Search Documents

By P. T. L. Koh

The effect of particle shape on the flotation process has been investigated in laboratory experiments with monosized spherical ballotini and roughly ground ballotini. The particles were treated by partial methylation with trimethylchlorosilane to achieve varying degrees of hydrophobicity. In flotation, the process of film thinning and liquid drainage is critical in the formation of a stable bubble-particle attachment and this is affected by the particle shape and surface hydrophobicity. The rate of attachment affects the overall flotation rate. Flotation tests with different particle sizes at various degrees of partial methylation have been performed in a modified Denver cell. Predictions from a computational fluid dynamic model of the cell which incorporates fundamental aspects of bubble-particle attachment are compared against flotation test results. Contact angles of the particles have also been measured using the capillary rise technique to indicate surface hydrophobicity.

Jan 1, 2014

By Donald F. Reed

In the latter half of 1948 the Bureau of Mines investigated the Magnet Cove Rutile Co.'s prerty in northern Hot Spring County, Ark. This work was supplemental to the work done by the Bureau on the same property in 1945.2/ It was undertaken for the purpose of investigating the extent of the ore body toward the south and west and at depth and to obtain representative samples of the ore for metallurgical tests. For the latter purpose, the samples were so taken as to minimize alteration of the physical characteristics of the ore, these characteristics being determining factors in working out processes of bencficiation. During the investigation, 27 holes were drilled, 10 with a diamond-coro drill end 17 with churn-drill rigs using a Baker standard cable-tool core barrel. Drilling developed an extension of the ore deposit westward from the previously mined area but did not disclose the full depth of mineralization. Metallurgical tests to determine methods of beneficiating the ore and utilizing the resultant products are now in progress.

Dec 1, 1949

By H. R. Butler

"The Ontario Division of Inca Metals Company, a Unit of Inca Limited, operates eleven mines, four mills, three refineries, one smelter and one iron ore recovery plant. All but one mine, mill and refinery are located within a fifty kilometer radius of Sudbury, Ontario. A mine-mill complex is located some 100 kilometers west of Thunder Bay on the shore of Lake Shebandowan and a nickel refinery at Port Colborne.During the past 10 years the use of recycled water in our milling operations has increased to more than 95% at each mill. This high degree of water reuse has reduced the (a) need for fresh water and (b) the contaminant level of the downstream aquatic environment. The aggregating of effluents in a common receptor provides a process water having a consistent quality thereby minimizing upsets in mill metallurgy while concurrently improving the operating economies and the downstream aquatic environment."

Jan 1, 1980

By Rafael Pereira Ferreira

O objetivo deste trabalho consiste em caracterizar o comportamento termomecânico do aço inoxidável austenítico AISI 316L a partir dos parâmetros de encruamento (h), recuperação dinâmica (r) e recristalização dinâmica (n, t0,5). Na parte inicial das curvas de escoamento plástico a relação sc/sp = 0,92 é relativamente alta, sendo um indicativo que o amaciamento promovido pela DRV é intenso, corroborado a moderada EFE, ?sfe = 66,86 mJ/m2. Na segunda parte das curvas vê-se que há um atraso na cinética de amaciamento dinâmico com maior valor para t0,5 e menores valores do expoente de Avrami n, devido à competição entre os mecanismos DRV-DRX

Aug 17, 2017

By E. O. Wagner, V. F. Parry

This paper summarizes investigations during 1949 on three pilot plants for drying low-rank fine cool by entrainment in hot gases. Detailed operating results on processing seven coals having moisture ranging from 24 to 62 pct, formulas and data for calculating performance of large units, and general conclusions on the problem of drying fine coal are presented.

Jan 1, 1950

By T. E. Gray

This report describes the preparation characteristics of the signifi¬cant coalbeds in Preston County, W. Va. It is one in a series of reports planned to determine coals suitable for the production of metallurgical coke, either as mined or after beneficiation. Over 2 million tons of coal was produced in Preston County, W. Va. in 190, none of which was cleaned mechanically. Estimates as of January 1, 1959, indicate that more than 3 billion tons of coal remained in the county in beds 12 inches or more thick. The Bakerstown, Mahoning, Upper Freeport, and Upper Kittanning beds were selected by the Bureau of Mines for study based on current production and estimated minable reserves. Sample locations were selected after study of the literature, conferences with mining engineers and mining company offi¬cials in the field, and examination of available sites. Four samples were collected from the Bakerstown and Upper Freeport beds and one each from the Mahoning and Upper Kittanning beds.

