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By Ralph H. Sweetser

AT the end of 1943 the charcoal pig iron capacity of the United States was at the lowest point in over 1110 years, with only one strictly charcoal blast furnace in operation, and all others permanently out of blast except one in Tennessee d reported to he running on part charcoal and part coke. Such a decrease in production has taken place in spite of the O.P A.'s high-premium price on charcoal pig iron of +34 per ton f.o.b. furnace in Michigan. Depletion of the hardwood supply within fifty mlles or inure of the blast furnace is the reason why; the deplorable lack of reforesting is the cause.

Jan 1, 1944

By Edwin B. Wilson, Charles F. Cockrell

The application of evolutionary operation is proposed for the cleaning of coal by the heavy media process. Analysis of the data given suggests some benefits that may not be immediately appreciated unless evolutionary operation is applied. For example, while it may seem obvious to increase specific gravity when the ash and sulfur content of the clean coal is lower than that allowed, evolutionary operation may show that an increase in feed rate or an increase in both feed rate and specific gravity would be a more profitable alternative. In addition, by using evolutionary operation, up-to-date knowledge of the effect of change of feed rate or specific gravity on yield and product quality is available. This information facilitates confidence about decisions made in regard to the day-to-day operation of these units. A number of other applications in the minerals industry are proposed. An application of evolutionary operation in a related field is also given where a large number of variables were required to be optimized.

Jan 1, 1969

By Charles Will Wright

ALTHOUGH the United States has long led all other countries in both the production and consumption of mineral products, the trend seems definitely toward an increasing dependence upon foreign sources of supply. This is not to take the position that we are either a have or a have-not nation. For years we shall continue to secure a large proportion of our needed minerals: from our own mines, but we must face the fact that this century has seen "a more thorough and intense development of the mineral resources of the United States and a greater depletion of its irreplaceable mineral reserves than has occurred in most other countries. An audit of our mineral production given in the attached charts discloses the extent of our deficiencies. Because of these facts, low-cost foreign sources offer a promising field for the investment of a portion of our mining capital and an opportunity to obtain for the United States a greater supply of strategic metals and minerals. How. ever, to reach this end, the industrialist investing in the foreign field must have the full co-operation and strong backing of the Federal Government and the involved Federal agencies.

Jan 1, 1947

By F. G. Miller

Earlier studies of the mechanism of flotation showed that coal flotation products are contaminated by composite coal and mineral particles. The mineral matter of these particles has the dual effect of increasing the specific gravity and decreasing the coal surface of the particle available for bubble attachment. The present study showed that these particles are more loosely held in the froth column than the high grade coal particles, especially in the coarser sizes. Consequently, it is possible in the laboratory to produce a secondary concentration of the product by sprinkling the froth product with water to wash these loosely held particles from the froth during formation and recovery. To improve coal flotation, Bethlehem Steel Corp.'s research department has been working on a number of related problems based on both physical and chemical factors. The ideal is of course full understanding of the interrelated effects of both sets of factors. However, detailed studies1 of each physical factor have produced immediately usable results in commercial coal flotation and are providing the basis for our current work on the effect of chemical factors. Since these detailed studies provided the basis for the present investigation of froth sprinkling, their key results are highlighted here. For example, for a highly floatable bituminous coal, particle floatability was shown to be directly related to the percentage of coal surface available for bubble attachment and inversely related to particle mass. The data also underscored that in a given size range the addition of mineral matter to a particle makes flotation more difficult both by adding to the mass of the particle and by decreasing the amount of coal surface available for bubble attachment. Size also affects particle floatability in that as the size of particles of a given specific gravity increases, mass increases and the ratio between coal surface area and mass of the particle decreases. Flotation tests showed that any recovery of the coarsest particles in a coal feed is accompanied by progressively higher recovery of finer and finer particles. Consequently, fine high-specific-gravity particles are recovered with the coarse good coal. As a result, when the entire 14 mesh x 0 size range is processed by froth flotation, the good coarse coal is contaminated with high-specific-gravity fines. It is the small quantities of these fines that must be rejected from the froth product if flotation efficiency is to be increased above its present level. These principles and findings, together with work by Professor V. I. Klassen,' led to the froth sprinkling investigation reported in this paper. Working with Russian coals, Klassen had shown that froth sprinkling washes loosely held refuse particles from the froth and compensates for the water lost in the upper froth layers and increases its stability. As a result, the coal particles are retained in the froth and the loss of coarse coal from the froth is prevented. Decreases in ash of 0.1% to 1.5% were reported by Klassen. Working with a 28 mesh x 0 American coal, the author of the present paper found that single-stage flotation coupled with froth sprinkling produced a product comparable to that obtained by the more expensive method of roughing and cleaning.3 The investigation reported in the present paper expanded study of the effect of froth sprinkling to include each of the standard size fractions of a bituminous coal. The main findings are as follows: (1) For those size fractions between 48 mesh and 150 mesh, froth sprinkling produces a marked reduction in both sulfur and ash. In the case of those sizes coarser than 48 mesh, while this reduction is not as significant, the additional benefit of shorter retention time is still a plus for froth sprinkling. Furthermore, when froth sprinkling is coupled with normal fast flotation, the product purity approaches that obtained by starvation reagent feeding, i.e., gradual feeding of flotation reagent to float the recoverable coal from the pulp slowly in several increments. The specific results for these two size groups are: (a) 14 x 48 Mesh. By using froth sprinkling with fast flotation, product sulfur can be reduced to a level

