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By W. C. T. Yeh, T. G. Oakwood, A. A. Hendrickson, R. H. Hammar

The objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for by the influence of the solute addition on the dislocation structure oj- the crystals. The additions of both tin and indium produced only small changes in the dislocation densities and arrangements in silver crystals. However, as found previously, small solute additions have large effects on the tensile properties; the inj-luence of the tin and indium additions on the temperature dependence of the flow stress and the easy-glide range is especially strong; It is concluded that the indirect strengthening effect of the solute due to variations in the dislocation density as proposed by Seeger is of minor importance and that solute atom-dislocation interactions are responsible for the observed strengthenirzg effects. The experimental results were combined with those of Rogausch to test the concenlvatiorz dependence of solute strengthening. Both the first and one-half power dependences of the critical resoleed shear stress on concentratiorz fail in very dilute solutions. THE objective of the research is to determine whether solid-solution strengthening effects observed in dilute solutions of silver can be accounted for, at least in part, by the influence of the solute addition on the dislocation structure of the crystals. It is recognized that the addition of solute atoms may influence the strength properties of a metal through both "direct" and "indirect" effects. The former refer to the strengthening mechanisms that result from the interaction of solute atoms with dislocations; in the latter case, the strengthening effects arise as a result of solute's influence on quantities such as dislocation density, dislocation arrangement, stacking-fault energy, diffusivities, the elastic constants, and so forth. It is clear that the correct interpretation of solid-solution strengthening phenomena cannot be given until the importance of indirect strengthening effects is properly evaluated. In the particular case of close-packed metal crystals, Seeger showed that solute strengthening effects in dilute solutions of copper and silver might be accounted for by an increase in dislocation density due to the addition of the solute. Seeger's argument was that the strengthening effects extrapolated from more concentrated solutions indicate that small concentrations of impurities raise the critical resolved shear stress much more than is predicted by a concentration-independent dislocation density. The above idea was a very reasonable one. The dislocation theories of work hardening of Taylor,2 Cot-trell, 3 Mott, 4 and seeger5 had already associated the increased flow stresses with increased dislocation densities in deformed metals; investigations of the dislocation structure of metal crystals had provided a logical basis for expecting an increased dislocation density in crystals containing impurities (see for example, Ref. 6). The numbers involved seem reasonable, too. It can be expected that the flow stress of the crystal would increase as the one-half power of the dislocation density.' Solute additions of 1 at. pct to metal crystals result in strength increases by factors in the range of three to ten. If one assumes that the strengths of the pure metal crystals are determined by their dislocation densities, then dislocation-density increases of one to two orders of magnitude as a result of solute addition would be required to account for the observed strengthening—not an unreasonable expectation. In addition to the effect of the solute addition on dislocation density, one might also anticipate important strengthening contributions to result from the solute's influence on the dislocation arrangement. Parker and washburns have reviewed a number of experimental evidences which show important strengthening effects due to the presence of subboundaries. Further, lattice strains due to impurity segregation would be expected to influence the distribution as well as the dislocation density of the as-grown crystal. As pointed out in the reviews of Chalmers,6 Elbaum,9 and winegard,lo micro segregation of impurities occurs at all interfaces of crystals in cellular growth; the impurity gradient results in lattice strains which can be reduced with the presence of dislocation arrays in the region of the impurity gradient. Hence, one would expect the presence of a solute to favor the formation of dislocation subgrain structures and that the subgrains would have an important influence on the strength of the crystal. The experimental observations that concern the possibility of an important strengthening contribution through the influence of the solute on the dislocation density or arrangement are not in agreement. Haasen has reviewed the observations of Meakin and Wils-dorf,12 Howie,13 and Bocek 36 and concluded that the solute's influence on dislocation density is not sufficient to account for strengthening effects in concentrated solutions but might, as seegerl suggested, make an important contribution in very dilute solutions. On the other hand, Hendrickson and Fine 14 concluded that changes in the dislocation density and dislocation width accounted for the solid-solution strengthening effects observed in silver-based aluminum solid solutions. Goss et a 1.I5 observed dislocation arrays in Ge-6 at. pct Si, Ge-0.2 at. pct Sn, and Ge-0.2 at. pct B crystals that were not observed in germanium crystals of

