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By J. C. Martin

Stmplified equations are developed for the flow of fluids in gas drive reservoirs in which the effects of gravity can be neglected. The results show that the pressure distribution is governed by a nonlinear heat flow type of equation, and the saturation distributions are related to the pressure by the same equations QS those developed by Muskat for the average pressure and saturations in gas drive reservoirs. Unrler certain conditions the equation for the pressure can be approximated by the linear form of the heat flow equatlon. This equation tk analogous to the equation for the pressure in single-phase compressible flow The analysis reveals that the equation for the pressure in n~ultiphase flows can be obtained directly from the equation for the pressure in slngle-phase flows by simply replacing the single-phase compressibility by the total compressibility and the single-phase mobility by the sum of the mobilities of all the fluids present. Perrine's method of pressure buildup analysis for multiphme flows is based on these same substitutions. Thus, the development presented in this paper constitutes a theoretical justification for Perrine's method of pressure buildup analysis. One of the most difficult problems associated with the production of oil is the determination of the flow of the fluids within the reservoirs. One purpose of this paper is to present the development of simplified equations for the flow in gas drive reservoirs. The other purpose is to present some of the needed theoretical foundation for the methods currently being used in the analysis of multiphase pressure buildup data. The analysis presented in this paper makes use of a partial linearization of the equations governing multiphase flows. It is felt that the process of linearizing or partially linearizing the nonlinear equations of multiphase flows can lead to useful results since this process has proved extremely valuable in the study of other fields of science and engineering where nonlinear equations are encountered. Pressure buildup data of shut-in wells have been used for many years to estimate the static reservoir pressure. These data have also been used in studying the aver- age permeability both away from and close to the well-bores. The majority of the buildup data are obtained from wells producing two or three fluids. As yet the theoretical foundations for the methods of buildup analysis used in connection with rnultiphase buildup data have not been established. A number of methods of analysis of pressure buildup data have been developed." Most of these methods apply only to single-phase flows, and almost all of the theoretical analysis is confined to single-phase flows. Perrine' developed a method of analysis for rnultiphase flows from the method for single-phase flows of Miller, Dyes, and Hutchinson.' He did this by simply replacing the single-phase compressibility by the multiphase compressibility and replacing the single-phase mobility by the sum of the mobilities of the fluids in the rnultiphase flows. Obviously, such a procedure lacks a certain amount of theoretical justification, and such practices can lead to erroneous results. Fortunately, Perrine's results have a theoretical justification, and this justification is presented in the following discussion. It is assumed that gravitational effects and the cornpressibility of the rock can be neglected. Under these assumptions the equations governing the simultaneous flow of gas, oil and water in porous media areo* The preceding equations can be expanded into the following expressions.

By W. L. Dumoulin

A RATHER detailed description of the entire plant and leaching process was given in a paper recently presented to the Institute,1 so this paper will cover briefly only the crushing practice of the New Cornelia Copper Co. for the year, 1918. The ore, which is mined by steam shovels and loaded in side-dump cars, passes through two crushing plants. These crushing plants were constructed to crush the ore required by a leaching plant of 5000 tons daily, capacity, during a crushing period of 16 hours. The primary plant reduces to less than 3 in. (76 mm.) and the secondary plant, to ¼ in. (6.35 mm.), which is sufficiently fine for satisfactory percolation of solution through the ore in the leaching tanks, and to give good extraction. The ore is then conveyed to the leaching tanks by a system of 28-in.. (71-cm.) belt conveyors. On the way to the leaching tanks, it passes through an automatic sampling plant, where a 1-per cent. sample is taken. From the primary crushing plant, the ore is conveyed by two 36-in. (91-cm.) belt conveyors to a 10,000-ton steel storage bin, with a reinforced-concrete flat bottom. The ore discharges from the bottom of this bin onto four 20-in. belt conveyors, which deliver it to the four units of crushers in the secondary crushing plant. There is no storage bin between the mine and the primary crushing plant. The ore breaks very coarse, is very hard, and contains a great many boulders, some as large as 4 ½ by 4 1/2 by 10 ft. (1.3 by 1.3 by 3 m.). Jams form in the bowl of the coarse crusher in the primary crushing plant, as a consequence, and are freed by means of an immense steel hook operated from a 40-ton electric traveling crane.