Jan 1, 1970

[Executive HENRY A. BUEHLER, Chairman ERLE V. DAVELER EDGAR RICHARD JOHN M. LOVEJOY WILLIAM WRAITH J. V. W. REYNDERS, Consultant Finance HENRY KRUMB, Chairman E. E. ELLIS PAUL D. MERICA H. G. MOULTON, Consultant]

Jan 1, 1936

By S. A. TAYLOR

THERE is probably no other mineral industry of which the public has as much information and misinformation as it has of the coal industry. Unfortunately, however, the general public's knowledge of the coal industry, outside of the particular kind of coal it is accustomed to, by reason of use, is largely made up of information received from newspaper and popular magazine articles, in which the mine workers are depicted as overworked and mistreated men, and the coal operators as "coal barons." Those who have any specific knowledge of exact conditions in the coal industry know how unjust and un- fair such an opinion of the coal industry is, not only to the miner but to the operator as well. Many reporters and writers of magazine articles are misled by statements regarding the condition of the miners that are exaggerated and not founded on facts and, if an investigation of the conditions of the miner's work, his habitation and surroundings were fairly made, it would at least compel more truthful statements by those who write for public reading. That such an investigation would not reveal anything that was wrong, or anything to be censured or cured, no one, I think, would maintain, but I do think that any fair investigation of the facts would show that conditions in and around the newer and later-developed coal mines and communities would compare favorably with those of manufacturing districts, and that where the mines and com- munities are old and not very attractive places to work, or live in, they carry with them other considerations, compensating for these conditions, and cannot be remedied by reason of a lack of sufficient coal to warrant economically any costly changes.

Jan 1, 1926

By AIME AIME

ON MAY 22 the American Institute of Mining and Metallurgical Engineers will commemorate the sixtieth anniversary of its founding at Wilkes- Barre, Pa., in May, 1871. The Directors have transferred the May meeting of the Board to Wilkes-Barre, and the Pennsylvania Anthracite Section has invited as many members of the Institute as can to be present at this time and to join with their fellow-engineers at Wilkes-Barre in the inspection trip through a portion of the anthracite district that has been planned. Ac- cess to Wilkes-Barre is easy, from nearby points, over excellent automobile roads, or by train. The distance from New York is only about 140 miles. , It is hoped to engage a special car for those travelling by train from New York, which will leave the Pennsylvania Station over the Lehigh Valley Railroad at 11:50 p.m., arriving in Wilkes-Barre the next morning. Return can be made from Wilkes-Barre by sleeper the same evening, arriving in New York Saturday morning. Other trains are available for those who prefer a daylight journey.

