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By R. E. Zinkham

An investigation has been conducted to compare short transverse and longitudinal fatigue and fracture properties in 4.25-in.-thick, high strength aluminum alloy plates. One plate was produced using standard rolling techniques while the other was pre.forged before rolling. Little difference was shown in fatigue strength of longitudinal specimens taken from mid-thickness of the plate. Howeuer, in the short transverse orientation fatigue strengths at 107 cycles were about 25 and 50 pct less, respectively, for the preforged and standard rolled plate. Differences in fatigue strengths were attributed to grain size and shape as well US orientation of constituents. Fatigue crack propagation rates and fracture toughness were compared at three different stress intensity (K) levels, using a constant compliance, double cantilever, wedge-shaped specimen. In a given plate, comparable fatigue crack Propagation rates were observed in the longitudinal (i9W) and short transverse (TW) orientations. Somezuhat gveater rates were observed in the short transzerse (TR) orientation. The preforged plute gave a lower rate for all three directions. Considerable secondary cracking developed, at times, over portions of the fatigue crack in both plates, particularly at the lower stress intensity levels in the short transverse specimens. Micro structure revealed constituent stringers as possible causes of the crack branching. Fracture toughness was considerably less in both plates in the short transuerse orientation. It is concluded that preforging not only improved directional tensile properties but also the fatigue and fracture properties in general. On occasion, aluminum plates have been milled away for hinges or bolted connections and stressed through the thickness or short transverse direction. Little or no information is available concerning fatigue characteristics or fracture toughness in this loading orientation in aluminum plate, or of the effect of fabrication on these properties. It was the intent of this project to examine, develop, and apply a unique specimen that has been advocated by others to study the fatigue characteristics and fracture toughness of two differently fabricated high strength aluminum plates. Linear elastic fracture mechanics criteria may be applied to the specimen so that the fatigue crack propagation rate and fracture toughness data may be of use for design or inspection applications. Fatigue characteristics are generally measured in the longtudinal or long transverse direction, where fairly large specimens such as center notched panels,' are usually employed. Limitations are evident due to plate thickness, however, in the type and size of specimen that may be tested in the short transverse direction without extensions. Therefore, a specimen that is to be loaded in this direction should, for convenience, be compact. The general type of fatigue crack propagation specimens discussed and employed herein meet this requirement. These specimens are commonly called double cantilever beam specimens and lately "crackline-loaded edge-crack specimens".2 They may vary from a slope of zero (parallel-sides) to a wedge shape, the type employed herein. In general for most specimens the stress intensity KI at the tip of a crack is a function of the load, P and crack length, a. Some varieties of the wedge shaped specimen, however, give essentially a constant stress intensity KI over a considerable range of crack length.' This feature can be a valuable asset in fatigue crack propagation experiments because the stress-intensity can be controlled simply by controlling the load without regard to crack length. MATERIAL AND METHODS Material. A standard rolled (light pass reduction) and a ~reforged and rolled (heavy pass reduction) plate of 7179-T651 material were used for the evaluation. The chemistry, processing history and average tensile properties are shown in Table I. Specimen Selection and Preparation. The specimen selected for the generation of fatigue initiation or S-N data was an axial tension type and is shown in Fig. 1. Specimens were taken from mid-thickness in the longitudinal and short transverse directions from both plates. Specimens were polished with 500 grit paper in a direction parallel to the loading axis. For the fatigue crack propagation tests, the specimen shown in Fig. 2 was used. This is similar to a specimen that has been employed by Mostovoy3 for fracture toughness studies on 7075-T6 aluminum alloy. It also fortuitiously agrees quite well with the dimensions of a specimen for which Srawley and Gross2

Jan 1, 1970

By Owen Thornton

Recently equations have been presented by Rose and Bruce' and by Rose², showing how the relative permeability of a reservoir rock may be determined from the capillary character of the rock. In particular, equations were developed to show the relationship between capillary pressure and the effective permeability to the wetting phase in a poly-phase flow system. The equations are as follows (nomenclature the same as in the Rose and Bruce paper) Rose and Bruce assume that the average length of path (L,), which the wetting fluid follows in flowing through a porous media is independent of the saturation to the wetting phase, so that 1 is a constant dependent only on the k rock, and the permeability to the wetting phase is a function of the saturation and of the capillnry pressure: In measuring the flow of ekctric current through partially saturated core samples, it has been observed that the electrical resistance usually is not a simple linear function of saturation. This fact indicates that the average length of path in the flow of electric current is not independent of saturation, but rather that the tortuosity of the path depends upon the average saturation to the conducting fluid as well as upon the characteristics of the rock. itself. Inasmuch as the flow of fluid and the flow of electric current in many respects are analogous, it may be indicated further that the length of path for fluid also may not be independent of saturation. The following relationship can be derived to express the resistance to flow of electric current through a core sample partially saturated with conductive wetting phase, the non-wetting phase being non-conductive: where L is the average length of path followed by the current in flowing through a length L of partially saturated core, where L is the length of current path when the core is fully saturated, and where Rs and R, are the specific resistivities of the partially saturated and saturated core sample, respectively. It will be noted that R., the specific resistivity of the core sample when S, = 1.0, is equal to the "formation resistivity factor"' multiplied by the specific resistivity of the saturating fluid. If it be assumed that the average lengths of path for fluid flow and for the flow of electric current are the same, then equation (5) may be combined with equations (l), (2) and (3) to give the following relationship: The above equation suggests including a correction for tortuosity when calculating the relative permeability of a reservoir rock to a wetting phase. The correction factor may be obtained from the resistivity-saturation relationship. For instance, the following calcu- lations are obtained for the unconsoli-dated sands described by Leverett Kw Kw Sw R°/Rs Pt/Pc¹ (Calc.) (Obs.) 0.30 0.08 0.88 0.02 0.0 0.40 0.16 0.94 0.06 0.04 0.50 0.27 0.97 0.14 0.11 0.60 0.40 0.98 0.26 0.21 0.70 0.53 0.98 0.39 0.35 0.80 0.68 0.99 0.57 0.54 0.90 0.84 0.99 0.77 0.76 1.00 1.00 1.00 1.00 1.00 It will be noted that the agreement between the calculated points and the observed data is rather good. Further investigation of the above method for obtaining relative permeabilities may be merited. For many sands within specified ranges of saturations the following relationship has been found to hold approximately': — =SW"......(7) Rs The exponent n in the above equation has been found to equal two for many sands so that equation (6) reduces to the following: The writer acknowledges the permission of The Texas Co. to submit this note for publication. 1. Walter Rose and W. A. Bruce—Jnl. of Pet. Tech., Vol. 1, No. 5, p. 127 (1949). 2. Walter Rose—Jnl. of Petr. Tech., Vol. 1, No. 5, p. 111 (1949). 3. G. E. Archie— -Trans. AIME, 146, 54 (1942). 4. M. C. Leverett— Trans. AIME, 142, 152 (1941). 5. M. C. Leverett—Trans. AIME, 132, 149 (1939).

