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By P. Samanta, Mohammed N. Azad, Gustad F. Taraporewalla, A. K. Mukherjee, Abhay S. Patra, D. Sachinraj

Beneficiation of coal is a water intensive process, and the water is recovered in downstream operations in the high rate thickener (HRT) and vacuum belt filtration (VBF). Clean coal particles entering the HRT have an inherent tendency to enter the overflow because they are extremely fine and hydrophobic. Hence, flocculants (polymers) are used to floc the ultrafine particles so that they settle and enter the underflow. Ultrafine coal particles (−37 μ), which are highly hydrophobic, if present in the stream, will not be efficiently captured by using flocculants alone. This is observed in the normal plant operation at one of the beneficiation plants in the Jharia region, Jharkhand, India. Approximately 6–7% of the feed to the HRT enters the over flow (supernatant water). Hence, this amount of clean coal particles is not recovered and account for production losses. A comprehensive settling and dewatering test work was conducted with clean coal slurry using several commercially available reagents. Studies were also done on different combinations of reagents, including coagulants and surfactants along with flocculants, to improve the settling behavior of the coal particles. The reagents were assessed based on their performance with respect to settling rates, overflow water clarity, and compaction of the underflow solids. Emphasis was given to the ability of the reagents in compacting thickener underflow to higher densities so that maximum water could be recovered from the thickener. Pretreatment of highly hydrophobic coal slurry with a combination of coagulant and surfactant followed by flocculation showed very good settling characteristics with clear overflow.

Sep 30, 2021

By Charles B. Carpenter

[The Bureau of Mines selected Anahuac for a petroleum-engineering study because it is one of the notable fields of the Gulf Coast region. It is outstanding because the producing for is very thick; every modern technique of drilling' and development has been applied; complete records of all operations,, including detailed subsurface information have been kept; the field has been developed systematically; and every effort has been made to utilize the reservoir energy efficiently Data and information pertaining to the development anal operation were collected, compiled, and studied by the writers as if the field were under single ownership. The chief aim-of the stud,, was to increase the accuracy of the existing methods of estimating reserves by applying all the data collected during the modern development of an oil-field, These scientific aids include coring; electric logging; micropaleontology determinations of porosity, permeability of oil-bearing sands, and their connate water content; subsurface sampling of the reservoir oil; and depth-pressure measurements. Because the reservoir structure in the Anahuac field is extremely complex, special attention was given to methods of calculating the reservoir volume.]

Jan 1, 1941

By Ludovic Charpentier

Production of metallic wires directly from liquid jets would avoid drawbacks of extrusion (space needed, damaging, cost?) and enable recycling. But liquid jets tend to break, due to capillary instabilities, unless a solid layer (coating or start of solidification) surrounds it. We recently developed a process to produce tin wires, cooled by water flow parallel to the jet. Superficial oxidization of tin produces a glass coating around the jet. Studies showed the length of wires increased when increasing speed of tin jets, and that water average speed should be the closest possible to the jet one to have smooth fibers. Producing 1 mm diameter wires is possible. The length of wires is limited by the experimental setup, which does not provide possibilities to coil the wire. Most of other metals do not generate glass-like oxides. The lack of coatings makes it necessary to reduce the capillary instabilities to obtain fibers.

Jan 1, 2006

By W. J. Kingwell

My comments and questions are addressed to Mr. Troughton. It seems to me that the tests were very well tailored to determine long term effects on performance of bearing piles as groundwater pressures rise in the London Basin. This rise is being simulated by means of a groundwater recharge system but it would be informative to have further details of the controls of conditions simulated. Ideally the porewater pressure in Standpipes 1, 2 and 3 should be the same throughout the test. Under test conditions are there not practical dif­ficulties? Recharge Well C2 is a lesser dis­tance from the pile than the other wells. Was the rate of recharge to C2 regulated to a lesser rate than the other three? In my experience the rate of acceptance usually varies from well to well. Under a common feed pressure were mea­sures taken to compensate for this? Since the problem does not only affect London, but also Liverpool, Nottingham, Birmingham and to a lesser extent, Manchester, I question whether an ideal procedure is being used. It is well known that rates of acceptance decrease with time and often recharge wells need to be flushed out at regular intervals. Other pro­cedures may need to be adopted to accurately simulate the effect of groundwater rise, if tests of longer duration are to be considered.

