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By Andrew Peterson

The Maine Department of Transportation offered this challenging design-build project for a new, 12-span, bridge over the Kennebec River in Bath, Maine. This structure would be built to replace the existing Carlton Bridge connecting the village of Bath, Maine to neighboring Woolwich, Maine. The design build team of Flatiron Structures, Inc., and Figg Engineers, Inc., elected to design and build a segmental concrete bridge. Site conditions dictated that this bridge would be supported primarily on deep foundations. Case Foundation Company joined the project team in the winter of 1997 to install twenty-two, eight foot diameter drilled shafts. The drilled shafts were designed with 8' diameter, permanently cased shaft sections and 7.5' diameter rock sockets. Shaft lengths ranged from 20' long near the river's edge to 100' deep in the middle of the river. Rock socket lengths ranged from 12' to 30' deep. Two Osterberg Cell load tests were conducted on production drilled shafts. Figg Engineers utilized the results of the load tests to "fine-tune" the rock socket design during construction of the drilled shafts. Construction of the drilled shafts proved to be very challenging and called on every member of the design-build team to work together throughout the project. One of the most challenging aspects of this project was in the installation of the 8' diameter permanent casing and drilling of the rock sockets. Early in the project, it became apparent that the top of bedrock was broken and unstable. This condition limited the advancement of the permanent casing and the affect of a "seal" at the top of rock socket. As a result, as the rock socket was advanced, loose material spilled into the hole and stopped progress of the socket. In order to resolve this problem, the design-build team developed a redesigned drilled shaft which included the installation of a steel sleeve to seal off the unstable rock formation. Following installation of the sleeve, the rock socket diameter was reduced to 7' diameter and advanced additional length to achieve required design capacity. All drilled shafts were installed with equipment supported on floating barges. Water access, along with the long shaft lengths and very hard bedrock required the use of cranes and drilling equipment that far exceeded the requirements of typical drilled shaft projects. This paper will discuss the relationship between design, construction, and equipment utilization on this challenging design-build project. [ ]

Jan 1, 1999

By Fazel G. Jahromi, Ahmad Ghahreman

"Atmospheric leaching of arsenical sulfide concentrates, and especially enargite leaching, is one of the major challenges within the current hydrometallurgy research area. One of the recent processes developed for sulfide ore treatment is atmospheric leaching in the presence of AF 5, a novel carbon based catalyst, in chloride media. The quantification of different ion concentrations during enargite and chalcopyrite leaching in the presence of AF 5 were measured and the copper recovery rates of 97% and 96% were achieved. The objective of this study is to shed light on the leaching mechanism of the sulfide minerals. Based on the speciation of iron and copper by different titration methods, the AF 5 catalyst first reduced ferric and cupric ions and then oxidized ferrous, cuprous and arsenite ions. The oxidation behavior of the catalyst enhanced the leaching results. The AF 5 catalyst also caused in situ precipitation of scorodite in leaching experiment. The speciation of ions in the chloride media were simulated by Phreeqc software and the dominant species in the leaching solution were determined.INTRODUCTION The hydrometallurgy of copper has been used for several decades and is still under development for more complex copper sulfide minerals due to their refractory nature. Most of the world copper reserves are in the form of chalcopyrite; and enargite is known as a major contaminant. Pyrometallurgical processing of enargite is problematic due to arsenic release and tight environmental regulations (Peacey, Gupta, and Ford n.d.). On the other hand, lower recoveries in the hydrometallurgical processes make most of these processes impractical. Several leaching processes have been developed for the leaching of copper sulfide minerals. Some of the common treatment methods for copper sulfide minerals are pressure oxidation leaching (POX), CESL, Activox, Albion process, atmospheric ferric sulfate leaching, Dynatec, Galvanox, and Hydro copper process (Barr, Defreyne, and Mayhew 2005; Conner and Anderson 2013; D.G. Dixon, Mayne, and Baxter 2008; Hyvärinen and Hämäläinen 2005; Palmer and Johnson 2005; Rohner, Bartsch, and Ngoviky 2012). Generally it is not viable to dissolve copper sulfide minerals at ambient pressure in mild acidic media and dissolution of these refractory minerals requires harsh conditions in the presence of oxidant materials (Biswas and Davenport 2002). Ferric ions have been used as an oxidant in different media in copper sulfide leaching processes. U. S. Bureau of Mines’ Reno Metallurgy Research Center in 1969 (Haver and Wong 1971) investigated ferric chloride leaching of chalcopyrite. Dutrizac and Macdonald (1972) studied ferric sulfate leaching of enargite. Based on this study, 50% of the copper was recovered at 80-85 ºC after 7 days of leaching. Cupric ions can also be used as an oxidant. Parker, Paul, and Power (1981) stated that cupric/cuprous couples are more effective than ferric/ferrous couples in chloride media because they are rapid and reversible. The Hydro Copper process leaches copper sulfide minerals in chloride solution catalyzed by cupric ions. In this process, copper dissolves as cuprous ions in presence of cupric ions (about 10 g/L) (Hyvärinen and Hämäläinen 2005)."