Jan 1, 1949

By Owen Thornton

Recently equations have been presented by Rose and Bruce' and by Rose², showing how the relative permeability of a reservoir rock may be determined from the capillary character of the rock. In particular, equations were developed to show the relationship between capillary pressure and the effective permeability to the wetting phase in a poly-phase flow system. The equations are as follows (nomenclature the same as in the Rose and Bruce paper) Rose and Bruce assume that the average length of path (L,), which the wetting fluid follows in flowing through a porous media is independent of the saturation to the wetting phase, so that 1 is a constant dependent only on the k rock, and the permeability to the wetting phase is a function of the saturation and of the capillnry pressure: In measuring the flow of ekctric current through partially saturated core samples, it has been observed that the electrical resistance usually is not a simple linear function of saturation. This fact indicates that the average length of path in the flow of electric current is not independent of saturation, but rather that the tortuosity of the path depends upon the average saturation to the conducting fluid as well as upon the characteristics of the rock. itself. Inasmuch as the flow of fluid and the flow of electric current in many respects are analogous, it may be indicated further that the length of path for fluid also may not be independent of saturation. The following relationship can be derived to express the resistance to flow of electric current through a core sample partially saturated with conductive wetting phase, the non-wetting phase being non-conductive: where L is the average length of path followed by the current in flowing through a length L of partially saturated core, where L is the length of current path when the core is fully saturated, and where Rs and R, are the specific resistivities of the partially saturated and saturated core sample, respectively. It will be noted that R., the specific resistivity of the core sample when S, = 1.0, is equal to the "formation resistivity factor"' multiplied by the specific resistivity of the saturating fluid. If it be assumed that the average lengths of path for fluid flow and for the flow of electric current are the same, then equation (5) may be combined with equations (l), (2) and (3) to give the following relationship: The above equation suggests including a correction for tortuosity when calculating the relative permeability of a reservoir rock to a wetting phase. The correction factor may be obtained from the resistivity-saturation relationship. For instance, the following calcu- lations are obtained for the unconsoli-dated sands described by Leverett Kw Kw Sw R°/Rs Pt/Pc¹ (Calc.) (Obs.) 0.30 0.08 0.88 0.02 0.0 0.40 0.16 0.94 0.06 0.04 0.50 0.27 0.97 0.14 0.11 0.60 0.40 0.98 0.26 0.21 0.70 0.53 0.98 0.39 0.35 0.80 0.68 0.99 0.57 0.54 0.90 0.84 0.99 0.77 0.76 1.00 1.00 1.00 1.00 1.00 It will be noted that the agreement between the calculated points and the observed data is rather good. Further investigation of the above method for obtaining relative permeabilities may be merited. For many sands within specified ranges of saturations the following relationship has been found to hold approximately': — =SW"......(7) Rs The exponent n in the above equation has been found to equal two for many sands so that equation (6) reduces to the following: The writer acknowledges the permission of The Texas Co. to submit this note for publication. 1. Walter Rose and W. A. Bruce—Jnl. of Pet. Tech., Vol. 1, No. 5, p. 127 (1949). 2. Walter Rose—Jnl. of Petr. Tech., Vol. 1, No. 5, p. 111 (1949). 3. G. E. Archie— -Trans. AIME, 146, 54 (1942). 4. M. C. Leverett— Trans. AIME, 142, 152 (1941). 5. M. C. Leverett—Trans. AIME, 132, 149 (1939).

Jan 1, 1949

By Walter Rose

In a recent technical note, Owen Thornton&apos; suggests that wetting liquid relative permeability may be derived from the relationship: where Pd/Pc is the ratio of displacement pressure to capillary pressure at the wetting liquid satdration Sw, and I is the resistivity index at this saturation. Thornton shows that this expression gives values for relative permeability in good agreement with those experimentally determined by Leverett. We have recently developed another expression for krw which seems preferable to Equation 1 since it requires fewer experimental data for its verification. This equation may be derived in the following manner. Making use of the analogy between mass transfer of fluid in a porous medium and electrical conductivity through the fluid in the same medium, we can postulate a hydraulic formation resistivity factor analogous to an electrical formation resistivity factor. From Poiseuille&apos;s Law the resistivity to flow in a tube of radius R is of the form 8u/R², where is the viscosity of the fluid. Similarly7 the resistivity to flow in a porous medium of the same dimensions as the tube is given by D&apos;Arcy&apos;s Law as where k is the permeability of the medium. The hydraulic formation resistivity factor, Ff, is thus the quotient of these two resistivities, or: But permeability is defined by the KO-zeny equation as: where: r is the average pore radius of the porous medium, L. is the average tortuous length of the average pore, + is the porosity, and L is the bed length. This gives Fr as a function of the (La/L) .-.-.tortuosity ratio and porosity, or in explicit form: where: T = (La/L)&apos;, and N is the number of pores of radius, r, which will be found in any cross sectional area, x R&apos;. That is, N = R²/r². It will be clear from the foregoing considerations that the hydraulic formation fat. tor should be dependent on the value of R which in every case must be arbitrarily selected. By analogy, the hydrauiic formation factor, Fcf, characterizing the porous medium at Sw<1,will be given by: R² NT. where ke is the effective wetting liquid permeability obtaining at Sw<l, and Te is the square of the (Las/L) ratio defined by Thornton. Therefore, the hydraulic resistivity index, If, is: However, Thrnton gives I as: and it follows that: Equation 2, when checked against the data of wyckoff and Botset² and some of the Morse et al data³, gives comparisons as shown at the bottom of this page. Computations based on Leverett&apos;s data, quoted by Thorntaon, gives computed krw values somewhat lower than the experimental values. Moreover, other instances can be cited where we find that neither Equation 1 nor Equa tion 2 is checked by experimental data. The work of Botset&apos; on the Nichols Buff sandstone and Morse et a1 on oil wetted Bradford sandstone are such instances. A reason for these discrepancies may lie in the fact that if both Equations 1 and 2 are presumed always to give accurate values for krw, it follows that PC = Pd/Sw". Such an expression, it is well known, is too simple to describe accurately the capillary pressure behavior of all porous media. However, it is believed that a particular advantage resides on the use of Equation 2, since it is not dependent for its utility on a knowledge of the capillary pressures obtaining in dynamic flow svsterns. No practical technique for measuring the capillary pressures characterizing the fluid distributions in dynamic flow systems has yet been proposed. Acknowledgment is given to Dr. Paul D. Foote, executive vice-president of the Gulf Research and Development Company, for permission to publish this note. 1. Owen F. Thornton, "A Note on the Valuation of Relative Permeability," J. Pet. Tech., 1:7, Section 1, July, 1949. 2. R. D. Wyckoff arid H. G. Botset, "The Flow of Gas-Liquid Mixtures through Porous Media," Physics, 7:325-345, 1936. 3. R. A. Morse, P: L. Terwilliger, .and S. T. Yuster, "Relative Permeability Measurements of Small Core Samples," Oil and Gas J., 46:109-125, Aug. 23, 1947. 4. H. G. Botset, "Flow of Gas-Liquid Mixtures Through Consolidated Sand," Trans. AIME, 136:91, 1940.

Jan 1, 1949

By Walter Rose

In a recent technical note, Owen Thornton&apos; suggests that wetting liquid relative permeability may be derived from the relationship: where Pd/Pc is the ratio of displacement pressure to capillary pressure at the wetting liquid satdration Sw, and I is the resistivity index at this saturation. Thornton shows that this expression gives values for relative permeability in good agreement with those experimentally determined by Leverett. We have recently developed another expression for krw which seems preferable to Equation 1 since it requires fewer experimental data for its verification. This equation may be derived in the following manner. Making use of the analogy between mass transfer of fluid in a porous medium and electrical conductivity through the fluid in the same medium, we can postulate a hydraulic formation resistivity factor analogous to an electrical formation resistivity factor. From Poiseuille&apos;s Law the resistivity to flow in a tube of radius R is of the form 8u/R², where is the viscosity of the fluid. Similarly7 the resistivity to flow in a porous medium of the same dimensions as the tube is given by D&apos;Arcy&apos;s Law as where k is the permeability of the medium. The hydraulic formation resistivity factor, Ff, is thus the quotient of these two resistivities, or: But permeability is defined by the KO-zeny equation as: where: r is the average pore radius of the porous medium, L. is the average tortuous length of the average pore, + is the porosity, and L is the bed length. This gives Fr as a function of the (La/L) .-.-.tortuosity ratio and porosity, or in explicit form: where: T = (La/L)&apos;, and N is the number of pores of radius, r, which will be found in any cross sectional area, x R&apos;. That is, N = R²/r². It will be clear from the foregoing considerations that the hydraulic formation fat. tor should be dependent on the value of R which in every case must be arbitrarily selected. By analogy, the hydrauiic formation factor, Fcf, characterizing the porous medium at Sw<1,will be given by: R² NT. where ke is the effective wetting liquid permeability obtaining at Sw<l, and Te is the square of the (Las/L) ratio defined by Thornton. Therefore, the hydraulic resistivity index, If, is: However, Thrnton gives I as: and it follows that: Equation 2, when checked against the data of wyckoff and Botset² and some of the Morse et al data³, gives comparisons as shown at the bottom of this page. Computations based on Leverett&apos;s data, quoted by Thorntaon, gives computed krw values somewhat lower than the experimental values. Moreover, other instances can be cited where we find that neither Equation 1 nor Equa tion 2 is checked by experimental data. The work of Botset&apos; on the Nichols Buff sandstone and Morse et a1 on oil wetted Bradford sandstone are such instances. A reason for these discrepancies may lie in the fact that if both Equations 1 and 2 are presumed always to give accurate values for krw, it follows that PC = Pd/Sw". Such an expression, it is well known, is too simple to describe accurately the capillary pressure behavior of all porous media. However, it is believed that a particular advantage resides on the use of Equation 2, since it is not dependent for its utility on a knowledge of the capillary pressures obtaining in dynamic flow svsterns. No practical technique for measuring the capillary pressures characterizing the fluid distributions in dynamic flow systems has yet been proposed. Acknowledgment is given to Dr. Paul D. Foote, executive vice-president of the Gulf Research and Development Company, for permission to publish this note. 1. Owen F. Thornton, "A Note on the Valuation of Relative Permeability," J. Pet. Tech., 1:7, Section 1, July, 1949. 2. R. D. Wyckoff arid H. G. Botset, "The Flow of Gas-Liquid Mixtures through Porous Media," Physics, 7:325-345, 1936. 3. R. A. Morse, P: L. Terwilliger, .and S. T. Yuster, "Relative Permeability Measurements of Small Core Samples," Oil and Gas J., 46:109-125, Aug. 23, 1947. 4. H. G. Botset, "Flow of Gas-Liquid Mixtures Through Consolidated Sand," Trans. AIME, 136:91, 1940.

