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By J. E. Burke, C. W. Mason

In attempting to study precipitation from a tetragonal lattice, using solid solutione of bismuth in tin, it was found that although a Widmanstätten pattern is observed1,4 only a qualitative analysis of the orientation relationships is possible, because of the unusual structural changes that accompany the precipitation process. Microscopical Studies Alloys were made from Chempur tin (Standard samples 42b and 426, National Bureau of Standards), and bismuth (Kahl-baum C.P.) by melting weighed quantities together under palm oil, stirring well, and castilig in a heated graphite mold. The polishing and etching techniques employed largely govern the visibility of the structural changes. The preliminary surfacing operations were similar to those recommended by Villela and Bergekoff,5 through Behr-Manning 3/0 abrasive papers, lubricated by a solution of paraffin in kerosene. A rough metallographic polish was next given, using a thin cotton cloth charged with relevigated alumina (maximum particle size of about 4µ) and soap solution; repeated etching and polishing served to remove disturbed metal. For high-power examination better preparation was necessary. It was found that on such soft metals the threads of the fabric, rather than the abrasive, cause most of the scratching. Cotton outing flannel, which had been brushed so that the nap lay down, was fairly satisfactory, but a heavy grade of silk velvet (not the noncrushable kind) was found to be better, especially after some use. A better procedure was as follows: The metal lap was warmed slightly, and a 4-in. circle of woolen broadcloth was cemented to its center by a thin film of melted paraffin. The broadcloth was then moistened with water, and a 30 to 40 per cent solution of sodium hydroxide heated to about 50°C. was poured over it, allowed to stand for I to 2 min. and then washed off. It was neither necessary nor desirable to remove all the sodium hydroxide from the cloth, since its etching action aided in the removal of the flowed layer from the sample. The cloth was then charged with a paste of the relevigated alumina in water. Since this lap did not remove deep scratches, it was necessary previously to polish the specimen on some material such as the silk velvet. The sodium hydroxide softens and partly gelatinizes the woolen lap covering, permitting a scratch-free polish, but its action continues, and the cloth deterioratcs after about 24 hr. This is not serious, because a new lap can be prepared in about 5 min., and only small pieces of cloth are used. Etching with a strongly acid solution of ferric chloride was found satisfactory for removing the flowed layer. For the final etching, the most satisfactory reagent was that of Tafls,7 the formula for which is: FeC13.6H2O, 2 grams; HC1, 5 c.c.; H2O, 30 c.c.; C2H5OH (95 per cent), 60 C.C. This etchant reveals differences in com-

Jan 1, 1942

By J. E. Burke, C. W. Mason

In attempting to study precipitation from a tetragonal lattice, using solid solutione of bismuth in tin, it was found that although a Widmanstätten pattern is observed1,4 only a qualitative analysis of the orientation relationships is possible, because of the unusual structural changes that accompany the precipitation process. Microscopical Studies Alloys were made from Chempur tin (Standard samples 42b and 426, National Bureau of Standards), and bismuth (Kahl-baum C.P.) by melting weighed quantities together under palm oil, stirring well, and castilig in a heated graphite mold. The polishing and etching techniques employed largely govern the visibility of the structural changes. The preliminary surfacing operations were similar to those recommended by Villela and Bergekoff,5 through Behr-Manning 3/0 abrasive papers, lubricated by a solution of paraffin in kerosene. A rough metallographic polish was next given, using a thin cotton cloth charged with relevigated alumina (maximum particle size of about 4µ) and soap solution; repeated etching and polishing served to remove disturbed metal. For high-power examination better preparation was necessary. It was found that on such soft metals the threads of the fabric, rather than the abrasive, cause most of the scratching. Cotton outing flannel, which had been brushed so that the nap lay down, was fairly satisfactory, but a heavy grade of silk velvet (not the noncrushable kind) was found to be better, especially after some use. A better procedure was as follows: The metal lap was warmed slightly, and a 4-in. circle of woolen broadcloth was cemented to its center by a thin film of melted paraffin. The broadcloth was then moistened with water, and a 30 to 40 per cent solution of sodium hydroxide heated to about 50°C. was poured over it, allowed to stand for I to 2 min. and then washed off. It was neither necessary nor desirable to remove all the sodium hydroxide from the cloth, since its etching action aided in the removal of the flowed layer from the sample. The cloth was then charged with a paste of the relevigated alumina in water. Since this lap did not remove deep scratches, it was necessary previously to polish the specimen on some material such as the silk velvet. The sodium hydroxide softens and partly gelatinizes the woolen lap covering, permitting a scratch-free polish, but its action continues, and the cloth deterioratcs after about 24 hr. This is not serious, because a new lap can be prepared in about 5 min., and only small pieces of cloth are used. Etching with a strongly acid solution of ferric chloride was found satisfactory for removing the flowed layer. For the final etching, the most satisfactory reagent was that of Tafls,7 the formula for which is: FeC13.6H2O, 2 grams; HC1, 5 c.c.; H2O, 30 c.c.; C2H5OH (95 per cent), 60 C.C. This etchant reveals differences in com-

