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By D. M. Schuster, E. Scala

The elastic effects occurring in the matrix of a composite reinforced by discontinuous fibers were studied by means of photoelastic techniques. A hirefringent plastic was employed as the matrix material with high-strength a Al2O3 whiskers as the reinforcing fibers. It was found that for whiskers aligned parallel to the tensile load direction: (I) Matrix reinforcement occurred along the length of the whisker to within about 5 diameters of the whisker tip for a length to diameter ratio, L/D, of 40. (2) Significant stress concentrations were created in regions immediately surrounding the tips; the fine as-formed tapered ends exhibited the minimum stress concentration whereas the square-ended whisker produced relatively high values, K r 2.5 for L/D = 40. (3) The axial and radial stress distributions could he determined quantitatively; the stress distribution at the whisker-matrix interface was in general agreement with theoretical calculations. (4) The highest source of stress concentration occurred at points of fracture in whiskers which had ruptured after incorporation into the composite. Whiskers aligned perpendicular to the load direction neither reinforced nor caused appreciahle stress concentrations in the matrix. ThE properties of composites have generally been formulated empirically on the basis of macroscopic tests. There are still many questions concerning the mechanical and chemical interactions occurring at the interface between the reinforcing fiber and its matrix. Continuously reinforced plastics and dispersion-hardened metals represent the two extremes of composite reinforcement. Whether artificially produced or formed in situ, the whisker composite falls between these two extremes and is an example of discontinuous fiber reinforcement. The effect of fiber shape, size, surface condition, and end configuration on the stress distribution in the matrix is important since the presence of stress concentrations, especially in any high-strength, thin-wall structure, could become the cause of catastrophic failure. DOW,' in his theoretical discussion of discontinuous fiber reinforcement, has pointed out that appreciable stress concentrations occur at the tips or ends of the reinforcing fibers. It is the purpose of this study to examine directly, by means of the photoelastic technique, the stresses which occur in the vicinity of a discontinuity or whisker tip and to measure qualitatively and quantitatively the effects of whisker geometry when embedded in a birefringent matrix material. The use of sapphire (a A1,O3) whiskers was decided upon as the reinforcing agent because of their high elastic modulus (E- 60 X 106 psi) and in some cases strengths in excess of one and a half million psi. Sapphire whiskers are of further practical interest since they retain large fractions of their strength up to temperatures approaching the melting point (3720oF).2 The whiskers were grown, by the vapor-phase reaction commonly employed,3 as part of this study to insure a physically uniform supply. Tensile and bend tests were performed to verify that the whiskers were of the expected ultra-high strength. The high-strength whiskers can be identified and selected from the combustion boats by surface perfection, shape, and size; otherwise, strength values can vary by a factor of ten or more. Macroscopic defects are quite common on the surface of large bladed whiskers and the principal experiments were conducted with hexagonal whiskers of about 0.002 in. diameter and lengths ranging from 0.1 to 0.4 in. Upon completion of these two phases of the experiment, several birefringent resins were evaluated. A plastic, developed by Zandman,4 which is supplied by the Budd Co., was found most suitable and was used as the matrix material for the whisker composite throughout the study. It has a sensitivity of 60.5 lb per in. order, calibrated in tension and cures without introducing residual stresses. Young's modulus for this matrix material is 430,000 psi in the fully cured condition. Since good wetting and bonding between the sapphire and the matrix material is essential to the interpretation of the results, a wettability test was performed. The contact angle was measured to be 168 deg where perfect wetting is defined as 180 deg; therefore, the Budd Plastic wets the sapphire