Jan 1, 1949

By H. Dykstra

Calculated wellbore pressures were obtained for parameters of radilcs ratio and permeability. In all cases bur two, after-production was allowed to occur for one day. The calculated pressure build-up data were compared with actual pressure build-up data from a condensate well. The paper discusses the comparison, gives reasons for, inability to match calculated (2nd actual data, and presents conc1usions derived from the comparison. INTRODUCTION Considerable information has been published on the decline in wellbore pressure for oil and gas fields resulting from production of fluids. Considerable information also has been published on pressure build-up for oil fields, but relatively little has been published for gas and condensate fields. Perrine&apos; summarized the equations derived for pressure build-up in oil wells and showed how the different methods could be applied. On the other hand, very little theoretical information has been published on pressure build-up in gas or gas-condensate wells.2-4 Tracy,&apos; by pointing out the similarity between the equation describing oil wellbore pressure decline and the equation describing gas wellbore pressure decline, showed how methods of pressure build-up analysis could be applied to a gas well. In analyzing pressure build-up data for gas or gas-condensate wells, it would be very desirable to compare actual pressure build-up data with calculated pressure build-up data. Such a comparison would lead to a better feeling for the quantitative picture of gas-well build-up curves and would help to establish a degree of confidence in a given build-up curve. This paper discusses the comparison and presents conclusions made from it. Calculated wellbore pressures are given for parameters of radius ratio and permeability. In all cases but two, after-production was allowed to occur for one day. The work was done in an attempt to evaluate the reserves of a gas-condensate field. As will be discussed later, it was not possible to make an evaluation. METHOD OF CALCULATION The method used for solving the depletion and pressure build-up behavior for a gas-condensate well was that developed by West, Garvin and Sheldon.5 or the IBM 704 computer program used, it was assumed that liquid condensing out of solution would have only a minor effect on the flow behavior. Therefore, the field was treated as having single-phase flow, with the gas saturation S, remaining constant at unity minus the connate-water saturation Sw. As will be discussed later, this may not have been a good assumption. It also was assumed that oil production could be considered as equivalent gas production by using a conversion factor based on an analysis of the liquid produced. An outer boundary condition of no-flow was assumed. BASIC DATA The data required for the study were reservoir properties, fluid properties and production data. Reservoir properties included the following: thickness h, 179 ft; porosity, 0.194; connate-water saturation, 0.43; gas saturation, 0.57; permeabilities k, 1.0, 0.5, 0.25 and 0.15 md; radius ratios re/rw, 800, 1,000 and 2,000; wellbore radius rw, 5 in.; initial reservoir pressure P, 6,529 psia; and reservoir temperature, 272°F. The selection of permeabilities was based on core-analysis data showing an average air permeability of about 2 md. With a relatively high connate-water saturation, the average effective gas permeability would be about one-half, or less, of the air permeability. The selection of radius ratios was based partly on the observed rapid decline in wellbore pressure during production and partly on the fact that the well was believed to be located in a relatively small fault block. Reservoir fluid properties were obtained from a reservoir fluid study on a recombined sample of gas and condensate. Gas formation-volume factors were calculated from pressure-volume measurements made at reservoir temperature. Gas viscosities were calculated by the method of Carr, et al,G from an analysis of the re-combined sample. These data are shown as a function of pressure in Table 1. The production schedule from the gas-condensate

By R. L. Mauger, P. E. Damon, B. J. Giletti

This report includes the lead isotopic dating of a suite of galenas from Arizona and an application of the K-Ar method to the dating of a Laramide porphyry copper deposit, the Silver Bell Mining District. The lead isotopic data supports prior age assignments based upon geologic inference. The Silver Bell study illustrates the necessity of correlative geologic and petrographic investigations for the interpretation of the results of potassium-argon dating. LEAD ISOTOPIC DATING OF GALENAS FROM ARIZONA ORE DEPOSITS A group of galenas from Arizona ore deposits have been analyzed for lead isotope ratios. The results were used to calculate model ages by the. method of Russell, Stanton and Farquhar,l6 in which the age is calculated directly from the Pb206/Pb207 ratio. The use of Pb206/Pb207 ratios eliminates the errors inherent in measuring the abundance of Pb204. The Holmes-Houtermanns model is the other model commonly used for calculating model ages. Both models assume that any lead sample is composed of primeval and radiogenic components and the calculated age is the time at which the lead was extracted from its source area. Using the Holmes-Houtermanns model, a lead is ordinary if its isotopic ratios lie on an isochron. The growth curve that passes through the experimental point determines the U/Pb ratio in the source area. The RSF model assumes the source area for conformable leads is the mantle, that this has a uniform U/Pb ratio, and thus all ordinary leads must lie on a single growth curve, having a mantle U/Pb ratio. The definition of an ordinary lead differs between the models, and differences in age arise mainly from the assumptions made to evaluate parameters in the model equations. These assumptions depend on the hypothesis chosen to explain ore genesis. In the RSF Model, the Pb206/Pb207 ratio is derived as a function of time. The equation contains three undetermined parameters which are evaluated by assuming three known points lie on the curve. These are the following: 1) Primeval lead from the Canyon Diablo and Henbury meteorites, 2) Modern conformable leads which lie on Patterson&apos;s zero isochron, 3) Lead from the Bathurst, New Brunswick base metal deposits. The Bathurst deposits are postulated to be examples of "conformable base metal deposits", as proposed by Stanton.l9 A conformable deposit has a particular genetic history and, as a result, the orebody conforms to stratigraphic layering in the host rock. The metals are brought to the surface in volcanic rocks which originated in the mantle. Weathering products of these rocks, including sulfur and metals, accumulate in areas undergoing sedimentation. The formation of sulfide ion in the sediments by the action of sulfate reducing bacteria causes fixation of iron as pyrite. If the pyrite becomes concentrated in favorable stratigraphic horizons, any base metal deposit eventually formed by replacement of pyrite will have a strata bound character. Compaction and expulsion of pore water from the sediments at depth result in upward mobility of solutions containing soluble base metal chlorides. The strata with high pyrite content act as chemical traps for the base metal ions and replacement occurs. An important result of this general evolutionary model is that, if complete separation of lead and parent isotopes occurred during accumulation of the sediments, any ore deposit formed solely of metals derived from those sedimentary rocks will contain "conformable" lead. This would be true even if the actual ore deposit were formed at a later date by some epigenetic process. In this case, mineralization would be controlled by local conditions, and need not conform to stratigraphic layering. Also, any ore deposit containing lead derived from a mantle or mantle-like source, even though not conformable in Stanton&apos;s sense, will fall on the curve for conformable ores and thus give a meaningful model age. Model ages for Arizona galena deposits are listed in Table 1. Fig. 1 is a location map. Jerome-Humbolt District: Galenas from the United Verde mine at Jerome and the Iron King mine at Humbolt give model ages of 1750 m.y. and 1640 m.y. respectively. Both deposits are massive sulfide bodies in a host rock of older Precambrian