Jan 1, 2017

By M. R. Geer, H. F. Yancey

0. R. LYONS*—I know that we are all interested in hearing about problems that other people have. To most of the people from the eastern part of the United States, this kind of coal preparation is completely different. It represents washing difficulties that most operators have never experienced, or, if they have, they have refused to consider them because there are coals that are much easier to wash and, therefore. they leave the more difficult ones alone for the time being. E. R. McMILLAN†—I think the au-thors have summarized the material very well. Dr. Yancey has spent a great many years in the study of washing coals, as has Mr. Geer. I might comment briefly on some of the plants that were mentioned, plants with which I have had some con-nection, particularly those of our own company, the Northwestern Improve-ment Co. I would like to point out this: that ill each case, a great deal of work was done in the way of preliminary studies of washability of the coal before plants were built. The first plant of any size built in Roslyn field was mentioned in the paper. This central cleaning plant was designed and built to handle coal from three different mines. I might say that prior to 1935, the year in which the plant was built, the coal was used largely as railway fuel, close to a million tons annually. But as mining increased in depth, it became increasingly difficult to separate and gob much of the impurities underground, with the result that the run-of-mine coal became so high in ash that the railroad eventually was forced to consider installing some kind of preparation plant at the mine. We spent about a year in preliminary studies in cooperation with the Bureau of Mines to find out the best type of plant that would clean the coal. The result, as Mr. Geer has explained to you, is a rather complicated plant, but it is doing a very satisfactory job. We have, however, made a number of changes and improve-n~euts since it was first built. The last addition was the, installation of a cen- trifugal drier to dewater the minus ¼ in. size. We are now contemplating installing heat driers for further drying of minus ¼ in. We use Vissac heat driers for drying the stoker coal, the ¾ to in. The demand for drier coal, for both railway and industrial use, is forcing us to further drying of the coal. The plant that was mentioned as having been built in Pierce County, during the war, was a government sponsored plant. I happen to have had some connection with its design, construction and initial operation. We did what we thought then, and still think, was a very thorough job of preliminary studies in cooperation with the Burea of Mines of the coal from that field. The plant was as good a plant as could be built with the equipment available at that time, 1943. The plant that was mentioned as having been built at Ravensdale for treating the McKay coal was rebuilt about two years ago, and in addition to the modified Elmore jig washer that was mentioned. we added a coucentrating table for re-cleaning the minus 3/32 in. Our object there was to produce a commercial

Jan 1, 1950

By Stanley J. LeFond

The Republic of Botswana, one of the newer countries of southern Africa, attained independence on September 30, 1966. It covers an area of about 225,000 square miles (582,000 square kilometers) which makes it slightly larger than France, or slightly smaller than Texas. It is bounded by Zimbabwe, the Republic of South Africa and Namibia, including the Caprivi Strip. Angola and Zambia are close neighbors. (Map 1). Botswana lies at the center of the southern African plateau at a mean elevation of 3,300 feet (1,000 m). It is a natural habitat for most species of African fauna. The rolling sands and extensive grasslands of the Kalahari Desert cover the southwest. The climate is sub- tropical. Summers, although tempered by north- easterly breezes, are hot, but mean maximum temperature seldom rises above 100°F (38°C). Winters are dry with wide temperature variations, which often give rise to frosts.