Jan 1, 1964

By R. W. Guard

ALTHOUGH etching techniques have been developed for revealing dislocation sites in several metals and ionic crystals,h t is valuable to extend the technique to new metals. An etch pit method for nickel has been developed on the basis some suggestions of Dr. John R. Cuthill of the National Bureau of Standards who had observed etch pits in creep specimens of nickel. The etchant used was proposed first by wensch2 for revealing grain size in nickel. The present paper describes the evidence that the technique can be used to reveal dislocations and gives the conditions under which etching can be carried out. The specimens examined were vacuum melted high-purity Ni (99.985 pct Ni) and commercial "A" nickel (99.8 pct Ni). Both materials contained greater than 0.008 pet C and had been annealed in nitrogen or dry hydrogen at 1100o to 1200°C. This gave a grain size of 1.5 mm in the high-purity nickel and 0.050 mm in "A" nickel. Tensile specimens (0.254 in. diam) were deformed from 0.25 to 10 pct at room temperature and then heated for 1/2 hr at different temperatures from 400" to 900°C. The specimens were sectioned longitudinally then polished electrolytically in 60 pct H2SO4 and etched in 35 pct H3PO4 solution at 0.2 to 0.4 v for 30 sec to 3 min. The best method for setting the proper voltage for etching is to increase the voltage until gas bubbles are evolved vigorously from the specimen and then cut it back by 10 pct. It is necessary to heat the specimen above 500°C after deformation in order that etch pits will be formed. This "decoration" treatment permits carbon to segregate to the dislocation rendering them sensitive to etching. It was demonstrated that carbon was the decorating impurity by decarburizing some specimens in wet H2 at 1200°C. The susceptibility to etch pitting was lost following this treatment but could be restored by carburizing in contact with graphite. Some rearrangement of the dislocations in the as-deformed structure occurs on heating at 500oC and above so that the technique can not be used to study the nature of dislocation patterns in deformed specimens. Extended etching does not change the number of pits although the background becomes rough and the pits quite large. The polycrystalline specimens with various strains were examined after annealing at different temperatures. Typical patterns are shown in Figs. 1 and 2. In the unstrained specimen, Fig. 1, the density of pits is 2.5 X 10' per sq cm. All grains show pits regardless of their orientation although there is a

Jan 1, 1961

By M. D. Scott

A second generation tailings system, consisting of 8 km (5 mile) of large diameter 914- mm (36-in.) po1yethylene pipeline, the bulk of which was laid on a 0.2% grade, has been successfully operated by Lornex Mining Corp. for the past 2 yr. The system was designed to operate as a partial flow pipeline during average flows with the ability to pressurize itself and operate as a pressure pipeline under high flows, or clean itself out under sanding conditions. The system has exceeded design capacity and has had very little downtime. Polyethylene pipe was easily and inexpensively installed and has exhibited superior abrasion resistance characteristics.

Jan 1, 1978

Prof. Henry M Howe, New York: It is extremely probable that this efflorescence of silica is due to the liquation either of silicon or of a silicide, and the subsequent oxidation of the silicon to silica. As Mr. Fackenthal says, it is very hard to see why silicon should liquate from an iron containing so little silicon, and it seems more probable that some silicide of some volatile element has liquated, and has dissociated on reaching the air, and that the volatile element has volatilized, leaving the silicon to oxidize to silica. The volatile elements present which might thus liquate in combination with the silicon are sulphur, zinc, and lead. It is hard to see why sulphide of silicon should have liquated from an iron containing so little of either sulphur or silicon. At first, one naturally thinks that either the zinc or the lead present in this furnace might have liquated as silicide. It is true that they are both volatile at the temperature within the furnace, but then the vapor-tension* of each of them within

Jan 1, 1901

J. M. TIPPETT? Colorado Springs, Co1o.-There are several points which offer ground for discussion, although the authors' indicated results leave small chance for argument. Under classification of the ores as they come to the mill, it will be noted that these are classified according to their lime contents. In previous years the classification was based upon sulfur contents, CaO not being considered; class A would be called the oxidized ore and class B the sulfides. Classification according to CaO is the first public indication that a decided change in the ore has necessitated improved methods of treatment. The very serious effect that CaO, even in small quantities, has upon extraction has been noted for some years.

Jan 11, 1918

FRANCIS B. SILSBE,* Washington, D. C. (written discussion?). ?This paper is an interesting example of the -solution by the methods of metallography of what seemed at first a purely chemical problem. The authors have shown: in detail, how the well-known corrosion of spark-plug terminals is due to the dropping out of the individual crystals of the metal as it becomes surrounded by an oxide film. This corrosion is usually quite slow but in special cases may become a serious factor in limiting the life of spark plugs. There still remains the problem for the metallurgist to produce a material that will be entirely free from, this trouble. One of the most startling results of the work is. the demonstration that it affords of the deleterious effect of a mechanical stress continuously applied to material that is at the same time subject to adverse chemical or thermal conditions. The particular style of spark plug shown in the illustration, and in which serious trouble was caused by this corrosion, has the side terminals fastened at both ends and the method of assem-bling is such that a considerable initial tension is applied to the wire. It is without doubt this superimposed tension that causes the inter-crystal-line network to line up, as it were, into a few continuous and deeply penetrating transverse fissures instead of forming a great number of shallow surface cracks. This result is clearly shown both in the case of