Jan 1, 1965

By B. J. Kochanowsky

TO improve blasting methods it is necessary to know how the explosive force acts and how rock resists this force. Because of the tremendous power developed within milliseconds and the great number of other factors directly affecting the technical and economic results, an analysis of the fundamentals of blasting theory is difficult. But since the rules used for layout design and for calculations of size of explosive charges are based on theoretical assumptions, complete knowledge of blasting theory has great practical importance in mining. Analysis of Blasting Theory: It is interesting to note the opinion of blasting experts with respect to contemporary blasting theories. F. Stussi; Professor of the University of Zurich, stated: "We do not have enough experience yet to change our army engineering regulations in blasting and base it on new fundamentals. It is our duty to collect more practical data and to do more research in blasting to close this gap." K. H. Fraenkel,2 editor of the Manual on Rock Blasting published in 1953 in Sweden and written by well-known Swedish, German, Swiss, and French blasting and explosive experts, said: "To the best of our knowledge no suitable formulas for civil blasting work are to be found in the American, French or German literature." Present blasting theory is based upon two assumptions. 1) The blasting force of explosive acts in concentrical and spherical form. 2) Rock resistance against the explosive force is directly proportional to the strength characteristics of the rock. The first classical formula based on theoretical fundamental in blasting theory for explosive charge calculation was introduced by Vauban, a military engineer who lived 300 years ago. It was Vauban who proposed the famous formula L = w3 q, where L is the explosive charge, w = line of least resistance, and q = specific explosive consumption proportional to the weight of rock. Later engineers used q as proportional to the strength of the rock. Since Vauban&apos;s time different suggestions concerning blasting theory have been proposed. However, the principles stated at that time so affected the thinking of later generations that his formula is still in use and practically unchanged. The first controversy concerned the form of crater. It was found that geological features of rock affected its form. The factor q was analyzed thoroughly by Lares3 and later by Ohnesorge," Weichelt,5 Bendel,6 and others, but the assumption remained that resistance against explosive force is directly proportional to the strength of the rock blasted. The greatest controversy, which has not yet been settled, concerned w. It was noted that w3 is more appropriate for long lines of resistance and w2 for lines of resistance less than 15 ft. Based on the assumption that the explosive force acts concentrically and spherically, spacings between charges were limited to distances not greater than the length of line of least resistance. Sometimes larger spacing is recommended, but this is due to the advantageous geological and physical properties of rock and not to the action of an explosive force as such. In addition to the classical formula, empirical formulas are used widely. These state that the explosive charge is directly proportional to the volume of blasted rock in cubic yards, and the amounts of explosive required are usually expressed in pounds of explosive per cubic yard of rock. Empirical and classical formulas are contradictory. In the empirical formula, but not in the classical formula, explosive charge is taken proportional to all three space axes: line of least resistance, spacing, and bench height. In spite of this contradiction, both formulas give good results. This is possible because as now practiced the explosive charge calculation for heavy burdens need not be highly accurate. Each, open pit or quarry, usually works with a certain relation between bench height and line of least resistance and between charge spacing and line of least resistance. When these relations are changed, however, the specific explosive consumption q changes greatly. This is one of the reasons why the principles on which the formulas are based appear to be incorrect. In addition to the formulas discussed, others exist and are based more or less on the same theoretical

Jan 1, 1956

By J. E. Burke, A. M. Turkalo

IN 1923 Desch¹ pointed out that the grains in a metal which is anisotropic with respect to its thermal coefficient of expansion would contract differently upon cooling, and that the stresses developed might approximate the plastic strength of the metal. More recently Boas and Honeycombe2-5 studied the behavior of several metals upon thermal cycling and observed that the stresses developed in arlisotropic metals are great enough to produce slip lines in individual grains and a roughening of the specimen surface. This phenomenon they have named "thermal fatigue." The mechanism they propose involves essentially a kneading of the grains, the deformation being alternately in compression and tension in a given grain as the temperature is changed in one direction and then the other. The present work was undertaken to investigate the possibility that an additional mechanism might operate to produce plastic deformation during thermal cycling—a "thermal ratchet" that depends upon a combination of grain boundary flow to relax the stress that develops between differently oriented grains upon raising the temperature and transcrys-talline slip to relax the oppositely directed stress which develops on lowering the temperature. Thus, thermal cycling should produce a nonreversible distortion such that certain grains will change shape differently from their neighbors with a simultaneous displacement being produced at the grain boundary. Temperature Dependence of Grain Boundary and Grain Strength The critical resolved stress for the initiation of slip in metal grains is only mildly affected by temperature." For example, in cadmium it decreases from 0.15 to about 0.05 kg per sq mm when the temperature is increased from 20° to 458°K and further temperature increase causes little further decrease. On the other hand, the work of KG1 indicates that the grain boundaries behave in a viscous fashion that can be described8 by the expression: t = BVexp(Q/RT) [1] t is the shearing stress on the boundary; B, a constant; V, the flow rate at the boundary; Q, the activation energy for grain boundary flow; R, the gas law&apos;s constant; and T, the absolute temperature. Eq 1 indicates that the stress necessary to cause a given grain boundary flow rate, V, decreases rapidly with increasing temperature. The value of the constant B is such that at sufficiently low temperature and ordinary strain rates deformation will occur preferentially by slip rather than by grain boundary flow. There is considerable evidence to indicate Consider the bicrystal shown in Fig. 1. In grain 1 the slip plane lies 45 " to the boundary while in grain 2 the slip plane is 90" to the boundary. The coefficients of expansion of the grains in a direction parallel to the length of the crystal are a1 and a, with a, > a2 for the orientations shown. The sequence of events that can occur upon heating and cooling this specimen is illustrated schematically in Fig. 2. Initially there is assumed to be no stress in the specimen (A). Upon heating, grain 1 attempts to become longer than grain 2, but is constrained by grain 2. Thus grain 1 is loaded in compression and grain 2 is loaded in tension, and a shearing stress is present across the boundary (B). As the temperature is increased, the stress will build up, and finally grain 1 will be plastically deformed by slip, since the greater stress is resolved on its slip planes. Any further heating will result in more slip and the stress will remain constant until some temperature T* is reached where the stress can be relaxed by grain boundary flow.† At this relaxation temperature (C) a step will appear between grain 1 and grain 2. Further heating above T* will cause grain 1 to become relatively longer, but no stress will appear because the grain boundary is too weak to support the stress (D). Upon cooling again, at T* (E), the grain boundary will again be able to support a shearing stress, and upon cooling further, grain 1 will be loaded in tension and grain 2 in compression (F). When the decrease in temperature below T* is sufficient to impose the critical shear stress upon the slip plane of grain 1, it will be stretched by slip.

Jan 1, 1953

By William Y. Holland, Roger M. Cook

In view of the increasingly widespread deterioration of concrete structures as the result of the interaction of the alkalies sodium and potassium released by hydration of portland cement and susceptible rocks and minerals in aggregates, it is believed that a paper summarizing the geographic distribution of these aggregates will be of interest to producers and users of concrete, concrete products, and concrete-making materials. THIS paper reviews the problem of alkali-aggre-gate reaction in concrete and describes the geologic and geographic occurrence and distribution of alkali-reactive sand and gravel in western United States. It includes no discussion of crushed stone or synthetic aggregates. Most deposits of sand and gravel are accumulations of particles of rocks and minerals from a variety of sources, and it is not unusual for at least one or two varieties of the rocks to contain some form of reactive material. Examination by petro-graphic methods of many sands and gravels, as well as manufactured aggregates, has shown that a comparatively high proportion of the deposits does contain, in greater or lesser degree, rocks and minerals known to be deleteriously reactive with the alkalies of cement. Fortunately the amount of reactive materials is commonly less than that necessary to cause deleterious effects in concrete. As investigation of unsound concrete structures progresses, it becomes evident that the alkali-aggre-gate reaction is even more widespread than supposed, Figs. 1 and 2. Even though some parts of the country appear at present to be immune, further investigations will probably show that the effects of alkali-aggregate reaction can be seen in many structures in these areas, although only on a small scale in most of them. Many concrete structures will, of course, have lived their useful life before disintegration from this cause is serious, and in others the alkali-aggregate reaction may never become significant even though the microscopic evidence of reaction is present. The alkali-aggregate reaction first was reported to be a cause of deterioration of concrete in 1940 when Stanton1 described expansion of concrete pavements in California. Similar expansion and deterioration of concrete was recognized during succeeding years in concrete structures located in many parts of the country, but particularly in the western states. A number of concrete laboratories2 became interested in the problem. It was soon determined that only certain combinations of aggregate and cement caused the alkali-aggregate reaction to take place, and moreover that the reaction progresses only in the presence of water. Further research proved that cements containing more than 0.60 pct total alkalies (pct Na,O + 0.658 x pct K2O), when used with aggregates containing appreciable amounts of reactive ingredients, caused the reaction to take place, usually with subsequent deterioration of the concrete. During the last few years this limitation has been adhered to in both government and private construction as the maximum allowable alkali content of cement to be used with aggregates of known alkali reactivity. Because of this limitation, it appears that deleterious reaction either has been reduced or eliminated in many recently built structures in which it probably would otherwise have occurred. Recent tests have shown that the degree of expansion obtained with any particular cement-aggre-gate combination depends not only on the alkali content of the cement but also upon the relation of this alkali content to the amount and degree of reactivity of reactive constituents in the aggregate.&apos; In laboratory mortar bars, opal and cements with alkali content of as low as 0.2 pct (as equivalent of Na2O) have produced deleterious expansion as the result of alkali-aggregate reaction. These experiments demonstrate that aggregates containing even 0.1 pct of opal are deleteriously reactive. It was soon determined that alkali-silica gels were formed by the interaction of the alkalies of the cement and the reactive aggregate, Figs. 3 and 4. Osmotic or swelling pressures produced by the continued hydration of these gels cause expansion of the concrete with resulting cracking, warping, and dislocation. Evidence of the alkali-aggregate reaction can be seen by a petrographic study of the deteriorated concrete. Among the first structures studied by this method was Parker Dam on the Colorado River, California-Arizona. In the concrete from this dam pebbles of rhyolite, andesite, siliceous limestone, and chalcedonic chert were found to be reactive.