Jan 1, 1981

By Aris Tambunan, Nella Lubis, Nurafrianti Saala, Komang Widhiayanto, Herry Saputra, Rudolf Sitorus

Maximizing mining recovery rates and minimizing ore loss are pivotal objectives for economic efficiency and operational effectiveness. This study explores methods to address these imperatives by enhancing ore production and recovery through improved blasting techniques and spillage control in the Martabe Gold Mine Project in North Sumatra Province, Indonesia. Between 2018 and 2021, the average mining recovery rate stood at 93%, resulting in a potential annual ore loss of 7% and a potential quarterly financial impact of close to $2 million. Maintaining and enhancing mining recovery became crucial, with a planned 30% increase in total material movement for 2022. The mining recovery target for 2022 was set at 96% based on best achievement historical data from 2021 to increase ore tonnage by 203 KTon per annum. To achieve the primary objective of increasing ore production by improving mining recovery, the study focused on predicting and controlling the movement of blasted ore to reduce spillage and enhancing the grade control model to reflect actual conditions post-blasting. Several alternative solutions were explored, primarily emphasizing drilling and blasting activities. Essential methods included capturing the actual blasting movement to adjust the ore block based on blasting design data and post-blasting muckpile topography. This approach minimizes ore loss by providing output as ore block adjustment based on post-blast movement data. In addition, the tie-up design was adjusted to control ore spillage outside the pit ridge. The implementation of these methods yielded significant improvements. Adjusting the ore block based on actual blasting movement contributed $1,545,764 in benefits. Controlling ore spillage outside the pit ridge achieved a 10% reduction in spillage, contributing $79,184 in benefits. These enhancements successfully met the 2022 mining recovery target of 96%, marking a 3% increase from 2021. Consequently, ore loss was reduced by 178 KTon throughout 2022, resulting in a financial impact of $7.3 million. The study underscores the significance of precise blasting techniques and effective spillage control in enhancing mining recovery rates.

Jan 21, 2025

By A. J. Bartlett

Island Creek conditions are generally referred to as ideal; yet, as at all other properties, there are all known hazards of coal mining. The hardest of these hazards to combat is the human element. The basic thought in the minds of the management of these properties is to produce coal with the utmost safety, and it has impressed upon its supervisory force that it does not want a ton of coal unless it can be produced safely. This company has instituted a mine inspection department, which reports direct to the general manager, arid all matters pertaining to safety come under the direction of this department. Through the medium of the inspection department, the management is kept in touch with the actual conditions existing in general at all mines. Inspections are made regularly arid continuously; that is, at all times while the mine!: are in operation some sections of some mines are being examined. These inspections cover all active and inactive workings. Miners are contacted in their working places and other employees at their respective, work. A thorough check is made to see that the state mining laws are complied with and that company safety rules arc being observed. Night shifts receive the same attention as day shifts. All violations and dangerous practices are brought to the attention of the plant supervisory force with suggestions and recommendations; major hazards of emergency nature are taken up immediately with the management. Periodical inspections are also made of all tipples, preparation plants, dumping and hoisting equipment, to see that all machinery is properly guarded, and walkways and platforms properly fenced; conditions of equipmcnt and mechanical defects are also reported. Reports of inspection are written in letter form and in such a manner as to give the management a picture of the existing conditions at the time of inspection. Copies of inspection reports are forwarded to the superintendents with the general manager'? comments. It has been said, "There is nothing under God's heaven that justifies. your creation or your citizenship but this gospel: ' That the next greatest