Jan 1, 1968

By Bruce N. McIver, Leo Casagrande

Similarities are noted in the practices and problems of constructing dams to impound mine tailings, fly ash, and chemical wastes. The comparison of a typical tailings dam with a conventional water-retaining earth dam shows that the former is inherently less stable and can be susceptible to cracking, liquefaction, erosion, and frost action, as illustrated by examples. Several methods are presented for building safe tailings dams using either the coarse fraction of the tailings or local soils, the important factor in each method being proper compaction of the material. The safety of existing tailings dams can be improved by flattening the overall slope, preferably by adding berms, or by decreasing the height. Where neither remedy is possible, the installation of electro-osmotic tie-backs is suggested. Dumps of mine spoil can be stabilized economically by compacting the material in layers along the toe to form a dam.

Jan 1, 1971

By E. R. Morgan

A series of manganese-rich ferromagnetic alloys has been studied. The alloys are based upon an interstitial solution of carbon in manganese. In each of the systems investigated, the ferromagnetic phase was found to be face-centered-cubic in structure. This magnetic phase is based upon the composition (Mn, X)4C; where X is a metallic element which has both a positive size factor with respect to manganese and a high positive valence. Typical elements of this type are aluminum, indium, and tin. Preliminary magnetic measurements indicate that the effective magnetic moment of manganese in the alloys is at least 1.0 Bohr magneton per atom. It is emphasized that the critical atomic separation beyond which ferromagnetism can occur will be governed by the electronic configuration of the manganese atoms. Lattice parameter measurements show that the ferromagnetic condition in the present alloys is associated with an increased atomic separation of only 3 to 6 pct compared with a hypothetical face-centered-cubic lattice of pure manganese. MANGANESE which is paramagnetic and not ferromagnetic in the pure state can become ferromagnetic if suitably alloyed. Under favorable conditions manganese can have an effective ferromagnetic moment of the order of 3.41,2 or even 4.0 compared with a moment of 2.2 Bohr magnetons for iron. The incidence of ferromagnetism is believed to be controlled by the degree of atomic separation.4,5 This is consistent with the fact that the atomic separation, when considered in terms of the ratio of the atomic diameter R to the diameter r of the 3d-shell, is larger in the ferromagnetic metals. The values of R/r calculated by Slater,' for metals of the iron group are given in Table I, and Slater has suggested that the critical ratio of R/r is 1.5. Consideration of the criterion of atomic separation alone would suggest that there are three classes of possible ferromagnetic manganese alloys: 1— Ordered structures, of either solution or compound types, such that manganese atoms are not near neighbors; 2—Structures in which the separation of near-neighbor manganese atoms is sufficiently increased by the presence of suitable solute atoms; and 3—Dilute solutions of manganese. Typical ferro- magnetic alloys of types 1 and 2 are the Heusler alloys and Mn4N, respectively. There are no recognized ferromagnetic alloys of type 3. In view of the proximity of the ratio R/r for manganese to the critical ratio of 1.5, the present work was concentrated on manganese-rich alloys rather than on ferromagnetic alloys of low manganese content, several examples of which are already known. Calculation of the distance of closest approach of manganese atoms in each of its allotropic forms, Table 11, indicates that the high temperature ? phase provides the most suitable basis for ferromagnetic alloys of high manganese content. However the high temperature forms of pure manganese cannot be retained on quenching, although a face-centered-tetragonal form apparently can be produced by electrodeposition. Since the critical separation which must be exceeded in order to obtain ferromagnetism is dependent upon the number of electrons in the d-shell, no exact critical value of R/r can be assumed. Not only will this separation vary from one pure metal to another, but it will also vary with the valency of the given type of atom when it is in an alloy. Raynor8 has shown that metals of the iron group probably