Jan 1, 1954

By E. T. Hayes, A. H. Roberson, M. H. Davies

R. F. Dornagala and D. J. McPherson (Armour Research Foundation, Chicago)—I should like to compliment the authors for a workmanlike job in determining the partial phase diagram of a system comprised of two rnetals which are certainly not easy to work with. We are completing work at Armour Research Foundation on an Atomic Energy Commission-sponsored project for the determination of eight zirconium binary diagrams. Work on the Zr-Cr system has been completed and should be published within the next year. For our work, Westinghouse Grade 3 iodide crystal bar served as the zirconium melting stock. Johnson-Matthey, electrolytic chromium, specially treated for oxygen removal, was employed. The overall constitution of the system determined at Armour Research Foundation is in very good agreement with the present work. We found a eutectic at 18 pct Cr and 1280 °C, somewhat lower than the value reported. This temperature was confirmed by thermal analysis, incipient melting studies, and regular isothermal anneals. The eutectoid was located close to 1 pct Cr and 835°C by metallographic analysis of annealed specimens. Maximum solubility of chromium in /S zirconium was 4.5 pct at the eutectic temperature. Chromium solubility in a zirconium was less than 0.28 pct at all temperatures. We found the compound at 53 pct to melt around 1700°C, with an open maximum, but determined its crystal structure to be hexagonal close-packed (MgZn, type). The lattice parameters were in excellent agreement with those determined by Wallbaum in 1942. The diagrams are in substantial agreement, and .part of the differences are undoubtedly due to the use of different zirconium melting stock. M. K. McQuillan (Birmingham, England)—I read this paper with a great deal of interest, as it covered the same field as some work of my own.&apos; There are a number of points in the present paper on which I would like to comment. First, I should say that I, too, used zirconium prepared by magnesium reduction of the tetrachloride and electrolytically prepared chromium, and melted the alloys in a Kroll-type arc furnace. The purity of my alloys should, therefore, be comparable with the purity of those of the present authors, and any differences in our observations would not be expected to be attributable to this cause. The differences between my observations and theirs concern the presence of the eutectic, the temperature of the eutectoid, and the melting point of the compound. I would be very much interested in any further evidence the authors may have for the occurrence of the eutectic at 1380°C. During the course of my work I noted that a number of my alloys containing 60 to 90 pct Zr melted at about 1400 °C, and for a time assumed that a eutectic occurred at this temperature as described in the paper. On further investigation, however, I found that the structures of the as-melted alloys could not be made to fit in with this interpretation of the system. If a eutectic exists in this region of the system it would be expected that the as-melted alloys would show the usual type of cast structure, i.e., dendrites of the compound plus eutectic. This, however, does not occur, as may be seen from Fig. 9. The compound seen there is not dendritic in form, and the remaining material is by no means certainly eutectic. It may be argued that a compound such as ZrCrl would not form dendrites but would tend to crystallize in geometric shapes. In this case, however, I have evidence to the contrary, as on the chromium side of the compound, where a eutectic occurs at about 1545"C, the compound formed from the liquid takes on a conventional dendritic form, and the eutectic is observed in the interdendritic spaces in the usual way. There is no reason to suppose that the compound would behave differently in an alloy lying on the zirconium side of the compound composition if a eutectic existed there too.

Jan 1, 1953

By E. C. Smith

THE CHAIRMAN.-Mr. Earle Smith- has kindly offered to make some remarks in connection with segregation in the product, Mr. Smith: E. C. SMITH,* Cleveland, Ohio-I will start this off by a story of the code days of the American Iron and Steel Institute. In those days, Republic did not have a big strip mill, and the question came up of the check analysis of rimmed steel. I suggested that they let me be the chairman of the Committee on Accumulating the Information on the Variation of the Composition of the Ingots of Rimmed Steel. Somebody wanted to know why I wanted to be the chairman. I said, "We don&apos;t make any of the big ingots of rimmed steel, and no matter who makes them they are so bad that you don&apos;t dare publish the information. So if I collect it and hide it you can&apos;t charge me with having done anything that really disrupted the commercial situation. So, everybody furnished me with a rather complete story as to the horrible variations in big rimmed ingots. I took it out to my house and put it away, and it is still there. Now, segregation in the big ingot is no longer an "-academic-matter-as far as II am concerned. ¬I am in a situation like that of the German who was told in 1936 about the coming war. He said: "Until it is your throat that is going to be cut, you don&apos;t pay any attention to what is happening to the other man." That is the way with the problem that we have in front of us. Recently I have been told that the comptroller was questioning the payment for certain articles of stamped steel that had been made from rimmed steel, because upon check analysis of the rimmed steel it had been determined that these stamped articles were not within the compositions that were included in the specification, and therefore he as the comptroller had no alternative. It was not meeting the specification; therefore, no payment. So I would say to all of you: You can very seriously consider this matter of segregation now and on into the future on the basis of the fact that it is actually going to cost your companies, which are making these products, money unless there is some new idea about the infallibility of quantitative chemists who analyze some of these products or lawyers who read specifications. I don&apos;t know which man is going to be the major factor in the future. If the National Bureau of Standards could in some way show the specification writers the variation between good chemists analyzing for what they expect to be umpire results, the writers would certainly realize that some of the specifications to which we have calmly signed our names as being O.K. are well, as one man said to me, they might be filled by the devil, and they, certainly could be filled by the Lord, but they could not be filled by mankind. I would like to inject two or three things into a segregation study which I want you to think about, because I would be a little surprised if there is very much discussion of them. In the first place, we generally make steel in the United States in the basic open hearth, and I do not think there has been nearly enough consideration given to segregation within the bath before it moves into the ladle. I am sure that any of the people who handled the 9400 series of the NE series when it contained the 0.60 per cent silicon have more respect than they had previously for the segregation that is within the ladle; that is, before the metal reaches the ingot mold, the frozen ingots and the segregation in them. Another point to which I think we ought to give serious consideration is the segregation of iron oxide in the ingot-iron type of material, where the distinction between that and the steel segregation is that it is actually segregating iron oxide. Normally we are segregating some form of carbon or sulphur, or something like. that, with the stamping steel industry now coming down into the ranges of chemistry, where the segregation of iron oxide will be just

Jan 1, 1944

By Earle C. Smith

The Chairman.—Mr. Earle Smith has kindly offered to make some remarks in connection with segregation in the product, Mr. Smith: E. C. Smith,* Cleveland, Ohio—I will start this Off by a story oF the code days of the American Iron and Steel Institute. In those days, Republic did not have a big strip mill, and the question came up of the check analysis of rimmed steel. I suggested that they let me be the chairman of the Committee on Accumulating the Information on the Variation of the Composition of the Ingots of Rimmed Steel. Somebody wanted to know why I wanted to be the chairman. I said, "we don&apos;t make any of the big ingots of rimmed steel, and no matter who makes them they are so bad that you don&apos;t dare publish the information. So if 1 collect it and hide it you can&apos;t charge me with having done anything that really disrupted the commercial situation." So, everybody furnished me with a rather complete story as to the horrible variations in big rimmed ingots. I took it out to my house and put it away, and it is still there. Now, segregation in the big ingot is no longer an "academic " matter as far as I am concerned. I am in a situation like that of the German who was told in 1956 about the coming war. He said: "until it is your throat that is going to be cut, you don&apos;t pay any attention to what is happening to the otherman." &apos;That is the way with the problem that we have in front of us. Recently I have been told that the &apos;Omptroller was questioning the payment for certain articles of stamped steel that had been made from rimmed steel, because upon check analysis of the rimmed steel it had been determined that these stamped articles were nut within the compositions that were included in the specification, and therefore he as the camptroller had no alternative. It was not meeting the specification; therefore, no payment. So I I say to all of you: You can very seriously consider this matter of segregation now and on into the future on the basis of the fact that it is actually going to cost your companies, which are making these products, money unless there is some new idea about the infallibility of quantitative , chemists who analyze some of these products or lawyers who read specifications, I don&apos;t know which man is going to be the major factor in the future. if the National Bureau of Standards could in some way show the specification writers the variation between good chemists analyzing for That they expect to be umpire eel. the writers would certainly realize that some of the to to which we have calmly signed our names as being O.K. are— well, as one man said to me, they might be filled by the devil, and they certainly could be filled by the Lord, but they could not he me by mankind. I would like to inject two or three things into a segregation study which I Want you to think about, because 1 would be a little surprised if there is very much discussion of them, In the first place, we generslly make steel in the United States in the basic open hearth, and I do not think there has bee,, nearly enough consideration given to segregation German the bath before it moves into the ladle. I am sure that any of the people who handled the 9400 series of the NE series when it contained the 0,60 per cent silicon have more respect than they had previously for the segregation that is within, the ladle; that is, before the metal reaches the ingot mold, the frozen ingots and the segregation in them. Another pint to which I think We ought to sis serious consideration is the segregation of iron oxide in the ingot-iron type of material, where the distinction between that and the steel segregation is that it is actually segregat. ing iron oxide, Normally we are segregating some form of carbon or sulphur, or something like that, with the stamping steel industry now coming down into the ranges of chemistry, where the segregation of iron oxide will be just