Jan 8, 1919

Jan 1, 1969

By C. E. Richards, C. N. Reid

The influence of preferred orientation on the incidence of defbrtnation tuinning has been studied. High-purity iron with almost vandonz grain orientation was cotnpared uitll iron of the sa)ne grain size and composilion lza,ing a strong (110) fiber texture. As expected from published work on single crgslfls, /he ))lean stress for the onset of luitzning-, and the l,olu)nt. fraclion of twinned nzaterial obserlled in lension differed fron the 1-a1ue.s it2 co?nPression for tnolerial with a slrong texlure. The llinning stress of "rctndorrl " )zalerial did not 17ary with the sense of the aPPlied unin.via1 stress, but sirprisinglg the incidence of 1c)i)zning- was about three 1i))zes greater ill conzp?&apos;ession Illon in lension. These results (Ire attributed entirely to ovienbation and may be nderslood in ler?ns of the shear slresses acting on the allowed twinning syster)is. J. HE twins most commonly formed in bcc metals may be described as regions of the crystal in which a particular set of (112) planes is homogeneously sheared by 0.707 in the appropriate ( 111) direction. A similar twin-related crystal could be produced by a shear of 1.414 in the reverse (111) direction but twinning by this large displacement has never been reported. Thus, twinning is unidirectional and a shear stress which produces twinning does not do so when its sense is reversed. The sense of a shear Stress is reversed when the loading is changed from tension to compression, or vice versa. Consequently, for a given orientation of a crystal relative to a uniaxial stress, only a fraction of the twelve (112) twinning systems are geometrically capable of operating in tension, and the remaining systems may operate only in compression. Therefore, when twinning is involved, there are expected to be differences in behavior between crystals tested in uniaxial tension and those tested in compression. This has been verified experimentally by Reid et 01.&apos; and Sherwood el al.,&apos; although a critical stress criterion was not encountered. Furthermore, twinning stresses in colmbium," tungten, tantalum,&apos; irn,&apos; i-Fe,\ nd molybdenum7 single crystals have been shown to depend critically on orientation, although again twinning did not occur at a critical value of the macroscopic shear stress. However, when twinning occurs, it generally does so on the most highly stressed systems, 1--4&apos;6&apos;8&apos;9 implying that the stress level does have some relevance to twin formation. In view of the large orientation dependence of twinning in bee single crystals, it might be expected that such an effect would be present in poly crystalline material which possesses a recrystallisation texture. Indeed, riestner" showed that the twinning stress in tension is very orientation-sensitive it1 <&apos;grain-oriented, silicon-iron;" this material possessed a very strong t c m^ii a nnr x_____k . i-_ii__ ri_______j. _x r»i_._:__i preferred orientation obtained by secondary recrystallisation. Reid et a/.&apos; observed a marked difference in the tensile and compressive yield stresses of polycrys-talline columbium which was rationalised in terms of the effect of a preferred orientation on twinning. No other such illformation is known to the authors. Several investigations of twinning in polycrystalline bcc metals have been reported in which the possible existence of a preferred orientation was not even mentioned. It is the purpose of this paper to show that there is a strong effect of texture on twinning in polycrystalline iron, and to poilt out the difficulty in eliminating preferred orientation in recrystallised metals. 1. EXPERIMENTAL METHOD Material and Specimen Preparation. Low-carbon, high-purity iron was obtained from the National Physical Laboratory in the form of $-in. diam rod which had been cold-swaged from a diam of 1 in. The composition of the material is given in Table I. The as-received bar was cold-swaged directly to 0.185 in. diam from which cylindrical tensile and compression specimens were machined. Specimen geometry is illustrated in Fig. 1. The gage length was 0.30 in. long and 0.10 in. diam; it should be noted that, apart from the extra heads which are necessary for tensile loading, the geometry and dimensions of the two types of specimen are identical. The specimens were heat treated either by sequence A or B outlined in Table 11. The essential difference between these two treatments is that in one case the material was repeatedly cycled through the y- to a-phase change in order to produce grains of almost random orientation ("random" iron)

Jan 1, 1969

By Thunaes, Arvid

Pilot plant test work in 1942 and 1943 showed that by a combination of desliming, fine-size classification, and Sullivan deck concentration it is possible to recover heavy minerals such as cassiterite at least as fine as 10 microns in size. This appreciable improvement in gravity concentration practice has been substantiated by several full-sized plants.