Jan 1, 1931

By L. C. Snider

All important industries have certain basic principles in common which govern them and give them a family resemblance. In addition, each industry has a certain individuality due to some principle or principles which govern, or are accepted as governing, that industry and which is not effective in others. The customs and practices of an industry depend on these basic principles much as the corollaries follow a proposition in geometry. After the proposition is proved or is accepted as proved, the corollaries are seen to be true almost without additional evidence or proof. In many cases, the corollaries are more important in practical affairs than the proposition on which they depend. By continued application the corollaries may come to be accepted as law and the fact that their truth depends on the correctness of the fundamental proposition is forgotten or ignored. If it is discovered that an error was made in demonstrating the proposition and that the proposition is untrue, the corollaries are, in most cases at least, equally untrue. Considerable time may be required, however, to realize the fact that the corollaries have failed, particularly if they have been embodied in custom and law. For example, in the business of government the proposition that women are intellectually inferior to men was formerly considered, by most men at least, to be duly proved if not axiomatic. This propositiot was never embodied in law, but its corollaries—that the rights of the wife in property and even in her own children were inferior to the rights of the husband, and that women had no place in governmental affairs—were duly incorporated in law or so completely approved by custom that they had the effect of law. Developments of the past few decades have proved, to the satisfaction of the majority, that woman's intellectual inferiority to man had not been satisfactorily demonstrated, and that the proposition that she was inferior, although accepted for many generations, was untrue. It was not so great a shock to men to discover that this proposition was wrong as it was to find out that its corollaries were also untrue and that the laws embodying them were not good laws and were subject to repeal. The adjustments which give women equal rights with men

Jan 1, 1932

By E. W. Parker

THE anthracite region, from which there is produced annually about 80,000,000 tons, or approximately 15 per cent. of the total coal supply of the United States, has a combined area of a little less than 500 sq. mi. The total area occupied by the bituminous fields (including the sub-bituminous and lignite fields) is in the neighborhood of 400,000 sq. mi., so that 15 per cent. of the total output comes from this small area of only a little more than 0.1 per cent. of the coal-producing territory. of the United States. The productive anthracite area is divided into a series of basins or troughs, roughly parallel, extending. in a northeast-southwest direction through the. Counties

Jan 1, 1921

By PDF

C. 0. FAIRCHILD, Washington, D. C. (written discussion*).-Referring to the paragraph entitled "Effect of change in temperature of absorbing glass on its transmission," Dr. Foote and the writer have been using, since

Jan 11, 1919

WILLIAM YOUNG WESTERVELT, Chairman, Representing A. T. M. E. and M. and M. Soc. of Am. ALFRED G. WHITE, Secretary, Representing U. S. Bureau of Mines. W. 0. HOTCHKISS, Representing Association of American State Geologists. DAVID WHITE, Representing U. S. Geological Survey. The organization and purpose of the War Minerals Committee was explained in a special war notice in the-August Bulletin. The first work of this Committee is to secure and condense information as to the relative importance of different properties from the standpoint of domestic mineral production. When the possibilities of ore deposits are known, involving, in some cases, further examination through the voluntary services of, Engineers and Geologists, then the necessary policy required to stimulate such development can be determined. Proper recommendation has been and will be made to .the various agencies controlling the situation during the war. This will insure a complete presentation of the needs of the situation. Every legitimate effort will be made to stimulate the production of domestic minerals and to put the industries on a permanent basis. The following information forms indicate the type of information required by the Committee. Engineers and Geologists can assist in one of several ways in furnishing information to the War Minerals Committee:

