperature. The charges were made up of electrolytic iron, pure iron sulfide, and desired alloying elements, which were pure metal or master alloys made in the laboratory. The weighed samples were held for 4 to 12 hr in the prepared atmosphere at 1550°C. They were then low- ered to be cooled as quickly as possible. The quenched metal beads were crushed to avoid the errors of segregation in the ingot. The sulfur content was determined gravimetrically and alloy content by appropriate chemical analysis. CALCULATIONS The apparent equilibrium constants of Eq. [I] are expressed as follows from the corrected gas ratios and sulfur concentrations: The term K" is the observed equilibrium constant in any given ternary solution, K' is the value for the Fe-S binary solution. and the limiting value of K' in the infinitely dilute solution is designated by K, which is the true equilibrium constant in Eq. [I]. In the thermodynamic treatment of nonmetallic elements in a metallic solution, it has been suggested1' that the lattice ratio has certain advantages over other variables to express the concentration of solute. In interstitial solid solutions the lattice ratio zj is proportional to the ratio of filled interstitial sites to those which remain unfilled. The equations derived for the activity of the solute using zj as the concentration variable are found also to be applicable to liquid solutions containing nonmetallic solutes when the nonmetal is treated as if it were interstitial. For this purpose we adopt the following definitions: The quantity vj which is negative for interstitial solutes is taken as -1 for nonmetallic and +1 for metallic solutes. For purposes of calculation however ; j may be assigned a value which results in a linear relation such as shown in Figs. 1 to 15. The activity coefficient of sulfur, Qs, and equilibrium constant. K(z). are defined as follows: According to a Taylor series expansion. the logarithm of the activity coefficient of sulfur in Fe-S-j ternary system is: However, the value of 6 In */6zi remains constant through a broad range of dilute solutions and the terms of higher order are negligibly small. As a consequence, Eq. [6] is simplified as follows:

Jan 1, 1970

By Roy F. Abernethy

This report describes a method developed by the Bureau of Mines for the determination of beryllium in coal ash. Samples are put into solution by standard wet chemical procedures. Interfering elements are complexed with Na2EDTA, and the beryllium is separated by extraction of its acetyl acetone complex with chloroform or carbon tetrachloride. Final determination is made with Beryllon II.

Jan 1, 1970

By E. M. Bennett

HISTORY In 1923 John Campbell Miles discovered the Mount Isa deposit after finding and submitting for assay some “unusual and heavy rocks”. Six months after submission he received the assays of his original samples which indicated high lead-silver values. The deposit area was isolated and unknown geographically and not served by even a rough country road. The isolation of Mount Isa coupled with the depression years had a strong influence on the rate of development of the area. These two factors resulted in a slow amalgamation of the early individually held leases and the lack of ready finance to begin serious mining of the deposit. Initially, surface lead-silver-zinc mineralisation was proved and diamond drilling to shallow depths showed the presence of a viable orebody. Limited underground development work was initiated and open cutting associated with glory holing commenced. Due to the metallurgical problems associated with the ore and due also to unsuspected change in metallurgical conditions as the ore deepened into what is known today as the transition zone, major problems of finance were recurring at frequent intervals. Despite low metal prices the development of the mine continued due to continuing infusion of capital. During the 1939-45 war years a surplus of lead was being produced in Australia, but a grave shortage of copper was apparent. About this time copper ore had been found to the hanging wall of the then known major lead orebodies. At the request of the Australian Government, lead production ceased and copper production commenced.

Jan 1, 1970

By Bert C. Morrison

In 1961. American Smelting and Refining Company was conducting exploration for lead in southeastern Missouri using several geophysical methods. Electrical methods were used in almost every hole drilled during this period. These methods met with only limited success, with one exception. This paper deals with that exception: An Electrical Potential Method used at a single hole to indicate direction to better mineralization. This method was notably successful in the program.