Jan 1, 1950

By R. Kossowsky

USING etch-pit techniques, Johnston and Gilman&apos; have shown that the stress dependence of dislocation velocity can be represented by the expression where r, is the dislocation velocity, a is the applied stress, and oa, is the stress to produce a unit velocity. Noble and Hul12 showed that the exponent m is strain-dependent and increases rapidly in the work-hardening region. This was explained by arguing that in the work-hardened material the applied stress required for any given velocity will be greater than in the annealed material by an amount equal to a back stress due to work hardening. schadler3 has stressed the importance of substructure as a possible source of error in dislocation velocity measurements, and took care to make velocity measurements in which dislocations moved such short distances that interactions with boundaries were avoided. schadler3 also pointed out that, if standard testing equipment is used, measurements of m from flow stress data could be seriously in error in materials with a high initial work-hardening rate. Noble and Hu112 have further argued that, due to the strain dependence of m , the extrapolation to zero strain4 to obtain the true value of m can be justified only in the preyield region. Microstrain experiments in high-purity iron5,6 have led to the conclusion that aiA (Ref. 5) (defined as the stress to first produce a permanent set of 10-6 in. per in.) and oflow are not controlled by the same deformation mechanism. It has been proposed5,6 that aA is governed by the lattice resistance to the motion of screw dislocations in a given slip plane and that oflow is controlled by the lattice resistance to a full-scale cross slip. The purpose of this note is to extend Noble and Hull&apos;s argument further and to show that measurements of m from flow stress data can be in error due to the rapid increase in stress in the microstrain region6 when stress is increased beyond aA. Double z-one-refined single crystals of molybdenum (with the (101)[ 111] slip system operating and a Schmidt factor of 0.475) were used in an experimen-

Jan 1, 1968

By Bezalel C. Haimson

Anna, Ohio, at the junction of Cincinnati, Findlay and Kankakee arches, has been the site of repeated and sometimes damaging earthquakes. As part of a seismicity investigation near-surface (0.15-1 m depth) overcoring strain measurements were conducted in four limestone and dolomite quarries surrounding Anna, the results of which suggest a complicated regional stress pattern, with changes in the maximum horizontal stress direction from N45ºE to N15ºW. Since such abrupt stress fluctuations are rather atypical in the Midwest and since the reliability of near-surface tests in defining regional stress had not been established, we decided to remeasure the stresses at the same locations but at greater depths (0-200 m) using the hydrofracturing method. Owing to the weak horizontal bedding planes of the Silurian shaly limestones and shaly dolomites and the relatively shallow depths, many of the tests yielded horizontal fractures, providing information only on the vertical principal stress (-0.029 MPa/m depth). However, sufficient tests in each of three testholes resulted in vertical hydrofractures to enable the calculation of all three principal stresses. Within 50-170 m depth the horizontal stresses in all three quarries appear to belong to a uniform regional Stress field defined by the following relations: [&apos;]Hmin = 5.1 + 0.014 D; [0] Hmax = 10.1 + 0.014 D, where D is depth in meters. The direction of [O]Hmax within 50-170 m depth is uniform at N70°E (±15º). The hydro- fracturing results obtained at Anna, Ohio are in agreement with the prevailing stress regime in the midcontinent both with respect to magnitudes and directions. The results suggest a possible thrust mechanism for a proposed NW-SE fault along which most of the earthquake epicenters have been located, and a left lateral strike-slip at greater depths. The focal mechanism solution of a recent major earthquake near Sharpsburg, Kentucky, some 200 km south of Anna, also indicates strike-