Jan 10, 1917

By G. T. Higgins

PREVIOUS workers1,2 have found evidence of exaggerated grain growth or secondary recrystallization on annealing sponge zirconium at temperatures high in the a, phase field, but no details of the orientation relationship between the secondary grains and "as-recrystallized" matrix were reported. In other hexagonal metals, namely dilute Mg-A13 and Cd-zn4 alloys, secondary recrystallization has been observed in which the secondary grains are related to the primary recrystallized structure by rotations about the c axis. These rotations are thus comparable with the rotations about the (111) axis observed in the secondary recrystallization of fcc metals. In the current work secondary recrystallization has been observed on annealing iodide zirconium at 800°C and the associated changes in crystallographic texture have been examined. The material employed was arc-melted iodide zirconium of the following composition: Impurity O H Fe Hf Pb I Ni C1 A1 ppm by wt 130 5 230 98 23 28 200 39 30 This was received as 0.25-in. plate, and, prior to the annealing studies, was cold-rolled to 0.040 in. Specimens 1 in. sq were chemically polished and annealed for various times at 800°C in a vacuum better than 5x 10-6 Torr. For metallographic examination specimens were first chemically polished and then anodized8 to enhance contrast between the grains when examined under polarized light. Changes in crystallographic orientation associated with the development of secondary grains were followed by (1011) and (0002) pole-figure determinations using a conventional Schulz goniometer in reflection. Filtered Cr Ka radiation was employed and great care was taken to avoid spurious re- sults due to the close proximity of the Bragg angles for the (1011) and (0002) reflections. Figs. 1 and 2 illustrate the change in grain structure on annealing at 800°C. After 24 hr the structure has ceased to be equiaxed due to the development of certain grains in preference to others. It is notable that the secondary grains do not grow to the extent observed in sponge zirconium.1,2 This appears to be due in part to the fact that normal grain growth is inhibited in the less pure sponge zirconium, with the result that the driving force for secondary recrystallization remains high, while at the same time the number of grains able to develop in the presence of the impurities is also smaller. As a consequence, in sponge zirconium those grains that do develop preferentially are able to grow into the fine -grained matrix without impingement, while in iodide zirconium the preferential growth of many grains leads to early impingement. The pole figures determined for specimens annealed for 5 min and 24 hr at 800°C are illustrated respectively in Figs. 3 and 4. These indicate that the dominant feature of the initial recrystallized texture consists of basal planes at an angle of 321/2 deg to the sheet surface, with a (1120) axis lying parallel to the

Jan 1, 1967

No. 526.-At liberty about Mar. 1, 1919. Just returned from France, a Captain of Engineers. Member A. I. M. E., A. I. E. E., 35 years old, technical education. Last six years of civil life as electrical engineer, master mechanic and superintendent of construction with large mining company. Salary expected, $3600 per year. No. 535.-Member, 'mining engineer, technical graduate, age 34 years, experience as engineer for coal companies. Three and one-half years with one company and five years with another. Have good recommendations. Recently honorably discharged, First Lieutenant, U. S. Army. Desires position, preferably in West. Salary last received, $175 per month. No. 555.-Metallurgical engineer having 18 years' experience in positions from chemist to manager, specializing in the smelting of copper, gold and silver ores, and now returning to the U. S. Available about May 15. No. 556.-Manager or superintendent, member, technical graduate, age 44, married, desires position. Good references, 18 years' experience in positions of responsibility and administration. Familiar with development, mining, milling, operation, construction and management. Available on short notice. , No. 557.-Member, technical education, married, age 30. Five. years' experience in construction work, four years superintendent of mining and milling operations. Looking for wider experience. Free Apr. 1.