Jan 1, 1942

By J. K. Furst

The reasons for manufacturing steel by the deplex process are, briefly…

Jan 1, 1915

By Richard A. Arnold

The evolution of planning processes in the United States from the early 1900's is briefly examined. From one year operating budgets, planning processes have evolved into sophisticated analyses of alternative long-term future strategies and the management issues and practices which relate to their implementation. Increasing complexity within the business environment has led to numerous planning methodologies and extensive use of computers to analyze operating and financial information. All of these developments, however, have not supplanted the real need for decision-makers to continue to give important weight to the intuitive or soft data inputs into the planning process.

Jan 1, 1985

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

This communication points out that serious errors exist in some current treatments of the random fracture of solids, including the prior treatments by Klimpel and Austin, Gilvarry, and Gaudin and Meloy. The problem considered in all of these papers is: what cumulative weight versus size distribution is expected for the fragments produced by fracture of a particle? The basic assumption made is that fracture surfaces propagate in random directions from weak flaws in the solid (these weak flaws being activated to fracture by applied stress), with the activated weak flaws distributed at random spatially within the solid. The previous treatments considered fracture in three dimensions, and all use similar physical models, although the mathematical techniques were somewhat different. We first noticed that these treatments were in error when we attempted to reduce the equations developed to the simple case of fracture of a one-dimensional particle, e.g. a long, thin fiber which breaks along its length. For this simple case, it is readily shown that the assumption of random fracture leads to the expression P(V) = (r/Vo) (1-V/Vo) r-1 dV (1) is the probability of occurrence of a fragment of length within the range V to V + dV; V being length dimension, from r random fractures passing through an original size of Vo to produce r + 1 fragments. This equation agreed with the one-dimensional form of an equivalent equation in the original Klimpel-Austin treatment. However, in this treatment it was then stated that, "The fractional weight below size V is [ ]

Jan 8, 1968

By N. K. Chen, C. H. Mathewson

Recrystallization of aluminum single crystals after plastic extension is carefully studied in relation to the structure of the deformed matrix. The shapes of the new grains are analyzed with regard to slip planes and to the presence or absence of deformation bands. A mechanism by which the orientations of the grains are related to the parent lattice is described. EXPERIMENTS previously reported&apos; have been extended to develop some of the characteristics of the new crystals which are formed on annealing axially strained crystals whose deformational characteristics had been documented with special care. Thus, the presence of deformation bands affects the growth contours of the crystals, some of the strained crystals produced single crystals anew, and some, polycrystals, on annealing, while others merely "recovered" or "polygonalized" after the 600°C annealing treatment generally adopted in these tests. In the matter of orientational relationships between new crystals and the strained matrix, the present experiments have added little to previous experience, which had demonstrated great variety in the range of orientations encountered and no simple theory or correlation. For example, there has been ample evidence for the predominance in various face-centered cubic metals of a favored orientational relationship; viz., a rotation of 30° to 40° around a <1ll> axis, between grains growing in a matrix with a strong single orientation texture and the matrix itself.&apos;-&apos; This reorientation has been interpreted by various investigators in support of both the "oriented nucleation" and the "oriented growth" hypothesis. In the case of axially extended single crystals of aluminum, no general relationship, such as the one stated above, can be used to correlate the orientations of the recrystallized grains with that of the original crystal. Thus, Carpenter and Elama and Burgers and Basart7 were content to assume that the orientational relationships so developed were random in nature. Mathewson, however, in the Campbell Lecture of 1943 "rgued on the basis of <112> slip that a complex strain, chiefly characterized by rotation around a variable axis in the slip plane combined with a principal rotation around the pole of the slip plane, could be responsible for such devious relationships. Nevertheless, owing to the limited data now available dealing with orientational relationships between new grains and the single crystals strained in tension from which they have recrystallized, no adequate examination of the above generalization could be made. Here, there is the disturbing preliminary condition that any desired orientational relationship may be expressed by means of two rotations about mutually perpendicular axes, so the process lacks a certain critical flavor and any successful choice of axes meeting certain theoretical requirements could be replaced by another differently selected pair. With this reservation clearly in mind the process of double rotations, as previously indicated, was used to relate the orientations of the single crystals which grew out of the strained single crystalline matrix and was construed as certain evidence in favor of the theory of incongruent shearing action proposed by Mathewsons as a necessary element in the (111) slip process with close-packed metals. There is here