Jan 1, 1991

By E. Özberk

Uranium minerals are often associated with iron minerals, and during the hydrometallurgical processing of the uranium ores, iron plays several significant roles. The presence of Fe(III) in solution promotes the oxidative acid leaching for the recovery of uranium. The control of the distribution of impurities in milling and refining is also affected by dissolved iron. When rejected from the process streams, iron usually collects other impurities and contributes to the stabilization of the wastes for final disposal. These roles of iron, as they relate to current uranium processing operations, are discussed in detail, and some broad and historical perspectives are also presented.

Jan 1, 2006

Effects of High Pressure Grinding Rolls on Platinum-Bearing Ores and the Flotation Response as Compared to the Conventional Ball Mill Three major PGM ore types from the Bushveld Complex of South Africa: Merensky, UG2 and Platreef were comminuted with the use of the high pressure grinding rolls (HPGR). The influence of the feed characteristics and the various operational and design features of the HPGR on energy consumption, throughput, mineral liberation and PGM flotation recovery were investigated. The test work variables included two feed top sizes of 12 mm and 6 mm, specific grinding forces ranging between 3 - 7.5N/ mm2 and zero gaps of 1.5 mm and 3 mm. The results show that the influence of the HPGR operational and design features on energy consumption, throughput, mineral liberation and PGM recovery are ore dependent. The size reduction-specific energy relationships show that the most energy efficient utilisation of the HPGR for Platreef ore was at the lower specific grinding force of 3N/mm2 and the zero gap at 3 mm. For Merensky and UG2 ore on the other hand, the most energy efficient operation was at the higher specific grinding force of 7.5N/mm2 and the zero gap of 1.5 mm. At a specific energy input of 3 kWh/t, reduction ratios (F50/P50) of 6.5, 3.8 and 10 were obtained for Merensky, UG2 and Platreef, respectively for feed top sizes of 12mm. Further application of the HPGR as a pregrinding stage to a ball mill showed a 25 - 30 per cent increase in throughput for Merensky and UG2 ore. Batch flotation tests performed on selected samples appear to indicate that ore comminuted with the ball mill had superior grades compared with that ground with the HPGR. However, Merensky and UG2 ore comminuted at different HPGR operating conditions showed distinctions in PGM recovery. Platreef on the other hand did not appear to show any differences. Therefore, this study highlights the significance of ore type and operating variables in HPGR applications with regards to energy efficiency, throughput and PGM recovery.

Sep 13, 2010

By Earl Redman

The Juneau Gold Belt portion of the Juneau Mining District has historically had the greatest mining and exploration activity within the district. Between 1880 and 1983, the mines within the Juneau Gold Belt produced 6.7 MM oz gold, 3.1 MM oz silver, and 45 MM lbs lead, which had a total value of about $157,000,000 at the time of production. This report summarizes Bureau of Mines work completed in 1986, the second year of the Juneau Mining District study. Fifty mines, prospects, and occurrences were examined and 638 samples were collected for analysis during 1986. Metallurgical samples were collected from seven deposits and preliminary tests of cyanide amenability have been completed for five of these. The simultaneous discovery by private industry and the Bureau of gold-bearing quartz veins cutting diorite gneiss recently exposed by the retreat of the Herbert Glacier is the most notable result of work during 1986. This location yielded gold values up to 7 oz/st.