Jan 11, 1919

By Thomas M. Dr. Drown

IN experimenting in connection with Mr. P. W. Shimer (now chemist of the Thomas Iron Company, Hokendauqua, Pa.) on methods for the determination of silicon in pig iron, in order to find one which should be accurate and yet give results in a few hours, I have adopted the following procedure, which, as far as my experience goes, leaves nothing to be desired. About one gram of pig iron or steel is treated in a platinum or porcelain dish with 25 cubic centimeters of nitric acid (sp. gr. 1, 2). When action has ceased, 25 to 30 cubic centimeters of dilute sulphuric acid (one of acid and three of water) are added, and heat applied until the nitric acid is nearly or quite driven off. The heat of a water-bath is sufficient, though the process may be hastened by heating higher on a sand-bath. Water is then cautiously added (as soon as the free sulphuric acid is sufficiently cool) and the contents of the dish heated until the crystals of ferric sulphate are completely dissolved. The solution is then filtered as hot as possible, the residue washed first with hot water, then with 25 to 30 cubic centimeters of hydrochloric acid (sp. gr. 1, 12), and finally with hot water. After drying and igniting, the silica will be found to be snow-white and granular. The following are some results obtained by this method compared

Jan 1, 1879

By Thomas M. Drown

In experimenting in connection with Mr. P. W. Shimer (now chemist of the Thomas Iron Company, Hokendauqua, Pa.) on methods for the determination of silicon in pig iron, in order to find one which should be accurate and yet give results in a few hours, I have adopted the following procedure, which, as far as my experience goes, leaves nothing to be desired. About one gram of pig iron or steel is treated in a platinum or porcelain dish with 25 cubic centimeters of nitric acid (sp. gr. 1, 2). When action has ceased, 25 to 30 cubic centimeters of dilute sulphuric acid (one of acid and three of water) are added, and heat applied until the nitric acid is nearly or quite driven off. The heat of a water-bath is sufficient, though the process may be hastened by heating higher on a sand-bath. Water is then cautiously added (as soon as the free sulphuric acid is sufficiently cool) and the contents of the dish heated until the crystals of ferric sulphate are completely dissolved. The solution is then filtered as hot as possible, the residue washed first with hot water, then with 25 to 30 cubic centimeters of hydrochloric acid (sp. gr. 1, 12), and finally with hot water. After drying and igniting, the silica will be found to be snow-white and granular. The following are some results obtained by this method compared

Jan 1, 1879

By C. B. Barlow, T. A. Mekelburg

Due to a tight ash constraint on the clean coal product and difficult middlings washability characteristics, a considerable amount of coal was being lost in the jig middlings at the Monterey No. 2 Mine. An investigation was conducted into circuitry to recover this lost coal with minimal effect on the total clean coal ash. A reverse two-stage hydrocyclone system cleaning at low specific gravities was selected. This system is currently recovering approximately 5.8 kg/s (23 stph) of 11.5% to 12.5% ash coal. The specific gravity of separation for the system is about 1.5 and the probable error is 0.13.

Jan 1, 1986

Henry Louis, Newcastle-upon-Tyne, England (communica, tion to the Secretary): I have been much interested in Mr. Schmitz's description of the copper-ore bed in the Permian formation of Texas. He compares it with the Mansfeld Kupferschiefer; but it seems to me to present closer analogies with a small deposit on the same side of the Atlantic, in Nova Scotia, which I examined in 1877. I quote entirely from my fieldnotes, made then, and from specimens still in my possession. These copper-deposits are known in several places; but I examined them at the village of New Annan, on the banks of the French river. This district has been determined by Sir J. W. Dawson as being of Permian age, and this determination seems to have been confirmed as recently as 1891 by the operations of the Canadian Geological Survey. The following is the section, very imperfectly exposed in a few shallow levels, described in ascending order: Red sandstone, moderately fissile and markedly false-bedded. Lower nodule-bed, 1 inch to 6 inches thick, of fissile mica, ceous sandstone, containing obscure plant-remains converted into anthracite, chalcopyrite, chalcocite and iron pyrites. Very coarse grit or, in places, red sandstone; thickness and character variable. Upper nodule-bed, 6 inches to 2 feet thick exceptionally, generally about 10 inches. Soft, gray, friable shaly sandstone, with nodules of copper-ore. Red sandstone. All these strata lie flat, in places quite horizontal, in places dipping towards the river at 5° to 10°.

