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By A. Mosqueda Martinez, L. C. Trytten, R. P. Kofluk, J. J. Budac

The Corefco ammonia leach nickel refinery treats Ni-Co mixed sulphides from the high-pressure acid leaching of Moa Bay nickel laterite. Due to the low iron content of the feed, the ammonia leach process generates a leach residue with ~10% Ni+Co. Since commissioning a leach residue pressure filtration circuit in 2002, this residue has been stockpiled, dried, and sold commercially. For several years, the residue was sold to nickel smelters overseas. In 2014, re-processing of the residue in the high-pressure acid leach was tested. Lab test work was completed showing excellent extraction of the contained nickel and cobalt, and additional beneficial effects in the high-pressure acid leach circuit. A plant test in Moa confirmed the results, and preparation for shipment of the valuable leach residue for re-processing has begun. This paper outlines the test work and results, and some commercial considerations.

Jan 1, 2015

By T. C. Goel, A. Venna, R. G. Mendiratta

"Processing of ferrites has gained tremendous importance in recent times to meet the high performance demands on ferrites in keeping with the fast emerging· technologies. The quality of ferrite powders has strong influence on ·the performance of final device. Fabrication· of high performing ferrite components requires starting ferrite powders of precise stoichiometry, purity and microstructure. It is difficult to obtain these attributes by the conventional ceramic method. The key to obtaining quality powders lies in the· solution techniques. With this in view soft ferrites have been prepared by a wet chemical process, known as the citrate precursor method, which involves the formation of citrate complexes of the constituent cations. The advantages of this process are the ease of preparation and close control of composition, homogeneity, purity and particle size. Electrical and magnetic measurements on lithium ferrites have shown resistivity higher by more than two orders of magnitude compared to that observed for samples prepared by the conventional ceramic method, and low magnetic losses, making the ferrites specially suitable for high frequency applications.IntroductionProperties of ferrites are known to be sensitive to .their processing technique. A small deviation in the compositional stoichiometry of the ferrite affects its properties greatly. Soft ferrites such as Ni-Zn, Mn-Zn and Mg-Mn. are well known ferrites covering wide-ranging applications [1,2]. Lithiiim ferrites have also assumed technological importance for microwave applications and are potential substitutes for the expensive garnets [3]. Lithium ferrites are often doped with zinc to tailor the saturation magnetization required at high frequencies. Lithium and lithium-zinc ferrites, however, present difficulty to processing due to the volatile nature of both the cation components, namely Li and Zn. These ions are volatile at temperatures > 1000°C which makes their processing difficult. One of the main considerations of high frequency performance of ferrites is the high eddy current losses which prevent the interaction of the magnetic field with the ferrite component and hence impair device performance. These losses can be reduced by having a material of high resistivity. Electrical conductivity in lithium ferrite has been attributed to electron hopping [4] between the two vaience states of iron, Fe2+ <=> Fe3+, on octahedral sites. Maintaining the + 3 valence state of otahedral- Fe ions is thus a prerequisite for achieving high resistivity. The resistivity of ferrites is normally found to be low when processed by the conventional solid-state or the ceramic method [5]. This is attributed to (a) extensive ball-milling employed in the method to mix the component oxides results in non-stoichiometric compositions due to introduction of additional Fe ions on abrasion of steel balls during milling, (b) high processing temperatures involved which result in significant volatilization of Li and Zn ions creating thereby oxygen non-stoichiometry which results in reduction of Fe3 + to Fe2 +, (c) large and non-uniform grain sizes. In the present work, preparation of Li and Li-Zn ferrites by a non-conventional method known as a citrate precursor method [6, 7] which requires lower processing temperatures and duration is reported. The method gives stoichiometric compositions on account of homogeneous atomic-scale mixing of the constituent cations via the formation of metal-citrate complexes mixed in solution state. The method is also capable of giving small grain size which aids the oxidation ofFe2+ ions."

Jan 1, 2000

By T. T. Chen

A mineralogical study of copper anodes and copper anode slimes was carried out to elucidate the silver phases present and the behaviour of silver during copper electrorefining. Most of the silver in the anodes is in metastable solid solution in the copper metal. As the copper dissolves, silver also dissolves, but is rapidly removed from solution by a variety of reactions. Some of the silver is precipitated as Ag by cuprous ions and some is precipitated as a complex CU-Ag-Pb-As-Se oxidate phase. Much of the silver, however, reacts with copper selenides to form, progressively, (CU,Ag) 2se, AgCuSe and Ag2se. The reaction commences at the periphery of the selenide grains and progresses inward; the result is commonly a silver-rich species on the outside of a silver-deficient core. Slimes collected periodically throughout the electrorefining cycle show a progressive silver enrichment of the selenides. Traces of Ag2Te also may be present, but the telluride seems to J:ie a rare constituent of most raw anode slimes.