Jan 1, 1961

By Sabry A. Sabour

Metal price is among the key variables in the open pit optimization and the economic evaluation process. The common approach to handle metal prices in open pit mine planning is to optimize the ultimate pit and the mining schedules using a fixed, flat metal price. In this respect, metal price is assumed to be known with certainty throughout the entire mine life, which in some cases can reach 80 years. Given the volatile nature of metal markets and the metal price cycles, the conventional pit optimization approach may generate sub-optimized mining plans, which results in either extra costs to mining projects or lost revenues, or both. Long-term operational decisions such as future pit expansions, beyond the currently optimized limits, cannot be handled using the pit optimization approach based on flat metal prices. There is a growing interest in the mining industry to model and manage such market uncertainty in the pit optimization as well as the project evaluations in order to maximize the value of mining operations. In this paper, the author will outline a practical approach to optimize the ultimate pit taking into account the volatility and variability of metal markets. The proposed approach uses a combination of the pit optimizer of the commercial MineSight package and a simulation-based economic modeling real options valuation approach employing the least-squares Monte Carlo algorithm. MineSight pit optimizer employs both the floating cone for initial optimization exercise and the standard Lerchs-Grossmann algorithm. In this paper, Lerchs-Grossmann option will be used to generate the pit shells. Real options valuation approach used in this study is based on generating multiple metal price scenarios. Metal price uncertainty is modeled using stochastic metal price models such as the geometric Brownian motion and the mean-reverting process. The mining operational scenarios corresponding to the simulated metal prices are then optimized using the least-square Monte Carlo approach. The objective is to maximize the discounted cash flow value of the project while incorporating the operating flexibility to revise the operating status of the open pit with time as new information becomes available. The focus of this work is on the practicality of the proposed uncertainty-based pit optimization approach and the difference it can make to the technical operational mining decisions. A case study of a hypothetical open pit poly-metallic mine is provided. The deposit contains copper, gold and silver grades. The run of mine ore is sent to the process plant that produces copper concentrate with copper as the main metal and gold and silver as the by-products. Four uncertain variables are considered here include copper, gold, silver prices and foreign exchange rate. Both copper price and exchange rate are modeled using the mean-reverting process while gold and silver prices are modeled using the geometric Brownian motion. The case study is performed using both the conventional flat price pit optimization approach and the proposed uncertainty-based one to compare results.

Aug 1, 2013

By Alexander Ciccone, John H. Gill

Jet grouting is a highly versatile ground modification technique that can offer significant commercial and technical advantages over traditional concrete pit underpinning applications. Despite these advantages, jet grouting remains an underutilized technique in the construction industry due to its perceived complexity, cost, and risk. When performed thoughtfully, underpinning by jet grouting offers significant safety and schedule advantages over traditional underpinning approaches. The New England construction market has seen a recent acceptance in the use of jet grout underpinning on congested project sites across a variety of subsurface conditions. The reduction of the cement batch plant footprint due to equipment advances has allowed the use of this technique in urban sites where its use would be previously infeasible. Furthermore, jet grout underpinning has been utilized for support of historic and sensitive structures with generally lower tolerance to settlement than is typically feasible with conventional pit underpinning. Robust, real-time geotechnical instrumentation monitoring systems have helped reduce the uncertainty and further expand the feasibility of jet grout underpinning applications. When properly designed and constructed by qualified and experienced jet grouting contractors, the flexibility of soilcrete for design and construction may be utilized to overcome the many inherent challenges which complicate underpinning and earth retention systems. INTRODUCTION The construction of buildings and infrastructure in our increasingly dense urban spaces often requires excavations below the elevation of existing structures immediately adjacent to the proposed work. Where a proposed excavation system encroaches into an existing structure’s zone of influence, additional measures, such as the construction of an underpinning or excavation support system, are required to safely excavate and minimize the impacts on the adjacent structures. Jet grouting is one method of underpinning that offers significant commercial and technical advantages over many other techniques. Though it was first used to the United States in the 1980s and has grown in popularity elsewhere, jet grout underpinning remains underutilized domestically due to its perceived cost and risk premium. Jet grouting has significant technical advantages over other underpinning methods due to its applicability in a wide range of soil types and its flexibility of design and installation. The jet grouting process is capable of limiting the movement of foundations during construction and excavation to lower thresholds than most traditional underpinning methods (Droof, Furth, & Scarborough, 1995). Its use for underpinning historic and sensitive structures with lower settlement criteria provides additional evidence to its technical utility. Through thoughtful design, adequate planning, and experienced installation, jet grouting can be an appropriate underpinning solution that can provide significant cost and schedule savings.