Jan 1, 1897

By J. L. Bruce, G. W. Nicolson

THE country rock of the Mavrovouni mine of the Cyprus Mines Corp. is hydrothermally altered, disintegrated pillow lava, with very little tensile strength ("short" ground). In places, especially when wet, it is heavy ground, though not extremely heavy except where movement has been caused by underlying or nearby stoping operations. Damage by caving from roof or sides of galleries is not sudden but progressively faster when the size of the cave increases as a result of the fall of small pieces. CEMENT AND CONCRETE LININGS During early operations, galleries in the country rock were supported by customary mine-timbering methods. Available timber, however, was of poor quality and of relatively high price, and replacements were frequent and expensive. Furthermore, the massive sulphide ore bodies required large volumes of fresh air for ventilation and cooling, and it was therefore desirable to provide smooth-lined galleries with low resistance for the introduction of air to the ore bodies. It was also desirable to eliminate hazards of fire in shafts and underground workings insofar as this would be practical. Cement and concrete were relatively cheap, and plans for using these in support of shafts, underground galleries, raises, and chutes, were developed steadily. Circular shafts with diameters ranging from 10 to 15 ft were adopted for all permanent shafts and airways. In places these were lined with concrete poured behind sectional pressed-steel forms especially constructed for this purpose. In other places, they were lined with precast-concrete blocks. It was found that such precast concrete of good quality could be produced on mass production scale and delivered at the mine from most favorable point of manufacture, at a cost of about 25 cents per cubic foot of concrete. This refers to prewar costs. As the use of concrete blocks in circular lined galleries was developed, it was found that there were very great advantages in the reduction of air resistance as compared with customary timber supports. After best methods had been developed, it was found that breakage and replacements were extraordinarily low, averaging only about 1 ½ pct per year during a period of about 15 years. Furthermore, it has been possible to reclaim for re-use a very large percentage of the concrete blocks from abandoned galleries. During the history of the operations precast-concrete blocks have been used for lining shafts, raises, ore chutes, galleries, and shaft stations, ranging from 3 to 16 ft id. The thickness of lining has varied from 5 to 10 in.; with I2 in. thickness in a few cases. Junctions of two galleries at angles ranging from about 30 to 60° are usually made of poured concrete behind sectional forms, or of a combination of poured concrete and precast blocks. In nearly all cases it has been found advisable to make the point of the wedge at the junction, of

Jan 1, 1947

By T. E. Leontis

Several publications1-7 during the past few years have demonstrated the markedly greater effect of cerium, as compared to all other alloying elements, in enhancing the strength and creep resistance of magnesium at elevated temperature either with or without the presence of other elements. In the work reported in Ref. 1-6, the cerium was added in the form of Mischmetal, which contains all the rare earth elements in essentially the same proportions as they occur in monazite sand, the principal ore of these metals. Mellor and Ridley7 have presented the creep characteristics at 200°C of magnesium alloys prepared both with pure cerium and with Mischmetal. Up to the present time, however, no comprehensive study of the effect of the various component elements of Mischmetal on the properties of sand-cast magnesium has been made. This hiatus in magnesium technology undoubtedly is associated with the difficulty in obtaining the rare earth metals separately. This investigation provides such a survey, the object of which was to determine which of the elements present in Mischmetal contributes the greatest effect in developing high strength and high resistance to creep at elevated temperatures. Toward this end the compositional variation of these properties has been determined as a function of temperature in the following alloy systems: 1. Magnesium-Mischmetal 2. Magnesium-cerium-free Misch- metal 3. Magnesium-didymiuin 4. Magnesium-praseodymium- lanthanum 5. Magnesium-cerium 6. Magnesium-lanthanum This designation, based on the names of the metals as furnished by the producer, is used throughout the paper in order to avoid the complicated system of listing all the elements present in the more complex alloys. The composition of the metals and the alloys is discussed in detail below. Preparation of Alloys ALLOYING INGREDIENTS The chemical composition of each of the six alloying ingredients used to prepare the alloys reported in this paper is given in Table 1. In each case, the percent total rare earths, percent cerium, percent neodymium, percent praseodymium, and percent thorium were determined in addition to the listed impurities. The percent lanthanum was determined by difference from the total rare earth content and consequently includes the other elements (samarium, terbium, yttrium, etc.) present in Mischmetal. These additional elements, however, seldom amount to more than 1 to 2 pet of the total rare earth content of Mischmetal. The iron content of the Mischmetal is considerably lower than that of the other metals. This grade of Mischmetal is now readily available. The metals are listed in the order of decreasing complexity. Elimination of the cerium from Mischmetal results in what the trade calls "Cerium-free Mischmetal." Carrying the separation a step further by eliminating the lantha-