Jan 1, 1989

By Gheorghe Oncioiu

The phenomena developed on the influence of thick coal seam no.3 mining, by horizontal slices and rocks caving roof control, in the Jiu Valley coal basin, are very complex. By analyzing the influence volume of underground faces and defining the stress and strain zones, around the faces, it is possible to evaluate the suitable powered support performances. Also, Jiu Valley thick coal seams involve about 50% of reserve balance in the main safety pillars of social, industrial and natural objectives, situated on the mining surface perimeters. For a correct design and drawing of main safety pillars complex research was done with the aim of establishing the subsidence parameters. Upper face rocks medium could be assimilated as a granular medium, which is in a permanent movement. For describing the rocks movement, respectively the ground surface displacement, was taken into account the stochastic mechanics principles. The theoretical solutions are in accordance within situ measurements.

Jan 1, 1999

By V. A. Zhilina, I. V. Shadrunova, O. E. Gorlova

"The aim of the study is to develop and scientifically justify a new adaptive approach to the separating processes of deep and complex processing technogenic mineral raw materials. Technogenic mineral resources as a waste of mining and processing industry are mostly complex objects that have specific features of material composition and technological properties and make it processing ineffective with traditional schemes of mineral raw materials enrichment. Mineral wastes are regarded in this study as a complex object with a large number of signs in conditions of uncertain environment and object. However, adaptation is regarded as the process management system’ adaptation to the specific the properties of the object and the environment that has several hierarchical levels corresponding to different stages in the management of complex object. An adaptive approach is considered as a methodological basis of multivariate schemes for opening the mineral resources and creating mechanisms that could transfer these potential technogenic resources to the actual that significantly expand the mineral resource base of the country's black, coloured, rare, noble metals and construction materials. In this case, potentially the solution to the most pressing social and environmental problems associated with the adverse effects of past economic activity simultaneously with the commercial objectives. This approach to the wastes mining and related processing manufacturers meets the core idea of sustainable development as the balance of interests of State, society, business, private enterprise and each person in the areas of rational use of resources, economic efficiency and environmental safety. On the example of metal-containing raw materials in the form of slags of ferrous and nonferrous metallurgy, ferrous metallurgy sludge, mature fine tailings, the application of adaptive approach illustrates to the development of technologies of its deep and complex processing as phased, thoughtful movement from a comprehensive study of technogenic raw materials to build optimal topologies of technological schemes for processing the mineral wastes. INTRODUCTION Involving the Russian economy in the system of global economic relations significantly changes the nature of the country's competitiveness in the development of the world market and urgently requires competent management of its own natural and mineral resources. The latter at the present time in real economic processes cease to be a passive material foundation and become the producing basis in the production processes in the status of so-called natural capital. Introduced in the field of economic theory at the end of the 20th century, this term means both the flow of natural services and real natural resources. Consequently, natural objects, which act as natural resources of a certain production, today must necessarily be evaluated in a strategic sense. Modern standards of sustainable development presuppose that the economy should equally be oriented to balance the interests of the state, society, business, individual enterprise and each person in the spheres of rational use of resources, preservation of healthy ecosystems, ensuring well-being, high quality of life and environmental safety of not only the current generation, but also respect for the rights of future generations, that is, intergenerational equality. Most types of minerals are classified as non-renewable resources, therefore resource-saving in the sphere of mineral and raw materials complexes is one of the most important factors-indicators characterizing the degree of approximation to the model of rational subsoil use, and, consequently, sustainable development (State Report, 2017)."

Jan 1, 2018

By W. K. Connor, O&apos

Thermal Treatment Technology Division Albany Research Center, U.S. Dept. of Energy Oregon. This evaluation included a characterization study and direct smelting tests conducted in a bench-scale electric arc furnace (EAF). In contrast to other thermal treatment technologies considered for these wastes (i.e., fluidized bed combustion), direct smelting in the EAF can process 100% of the wastes without prior beneficiation, and utilizes solid oxidant additions (in this case iron ore) rather than air to oxidize the carbon. This solid oxidant addition is advantageous because it results in the production of several value-added furnace products. These products include cast iron resulting from the reduction of the iron oxides, baghouse dust containing virtually all of the zinc from the residues, and a clean (nonhazardous) slag product suitable for recycle as concrete aggregate or construction fill. Offgas from the smelting furnace also holds potential as fuel gas for cogeneration. The direct smelting tests conducted thus far were successful at producing the desired furnace products, exhibiting the potential for complete recycle of the waste pile. A cast iron product of comparable quality to conventional cast irons was produced, at nearly 80% iron recovery to the metal. The slag product was determined to be nonhazardous, based on the EPA TCLP. Lead and zinc partitioning to the dust product was greater than 99%. The material balance over the furnace indicates that for every ton of feed processed, 540 lb. of cast iron, 600 lb. of slag, and 150 lb. of dust would be produced. Energy consumption was roughly 1.10 kWxh/lb of feed material. Prior experience suggests that these figures measured in the bench-scale furnace would translate to 0040 to 0.50 kWxh/lb at the industrial-scale.