Jan 1, 1955

By W. G. Pariseau, C. H. Schmuck, Fei Duan

The Homestake Mine is located in steeply dipping Precambrian metasediaents, an environment common to a number of world class ore bodies. Development of a pronounced plane of schistosity raises a question concerning the importance of anisotropy to the design of vertical crater retreat stopes. Little is known about the actual influence of elastic anisotropy in such -circumstances; even less is known about strength anisotropy. A cautious step- by-step approach was therefore taken towards a numerical assessment of the role of anisotropy in the analysis of stress and stability. The sequence of analyses begins with elementary test problems for computer program checks and proceeds to the analysis of a study stope area between the 6950 and 7100 Levels of the Homestake Mine. Anisotropy (orthotropy) is important at the Homestake Yine. No simple guidelines for evaluating in advance the need for plastic and strength anisotropy in design analysis appear to be forthcoming, ;o that some physical properties testing is necessary where the question is in doubt

Jan 1, 1984

By E. H. Roberts, L. G. Swenson, F. C. Nix, R. A. Morgen

The binary system lead-antimony has been the subject of comprehensive investigations in these laboratories by Dean1 and his associates. The effect of a third constituent on this system, particularly on the lead-rich alloys in which dispersion hardening was found, has a commercial value as well as an academic interest. This paper covers the effect of the addition of copper, bismuth and tin, all of which are likely to be found in commercial lead-antimony alloys, and is divided into three parts, as follows: I. The System Lead-A~ili~r~ony-Copper II. The System Lead-Antimony-Bismuth III. The Lead Corner of the System Lead-Antimony-Ti11 These three systerrls are of three different types, and hence may be considered as covering three general kinds of additions. Bismuth forms no compounds with either lead or antimony and forms solid solutions with both. Copper forms several compounds with antimony as well as solid solutions but with lead it forms a two liquid layer system and no appreciable solid solution. Tin is soluble in both lead and antimony in the solid state and also forms a compound with antimony. The effect of small amounts of bismuth on the lead-antimony alloys is small, having no appreciable effect on the solubility of antimony. The temperature of the solidus floor is lowered appreciably by the presence of bismuth, cutting down the range of heat treatment. Copper, on the other hand, due to compound formation, increases the apparent solubility of antimony. The excess antimony is tied up with the copper finally and so is not available for dispersion hardening. The net result of addition of small amounts of copper is to shift the dispersion hardening peak of the

By W. R. Crane

MINING of the red iron ores of the Birmingham district has been carried on energetically during the past 50, years, and their development has created a large iron and steel manufacturing, center, the only important one in the South. The district produces approximately 10 per cent. of all the iron ore of the United States (80 per cent. of the Alabama ore mined is red ore) ; also, 43 of the 419 blast furnaces of the country are in the district tributary to Birmingham. The rapid growth of the district has been made possible through investigations that resulted in radical changes in furnace practice, and a still greater impetus will come from the study of the low-grade, high-silica ores, as a result of which they will be made amenable to treatment by concentration. Mining practice in this district has been comparatively simple because of the occurrence of the ore; but with the-rapid extension of the work-ings and the disturbed condition of the ore bed at some distance from the outcrop, more difficult conditions are encountered and the tendency is toward worse rather than better conditions. Should the high-silica ores of the lower bench of the Big Seam become available through beneficiation, mining practice will have to be modified to meet the new conditions, which will be rendered more difficult by the increased weight of cover that will exist at considerable distances from the outcrop. Support of workings will require greater attention and the efficient and economical operation of the mines will depend largely on the successful solution of the problems of working-and handling the ore.

