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By Ben-Zion Weiss, Melvin R. Meyerson

Chromium diffusion coatings on commercial Armco iron lead to carbide precipitation at the grain boundaries in and below the coatings. High compressive stresses are introduced into the coating and, as a result, tensile stresses are introduced into the base material below the coating. In coated samples, fatigue cracks form at the grain boundaries below the coating after only a limited portion of the total lifetime (5 to 10 pct). Residual tensile stresses and a stress concentration caused by precipitated carbides seems to be responsible for early crack nucleation. Stage I of Propagation may be divided into two substages: I-a in which the crack Propagates along grain boundaries, and I-b in which the crack propagates along slip boundaries according to a shear mode. In uncoated samples, the cracks form at slip bands after 40 to 50 pct of the total lifetime. In coated samples the Propagation process takes longer than in uncoated samples because of the moderate rate of crack extension until the crack breaks through the coating. The chromium-diffusion coating causes little if any increase in fatigue life. CHROMIUM diffusion is one of the most popular processes used to apply coatings to iron alloys. This popularity stems from the fact that the diffusion treatment is comparatively easy to carry out, and it improves certain surface properties such as corrosion and wear resistance as well as some other properties. Very little effort has been devoted to the investigation of the effect of chromium-diffusion coatings on mechanical properties and particularly on fatigue properties. Since the chromium coating usually represents a small fraction of the total volume of the base material it is generally assumed that the macro properties are dependent principally on the base material rather than the coating. Insofar as fatigue is concerned, there are indications that the fatigue life of the chromium coating is not less than that of the basic material and the fatigue properties are generally not reduced by it.' But chromium diffusion causes drastic structural and chemical changes in the region of the material surface2-4 which introduce additional residual stresses. Such changes must affect fatigue crack nucleation and may sometimes affect the initial stages of propagation. Furthermore, it is conceivable that the secondary stages of the crack propagation could be influenced by some irreversible structural changes in the core of the material, which stem from the long-time heat treatment at high temperatures required to apply the coating. This paper analyses the structural and compositional changes produced in commercial Armco iron by a chromium-diffusion coating and the effect of the coating on fatigue crack initiation and propagation. EXPERIMENTAL PROCEDURES The investigations were carried out with commercial Armco iron. The chemical composition of the iron, the number of specimens tested, the grain size produced during chromizing and heat treating, and the thickness and microhardness of the chromized layers are shown in Table I. Samples were chromized by a gas diffusion process. The temperature and time of the diffusion coating process were chosen according to a previous grain growth study. It had been found that at a temperature of 970°C and a holding time of between 3 and 9 hr there are practically no changes in grain size. To describe the grain size more accurately the ASTM method5 was supplemented by a statistical analysis of the mean volume diameter as outlined by Fullman6 and The The mean volume diameter was deter- mined from D = p/2m where D is the mean volume diameter, and m is the mean reciprocal value of grain diameters as seen on the micrograph. The shape and the size of the asymmetrical sample, see Fig. 1, were chosen so as to facilitate the study of fatigue crack initiation. Before coating, the samples were machined and the surface of the groove was polished. After chromizing, the two side surfaces were machined and polished so as to retain the coating only on the top surface of the groove. Residual stress in the chromized layer was measured on the top of the grooved section of the specimen after the diffusion process. The inclined incident X-ray beam procedure was used.9'10 The computations were performed with the initial assumption of a zero surface normal stress component. An electron microprobe analyzer was used to obtain the relative amounts of chromium and iron con-

Jan 1, 1970

By T. E. Leontis

Data are presented in this paper to show that addition of zirconium to sand-cast Mg-Th alloys effects a marked decrease in the grain size of these alloys which is accompanied by a significant increase in the mechanical properties over the entire range of thorium content investigated. The beneficial effect of zirconium on the strength properties is maintained at elevated temperatures up to 700°F. In addition the alloys exhibit exceptionally high creep resistance at temperatures up to 600°F. Zirconium does not greatly improve the strength or creep characteristics of extruded Mg-'Th alloys. Cerium is not a desirable addition to Mg-Th-Zr alloys. IN a previous paper,' it was shown that addition of thorium to magnesium imparts exceptionally high resistance to creep at elevated temperatures both in the sand-cast and in the extruded states. The large grain size of the sand-cast alloys, however, renders them of questionable value as engineering materials. Sauerwald² showed that the grain size can be reduced effectively by the addition of zirconium. Results of a detailed study of the properties of Mg-Th-Zr alloys over a wide range of thorium content are presented in this paper. In accordance with the preliminary findings of Sauerwald,² it is shown here that Mg-Th-Zr alloys possess the unusual combination of fine grain size and a high level of strength and creep resistance at elevated temperatures. Some information on the effect of cerium on the properties of Mg-Th-Zr alloys is presented also. Effect of Th on Solubility of Zr in Molten Mg Sand-cast test bars and 3 in. diam extrusion billets of Mg-Th-Zr and Mg-Th-Ce-Zr alloys* were pre- pared according to the procedures described in the previous paper.' The zirconium was added in the form of sponge metal as supplied by the Bureau of Mines.' The maximum amount of zirconium that usually can be introduced into magnesium at the customary alloying temperature of 1350° F is about 0.7 pct. The analyses in Table I clearly show that thorium in- creases the solubility of zirconium in liquid magnesium. The tabulated zirconium contents are designated as "acid soluble;" this serves to distinguish these values from the small amount of zirconium that is not dissolved when the alloy is subjected to the action of a dilute acid solution. The "acid-insoluble" zirconium is believed to be ineffective as an alloying ingredient. The acid-insoluble zirconium contents ranged between 0.03 and 0.16 pct in the present alloys, the tendency was toward higher values in alloys with higher thorium content. In contrast to the effect of thorium, cerium decreases the solubility of zirconium in magnesium. This is shown by the three Mg-Th-Ce-Zr alloyst in- cluded in Table I and stands in agreement with the observations of Nelson and Stricter".' on Mg-misch-metal-Zr alloys. Effect of Zr on Grain Size of Mg-Th Alloys The potent effect of zirconium as a grain refiner has been demonstrated for many types of magnesium alloys.3-8 Of greatest importance to date are Mg-Zn-Zr alloys5,6,8 and Mg-mischmetal-Zr alloys.3,4,7 Zirconium has also been found to exert a marked grain-refining action on Mg-Th alloys. All the Mg-Th-Zr alloys cast in the form of ½ in. diam test bars have an exceedingly fine grain size (Table I). Reference to the previous paper' will show that binary Mg-Th alloys containing up to 6 pct Th are almost completely columnar even in the M in. diam reduced section of a test bar, and that 10 to 50 pct Th alloys have an equiaxed grain structure of 0.03 to 0.08 in. The data in Table I also show that addition of cerium to Mg-Th-Zr alloys has no effect on the grain size. In addition to increasing the strength properties, the fine grain size of Mg-Th-Zr alloys