Jan 1, 1950

By E. F. Koch, J. L. Walter

In a study of the structure and properties of tungsten wire used for lamp filaments, it became desirable to perform transmission electron microscopy on the wire in the annealed as well as in the drawn condition. Wire used for lamp filaments is generally drawn to diameters less than 0.010 in. which is too fine for the preparation of transmission samples from single wires. Thus, it is clear that some assembly of wires must be used to form a "wire sheet" similar to that used by Glenn and Duff.' Also, because recrystallized tungsten wire is brittle at room temperature, the "wire sheetJ' must be rigidly contained during any subsequent grinding and polishing operation. With these conditions in mind, a technique was devised for thinning tungsten wire of 0.001 to 0.010 in. diam for transmission electron microscopv. Sample Preparation. The commercially doped (218) tungsten filament wire was obtained from the Lamp

Jan 1, 1969

By Clifford J. Lewis, James L. Drobnick

Vexed with competition from relatively high grade foreign orebodies, perplexed by marginal, low grade domestic orebodies, and ironically faced with the fact that practically every metal needed in our economy is available domestically in ample quantity in the ground, our mining industry awaits the advancements in beneficiation technology that will bridge the gap between the ground and the market place for our presently unexploited mineral reserves. Among the vast number of research and development projects underway in the metals mining industry, there are a few chemical techniques in metals winning that, with further development or wider application, could have a profound effect on the industry. These techniques include the Imperial Smelting and Refining Process for complex lead-zinc ores, chlorination and fused salt procedures, the liquid ion exchange process, and the field of non-aqueous leaching. IMPERIAL SMELTING PROCESS The Imperial Smelting and Refining Process is of interest because it offers a possible economic route for the processing of complex zinc-lead-copper ores. The process represents the outcome of the combined efforts of metallurgists and engineers of Imperial Smelting Corporation. Ltd., the United Kingdom Subsidiary of the Consolidated Zinc Corporation, Ltd., and is the subject of patents throughout the world. This process is essentially the employment of the blast furnace for the production of zinc. Zinc has always resisted blast furnace technology, primarily because of the difficulty of condensing zinc vapor from dilute gases. The Imperial Smelting Process employs a blast furnace working at ordinary pressures and in a system which is able to con- dense a blast furnace gas of a very low zinc content.

Jan 11, 1963

By Harry A. Roe

THE power drag scrapers and the slackline cableway excavator have been called "long-range excavators." Broadly, their field of usefulness is restricted to work in which their long range of action permits them to operate economically, and which other, possibly more conventional, excavating units cannot do. Both of these machines dig or lift material and transport it to a remote dumping point. They combine these two functions in a single machine, nearly always in a single straight-line motion. [ ] The purpose of this paper is to examine the important features that distinguish the machines in this group from each other, as well as from other groups. The Machines The "power drag scraper" is a long-range excavating machine that employs a bottomless drag scraper operated back and forth between digging and dumping points by two haulage cables. The typical arrangement is that of Fig. 1. This is the "slusher" of the underground mine, as well as the "dragline scraper" of the sand and gravel industry, and other open-pit mining operations.