Jan 1, 1938

By A. J. Bartlett

Island Creek conditions are generally referred to as ideal; yet, as at all other properties, there are all known hazards of coal mining. The hardest of these hazards to combat is the human element. The basic thought in the minds of the management of these properties is to produce coal with the utmost safety, and it has impressed upon its supervisory force that it does not want a ton of coal unless it can be produced safely. This company has instituted a mine inspection department, which reports direct to the general manager, arid all matters pertaining to safety come under the direction of this department. Through the medium of the inspection department, the management is kept in touch with the actual conditions existing in general at all mines. Inspections are made regularly arid continuously; that is, at all times while the mine!: are in operation some sections of some mines are being examined. These inspections cover all active and inactive workings. Miners are contacted in their working places and other employees at their respective, work. A thorough check is made to see that the state mining laws are complied with and that company safety rules arc being observed. Night shifts receive the same attention as day shifts. All violations and dangerous practices are brought to the attention of the plant supervisory force with suggestions and recommendations; major hazards of emergency nature are taken up immediately with the management. Periodical inspections are also made of all tipples, preparation plants, dumping and hoisting equipment, to see that all machinery is properly guarded, and walkways and platforms properly fenced; conditions of equipmcnt and mechanical defects are also reported. Reports of inspection are written in letter form and in such a manner as to give the management a picture of the existing conditions at the time of inspection. Copies of inspection reports are forwarded to the superintendents with the general manager'? comments. It has been said, "There is nothing under God's heaven that justifies. your creation or your citizenship but this gospel: ' That the next greatest

Jan 1, 1938

In the human body, the balance between heat production and heat loss is continuously being disturbed, either by changes in metabolic rate (work being the most influential) or by changes in the external environment (heat stress), which alters heat loss. These changes in body temperature can adversely affect the function of body systems and organs. As a result, heat production or heat loss processes are triggered in order to restore normal body temperature (36 - 37¦C). If the heat generating systems of the body are excessive or the environment hostile then the capacity of the body to maintain thermal homeostasis is exceeded and can lead to a serious threat to health, or even death. This health deficit can severely affect an individualÆs capacity to work optimally; the end result is both poor productivity and health. Strategies to minimise or eliminate this effort will benefit both the health of workers and the productivity of companies. The principal strategies to reduce the effects of the environment on workers are: engineering interventions: to improve environmental conditions and reduce heat stress; and a comprehensive working in heat protocol: with provisions to identify risk situations and procedures to be adopted in relation to these. The above points will be discussed in detail with practical and simple strategies proposed to combat the deleterious effects of heat in mining.

Jan 1, 2005

By Reginald S. Dean

THE commercial availability of electrolytic manganese has greatly changed the position of manganese as a nonferrous alloying metal. Manganese metal commercially available up to about ten years ago was reduced with either silicon or aluminum and contained substantial amounts of the oxides of these metals and other impurities. Manganese was accordingly not available as an alloy base and its addition to copper-base and nickel-base alloys was generally limited to a manganese content of a few per cent. Several special alloys like manganin contained up to 12 pct of manganese. A method for the production of electrolytic manganese was developed by the Bureau of Mines in 1936 and commercial production was begun in 1938. At the present time (June 1951), production is about 12 tons per day but appears likely to be substantially increased. Electrolytic manganese is deposited from an aqueous electrolyte containing manganese and ammonium sulphates and is marketed as cathode fragments about 1/8 in. thick. The impurities in its composition are as follows: iron, 0.0015 pct; copper, 0.001; arsenic, 0.0005; cobalt, 0.0025; lead, 0.0025; molybdenum, 0.001; sulfide sulfur, 0.017; sulfate sulfur, 0.014; insoluble, 0.002; carbon, 0.002; hydrogen, 0.015. These figures are from Bulletin 463, U. S. Bureau of Mines. From an alloying standpoint, the most important impurity is hydrogen. This can be removed by heating; 95 pct of the hydrogen can be removed in this way without introducing significant amounts of oxygen or nitrogen. Much of the commercial electrolytic manganese used in alloys is dehydrogenited by the producer, since the amount

Jan 1, 1953

By Rafael Valencia-Dongo, Ernesto Ramírez, Julio Tapia

Enfocado en una novedosa metodología de resolución de conflictos basada en la teoría de juegos, este artículo propone estrategias para generar un equilibrio estable entre empresa, Estado y comunidad. Tras evaluar la tipología y características de la conflictividad socioambiental por acción de líderes opositores a la inversión, se desarrolla un marco de resolución de conflictos a través de lo que se denominan pactos de contrapeso, que cubren los ámbitos de comunicación, gestión sociopolítica y fidelización del trabajador minero. Estos pactos permiten cambiar la percepción, incentivos y acciones de los actores, lo que incluye la acción de terceros legítimos.

