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By M. Friedman

Applications of rock mechanics to the design of engineering structures in rock involve the assumption that the stresses are due entirely to the present applied loads. For instance, it is assumed that the vertical normal stress in undisturbed rock free of topographic effects is equal to the weight per unit area of the overburden. In fact, vertical dilatational strains associated with stresses of more than 100 times the present overburden pressure have been measured by strain-relief methods on outcrops. 1,2 The notion of residual strain (stress) or latent stress3 seems unassailable; and indeed this has long been recognized by metallurgists. It is difficult, however, to assess the residual component of the in-situ state of elastic strain with conventional strain relief methods employed in mines or down boreholes. That is, in principle, the in-situ state results from the superposition of present applied loads (natural or man- induced) and potentially recoverable elastic strains (stresses) that exist in a given volume of material even though there are no external forces across the boundaries of the body (Voight,4 and Fig, 1). Accordingly, only in unloaded blocks can the true residual strains be measured by strain relief methods. Using X-rays, the elastic strains locked within the quartz grains or crystals of a rock can be measured. These strains are known to persist even when the rock is reduced to small chips but to vanish when the rock is disaggregated and the grains are powdered. Although we have just begun to investigate the mechanisms by which the strains are stored (see Preliminary Results), we believe that "pressure solution'' at grain boundaries, secondary cementation under load, permanent ("plastic") deformation, and temperature changes are possible processes. In any event, in our study of naturally deformed rocks, it is significant that we are work-

Jan 1, 1972

By William H. R. Gibney

Pine Point Mines is located in the Canadian Northwest Territories about 1,200 kilometers north of Edmonton, Alberta, close to the south shore of Great Slave Lake. Originally staked in 1898 by prospectors en route to the Dondike gold rush, it was not until the mid-1940's that large scale exploration was undertaken and Pine Point Mines Limited was formed. Work was suspended in 1954 while studies were made to resolve one of the main problems, transportation. In 1961, under the Canadian Government "Roads to Resources" program, agreement was reached for the construction of the Great Slave Lake Railroad and plans made to put the property into production. A townsite was established in 1963 and plant construction commenced. The first production was in the form of high grade ore which was shipped to Kimberley, B.C. for concentration starting in late 1964. The Pine Point concentrator started up in late 1965 when hydroelectric power became available. Initially designed for 4,540 metric ton per day, facilities were expanded to a designed 7,250 metric ton per day in 1969. Problems associated with mining operations at Pine Point are not unique but are augmented by the isolation, climatic conditions, topography, high water table and spread out nature of the operation. Maintenance of a reasonably stable work force is the number one problem but this is gradually being overcome as more local people are trained and oriented from a nomadic type life to an industrial society. The purpose of this paper is to give a general description of the mining operations of Pine Point Mines Limited and to review some of the problems encountered in the operation along with problems associated with northern operations.

Jan 1, 1970

By Laurence Hicks

CONSIDERATION of the past work on the subject of the diffusion of chromium into iron suggested that additional information might be given by the use of X-ray spectroscopy in following the concentration changes through the diffusion zone. Grübe and Fleischbein1 packed rods of electrolytic iron in a mixture of alumina and chromium. These specimens were heated in an atmos-phere of purified hydrogen for varying lengths of time. After treatment the specimens were examined metallographically and showed the usual structure, consisting of a border of radially oriented columnar grains ending in a sharp boundary line. Reference is made to the fact that etching with certain reagents will attack only the material inside the border of columnar growth and also to the fact that polishing seems to develop a ridge at the position of the boundary between the etched and unetched areas. By chemical analysis of thin layers turned off on a precision lathe, the authors were able to obtain depth-concentration curves. These curves, reproduced in Fig. 1, show that 'in most cases a pronounced change of slope occurs, corresponding to the position of the boundary of the columnar grains. In a later paper Grübe extends his work to other systems which show the same characteristics.2 He concludes that the reason for the break in the curve is that a hindrance of diffusion occurs at the place where the regularly oriented grains of the diffusion zone meet the random grains of the interior portion, on the assumption that the diffusion velocity in one direction in a grain may be greater than in another direction, and that the grains in the diffusion zone orient themselves so as to give the maximum diffusion rate. Kelley3 points out that Grübe has failed to note that the boundary line does not consistently cross all grains and