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.' 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 R. F. Sheldon

The discovery of the Carlin deposit was the result of discriminating geologic research and prospecting devoted to the objective of finding a gold deposit that could be mined by open pit methods. By the late 1950s, Newmont Mining Corp. was becoming increasingly concerned about the trend of rapidly rising underground mining costs unless bulk mining methods could be applied. The desirability of finding an open-pittable gold deposit was apparent. The attention of Newmont geologists was directed to Nevada by the publication of two papers: "Paleozoic rocks in North-central Nevada" (1958) and "Alinements of Mining Districts in North-central Nevada" (1960), both authored or co-authored by Ralph J. Roberts of the United States Geological Survey. John Livermore, geologist of Newmont Exploration Ltd., attended a talk given by Roberts in Ely, Nevada in the summer of 1961. These papers and the address by Roberts gave details concerning the Roberts Mountain overthrust, a 483 km (300-mile) long, shallowdipping fault which pushed clastic and volcanic rocks of early and middle Paleozoic age eastward over younger marine formations. Subsequent uplift and doming with consequent erosion had locally removed the upper plate strata exposing windows of lower plate carbonate rocks. Roberts noted that the principal mineral deposits of the region, including gold, were associated with these windows which exhibited a preferred alinement. In the summer and fall of 1961 Newmont's exploration geologists John Livermore and J. Alan Coope began a systematic examination of gold occurrences associated with these windows, aided by further discussion with geologists of the US Geological Survey. Attention was directed to the Lynn and Carlin windows, particularly to those formations lying immediately above and below the Roberts Mountain fault. It was appreciated at the time that many of the gold occurrences in the region were unusual in that no colours were obtained even when panning high grade samples. A large number of rock samples were collected and analysed using fire assaying procedures, and background values for gold were established. This systematic rock sampling resulted in the identification of a distinct area of anomalous gold values, and a block of claims was staked in late October, 1961. These claims, plus an adjoining optioned 32.4 ha (80 acres) of ground, cover the main area of the present Carlin gold mine. Prior to snowfall that winter, one of the bulldozed assessment pits required to establish a claim's discovery exposed 24 m (80 ft) of mineralization assaying 0.007 kg/t (0.22 oz per st) gold. In the spring of 1962 a program of trenching, sampling, and geological mapping followed by rotary drilling was underway. Other properties in the area were acquired. The generally undistinguished nature of the dolomitic siltstones and silty dolomitic limestones hosting the micron-sized gold particles, coupled with the lack of visually associated guide minerals, made identification of the gold bearing areas very difficult. The entire drill column had to be assayed to ensure that values were not overlooked, as very often sections that might be assumed to be waste turned out to be high grade. On September 10, 1962 a high grade intersection of 24 m (80 ft) assaying over 0.03 kg/t (1 oz per st) gold was encountered in the third hole drilled. An expanded program of both rotary and diamond drilling led to the further delineation of the ore body. By December 1963, the exploration program had established an initial reserve of 10 Mt (11 million st) grading 0.01 kg/t (0.32 oz per st) gold. A 1.8 kt/d (2,000 stpd) processing plant was constructed and the first gold bullion was poured in May, 1965, just two years and eight months after the discovery hole was drilled. REFERENCES Roberts, R.J., Holz, P.E., Gilluly, J., and Ferguson, H.G., 1958, "Paleozoic Rocks in North-central Nevada," Bulletin American Association of Petroleum Geologists, Vol. 42, No. 12. Roberts, R.J., 1960, "Alinements of Mining Districts in North-central Nevada," Professional Paper 400-B, US Geological Survey, Article 9.