Sep 30, 2019

By E. A. Johnson

The Bureau of Mines determined the effect of slag additives on copper solubility and the distribution of typical impurity elements between copper-iron matte and silica-saturated fayalite (iron silicate) slag at 1,250° C, in CO-C02 atmospheres with 10 pct S02. Small additions (<10 pct) of CaO, A1203, and MgO were shown to decrease copper solubility in the slag. Additions of CaO increased the solubility of bismuth and tellurium in the slag at lower matte grades. Al 20 3 additions decreased the solubility of tellurium in the slag, but increased that of bismuth at lower matte grades. A1203 additions increased the solubility of both at lower matte grades. With no additives, matte grade did not affect the solubility of bismuth in slags, whereas increasing matte grade resulted in a slight decrease in the tellurium solubility in slag. Additions of CaO or As203 alone to the slag increased selenium and arsenic distribution to the matte, but had little or no effect on antimony distribution; whereas small MgO additions decreased antimony distribution to the matte but had no effect on arsenic and selenium distribution. In slags with no additives, selenium distribution to the matte increased with increasing matte grade, while that of antimony decreased and that of arsenic was unchanged.

Jan 1, 1982

By E. D. Gardner

"In recent years efficient safety organizations have been considered essential at all well-managed metal mines. Statistics from numerous mines throughout the country show that the expense of operation of these safety departments is repaid many times by the saving due to fewer accidents. Men trained in first aid, mine rescue and fire-fighting are important parts of the safety organization at most mines. It is more desirable, however, to lay stress ma accident prevention and fire precautions rather than on first aid and fire fighting. Both of these phases of safety work have been well developed in the Globe Miami district. The co-operative mine rescue organization* in this district under Orr Woodburn, is one of the best in the country. Mine rescue teams are kept trained at all the mines and the oxygen breathing apparatus is constantly maintained in good condition. Miners are also trained in first aid, and are offered incentives to make themselves proficient both in mine rescue and first-aid work.The Old Dominion Company is among the leaders in the safety movement in the Globe-Miami district. The safety department at this mine was established January 1, 1914, and has been developed to a high degree of efficiency. W. G. McBride, general manager of the company, takes an active part in the safety work and has given Albert Talon the safety inspector, his active support in developing the organization. The success of the department is dos largely to the ability, tact, and personality of the men directing the work.The following description of the establishment and operation of the safety organization at this mine was prepared from information supplied by Mr. Tallon."

Jun 1, 1921

By David Hoadley, Kenneth R. Maser, Ashok B. Boghani, James E. Billar, D. Randolph Berry, Mackenzie Burnett, Robert H. Trent

C 2 Complete Hoisting Systems A Above Ground Installations A total of seven companies were identified who supply complete emergency escape hoist units for above ground installations The units have been designed predominately to meet the needs of coal mine operators to satisfy the requirements of the Coal Mine Health and Safety Act of 1969. The seven companies are as follows 1 Dover Conveyor and Equipment Co. 2. Coeur d&apos; Alenes Co. 3. Connellsville Corp. 4. Scott Midland 5. W W Williams Co. 6. Equipment Corporation of America 7. Timberland Ellicott Table VIII contains detailed specifications and price information on each of these units. The units have a number of similarities

