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By Giovanni B. Barla, Stefan H. Boshkov

The block caving method is examined in this paper on the basis of experimental results and observations in the field, and through the use of numerical modeling by the Finite Element Method. The Grace Mine, developed by a panel caving method, served as a reference case. However, the results obtained and the simulation techniques which have been developed may find useful application in more general conditions as encountered in other mining operations by block caving. Following a brief description of the Grace Mine and of the mining method, the problems associated with the behavior of underground drifts at the production levels, during undercutting and caving, are addressed. The most important results obtained through monitoring of strains and loads in the supports of a runway are discussed, while giving relevance to the sequence of mining operations in the immediate vicinity. The most important geomechanical data, as provided for subsequent modeling, are described with reference to: (a) rock mass characterization and (b) in situ state of stress. Then, the numerical modeling procedures, developed by the Finite Element Method in order to predict the caving phenomena and the behavior of underground openings during undercutting, are discussed. Finally, an attempt is made to compare the pre- dictions of the numerical analyses with, the measurements carried out at the instrumented site. Suggestions as to how to improve the results both qualitatively and quantitatively are also given.

Jan 1, 1984

By J. L. Shafer, Christopher L. Caenepeel, Martha L. White

Often an in situ leach is the only practical economic method for copper recovery from small low grade oxide deposits. The decision to develop a copper property by an in situ blast and leach is strongly dependent on ore grade, tonnage, hydrology, and the copper extraction and acid consumption rates. The inherent leachability of the ore will in part determine the desired amount of fracturing of the ore deposit by the blast in order to obtain a copper extraction rate that is economical. For the last several years Occidental Research Corp. (ORC), has undertaken a modest effort to address the question of how to best identify and determine the information necessary to predict and control the operation of an in situ leach for the economic recovery of copper. Modelling of the Leaching Process During the past 10 years the activity in the mathematical modelling of the leaching of copper sulfides in copper dumps and heaps has increased dramatically. The modelling of copper oxide leaching has not received as much attention. The acid leaching of non-sulfide copper minerals while chemically less complex, compared to sulfides, does generate a vertical acid concentration gradient in the ore heap being leached due to the acid-base nature of the reaction. This is generally not observed in sulfide deposits that are biologically active, due to the buffering action of opposing reactions involving the generation of sulfuric acid from sulfide minerals and acid consuming host rock. Thus, the objective of ORC 's copper oxide modelling efforts is to determine the leaching parameters which will account for this vertical acid concentration gradient. Knowledge of this gradient will result in the correct choice of the feed acid concentration to the top of the ore dump or heap, such that the effluent will have the desired pH.

Jan 1, 1980

By Walter P. Jenney

An investigation, conducted by the author, was begun in September, 1889, by the United States Geological Survey, having for its object the study of the questions bearing upon the occurrence and manner of formation of the deposits of lead- and zinc-ores in Missouri and the adjoining States. The field-work was completed in December, 1891. During the first season the State Geological Survey of Missouri furnished an assistant, and in other ways co-operated in the research within the boundaries of that State. In order that the ore-deposits of the southwest might be compared with those of other sections of the Mississippi valley, an examination was made of the lead- and zinc-mining area of Wisconsin-Iowa, and of the argentiferous lead-mines of the region extending westward from Hot Springs, Arkansas, to Indian Territory. In the discussion of the general geology, and in comparisons between the ore-deposits of the Mississippi valley and those of the Rocky Mountains, the writer has drawn largely from his personal experience, having been engaged for many years in professional work as a geologist and mining engineer in that region. The Director of the U. S. Geological Survey and the Scate Geologist of Missouri have kindly consented to the publication of the present paper. While giving the more important economic results, an endeavor has been made to set forth the unity of plan which appears in the formation of the deposits of lead and zinc of the Mississippi basin, and to show their relation to the argentiferous ores of the Rocky Mountains—that the ores of gold, silver, and mercury, and also of copper, antimony, zinc, and lead, have a universal common origin, irrespective of the geological formations in which they occur.