Jan 1, 1982

By R. B. Mears, E. H. Dix, R. H. Brown

In the Institute of Metals Division Lecture of 1940, E. H. Dix, J~.(I)~ discussed the acceleration of the rate of corrosion by high constant stresses. Experimental data obtained on this subject at the Aluminum Research Laboratories and a theory compatible with these facts were included in that lecture. The present paper contains data and ideas subsequently developed at the Aluminum Research Laboratories. Dix pointed out that in order for acceleration of corrosion by constant stress to occur: (1) There must exist in the alloy a susceptibility to selective corrosion along more or less continuous paths, as for in- stance at grain boundaries, and (2) There must exist a condition of high stress acting in a direction tending to pull the metal apart along these continuous paths. Acceleration of corrosion rate by stress is not confined to any one alloy system. Table I lists some of the metals and alloys and some of the corroding environments in which acceleration of corrosion by stress was sufficient to cause cracking (stress- corrosion cracking). It will be noted that the variety of alloys in which stress-corrosion cracking has occurred is rather large. Also, it will be observed that

Jan 1, 1945

By R. M. Genevray, M. B. Bever, E. J. Suoninen

THE martensitic transformation in the ß-phase of the Cu-Zn system has been the subject of several investigations. The transformation is known to be reversible and to be affected by stress. Its temperature range has been determined as a function of composition. In the investigation reported here, the effect of tensile stresses on the transformation was investigated quantitatively. Some information was also obtained on the thermoelastic behavior of the martensite formed in the first stages of the transformation. Most of the experiments were done with alloy E of an earlier investigation;&apos; this alloy analyzed 60.49 pct Cu and 39.51 pet Zn by weight. The methods of shaping and heat treatment were also essentially the same as those previously used. The stress was applied to the specimen immersed in a cooling liquid. The transformation was followed by measuring the electrical resistance with a Kelvin bridge and the elongation with a cathetometer. Fig. 1 shows the M, temperature as a function of stress. Resistance and strain measurements gave essentially identical values. The results suggest a roughly linear relation between M. and in the range investigated, up to 12 kg s mm". At higher stresses, plastic deformation begins to interfere seriously with this relationship. The increase of M, with stress is consistent with published work on the effect of stress on the martensitic transformation. The slope of the curve, 4°C per kg mm ", is of the same order of magnitude as the corresponding value calculated for steel.&apos; Fig. 1 also shows the difference, AM, between the temperature of 50 pct transformation on cooling, as measured by changes in length, and that of 50 pct reverse transformation on heating. This difference, which may be considered a measure of the hysteresis, increases with stress; the decrease at highest stresses is probably associated with plastic deformation. Preliminary work using only resistance measurements was done with an alloy containing 60.15 pct Cu and 39.79 pct Zn by weight. The results indicated higher values o-F M, in agreement with the known variation of M. with composition.&apos; The effect of stress on M, (2°C per kg mm-&apos;) was of the same order of magnitude as that shown in Fig. 1 for composition E. An increase in hysteresis with stress was also found. The following experiment was made in order to investigate a partially transformed structure. A specimen of alloy E was cooled to — 85°C under a stress of 4.7 kg mm-&apos;. Under these conditions, the martensitic transformation started but did not go to completion. The stress was then released and the specimen cooled to — 105°C. Fig. 2 shows the measured elongation c. The first change in the slope of the curve indicates the beginning of the transformation under stress. Removing the load at —85°C caused a decrease in length to the value corresponding to the elastic elongation of the parent phase resulting from the applied stress. Hence, the marten-site formed in the first part of the experiment apparently disappears completely and without hysteresis upon the release of the stress. The increase in length on further cooling indicates renewed formation of martensite. These conclusions are consistent with the concept of "thermoelastic" martensite," which has been confirmed by test." Acknowledgments The authors are greatly indebted to Professor M. Cohen for his advice and encouragement. They also thank F. Paxton for assistance. Thanks are due the American Brass Co. which supplied the alloys. References E. Kaminsky and G. V. Kurdjumov: Zhur. Tekhn. Fiziki SSSR (1936) 6, p. 984. A. B. Greninger and V. G. Mooradian: Trans. AIME (1938) 128, p. 337. "J. E. Reynolds, Jr. and M. B. Bever: Trans. AIME (1952) 194, p. 1065; Journal of Metals (October 1952). &apos;A. L. Titchener and M. B. Bever: Trai~s. AIME (1954) 200, p. 303; Journal of Metals (February 1954). " 3. A. Kulin, M. Cohen, and B. L. Averbach: Trans. AIME (1952) 194. p. 661; Journal of Metals (June 1952). "J. K. Pate1 and M. Cohen: Acta Metallurgica (1953) 1, p. 531. &apos;C. Crussard: Comptes Rendus (1953) 237, p. 1709. &apos; G. V. Kurdjumov: Zhur. Tekhn. Fiziki SSSR (1948) 18, p. 999. G. V. Kurdjumov and L. G. Khandros: Dokl Akad. Nouk. SSSR (1949) 66. p. 211.