Jan 1, 1976

By Tianzu Yang, Weifeng Liu, Lin Chen, Wei Chen, DUCHAO ZHANG, HUI XIAO

Carbonaceous refractory materials are widely accepted in many reducing smelting processes such as iron and ferroalloys. Oxidizing processes such as copper concentrate smelting traditionally use magnesia and/or alumina/silica refractory materials. The main objection to the use of carbon-based refractories as the exposed working lining in oxidizing applications is the potential for free oxygen to react with the carbon at high temperature, which could rapidly degrade the refractory lining. In 2013, Outotec and GrafTech conducted joint trials of a thermally conductive, carbonaceous lining for smelting copper concentrates in the Outotec® pilot-scale top-submerged-lance (TSL) furnace in Dandenong, Australia. This testwork had two equally important goals; to demonstrate the ability of carbon refractories to withstand oxidizing process conditions, while ensuring that neither furnace operating conditions nor process stability were negatively affected by the refractory material. The paper discusses the input parameters of the trials, key observations during the testwork program, and the results and conclusions from both process and refractory design standpoints.

Jan 1, 2016

By J E. Powalisz

Obtaining a representative sample of bulk materials in process industries is critical to providing valid data for process control and custody transfer (valuation). The accuracy of a sample, that is to say how well the sample represents the material in the process, is directly related to how well the process can be controlled and to how much a product may be worth. Sampling accuracy then is in fact related to bottom line profitability.Sampling theory offers information and equations on how to take a representative sample from a process, however, the actual practice of extracting a sample from the process can be more of an art.Key sampling variables include product specifications such as bulk density, particle distribution, material conveyance, practical sampler location, sampler type and sample frequency and volume/mass.This paper discusses basic sampling theory, sampling methods, types of samplers, how to develop a ‘real world’ sampling system and current manual and automated samplers.Key points include ‘practical precision and variance’, material properties, flow properties, direct sampling versus indirect sampling, sampler types and applications.CITATION:Powalisz, J E, 2014. Bulk solids sampling, in Proceedings Sampling 2014 , pp 179–188 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Jul 29, 2014

By W. J. Birch, R. Farnfield, S. Hosein, C. Johnson

Modern smart phones include accelerometers based on MEMS (Micro Electro Mechanical System) technology giving the possibility to measure both acceleration and orientation. The widespread use of such phones has driven technological development to such a degree that it is now possible to obtain a triaxial accelerometer unit, that also include signal conditioning and analogue to digital conversion, in a package smaller than 1 cm2 (1/2 sq.in) for a relatively low cost.

Feb 6, 2023

By B. W. Naugle

This report describes the carbonizing properties of coals from the principal beds in Cambria County, Pa. Samples of coals from Upper and Lower Freeport and Upper and Lower Kittanning beds having estimated minable reserves of 50-million tons or more were studied by the Bureau of Mines. Cambria County coals rank either as medium-or low-volatile bituminous. A preparation study indicated that all coals tested in this county, except one sample from the Lower Freeport bed, were responsive to cleaning and would yield a product with satisfactory chemical properties for metallurgical coal. All coals tested from Cambria County yielded strong coke; however, they expand excessively when carbonized singly, and should be used only as minor constituents in metallurgical coking blends when carbonized in slot-type ovens.

Jan 1, 1959

By Michael R. King

The application and use of steel fibre reinforced concrete in precast tunnel lining design is a growing trend due to its advantages in performance over plain concrete, and ease of manufacture compared to traditionally reinforced concrete. However, the design process and performance characteristics of the material are poorly served by current codes and standards. This paper provides some basic design guidance for segmental linings, and compares the material properties for the different material options. A typical example is considered to compare the possible results of lining arrangement and thicknesses for a plain, reinforced, and fibre reinforced design solution.

Jan 1, 2005

By R. C. Miranda

The purpose of this work is to present ?state of the art? mass balances closing strategies in ore treatment plants. It presents a brief history of difficulties and challenges ahead. The current methodology is based on usage of an expert system, which seizes and filters the plant data, analyzes situations of equipment stops and mostly instruments failures. It is still possible to internally create a strategy to check the data of an instrument failure. The system is coupled to software with a Lagrangian model of mass balance closure that receives the pre-treated data. Thus, the data goes through filtering and reconciling processes to generate a reliable mass balance of the ore treatment plant. This made possible to obtain a system that is able to tell the real productivity of a ore plant through reliable mass balances. Residence times on equipments are critical to the balance, thus, they require good logic to eliminate errors due to the characteristics of non-steady state. Among the next challenges is the inclusion of a ?soft sensor? as a replacement of an instrument required for mass balance closure.