Jan 1, 1933

By W. N. Lacey, R. H. Olds, B. H. Sage

Samules of liquid and gas were obtained from the primary separator of a well in the Paloma field. The volumetric properties of the samples and of six systematically chosen mixtures of the samples were experimentally determined at 100°, 190°, and 250°F. at pressures up to 5000 lb. per sq. inch. From these data the influence ,of pressure and temperature upon the composition and specific volume of the bubble-point liquid and of the retrograde dew-point gas was established, The formation volumes and gas-oil ratios of the rnixtures investigated were calculated on the basis of the plant-product oil, which is defined as the isobutane and less volatile portion of each mixture. The results are presented in graphical and tabular form. The volumetric behavior of the mixture corresponding to that produced by the well at the time of sampling was determined for 235ºF., the reported reservoir temperature, by graphical interpolation of the experimental data with respect to composition and temperature. The results indicate that the well-production mixture probably existed as a gas at its retrograde dew point under the conditions of temperature and pressure believed to prevail in the producing zone at the time of sampling. The effect upon the phase behavim occasioned by the omission from the well-production mixture of certain components of intermediate molecular weight was investigated. In the first case, all of the isobutane and 11-butane, and substantially all of the iso-pentane, were removed from the mixture of trap samples corresponding to the well production. In the second case, all the propane, isobutane and n-butane, and substantially all of the isopentane, were removed. Both modifications led to considerable increases in the retrograde dew-point Pressure at 235ºF.; an increase of 558 lb. Per sq. in. above that of the unmodified well-production mixture in the first case, and an increase of 1208 lb. Per sq. in. in the second. It was concluded that the material? remaining after the removal of certain components of intermediate molecular weight could not be injected back into the reservoir in the saqe proportion in which they were produced without entailing appreciable loss of liquid material through condensation within the formation. Introduction Under the usual conditions of production practice, petroleum arrives at the surface of the earth in a physical state considerably different from that in which it existed in the underground reservoir. The relative rates of production and the properties of oil and gas measured at surface conditions do not constitute, in general, even a qualitative description of the fluids existing in the reservoir. The estimation of reserves and the attainment of optimum efficiency with regard to rate, quantity, and cost of production require accurate data concerning the physical properties of petroleum throughout large changes in pressure and temperature. Many schemes have been devised for predicting the behavior of propane, as it is encountered in nature? but the experimental work upon which these predictions are based has not, for the most part, been extended to the higher pressures that occur in practice, nor do these methods permit, as yet, the estima-

Jan 1, 1945

By R. E. Hook, R. L. McGaughey, A. M. Adair

The initial yielding characteristics of a vacuum-melted iron have been measured as a function of thertnal history after slow cooling or quenching from a 700°C recrystallizntion anneal. A thermal history favoring the segregation of interstitials to grairz boundaries results in a material having high values of upper and lower yield stress and long, irregutar Luders' plateaus, wheueas specimens treated to minimize grain boundary segregation have significantly lower values of these yielding characteristics. The struc- ture of typical grain boundary areas as revealed by electron transmission microscopy is consistent with these findings. The grain boundaries in iron are considered to be principally responsible for the release of dislocations during macroscopic yielding and it is suggested that strong locking results when a substantial amount of grain boundary segregution is present; it follows that weak locking results from a more random distribution of interstitials to grown in dislocations. RECENT years have seen an increased emphasis placed on a more quantitative study of the influence of grain boundaries on the yield behavior of bcc metals. The earlier picturk of dislocation pileups at grain boundaries building up a sufficient stress concentration to unlock dislocations in neighboring grains1

Jan 1, 1967

By Rex B. McLellan, M. L. Rudee, T. Ishibachi

A modelfor dilute quasi-regular interstitial solid solutions is proposed in which the solute atoms can occupy both the octahedral and tetrahedral interstices in the bee solvent lattice. The distribution function, according to which the solute atoms are apportioned between the two kinds of sites, is calculated. The partial thermodynamic functions of the solution are calculated from the distribution function. It is shown that such a solution model can explain the deviation from linearity of the Arrhenius plot of the temperature variation of the diffusivity of carbon through a iron. The published difiusivity data is analyzed to obtain numerical values for the distribution function. Finally it is shown from the numerical values of the distribution function that the possibility of dual-site occupancy will have a negligible effect on the solution thermodynamics for this system. DeSPITE the large amount of experimental data available on the thermodynamics and diffusion kinetics of dilute solid solutions of carbon in a iron, many of the elementary properties of these solutions are not understood due to real or apparent discrepancies in the experimental data. Basically there is a lack of agreement between the solubility and diffusion data obtained by anelastic damping techniques and by bulk chemical thermodynamic methods. SPecifically the heat of solution of cementite in ferrite estimated from thermodynamic measurement1, 2 is about twice as high as that determined from anelastic damping measurements.3 Furthermore the diffusion coefficient D of carbon in a iron in the range -40" to about 150°C (covering about ten orders of magnitude) determined from anelastic damping techniques is such that an Arrhenius plot of In D vs 1/T is linear. However in the range of about 300o to 850°C where mass flow measurements of D have been made (covering about four orders of magnitude), although the data merges with the low-temperature data, the Arrhenius plot departs from linearity. The object of this paper is to present a more refined model of dilute ferrite solutions in which the solute atoms can occupy two kinds of interstitial sites. The experimental data is analyzed in the light of this model and it is believed that thereby some of the anomalies can be resolved. snoek4 explained the room-temperature internal-friction peak (usually referred to as the Snoek peak) in iron as the stress-induced ordering of interstitial carbon and nitrogen atoms occupying the octahedral (0, 0, 1/2) interstices in the bee lattice. From the consideration of a hard-sphere lattice model the (0, 1/4, 1/4) tetrahedral interstices are larger than the octahedrons but their symmetry would not produce the strain dipole necessary to give rise to the Snoek peak. Thus the presence of the Snoek peak is direct evidence that the octahedrons are occupied. Since the publication of Snoek's explanation, most workers have assumed that all of the carbon and nitrogen in the a solid solution was located in the octahedral sites. This assumption of universal octahedral occupancy has been implicit in the theory of wert5 for interstitial