Jan 1, 1957

By C. E. Arnold

A brief description of this installation was included in a recent paper by H. Kenyon Burch.l The purpose of the present paper is to amplify Mr. Burch&apos;s description, as it is felt by the writer that the subject merits more than passing attention. In making a comparison between the common method of hoisting men in mine shafts, and elevator practice in high buildings, the former shows to great disadvantage both as regards safety measures and smoothness of operation. It is surprising that in view of the inducements offered, the step of applying the building equipment direct to the mine shaft has not been taken before, as in many respects the conditions of service are similar, and the objects to be attained are identical. Even without doing this, it is certain that safety to life and limb in the usual method of hoisting men underground can be greatly enhanced by the application to the mine hoist of some of the features of the building elevator. In the case under consideration, the elevator cage runs in a vertical, concrete-lined shaft compartment 5 ft. 11 in. by 5 ft. 6 in. (1.8 by 1.68 m.) in section and 585 ft. (178 m.) deep, while the counterweight runs in the pipe and ladder compartment of a twin shaft 102 ft. (31 m.) distant. The section of the division of this compartment occupied by the counterweight measures 2 ft. 4 1/4 in. by 3 ft. 101/2 in. (0.72 by 1.18 m.), and the counterweight is made in the form of a small cage which suffices to carry two men for the purpose of making inspections or repairs in the pipe and ladder way. The hoist is designed to carry a load of 7500 lb. (3401.94 kg.), ex-clusive of the cage, which weighs 7500 lb., at a maximum speed of 800 ft. (243 m.) per minute. It is installed in the main hoist and compressor building about 220 ft. away from the elevator shaft and is driven by a 160-hp. direct-current motor which is served by a 190-hp. motor generator set. A small direct-current generator mounted at the end of the motor generator set furnishes the current for the controller magnets, brake and fields of the hoist motor and generator. The drum, which is 72 in. (1.83 m.) in diameter, is driven through the medium of a single reduction herringbone gear. A Francke flexible coupling connects the

Jan 1, 1918

By Y. Wang, M. M. Singh, H. L. Hartman

Knowledge of the state of stress at the bottom of a drillhole is of practical importance in rock drilling, since the induced stresses must exceed the strength of the rock in order to cause fracture. This note reports on a numerical method to determine the stress distribution at the bottom of a borehole induced by a static bit load and overburden and fluid pressures. The procedure adopted is similar to that for the plane-strain, discrete model employed by Harper and Ang.1,2 The rock medium is considered to be homogeneous, isotropic, and elastic-perfectly-plastic. METHOD OF ANALYSIS AND PROGRAMMING The discrete model adopted consists of two types of points: mass points and stress points. The configuration and numbering notation are depicted in