Jan 1, 1985

By H. L. Marcus, C. D. Turk

Titanium was physically vapor-deposited by electron beam high rate evaporation. Rates of 50,000 and 85,000Å per min at deposition temperatures of 480°, 535°, and 595°C were used. Deposited thickness ranged front 0.004 to 0.010 in. The evaporated titanium had a high degree of basal Plane texture. The specimens were tested in tension at temperatures ranging from 78° to 520°K. From the data, the yield stress, thermal component of the yield stress, and work hardening characteristics were found as a function of temperature, deposition rate, and deposition temperature. It was found that Taylor's equation, best fit the work hardening data with m = 1/2. MANY investigations have been made on the tensile deformation characteristics of commercial- and high-purity titanium.1"7 The data obtained from these experiments emphasize the fact that the mechanical properties are generally related to the method of production. The correlation of mechanical properties to production history arises from the dependence of impurity concentration on the extraction and melting technique used. Additional effects are derived from crystallographic texturing which can result from fabrication history. Lee and Backofen8 and other investigators9 have shown that crystallographic texturing in titanium sheet has a significant effect on the deformation characteristics. Bunshah and Juntz10 prepared high-purity titanium by high rate physical evaporation techniques. These authors found the deposited material to have a columnar structure with grain sizes ranging from 12 to 104 µ, depending upon the substrate temperature. The room-temperature strengths of the coarse-grained distillate were similar to arc-melted, rolled. and annealed crystal bar titanium. Commercial-purity titanium was also produced experimentally in our laboratory using high rate physical vapor deposition techniques. The commercially pure material has a finer structure than the high-purity distillate,10 and is highly textured. Since the method of preparation and degree of texturing affect the mechanical properties, a research program was initiated to determine the temperature dependence of the yield stress and work hardening characteristics as a function of high rate deposition parameters. This paper relates the results of the investigation. EXPERIMENTAL A) Material Preparation. The titanium was received in the form of commercial-grade 0.096-in.-diam wire which has a composition of 0.016 pct C, 0.0037 pct N, 0.110 pct 0, 0.011 pct H, 0.05 pct Mn, 0.051 pct Fe. balance Ti. The wire was continuously fed into a vacuum evaporation unit as shown schematically in Fig. 1. The deposition chamber was evacuated, purged with argon, and reevacuated to a pressure of 10-5 Torr which was maintained during deposition. A focused electron beam was used to evaporate the titanium from a water-cooled copper crucible. The titanium vapor was condensed onto a preheated titanium substrate. The temperature of the substrate was controlled within ±5°C for the deposition temperatures of 480°, 535°, and 595°C. Control of the input power enabled the use of two deposition rates. 50,000 and 85,000Å per min. The evaporated titanium had a final analysis similar to that of the input titanium, within experimental limits. B) Testing. The evaporated titanium was physically stripped from the titanium substrate and machined into tensile specimens with 1-in. gage lengths. In addition, tensile specimens of as received annealed 35-A titanium sheet with a 20 µ grain size and 45 pct cold-rolled 35-A were also prepared. All specimens were tested in tension in an Instron at a strain rate of 3.3 x 10"4 in. per in. per sec. Proportional limit has been used as a measure of yield strength. Tests were conducted at 78°, 220°, 300°, and 520°K. Metallography, X-ray diffraction, and electron microscopy were used to correlate structure with the deposition parameters and mechanical properties. Room-temperature X-ray measurements were made to determine the phases present. Pole figures and a scans were made to determine deposition texture. Because the vapor deposition was symmetrical about the normal to the substrate, there was no preferred di-

Jan 1, 1969

By Michael Hoch, Walter C. Wyder

The Cr-Ni system was investigated between 900" and 1400°C and 45 to 100 wt pct Cr. The Cr-Fe system was studied between 1200" and 1385°C and 70 to 100 wt pct Cr. Powdered alloy compacts were produced from high-purity chromium, nickel, and iron poulders. The compacts were sintered in an argon atmosphere and then machined into small, 0.030-in. diam cylindrical specimens. These were then heated by induction in the high-temperature X-ray diJfractwn camem under a helium atmosphere and irradiated with copper Ka radiation. From the results of the high-temperature X-ray diffraction patterns it can be concluded that chromium exists only in the bcc form, and that no eutectoid reaction occurs in the Cr-Ni system in the temperature interval 900" to 1400°C. The X-ray diffraction patterns are in agreement with the Cr-Ni phase diagram of Bechtoldt and Vacher, and Williams. It is possible that chromium undergoes one or more allotropic transformations between room temperature and its melting point. Most of the evidence was gathered from the study of the chromium-rich ends of the Cr-Ni and Cr-Fe binary systems. All the investigations rely heavily on indirect methods: thermal analysis, electrical resistivity, and micro-graphic inspection of quenched samples. In the present work the chromium-rich side of the Cr-Ni and Cr-Fe binary systems is studied, using high-temperature X-ray diffraction techniques. Thus the coexistent structures can be observed directly at temperature. PREVIOUS INVESTIGATIONS ~ansenl shows two possible Cr-Ni phase diagrams 1) a simple eutectic [Liquid =a-Cr(bcc) + y-Ni(fcc)], 2) a eutectic [Liquid+ P-Cr(fcc) + y-Ni(fcc)] and euctectoid [p-Cr(fcc) ==a-Cr(bcc) + yNi(fcc)]. The latter is based on the work of Grant and co-workers.2 Stein and rant'" placed the eutectoid composition at 1215°C and 68 wt pct Cr; their diagram is shown in Fig. l. Similarly, Sully3 also discusses the two proposed diagrams. Price and Grant,4 working on an isothermal section of the Cr-Ni- Fe ternary diagram at 1300°C, made no mention of a ß-chromium phase (fcc). The ß-chromium structure was also reported by Misencik 5 in the Cr-Nb(Cb) system. Williams 6 studied the Cr-Ni system using precipitation techniques. His work included the chromium and nickel solvus lines below 1250°C. He reported no ß structure nor any eutectoid reaction. The solvus lines which he produced were very similar to those of Jette, et al 7 below 1000°C. He concluded that Grant and coworkers2 had misinterpreted their data, and that effects which they had reported were actually due to the rapid and extensive precipitation of the nickel-rich phase. Bechtoldt and vacher8 used sintered powdered alloy compacts in an attempt to find the ß phase. They used metallographic and room-temperature X-ray diffraction techniques and also failed to detect the fcc chromium phase. They attributed the low slope of the chromium solvus at approximately 1150°C as the probable cause of the abundant precipitation obtained. They also stated that the precipitation was the probable cause for the abrupt discontinuities in the thermal analysis and electrical resistivity data which led to the conclusion that a eutectoid reaction existed. Fig. 1 also shows their diagram. Grigor'ev and coworkers9 investigated the polymorphic changes of chromium in the Cr-Ni phase diagram. Using standard microstructural and thermal analysis techniques, they published a phase diagram which contained five polymorphic forms of pure chromium and four eutectoid reactions. They stated that the room-temperature bcc chromium transformed to a fcc structure at 930°C, to bcc at 1300°C, to hcp at 1650oC, and then finally to bcc at 1830°C. The eutectoid reactions were placed at 850°, 960o, 1140°, and 1220°C. Also to be noted was the fact that the uppermost phase, the bcc above 1830°C, was different from the upper phase of Grant and coworkers,2 the fcc above 1840°C. Their eutectoid reactions, temperatures and compositions fall