Jan 1, 2011

By Bruce W. Woolpert

During the SME Board of Directors’ midyear meeting in Monterey, CA Aug. 25, I discussed trends in the construction aggregates industry. Many construction-material suppliers may not have yet fully internalized the changes that are taking place. But the changes are significant. And they have shifted the focus in the aggregates industry from “assets” to “people and innovation.” Construction-material suppliers serve many customers. A typical quarrying operation at Graniterock would have more than 1,000 customers, mostly civil engineering contractors. Along with the push toward people and innovation, there is increased emphasis on vertical integration from aggregates to ready-mix concrete and hot mix asphalt, to final construction. If a company is not vertically integrated, it will at least have strong partnerships with other firms, to deliver a high-quality finished project on time.

Jan 1, 2002

By Harumasa Kurokawa

Since the initial start-up, the Toyo Smelter & Refinery has been operating in harmony with the ambient environment, and improvements have been implemented with technologies specifically developed for further protecting the environment. Toyo Smelter & Refinery is now planning to increase the copper production capacity from 280,000 tpy to 450,000 tpy, over a period of several years. In 2003, the first step of this smelter expansion and modernization plan was implemented. The production capacity of the P-S converter was increased dramatically, as it became possible to operate under a ?2 hot-2 blowing? schedule. In 2005, an additional converter will be installed, in order to allow operation under a ?3 hot-2 blowing? schedule. This report will describe the technical improvements on the P-S converters, as well as describe the Toyo expansion program and discuss the technologies applied to the fugitive gas collecting system.

Jan 1, 2005

By R. J. C. MacDonald

"The first recorded discovery of placer gold in Canada was on the Chaudiere River in Quebec's eastern townships in 1832 and the first major production came from placer deposits in British Columbia in 1858 (Verity 1974). Placer deposits were the major source of gold until the late 1890's, although lode deposits were found in Nova Scotia in 1862. In 1896 the Klondike Gold Rush commenced with the discovery of gold by Henderson and Carmack in the Yukon. The peak was reached in 1900 when over one million ounces of gold valued at approximately $22.3 million were recovered. With the exhaustion of the easily accessible deposits, more capital intensive operations were necessary such as those initiated in 1906 by the Yukon Gold Corporation. This giant dredging operation continued to produce until 1966. Today only a few small operations remain.The development of Canadian lode gold mining began in earnest around 1900 when the railroads were opening up the interior and western part of the country. At this time many discoveries occurred, particularly where mineral outcroppings were near surface. Tremendous impetus for exploration and the reopening of former producers followed the elimination of the gold standard by Great Britain around 1931, and more importantly the United States in 1933, with subsequent stabilization of the price of gold at $35 per ounce in 1934. Prior to this the price of gold was basically unchanged since 1717, approximately, $20 per ounce (Verity, 1974; Green, 1973).The depression of the 1930s adversely affected most industries, however for the gold producers it was a very profitable time. Prices of materials and equipment declined and labour was cheap and plentiful. Interest in gold mining was further stimulated in 1936 when a three year tax exemption was declared for all new metal mines. In 1938 a decline in the value of the Canadian dollar relative to the U.S. dollar benefitted the industry. The second world war provided yet again further incentive for gold production and in 1941 Canadian gold production reached a high of approximately 5.4 million ounces. This figure was not surpassed until 1991 when approximately 5.6 million ounces were produced (Natural Resources Canada, 1996 )."