Jan 1, 1937

By John J. Stokes

Literature on the electrolysis of aluminum from cryolite melts and on the structure of these melts is surveyed critically. Data on density, freezing point, and other properties are reviewed. Theories of the electrolysis are examined in the light of these data. Two theories are presented which account equally well for the observations. * * * * In the early days, the process was thought of as a simple one. The actual mechanisms must be tremendously more complex. This paper is devoted to a rather narrow part of the whole subject, namely, what ions are present in the bath, and by what mechanism the current is carried.

Jan 4, 1958

By Andrew Allen

WHEN a mine is changed from hand, to me-chanical loading, the character of the coal dumped at the tipple is changed in many ways. Selective mining is not so easy with mechanical load-ers, and where much picking is done at the face it is apt to be wasteful anyway. Much recoverable coal is apt to be lost by too free gobbing and, in my opinion, picking at the face should be confined to removal of heavy rock, such as pieces of roof or bottom or sulfur balls. and to such clearly defined and persistent bands as can be readily recognized and segregated. With mechanical loaders of the shovel type, even this amount of gobbing is almost impossible. When coal is shoveled into a conveyor there should be no difficulty in doing as much picking as now by hand loading. The size of lumps may be greatly increased, on ac-count of the ease of handling them with a shovel, as the miners will not break them up in order to lift them into cars. Fines may be increased. This is, of course, not universally true, yet it is my opinion that a shovel breaks the coal more, as a rule, than hand loading. This might not be true with all types of shovels and is cer-tainly not true with a conveyor, either with or without the "duck-bill." The average car load will be greatly reduced in fields such as Illinois and Indiana, in which it is the practice to build up the coal above the sides. Where "level full" regulations prevail there should be no material change. When the coal comes to the tipple these differences usually result in the discovery, that many changes are necessary in the preparation plant. The increase in the percentage of fine sizes will probably not bother the screen, but may overload the conveying apparatus. The larger size lump may clog the chute, but as a rule the efficiency of the sizing screens is not greatly affected. In one completely mechanized mine the proportions of 6-in. lump and 2-in. screenings, when loading by hand, were 16.9 and 51.3 per cent respectively. When loading mechanically, these proportions changed to 15 per cent lump and 53.5 per cent screenings. The picking force on the tipple has been increased from 14 on hand loading to 33 men on mechanically-loaded coal. This is for an output of about 5000 tons.

Jan 4, 1927

Spencer Gulf takes off from the Great Australian Bight cutting a 200 mile deep wedge of water into the South Australia coastline. A pale winter sun shines yellowly on the choppy surface of this body of water which is progressively more salty as it approaches Port Augusta at the head of the Gulf. Once Port Augusta thrived as a grain port and the speedy clipper ships began or ended their legendary races there. On the eastern shores of Spencer Gulf, farm land spreads away from the water's edge. The western side of the gulf meets marginal grazing land of acacia tree and salt bush. Part way down the gulf, there are two industrial towns facing each other from opposite shores; Port Pirie on the east and Whyalla on the west. These towns are like half brothers, the common parent being the founders of Broken Hill Pty. Ltd., (BHP) who began lead smelting at Port Pirie and discovered iron ore near Whyalla needed for the lead smelting process. The iron deposits later became the inspiration for BHP's iron and steel business.