Jan 1, 1963

By Y. C. Liu, W. R. Hibbard

Based on pole figure data and microstructural observations, the re-crystallization orientation found in a copper strip previously cold-rolled 99.5 pct from a single crystal with an initial (110) [112] orientation may be described as: a 30° rotation, clockwise and counterclockwise, about octahedral poles of the cold-rolled texture such that all four poles function at a low annealing temperature (400°C) and only three of them function at high temperatures (500' to 1050°C). The relative intensity of deformation stresses on various slip planes can be correlated with the choice of poles affecting the rotations found in the recrystallized orientations. ROTATIONAL reorientation about the poles of densely packed crystallographic planes is an important characteristic of secondary recrystallization" in face-centered cubic metals. Some evidence has also been interpreted to show that such a rotational relationship also exists in the primary recrys-tallization process." In an investigation of the crystallographic relationships in the recrystallization process, several aspects of the experimental procedure should be considered. With cold-rolled poly-crystalline metal as the initial material, pole figure analysis leaves many ambiguities as to whether or not simple indices can be assigned to adequately represent its orientation. The rolling texture does not consist of a single texture. Minor deformation textures are usually present. In all cases, twin textures are present. The presence of both minor and twin deformation textures influences the recrystallization texture. In order to study the recrystallization mechanism, a more precise knowledge of the history of the material before recrystallization is necessary. Tensile deformation of a single crystal usually produces residual stresses which are concentrated at slip bands. Since the exact nature and orientation of these potential nuclei sites cannot be experimentally evaluated, the tensile deformation of a single crystal was not considered adequate. From the work done by Barrett and Steadman6 n copper, it appeared that cold rolling of a single-crystal specimen with an initial (110) [112] orientation would yield a specimen which fulfills the conditions required for the present investigation, namely a highly preferred single rolling texture with relatively homogeneous stress distribution. By investigating the recrystallization texture of this material, additional details of reorientation during recrystallization might be obtained. The purpose of this paper is to describe such an investigation. Experimental Procedure Copper used in the present investigation was cathode sheet with a purity of 99.94 to 99.97 pct. A copper single-crystal specimen, 1.15x0.8720x0.5322 in. (thickness) was cut from a cylindrical crystal which was grown in a Bridgman furnace.' The cutting was accomplished on a horizontal milling machine operated at a very slow speed to obtain a (110) plane in the rolling plane and a [112] direction in the rolling direction. The disturbed surface was removed by electrolytic polishing in dilute orthophos-phoric acid (H3PO4) with a specific gravity of 1.14, and a current density of about 1 to 2 amp per sq cm. A 3-min polishing was needed to eliminate the disturbed surface causing Debye-Scherrer rings and a 45-min polish produced a surface which yielded sharp rounded Laue spots. It was estimated that about 1/16 in. of metal was removed from the original cut surface. The final orientation of this specimen before rolling was about 2" from the (110) plane in the rolling plane with a [112] direction aligned in the rolling direction. It is possible that a small amount of strain was still present in the cube despite the fact that the Laue spots seemed very sharp. It is doubtful, however, that this would be an important factor after a subsequent rolling reduction of 99.5 pct. This copper specimen was rolled on a laboratory rolling mill with two highly polished rolls 37/8 in. in diam in the following manner: 0.010 in. per pass to 50 pct reduction, 0.005 in. to 70 pct, 0.002 in. to 85 pct and, finally, 0.001 in. per pass to a 99.5 pct reduction. Specimens, about 1 in. sq with the rolling edges intact, were cut from the rolled strip by the electrolytic method previously described, after the strip