Jan 1, 1965

By J. H. Collier

The mother lode, or mineralized belt, at Angels, in Calaveras county, California, is 3 miles wide. At least, a region of that width has been, and is being, prospected which has shown considerable mineralization. The lode proper divides into three lodes, or groups of veins, at this point. On all of these branches, mines have been operated with more or less success.

Jan 1, 1900

By K. E. Gray, G. M. Myers

In previous publications,5 results of single-blow bit tooth impacts on saturated rocks at various stress states were reported. This paper extends these earlier works to include study of bit impact tests on salt water-saturated Berea and Bandera sandstone samples under conditions of elevated confining and pore pressure. During the tests dynamic filtration and deposition of a mud cake were occurring due to the presence of drilling mud in the borehole and a borebole-to-formation pressure differential. Results indicate that saturation of these sandstones with salt water tends to make them weaker than when saturated with nonreactive fluids. Plastic failure often occurs even when extremely high fluid-loss muds are present in the borehole. The failure mode tends toward plasticity with decreasing fluid loss. Brittle failure of sandstones in mud-filled holes is apparently relatively rare. Depending on the stress level, and the associated failure mode, withdrawal of the bit tooth induces a tensile force that seems rather important relative to the quantity of rock removed by vertical tooth impact. INTRODUCTION A vast majority of the oil wells drilled today involve the use of colloidal muds having a measurable mud filtrate loss. It is known from field experience that reduction of the water loss of a mud generally results in a reduction of the penetration rate. This paper describes an investigation of crater formation at simulated bottom-hole pressure conditions for drilling fluids having different water losses. The literature on single bit tooth impact (cratering) at atmospheric conditions is extensive, but only a limited amount of work has been performed at the stress conditions similar to that found in oil wells. Spherical penetrator cratering tests on rocks at hydrostatic pressure were performed by Payne and Chippenda1e.1 Chisel impact studies on limestone with independently varying overburden and borehole pressure and atmospheric pore pressure were reported by Garner, et al.2 Gnirk and Cheatham3 performed "static" penetrator tests on dry rocks at equal overburden and borehole pressures. Podio and Gray4 studied the effect of pore fluid viscosity at atmospheric pore and borehole pressures and varying overburden pressures. Their results illustrated the importance of fluid saturation of the rock. Yang and Gray5 reported single tooth impact tests on saturated rocks at elevated borehole, pore and confining pressures, but with equal pore and borehole pressures. For the work reported in Refs. 4 and 5, filtration across the hole bottom purposely was avoided. Maurer6 has investigated the effect of independently varying pore and borehole pressures at elevated overburden pressures by using a zero water-loss mud in the borehole. His tests were carried out under conditions that allowed independent control of overburden, pore and borehole pressures, but without control of filtration at the hole bottom. EXPERIMENTAL APPARATUS AND PROCEDURE APPARATUS The single blow chisel impact apparatus used by Garner,2 as modified for this study, is shown in Fig. 1. A cross section of the pressure vessel is shown in Fig. 2. Several pieces of auxiliary equipment were added to the original apparatus in order that the borehole and pore pressure could be applied in a manner analogous to the actual bottom-hole situation. The pore-pressure system included a filtrate volume-measuring transducer and had sufficient surge capacity to allow filtrate to be injected into the sample without significant changes in pore pressure at points remote to the borehole. The borehole-pressure system contained a cross connection to the pore-pressure system so that both systems could be pressured simultaneously. The borehole-pore pressure differential was applied rapidly by the use of a quick and full-opening valve. The operation of this valve triggered two industrial