Jan 1, 1970

By Laurance L. Oden

The Bureau of Mines is developing melting data for binary combinations of the alkaline earth fluorides and yttria to facilitate the formulation of slag compositions. The present report deals with the CaF2-Y203 system for which solidus and liquidus temperatures and solid solubilities were determined. The information is presented as the phase diagram. All specimen compositions were blended from high-purity materials and encapsulated in Mo or Pt20Rh prior toheat treatment. Liquidus temperatures were determined by ceramographic examination of heat-treated and quenched specimens. Solidus temperatures were determined by differential thermal analysis and by electron microprobe analysis of quenched specimens. Terminal solid solubilities were derived by parametric methods. The peritectic system was found to be pseudobinary due to the formation of yttrium oxyfluoride at temperatures near the liquidus. The peritectic point occurs at 7 mole pct Y203 and 1,438° ± 5°C. The terminal solid solubility of Y203 in CaF2 decreases from 7 mole pct at 1,438° C to 1 mole pct at 1,100° C, and the solubility of CaF2 in Y203 decreases from 9.5 to 7 mole pct over the same temperature interval.

Jan 1, 1970

By M. M. Fine

Development of a process for winning copper from pelletized chalcocite concentrate without matte smelting and converting is underway at the Twin Cities Metallurgy Research Center, Bureau of Mines. The new route from concentrate to metal includes 2-stage fluid-bed treatment; pelletized concentrate (33 percent Cu, 7 percent S) is first desulfurized (to about 0.5 percent S) in an oxidizing atmosphere, and in the second stage the calcine is metallized by reduction with hydrogen. Thereafter, the reduced product plus 10 percent CaO is routed to a smelting furnace to separate metallic copper from the gangue. Recovery and the Cu content of the product at this point are in the 97-98 percent range. The metal must be refined to remove sulfur and iron to make wirebar copper. An important feature of the process is the pelletizing of the fine concentrate into mini-pellets prior to fluid-bed treatment, which has permitted shorter reaction time, decreased dusting, and facilitated subsequent processing.