Jan 1, 1894

By H. C. Spaulding

The rapid increase, during the last few years, in the number and magnitude of applications of electric power-transmission to commer cial uses in this country, has been due principally to three causes: first, the ability and enterprise of those who have been identified with the progress of electrical industries, since electric illumination became an economic fact instead of a laboratory-experiment: sec ondly, the readiness of the American people to adopt new and ad vanced methods as soon as their superiority has been fairly demon strated; and thirdly, tile economy and flexibility of the apparatus employed, when properly designed and constructed, and installed under suitable conditions. Basing our judgment on the world's advance in scientific devel opments during the past century, we may reasonably conclude that in no other country would the pioneeis of electrical invention, whose names have now become household words, have received the prompt and plentiful financial support which has enabled them to inaugurate undertakings of exceptional magnitude, even in this era of tremendous monetary organizations. And, on the other hand, we have seen, in the numerous financial and engineering failures inseparable from such rapid development, the natural results of a too implicit faith in electrical omnipotence. It is not to be wondered at that conservative engineers have been slow to adopt this new and mighty agent in the solution of exten sive problems, and under circumstances where a single failure means not only a greater or less financial sacrifice, but the loss, in a greater or less degree, of professional reputation. Be mechanical engineer, while recognizing the fact that thousands of horse-power are to-day transmitted by electrical means, from sunning the lathe in a dentist's office to the operation of a fifty-ton travelling crane; from passing a cooling draught of air through a

Jan 1, 1891

Jan 1, 1902

By George Sachs, S. M. Clark, George Espey

he tendency of a commercially drawn cartridge case to crack in the mercury test and the relation of cracking tendency to residual stress retained after drawing were studied. The fourth drawpiece (next to the final) of caliber 0.30 cartridge cases produced by Frankford Arsenal were selected as test pieces. These exhibited an exceptionally high cracking tendency, making a detailed study possible. To obtain fast cracking in the mercury test, about 0.0015 to 0.003 in. must be removed from the wall thickness of the drawpiece by pickling, and it must be subjected to the mercury test immediately after washing. Removal of the adhering mercury by annealing and subsequent squeezing of the case in a vise was used to reveal definitely the presence or absence of cracks. Various lots of apparently identically fabricated cases were shown to possess a different cracking tendency. Machining off or boring a hole in the base gradually reduced and eventually eliminated the cracking tendency. On the contrary, shortening of the wall (body) reduced the cracking tendency only if the wall became so short that the cracking zone was directly affected. By boring out the base and pickling from the outside and then splitting the resulting rings, it was possible to determine the approximate stress distribution in the base and in the adjacent part of the wall. Small compression stresses were present in the core and the major part of the base, while the surface of the base and the adjacent wall contained high circumferential tensile stresses. On the contrary, the wall when parted from the base contained only insignificant residual stress. The conception is advanced, that the stress distribution in a drawn cartridge case corresponds fundamentally to that of a tube (wall) shrunk on a disk (base). Such a stress distribution results from the tendency of the base to recover elastically by an increase in diameter from the biaxial compression during drawing while the wall exhibits little tendency to change its diameter after progressing through the die. This is confirmed by measurements which show the base diameter to be slightly larger than the wall diameter.