Jan 1, 2000

By Michael J. Humenick

A laboratory experimental research project was conducted to evaluate the use of chlorine for the oxidative destruction of residual ammonia which may remain in ground water after in-situ uranium solution mining operations. The work tested the idea of the injection of high strength calcium hypochlorite solution into the mining zone to convert ammonia to nitrogen gas as a final clean-up process for ammonia removal from the ground water system. The paper details ammonia removal efficiency as a function of chlorine dose, reactant and product material balances, and how the concept may be used as a final ground water restoration process.

Jan 1, 1982

By Martin H. Stanczyk

The direct dissolution of a typical zinc sulfide flotation concentrate by elevated temperature and pressure leaching was investigated. The concentrate assayed about 55 percent Zn, 32 percent S, 6 percent Fe, and 1 percent Pb and contained minor quantities of copper and precious metals. The influence of various factors on the dissolution of the zinc in acidic and ammoniacal pulps when using oxygen as the oxidant was determined. The tests revealed that the sphalerite was difficult to oxidize. Complete dissolution of the mineral required vigorous and intimate nixing of the gaseous, liquid, and sold phases. The addition of pyrite or sulfuric acid to water slurries of the concentrate was required to obtain a high zinc extraction when leaching under acidic conditions. The quantity of pyrite and acid used was about 0.125 and 0.25 pound, respectively, per pound of zinc sulfide contained in the leach charge. In tests with acid, about 96 percent of the zinc was extracted from the concentrate in 1 hour at 200° C. when the oxygen partial pressure was 75 pounds per square inch gage or higher. Leaching with a continuous flow of air as the oxidant gave results that were almost as good as those obtained when oxygen was used, In tests with air fed through the autoclave at 320 liters per hour, 95 percent of the zinc was dissolved in 1 hour, Acid leach solutions assaying approximately 58 grams Zn per liter and containing Fe, Ni, Cr, and Cu impurities were produced in the better tests. The leached residue consisted essentially of red iron oxide together with substantially all of the lead and precious metals.

Jan 1, 1961

By Charles E. Whieldon, C. I. Pierce

Data on the oilfields in Mahoning , Columbiana , Carroll , Jefferson , and Harrison Counties , Ohio , were collected from scattered sources and compiled to make the information readily available to operators who may be interested in conducting secondary - recovery operations in the area . General geology , oil production , oil - productive acreage , core data , reservoir calculations by townships , and miscellaneous data and reference material are presented .

Jan 1, 1965

By Elaine Ellingham, Francis T. Manns

"Abstract -The Orostar and Scadding were two small gold mines owned and operated by Orofino Resources Limited. Conventional statistical treatment indicates an identical arithmetic mean grade of 0.22 oz/T Au for both mineable reserves. Further, the deposits are both shown to have cut weighted average reserve grade of 0.21 oz/T. Orostar mined out at 0.206 oz/T and Scadding at0.156 oz/TAu . The combined exploration and development database contained 1394 fire assays, more than enough for statistical confidence in a normal distribution. Therefore this study was initiated to determine, if possible, why the mill head grades were lower than the averages and to experiment with several methods to determine whether a reliable statistical mill head grade estimation method would emerge. Despite the identical reserve grades, distinct differences in the grade distribution histograms are present. By studying the arithmetic and log-normal grade distribution s, with some attention to South African practices, this paper reports on those differences which may account for the considerable divergence in the mill head grades. Furthermore, this study casts considerable doubt on the industry standard method of cut weighted averages.The global mill head grades of the two deposits have been derived from the arithmetic average grades by graphic means. This precise method of mill head grade prediction, if applied to complex orebodies, could permit selective grade control and result in direct cost savings by allowing the operator to detect false value stopes, benches or levels and emphasize reliable regions of not only gold mines, but also uranium or base metal deposits."