Jan 1, 1954

By A. E. Wraith, N. J. Petch, J. D. Embury, E. S. Wright

The two most important parameters controlling the fracture behavior of a solid are its intrinsic properties, e.g.,grain size, and the operative stress system. The latter may be modified in laminates by the presence of weak interfaces. This is studied in notch-impact tests on a mode1 system of mild steel laminates containing a variety of interfaces. The effect of these is evaluated in terms of the ductile/cleavage transition. Two laminate geometries are distinguished, here called "crack-arrester " and "crack-divider". In both, cleavage is inhibited. This arises because of relaxation of a state of triaxial tension. In the crack-avrester laminates, cleavage initiated at a notch is confined to the layer containing the notch. In crack-cliuider laminates, a thick specimen behaves as the Sum of a number of thinner ones. Additional benefit may derive from improved intritnsic propevties of- the lanlinate layers arising from greater deformation in their manufacture. It has long been recognized that the two most important parameters controlling the fracture behavior of solids are their intrinsic properties (e.g., grain size friction stress,3 distribution of second phase particles4) and the operative stress system under which fracture occurs. In solids that show a ductile/cleavage transition, cleavage is favored by the presence of a notch. This is because triaxial tensions, generated by the localized plastic constraint at the notch, are operative when fracture occurs.= Anything that suppresses these triaxial tensions will be unfavorable to cleavage. Such suppression may possibly occur in laminates containing weak interfaces and the purpose of the present paper is to explore this possibility. Two basic laminate geometries, here termed "crack-avrester" and "cvack-divider", are examined. They are illustrated in Fig. 1. With the crack-arrester laminates, there is the possibility that, when the fracture crack approaches the interface, this, if weak, may delaminate due to the tensile stress acting parallel to the plane of the crack.= If this happens, energy will be used in delamination, the crack will be completely blunted, and the triaxial tension associated with the crack will be relaxed. To fracture the second portion of the laminate, crack reinitiation will be necessary and, because of the relaxation of the triaxial tension, this reinitiation will occur under conditions of nearly uniaxial tension, which are unfavorable to cleavage. Thus there is the possibility of cleavage suppression in the second and subsequent subunits of a crack-arrester laminate. With the crack-divider geometry, there is again the possibility of delamination at the interfaces. This will divide the crack into a series of cracks propagating through the individual laminate subunits. If these are sufficiently thin, the triaxial tension will be relaxed towards a state of biaxial tension in each of them. Thus, with the crack-divider laminates, there is again the possibility of cleavage inhibition. In the present work, these possibilities are explored using a notched impact test on mild steel laminates bonded with soft solder, silver solder or copper. Even if delamination does not occur, it is still possible that cleavage may be inhibited in laminates. With the crack-arrester geometry, the cleavage crack in the first layer may be blunted and arrested by plastic deformation in the laminate bond, if this is ductile. Partial relaxation of the stress transmitted ahead of the crack into the second layer will then result and this will reduce the significance of this stress in the fracture of the second layer. With the crack-divider geometry, there cannot be much effect in the absence of delamination unless a large amount of energy is absorbed in rupturing the ductile material. EXPERIMENTAL DETAILS The composition of the mild steel (wt pet) was: 0.04 C, 0.29 Mn, 0.01 Si, 0.006 P, 0.008 S. "As-received" plate was annealed for 2 hr at 900°C and slowly cooled to give a grain size of 0.04 mm. The laminates were made by brazing or soldering together mild steel plates 8 by 3 in. by various thicknesses. These were obtained from the annealed plate by machining, so that the intrinsic material properties were .kept constant. Laminates containing two to six steel layers were studied using standard Charpy V-notch specimens cut from the bonded plates. Standard homogeneous specimens from the annealed plate and subsize ones from the laminate components

Jan 1, 1968

By Richard H. Jahns

Gem materials, comprising those minerals and closely allied natural substances used for personal adornment, for the fashioning of ornamental objects, or for other decorative purposes, have been valued in human commerce for thousands of years. Amber, jet, natural glasses, and at least 15 mineral species were sought and used by primitive man, and most of the materials in common use today were known well before the time of Christ. Their variety is remarkably great, and the traceable relationships among their respective sources, modes of occurrence, properties, and histories of production, preparation, and valuation are extremely complex. Their uses have been affected by numerous shifts in fashion, and from time to time by superstition, by decrees of church and state, by personal interpretations of religious significance, and by various presumptions concerning medicinal value and influence on human behavior (Ball, 1935, 1950; Kunz, 1913; Pogue, 1915; Whitlock, 1946). Thanks to their durability, portability, and relative scarcity, some gem stones have been employed as media of exchange, and the investment value of the more precious stones has long been recognized and exploited, especially in Asiatic and European countries. Demands for gem materials have stimulated trade among various peoples for centuries, and they also were responsible for much early geographic exploration. During more recent times they have prompted numerous geological studies and a considerable amount of research on the growth and properties of crystals. Apart from decorative uses, some naturally occurring gem materials also are employed directly in numerous fields of industry. Substances that are manufactured for gem or industrial uses are termed synthetic gem materials; most of these correspond in composition and crystal structure to certain minerals found in nature. Imitation materials are those whose use is based upon their resemblance to substances of different composition and greater intrinsic value. Gem stone is a designation commonly restricted to those materials suitable for personal adornment, and the complementary term ornamental stone is applied to the remaining materials not used industrially. This distinction is arbitrary and somewhat inconsistent, owing to numerous geographic differences and historical shifts in end uses. Further, there is a complete gradation between the category of ornamental stones and that of dimension stone. Substances that lose their identity in use are excluded from the gem category; thus a transparent crystal of beryl would not be classified as a gem stone if it were processed as a source of beryllium metal. The adjectives precious and semiprecious have been employed as a means for distinguishing different gem materials on the basis of recognized value. Diamond, emerald, ruby, and sapphire consistently have been regarded as precious stones, and in cut form they commonly are referred to as the noble gems. Opal, pearl, turquoise, and chrysoberyl also have been classed as precious at various times. In recent years, however, it has been increasingly recognized that no satisfactory distinction can be based upon assessed value or any group of specific properties, and now all gem stones normally are referred to as precious. Indeed, the tendency is to extend this term to include many of the so-called ornamental stones, and the designation semiprecious has been essentially discontinued. Unlike most mineral commodities of economic value, gem materials are little altered in processing for end uses. Some stones are used in essentially their natural form, and most are reshaped and polished without significant changes in their fundamental properties. Thus the preparation of gem and ornamental stones is intended chiefly to emphasize or enhance