Jan 1, 1953

By Ross W. Smith, Nikhil Trivedi

The variation of point of zero charge (PZC) of both simple and complex oxide minerals was studied as a function of aging time in water. In most cases the PZC&apos;s of the simple oxides moved toward more basic pH values with aging time. Evidence to date suggests that this phenomenon relates to dissolution of disturbed layers on the mineral&apos;s surface accompanied by later readsorption of metal hydroxy species back onto these surfaces. The readsorption takes place after the solution becomes supersaturated with respect to some crystalline phase. The variation of PZC&apos;s of complex oxides as a function of aging time in water is apparently related to several different mechanisms. In a few cases PZC shifted toward more basic values with time. This shift could be attributed to much the same mechanism as for simple oxides. In most cases, however, PZC of complex oxides shifted toward more acid values with aging time, probably because of loss to solution of soluble cations whose oxides possess basic PZC&apos;s.

Jan 1, 1975

By Hans Lundberg

IN last year&apos;s report on the progress of geophysics, the airborne magnetometer was the featured new development. At that time only a relatively small number of surveys had been made. During 1947, the airborne magnetometer was used in making many surveys and is again one of the high lights of the year in geophysics. This report is mainly concerned with geophysics as applied to the search for minerals exclusive of petroleum. In 194,5 and 1946, the use of the magnetic method reached a peak, partly because of an active period of prospecting brought on by an active mining market, particularly in Canada.

Jan 1, 1948

By P. S. Bagga, P. T. Luckie

Liberation (the process of destroying the interlock between unwanted materials, such as mineral matter and pyrite, and coal) is one of the most important precursors to the benefication of raw coal in order to produce high grade marketable coals at economical recovery levels. Liberation is achieved usually by comminuting the raw coal. However, because of the significant interaction between the production of fine particles to achieve liberation and the cost of separating fine particles, the coal industry needs a method projecting the change in washability with size reduction. Such a projection can be combined with size reduction and separation simulators in order to examine completely beneficiation circuitry to produce coals of stringent specification. This paper presents the development of an appropriate liberation model for coal and its solution by Monte Carlo simulation to predict the expected washability of the raw coal as a function of comminution. It includes model validation with a known binary mixture as well as with a known teritary mixture.

Jan 1, 1983

By AUGUSTUS J. MONKS, Norman L. Weiss

THE Santa Barbara Unit of the Compania Minera Asarco, of which the San Diego mill is a part, is in the Parral District of southern Chihuahua. Although the concentration of sulfide ores has been practised in Santa Barbara since 1900, the San Diego mill, completed in 1921, was the first plant in northern Mexico to attempt the treatment of oxidized lead ores. From the milling point of view the many ores that have been treated at San Diego are very similar, the differences among them being rather of degree than type. Since 1921 the number of ores from different sources treated simultaneously has varied from four to eleven; in no case have any distinctive characteristics warranted the separate treatment of any of these. The zone of oxidation, source of the ores milled at San Diego, extends to a depth of 300 to 400 ft. below the surface. These ores carry more gold and less silver, lead, copper, and zinc than the underlying sulfide ores; the gangue minerals appear comparatively unchanged by oxidation and leaching. Lead occurs in diverse minerals, chiefly in cerussite, galena, and angle-site, the proportion of the lead in galena varying considerably in the different mines. An average of the feed to the mill would show the following approximate distribution of the lead content:

Jan 1, 1930

By D. R. Walker, M. C. Shaw

Dimitri Kececioglu (Allis-Chalmers Manufacturing Co., Milwaukee)—The idea of applying metal cutting theory to comminution and vice versa is very impressive. Among others, the demarcation of wheel-grinding data into two regions, namely Kick&apos;s and Rittinger&apos;s, draws attention here. A study of Figs. 6 to 9 shows the following: In Fig. 6, 1 point out of 8; in Fig. 7, 4 points out of 26; in Fig. 8 only 1 point out of 13; and in Fig. 9 practically none out of 13 points fall out of curve No. 2. Also when grinding particles smaller than 5x10." in. it is difficult to measure very accurately the grinding forces, chip geometry, and particle size. In view of the above it would be difficult to make a positive and distinct demarcation of the Wheel-grinding data into two regions, namely, Kick&apos;s and Rittinger&apos;s. The idea of using machine grinding to determine the comminution properties of materials is indeed unique. The following cautions come to mind, however, regarding applicability of machine grinding data to comminution: 1—Grinding gives uniform particle size, whereas comminution gives a variety of particle sizes in the same process. The fact that grinding gives uniform particle size is not necessarily an advantage because in comminution the overall energy under actual comminution is desired and comminution invariably results in the production of a variety of particle sizes. 2—In grinding, a small particle is ground off a comparatively large surface. In comminution small bodies are broken down to smaller bodies. This makes it difficult to establish a concept of reduction ratio in machine grinding. 3—The mechanics of machine grinding involve direct shearing action under very high strain and comparatively high compression at the shear zone, whereas: comminution involves direct dynamic compression and surface friction with comparatively little strain and shear. Consequently the mechanics of machine grinding appear to be different from those involved in comminution. Hence one might arrive at erroneous con- clusions when comminution characteristics are eval-uated from machine grinding results. It is noticed also that functions other &apos;than Eq. 16 which do not involve the concept of direct proportionality of useful energy input to new surface area created (Eq. 2 and particularly Eq. 12) may be derived to fit the, data of curve No. 2. One such relationship may be u = ct-", where c is a positive constant and n is a positive constant less than unity. This, of course, is made possible because data of a very small range. of particle size are being fitted by the curves of No. 2 and the hereby suggested relationship. A sound comminution theory should be applicable to a relatively large range of particle size. George B. Clark (Department of Mining Engineering, University of Illinois)—While the experimental work of Walker and Shawin this article is of intrinsic value in revealing certain fundamental aspects of machine grinding, milling, and related processes and in adding to the store of information concerning the comminution of solid materials by this particular process, it appears doubtful that the results of their research can be employed to verify either Kick&apos;s or Rittinger&apos;s theories. Both these laws were originally developed and proposed on the basis of very simple, idealized hypotheses. The creation of parallel idealized physical laboratory conditions which would be required for either their proof or disproof appear to be well beyond the scope of human ingenuity, at least at present. One great weakness of the imputed verification is that the spread of the points plotted on the graphs is not sufficient to permit accurate &apos;curve fitting. The range of particle sizes included in the belt and wheel grinding is not extensive enough to show any general trends, particularly for the horizontal portion of the curves, said to represent Kick&apos;s laws. That the milling; grinding, and turning data obtained by Walker and Shaw for both metals and minerals happen to comply with. certain interpretations of these two theories under certain specialized conditions

Jan 1, 1955

After months of negotiations, the U. S. has agreed to buy between 6000 and 7000 long tons of Bolivian tin now stockpiled at Peruvian and Chilean ports, at $1.175 per lb, f.o.b. South American Ports. Harry A. McDonald of the Reconstruction Finance Corp. signed the contract with Victor Andrade, Bolivian ambassador. The Mercantile Metals and Ore Corp., of New York City, acted as the agent of Bolivia&apos;s Banco Minero in negotiating the deal. The contract is a short term one. Throughout the talks, the U. S. refused to make a long term agreement because of the possibility that Bolivia will soon nationalize its mines. The Bolivians desired to sell the U. S. 18,000 tons during a one-year pact. The price agreed upon is roughly the same as with Malayan producers. In the meantime, American Smelting & Refining Co., signed over control of its operations to the Bolivian Government. The formal act of leasing the mines to the Bolivian Government follows the announcement last July by the company that it was closing operations because of high costs. Contract terms were not disclosed.