Jan 1, 1967

By J. R. Martson

The arrangement of the larger furnace at the United Verde smelter, together with the boiler layout and connecting flues, is shown in Fig. 1. The important dimensions are given in the figure, and cross-sectional areas of combustion space, flues, etc., are recorded. The location and extent of the baffling in the boilers also are shown because of their importance in the interpretation of the data. Two boilers serve each reverberatory furnace. They are of the class M-26 Stirling type (rated at 713 boiler hp. each). Steam is generated at 178-lb. gage pressure at a total temperature of 528" F., from feed water at a temperature of 113" F. The feed water is condensate from turbogenerators plus make-up softened by the lime-soda process. The make-up is rather large in amount as it must match the amount of steam consumed in reciprocating blowing engines and the like, which are not served by surface condensers. As a result the boiler feed water has a hardness of 1.5 to 3.0 grains per gallon, but this results in the formation, during six months to one year of boiler operation, of scale only of "eggshell " thickness or less. The boilers are set at the same elevation as the tapping floor of the furnace, which results in the introduction of the waste-heat gases at the top of the front bank of tubes and necessitates the inversion of the usual baffling arrangements. The boilers are equipped with valve-in-the-head soot blowers, which keep most of the dust blown off the surface of the tubes, but it is necessary to supplement the soot blowers by high-pressure air lances, inserted by an attendant through side doors in the boiler setting. Deposits of coal ash and of dust from the furnace charge accumulate in the flues between the reverberatory furnaces and the boilers and this necessitates cleaning of these connecting flues by hand during the greater part of one of the three 8-hr. shifts during each 24 hr. This cleaning operation requires the opening of clean-out doors, which, of course, has some effect on the yield of steam. Revebberatory Furnace Practice The United Verde furnaces are fired with pulverized coal of sub-bituminous type of which the screen and chemical analyses are given in Table 1.

Jan 1, 1934

By J. H. Swisher

ALUMINUM deoxidation equilibrium in liquid iron has been the subject of many investigations. Sawamura and Sano1 have written a critical survey of the literature on this subject and consider the data of Gokcen and chipman2 and of d&apos;Entremont, Guernsey, and Chip-man3 to be most reliable. The present study was undertaken to check these data and extend the range of the experiments to lower temperature. The experiments consisted of equilibrating 5-lb Fe-Al melts with recrystallized alumina crucibles at 1580o + 10oC, and analyzing the solidified ingots for aluminum and oxygen. The electrolytic iron stock contained 100 ppm C, 20 ppm 0, and trace amounts of other elements.* The stock was induction-melted in an atmosphere of 5 pet H2 in argon to attain equilibrium between the melt and the crucible. The temperature was measured with a W, 3 pet Re/W, 26 pet Re thermocouple, and the equilibration time was about 4 hr. The results are plotted in Fig. 1 along with curves obtained from the data of d&apos;Entremont et al.,3 for temperatures of 1740o and 1910°C. The present results can be seen to be consistent with the previously reported high-temperature data. The reaction under study is AI2O3 (s) = 2 Al (l) +3O [1] for which the deoxidation product is Kl =[% Al]2 [%O]3 [2] (Under the experimental conditions, Fe A12O4 is not expected to form.4) In Fig. 2, values of log Ki evaluated at 0.01 pet A1 are plotted against 1/T, using data obtained from all the investigations under consideration. The deoxidation product is plotted in Fig. 2 in lieu of the equilibrium constant (normally obtained by evaluating Ki as pet A1 — 0) because of the uncertainty involved in extrapolating to zero concentration. The difficulty in extrapolating the present data for 1580°C is apparent curvature in the log Ki vs pet Al plot. This curvature is perhaps due to the uncertainty in oxygen analysis for concentrations of 5 ppm and below. For the data of Gokeen and chipman,&apos; the extrapolation is also difficult because of experimental scatter. The line drawn through the points plotted in Fig. 2 may be represented by the equation:

Jan 1, 1968

By E. J. Eisenach, Edward Matsen

AT the present time the Climax Molybdenum Co. is the largest molybdenum producer in the world and the operator of the largest underground mine in North America. It has grown steadily and rapidly since its beginning in 1917. Only 250,000 lb of MoS2 were produced during the first year from 1917 to 1918 when the company was formed. Operations were suspended shortly thereafter because of the lack of a market and knowledge of the uses of molybdenum. During World War I it was used as a substitute for some rare metals and for minor chemical purposes. After 5 years of intensive research and sales promotion, Climax metallurgists succeeded in finding proper applications for the newly discovered metal and the mine was reopened in 1924. Demand for molybdenum increased gradually and in 1930, 3.5 million lb of MoS2 were produced. In the meantime, research work for additional uses of molybdenum continued until it had established itself as one of the most important alloying elements in producing high quality steels. After the start of World War 11, from January 1942 to October 1953, 43 million tons of molybdenum ore were mined and 484 million lb of MoS2 were produced. Climax mine is located in Colorado, 100 miles southwest of Denver and 12 miles northeast of Leadville on the Continental Divide of the Rocky Mountains. The principal mine workings range from 11,170 to 12,000 ft in elevation. Topographically, it lies in the base of a large cirque that is surrounded by Mt. Bartlett to the north, Clinton Peak and McNamee Peak to the east and Ceresco Ridge to the south. This cirque opens to the west and to the Ten Mile Valley.