Jan 1, 1983

By Charles Wraith

THE property of the Roan Antelope Copper Mines, Ltd., is situated at Luanshya, north-central part of Northern Rhodesia, and is connected with the main line of the Rhodesia Railways, Ltd., by a 24-mile branch line from N'dola. Most of the material and supplies that are not available in Africa are shipped into the country via Beira, on the East Coast of Africa, a distance of 1473 miles from Luanshya and the nearest ocean port. The output of copper is shipped by rail to Beira and thence by boat to the market. Passenger travel is mostly via Cape Town, a distance of 2162 miles from Luanshya. Excellent passenger trains operate on regular schedules between Cape Town and Northern Rhodesia. Luanshya is 13° south of the equator at an elevation of 4000 ft. above sea level, and has a mild healthful climate. During the rainy season, from October to March, the rainfall averages 53 in. The area is pro-fusely covered with vegetation. An ample supply of water for industrial and domestic purposes is available throughout the year. The more important supplies for smelting purposes, such as wood, coal, limestone, silica, quartzite, and clay for "dolly" mud, are con-veniently available. Excellent grades of coal, coke and firebrick are obtained from the Wankie Colliery Co., Ltd., Southern Rhodesia. The Wankie colliery has just completed the erection of equipment for the manufacture of silica brick. An ample supply of quartzite of good grade is available for this purpose. Silica brick is also obtained from the Belgian Congo and from India. Limestone is quarried from a large deposit a few miles from Bwana Mkubwa, which is 30 miles by rail from the smelter. An abundant supply of clay for "dolly" mud and for lining launders is available within a short distance of the smelter.

Jan 1, 1933

By Raymond B. Ladoo

ABRASIVES include the substances, natural or artificial, that are used to grind, polish, abrade, scour, clean or otherwise remove solid material, usually by rubbing action but also by impact (sandblasting, for example). They do not include abrasive tools-for instance, lathe tools and files-or polishing agents such as waxes, which act by filling pores. Detergents and cleaners whose action is chemical rather than physical are omitted although some chemical action polishes and cleaners may also contain solid abrasives; for example, many metal polishes. GENERAL CONSIDERATIONS The most important physical properties of materials that qualify them for use as abrasives are hardness, toughness (or brittleness), grain shape and size, character of fracture or cleavage, purity or uniformity. For making bonded grain abrasives such as grinding wheels, additional important factors are stability under high heat and bonding characteristics of grain surfaces. The economic factors of cost and availability are always important. No one single property is paramount for any use. For some uses extreme hardness and toughness are needed, as in diamonds for drill bits; for others, the factors of greatest importance are hardness and ability to break down slowly under use, to develop fresh cutting edges when grains become worn-for example, in garnet for sandpaper, neither highly cleavable or friable grains nor extremely tough grains

Jan 1, 1949

By Clarence G. Merritt

Stainless iron, as mild stainless steel is usually called, an alloy ranging from 11.50 to 15.00 per cent chromium with carbon under 0.12 per cent, has been considered to be not appreciably affected in respect to corrosion resistance by heat treatment. This metal, while one of the most widely used of the "straight" chromium stainless alloys, has failed in many applications because of insufficient information regarding heat treatment. These failures have been attributed to many possible causes from an inherent lack of resistance to corrosion and misapplication to mlysterious electrolytic effects or comparatively minute non metallic inclusions. Many uses for a steel with such excellent physical properties as are latent in this alloy have been lost on account of corrosion failures which could have been avoided by applying proper heat treatment. The alloy has not received the recognition or attention it should because of the fact that the details of its metallurgical behavior were not thoroughly understood. Response to heat treatment of the steel is well known as regards tensile properties,1-2 but its application has been for improvement in tensile characteristics or on account of machining considerations rather than for corrosion prevention. The potential user of this steel has not been clearly advised in papers, either technical or commercial, that have been written about it in the last 10 years or more, of particular features that are of prime importance in developing the excellent properties of this metal. The data to be presented in this paper are concerned mainly with the effect of heat treatment on the corrosion resistance, but a study has also been made of the concurrent microstructural changes and an explanation developed for the phenomena revealed, as well as a correlation to the other physical properties—hardness, tensile characteristics and impact strength. Stainless steel, largely used for cutlery purposes, an alloy of approximately 13.00 per cent Cr with 0.30 per cent C;, must be hardened and the surface prepared by polishing or pickling for best resistance to staining and corrosion. Monypenny reports that a loss of hardness is

Jan 1, 1932

By A. Martens

When I was honored with an invitation from the American Institute of Mining Engineers to present a paper at the Chicago meeting on the microstructure of iron, I hesitated about accepting, as the short interval that would remain at my disposal, after other pressing matters had received attention, could not but seriously affect the work of preparing such a paper. Unfortunately my fears have been realized and my work is neither completed, nor yet as comprehensive as I should desire. Mindful of my promise, however, and recognizing that 1 have reached a point where the results of my researches may prove suggestive, I am led to present them now, trusting that this brief explanation map secure indulgence for whatever deficiencies the paper may disclose. So far as my knowledge of published memoirs and treatises extends, microscopy cannot yet be said to possess a really firm foundation. In few cases only has any systematic development of the methods of investigation been undertaken, and broad gaps remain to be filled. It is not yet possible, therefore, to give a complete survey of the field, or, indeed, to supply a text-book on microscopic metallography. As Mr. F. Osmond, of Paris, a distinguished member of our profession, has undertaken to prepare for the Chicago meeting a historic review of the work actually accomplished I need not touch on that branch of the subject; but before entering upon my special theme, it may not be out of place for me to introduce certain explanations, as furnishing reasons for the course 1 have hitherto pursued, and to offer some suggestions for the further development of the methods of microscopic investigation. In microscopic metallography, the examination has to be conducted principally with incident light. Objectives of low power, in which the distance between the front lens and the abject is considerable, are adapted for directly incident light, and in such cases the relatively great depth of the image renders it possible to examine