Jan 1, 1998

By P. R. Day, W. K. Webster

"The introduction of large boreholes underground initially involved taking the techniques of open-pit bench blasting to the production stope, but with deeper boreholes and narrower stopes more controlled techniques must be developed in order to maintain good stope walls and prevent dilution of ore or structural damage to pillars due to blasting overbreak. The points discussed are drilling accuracy and drill pattern, the relationship between open-pit wall control and underground mining, the varied explosives products and initiation devices available, and some of the many ways that variations in loading, such as deck charging, etc., can produce desirable results.IntroductionThe use of large-diameter blastholes for underground mining began ten years ago and today they are widely employed in a variety of orebodies and stope configurations. These big blastholes, which range in size from 4.5 to 8 inches in diameter, were originally employed in the same manner ' as open-pit bench blasts; that is, the stope was silled out to full width and all holes were drilled vertical and parallel. This was suitable for competent, massive orebodies, however the popularity of the big drills saw their usage in more narrow stopes, often with poor ground conditions. The dipping orebodies and small drill sublevels resulted in inclined drilling.Today, there is full-ring drilling of 4.5-inch holes. Some 6.5-inch holes are drilled up to 350 feet deep. A 350-foot borehole may contain 6000 to 7000 pounds of explosive. The detonation of this size of charge weight within the confines of an underground stope can have considerable effect on the stability of stope walls and adjacent pillars. Obviously, precautions must be taken to minimize the damage which would result from the large charge weights possible with these big boreholes."

Jan 1, 1982

By Marc Ruest, Lewis Martin

A new instrumented cable bolt has been developed by the National Institute for Occupational Safety and Health at the Spokane Research Laboratory in Spokane, WA. Although various instruments are available to measure load distribution and magnitude along a grouted cable, this instrument is innovative in that it uses strain gauges internal to the cable as load-measuring sensors. The instrument has been successfully tested in the field at FMC’s Granger Mine, Meikle Mine, and Getchell Mine. A “split-pipe” laboratory pull test was performed on each of three cable bolts instrumented with the new device. Each test consisted of grouting a 1.83-m-long cable in two 0.91-m-long sections of schedule 80 pipe. A numerical analysis was then performed in which laboratory boundary conditions were simulated and model properties derived from textbook guidelines. The loads calculated by the model were then compared to the measured loads.

By Marc Ruest

A new instrumented cable bolt has been developed by the National Institute for Occupational Safety and Health at the Spokane Research Laboratory in Spokane, WA. Although various instruments are available to measure load distribution and magnitude along a grouted cable, this instrument is innovative in that it uses strain gauges internal to the cable as load-measuring sensors. The instrument has been successfully tested in the field at FMC?s Granger Mine, Meikle Mine, and Getchell Mine. A ?split-pipe? laboratory pull test was performed on each of three cable bolts instrumented with the new device. Each test consisted of grouting a 1.83-m-long cable in two 0.91-m-long sections of schedule 80 pipe. A numerical analysis was then performed in which laboratory boundary conditions were simulated and model properties derived from textbook guidelines. The loads calculated by the model were then compared to the measured loads.

May 1, 2002

By D. W. Cooper

The AMAX of Canada Limited Kitsault mine is located approximately 150 kilometers, by air, north of Prince Rupert, British Columbia at the head end of A1 ice Arm, just east of the southern tip of the Alaskan Panhandle. It is presently only accessible by sea or air, although a road is being constructed by the company which will provide access to Terrace, a commercial centre with a population of about 15,000. The topography is typically coastal mountainous with peaks rising to 2,100 meters around the head end of the inlet. The concentrator is at an elevation of 515 meters with the mine at 630 meters. This open pit molybdenum mine was previously operated between 1968 and 1972 by British Columbia Molybdenum Limited, a subsidiary of Kennecott Copper Corporation. AMAX of Canada Limited has spent $194 million to refurbish and expand this operation.