Jan 1, 1945

By M. Sheffield

This paper presents a technique lor predicting the flow of oil, gas and water through a petroleum reservoir. Gravitational, viscous arid capillary lorces are considered, and all fluids are considered to be slightly compressible. Some theoretical work concerning the fluid flow in one-, two- and three-space dimensions is given along with example performance predictions in one- and two-space dimensions. INTRODUCTION Since the introduction of high speed computing equipment, one of the goals of reservoir engineering research has been to develop more accurate methods of describing fluid movement through underground reservoirs. Various mathematical methods have been developed or used by reservoir engineers to predict reservoir performance, 193-5,7,8 The work reported in this paper extends previously published work on three-phase fluid flow (1) by including a rigorous treatment of capillary forces and (2) by showing certain theoretical mathematical results proving that these equations can be approximated by certain numerical techniques and that a unique solution exists. DISCUSSION The method of predicting three-phase compressible fluid flow. in a reservoir can be summarized briefly by the following steps. 1. The reservoir, or a section of a reservoir, is characterized by a series of mesh points with varying rock and fluid properties simulated at each mesh point. 2. Three partial differential equations are written to describe the movement at any point in the reservoir of each of the three compressible fluids. All forces influencing movement are considered in the equations. 3. At each mesh point, the partial differential equations are replaced by a system of analogous difference equations. 4. A numerical technique is used to solve the resulting system of difference equations. Capillary forces have been included in two-phase flow calculations.1,4,8 The literature, however, does not contain examples of prediction techniques for three-phase flow that include capillary forces. Where capillary forces are considered, each of the three partial differential equations previously discussed has a different dependent variable, namely pressure in one of the three fluid phases. Therefore, three difference equations must be solved at each point in the reservoir. Where large systems of equations must be solved simultaneously, an engineer might question whether a unique solution to this system of equations actually exists and, if so, what numerical techniques may be used to obtain a good approximation to the solution. It is shown in the Appendix that a unique solution to the three-phase flow problem, as formulated, always exists. It is also shown that several methods may be used to obtain a good approximation to the solution. The partial differential equations and differenceequations used are shown in the Appendix. Matrix notation has been used in developing the mathematical results. Two sample problems were solved on a CDC 1604. They illustrate the type of problems that can be solved using a three-phase prediction technique. SAMPLE ONE-DIMENSIONAL RESERVOIR PERFORMANCE PREDICTION A hypothetical reservoir was studied to provide an example of a one-dimensional problem that can be solved. Of the several techniques available, the direct method of solution as shown in the Appendix was used. The reservoir section studied was a truncated, wedge-shaped section, 2,400 ft long, with a 6' dip. (A schematic is shown in Fig. 1.) This section was represented by 49 mesh points, uniformly spaced at 50-ft intervals. The upper end of the wedge was 2 ft wide, and the lower end was 6 ft wide. The section

Jan 1, 1970

NORTH AMERICA. CANADA Canadian Army Overseas. Ball, H. D. Bridges. C. Butterill, H. J. If. Ladner, F. E. Lane, H. C. Alillar, W. A. ALBERTA Calgary.-Chonette, W. C. Clark, L. At. Corbett, C. S. de Hart, J. B. Dingman, C. W. Fath. A. E. Fulton. J. If. Cray, J. G. Johnson. R. V. McCutchin, J. A. *Slipper, S. E. Vin Buckirk H. A.

Jan 1, 1944

THE composition and quality of finished steel depend upon selection and proportioning of the raw materials of the charge as well as upon control of furnace practice. This chapter deals only with the raw materials of the basic open-hearth process that are important in determining the composition of the steel or slag. They are the metallic charge, oxygen-bearing materials, fluxes, alloying and deoxidizing additions, and certain refractory materials used for maintenance of bottoms. Other refractories, which may affect the slag composition, are discussed in Chapter 3. Wide variations are possible in the type and composition of charged materials but certain limiting relations among the elements of the charge must be observed. Since the process consists essentially of refining by the oxidation of undesired dements, a balance must be established between the sources of oxygen and the elements in the charge that are subject to oxidation (see Chapters 2 and 7). For example, if it is desired to use a high ratio of blast-furnace hot metal to scrap, it is necessary to add an oxygen-bearing material such as ore or mill scale to eliminate the excess carbon and silicon that are present in the hot metal. An example of the opposite extreme is the use of a metallic charge composed entirely of steel scrap. With this type of charge, it is common practice to substitute burnt lime for limestone as a flux and to charge some carbonaceous material such as coke to avoid an excess of oxygen in relation to the elements of the charge that are subject to oxidation. Elements such as copper and nickel, which are not oxidized or eliminated by, any other reaction, may be introduced into the charge only to the extent to which they are permissible in the finished steel. An example of adjustment of the charge for elements of this type is found in the use of steel scrap high in copper. In this case, metallic components of the charge other than the scrap should be low in copper, or a sufficiently high ratio of pig iron to scrap should be charged to dilute the copper from the