Jan 1, 1992

By Atsushi Shibayama, Toyohisa Fujita, Wan-Tai Yen, Ke-jun Liu

"In this investigation, a sponge gold sample (99.92% pure) has been leached with ammonium thiosulfate solution. The effects of CuSO4, (NH4)2S2O3, (NH4)2SO4, NH4OH and retention time on the gold leaching % (extraction %) and thiosulfate oxidation % (consumption %) have been studied. The copper ion acts as a catalyst in gold dissolution. On the other hand, it also accelerates oxidation of thiosulfate (consumption). It was found in this study that the best gold extraction condition was obtained at 43.2 ks with 0.8 - 1.0x103 mol/m3 (NH4)2S2O3, 30 mol/m3 CuSO4, 2.0 - 3.0x103 mol/m3 NH4OH, 0.4 - 0.5x103 mol/m3 (NH4)2SO4, pH 10±0.2 and 150 rpm. The thiosulfate oxidation was about 15% of the initial concentration.For gold recovery from the pregnant solution, the trioctylmethyl ammonium chloride (TOMAC) was used in this investigation as an extractant to extract gold from thiosulfate solution without pH and other adjustments. The effects of gold concentration, pH, ammonia, thiosulfate and cupric ionic concentrations, extractant and diluent concentrations and retention time on the gold recovery were investigated. It was found that 180 mol/m3 extractant diluted with n-octant at O/A ratio of 1:1 could extracted the 100% of gold in 0.6 ks from the thiosulfate solution at the optimal leaching conditions. The 100% gold stripping could be achieved with 10% thiourea solution."

Jan 1, 2003

By Pedone Ezio Michele, Mohamed Dahir Holad

"The 4c segment is a part of the ""Oman National Railway Project” linking the mining area in the surroundings of Thumrait and the port of Salalah. It is 90 km long and the last 40 km stretch crosses a mountainous area near the city of Salalah. The project includes the excavation of a 33 km double and single bore tunnel and 10 km of safety tunnels. This mountainous area is a holiday destination for Omanis, thanks to its beautiful landscapes, especially in summer time due to the monsoon rains. The tunnelling design had to take into account both these environmental constraints and the limestone rock formations crossed, which are affected by significant karst features. Given the context, the conventional tunnelling method has been preferred. INTRODUCTION The Oman Railway Project (Fig. 1) covers the construction of approximately 2,150 km of railway line for freight and passenger transport which will connect together Oman’s main towns and industrial sites and it will form part of the Arabian Peninsula railway system “GCC Project”. The non-electrified double-track railway line must guarantee a speed of 220 km/h for passenger trains and 120 km/h for freight trains and must guarantee the transit of AAR (Association of American Railroad) H and D plates using clearance envelope according to AREMA (American Railway Engineering and Maintenance-of-Way Association) requirements. The design alignment must have maximum radiuses of curvature of 3,250m and a maximum gradient of 1.0%. The project is divided into 9 constructional and functional segments. •,Segment 4c will be constructed in the southern region of Oman, close to the border with Yemen, to connect the town of Thumrait with the Port of Salalah. •,Segment 4c will run through the Dhofar region and will be mainly used by the freight traffic which currently travels by road."

Jan 1, 2016

By Filippos Patsiogiannis

Laboratory size (4.5 kg) low carbon steel melts were deoxidized using Al and FeAl (33% Al), with and without synthetic fluxes, in alumina and zirconia crucibles. The dissolved oxygen, total oxygen, soluble aluminum, insoluble aluminum, silicon and carbon contents in the melt were determined as a function of refining time and temperature. It was observed that the reaction between aluminum and oxygen in solution closely follows thermodynamic equilibrium. Silica present in the alumina crucibles was found to be a source of oxygen for the melt, while this was not the case for zirconia crucibles. Reoxidation of the melt occurred through oxygen pick-up from the atmosphere. The extent of this reoxidation was found to be a function of oxygen content of the bath and the slag cover on the surface of the melt. The effectiveness of calcium-aluminate based fluxes in protecting the melt from the reoxidation and in increasing the rate of removal of inclusions was evaluated.

Jan 1, 1992

By J. A. Organiscak

Water spray applications are one of the principal means of controlling airborne respirable dust in coal mines. Since many coals are hydrophobic and not easily wetted by water, wetting agents can be added to the spray water in an effort to improve coal wetting and assist with dust capture. In order to study wetting agent effects on coal dust capture, laboratory experiments were conducted with three wetting agents used by the coal industry on -325 mesh sized Pocahontas No. 3 coal dust. Significant differences in coal dust sink times were observed among the three wetting agents at water mixture concentrations of 0.05%, 0.1% and 0.2%. The best wetting agent as identified by the coal dust sink test was only tested at the lowest 0.05% water mixture concentration and was found to have a negligible effect on spray airborne dust capture. Water spray airborne dust capture results for all three wetting agents tested at a 0.2% water mixture concentration showed that all three wetting agents exhibit similar but small improvements in dust capture efficiency as compared with water. These results indicate that the coal dust sink test may not be a good predictor for the capture of airborne dust. Additional research is needed to examine if the coal dust sink test is a better predictor of wetting agent dust suppression effects during cutting, loading, conveying and dumping of coal products by comparison to airborne dust capture from sprays.