Jan 1, 1970

By James C. Word, R. M. McLouski

This paper will describe the development and application of large-scale integration techniques employed in the fabrication of a germanium multielement array. The array consists of 100 by 228 PNP bipolar transistors fabricated on 5 mi1 centers. Back-biased p-n junction techniques are used for electrical isolation of the individual elements. The end use of the array is a high resolution, large area IR sensor. The monolithic array is fabricated in 1 ohm-cm p-type germanium epitaxially deposited on 6 ohm-cm n-type substrate. Epitaxy was accomplished through the hydrogen reduction of germanium te trachloride. Di-borane was used as the dopant. Base regions are achieved by the diffusion of arsenic from doped oxide or arsine sources. Oxide-masking of the arsenic im-pzlvity was achieved by the chemical deposition of a boron doped glass. The emitter is formed by an aluminum alloy diffusion technique. Vacuum deposited aluminum is used for the emitter, interconnections, and for the contact and bonding pads. ALTHOUGH a great volume of literature pertaining to the development of large scale integration techniques (LSI) has been published for silicon and in particular silicon imaging applications,' to date only a small number of similar devices have been constructed using germanium technology.' Since the physical and chemical properties of germanium are vastly different from those of silicon, the fabrication technology for integrated structures in germanium is also different from that of silicon. In particular germanium does not possess a stable oxide as can be grown on silicon by heating in an oxidizing ambient for masking of dopants and passivation. This paper describes the application of germanium LSI techniques employed in the fabrication of a multielement infrared sensor array. The array is used in a high resolution, large area infrared sensor for operation in the 0.8- to 1.5-u spectral range. Back biased p-n junction techniques are used for electrical isolation of individual elements. Discrete germanium devices have been fabricated routinely for some time. However, mainly due to the lack of a suitable mask for selective doping and the high current leakages inherent in germanium p-n isolation, few monolithic germanium structures have been constructed. THE INFRARED MOSAIC A cross-sectional view of the array is shown in Fig. 1. The monolithic structure consists of 12,800 PNP transistor elements in a 100 by 128 matrix fab- ricated on 5 mil centers. The emitters of each line of transistors are connected together using aluminum interconnects while the strip collectors are connected together in series at right angles to the emitter lines. The selection of this structure is dictated by the readout technique involved. Access to each element transistor is obtained by applying a bias voltage to a particular collector strip and separately interrogating each emitter row. A charge storage, i.e., an integration mode is used for reading out this particular array Construction techniques available for use with germanium do not include a selective p-type diffusion capability for surface concentrations greater than 10" per cu cm and junction depths greater than about 10 u. This fact limits the type of structure that may be used. Therefore, an array of PNP transistors that did not employ p-type diffusions was chosen. The structure was fabricated by growing a 1 ohm-cm p-type epitaxial layer on a carefully prepared 6 ohm-cm n-type substrate. N-type dopants were used for the isolation and base diffusions and alloyed aluminum was used to form the emitter junctions. The array was then completed by evaporation of aluminum interconnections and contact pads. SUBSTRATE AND SUBSTRATE PREPARATION Germanium substrates of (111) orientation grown by both Czochralski and zone leveling techniques were utilized for mosaic fabrication. Czochralski substrates were preferred because of the lower dislocation densities available in this type of material. Dislocation densities for the Czochralski material were typically less than 3000 per sq cm, while those for the zone leveled material were typically less than 5000 per sq cm. All substrates were uncompensated to minimize thermal conversion problems in subsequent epitaxial and diffusion processing. Both in-house and vendor polished wafers were used. The in-house polishing technique employed consisted of an initial gross chemical etch in CP4 to remove saw damage from both surfaces. This was followed by a chemical-mechanical polishing operation of one side of the wafer. The chemical-mechanical polishing solution used was Lustrox 1000 (Tizon Chemical Co.), and consists of zirconium dioxide, sodium hypochlorite, water and a surfactant. The wafer thickness before and after polishing was typically 0.020 and 0.010 in, respectively. THERMAL CONVERSION The problem of thermal conversion of both the substrate and epitaxial layer was particularly acute because of the relatively low carrier concentrations employed in both regions. This problem has been encountered by other workers in the past.3 Without special treatment before epitaxial growth substrate conversion (n-type to p-type) and changes in the re-

Jan 1, 1970

By A. J. Barry

A practical method has been developed and field tested which provides an estimate of the bearing capacity of mine roof and floor. The relationship between penetration of the strata and imposed loads is determined by in situ tests. Information of this type is needed to determine the maximum allowable pressure that may be applied by self-advancing supports on roof and floor of a longwall face without causing a punching type of failure.

Jan 1, 1970

By James P. Connell

The Montana Operations of the Anaconda Company constitute an integrated, though geographically separated, non-ferrous metal production complex. The mines are located at Butte and consist of one large open-pit mine, two small underground mines, a precipitation plant for both underground and pit-dump leach water, and the Weed Copper Concentrator. The smelter, located at Anaconda, Montana 25 miles to the west, processes all Butte copper shipments as well as copper materials from both Anaconda and private mines. Copper and zinc are refined at Great Falls, Montana, 165 miles to the north. Other facilities developed over the years include the Anaconda Forest Products Division, the Butte, Anaconda, and Little. Chicago Water Companies, and the Montana Hardware Company. Data processing for these operations has been performed on an IBM 360 Series, Model 30 computer, utilizing a Disc Operating System. This was replaced in September 1970 with a 360 Series, Model 40 128K unit. In addition, some data processing is also done for Anaconda Company operations located at Britannia Beach, British Columbia; Columbia Falls, Montana; Yerington, Nevada; and Twin Buttes and Tuscon, Arizona. The material under discussion in this paper will be concerned primarily with the mining operations at Butte.