Jan 9, 1924

Jan 1, 1897

By Clair Upthegrove, Elbert S. Rowland

THE widespread interest in the alloys of beryllium with copper is due principally to the fact that certain compositions show very favorable precipitation-hardening characteristics and are, in fact, the strongest nonferrous alloys known at the present time. Investigations have been conducted by Masing and Dahl and others on the physical characteristics of ternary beryllium alloys, in an attempt to produce precipitation-hardening effects with a smaller amount of beryllium than that required in the binary copper-beryllium alloys (2.0 to 2.5 per cent Be). The results of these investigations show that ternary alloys of beryllium with Cu-Sn, Cu-Al and Cu-Zn, among others, exhibit promising improvements in physical properties after precipitation-hardening treatment and, while the increases in properties obtained are not as high as those realized from the binary copper-beryllium alloys, excellent properties are: obtained with beryllium contents averaging about one-half the amount required in the binary alloys. This paper presents the results of an investigation of the equilibrium relations of certain alloys containing copper, tin and beryllium. The alpha-phase boundary of the ternary system is given for alloys containing from. 0 to 1 per cent beryllium. The equilibrium conditions beyond the alpha-phase boundary are presented for alloys containing up to 32 per cent tin and 1 per cent beryllium. The data were collected by means of

Jan 1, 1935

By Wm. Reuben Webster

THE greatly enlarged demand for small sizes of seamless copper tube which has recently occurred, due particularly to the rapid growth of the electric household-refrigerator industry, has emphasized the superiority of phosphorized to tough pitch copper for the purpose of producing this commodity. In the manufacture of this material exceedingly heavy reductions by cold drawing are employed, customary practice involving as much as 90 per cent. reduction of cross-sectional area in four runs without intermediate annealing. Although this superiority has long been recognized by tube makers, no quantitative expression of it has heretofore been published. It is believed that the data herewith presented will serve this purpose. Recent investigators are not in agreement as to the relative mechanical properties of copper containing small amounts of oxygen as compared with copper containing sufficient oxygen to produce that condition known as tough pitch. Hanson, Marryat and Ford' found that "oxygen has a relatively small effect on the properties of copper." Johnson,2 on the contrary, states "it cannot be denied that it (tough pitch copper) is inferior, to deoxidized copper where severe mechanical manipulation is concerned." These authorities in the reports of their investigations, as might be expected from their conclusions, do not present data of a character requisite to a conclusive determination of the question.

Jan 1, 1927

By Herbert R. Mosley, Paul M. Tyler

STRATEGICALLY situated in almost the heart of the leading fertilizer- consuming area of the United States, Tennessee long has ranked second only to Florida as a phosphate-producing state. Since 1932 its share of the national output of phosphate rock has increased steadily, and in 1937 its production mounted to an all-time record. More significant even than the increase in tonnage are the forward strides in technology. The Tennessee Valley Authority's research program has led to quasicommercial operations using hydroelectric power to manufacture concentrated phosphatic fertilizer that is used to further the farmer education program designed to streamline the fertilizer business and halt the appalling waste of farm land by soil erosion. Even more stimulating to chemically minded imaginations is the production of elemental phosphorus by a private company that not only has succeeded in extracting it from the phosphate rock in electric furnaces but actually has contrived to capture it and to transport it safely in tank cars. New values have been created for low-grade phosphate deposits, and the economic life of reserves has been lengthened while the waste of former years goes back into the mills for recovery of its values by modernized methods. Tennessee's phosphate-mining industry dates from the discovery of blue rock in-lewis County in December 1893. Its known reserves are of the order of 101,500,000 tons, which compares with the production of 825,099 tons in 1937; that is, 21 per cent of the phosphate-rock output of the whole nation. The total output reported from 1894 until July 1, 1938, was approximately 19,000,000 tons. Official estimates of reserves are overly conservative and evidence submitted before a joint Congressional committee in November 1938 places "probable" reserves at more than 6,000,000,000 tons.