Jan 1, 2013

By AIME

Burton J. Westman-Besides decreasing the diamond size, there appear to be two other approaches open to overcome excessive diamond loss and, more particularly, the rapid diamond polish that took place in this quartz-feldspar rock. First, however, a short discussion of the diamond characteristics should be made in order to discuss the situation more clearly. The West African diamonds which we can assume were used. for this drilling have two disadvantages when drilling hard, exceptionally fine-grained rocks. These are rapid polishing and, if .the bit isn&apos;t "drilled in" carefully, a tendency to damage, resulting in excessive diamond loss. The normal wear resistance of any diamond is inversely proportional to the compressive strength of the diamond, therefore only the highest grade, of diamonds free from insipient fractures should be employed. Using upwards of 90 diamonds per carat instead of the20 to 30 per carat not only decreases the total projected area of the cutting points but increases the stress per point which, in turn, causes greater depth of penetration into the rock. Considering this depth of penetration, therefore, suggests an approach other than increasing the, number of diamonds per carat and that is to decrease the actual number of diamond points (also the carat weight per bit) so that the penetrating force on an individual diamond is increased. This penetration increases the chipping or rock shearing action.

Jan 1, 1950

By A. J. Dickson, A. M. Starfield

This paper reviews the progress made to date in the development of computer models of heat and moisture transfer from rock surfaces to the ventilating air in deep-level mines. The application of these programs to ventilation planning and design is discussed.

Jan 1, 2014

By L. P. Larson

In this Bureau of Mines evaluation of the domestic supply position of tungsten, certain tungsten resources in the United States are estimated as to quantity and grade and then are systematically costed in detail (excluding exploration costs). A supply curve is developed which depicts the quantity of tungsten (WO3) up to about 15.5 million short ton units that is producible at calculated price levels ranging from about $13 to $125 per short ton unit. About 10.4 million short ton units are available at a calculated price that is less than the present market price ($40). Total known resources amount to about 40.2 million short ton units. A very large portion of that quantity was not costed due to inadequate information on either resources or processing methods. Further exploration and research would have a significant effect on the availability of tungsten in the United States.

Jan 1, 1971

By Cheryl Devine, Radhakrishnan Mahadevan, Vladimiros G. Papangelakis, Srinath Garg

The microbial-mediated recovery of valuable metals locked in mining wastes presents an economical alternative to conventional hydrometallurgical processes. The present study investigated the bioleaching response of a low-grade nickeliferous pyrrhotite tailings (0.6 wt% Ni) and an upgraded pyrrhotite tailings (1 wt% Ni) produced by Vale Base Metals in the Sudbury Basin of Ontario, with the ultimate aim of maximizing Ni recovery. The initial part of the study focused on the bacterial adaptive evolution protocol, by repeatedly sub-culturing an indigenous culture from an acid mine drainage site on 2% (w/v) pyrrhotite tailings. The results showed that the extent of Ni dissolution is positively correlated with microbial activity. Microbial profiling revealed A. ferroxidans to be the dominant member of the microbial consortium. The enriched culture was used for optimizing the growth medium by varying the concentration of essential growth nutrients. Finally, an aerated biotic and abiotic leach of a 10% (w/v) upgraded pyrrhotite tailings with and without pH control, showed a higher recovery of Ni in the pH controlled experiments. These results demonstrate that a high concentration of the oxidant Fe3+ in solution promotes the dissolution of Ni. Furthermore, the sulphide conversion into So was found to be higher in the pH controlled experiments (32%), relative to the experiment without pH control (10%).

Jan 1, 2015

By F. Albayrak

This report is a study of the impact of Federal laws and regulations on the domestic supply of metallic and nonmetallic minerals. The study was confined to pertinent environmental legislation and the recently enacted Federal Mine Safety and Health Act of 1977. Emphasized were the legal requirements placed on individual selected mineral industries, and the economic impact of these requirements. A certain amount of attention was also directed to the particular environmental and health and safety problems generated by selected mineral industries. The study also pinpointed a list of major problem areas having significant impact on the domestic mineral supply.

Jan 1, 1978

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

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

Jan 1, 1970