Jan 1, 1982

By Sanchita Chakravarty, Sumantra Bhattacharya, Divya Jyoti, A. K. Mukherjee, Soni Jaiswal

"Release analysis is independent of collector and frother dosage and type, but it is primarily influenced by the degree of liberation or “state of release of the sample”. The shape of release curve is an indication of the degree of liberation. This paper briefs about the effect of reagent combination, particle size and surface characteristics on the release analysis of difficult-to-clean LVC coal.Release analysis of three LVC coal fines obtained from two different coalfields of India was carried out at three different size levels such as -0.5mm, (-0.5+0.1) mm, and -0.1mm. The collectors used were n-dodecane and commercial diesel oil. Incomplete liberation of coal fines even at a size of -100µm, corroborated by photomicrographs of ROM and clean coal macerals, in a great measure reduced the flotation-based cleaning potential of the fines. FESEM images of fines reveals that the adherence of ultrafine onto the surface of relatively coarser particles reduced the clean coal recovery. The results obtained also appear to be coal, reagent combination and, particle size and particle surface specific. Only one coal indicated the liberation as is usually expected for -0.1mm particles with a reasonable yield of 65% at 18% ash. INTRODUCTION Froth flotation has a long history of being used to treat coal fines. Coal flotation is considered to be difficult, if the percentage of Near Gravity Material (NGM), i.e. essentially locked particles, in flotation feed is >10% [Aplan, 1993], which is usually the case with all the coking coal fines in India. The fines are rich in vitrinite, so valuable for coking coal. Unfortunately, there appears to be no standard procedures to determine the separation efficiency of froth floatation. Release analysis proposed by C.C. Dell in 1953 [Dell, 1953], aimed to determine the ultimate floatability of coal. Several other techniques had been proposed but release analysis technique has been considered to be a vast improvement over the batch flotation process [Forrest et al. 1994]."

Jan 1, 2018

By J. P. Germiquet

"Rock properties have a material impact on mining processes, including drilling performance. An investigation using point loaded index (PLI) data converted to uniaxial compressive strength (UCS) has revealed that a direct relationship between grain size and UCS exists at Mogalakwena Mine. This correlation is best seen in unaltered rock, with lower correlations for altered rock types. Measurements from the new RockMa system installed on drill rigs can be used to obtain rock strength data to validate the current rock strength domains and create additional data for the next benches below. An investigation of penetration rates in different lithologies shows that rock composition plays an important role in determining drill performance. Additionally, there is an inverse relationship between rock strength and drilling penetration rate – a measure of how efficiently a hole is drilled.The domaining of grain-size-adjusted UCS at Mogalakwena Mine will allow more accurate scheduling of drill rigs through increased knowledge of rock strength in various areas. Successful rock strength domaining has the potential to be incorporated into blast indexing and predicting crushing/milling performance.IntroductionThe optimization of mining and processing through geometallurgical characterization of ore are key drivers of value realization (Deutch, 2013). Rock strength is one such property and is affected by, among other variables, composition, texture, and grain size (Ozturk, Nasuf, and Kahraman, 2014). Mogalakwena Mine is exploiting the intrusive Platreef PGE (platinum group element)-bearing orebody which forms part of the northern limb of the Bushveld Complex. This complex orebody exhibits areas of metasomatic alteration, metamorphism, and sporadic mineralization of the footwall and hangingwall (Nex et al., 2006). Understanding this variability is paramount due to the implications for rock strength and hardness, which in turn affect crushing, milling, and liberation efficiency. These variables must be known prior to blasting in order to optimize mine and plant processes using in-situ variables. This necessitates predictive modelling (Deutch, 2013). Geological and geotechnical data was sourced from the Overysel (OY) exploration database for the study. Point load testing was done for each borehole and the results converted to uniaxial compressive strength (UCS) (Akram and Bakar, 2007). The relationship of lithology, texture, and grain size with UCS revealed an inverse relationship between grain size and UCS in unaltered rock. The relationship was not present in altered rock types. A comparison of mean strength and hardness results indicated that Bond work index and UCS may be related. Drilling performance is affected by UCS (Bourgoyne et al., 1986), and this was proven using recent measurements obtained during drilling. Lastly, grain-sizeadjusted UCS values were applied to a 3D model for the OY property."