Jan 1, 2019

By T. Grounds, K. Singh, W. R. Reed, R. Cross, G. Ross, S. Klima, M. Shahan

"A 2nd generation roof bolter canopy air curtain (CAC) design was tested by National Institute for Occupational Safety and Health (NIOSH) at a Midwestern underground coal mine. During the study, the roof bolter never operated downwind of the continuous miner. Using a combination of personal Data Rams (pDR) and gravimetric samplers, the dust control efficiency of the roof bolter CAC was ascertained. Performance evaluation was determined using three methods: (1) comparing roof bolter operator concentrations underneath the CAC to roof bolter concentrations outside the CAC, (2) comparing roof bolter operator concentrations underneath the CAC to the concentrations at the rear of the bolter, and finally, (3) using the gravimetric data directly underneath the CAC to correct roof bolter operator concentrations underneath the CAC and comparing them to the concentrations at the rear of the bolter. Method 1 dust control efficiencies ranged from -53.9% to 60.4%. Method 2 efficiencies ranged from -150.5% to 52.2%, and Method 3 efficiencies ranged from 40.7% to 91%. Reasons for negative and low dust control efficiencies are provided in this paper and include: incorrect sampling locations, large distance between CAC and operator, and contamination of intake air from line curtain. Low dust concentrations encountered during the testing made it difficult to discern whether differences in concentrations were due to the CAC or due to variances inherent in experimental dust measurement. However, the analyses, especially the Method 3 analysis, show that the CAC can be an effective dust control device. INTRODUCTION Canopy air curtains (CAC) have been shown to be an effective respirable coal mine dust control for roof bolters in a laboratory setting with dust control efficiencies ranging from 14% up to 75% [Goodman and Organiscak 2001, Listak and Beck 2012, Reed et al. 2017]. Unfortunately, there is limited information on their effectiveness for controlling respirable coal mine dust in the field. On continuous miners, CAC dust control efficiencies ranged from 23% to 69% [Krisko 1975]. Two underground tests of the CAC on roof bolters demonstrated dust control efficiencies of 35% and 53% [Listak and Beck 2012] before problems occurred with operation of the CAC. Since the implementation of the new respirable coal mine dust limit from 2.0 mg/m3 to 1.5 mg/m3 (Code of Federal Regulations, 30 CFR 70.100, 2015), roof bolter CACs are becoming more commonplace in underground coal mines as a dust control tool to prevent roof bolter operator overexposure to respirable coal mine dust. J.H. Fletcher & Co. has been instrumental in delivering an effective design which incorporates the filter, blower, and canopy plenum seamlessly into the design of the roof bolter, resulting in a successful operational roof bolter CAC."

Jan 1, 2018

By Lloyd Robert Nelson

The historical progression in installed electric furnace smelting capacity of some 1650 calcium, chromium, manganese, nickel and silicon ferro-alloys furnaces is reviewed. Key increases in the inherent installed electrical capacity, often achieved through uprating furnaces, are identified. Possible factors facilitating such advances are explored, including: specific process engineering and pyrometallurgical enhancements (e.g., improved control over the consistency, size and chemical form of raw materials, extents of preheating and pre-reduction delivered into the furnace; and patterns of feed distribution); furnace electrical configuration (AC or DC; immersed, submerged-, shielded- or open-arc); form of electrode (graphite, self-baking or composite); furnace configuration (circular or rectangular; closed or open and 1-, 3- or 6- electrodes); better engineering and equipment designs (e.g., high-intensity cooling) and state of furnace electrical and metallurgical control systems. A view is presented on the prevailing state of evolution of the Mega-scale in ferro-alloy smelting and opportunities for still further improvements.

Jan 1, 2014

By D Ford

BHP BillitonÆs new rotary iron ore car dumper installation at Finucane Island (Port Hedland) was constructed to increase the total capacity of the port facility from 110 Mtpa to 120 Mtpa and to allow for incremental capacity increases in future. The arrangement of the dumper is similar to other car dumper installations existing on site. To construct the facility, approximately 120 000 m3 of material was excavated in six months, to a total depth of 22 m. The saline water table was nominally 6 m below ground level and the materials excavated varied depending on depth, ranging from sand to mangrove muds. There was a need to retain the sides of the excavation and limit the amount of water from entering the excavated area. This was required to allow excavation to progress and had to be maintained during construction of the permanent concrete and steel facility. The excavation was backfilled progressively as construction progressed. Various retaining wall methods were investigated with the preferred option being sheet piles secured by walers and ground anchors. Detailed electronic models were developed and assessed to complete the final design arrangement. Dewatering bores around the perimeter of the excavation removed the groundwater to intercepted sumps within the site. A strict and methodical program was developed to monitor the integrity of the temporary works and the quality of the groundwater. The works were completed on time despite the following challenges being encountered: availability of resources and equipment, movement of mobile plant on æboggyÆ materials, difficulty driving sheet piles into material at depth, drilling of ground anchors to 32 m, grouting of ground anchors, greater than expected groundwater flows, and the risk of hydrocarbons within the groundwater. The lessons learned from the use of the retention system and, in particular, the associated construction challenges overcome, provide a sound basis for similar work in this buoyant resource market. The conference paper describes the temporary works options investigated, design considerations and processes, construction methodology and challenges encountered, and the monitoring systems developed. Lessons learned are also discussed.