Jan 1, 1970

By Howard L. Hartman

In 1969, the OECD conducted a survey internationally to determine the status and needs for research and development in the field of tunneling. The findings also have some validity for underground excavation in general and for underground mining per se. Of the 17 countries responding to the survey, the U.S. leads in the level of support: $21.8 million and 720 man-years of effort over the last ten-year period. The total volume of R/D for the 17 countries was estimated to be $86 million and 5800 man-years. Performance of research was primarily by government agencies and public utilities (70%); the balance was conducted by private organizations and universities (15% each). In the categories of R/D subjects surveyed, three--Wk mechanics, soil mechanics, and geological exploration--outstripped all the rest in priority of effort to date. Ground support, equipment development, excavation, and environmental control received intermediate attention. The subject areas in which the least R/D effort has been expended are materials handling and systems evaluation. For the future, those R/D areas rated the most crucial to achieve technological progress in tunneling were excavation, ground support, and materials handling. The survey findings of tunneling activity indicated (1) a disturbingly low level of R/D activity in the private sector, (2) the necessity for a reordering of priorities in directing research efforts in the future, and (3) a lack of recognition to date of the importance of systems evaluation in R/D activities.

Jan 1, 1970

By Rodney L. Stone

In past attempts to characterize green and dry iron ore pellets, the authors have found large variations in the results of strength tests performed on closely sized pellets from the same batch. Where bentonite was the binder, such variations in the pellet quality were attributed to the presence of internal flaws and the nonuniform distribution of the binder. Studies have shown that pellet strength is strongly dependent on the degree of "mixedness" of the iron ore concentrate and the bentonite binder. However, before such a relationship can serve as a guide for the development of better mixing techniques and the associated economy of bentonite consumption, more precise knowledge of the bentonite-concentrate mixtures is needed. For example, what is the bentonitc distribution from pellet to pellet and within pellets?

Jan 1, 1970

By D. M. Thayer

In the last decade public awareness of the need for pollution abatement has increased greatly. The concern that had been previously shared by local and state conservation groups has spread to create a national concern for preservation of our non-polluted environmental assets and regeneration of those that have been wasted. Because other current matters such as inflation, civil rights,' tax reform and the Vietnam situation have been the object of most national concern, an extremely strong national pressure base has not been brought to bear on the pollution control crisis. Yes, the word is crisis, for in many areas pollution is of critical concern. One has only to look at Lake Erie, the skies about our major urban areas and many of our major rivers and streams to see this crisis These are not situations that can be corrected overnight. We are faced with two basic problems that should be attacked simultaneously: (1) Cleaning up the present sources of pollution and (2) preventing the generation of new pollution sources. What approach should be taken? As in any engineering problem, the limits must be well defined before a final solution is attempted. Pollution must be defined on a national basis. This means that basic Federal legislation and control is necessary. This should reduce any competitive advantage that can presently be gained by movement of operations from one state or geographical area to another on the basis of differences in local legislation .and enforcement. By giving real numbers as guidelines, selective enforcement can be avoided. As a starting point, for a definition of pollution let us use the following - "Any change in the environment occurring from other than natural causes." This definition may not be satisfactory to all but surely we must be somewhat dramatic in our statements to counteract the present prevailing philosophy. Our statement of this philosophy - "At what level of pollution can we afford to operate?" On the basis of our general definition we would like to state what we feel should be the philosophical statement - "How little can we change our physical environment as a result of operations?"

Jan 1, 1970

The suitability of char from Yallourn brown coal as a filler for carbon electrodes used in the aluminium smelting industry has been assessed on the basis of the specifications usually laid down by electrode manufacturers for petroleum coke fillers. The purity specifications can be met by a simple acid leaching of the coal before carbonization. The true density of char produced at 1200°C is within 5 per cent of the specification figure, but the bulk density of char obtained from as-mined coal is only half that specified for petroleum coke.Although this can be increased to three-quarters of the specified figure by briquetting the coal before carbonization, further increases would be very difficult to achieve, as the remaining shortfall in density is due to an extensive microporosity developed in the particles of char during carbonization.