Jan 1, 1952

By J. L. SILSBEE

THE existence of large saline deposits in that flat arid basin, known as the Great Salt Lake Desert, has long been recognized, but the extent and great commercial value of these deposits has not been generally appreciated. That a very considerable interest has recently developed is indicated by the fact that about 263 prospecting permits-each covering about 2560 acres of land in this Desert-have been issued under the Potash Leasing Act (Act of 0ct. 2, 1917-40 Stat. 297), and patents granted on approximately 40,000 acres. It is reported that patents and leases have, or will be applied for on an additional 80,000 acres in the basin. , Tests have been made on probably less than 10 per cent. of the total area of the basin, but these have proved a practically unlimited supply of brine available -sufficient, probably, to. furnish the potassium and magnesium chloride requirements of this country for at least a hundred years.

Jan 1, 1925

By Tommy Wilson

OIL well drilling fluids have become a vital part of the drilling industry during the past 25 years. From chance usage of drilling mud at the fabulous Splindletop field in 1901, drilling fluid control has become an extremely technical and exacting science. Drilling for oil today involves exploration at depths ranging to 21,000 ft, nearly 4 miles. Geological formations encountered at these depths offer a tremendous challenge to the production, research, and service facilities of any drilling mud company.

Jan 5, 1954

By W. C. McClain

In the design of underground excavations, rock mechanics considerations are nearly always based on an elastic behavior of rock. Most rocks do exhibit a certain amount of elasticity, and the application of principles and concepts of elasticity to rock mechanics problems has been largely responsible for progress in the field over the past 10 or 15 years. No doubt the theory of elasticity will remain the most useful analytical tool available for both the design of underground openings and the interpretation of phenomenological data.

Jan 1, 1967

By AIME AIME

BERYLLIUM is one of the most interesting of the minor metals and distinctly a modern development, for until the last two decades it had practically no commercial importance whatever. Then it was discovered that when small quantities of it were alloyed with copper, a copper alloy of unusual and valuable qualities resulted. This is by far its major use-in the manufacture of strong, heat-treated copper-base alloys in which the beryllium content varies from about 0.3 to 2.5 per cent. Its second most important use, though much smaller, is in the form of oxide or other nonmetallic products in the fluorescent lamp, X-ray, cathode ray, and television industries. Certain beryllium salts have the quality, in common with several other materials, of transforming short-wave radiation and cathode rays to visible radiation. Such materials are commonly known as phosphors, and the beryllium salts are the most important phosphors now in use. The third largest use for beryllium is for ceramics, including refractories. Beryllium is also used in small quantities in the form of the metal itself.

Jan 1, 1943

By Ernest Stütz

(New York Meeting, October, 1918.) THE problem of increasing blast: furnace efficiency through diminution of flue-dust production while operating with burdens consisting largely of fine ores has of recent years attracted the attention of metallurgists, whether directly or indirectly interested in the economies of iron smelting, and the various methods evolved from theory or practice have been submitted to wide discussion. After the very thorough and, at that time, exhaustive view of the whole subject, which was afforded to the industry by the meeting of this Institute in February, 1912, the subject was again taken up at the meeting of the Verein deutscher Eisenhüttenleute at Diisseldorf in December, 1912. While American and German conditions are not entirely identical, it may be of interest to give here the words of the gentleman summing up the discussion at the Diisseldorf meeting: &apos; The chief advantage offered by the use of briquettes lies in the fact that disturbances in the furnace, caused mostly by the presence of fine ores in the burden, are avoided, and that blast pressure can be considerably reduced. The resulting economies cannot be overrated, as, with lower blast consumption per ton of product, the installation will be able to take care of increased production. In consequence of lower pressure and speed of blast, heat is more efficiently utilized, flue gas temperature is lowered, and coke particles are less liable to be carried along with the flue dust, of which considerably less is produced. Finally, by increased regularity of operation and higher . temperature in the lower parts of the furnace, the quality of the product is improved. The question of briquetting iron ores has grown to be one of the most important in the iron industry, and, it is not any more a question of what is the cost of briquetting ton of ore, but what, in using ore briquettes, is the cost of production of a ton of iron.&apos;

Jan 7, 1913

"With a total value to date of well over $200,000,000.00 for its ore production, the Tintic mining district, which is about 100 miles southwest of Salt Lake City, ranks as one of the three main ore producing areas of Utah. In it are located the biggest silver mines of the country, silver having been the chief metal produced in the camp since its start. Tintic's silver production to date has a total value of over $ 100,000,000, approximately half of the value of the camp's ore production, the balance being roughly divided among lead, gold and copper.Discovery of the camp was made in the late sixties. Lack of transportation and ore reduction facilities delayed extensive development of the area for nearly a decade.In recent years Tintic's ore production has ranged from 350,000 to 400,000 tons annually. In 1 924 the camp produced one-eighth of the silver produced in the nation with an output of 7,729,700 ounces. Its lead production was 77,765,000 pounds and its gold production 26,285 ounces.The known mineralized area of the district is found in a broad syncline striking north and south. The west limb plunges sharply and extends for a distance on its dip of approximately one and a half miles to the trough. The east limb raises gently through a distance of about two miles to the east limit of known mineralization. This general structure is broken by local faulting throughout the district, the local structural conditions playing an important part in the ore deposition. The north end of the fold is obscured by a rhyolite flow and the south end stops against a monzonite stock."