Jan 1, 1939

By W. F. Holbrook, C. E. Wood, E. P. Barrett

The high-frequency laboratory induction furnace with a rotating liquid crucible enables research workers to conduct certain investigations heretofore very difficult or impossible to realize because vessels are not obtainable that are capable of resisting the physical conditions or the chemical actions to which they are subjected. Applications for patents covering commercial uses of centrifugal liquid crucibles were filed in the United States in 1919,' in France in 1925, in the United States and Germany in 1926,2 and in France in 1927.3 In 1928, Schuette and Maier,4 of the Bureau of Mines, reported the construction of a whirling table beneath a high-frequency induction furnace. Shape and Size of Centrifugal Liquid Crucibles When a vessel containing a liquid is rotated, the inner surface of the liquid takes the shape of a paraboloid under the simultaneous action of centrifugal force and gravity. The internal dimensions of the paraboloid rotating liquid crucible are governed by the diameter of the container and its speed of rotation. Melted Wood's metal was poured into cylinders 2 1/2 in. in diameter, which were rotated at 180, 300, and 468 r.p.m. When the metal was solid, a slurry of plaster of Paris was added, and rotation continued until the plaster had set. Fig. 1, a photograph of sections of the cylinders, shows the effect of speed of rotation of the containers upon the shape of the inner surface of the rotating liquid crucibles. Types of Furnaces Three types of high-frequency induction laboratory furnaces using liquid-metal crucibles were designed and constructed by the Blast

Jan 1, 1939

By W. F. Holbrook, C. E. Wood, E. P. Barrett

The high-frequency laboratory induction furnace with a rotating liquid crucible enables research workers to conduct certain investigations heretofore very difficult or impossible to realize because vessels are not obtainable that are capable of resisting the physical conditions or the chemical actions to which they are subjected. Applications for patents covering commercial uses of centrifugal liquid crucibles were filed in the United States in 1919,' in France in 1925, in the United States and Germany in 1926,2 and in France in 1927.3 In 1928, Schuette and Maier,4 of the Bureau of Mines, reported the construction of a whirling table beneath a high-frequency induction furnace. Shape and Size of Centrifugal Liquid Crucibles When a vessel containing a liquid is rotated, the inner surface of the liquid takes the shape of a paraboloid under the simultaneous action of centrifugal force and gravity. The internal dimensions of the paraboloid rotating liquid crucible are governed by the diameter of the container and its speed of rotation. Melted Wood's metal was poured into cylinders 2 1/2 in. in diameter, which were rotated at 180, 300, and 468 r.p.m. When the metal was solid, a slurry of plaster of Paris was added, and rotation continued until the plaster had set. Fig. 1, a photograph of sections of the cylinders, shows the effect of speed of rotation of the containers upon the shape of the inner surface of the rotating liquid crucibles. Types of Furnaces Three types of high-frequency induction laboratory furnaces using liquid-metal crucibles were designed and constructed by the Blast

Jan 1, 1939

By Zay Jeffries

Page Introduction............................. 474 Nature of Experiments ........................ 476 Materials Used in Experiments..................... 476 Description of Samples........................ 476 Details of Tests and Apparatus .................... 486 Determination of Elongation...................... 488 Determination of Reduction of Area .................. 488 Results of Tests........................... 489 Quantity and Arrangement of Amorphous Phase............. 497 Properties of Amorphous and Crystalline Phases............. 501 Intercrystalline Fracture........................ 530 Trans-crystalline Fracture....................... 531 Rupture ............................... 535 Explanation of Beilby's Results..................... 536 Mechanical Properties of Copper Wires................. 537 Mechanical Properties of Tungsten Wires................ 542 Mechanical Properties of Iron Wire................... 546 Effect of Diameter of Wire on Mechanical Properties........... 554 General Considerations on Properties of Metals at Very Low Temperatures .. 556 General Considerations on Physical Properties of Complex Alloys...... 557 Summary.............................. 559 Discussion.............................. 562 Introduction DuRing the period 1914 to 1916. the writer observed many times that tungsten wire could be drawn hot until it became brittle but on cooling to room temperature it became ductile again. In searching the literature for parallel cases. it was found that Beilbyl had produced hard-drawn wires of gold. silver. and copper that showed less than 1 per cent.