Jan 1, 1970

By R. W. Heckel, H. P. Cheskis, A. Lawley, M. R. Pinnel

THERE are discrepancies reported in the literature regarding the micro and macro stress-strain behavior of metals and alloys. In particular, Young's modulus and micro yield measurements often show significant variations depending upon the techniques employed.'-" The purpose of this note is to correlate measurements made with four techniques and to indicate where some of these discrepancies might arise. Allied use of these techniques can provide a complete and consistent characterization of micro and macro stress-strain behavior (over the strain range of 10-9 to 10--2 in. in.-') from a minimum number of samples. Techniques. The techniques employed for measuring stress-strain behavior involved the use of a) linear differential transformers, b) SR-4 strain gages, c) longitudinal resonance waves, and d) X-ray diffraction. Specimen geometries and preparations are summarized in Table I for each technique. Differential Transformer and Strain Measurements. An Instron universal testing machine, modified with an alignment device, was used to apply the load via parallel-jaw grips. The signal from the load cell was applied to the Y scale of a Moseley X-Y recorder (sensitivity of 10 lb load per in. chart). The elongation was monitored simultaneously with strain gages mounted on three sides of the rectangular specimen, and with two linear variable differential transformers (LVDT) mounted at 90 deg to one another on faces that also contained the strain gages, Fig. 1. The signal from one of the LVDT's was applied to the X scale of the recorder (sensitivity 40 µ in. elongation per in. chart) in order to trace a continuous load-elonga-tion curve. Concurrently, the strain on the same face (i.e., the face monitored by the LVDT) was recorded by the corresponding strain gage. A stress-strain curve was plotted from the load cell-strain gage data and was compared to the stress-strain curve (converted from load-elongation) plotted from the continuous load cell-LVDT trace. Identical Table I. Description of Specimens Used in the Present Study Material Dimerisions Preparation Condition 99.99 pct A1 tensile 318 by 3/16 by 3 in. as cast ingot; cut annealed specimen on diamond wheel 2024 A1 tensile 318 by 3/20 by 31/2 in. vacuum hot annealed specimen pressed sheets; cut on diamond wheel 99.99 pct Al 3116 by 3/16 by 2 in. cut from tensile prestrained dynamic modulus specimen after 10"* in. specimen test per in. 2024 A1 dynamic 3/20 by 3/20 by 2 in. vacuum hot annealed modulus specimen pressed sheets; cut on diamond wheel 2024 A1 X-ray gage section 112 by vacuum hot annealed specimens 1/4by1/20in. pressed sheets; cut on diamond wheel

Jan 1, 1970

By A. Vignes, J. P. Sabatier

A study of ternary diffusion at 1315°C in the Fe-Co-Ni system covering the entire ternary phase diagram has been carried out. Experimental values of the four interdiffusion coefficients DFeNico,DFeCoCo, DFeCoNi were computed at 33 points of the ternary diagram. The limiting values of these coefficients on the three sides of the ternary diizgram have also been determined. This set of data is presented as a contour map on the ternary isotherm for each of the four coefficients. Assuming that the Fe-Co-Ni system can be considered as ideal, the phenomenological coefficients Lk ij (with k = Fe) have been computed and the Onsager reciprocal relutions verified. It is shown that, in the Fe-Co-Ni system, the diffusion process can also be described by only two interdiffusion coefficients DFeFe and DCoNiFe, the second cross diffusion coefficient DCoFeNi being equal to zero and the second direct difusion coefficient being given by The values of the cross interdiffusion coefficients and of the Onsager coefficients are explained in terms of atomic mobilities of the three components with the help of a kinetic calculation due to Lane and Kirkaldy.8 It is shown that all the results are explained if the tracer difusion coefficients of the three components are such that DFe > DNi ~ DCo in complete agreement with experimental data on the three binary systems. DIFFUSION in a ternary alloy system is basically and significantly different from diffusion in binary alloys. In binary diffusion, there is just one independent composition variable and only one coefficient Dij is needed to describe the interdiffusion process. In ternary diffusion, we must allow for cross interaction between two independent species, and four interdiffusion coefficients are necessary to describe the transport process. Kirkaldy et al.1,2 have determined interdiffusion coefficients in the systems, Cu-Mn-A1 and Zn-Cu-Al. Guy and Leroy4 have reported intrinsic diffusion coefficients for the r phase at 1300°C of Co-Ni-Cr alloys as a function of composition using the analysis of Philibert and Guy.3 Interdiffusion coefficients were measured at three different compositions at 850°C in the single phase copper-rich corner of the Cu-Zn-Mn system by Dayananda and race.5 Zie-bold and Ogilvie6 have determined interdiffusion coefficients in the single-phase field of the Cu-Ag-Au system at 725°C. Preliminary results on diffusion at 1136°C in the system Fe-Co-Ni have been reported.7 In this study, data are reported on a more complete determination of interdiffusion coefficients in the Fe-Co-Ni system in the entire ternary at 1315°C. There is complete solid solubility with the fcc structures at 1315ºC, and this system can be considered as nearly ideal. This approximation allows the computation of the Onsager phenomenological coefficients. These values can then be used to test a kinetic calculation of the Onsager L coefficients in ternary substitutional solid solutions due to Lane and Kirkaldy.8