Jan 1, 2007

By Joachiim Lehner

The application of post-combustion (secondary oxygen) to avoid skull formation on BOF lances was tested in industrial trials. The main findings are that no negative impact on the metallurgical targets (i.e. carbon, temperature and phosphorus at end of blow as well as iron–oxide in the slag) could be observed. The technology is capable of avoiding the buildup of lance skull and consequently increasing the average life of lance tips. The application of post-combustion not only affects the skull formation, there are also interactions with the refractory lining, especially thermal wear, and the utilization of the process gases (CO Recovery) that have to be considered. Special attention has to be paid to the parameters determining the use of secondary oxygen because rather small changes can strongly affect the points mentioned above. Since August 2016, the PCD (Post-CombustionDistributor) lances are used on a daily basis in the steelplant LD3 in Linz.

Oct 30, 2017

By R. D. Alorro

Melting has become a popular pre-treatment method for municipal solid waste (MSW) incineration residues in Japan. Although the method is effective in stabilizing the hazardous organic sub-stances such as dioxin, it concentrates the heavy metals such as Zn, Pb, Cu, and Cd in a newly formed fly ash (melting fly ash). Melting fly ash is classified as a hazardous waste because of the leaching potential of these heavy metals in landfill environment. Extraction and recovery of these metals seem to be more environmentally and economically attractive than disposing the material to landfill after immobilization process. This study proposes a Carrier-in-Pulp (CIP) method as a new hydrometallurgical route to reject and recover heavy metals from fly ash. In this method, a carrier material which recovers the extracted metals is added simultaneously with fly ash to leaching solutions and is harvested from the pulp by physical separation method like magnetic separation or sieving. To demonstrate the effect of CIP method, shaking flask experiments were conducted under various conditions using NaCl solution as lixiviant and iron powder or granular activated carbon as carrier materials. In the CIP method using iron powder, more than 97 wt% of Pb and Zn were extracted from the ash to the solution phase. However, the iron powder which was harvested from the pulp by magnetic separation, recovered only Pb (more than 94%) through cementation, leaving behind Zn ions in the solution phase. Due to this problem, granular activated carbon (GAC) was considered as an alternative carrier material. Single- and multi-metal adsorption experiments using granular activated carbon were conducted as a preliminary study. Around 85% Pb and 88% Zn were recovered by GAC in the single-metal adsorption experiment, while 60% Pb and 70% Zn in the multi-metal experiment. These results showed that activated carbon was superior to the iron powder since it was able to recover both Pb and Zn through adsorption. The leaching test conducted on the residue after the CIP-Fe treatment revealed that the solubilisation of Pb was successfully suppressed to meet landfilling guidelines.

Jan 1, 2014

By P. H. Agson Gani, T. Sitorus, N. P. Widodo

"PT ANTAM UBPE Pongkor underground mine use blasting to develop its tunnels which will cause poisonous and dangerous gases trapped inside mine. To analyze this case, a study of mine ventilation, the dispersion of carbon monoxide (CO) gas concentration and diffusion coefficient is commenced. At the end, the re-entry time formula will be determined. Results indicate that this study is site specific and could only be applied in the place this study executed. The aim of this study is to be further developed by applying Principal Component Analysis (PCA) to find a universal re-entry formula. KEYWORDS Mine Ventilation, Re-Entry, Smoke Clearing, Diffusion Coefficient, Carbon Monoxide Gas, Gas Dispersion INTRODUCTION Pongkor underground mine is using cut and fill as its mining method. Thus, its development and production processes require blasting to develop its tunnel. This process caused poisonous and dangerous gases spread and trapped inside the mine, one of them is carbon monoxide (CO) gas. CO is formed in an unbalanced reaction of explosives detonation and could be the cause of headache, blackout and death to people who inhale CO at certain concentration (McPherson, 2011; Hartman, Mutmansky, Ramani, & Wang, 2012). Mine ventilation system is installed in the mine to resolve this problem. Mine ventilation play an important role to disperse CO gas by absorb the poisonous/dangerous gases and deliver clean air into mine. The important parameter is diffusion coefficient, because diffusion is affecting particulates or gasses spreading from its sources throughout the mine. Diffusion coefficient is the total diffusion in axial direction of turbulent flow mainly by convection of bulk motion, advection and eddy diffusion, while the effect of molecular diffusion is appreciably negligible (Widiatmojo et al, 2015). Taylor (1953, 1954) develops a theory about the dispersion by inducing a slow stream of solvent into a capillary tube. Taylor used Reynolds assumption of radial diffusivity to be analogous with the transfer of the matter in turbulent flow as well as the transfer of momentum and heat. Then, Taylor proposed the formula of diffusion coefficient, D (m2/s), against pipe diameter and turbulent shear velocity are as follow:"