Jan 1, 1945

By P. G. Winchell, A. J. Heckler

An experimentally simple method for determining the effect of alloying elements on the activity of carbon is validated in Fe-Ni-C austenite. The technique consists of the equilibration of carbon between specimens of different nickel contents within a sealed silica capsule. The attainment of carbon equilibrium within each capsule is evidenced by: 1) in each capsule specimens of the same nickel content attained the same final carbon content regardless of their initial carbon contents, 2) in every capsule the final carbon content was reached for most nickel contents by carburizing and by decarburizing. The activity of carbon attained within each capsule was calculated from the carbon content of a binary Fe-C alloy placed within the capsule, and from the activity coefficient of carbon in the Fe-C system as found by Smith for CO/CO2/C equilibrium. The activity of carbon in Fe-Ni-C austenite determined by this method at 1000°C agrees with prior work by Smith, who used mother method. The measurements are extended to 800°and 1200°C. The activity coefficient of carbon 7c, in Fe-Ni-C austenite is given by: where xC is the ratio of carbon to metal atoms and XNi is the ratio of nickel to metal atoms and where the standard state is chosen such that yC = 1 as xc approaches zero in Fe-C alloys. This equation appears to be valid for xni < 0.3, and 1073° < T<1473°K. ThE activity of carbon in Fe-C austenite has been measured by smithL at 800°, 1000°, and 1200°C. Smith has also studied the effect of nickel on the activity A. J, HECKLER and P. G. WINCHELL are Graduate Student and Associate Professor of Metallurgical Engineering, respectively, School of Metallurgical Engineering, Purdue University, Lafayette, Ind. This paper is based on a thesis submitted ty,to Purdue University, in partial fulfillment of the requirements for the degree of M.S. in Metallurgical Engineering which A. J. HECKLER received from Purdue in January 1962. Manuscript submitted August 13, 1962. IMD of carbon in austenite at 1000°C. In both these studies the activity of carbon was fixed by a flowing CO-C02* *Gas mixtures of hydrogen and methane were also used in Ref. 1 but these results are not incorporated in Ref. 2 or in the present study. gas mixture. In the present work, Smith&apos;s results for Fe-Ni-C austenite are confirmed and extended to 800" and 1200°C by a different experimental technique. EXPERIMENTAL PROCEDURE In essence the experimental technique consisted of enclosing specimens of various nickel contents in an initially evacuated silica capsule and annealing the capsule until carbon equilibrium was attained among the enclosed specimens. The carbon activity obtained within the capsule was determined from the final carbon content of the binary Fe-C alloy included in each capsule and the results of smith.&apos; In order to evaluate this method the absence of nickel transfer between specimens must be established and the attainment of carbon equilibrium between samples must be assured. The absence of nickel transfer was demonstrated in the case of an originally pure iron sample which was annealed at 1200°C in a capsule with a 27.3 at. pct Ni alloy. The final nickel content of the iron specimen was less than 0.1 at. pct, a change which has a negligible effect on carbon activity. The attainment of carbon equilibrium was demonstrated within every capsule and in over half the results by achieving the same final carbon content in a sample which carburized during equilibration and in a sample of the same nickel content which decarburized during equilibration. The base Fe-Ni alloys were vacuum melted from Ferrovac E or electrolytic iron and Mond or electrolytic nickel. The samples were rolled and/or swaged and their carbon content adjusted to the desired pre-equilibration level either by methane-hydrogen carburization or by direct carbon transfer from a graphite source in a sealed silica capsule. As mentioned previously, high-carbon and low-carbon samples were prepared for most nickel levels in each capsule. The specimens were cleaned and

Jan 1, 1963

By M. R. Tek

General equations relating the pressure drop necessary to sustain the flow of a fluid through a porous matrix at a given rate have been developed. The results indicate that at high values of flow rate the pressure-flow behavior may not necessarily satisfy the usual Darcy equation. The mathematical analysis, carried through the micro-pore geometry and extended through the macro-reservoir scale, indicate that Darcy&apos;s law, of limited applicability to certain ranges of Reynolds numbers, can be generalized through the inclusion of some additional parameters. The "generalized Darcy equation" has also been formulated in dimen-sionless form permitting the evaluation of its predictive accuracy with regard to literature data. A comparison between predicted and experimental values indicates that the generalized Darcy equation predicts the pressure drops with good agreement over all possible ranges of Reynolds numbers. INTRODUCTION The limits and the nature of validity of Darcy&apos;s law&apos; has been a subject of every-day interest to the industry for many years. It is well known that as the Reynolds number, characteristic of the fluid flow through porous media, becomes large, Darcy&apos;s law gradually loses its predictive accuracy and ultimately becomes completely void. For the last 20 years much has been said and written on this subject. Unfortunately little has been accomplished to bring about a satisfactory agreement, at least on the nature of the threshold of validity of Darcy.&apos;s law. Fluid dynamists, geo-physicists, and engineers all had their individual views, explanations, interpretations and concepts on the subject. To some, a mechanistic analogy with pipe-flow proved a satisfactory explanation.&apos; To others,&apos; turbulence, in its random character, was incompatible with the geometric structure of consolidated porous systems. To some,4 turbulence merely represented a factor influencing the permeability measurements and again to others5,6,7 em-pirical or semi-empirical correlations proved satisfactory from an engineering viewpoint. Deviations from Darcy&apos;s law at high flow rates have been studied by systematic experiments by Fancher, Lewis, and Barnes.&apos; In an article on the flow of gases through porous metals, Green and Duwezs conclude that the onset of turbulence within the pores appears unsatisfactory to explain deviations from Darcy&apos;s law. This view is held by many others. While the subject remained controversial for many years, the development of vast natural gas reserves throughout recent years further justified considerable interest on this problem from the standpoint of gas reservoir behavior. As large amounts of field data became available from the operation of many gas fields, it became evident that the steady-state behavior of gas wells was not, in general, in agreement or compatible with Darcy&apos;s law. This suggested a careful reconsideration of all mechanisms which may account for pressure drops in addition to viscous shear. In a series of articles9,10 . Hou-peurt indicated that deviations from Darcy&apos;s law may be explained on the basis of kinetic energy variations and jetting effects without resorting to assumptions on turbulent flow conditions. Another article by Schneebeli11 indicates that special experiments by Lindquist clearly demonstrated that the onset of turbulence does not necessarily coincide with conditions of deviation from Darcy&apos;s law. This view is also held by M. King Hubbert.12 Starting with the basic pressure-flow relations suggested by Houpeurt, the derivation, development and extension of analytical expressions to -supplement and generalize Darcy&apos;s law has been the objective of this work. MATHEMATICAL ANALYSIS Derivation of Dimensionless Pressure-drop, Flow-rate Relations In considering the flow of a fluid through a porous matrix geometrically represented by a succession of capillary passages in the shape of truncated cones,810 an approximate expression may be derived relating viscous and inertial, i.e., total pressure drop to the physical properties of the fluid, geometric properties of the rock matrix and the rate of flow: ?P/?r = µ/k V [ 1 + c(m4 - 1) p V/16n" mµ w] ..........(1) Let us formally set: c (m4 - 1) / 16n" m = a d ......(2) Such a representation is equivalent to assert that the term [c(m4 — 1)/ 16n"m], variable with various porous media and probably highly variable within a given porous medium, may be macroscopically defined as equal to a lithology factor times the aver-age grain diameter d. In view of the usual grain and pore size distribu-