Jan 1, 1970

By Alfred E. Schwaneke

An improved maximum-bubble-pressure system using the Sugden twin-capillary method for measuring the surface tension and density of molten metals is described. Improvements include (1) internally ground capillary tips, (2) electronic pressure transducers, (3) micrometer adjustment of immersion depth for density measurements, (4) valuing arrangements to allow operation at other than atmospheric pressure, (5) temperature range to 1,100° C, and (6) recorder readout of pressures. Data for surface tension of mercury from 20° to 300° C are given.

Jan 1, 1970

By Peter L. Raffo, Walter R. Witzke

RHENIUM has a melting point of 5750°F, the second highest value among the metals.1 Its refractory nature should thus make it a useful material at high temperatures. The only available data on the high-temperature properties of bulk rhenium are from the work of Flagella and Tarr.2 These authors have shown that, over a wide range of temperatures and stresses, no appreciable linearity exists in a log-log plot of the minimum creep rate or rupture life vs stress. The purpose of the present letter is to describe some exploratory experiments designed to study the creep rate-stress-temperature relation and other facets of the creep of rhenium. The tests were carried out in vacuum in the temperature range 2200" to 4000°F (0.43 to 0.72 Tm,) at stresses ranging from 4 to 20 ksi. The powder metallurgy rhenium was purchased as 0.04-in.-thick sheet. The sheet is nominally 99.97 pct pure with the major impurities being iron (70 ppm) and molybdenum (25 ppm). The sheet was machined into specimens having a 1-in. gage length and a 0.25-in. gage width. The specimens were preannealed in hydrogen at 3000°F for 1 hr. This treatment produced

Jan 1, 1970

By Ted C. Briggs

A removable-jacket distortion apparatus was constructed and used to measure distortion coefficients for two high-pressure vessels. The measured distortion coefficients were used to compute distortion coefficients for volumes VI and (V1+V2) of a 1,000-atmosphere Burnett compressibility apparatus for the temperature range 0° to 75° C. Young?s modulus for Armco 17-4 PH stainless steel, heat treated to condition H1150-M, was computed from experimentally determined distortion coefficients. A 10-to 14-percent correction to the values obtained for Young's modulus may be required because pressure vessel end effects were neglected. The distortion coefficients of the compressibility apparatus are believed to be accurate to about 1 percent.