Jan 3, 1954

By I. R. Kramer

The apparent activation energy, U, JOY plastic deformation of aluminium, copper, and gold single crystals and polycrystalline aluminum was found to he dependent upon surface condition. At low strains, the value for U for aluminum single crystals was 4200 cal per mole ; however, this value decreased to 920 cal per mole when the specimens were polished during the test at a rate of 50 X 10-5 win-1 The activated volume also was found to increase with the rate of metal removal. That the surface plays an important role in plastic-deformation processes has been adequately demonstrated.1-4 Of particular interest at this time are the observations4 that the creep rate of single crystals of fee metals is increased markedly when specimens are polished during the deformation process. These observations were interpreted in terms of a dislocation debris layer at the surface regions of the crystal. This layer, which appears to be a region containing a high concentration of dislocations or segments of dislocations, not only will impede the egress of dislocations on the primary slip system, but will also provide a barrier against which dislocations may pile up. By this means, a stress which opposes the motion of dislocations will be generated. It is considered that this stress must be taken into account in any theory which describes the plastic-deformation process. Although a detailed dislocation model cannot be given at this time, it may be stated that the stresses opposing the motion of dislocations arise from the dislocations in the debris layer, Ts, and ti due to the resistance to motion imposed by internal obstacles such as Lomer-Cottrell barriers, subgrain and grain boundaries, forest dislocations, and so forth, as well as the resistance due to the presence of jogs on dislocations and the interaction of the stress fields of dislocations, and so forth. In essence, we have added an additional term, ts, to the usual form of the equation T = Ta- Tb, where Tb is the back stress due to the various types of obstacles which impede the motion of dislocation. Accordingly, the net stress, t, acting on a dislocation may be written as where Ta is the applied shear stress. For deformation which occurs by a thermally activated process5,8 ?=Ae-u/kT = A e(u,-VT)/kT [2] and U = Uo- Vt PI where U = activation energy for plastic flow, y = shear strain rate, Uo = activated energy for plastic deformation in the absence of stress and depends upon the particular deformation process, V = activated volume, k = Boltzmann constant, T = temperature, OK, and A = frequency factor. From Eqs. [I] and [3], U = Uo- V(Ta - Ti - TS) [4] and it is seen that if Ts decreases, the activation energy, U, must decrease if V remains constant. However, as will be shown, V is a function of the surface conditions. In their work on aluminum, Lytton and coworkers7 reported that at low strains the activation energy was 3400 cal per mole and at high strains it was 28,000 cal per mole. The lower value was interpreted in terms of the energy necessary to overcome the Peierls force, while the higher value was associated with the energy necessary for dislocations to move by a cross-slip process. It will be shown that the lower activation energy is associated with the surface debris layer rather than with the Peierls force. EXPERIMENTAL PROCEDURE Single crystals having a nominal cross section of 1/8 in. and a 3-in. gage length were prepared by a modified Bridgman technique using a multiple-cavity graphite mold. The initial purity of the metals was 99.997, 99.999, and 99.999 pet for aluminum, copper, and gold, respectively. The orientation of the specimens is given in Fig. 1. The measurement of the activation energy as a