Jan 1, 1951

Jan 1, 1969

By Grover R. Castle

INTRODUCTION "Project Financing" or "Project Loans" have become increasingly popular in recent years, and commercial banks are being asked to consider more and more of such financing. However, the analysis of this type of loan is quite different from the analysis of a loan to a financially sound corporation based on the company's balance sheet. For this reason Chemical Bank did a study of project loans in an attempt to be more sophisticated in our approach to them. As part of this study, we examined 29 project financings for which information was available. In this article I shall describe project loans and set forth the guidelines we developed, as an aid to credit officers who might have occasion to analyse this type of financing. DEFINITION OF "PROJECT FINANCING" OR "PROJECT LOAN" The terms "project financing" and "project loan" commonly describe the various methods that banks and institutional lenders use to finance the construction of new projects on a basis whereby payout is anticipated from the revenue stream generated by the project. A project financing often involves a loan to a new entity formed specifically to own the project. The analysis of a project loan proposal is quite different from the analysis of other term-loan proposals since it involves a credit decision based on the review of a projection or forecast rather than of historical earnings and/or it involves the reliance on contractual obligations of third parties. Lenders are asked to assume the added risks associated with project loans because: 1. Project financing may permit a company to obtain additional leverage. It is possible for companies to arrange financing on a project basis that could not be arranged as a direct borrowing. For example, a company may not be permitted to borrow more money directly, due to a limitation in a bond indenture. However, a project financing can sometimes be negotiated on a basis not prohibited by the indenture. 2. Often the sponsors of, or the stockholders in, the project are seeking an off-balance-sheet financing. For example, 11 of the 29 projects in our study were arranged on an off-balance-sheet basis and one showed on the balance sheet as a deferred income item. An off-balance-sheet financing, for the purpose of this article, is a financing which does not show as a direct liability on the balance sheet of the sponsors of or stockholders in a project. 3. Projects are often located in a foreign country. The financing is arranged so that the lenders assume the political risk on the loan because many companies rightly believe that this arrangement affords a degree of insulation from political risk not otherwise obtainable. 4. Many projects are jointly owned by several sponsors. This form of financing lends itself well to a situation where a new entity is formed to own a project and do the borrowing. Project loans can be used to finance a variety of activities including development of iron-ore deposits and associated pelletizing plants; development of coal reserves; construction of pipelines, alumina plants, fertilizer plants and refineries; etc. The specific areas of analysis can be quite different, depending upon the type of project being financed. It is important, therefore, to classify the proposal according to the type of project, and also by the nature of the financing - nonrecourse financing, financing covered by a guarantee of completion and financing supported by an undertaking lasting for the life of the financing. I will discuss each of these types in more detail later, but first, I should like to make some