Jan 1, 1919

By H. A. Wheeler

. Page History.................................533 Location .........:.....................536 Geology...............................539 Description of the Eastern Field ... :..................543 Description of the Western Field .........,...........546 Quality of the Oil ................ ,........549 The Oil Sands .,.............................549 Drilling Features'........................., . 551 Well Density...........,.'...............:. 552 Plant Equipment.......................:.'., .554 Market Features..........................555 Production Prices.........,...................557 Royalties and Rentals.........................558 Cost of Oil Leases............................'.558 Operating Expenses..........................559 Operating 'Profits...........................559 Gas Developments ........................560 Gas-Gasoline production ... :....................561 Statistics.......562 History Illinois has SO recently attained the third place in the oil production of the United States that few realize its great importance, or are aware of its highly profitable character. Since 1907 Illinois has furnished about 15 per cent. of the United States output and about 10 per cent, of the world's production. The value of the output in 1913 is estimated at $307000,000, of which about $20,000,000 is profit. The present prosperity dates from 1905, but efforts have been made since 1865 to develop production and geologists have been very sanguine as to its future for over 25 years. Had the oil operators been as confident as the geologists, the field would have been opened at least 30 years earlier. For the rich Eastern Illinois oil field is located along the La Salle anticline, that was mapped 46 years ago by Professor Worthen in the

Jan 1, 1915

By J. E. Johnson

It is the purpose of the present paper, while not excluding chemical considerations, to deal more extensively with some of the physical and mechanical aspects of the blast-furnace process, and to point out its dependence, in these respects, on well-known laws. The quantity and cost of ore and flux required to make a ton of iron being determined by circumstances over which the furnace-man, under given conditions as to quality and quantity of product, has commonly little control, the principal item of cost, apart from the saving of labor, which he can aspire to reduce, is that of fuel. To determine the limits of possibility in this direction is clearly the first step in a practical inquiry; and this step is represented herewith in Fig. 1, a diagram showing the total useful effect obtained from a pound of fuel under various conditions, and thus permitting direct comparison, under any given conditions, between actual results and the maximum possible results. The following statements will explain the basis upon which this diagram has been constructed. One pound of fuel, containing 90 per cent. of fixed carbon (which represents average conditions), is taken as the unit. The degree of oxidation of the carbon is measured by the ratio of the two oxides of carbon contained in the top-gases. It is necessary to remember that a considerable quantity of carbon is brought in as carbon dioxide by the flux, and to take account of it and of its condition. It is here considered that the carbon dioxide liberated by the limestone does not affect the analysis of the top-gases, and that the ratio of CO to CO2 will remain unchanged by the addition of limestone; enough CO, being reduced by the solution

Jan 1, 1906

By C. A. Heiland

Geophysical methods are playing an ever increasing part in various engineering fields. About ten years ago, geophysical exploration was first applied in civil engineering to the study of foundations and the location of construction materials and water. Its usefulness is now being extended into the field of structural engineering. Almost every structure has to be so designed that it will withstand any force to which it may be subjected. Such forces may result from its own weight, applied loads, pressures of various kinds, including those due to wind and water, ground subsidence and vibrations. The last two, problems involving the nature and dynamic behavior of surface and subsurface formations, are within the scope of geophysical investigations. In the design of any structure, the disposition and dimensions of its members as well as their materials must be so selected that they will withstand any or all of the forces enumerated above. In other words, its "resistance" to such forces must be sufficient, allowing for a definite margin of safety. Often a static treatment of the problem leads to satisfactory results, but the static method entails serious errors when vibrations are involved, as in resonance with an impressed vibration the displacements of a structure or parts thereof may dangerously exceed the allowable values. The principle of "dynamic design"† is, therefore, avoiding or reducing resonance by suitable selection of the natural frequency of a structure, or by the provision of damping. Methods of Investigation Dynamic design of structures is required where ground vibrations occur naturally or are produced artificially. Earthquake regions fall in the first group; areas of industrial activity where vibrations are produced by machinery, blasting, etc., fall in the second. In either case, dynamic