Jan 1, 1964

By A. R. Troiano, E. A. Steigerwald, F. W. Schaller

D. N. Williams(BatteZle Memorial Institute)-The authors have presented an extensive collection of arguments pertaining to the role of stress in hydrogen embrittlement. The basic assumption of these arguments is that stress is essential as a driving force for diffusion of hydrogen. However, in view of the rapid diffusion rate of hydrogen in steel at low temperatures as evidenced by the ability to alloy with hydrogen by electrolytic charging, it seems unlikely to me that stress acts in this manner. Instead, I would like to suggest that stress may be essential for the nucleation of hydrogen in steel. I believe that such an assumption would equally well satisfy the experimental data presented by the authors. I should also like to comment on the interpretation of the data presented in Figs. 5 and 6. Fig. 5 shows the effect of hydrogen content on ductility in a rupture test. The curve as drawn by the authors indicates an abrupt transition from ductile to brittle behavior at about 0.001 amp per sq in. (5 ppm). The data points would equally well support a gradual transition from ductile to brittle behavior extending over the range from 0.0008 to 0.02 amp per sq in. (4 to 8 ppm). A gradual transition would be the ex-

Jan 1, 1962

In any earth-moving operation, more profit may be earned or lost by equipment scheduling than by any other single facet of the project. Many now-defunct earth movers would have survived the cost-profit squeeze had they followed an efficient, cost saving, equipment scheduling program. The ideal program would have every item of the equipment fleet working all of the time. In practice this ideal situation is not possible. Several basic methods of equipment scheduling, with an infinite number of minor variations, are used. The first approach is the use of a "minimum equipment fleet," of which all items or equipment are scheduled each working shift.

Jan 10, 1967

By J. H. Curran

In this paper, a numerical model for determining the stress and displacement fields around a crack of arbitrary geometry in a linear elastic medium is described. Accuracy and computational speed were the main considerations in selecting the numerical method and Propagation criteria used to model the growing crack. Some results regarding the stresses and displacements around a two-dimensional crack of arbitrary geometry are discussed.

Jan 1, 1984

By E. W. Engelmann

RAPID progress has been made during the past year in the copper mills throughout the country. Particular efforts have been made to increase the fine-grinding efficiency by the installation of larger classifying units operating in closed circuit with ball mills, such as the 78-in. high-weir Akins installation at the Phelps Dodge plant at Ajo, Ariz.; also the Type "FX" Dorr classifiers of Nevada Consolidated at McGill. Nev. and the "FX" Dorr bowl classifier of the Braden Copper Co. in Chile. Some of the copper milling plants in the Southwest, such as Chino in New Mexico and Ray Con. in Arizona, have replaced rolls operating wet in their fine-grinding circuit by rod mills. At Hollinger primary rod mills were formerly used in open circuit followed by pebble mills in closed circuit with classifiers. They now have primary ball mills in closed circuit with large extra heavy classifiers and no secondary mills. This new installation is producing the same grinding on 5000 tons per day with a reduction in cost of nearly 4c. per ton. At the Braden plant, in Chile, short-head Symons crushers have replaced 54-in. rolls, thereby in- creasing crushing capacity with some saving in maintenance cost.

Jan 1, 1939

By T. A. Rickard

MILLING is one of the metallurgical arts whereby the extraction of the largest possible proportion of the value in an ore is effected at the least possible expense. Stamp-milling* is that particular process in which a heavy body of iron is caused to fall upon the ore so as to disintegrate it and thereby induce a separation between what is valuable and what is worthless. The latter is usually less in specific gravity, and is therefore, by the further aid of water, removed from the former, which is then collected by the use of mercury. Several similes have been employed to describe this process. The stamp has been likened to a hammer of which the stem is the handle and the die the anvil. The ore upon which the stamp falls has been compared to a nut awaiting the descent of the hammer whose blow is to separate the valueless shell, the quartz, from the valuable kernel, the gold. When we begin to pursue our inquiries, however, we find that the analogy is just sufficiently true to emphasize the departures from it. The hammer falls, the anvil is fixed; so with the stamps and the mortar. The anvil is made of softer metal than the hammer; so also the die is often, and should be always, of steel or iron less hard and more tough than that of the shoe. The movement of the hammer and the drop of the stamp are both intermittent. In regard to their intermittent action, as in many other respects, stamp-mills arrange themselves under two types, which, though apparently contradictory, have both been evolved from a common original, and are united by a great variety of intermediate modifications. The slow speed and the high drop of the mills of Gilpin county Colorado, appear to have very little in common with the fast speed and short drop of those of the main gold belt of California; yet the practice of the one was largely derived from that of the other,

Jan 1, 1894