Jan 1, 2016

By D. P. Roberts

The stoping of platinum orebodies in the Bushveld has in the past been accomplished by using in-stope pillars to ensure stability of the workings. In the future, the use of continuous mining machines to mine the platinum orebodies is probable. It is not envisaged that such machines will cut in-stope pillars. This paper describes the alternative support systems that will replace the pillars and the stope geometries that will be required for this type of mining. The paper describes how the support resistance provided by in-stope pillars in current mining was determined and then evaluates support systems that can substitute for these pillars. Conceptual layouts based on existing breast mining layouts are presented. The layouts consist of panels of up to 100 m face length between rigid strike stabilizing pillars. A number of design charts are then proposed that allow for the design of appropriate support systems.

Jan 1, 2005

By J. E. Nesset, S. R. Rao, J. A. Finch

"For base metal sulphides, iron rejection starts in mineral processing. This review focuses on changes in plant practice specifically to improve iron sulphide rejection by control of contaminant ion effects and discusses selected general innovations in mineral processing that can be expected to play a role. One group of changes to control contaminant ions is in size reduction (the use of stage grinding and inert stirred milling) and another is in system chemistry (order of reagent addition and exploitation of the flexibility of sulphoxy reagents). Plant examples illustrate the successes, indicating that there are several options available. The general innovations start by considering the new tools for measuring gas dispersion properties and quantifying froth characteristics by imaging. Examples of their application to improve concentrate quality illustrate the potential. Other innovations stress adapting geostatistics to model variation in milling and flotation response to provide feed forward control and rigorous application of statistical experimental methodology in plant test work. An example from one concentrator shows improvements in concentrate quality from application of basic principles can be impressive.INTRODUCTIONThe more iron control (rejection) that can be accomplished in mineral processing the lower the subsequent metal extraction costs and environmental implications of iron disposal, particularly in hydrometallurgical processes. Iron rejection has been a contributing target to periodic attempts to apply mineral processing to nickel laterites and bauxites but the prime application is control of pyrite and pyrrhotite (iron sulphides) in the treatment of sulphide ores by flotation. In this paper some new concepts and innovations introduced in sulphide flotation plants over the past ten years or so (i.e., since a previous review [1]) will be outlined with examples of how they have contributed to improved “iron control”.To increase rejection of iron minerals, first the recovery mechanism should be understood. There are four principal ones, two physical in origin: 1, via locked particles (i.e., flotation of composite particles due to insufficient size reduction to liberate the minerals) and 2, through entrainment in the water reporting to the float product (an unselective process); and two originating from a response to the system chemistry: 1, true flotation (i.e., iron sulphides becoming hydrophobic) and 2, as a result of iron sulphides forming aggregates with hydrophobic particles (e.g., ”slime” coatings). There has been considerable effort to diagnose which of these dominates iron sulphide recovery; in many cases it is due to “chemistry”, in particular true flotation. The flotation effect often appears related to contamination by metal ions [1]. This can reduce selectivity in two ways: 1, metal ion species may activate iron sulphides, or 2, cause general depression which demands more vigorous flotation conditions (e.g., additional collector) with consequent loss of selectivity. This is where the review will start, by considering ways to control contaminant ions."

Jan 1, 2007

By Lowell Stroud

This report is the third in a series presenting equilibrium vapor-liquid data for helium-bearing natural gases. The first two reports contained phase data for the gases processed for helium at the Bureau of Mines Amarillo and Exell, Tex., helium plants. The present report offers similar information for a lower-helium-content (0.75 mole-percent) natural gas to be processed in the Department of the Interior's long-range helium-conservation program. A windowed-cell apparatus was used to obtain 218 samples of equilibrium vapor and liquid phases at 73 experimental conditions ranging in temperature from -100° F to -275° F and in pressure from 100 to 500 psi. From the phase data, the condensation characteristics, helium solubility, and equilibrium-vaporization-coefficient data for helium, nitrogen, and methane were evaluated. The effect of using a. preliminary hydrocarbon trap upon the subsequent vapor-liquid compositions is reported. A brief comment regarding the composition effect of passing the gas through a gasoline-removal unit is also included.