Jan 10, 1964

By H. B. Hunter, F. G. Stone, F. J. Dunkerley

Introduction and Literature Survey This is the second in a series of papers coming from this laboratory on the correlation of the low temperature tensile properties of tin-binary alloys with microstructure. These engineering data and those of the previous paper1 were obtained as the initial part of a long-range program to determine the changes in the fundamental mechanical properties accompanying the beta to alpha phase change in tin and its binary alloys below 13.2°C. Since it appears now that the more fundamental studies will be delayed,* and since no summary of the low temperature properties of these tin-base white bearing alloys was found in the literature, it was decided to publish all the engineering data thus far obtained. Accordingly, the tensile properties of thirteen binary alloys containing from 0.1 to 60 pet cadmium and 0.1 to 10.43 pet antimony measured at six temperatures from —196 to +23°C are presented here and their variations rationalized in terms of microstructure. A literature search showed that these systems had not been investigated at low temperatures, although both the tin-cadmium and tin-antimony2,3,4,5 and the tin-rich corner of the ternary system67 have been studied at room temperature. Hanson and Pell-Wal-pole5 and Homer and Plummer4 determined the tensile properties of alloys containing from 0 to 10 pet cadmium. The same authors3 determined the tensile strength and elongation in the tin-antimony system from 2 to 18 pet antimony at room temperature while Pell-Walpole et al.6,7 studied the properties of high tin and tin-antimony-cadmium alloys. Since there were many variables besides composition in these tests, it was difficult to make a valid comparison with the room temperature data of the present study, but in general the tensile strength and ductility values are in reasonable agreement. Pell-Walpole2 also determined the effect of grain size on the tensile strength of pure tin and 1 pet alloys of both antimony and cadmium. The true maximum stress was found to decrease exponentially as the number of grains in the cross-section increased. This effect of grain size was strikingly revealed in the present work, as indicated in a later section. Hanson and Pell-Walpole8 placed the solid solubility limit of antimony in tin at 3.5 pet at 20°C, increasing to 4 pet at 190°C, and then sharply increasing to 10.3 pet at 246°C (the latter being a peritectic point). Their results are in disagreement with those of previous investigators,9 and the discrepancy seems to lie in the micro-graphic observation of the second phase

Jan 1, 1950

By B. Haimson, C. Fairhurst

A criterion is Proposed for the initiation of vertical hydraulic fracturing taking into consideration the three stress fields around the wellbore. These fields arise from (1) nonhydrostatic regional stresses in earth, (2) the difference between the fluid pressure in the wellbore and the formation fluid pressure and (3) the radial fluid flow through porous rock from the wellbore into the formation due to this pressure difference. The wellbore fluid pressure required to initiate a fracture (assuming elastic rock and a smooth wellbore wall) is a function of the porous elastic constants of the rock, the two unequal horizontal principal regional stresses, the tensile strength of the rock and the formation fluid pressure. A constant injection rate will extend the fracture to a point where equilibrium is reached and then, to keep the fracture open, the pressure required is a function of the porous elastic constants of the rock, the component of the regional stress normal to the plane of the fracture, the formation fluid pressure and the dimensions of the crack. The same expression may also be used to estimate the vertical fracture width, provided all other variables are known. The derived equations for the initiation and extension pressures in vertical fracturing may be employed to solve for the two horizontal, regional, principal stresses in the rock. INTRODUCTION Well stimulation by hydraulic fracturing is a common practice today in the petroleum industry. However, this stimulation process is not a guaranteed success; hence, the deep interest shown by the petroleum companies in better understanding the mechanism that brings about rock fracturing, fracture extension and productivity increase. Geologists and mining people became interested in hydraulic fracturing from a different point of view: the method may possibly be employed to determine the magnitude and direction of the principal stresses of great depth. Numerous articles in past years have dealt with the theory of hydraulic fracturing, but they all seem to underestimate the effect of stresses around the wellbore due to penetration of some of the injected fluid into the porous formation.1-4 Excellent papers on stresses in porous materials due to fluid flow have been published5,6 but no real attempt has been made to show the effect of these stresses in the form of a more complete criterion for vertical hydraulic fracturing initiation and extension. This paper is such an attempt. ASSUMPTIONS It is assumed that rock in the oil-bearing formation is elastic, porous, isotropic and homogeneous. The formation is under a nonhydrostatic state of regional stress with one of the principal regional stresses acting parallel to the vertical axis of the wellbore. This assumption is justified in areas where rock formations do not dip at steep angles and where the surface of the earth is relatively flat. This vertical principal regional stress equals the pressure of the overlying rock, i.e., S33 = —pD, where S33 is the total vertical principal stress (positive for tension), p is average density of the overlying material and D is the depth of the point where S33 is calculated. The wellbore wall in the formation is considered to be smooth and circular in cross-section. The fluid flow through the porous elastic rock obeys Darcy's law. The whole medium is looked upon as an infinitely long cylinder with its axis along the axis of the wellbore. The radius of the cylinder is also very large. Over the range of depth at which the oil-bearing formation occurs, it will be assumed that any horizontal cross-section of the cylinder is subjected to the same stress distribution, and likewise that it will deform in the same manner. STATE OF STRESS PRIOR TO DRILLING OF WELLBORE At a depth D from the earth surface within the oil-bearing strata, it is assumed that the following are 1References given at end of paper.