Jan 1, 1894

By Thomas O. Ziebold, Robert E. Ogilvie

Experimental analysis of diffusion samples covering the entire Cu-Ag-Au system at 725°C has been carried out. Experimental coefficients are computed at twenty-eight points in the lermary system. It is found that the direct coefficienl for copper is nearly independent of the silver, content for 1ow-silver alloys and that the cross coefficient for silver correlates with the ther-nzodynatnic properlies. This lalter observalion leads to the conclusion that the mobililies of copper and gold are nearly equal. Thermodynarmic actiuilies for Cu-Ag-Au were computed from binary data and adjusted to be consistent with neasured tie lines across the two-phase region which extends into the ternary diagram at 725°C. Application of these therknodynarnic calculaliorls to the dijftcsion data terifies the Onsager reciprocal relations to the extent that experimental uncertainlies will allow. It is jound that diffusion neav the critical point of the 1200-phase field in the isothermal section at 725°C causes the composition gradients for copper and silver to approach infinity while the direct and cross coeficients become equal. From the standpoint of experimental Procedures, it has been shown that microanalysis of ternary samples may be carried out using a simple expression for the conversion of X-ray zntensily to composilion. The accuracy of' this method has been demonstrated by the analysis of standard alloys and by the reproducibility of composition determinations using differed X-ray lines. DIFFUSION in a ternary alloy system is basically and significantly different from diffusion in binary alloys. When only two elements are present there is just one independent composition variable, and the diffusion profile of composition vs distance across a sample must change monotonically through all solid solutions bracketed by the terminal alloys. If two-phase regions are stable for compositions between the terminal values, these must appear as planar interfaces in the diffused sample, with the composition profile exhibiting sharp discontinuities. Adding a third element may alter this picture completely. Because of the additional degree of freedom in the composition, we may see composition profiles which do not change monotonically through solid-solution ranges, and stable, nonplanar phase interfaces. Even though two-phase regions may lie between the terminal compositions of a diffusion sample on the constitution diagram, they will not necessarily appear in the diffusion profiles. In binary diffusion only one coefficient is needed to describe the interdiffusion process. From Fick's law this coefficient relates the diffusive flux of one component to its own composition gradient. In ternary diffusion we must allow for cross interaction between the two independent species. By a linear extension of Fick's law we introduce "cross" or "off-diagonal" diffusion coefficients which relate the flux of one component to the composition gradient of the other independent constituent. Thus, we require four interdiffusion coefficients to describe the transport process in a ternary system. In its most general form,1,2 the rate equation for mass transport by isothermal diffusion in a system of s components states that the diffusive flux of component i, Ji, is a linear summation of all driving forces, Xk, each force being multiplied by an appropriate compliance coefficient:

Jan 1, 1968

By John Alden

A CONSIDERABLE PROPORTION of the tonnage of aluminum used today has at some stage during its manufacture, been rolled. I. For one, therefore, was particularly pleased to hear that this Society was to hold a symposium on rolling of nonferrous metals. Metallurgists can well afford to direct their close attention to the metallurgy involved in this important operation. To one who has seen today's high production rolling mills for aluminum it is difficult to realize that the first aluminum rolling mill For sheet was installed a scant 55 yr ago, in 1892. This mill was a three-stand train of 2-high mills, driven by a steam engine and was operated for many years successfully rolling aluminum sheet. Mills for the rolling of aluminum rod were installed in 1899 to meet the demand For manufacture of electrical conductor wires and cables. Bars and rods in straight lengths were also made. While these mills were the first built for rolling aluminum products of these types some rod had previously been rolled on brass and copper mills. Not until many years later, in 1929, however, Were facilities provided for the rolling of structural shapes, such as I-beams and channels. Growth of the aluminum sheet business and the necessity for economical manufacture soon brought the realization of the economies resulting From-the rolling of sheet in long lengths and coiling it. A five-stand continuous mill driven by a steam engine, was in operation late in 1907. This took aluminum slabs coating from

Jan 1, 1948

By B. J. Harlan

THE trying times experienced by the steel industry during the past four years have emphasized the necessity of producing pig iron at the lowest possible cost. The trend in both design and operation of blast furnaces has been toward this end rather than securing maximum production from a unit or group of units. In the following discussion the trend in design of stacks and auxiliary equipment will be taken up before operation is considered. Although few furnaces have been constructed in the past few years, the trend is definitely toward larger furnaces with a hearth diameter of 24 or 25 ft. Such a furnace is very flexible, being able to produce efficiently any desired daily tonnage between 500 and 1000 or more. The detail of the design of furnace stacks, with the exception of the top, has changed little in recent years.

Jan 1, 1934

By John Drew Ridge

For the early conservationists before the first decade of the twentieth century, conservation meant largely the planned preservation of water, forest, soil, and wildlife resources-renewable natural resources-through efficient use. Water was primarily thought of as a resource that must be kept available for humans to enjoy in a recreational sense and as a habitat for wild animals, birds, and fish. Little thought was given to conserving water for actual human or industrial needs. If industry entered the picture it was as an actual or potential polluter of water, which was the basic necessity for drinking and bathing and for outdoor recreation. Even the forests were only held worthy of conservation largely because they were areas in which wildlife could, or should, abound and in which human beings might find relief from the cares and problems of everyday life. Finally, the soil was to be preserved in its natural fertility through proper fertilization, cultivation, and crop rotation; in this the conservation program did enter the realm of the practical. For through soil conservation, the world was to be able to raise increasingly large crops of constantly improved organic foods which the steadily growing population of the earth was to need to survive and improve. Relatively little time, however, was spent on considering what profit the farmers of the world were to make from the scientific farming on which they were to embark. In short, the appeal of the early conservationist program was much the same as that of the entire era of Theodore Roosevelt of which it was a part; it was to the heart rather than to the mind; it was to emotion rather than to reason. Because of the way in which the problem was approached, conservation took on the character of a crusade rather than that of a practical plan for the betterment of man through economically sound methods of improving his environment and the uses he makes of it. Conservation had, then, all the advantages of a stirring appeal to the emotions, but it did not have the lasting results that would have been achieved by a program with a sound economic basis.