Jan 1, 1958

By G. C. Rauch, T. H. Courtney, J. Wulff

The superconducting behavior of Nb-Ti alloys containing 40 and higher wt pct of Nb and variable oxygen content was studied as a function of thermomechanical processing. Critical current density (Jc) us applied transverse magnetic field (H) data were obtained for 0.010 in. diam wires at 4.2° Kin steady fields up to 120 kOe. The precipitate responsible for increase in Jc in each of the alloys studied was related to niobium and oxygen content. In alloys containing 40 to 60 wt pct Nb with less than about 1600 ppm of oxygen, w precipitation in the range 350° to 450°C appears to be responsible for the maximum value of Jc observed. In alloys of higher oxygen content (-2500 ppm), the oxygen-enriched a phase which precipitates in the temperature range 450° to 550°C is a more effective fluxoid pinner. Maximum Jc in low oxygen (350 ppm) 80 wt pct Nb alloys was achieved by 600°C aging heat treatments. Measurements of resistive critical field also reflect the changes in composition accompanying precipitation in these alloys. It is well known that the superconducting critical current density, Jc, of solid solution superconducting alloys can be increased by precipitation heat treatments.1-4 The precipitate, to serve as an effective superconzlucting fluxoid pinner and increase Jc, must be of proper size and spacing.&apos; Its electronic properties must also be different from those of the matrix.6 As in age-hardenable systems, optimum temperature and time of aging are dictated by the composition and history of the particular solid-solution alloy under consideration. The alloy diagram of Ti-Nb7-9 shown in Fig. 1 is typical of ß-stabilized Ti alloys. Precipitation to achieve high Jc in Ti-Nb and Ti-Ta alloys is usually carried out in what is believed to be a two-phase a + ß region.1,2,4,10 Previous work on Ti-Nb4,11 and on other ß-stabilized systems such as Ti-V, Ti-Mo,12-14 has shown, however, that the first precipitate to appear is not necessarily (Y. Under specific conditions the meta-stable w phase is precipitated instead. A further complication arises in such alloys from the strong influence of contained oxygen on the phase stability and on the kinetics of precipitation.15,16 The superconducting critical current density of Nb-Ti alloy containing less than 36 wt pct Nb has been studied by Vetrano and Boom1 and Kramer and Rhodes.4 The most effective aging temperature was found to be about 425°C; fluxoid pinning was attributed to the precipita- tion of a by Vetrano and Boom and of w by Kramer and Rhodes. Although the latter workers used recrystal-lized material and the former cold-worked, studies carried out in our laboratory lead us to believe that the type of precipitate responsible for increased Jc is unaffected by prior cold-work.17 That other types of precipitates may also be effective, especially in higher oxygen-containing alloys, has been demonstrated by Reuter, et al.2 in this laboratory with the aid of electron microscopy. Reuter et al. found that at an aging temperature of 600°C, fee-TiO is precipitated, resulting in high values of Jc. Even higher values of Jc were observed after heat treatment at 500°C, but the precipitate could not be indexed as fee-TiO. Whether the precipitate was oxygen-rich w or a could not be clearly distinguished. The work nevertheless indicates that appreciable amounts of oxygen alter the nature of the phases precipitated at different temperatures, at least in alloys containing more than 36 wt pct Nb. Since such compositions are more readily worked into suitable wire than lesser niobium content alloys, it was decided to study the response to aging of the alloy compositions reported in the present paper with the hope of clarifying the effect of composition on the precipitation processes responsible for high values of Jc. I. EXPERIMENTAL Nb-Ti alloys containing 40, 50, 60, and 80 wt pct Nb were prepared by are-melting 35 g ingots of iodide crystal bar titanium and electron-beam melted niobium.

Jan 1, 1969

By K. E. Beu

IN the measurement of retained austenite concentrations in steels using the integrated intensity method,1 Averbach has pointed out" that the absorption factor A(0) for a flat sample making a glancing angle 4 with the incident X-ray beam can be combined with his constant factor R to obtain our constant factor" G provided that "1—There is no preferred orientation in the sample, and 2—The geometric requirements [for the sample, film, and X-ray beam] have been met precisely."&apos; If A(0) can be combined with R to give G according to the equation G = R . A(0) [14] then the possibility for making non-compensating errors in the austenite determination has been eliminated. This has been described previously in a technical note." Because of the brevity of the previous note,3 it was impossible to emphasize the fact that the two conditions on preferred orientation and geometry can be easily met experimentally, contrary to Aver-bach&apos;s statement that: ". . . the necessary conditions must be tested experimentally for each determination, and this is done most easily by observing whether the apparent absorption has the form of Eq. 2 [the theoretical equation for A(0)]."" he way in which these two conditions can be met experimentally will be discussed briefly to help clear up this point. In addition to these two conditions, other factors such as sample shape, homogeneity, and grain size which also affect A will be included in this discussion. A (0) depends on sample shape. The theoretical function for A was derived originally for a flat surface.&apos; In general we have found that a flat sample surface is readily obtainable." If such a surface can * The effect of surfaces which are not flat on the measurement of retained austenite will be discussed later. be obtained, it has the following advantages: 1—it is easily reproducible from sample to sample, 2—it is the form required for metallurgical examination —this type of examination being frequently desirable for this work, and 3—it is an efficient shape for diffraction purposes. Perhaps the most important of these features is that a flat sample surface is easily reproducible; hence, this requirement on the repro-ducibility of A from sample to sample is met for all such samples. Fig. 1—Schematic diagram of the quartz crystal monochromator diffraction unit. The centerline of the main beam is at 6&apos; to the target face. The tangent to the crystal face is at 16.8&apos; to the moin beam. The centerline of the monochromatic beam is at 33.6 to the main beam. The sample surface can be rotated in its own plane. The angle of the sample surface and the monochromatic beam can be adjusted by rotating about the vertical axis, The film holder can also be rotated about B so that the film can be exposed over the desired angular range. For Fe K, X = 1.932A. 1011 planes of quartz have d = 3.35A. A(0) depends on homogeneity and grain size. If the sample is badly segregated or the grain size is large, the effect of micro-absorption and primary extinction1. &apos; must be considered. It has been shown, however, that for most plain carbon or low alloy hardened steels, neither micro-absorption nor primary extinction effects are present.&apos; A (0) depends on camera geometry. For a given angle 0, A remains theoretically constant from a geometrical viewpoint only if the following factors are kept constant: 1—the angle of inclination .+ of the sample to the X-ray beam, and 2—the centering of the sample with respect to the film cylinder. These are mechanical problems which can be solved readily if the facilities of a good machine shop are available. The arrangement used to insure that the angle 4 remains constant and the centering of the sample is reproducible is indicated schematically in Fig. 1. The sample is clamped against a thin plate with a hole in it by means of a spring-loaded pres-

Jan 1, 1954

By R. D. Russell, R. M. Farquhar

SOTOPIC tracers have become an important aid in following the progress of chemical processes in the laboratory. It has recently been found possible to utilize a system of naturally existing iso-topic tracers to obtain information about the geological history of lead ores. Common lead, such as is found in lead deposits, is a mixture of four stable isotopes having atomic weights 204, 206, 207, and 208. Of these, the last three are identical with the lead isotopes produced as stable end products of the radioactive decays of uranium and thorium: the first, lead-204, is not known to be produced on the surface of the earth by any process. Since uranium and thorium Occur in the surface regions of the earth in amounts comparable with lead, and since the half-lives of uranium and thorium isotopes are of the same order as the age of the earth, they produce the radiogenic lead isotopes in amounts comparable to the amount of nonradiogenic lead present. Every significant exposure of a sample of lead to uranium and thorium will therefore lead to the permanent alteration of the lead isotope ratios in that sample. It is this unique property of lead that serves as a means of tracing the history of a lead sample in terms of its contacts with the radioactive elements. If lead from a lead mineral has been analyzed with a mass spectrometer, the measured isotope ratios are determined entirely by the isotope ratios of primeval lead, which are identical for all minerals, and by the particular history of the sample. It follows that for samples from any particular geological area, observed differences in the isotopic composition are enough to distinguish different geological histories. An illustration of the qualitative application of this statement is given in Table I by analyses of some galenas from the western Cordillera. Samples from deposits in Pre-Cambrian sediments have very different lead isotope ratios from those of the ores in the Paleozoic sediments. Although the two types are associated closely geographically, it is apparent that they have had quite different histories and have probably been emplaced at quite different times, as the ideas outlined in the following section suggest. Even when applied quantitatively, a lead isotope analysis can never indicate a unique history of any lead sample. However, it greatly restricts the choices available and combined with other geological and geochemical data can lead to a much better understanding of the genesis of lead ores. General Character of Lead Isotope Variations: Early isotopic analyses of common leads by Nierl showed that geologically younger leads were generally richer in isotopes of masses 206, 207, and 208, with respect to that of mass 204. This regularity of measured lead isotope ratios can be easily observed by plotting each of the ratios Pb207/Pbm and Pb205/ Pb204 against the ratio Pb206/Pb204. In both graphs the points lie scattered closely about a well defined mean curve. It was immediately supposed that this regularity resulted from the growth of all leads from a common primeval lead present at some time, To, early in the earth&apos;s history. Lead in the outer part of the earth would become continually enriched in the radiogenic isotopes as a result of the uranium and thorium intimately associated with it. The subsequent extraction of some of this lead and formation of a lead mineral free of the radioactive parents provide samples of lead existing in the earth at the time of mineralization, T. Younger leads in general will be richer in the radiogenic isotopes because they have been associated with uranium and thorium for a longer time. Then lead ratios would be given by the formulae: (Pb206/Pb204)YTPb^/Pb204) +f "(u201) kdt T (Pb207Pb204)r = (Pb208/Pb204)T0 + J (U295/Pb204) k&apos; dt T (Pb208/Pb204) t = (Pb208Pb204 + J (Th204) A." dt [1] where A, A&apos;, and A" are the decay constants of U238, U285 and Th232. Summaries of measurements of radioactivity of surface rocks, such as given by Faul,2 are of limited