Sep 1, 2012

By C. Graeme-Barber, R. L. Bell, T. G. Langdon

An analysis is made of the formulas and ,methods used to estimate the contribution of grain boundary sliding to the overall strain of a polycrystal. The errors involved in the approximations and/or ,mistakes in earlier work are assessed quantitatively so as to make possible the critical use of previously published data. SINCE it has been found that, under conditions of very slow creep, the strain due to grain boundary sliding (?gb) may contribute as much as 80 pct of the total creep strain,1,2 it is obviously important to have reliable methods for estimating this grain boundary strain. In two recent papers Stevens3,4 has drawn attention to the pitfalls encountered in assessing ?gb. He criticizes 1) the assumptions made in the derivation of some of the formulas for ?gb, and 2) the indiscriminate averaging procedures used for obtaining the quantities substituted in these formulas. These and further criticisms of earlier work are mostly valid. Unfortunately the only formulas and procedures recommended are either impossible or very difficult to apply in practice. Furthermore no attempt is made to assess the errors involved by the earlier approximations or mistakes, and so it is not possible to make critical use of any of these early dab. The present article attempts to improve on these shortcomings by reference to empirical verification of easily applied formulas whose theoretical derivations involve some otherwise unjustifiable assumptions, and by a quantitative assessment of the errors in previous work. DEFINITIONS First it is necessary to define the terms and symbols to be used. The choice of symbols preferred here is a logical combination and extension of the v introduced by McLean5 and the u by Brunner and rant.&apos; In Fig. 1 the two grains X and Y are displaced by the sliding vector AC. u is the component of sliding resolved along the stress axis, v is that measured perpendicular both to the stress axis and to the specimen surface, and w is that measured perpendicular to the stress axis but in the plane of the surface. Two angles define the orientation of the grain boundary: 8, between the stress axis and the surface trace of the boundary, and +, the internal angle on a longitudinal section cut perpendicular to the surface. In computing the strain resulting from the boundary displacement at all the in- dividual boundaries in a polycrystal the components u, v, or w are sometimes averaged along a longitudinal line (i.e., parallel to the stress axis), sometimes along a transverse line, and sometimes at randomly chosen boundaries. Averages obtained in these three ways are given subscripts 1, t, and r, respectively. Stevens rightly calls attention to the possibility of non-equiaxed grain shapes either at the start or at the end of deformation. In this article all values of numbers of grains per unit length will refer to measurements made before deformation. The subscripts 1 and t will be used for the number of grains per unit length obtained along longitudinal and transverse lines, r for that obtained by averaging along a number of randomly directed lines. FORMULAS FOR ?gb ?gt, as a Function of u. An obvious truth is that cgb can, in principle, be obtained by summation of all the v components at the boundaries intersected by a longitudinal line of known length I, viz.: where nl is the number of grains per unit length, parallel to the stress axis, in the unstrained specimen. There are assumptions in the analytic derivation of Eq. [I] due to Brunner and rant&apos; but ~achinger&apos; arrived at Eq. [la] by a rigorous method. Unfortunately the experimental procedure required by Eq. [ la] proves very difficult as boundary migration tends to obscure the points at which the longitudinal line meets the grain boundary and the errors on such measurements tend to be large, see Fig. 2. For example, on a specimen of Magnox AL 80 at a creep strain of 9.7 pct, 300 measurements of u obtained from the points of intersection of a longitudinal line with the grain boundaries gave ul = 8.95 ± 3.58 pm, or an error of ±40 pct, at the 95 pct confidence limit. These large errors due to migration may be avoided by measuring u from the separation of the segments

Jan 1, 1968