Jan 4, 1919

By A. J. Griest, P. D. Frost, H. A. Robinson

The flow characteristics and uniform elongation of alpha-beta titanium alloys in the solution-treated condition were shown to be markedly affected by the solution temperature. Two classes of alpha-beta alloys were distinguished, based on the effect of solution temperature on the uniform elongation. Martensitic alpha-beta alloys, which are relatively weakly beta-stabilized, showed decreasing values of uniform elongation as the solution temperature was initially increased. However, after solution-treatment at still higher temperatures in the alpha-beta field, the uniform elongation of these alloys was again high, and often attained its maximum value. Nonmartensitic alpha-beta alloys, which are more heavily beta-stabilized, showed a continuous decrease of uniform elongation with increasing solution temperature. The behavior was rationalized in terms of the alpha-beta ratio and the alloy content of the beta existing at the solution temperature. The data indicate that in commercial practice close temperature control may be required to get maximum uniform elongotion, and hence, maximum potential formability, in solution-treated sheet. Bend-test data also were obtained for the solution-treated conditions. A MOST important objective of current titanium research is the development of age-hardenable alloys with superior formability in the solution -treated condition. Alpha-beta titanium alloys have been shown to be amenable to high-strength aging treatments after solution-treatment in the alpha-beta field.' However, heat-treatment data on the properties of solution-treated sheet, such as uniform elongation, minimum bend radius, and flow properties, which have a bearing on the potential formability, have not been widely available. This paper presents only the most significant results of a research program conducted at Battelle for the Air Force in an effort to develop sheet alloys that can be formed readily as solution-treated and subsequently aged to very high strengths. Data for 10 compositions representative of the more than 25 alloys studied in this program are presented. A primary objective of the paper is to demonstrate the pronounced dependence of the flow characteristics and uniform elongation on solution-treatment temperature. This effect is believed to be vitally important in the commercial heat-treatment of age-hardenable titanium sheet alloys. Experimental Procedures Melting and Fabrication—The nominal and actual compositions, beta transi temperatures, and rolling temperatures of 10 of the 30 alloys studied are presented in Table I. Stock :€or two of the alloys, E (Ti- 8Mn) and J (Ti-6A1-4V) was obtained from commercial heats. The remaining heats, except D and I, were double melted as 10-lb heats in a consumable-electrode furnace. Melting stock was 120 Brine11 hardness sponge. The oxygen and hydrogen analyses spotted throughout the heats indicate the range of interstitial levels resulting from the melting practice used. Heats D and I were melted as 20-lb ingots with the same grade of sponge. These ingots were cut in half and one portion used in the present evaluation. The ingots, which were about 4 in. diam and 4 in. in height, were upset forged and drawn at 1750°F to sheet bar 5/8 in. thick by 2 1/2 in. wide in such a manner that the top of the ingot corresponded to the top of the sheet bar. Slabs of the sheet bar, 5 1/2 in. in length were scalped to 1/2 in. thickness and rolled at the temperatures indicated in Table I to approximately 0.055 in. sheet. Elongation during rolling took place at 90" to the original forged length. The fabrication procedure used is described in some detail since the experimental heats showed considerable directionality in mechanical properties. The rolling procedures for the commercial heats were unknown, but were such as to produce essentially isotropic properties. All heats, as rolled, showed microstructures typical of alpha-beta alloys worked in the alpha-beta field; that is, the structures consisted of equiaxed alpha particles in a beta matrix. Heat Treatment— The effects of solution and aging heat-treatments on the properties of the alloys were evaluated uSing longitudinal and transverse tensile and bend coupons sheared from the sheet. Two or three solution-treated conditions were evaluated for each alloy. In addition, the alloys were also tested after annealing at 1200°F for 4 hr and furnace cooling. The solution-treated and annealed conditions were those in which the alloys might be expected to

Jan 1, 1959

[A Aamodt, H. C., A55 C Sales, Great Lakes Carbon Corp., 18 E. 48th St., New York, N.Y. Aamot, Olav Crone, M29 2126 M4, Galveston, Texas Aaronson, Hubert I., M47 E Prin Res Engr, Ford Motor Co., Met. Dept., Sci. Lab., Engrg. Staff, P. O. Box 2053, Dearborn, Mich. Aase, Glenn D., M54 D Prin Engr, Air Pollution Control Dist., 1480 Mission St., San Francisco 3, Calif. Abbett, W. A., Jr., M56 8629 Beverly St., Duluth 8, Minn. Abbey, Robert G., M56 138 Dartmouth Rd., Bala Cynwyd, Pa. Abbott, A. G., Jr., J52 E Test, Dev Engr, Chrysler Corp. Missile Div., P. O. Box 2628, Detroit 31, Mich. Abbott, Mark L., A58 Rep, General Refractories Co., 208 S. LaSalle St., Chicago, Ill. Abbott, W. K., J58 E Dev Met, Int'l Nickel Co., Inc., 67 Wall St., New York 5, N.Y.]

Jan 1, 1961

By S. F. Willey

Difficulties encountered in justifying replacements for overage mobile mine equipment at the Gay mine are common to most mining operations. More critical management reviews, resulting from ever rising capital expenses, increased such difficulties. These increased difficulties are especially apparent to those who are primarily operators and are not statisticians, mathematicians or computer men. The Gay mine is located 17 mi east of the town of Fort Hall in southern Idaho. This open pit operation annually supplies the J. R. Simplot Co. and the FMC Corp. with 1.5-2.0 million tons of phosphate ore. Stripping ratios average approximately three bank cubic yards of waste per ton of ore mined. The mobile mine equipment fleet consists of ten 24-cu yd scrapers; twenty-one 30-50-ton end-dump trucks; four 3%-4%- cu yd shovels; fifteen dozers in the D-8 and D-9 classes; and three road patrols. Equipment replacement is based on the results of evaluations made on individual units.