Jan 1, 1958

By R. J. Wasilewski

Electrical resistivity variation with temperature was measured on a series of alloys containting up to 33 at. pct of oxygen over the range 77° to1500°K. The resistivity behavior is highly anomalous and itzconsistent with simple metallic conduction. Both composition and temperature-depended resistivity singularities were observed. A few experiments carried out on Ti-N and Zr-O alloys indicate the presence of similar anomalies. These observations, together with the published data on effects of substi-tutional alloying on the resistiuity of titanium, suggest that the anomalies are inhevent in the electron structure of this group oj metals. The existence of two-band conduction, and a significant shift of bands relative to each other with temperature and/or the electron concentration are suggested. CONSIDERABLE advances have been made in recent years in the alloy theory of simple metals. Very little, however, is known about the bonding in transition metals and their alloys.&apos; Titanium, with its relatively few electrons, may be expected to show simpler alloying behavior than the more complex transition elements. Its alloys with the interstitial elements appear particularly attractive in an investigation of bonding characteristics because of a) the simple nature of the solute elements, b) the remarkable similarity between the equiatomic structures Tic, TiN, and TiO, and c) the extensive solid solubility ranges of oxygen and nitrogen in a titanium reported.2,3 The Ti-O system was chosen for the most extensive investigation because of the relative ease of preparation of suitable specimens. Since the main object of the work was to obtain data on the bonding and its changes on alloying, electron-sensitive properties were primarily investigated. The present work describes the investigation on the electrical resistivity-temperature-oxygen content relationships. A few experiments were also carried out at selected compositions in the Ti-N and Zr-O systems. EXPERIMENTAL Materials and Method. Polycrystalline specimens were prepared in the form of hairpin strips some 50 by 5 by 0.15 to 0.50 mm by direct metal-gas reaction. This was carried out by controlled oxidation followed by a homogenizing anneal at a higher temperature. All the test specimens were fully homogenized as judged from the uniform microstructure and microhardness. To avoid preferred orientation, each strip specimen was annealed in the ß range prior to the oxidation, this procedure assuring random orientation in the strip;4 hence any texture resulting from the oxidation reaction itself affected all the specimens to a similar extent. Titanium used was of high purity (66 DPN, 10 Kg load; major impurities 0,-43G ppm, N,-70 ppm, C-25 ppm, Fe-14G ppm). The solute content of the alloys was determined by weighing, after the reaction with a known amount of oxygen. The specimens in which the discrepancy between the volumetric and gravimetric measurements exceeded 2 pct (or 0.2 mg for the low oxygen alloys) were rejected. The mean between the two measurements was then taken as the oxygen content of the alloy. Check analyses showed no measurable nitrogen contamination. All oxygen contents are given in atomic percent. Zr-O alloys were prepared in identical manner from hafnium-free crystal bar metal, cold-rolled to strip 0.25 mm thick. Ti-N alloys required very long reaction times at the maximum temperature available (1250°C). In order, therefore, to detect possible oxygen contamination, duplicate specimens were reacted in every experimental run, and one of these was analyzed both for oxygen (vacuum fusion) and for nitrogen (Kjeldahl). Only the specimens in which the check analysis showed < 1000 ppm O were then used for resistivity investigation. Since only relatively high nitrogen alloys (7.1 at. pct; i.e., 2 wt pct N,) were investigated, this oxygen contamination was considered permissible. Dc resistance was measured by the four-probe method as previously described.= The temperature was determined with a calibrated thermocouple placed in the center of the specimen hairpin. The errors in the specimen resistance values thus obtained were estimated at 1 pct due almost exclusively to the finite thickness of the potential wires and the consequent uncertainty as regards the true resistance length of the specimen. For the calculation of the specific resistance, however, no dimensional measurements could be carried out on most of the

Jan 1, 1962

By W. G. Pfann

The simultaneous segregation of two solutes during the directional solidification of an ingot is treated mathematically on the basis of simplifying assumptions. Expressions are derived for the difference in concentration of two solutes, and for the location and concentration gradient of a pn barrier formed in a semiconductor by the segregation of a donor and an acceptor. THE problem of normal segregation of a single solute during the freezing of an alloy has been treated mathematically by a number of investigators. Gulliver&apos; showed that coring increases the quantity of eutectic above that to be expected at equilibrium, for a system having limited solid solubility and, on the basis of simplifying assumptions, calculated the fraction of eutectic to be expected. Scheuer2 expressed composition of solid solution in terms of a distribution coefficient and the fraction solidified and compared experiment with calculation for the systems A1-Cu, Al-Zn, Cu-Sn, Cu-Zn. Hayes and Chipman,3 in a detailed study of segregation in a low carbon, rimming steel ingot, calculated distribution coefficients for a number of solutes in iron, compared calculated and experimental segregation curves, and discussed the effects of process variables such as rate of solidification and stirring. In the present paper a mathematical analysis is made of the simultaneous segregation of two solutes during the orderly freezing of a solid solution system, with particular emphasis on the difference in solute concentrations. Although the analysis is quite general and can be applied to the segregation of minor elements in alloys, it is directed in particular at the solidification of a semiconductor containing a donor and an acceptor. Normal segregation has unique aspects in a semiconductor, because of the ways in which donors and acceptors affect the electrical properties. The difference between two solute concentrations becomes of importance, as does also the gradient of the difference where the difference goes through zero, this being the concentration gradient of excess carriers at a pn barrier. A primary object of this paper is to extend the mathematical treatment of segregation to include these newer aspects which are of particular significance for semiconductors. One property of interest is the electrical conduc- tivity, which arises from the presence of donors &apos;or acceptors in solid solution. The conductivity may be either n-type or p-type depending on whether donors or acceptors, respectively, are in atomic excess. For both germanium and silicon, elements of Group V of the Periodic System, such as P, As, and Sb, are donors and elements of Group 111, as B, Al, In, and Ga, are acceptors.4-6 If a donor or acceptor is present alone in solid solution, the conductivity is proportional to its concentration." If both a donor and an acceptor are present, then the conductivity is proportional to the difference in their atomic concentrations. If the donor and acceptor segregate at different rates then a pn barrier in certain circumstances may form at some point in the ingot. Accordingly, equations are derived and illustrated which express the effect of segregation on: 1—the concentration of a single solute with a discussion of the assumptions; 2—the difference between two solute concentrations and means for minimizing its variation in an ingot; and 3—the location and concentration gradient of a pn barrier. The analysis is applicable to processes in which the entire charge is melted and then progressively frozen from one end. The method in which an ingot is solidified in a crucible7 and that in which a solidifying rod is pulled from the melt8 both fall into this category. Segregation of One Solute If a cylinder of molten alloy is caused to freeze slowly from one end, a normal segregation of solutes will usually occur, producing a lengthwise concentration gradient in the ingot. Depending on whether a solute raises or lowers the melting point of the solvent, it will become concentrated in the first or last regions, respectively, to freeze. If it is assumed that freezing is such that there is no diffusion of solute in the solid, complete diffusion in the liquid, and that k, the distribution coefficient, defined as the ratio of solute concentration in the just-freezing solid to that in the liquid, is constant, then the

Jan 1, 1953