Jan 1, 1925

By F. P. Dewey

The most serious problem that confronts the lead-smelter is the waste caused during smelting by the volatilization of both lead and silver, which are consequently lost in the form of fume. It is not difficult to collect a portion of the solid materials passing out of the

Jan 1, 1890

By J. P. Hirth, A. H. Clauer

A simple graphical method is presented for the determination of climb forces on dislocations exerted by uniaxial stresses. In conjunction with standard stereographic projections, the technique is applicable for any crystal system. Climb forces on glide dislocations in bcc crystals are determined as an application. In connection with a study1 of elevated temperature creep of molybdenum single crystals, a detailed analysis of the climb force on a dislocation was necessary. In general, such forces can be calculated for an arbitrary dislocation segment from the Peach-Koehler equation2 (or one of its variants3"6) where Fk are the components of the force per unit length of dislocation line, ?i of the unit sense vector tangent to the line, ojl of the stress tensor, bl of the dislocation Burgers vector, and is the Einstein permutation operator with components ?123 = ?231 = ?321 = —?132 = — ?321 = —?—213 = unity, and all other components zero. It is understood in the suffix notation of Eq. [I.] that repeated indices are to be summed over 1, 2, and 3. For the most general coordinate system, the matrix manipulations required to solve Eq. [I] are fairly complex. However, a simplification can be achieved by specifying a coordinate system based on the dislocation in question. The pertinent system involves cartesian coordinates xi, x;, xi, with attendant unit vectors e&apos;i; ei being parallel to the Burgers vector b, and e&apos;3; being parallel to the climb directions (b x ?), i.e., normal to the slip plane. In this coordnate system b = (bi, 0, 0) and ? = (?&apos;1,?&apos;2, 0). Hence, Eq. [I] yields for the climb force per unit length F3 = ?&apos;2s&apos;11b&apos;1—?&apos;1s&apos;12b&apos;1 [2] The first term on the right side of Eq. [2] is the climb force on the edge component of the dislocation, while the second is the (cross-slip) force normal to the glide plane acting on the screw component. Thus, the problem of determining the climb force reduces to that of resolving the stress components —il and s&apos;12 in the xi coordinate system. Several authors7- l0 have shown, for the glide case, that such stress resolution can be performed most readily by graphical methods. Therefore, we present a similar method for the climb case. Of the suggested methods, we follow that of Hartley and Hirth,9 which can be performed directly with a standard stereographic projection for the crystal system in question. We treat the case of simple tension, or compression, this being the most common creep test in which climb is important. A set of cartesian coordinates (x1, x2, x3) is fixed with x3 parallel to the specimen axis. This set is connected to the x&apos;i set by the factors defined in Table I. A perspective view of the coordinate systems relating them to the glide ellipse, is given in Fig. 1, while a stereographic projection of the coordinate systems is presented in Fig. 2. The transformation matrix connecting the xi and xi coordinates is x&apos;i =aijXj [3] where an a11 a13 aij = a21 a22 a23 a31 a23 [4] s The corresponding transformation for the stresses is i [5] The only nonzero component of okl for the simple tension case is s33,. Hence, using Eqs. [4] and 151, we find that Eq. [2] becomes F3 = b&apos;1s33 sin2 cos ?[cos ? sin a - sin ? cos a] [6] = m1b&apos;1s033 sin a- rn2b&apos;s33 cos a where sin a = 5: and cos a = ?i, with a the angle measured from b to ?, i.e., a polar angle in the x1, x2 plane. The same equation with a sign change applies for compression. A graphical plot of the "Schmid" factor m1, relating to the climb force on the edge component, is presented in the stereographic projection of Fig. 3. In this projection the glide plane normal points toward the top of the page and the glide direction points normal to the plane of the page. To use the graph, one

Jan 1, 1970