Jan 9, 1972

By J. P. Dunlop

THE fact is-notable though probably little known that the United States is the only nation obtaining and distributing through its Government bureaus any data pertaining to waste metals and drosses. Some foreign governments do issue reports relating to mine or smelter production of primary metals, but none gives in scope and detail the information published now by the U. S. Bureau of Mines and formerly by the U. S. Geological Survey; and this is despite the fact that the funds annually allotted for those purposes are insignificant in comparison with allotments for the preparation of data relating to other industries of like importance. The earliest data on the production of metals from secondary sources in the United States were contained in a press bulletin issued by the U. S. Geological Survey on Jan. 4, 1909. The information published was that for the year 1907 obtained and compiled by C. E. Siebenthal, who was one of the first to visualize the growing importance of the scrap-metal industry. The National Conservation Commission had emphasized its opinion that the known domestic supply of certain kinds of the more important metals was being rapidly marketed and that while there was no immediate cause for concern it was best to conserve such resources. Not only had there. been a lamentable lack of any data regarding the quantity of scrap metals available or used but also gross carelessness and indifference in the segregation, collection, and effective use of scrap material. Siebenthal realized that even approximately correct statistics of recoveries from the more important base-metal scrap and drosses were nearly as essential to both producers and consumers as the statistics of the output of primary metals. There were not then nor are there now sufficient funds for complete collection of data, nor was it considered the province of the Geological Survey to do more than determine approximately the recovery of secondary metals for use in supplementing those given for the primary metals. Undoubtedly the first bulletins-issued did not give the full output, for it takes time to establish contacts for an inquiry covering so

Jan 1, 1928

During the past year the Committee on Coal and Coke has been collecting data concerning various phases of the bituminous industry about which considerable misinformation has been circulated even, in some cases, through the coal trade papers. The data here presented have been compiled by various members, from the most authentic sources available and, where possible, cover the period 1913-1924. They will enable comparisons to be made within the industry, and of this and other industries, and will explain some of the differences between conditions existing now and in the prewar period. Capacity and Over-development The capacity of bituminous mines is frequently stated at figures ranging between 800,000,000 to 1,400,000,000 tons per year. Table 1 shows statistics for the industry, mainly from U. S. Geological Survey sources but partly from U. S. Coal Commission reports. Column 3 gives the mine capacity with equipment and labor as of given date, as estimated from the data published by the U. S. Geological Survey. This is calculated for each State by obtaining the total man days worked as reported by the operators (multiplying average men employed by total days worked at each mine) and dividing this figure into the total production, getting the production per man day; this figure times number of men employed times 308 (a theoretical full working year) equals estimated full-time capacity. Two major objections are made to this method—one that the total number of men employed is used, instead of the number actually working, and the other that the number of days used only deducts Sundays and five holidays. The first objection is answered by the fact that the same number of men is used in estimating capacity as is used in actual production, and while this number is always from 12 to 20 per cent. more than are actually working, this condition exists at all times, although it is worse at times of maximum output. Few coal men will agree with the conclusion that the use of 308 days is correct, as it is practically impossible to keep any mine working full time at the same daily rate of production as when it is working part time, and the opinion is