Jan 1, 1985

By A. Goldberg, T. E. Tietz, J. E. Dorn

INTRODUCTION THE concept that the flow stress for plastic deformation of metals in the work hardening range is a function of the instantaneous values of the strain, strain rate and test temperature was promulgated by Ludwick1 many years ago. This thought has been more or less a guiding principle throughout the immediate period of development and growth of mechanical metallurgy. It has been tacitly assumed or knowingly applied to many investigations on the plastic behavior of metals. Spurred by the theoretical interest and practical importance of the plastic behavior of metals, many investigators have attempted to determine empirical, semi-empirical, and theoretical equations2-18 relating the flow stress with the strain, strain rate, and temperature. Although the applications of such equations have been extensive, the experimental verification of the existence of a mechanical equation of state is weak. Furthermore, some of the available evidence on plastic flow appears to suggest that no simple functional relation between stress, strain-rate, strain and temperature can exist. The mechanical equation of state demands that [a = a(e, E, T)[I]] Where o = true stress = load/instantaneous area e = true strain = In Instantaneous gauge lengths initial gauge length e = true strain rate T = temperature] This formulation implies that [da] is an exact differential. Therefore the flow stress (o) is a function of the instantaneous values of the strain (e) the strain rate (e) and the temperature (T), independent of the previous mechanical or thermal history. Having reached a certain strain, strain rate, and temperature, by any path whatsoever, a definite and fixed value of the flow stress should be obtained. One check on the validity of the mechanical equation of state is easily obtained. Consider the following three tests on the stress-strain curve at constant temperature: [A. Strain at rate [ei] B. Strain at rate i2 C. Strain at rate [Ei] to [ei] and continue test at i2] A graphical representation of possible results of such tests are shown in Fig I. If, for strains greater than [el], test (C) data coincide exactly with the data from test (B), as shown in Fig Ia, a limited verification of the mechanical equation of state is obtained for the range of strain rates from [ii] to [e2]. But if the data from test (C) differ from those of (B) beyond strain [el] where the strain rate is changed from [e,] to [€2i] the mechanical equation of state is not

Jan 1, 1948

By Nicholas J. Grant, Oliver Preston

PUBLICATION of data by Irmann' indicating outstanding thermal stability and elevated-temperature strength properties in a sintered aluminum powder product (SAP) stimulated interest in the strengthening of metals by means of a highly dispersed oxide phase. This material was produced by compacting, sintering and extruding a fine flake aluminum powder, resulting in a dense product containing 10 to 16 volume pct alumina, which arises from the thin oxide film on the starting powder, highly dispersed in a matrix of pure aluminum. The method of producing SAP, and the stable high-temperature properties obtained from it, introduced the possibility of developing superior materials for high-temperature service by powder metallurgy methods. The composition of the materials of this type which are presently under consideration is predominantly metallic, containing from less than 1 pct up to about 20 volume pct of the oxide. As a result, other properties of these materials, such as electrical and thermal conductivity, thermal shock resistance, and to a certain extent ductility, notch sensitivity, machinability and hot working properties, are also predominantly metallic. These alloys do not constitute, therefore, a completely new class of materials as do the cermets, but rather present a new means of modifying the properties of a metallic matrix. In this sense, SAP type alloys are more closely analogous to the alloy aging systems. While the strength properties realized in the oxide-pure metal systems at the lower temperatures are substantially less than the best attainable in the aging systems, the thermal instabilities in the latter make them of less value for use at temperature much above their optimum aging temperatures, as indicated in Fig. 1. While the means of obtaining an oxide dispersion are more difficult and costly than conventional aging processes, in the light of the as yet limited understanding of such systems there is considerable promise of improved high temperature properties arising from the thermal stability of these structures. Since the development of SAP in 1946, its properties and the properties of a series of similarAl,O,-A1 products containing from about 1 to 20 pct aluminum oxide have been fairly extensively studied and reported.'- "articular attention has been given to

Jan 1, 1958

By W. H. Furlonge

WHILE fulfilling professional engagements, my travels over this portion of the Transvaal have been quite extensive—always on horseback however, so that anything like a thorough investigation of the ground passed over has been necessarily impossible; still, the more minute examination of certain small areas, coupled with general observations, has enabled me to form some idea as to the prominent geological features of the country as a whole. Anything like a complete or comprehensive description is indeed out of the question, as there are no proper maps of the country and the facilities for observation are limited. A large plateau, called the "High Veldt," stretches from east to west across the Transvaal. It is generally level, or gently rolling, and has an average elevation of 6000 feet above the sea; it is destitute of timber, and in fact greatly resembles the western prairies of North America. Rock-outcrops are not common in it. It terminates very abruptly to the east and northeast, the descent of 2000 or 3000 feet into the mountainous country that occupies its borders being made in a