Jan 1, 1959

By Malcolm F. Hawkes

AUSTENITE grain size has long been recognized by metallurgists as an important property of steels because of its influence on toughness, hardenability, machinability and creep strength. Much research has been carried out on wrought steels to develop methods for disclosing austenite grain size, and to provide knowledge of the grain-size -characteristics of steels produced and heat-treated in various ways. Much less work in these fields has been done on steel castings; partly because, owing to the variable and complex microstructures of cast steels, it is frequently very difficult to obtain results that are not questionable. The object of this investigation, therefore, was to establish, for a wide variety of carbon and alloy cast steels, suitable methods for disclosing austenite grain size and some knowledge of the grain-size variations to be expected. The steel foundryman is interested in austenite grain size at two different stages in the manufacture of his products; one is just after the steel is cast, and the other is after any reheating operation carried out above the critical temperature range. In both, it must always be kept in mind that the grain size being sought is actually a previous austenite grain size, and that the austenite no longer exists once the steel has cooled to room temperature. The problem of the investigator is always to use evidence obtained from the structure at room temperature to deduce this previous austenite grain size, which was established the last time the steel existed at a temperature above the critical range. Since most steel castings today are at least annealed or normalized, the measurement of austenite grain size established by heat-treatment will be considered first. More than So commercially produced cast steels representing a wide variety of compositions and melting practices were used in the study. For each steel, grain-size determinations were made after each of three widely varying heat-treating schedules; namely, one hour at 1550°F, one hour at 1700°F, and six hours at 1700°F. The list of steels and results obtained on them will be found in the appendix. (See page 21.) A discussion of the knowledge gained on the applicability of various test methods and on grain-size characteristics of cast steels in general follows. MEASUREMENT OF AUSTENITE GRAIN SIZE ESTABLISHED BY HEAT TREATMENT METHODS SUITABLE FOR DETERMINING AUSTENITE GRAIN SIZE AFTER HEAT- TREATMENT AT ORDINARY TEMPERATURES AND TIMES It was desired, as one of the results of this investigation, to be able to recommend to steel foundries a method, or methods, of disclosing grain size best suited to accurate

Jan 1, 1947

By W. J. Leas, L. A. Rapoport

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas' which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy's law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy's law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951

By L. A. Rapoport, W. J. Leas

As a preliminary, consicleration is given to the conventional definition of relative permeability and to the conditions governing the simultaneous flow of oil and gas through porous media. For the conditions of flow prevailing throughout most of a gas drive reservoir, the oil and gas can reasonably be supposed to be in capillary equilibrium with each other. Under these conditions, and these conditions only, the relative permeability to liquid can be expressed as a function of saturation. The relative permeability to liquid in that case is dependent upon the distribution of fluids which itself is shown to be related to the capillary pressure, and, in turn, to the saturation. As a consequence, relative permeability to liquid can be expressed in terms of the volume and surface area of a network of liquid channels bounded by the rock and the gas phase. While the volume of this network can be evaluated accurately, the surface area cannot. However, for any such volume, maximum and minimum values of the corresponding surface area can be calculated from capillary pressure data. It is then possible to establish for any saturation the limits within which the value of the relative permeability to liquid must lie. As a consequence of the theoretical development, the validity of an experimental method for measuring relative permeability to liquid which utilizes a stationary gas phase is demonstrated. In this method capillary barriers are cemented to the ends of the core sample to permit the maintenance of capillary equilibrium between the two phases. At the same time, this procedure eliminates undesirable secondary phenomena such as end effects, fissure effects, etc., the presence of which adversely affect the results of other laboratory methods. The results obtained by theoretical calculations, and experimentally, are discussed. In view of the overall precision that can presently be obtained in reservoir calculations, the agreement between the calculated and measured relative permeability to liquid data can be considered satisfactory. In conclusion, for reasons of economy and simplicity, the procedure of calculating limiting relative permeability to liquid curves from capillary pressure data is indicated for general engineering purposes. It is shown that the above procedure can easily be extended to the cases where connate water is present. Its use for reservoir studies is particularly recommended in conjunction with the method for measuring relative permeability to gas' which simultaneously yields the capillary pressure data necessary for the calculations. THEORETICAL Definition of Relative Permeabilities — Basic Equations for Heterogeneous Flow The equations by which the relative permeability concept is defined and upon which the formulation of all of the gas-oil flow problems rests at the present time are expressed as: V, = — Grad PL = — Grad PL ....(la) PL µL, k k KG VG = —K - Grad PG k- Grad Pc .... (lb) Mo where ,. and G refer to liquid and gas; V is the volumetric rate of flow per unit gross area. µ the viscosity, Grad P the potential gradient. and k the specific permeability of the porous medium.* (For horizontal flow, Grad P becomes the pressure gradient; otherwise, gravity must be included.) According to these expressions, each of the constituent phases is considered similar to a homogeneous system where the volumetric rate of flow is proportional to the pressure gradient, and for each of which the constants of proportionality, k, and kG, are termed effective permeabilities. by analogy to the specific permeability as defined by Darcy's law in its original form. In order to obtain a convenient basis of comparison, the effective permeabilities are referred to the specific permeability, k, of the considered porous medium, with the help of the relations: k1. = KI. k kQ = Kn k..........(2) K,. and Kr. are defined as the relative permeabilities to the liquid and to the gas phase respectively, and frequently expressed in per cent of specific permeability. It may be seen that Equations (1); which appear to be a direct generalization of Darcy's law, correspond to the assignment at any given time of a set of "local" permeabilities to each point of the porous medium, and represent in a differential form the two fluid flow system as a simple superposition of the individual single flow systems. The above interpretation implies that the effective or relative permeabilities are independent of pressure or rate of flow,

Jan 1, 1951