Jan 1, 1940

By C. A. Heiland

Geophysical methods are playing an ever increasing part in various engineering fields. About ten years ago, geophysical exploration was first applied in civil engineering to the study of foundations and the location of construction materials and water. Its usefulness is now being extended into the field of structural engineering. Almost every structure has to be so designed that it will withstand any force to which it may be subjected. Such forces may result from its own weight, applied loads, pressures of various kinds, including those due to wind and water, ground subsidence and vibrations. The last two, problems involving the nature and dynamic behavior of surface and subsurface formations, are within the scope of geophysical investigations. In the design of any structure, the disposition and dimensions of its members as well as their materials must be so selected that they will withstand any or all of the forces enumerated above. In other words, its "resistance" to such forces must be sufficient, allowing for a definite margin of safety. Often a static treatment of the problem leads to satisfactory results, but the static method entails serious errors when vibrations are involved, as in resonance with an impressed vibration the displacements of a structure or parts thereof may dangerously exceed the allowable values. The principle of "dynamic design"† is, therefore, avoiding or reducing resonance by suitable selection of the natural frequency of a structure, or by the provision of damping. Methods of Investigation Dynamic design of structures is required where ground vibrations occur naturally or are produced artificially. Earthquake regions fall in the first group; areas of industrial activity where vibrations are produced by machinery, blasting, etc., fall in the second. In either case, dynamic

Jan 1, 1940

By P. F. Gnirk, J. B. Cheatham

The basic objective of this paper is to present a review of the state of knowledge concerning the fundamental mechanics of rock/bit-tooth interaction under downhole conditions. Of particular concern is the contributing significance of the various variables associated with the generation of rock chips by a single penetrating bit-tooth. The variables to be considered are fluid pressures which simulate borehole conditions, the mechanical properties of the rock, the shape and angle of attack of a bit-tooth, and the rate of load application on a bit-tooth. In addition, consideration is given to multiple bit-tooth penetration insofar as the effects of distance from and geometrical shape of adjacent penetration craters are concerned. Both experimental results and idealized theoretical models for single bit-tooth penetration are presented. Finally, the applicability of plasticity theory to drilling phenomena at depth, results of recent drag-bit studies, and several general theories of roller-bit drilling are briefly discussed. FUNDAMENTALS OF ROCK/BIT-TOOTH INTERACTION Drilling efficiency at depth in terms of penetration rate depends largely upon three essentially interdependent factors: 1) the bit, insofar as the mechanical motion, shape, and configuration of the bit-teeth are concerned; 2) the rock, as regards its mechanical behavior, or response to the penetrating action of the bit-teeth, when subjected to a state of stress induced by mud column, interstitial pore, and overburden pressure (and at great depths to high temperature) ; and