Jan 1, 1890

By Wilhelm Borchers

In all special branches of the chemical and metallurgical industries, in which large electric furnaces became necessary for carrying out new processes or for the improvement of old ones, the development of the electric furnaces took place on much the same lines. The endeavors to make a success of a new idea brought forth many ingenious designs, which, however, almost without exception, furnished the proof that the safest and shortest way to practical success is the utmost simplicity of construction of the necessary apparatus. Our knowledge of the qualities of materials for building electric furnaces and of the constituents of the furnace-charges, especially their electric conductivity and their chemical affinity towards one another at high temperatures, is still far from being complete, and from this fact we must conclude that the smaller the number of elements in the construction of a furnace, the fewer the number of unreliable factors both in the construction and in the operation of the electric furnace. This conclusion deserves special attention when an electric furnace for making steel has to be chosen from the constantly-growing number of inventions, inasmuch as the chief constituent of steel, the element iron, is a substance which in its liquid phase has so great an affinity for those elemen'ts which are to be removed from the charge, that it is very difficult to comply with the following conditions: 1, to heat the refining-slag to the highest point of its chemical activity ; 2, to prevent the iron from entering the slag, or, where this cannot be done, to make it enter so that it finally appears in the end-product

Jan 1, 1911

By Andrew Hyslop

IN our never ending search for new and better ways of underground mining, we find that transportation has had its share of new ideas in the past few years. The old and still effective method of track haulage has had some competition from rubber tired cars and belt conveyors, each of which has its own safety hazards which demand close scrutiny in any safety study. The use of shuttle cars, in particular, has introduced clearance hazards caused by the absence of the more or less positive guides formed by the rails of a track sys¬tem; likewise the requirement of greater clearance tends to increase roof hazards which we all know to be great enough with the best of methods. However, the subject of transportation hazards is too broad to be covered entirely in one paper, so I will confine myself to track methods which carry the preponderance of underground tonnage. I am quite sure that to this group it is an evident fact that haulage accidents are of major importance. However, to stress the point, it may be well to look at a few figures. Safety statistics can be quite boring and often are subject to question as to mathematical accuracy because of different

Jan 1, 1948

By Chester Fulton

IN Polk County, Florida, the mining of raw phosphates began some 50 years ago with dredging operations on the Peace River, and in other near-by places by removal of shallow overburden with negroes and wheelbarrows, or with mules and scrapers, and the excavation and screen-ing of deposits found close to the surface. There were many individual operations of comparatively short life. Later steam shovels removed the overburden, and still later hydraulic methods were substituted for the steam shovel. Within the last 10 years large electrically operated drag-lines have almost entirely replaced hydraulic mining for overburden removal. The matrix is still mined by hydraulic giants and pumped to the washer or recovery plant. The many small operations have long since disappeared and the most desirable phosphate lands have gradually been acquired through purchase or merger by the seven companies that are operating in the field today. These companies are producing and selling about 2,000,000 long tons of phosphate per annum, or about two-thirds of what the industry likes to think is the normal output, with 1929 and 1930 in mind. To produce these 2,000,000 long tons of raw phosphate, they mine and treat about 1,000,000 tons of tailings from older and less efficient opera-tions, about 11,000,000 tons of matrix, and remove from above this matrix some 22,000,000 tons of overburden. The mining practice that has made possible the excavation and handling of 34 million tons of material to win but 2 million tons of merchantable product, selling for probably an average of only $4 per long ton when dried, should be of interest to the mining profession, though little has been written of it. The Florida Pebble Field, as it has come to be known, comprises an area (Fig. 1) within a radius of about 18 to 20 miles centering around Mulberry in Polk County, a small town 30 miles east of Tampa, Florida's largest port on the gulf coast.