Jan 1, 1927

By J. P. Martin, A. H. Geisler, J. H. Crede, E. Both

The investigation of a 50 pct Co alloy was undertaken to determine whether there was any direct correlation between the structure and properties of Co-Fe alloys which were given various magnetic heat treatments. The magnetic anisotropy and texture of the 0.002-in. cold-reduced 98 pct material tend to decrease and change in nature with increasing temperature of the recrystallization anneal. Annealing samples in a magnetic field had little effect on either the magnetic properties or texture. However, cooling them in a magnetic field greatly improved their magnetic properties. THE beneficial influence of a magnetic field applied during the heat treatment of certain soft magnetic materials has been known for a long time. Early work showed that the presence of a magnetic field of a few oersteds during the heat treatment of Fe-Ni alloys will cause a large increase in maximum permeability. A pronounced increase in the residual induction which is produced by the magnetic anneal causes the hysteresis loop to approach the shape of a rectangle. Such results are beneficial since the desired properties are high permeability, high induction at maximum permeability, high residual induction, and low coercive force. More recently Libsch and coworkers1 studied the effect of magnetic annealing on the hysteresis properties of a series of Co-Fe alloys prepared from powders. They observed good response for the 35 and 50 pct Co alloys but little response for the 42 pct Co alloy. They pointed out that this was somewhat surprising since the 42 pct alloy has a high linear magnetostriction and zero crystal anisotropy and similar conditions in Fe-Ni alloys give excellent response to magnetic annealing. They found optimum properties to be at the 50 pct composition with residual induction, Br = 19,000 gauss and coercive force, Hc = 0.68 oersteds after the magnetic anneal. Before the magnetic anneal these values were B, = 12,600 gauss and Hc = 1.15 oersteds. The optimum treatment consisted of cooling from above the y-a transformation temperature to 900°C in a field of 20 oersteds, holding 11/2 hr at 900°C, then cooling at a rate of 20° to 25°C per min in the field to below 230°C. Cooling rate mainly affected coercive force with the value decreasing from 1.09 to 0.88 oersteds as the rate was increased from 3° to 48°C per min. Cooling from 1020" to 900°C in a field followed by further cooling to 230°C without the field gave properties decidedly inferior to those for samples annealed with the field applied throughout the cooling. They concluded that to get the best properties the samples must be cooled in a field to a threshold temperature above which the alloy is plastic enough to be affected by magnetostriction. In this respect the holding temperature must be high enough so that the alloy exhibits good plasticity to permit the optimum orienting of magnetic domains by relaxation of magnetostriction. In contrast, the holding time was of less significance for there was little improvement when the time exceeded 1/2 hr. The improvement in properties effected by magnetic annealing has usually been attributed to the establishment of a domain texture caused by the "freezing in" of magnetic strains. On the other hand, Smoluchowski and Turner2,3 apparently found that a magnetic field applied during recrystallization could alter the crystal texture. If this effect is real, improved properties would also be expected when

Jan 1, 1954

By L. G. Austin, R. R. Klimpel

This article demonstrates that the Gilvarry and Klimpel-Austin equations for the random fracture of solids are incorrect by deriving intuitively correct expressions for simple cases and showing that the foregoing equations do not reduce to right answers. It is the purpose of this article to point out serious errors in some existing treatments of the random fracture of solids. Gilvarry ' gives the equation where B(y,x) is the cumulative fraction by weight of particles which fall below size y when particles of size x are broken. The constants i, j, k contain shape factors and densities of flaws leading to propagating fracture surfaces. The authors believe this equation to be incorrect. Klimpel and usttin' give where r~ is the number of fracture planes originating from edge flaws (per L where L is the edge length of the original particle), rs is the number of fracture planes originating from flaws on the particle surface (per S where S is the surface of the original particle) and rv is the number of fracture planes originating from flaws within the particle volume. This equation is also incorrect. The failures of these equations will be demonstrated by deriving intuitively correct expressions for simple cases and showing that the Eqs. 1 and 2 do not reduce to the correct answer. In this process, the flaws in statistical reasoning inherent in the derivations of Eqs. 1 and 2 become apparent. THE KLIMPEL-AUSTIN EQUATION Eq. 2 was derived by considering a set number of fracture planes occurring spatially at random within a given particle. This case will be treated here in its simplest form: a line with 1, 2, 3, etc., fractures occurring at random. This is illustrated in Fig. 1, with the original length of the line as Vo. The breakage of a long, thin, brittle fiber is a corresponding physical case, with the volume of a fragment proportional to its length. Assuming independence of the occurrence of the fractures, the probability of any one fracture occurring in length dV is dV/V0. The probability of the first fracture occurring at a length V to V + dV is dV/Vo. For the case of only one fracture per particle, formation of a number-size distribution of the left-

Jan 1, 1969