Jan 1, 1967

By J. H. Jackson, P. D. Frost, C. H. Lorig, A. C. Loonam

THIS paper describes (1) the effect of sodium on the tensile ductility of magnesium-lithium base alloys, and (2) the precautions necessary to avoid sodium contamination. Effect of Sodium on Properties The harmful effect of sodium in magnesium-lithium base alloys has been recognized by other investigators.1,2 However, quantitative data on its effect have not hitherto been published. The effect of sodium on the ductility of an 87 pct Mg-9 pct Li-4 pct Zn alloy is shown in fig. 1. The sodium was introduced by adding sodium chloride to the flux, which consisted of 50 pct LiC1-50 pct KC1. Moderately high ductility was obtained at an indicated sodium content of about 0.05 pct. Actually, the value probably was less than 0.05 pct, be-cause analyses of the lithium, which were more accurate than those of the alloy, indicated that the highest ductility was obtained when its sodium content was 0.02 pct or less. In fact, in alloys having somewhat greater strength than this particular composition, the sodium content of the lithium must be under 0.01 pct to avoid embrittlement. The effect of sodium on the ductility of several alloys having fairly low strength levels is shown in fig. 2. These alloys were melted with a flux containing 75 pct LiC1-25 pct LiF, to which various quantities of sodium chloride had been added. Sodium had no significant effect in pure magnesium but markedly decreased the ductility of the magnesium-lithium-zinc alloy, even though the alloy contained only 3 pct Li. As the lithium content of the binary alloys was increased, the ductility of the sodium-free alloys also increased. However, the effect of sodium on ductility became progressively more pronounced. Sodium raised the minimum hot-rolling temperatures, particularly those of the high-strength alloys, but its effect, in this respect, was less critical than its effect on tensile ductility. For optimum cold roll-ability, a low-sodium content was required. No deleterious effect of sodium on the stability of properties at slightly elevated temperatures was found. Control of Sodium in the Alloys Optimum ductility is obtained in the magnesium-lithium base alloys when sodium-free materials are used. Commercial lithium was formerly the chief source of contamination. Now purified lithium is usually available. When lithium of ordinary purity is used, the effects of sodium can be minimized by using a flux consisting of 75 pct LiC1-25 pct LiF. Bubbling nitrogen through the melt also helps remove sodium. The damaging influence of sodium on the ductility of the magnesium-lithium base alloys was observed very early in the alloy development program. The discovery came about as a result of chemical analyses made on the lithium used in the alloys. Ductile alloys had been made from lithium containing about 0.2 pct Na, whereas the lithium used in the brittle alloys contained about 0.9 pct Na. The first magnesium-lithium alloys were melted under commercial fluxes ordinarily used in melting magnesium alloys. These fluxes were unsuited for scavenging the contaminating sodium, and the resulting alloys were not ductile. Next, a flux containing 50 pct KC1-50 pct LiCl was tried. This was somewhat more effective but still was not satisfactory. After a number of different experimental fluxes had been investigated, one containing 75 pct LiC1-25 pct LiF was adopted. This flux made it possible to obtain good ductility in the alloys. The

Jan 1, 1951

By George A. Grandy, D. W. Fuerstenau

Simulation of nonlinear grinding systems is discussed in the context of the size-discretized batch-grinding model. A linear approximation of environment-dependent (or nonlinear) selection functions is postulated for systems which exhibit feed grinding orders less than unity. For this, a convex linear combination of zero and first-order selection function forms is used to obtain an analytical solution that can be used for simulation. An example in which marked nonlinear behavior occurs is rod-mill grinding. Accordingly, a series of grinding experiments was carried out in a batch laboratory rod mill to test these techniques; agreement between experiment and the model was found to be very good. Recently, significant progress has been made in the simulation of linear grinding systems by using a population balance mathematical model. Herbst and Fuer-stenaul presented a parameter estimation scheme that can be used with the size-discretized batch-grinding model, and Gumtz and Fuerstenau3 have extended these techniques to the simulation of locked-cycle grinding. Grandy et aL." summarized the simulation of linear systems and noted important alternate solutions to the batch-grinding equation. Kelsall et a1.'-" discussed the dynamic simulation of linear batch grinding, as well as linear open and closed-circuit grinding. In all of these, the key word is linear, which certainly restricts the engineer trying to simulate a variety of grinding systems. This paper discusses an approach for the simulation of non-linear grinding systems, particularly those which exhibit grinding orders less than unity. Experimentally, dry rod-mill grinding is used to evaluate the technique presented. Batch Grinding Model The size-discretized batch-grinding model has been discussed in detail by Mika et al.'.' and by Herbst and Fuerstenau,' and therefore, will only be briefly developed here. The model is formulated by making a differential mass balance of each size fraction in such a manner that the equation parameters are precisely defined in terms of selection and breakage functions,' which can be either calculated'.' or estimated1 from experimental data. The model is phenomenological because it averages all stress-application events in the system and, therefore, does not distinguish the manner in which individual particles are stressed.' For this average environment, the resistance of all particles in a size fraction to breakage is defined by that size-frac-tion's selection function; and when fracture occurs from an average event, the breakage product size distribution is defined again by that size-fraction's breakage function. The model is deterministic and is derived in terms of a continuous time variable and a discretized size variable,' i.e., the n mass fractions associated with the n defined size intervals (see Table 1 for nomenclature).

Jan 1, 1971