Jan 1, 1936

By W. C. Roberts-Austin

The subject with which the Council of the American Institute of Mining Engineers has entrusted me is one of much interest. It has been so admirably treated in America by Prof. Carl Barus* that I should have hesitated to deal with it had not the adoption of pyrometric methods in England recently occupied much attention, especially in relation to metallurgical industries and research. I shall endeavor to show what is the present state of our knowledge of practical pyrometry by briefly tracing the history of the efforts which have been made to measure high temperatures. This paper will, therefore, be limited to the consideration of those forms of appliance which have either marked distinct stages of advance, or have remained in use with more or less modification through a considerable range of time. The earliest pyrometers were essentially thermoscopes, and although their graduation presented great difficulties, their importance as affording a means for the measurement of high temperatures has been recognized for centuries. It would be difficult to illustrate this better than by a brief record of the testimony which has from time to time been offered by those who have had to apply the heat of furnaces in research or in industry, and it is mainly for the sake of the light incidentally thrown on the progress of both that the following historical notes are offered. In the eighth century, Geber, the chemist, wrote a treatise on furnaces, and showed that he was familiar with many and varied means of applying heat; but he points to the difficulties that are met with in conducting operations at high temperatures, which he attributed to inability to measure heat, his actual words being: " sed quoniam non est res ignis, quae mensuari possit." t

Jan 1, 1894

By G. Y. Chin, M. T. Dolan, W. L. Mammel

In the case of plastic deformation by slip, von Mises&apos; showed that an arbitrary shape change of a crystal generally requires the activation of five independent slip systems. The selection of the five active systems was worked out by Taylor ,&apos; who hypothesized that, among all combinations of equivalent slip systems which are capable of accommodating a given imposed strain, the active combination is that one for which the sum of the absolute values of the glide shears is a minimum. Taylor analyzed the case of {lll}( 110) slip for fcc metals and applied the analysis to crystals undergoing axisymmetric flow, which approximates the shape change of an embedded grain in a polycrystalline aggregate deformed in tension (or compression). For the twelve equivalent (111) (110) slip systems, there are 384 independent combinations of five slip systems that satisfy the imposed strain.&apos; Taylor laboriously calculated the value of M = ZjIyj /E for each combination (although some were missed) and obtained the minimum M, hence the active combination, for a number of axial orientations distributed throughout the stereographic triangle. (yj is shear from slip on the th system and e is the tensile strain). Detailed contours of constant minimum M were recently obtained by Hosford and Backofen using a simplified but equivalent Bishop and ill&apos; analysis. Due to the numerous combinations of slip systems involved in the calculations, however, the full potential of the powerful Taylor analysis has not been exploited. For this reason, we have recently utilized techniques of linear programming to obtain solutions of the Taylor analysis for axisymmetric flow, for slip on {110)(< 111), {112)(111), and {123)(111) systems as well as mixed slip composed of these three systems. These slip modes are of obvious importance in the deformation of bcc crystals. Some of the salient results are summarized below. 1) Stress-Strain Data for Polycrystal. The value of M averaged over all axial orientations is the ratio of the tensile flow strength of a randomly oriented aggregate to the critical resolved shear stress for slip. This value enters importantly in theoretical deductions of the polycrystalline stress-strain curve from single-crystal data.2&apos;3&apos;5 Table I lists the values of Ma,, for the several cases of slip, as obtained by the present computer work. 2) Texture Hardening. Since the value of M depends on the axial orientation, the (tensile) flow strength of a specimen may be increased through texture control.&apos; An example of the computer results is shown in Fig. 1, where contours of minimum M have been computer-plotted for the case of mixed slip on {110}(111), {112)(111),and {123}(11 1) systems. It may be seen that, under axisymmetric flow, wires of (111) and (110) axial orientations are 50 pct stronger than those oriented at (100) .

Jan 1, 1968

Jan 1, 1970