Jan 1, 1963

By G. Sachs, A. W. Dana, C. C. Chow

A great number of the investigations on the plastic flow of metals have been concerned with the establishment of a "universal" stress-strain relation. In such a relation some stress function when plotted against a strain function should yield identical curves for the various stress states. In the first investigation of this type, Ludwik and Scheu1 plotted the maximum shearing stress as a function of the maximum principal strain. Later Ros and Eichinger2 introduced two universal stress-strain relations, the one relating the maximum shearing stress to the maximum shearing strain, and the other relating a stress invariant, suggested by von Mises and Haigh, to the corresponding strain invariant. (In more recent investigations the stress and strain invariants are frequently supplemented with some factor to render their meaning more lucid.) A further suggestion which has not attracted appreciable attention is that by Baranski³ who used stress and strain deviators. The most common means of experimentation to determine the relation between stress and strain consists in subjecting thin walled tubes to combined internal pressure and axial tension.4a,4b,4c This method allows the study of plastic flow under stresses which are variable in two directions. However, the plastic flow which can be obtained in this manner is comparatively small, being limited by either tension failure or instability. For copper,'. only the relation between maximum shearing stress and maximum shearing strain yielded good agreement. On the other hand, tests on a stee14b and on an aluminum alloy4c. resulted in systematic deviations if any of the discussed universal stress-strain relations were used. It would seem, therefore, that the agreement mentioned above for copper is only incidental and explained by its high rate of strain hardening compared to that of other metals. Much larger strains than experienced in the tube tests can be obtained by subjecting a thin membrane of a ductile metal, which is restrained at its periphery, to a uniform hydraulic pressure. The thin sheet forms a deep bulge before it fails. The stresses and strains in such a bulge increase with increasing distance from the edge of the clamping "die," the maximum stresses and strains occurring at the pole (crown) of the bulge. While the stress and strain states are determined by the contour of the bulge, the absolute magnitude of the stresses and strains depends upon the hydraulic pressure. The bulge contour is in turn correlated with the geometry of the die opening. The deformation and fracture characteristics of circular bulges, that is, bulges formed with circular clamping dies, have been the subject of numerous experimental and analytical investi-gations.5,6,7 It has been shown that plastically deformed circular bulges develop large and comparatively uniform strains before failure by instability"6b,6c,6d and closely assume a spherical shape.6d Also the distribution of strains across the contour of the bulge is dependent on the metal being investigated and is correlated with, but cannot be predicted from, the metal's stress-strain characteristics. On the other hand, oblong or elliptical bulges, that is, bulges formed with elliptical clamping dies, are not as susceptible to analytical analysis and have not been investigated to the extent that circular bulges have. The few available data6c,7c indicate that stress states are obtained at the poles of the bulges, varying between plane strain and balanced biaxial tension, depending upon the geometry of the die opening. In this paper, the strain state and curvatures exhibited by three bulge shapes, a circular and two elliptical bulges, Fig 1, are analyzed experimentally using methods described in previous publications.6a,6c An attempt is made to derive the stress-strain relations for these bulges, which represent strain states in which the ratio of the two positive principal strains varied between 1.0 and 0.35. In addition, tension tests yielded data for a value of —0.5 for this strain ratio. Such an analysis should indicate the applicability of the various laws correlating stress with strain to the stress and strain states occurring in bulged shapes. Definitions and Nomenclature The definitions of the major stress and strain quantities used in this paper are as follows: s1, s2, s3 = principal normal stresses Sl > s2 > S3 t = shear stress e = conventional (unit) strain e = In (1 + e) El, E2, E3 = principal natural strains 7 = shear strain The maximum shear stress: , _ S1 — S3 lmax = 2 Frequently, the flow stress, s1 — s3 = 2lmax rather than the maximum shear stress is used.

Jan 1, 1950