Jan 1, 1970

By B. C. Wonsiewicz, G. Y. Chin

THE presence of deformation bands in cold-worked metals is known to influence the development of deformation textures1 but has not been considered in any theoretical treatments. At the present time the most rigorous theory of deformation textures appears to be based on Taylor's concept of homogeneous deformation of a crystal within a polycrystalline aggregate.' For each crystal the Taylor theory allows the operation of several equivalent combinations of five or more slip systems. Hence deformation bands can arise from the operation of a separate combination of slips in each of several portions within a crystal. On the other hand, a second type of band may occur as a consequence of slip on systems other than those selected on the basis on homogeneous deformation. This type appears to be associated with crystals of symmetrical orientations, such as the [loo] and [lll.] axial orientations in drawn wires of fcc single crystals studied by Ahlborn.3 In this note we propose a simple mechanism of deformation banding of the second type, and compare the theoretical results for wire drawing of [loo] and [Ill] with Ahlborn's observations. In outlini the model requires that the work to accomplish a given overall shape change by banding be less than or equal to the work to accomplish the same change by homogeneous deformation. While the work by homogeneous deformation, WH = ?T ;dri, can be calculated exactly by the equivalent methods of Taylor2 or of Bishop and Hill,4 the work by banding, WB, is less certain. The latter consists of 1) Wi, work by slip within a band, 2) Wb, work associated with formation of a boundary between bands, and 3) Wc, work to correct the difference in shape change arising from banding and homogeneous deformation. The Wi term can be evaluated explicitly for a band with an assumed set of slip systems, but a satisfactory analysis of Wb and Wc has not been obtained. Since WB = Wi + Wb + Wc WH, for banding to occur, however, a necessary condition is Wi = WH . Hence it seems reasonable to choose a band with the lowest value of Wi among competing bands consistent with Wi = WH, and then minimize Wb and Wc by arranging the physical configuration of the selected band. Wc is minimized by combining neighboring bands such that their net strain matches the macroscopic strain as closely as possible, and Wb is minimized by enforcing strain compatibility across the boundary between two neighboring bands, similar to the case of a grain boundary.5 It is realized that this procedure is not completely satisfactory, but it does seem to explain Ahlborn's observations reasonably well. The procedure is now outlined for the two corner orientations. a) [l00]. Fig. 1 shows a (100) stereographic projection. The results of the Taylor analysis for axi-symmetric flow by homogeneous deformation6 show that, while [loo] itself is unstable, the rotation of the tensile axis will nevertheless be confined to within about 15 deg from [loo]. Alternatively, less work may be expended by banding with slip on a pair of systems with primary-conjugate relationship, e.g., (ll1)[10l.I + (li1.)[110]. The latter represents minimum Wi for all possible bands.* Since there are four symmetrically

Jan 1, 1970

By William G. Pariseau

The flexure of geologic strata, a phenomenon of interest to geologists and mining engineers alike, is examined as a sheet bending problem in Coulomb plasticity. Fonnulae for the distribution of stress, strain, and displacement increments; volume change; change in the length of the central surface; and power of dissipation, as well as for the neutral surface shift are given. Strains of any magnitude are considered. The analysis shows that deeply buried strata may bend and develop "tensile" cracks under generally compressive states of stress. It is also shown that bed separation and high capacity props are desirable in mechanized longwall mining, a result in keeping with operating experience. Although speculative at this time, the analysis provides a rational working hypothesis as regards the problem of strata flexure and control. | he purpose of this paper is to present an analysis of the flexure of geologic strata as a problem in the bending of a sheet of material failing in accordance with a Mohr-Coulomb criterion. The flexure of strata has an obvious academic interest to the geologist concerned with the mechanics of folding. It is of interest to the economic geologist as it relates to the structural control of certain types of ore deposits. It has an intimate association with mine subsidence phenomena, and is of concern to the mining engineer. Strata flexure is also the dominant feature of roof behavior about longwall workings. An improved understanding of strata flexure through a rational mechanical analysis thus appears desirable not only from the academic view but from the economic one as well. In the field, the most commonly observed feature of folding, subsidence, and longwall roof behavior is the permanent and therefore inelastic nature of the strata movement. Fig. 1 illustrates the physical disposition of strata in the vicinity of a longwall face. Inasmuch as most rocks (with the possible exception of certain evaporites) do not exhibit significant viscoelastic behavior, at least not over time spans of engineering interest, a plastic analysis is indicated. The analysis is meant to apply to strata whose deformation is dominantly that of bending such as might be expected in the remote roof about a longwall face.

Jan 1, 1970