Jan 1, 2019

By Max W. Ball

THE geologist or mining engineer, whose work takes him into the western United States, whether for the Government or private enterprises, is likely to be called upon to classify public lands as to their mineral character, or to review such classification already made, usually by a Government geologist or mineral inspector. The public-land law covering the matter is clear and logical, and a knowledge of its simpler principles is necessary to intelligent classification work. There are two classes of cases in which a classification of lands as mineral or non-mineral may be required: .first, cases in which lands classified as mineral will be retained by the Government and lands classified as non-mineral alienated; second, cases in which lands classified as mineral will be alienated and lands classified as non-mineral retained.

Jan 1, 1921

Palladium Alloys. E. M. Savitskii, V. P. Polyakova, M. A. Tylkina. Translated by: R. E. Howard. Published by Primary Services, New York, N.Y. 10012. $24.50. The output of palladium in the U.S.S.R. greatly exceeds the internal usage. The primary purpose of this 200 page volume is therefore to record details of fundamental researches on the properties of this metal with a view to expanding its marketability. Theoretical studies have revealed a number of alloys with great promise in electrical instruments and for the chemical industry. The success of these researches in the U.S.S.R. and in the U.S.A., resulted in the industrial usage of palladium exceeding that of platinum in 1957 and increasing its lead during the next decade. This volume is divided into three parts. Section I covers the mineralogy, extraction and the physical metallurgy of the metal. It records a considerable area where the resistance to corrosion of palladium equals that of platinum. Section II deals with the preparation and the properties of palladium in alloys and contains a comprehensive metallographic treatment of the many binary alloy systems. Section III is devoted to industrial applications. The 460 references which are quoted are mainly from the U.S.S.R. but otherwise have a world-wide coverage. H.B.

By R. V. Ramani, P. M. T. White, D. Sutton

Appendix I. Part 1: Description Of Geology & Reserves System Introduction The Ore Evaluation and Reserve programs have been developed to aid in the evaluation of coal deposits, both qualitatively and quantitatively. The "Weighted Moving Average" technique used provides considerable flexibility in dealing with diverse parameters with differing distribution characteristics. Determination of Model Constants "a" and "k" - Unit 1 The flexibility of the method in dealing with diverse value parameter distributions lies in its ability to cater to the individual characteristics of each. These characteristics are embodied in the values determined for constants "a" and "k", namely, local and regional variations in value distributions, respectively. The empirical method used attempts to optimize the "a" - "k" combination. Realistic values for "a" and "k" are entered into the program together with sample values for the required parameters and their respective coordinate location values. All the values within a specified radius from the point being evaluated are used to interpolate a value at that point. (Note, the interpolated point is the location of one of the boreholes, values of which are not used in the calcula¬tion.) 3n a similar manner, interpolated values are calculated for each borehole location and for each parameter. This is done for each possible combination of "a" and "k".

Jan 1, 1974

By Charles E. Locke

SHARP CONTRAST exists in the reports so helpfully contributed by the individual members of the Milling Committee for this review. Those engaged in the milling of gold and silver ores report great activity, of which some details will be given later. Those engaged in milling ores of base metals report continued depression and little progress. Copper production in the United States is running at about fifteen per cent of capacity. Some Arizona copper mills are closed. Anaconda is milling about 45.000 tons of copper ore per month, and the Utah Copper Co. 35,000 monthly. However, in Canada the International and Falconhridge copper-nickel mills and the Noranda copper-gold mill have increased production. Also the Climax molybdenum mill in Colorado is milling 4000 tons per day. Water shortage from the drought has caused curtailment or complete shutdown of mills in some parts of the West.

Jan 1, 1935

Once applied, EarthZyme reduces the tendency for a road to exhibit common maintenance issues: wash-boarding, rutting, heaving, potholing and dust.

Aug 1, 2013

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