Jan 1, 1969

By David Cole

The appearance of the Wilfley table in 1897 marked an epoch in the art of concentration of ores. The table has merited and received an almost unprecedented measure of public approval, lasting through its whole patent life. It has been very little improved in itself, or improved upon by competitors. The new machines bidding for popular favor have been of the Wilfley family, but without ability to do markedly better work than the parent machine, or to do more work except by the use of superimposed decks, the latter having obvious disadvantages. During the past three years there has been developed at Morenci a new type or arrangement of riffles applicable to the Wilfley type of concentrating table which corrects many of the objectionable features or limitations of the older system and obviates most of the difficulties encountered with it, particularly when handling ores having a low ratio of concentration. The new type is known as the Butchart1 riffle system, and its general arrangement is shown in Figs. 1 and 2. The old system accomplished stratification satisfactorily but has

Jan 1, 1915

By J. J. Gilman

IT is well established that dislocations exist in crystals and account for crystal plasticity.' However, the origins of the dislocations are not clear. Among the means by which dislocations might originate are: a) through crystal growth accidents, b) by the collapse of condensed sheets of vacancies, or c) by stress-induced nucleation. Theoretical calculations' have indicated that the last means should require very high stresses in order to operate. The purpose of this paper is to show that the stresses around the tips of cracks are large enough to nucleate large numbers of dislocation loops. Specifically, it will be shown that (100) cleavage cracks in LiF crystals nucleate dislocations in regions of the crystals where dislocations did not exist previously. It is believed that the use of LiF for this investigation does not restrict the significance of the 1 results. In fact, it is believed that this complements and extends previous papers by the same author which dealt with metal crystals.10,14 The dislocations were detected by means of the etching techniques that were described in a previous paper by Gilman and Johnston.3 In that paper it

Jan 1, 1958

By John Jermain Porter

PAGE. I. INtroduction............ 191 I1. Derivation of Formula foR Fuel-RequiRements.... 192 1. Heat Available in the Hearth........193 a. Method of Calculation..193 b. Data for the Determination of Critical Temperature.. 195 2. Heat Necessary in the Hearth ...... 197 a. To Care for Slag..197 b. To Care for Pig-Iron...198 c. To Reduce Silicon........198 d. For Other Items.........199 3. The Effects of Rate of Driving ..... 199 4. Loss of Carbon Between Throat and Hearth.....201 a. Solubility of Coke..201 b. Carbon-Loss Due to Flux....201 c. Effects of Reducibility of Ore..202 5. The Formula as Used........203 III. The LImitations of the Formula........ 204 1. Through Effects of Irregular Furnace-Work.....204 2. Through Ratio Between Heat-Requirements in Shaft and Hearth. 20.5 IV. The Formula Applied to Actual Furnace-Records,.. 209 1. Description of Furnace-Stock........ 209 2. Furnace Dam..........210 3. Application of Formula..211 4. Average Furnace-Practice..213 V. Sources of Error........... 214 VI. SuggesTions for Practical Methods of Fuel-Economy... 215 VII. Efficiency as a Factor in Furnace-Management.... 219 1. The Efficiency Principle........ 219 2. The Application to the Blast-Furnace..220 I. Introduction. The heat-balance of the blast-furnace has been a favorite subject for discussion for many years. and its study has contributed much to our knowledge. and still possesses a certain academic interest. As a means of accounting for differences in fuel-consumption, however. it has failed utterly. and it is evident that we must look elsewhere for the means of accomplishing this end.

Jan 1, 1912

By E. Robert Ruhlman

The term potash refers to potassium oxide (K2O), a compound not found in nature or produced by man but used as a basis for comparison of all potassium compounds and now is applied generally to various compounds of potassium used by agriculture and industry. Potassium, the last of the three major plant foods to be used in appreciable quantities by agriculture, was originally produced only from organic materials for chemical uses. The first recorded identification of a mineral source of potassium was in 1797; but, until the discovery in 1839 of the large deposits of soluble potassium salts in Germany and their development in 1860-61, nearly all potassium compounds continued to come from organic sources. With the importance of potash to plant life discovered in 1840 by von Liebig and the production of potash in Germany after 1861, agriculture soon became the major consumer of potash. In 1958 agriculture accounted for about 95 pct of the total potash consumption; the chemical industry used the remaining 5 pct. Mineralogy and Geology Potassium, an important constituent of the earth's crust, occurs in many forms in numerous rocks and minerals, including water solutions, but is not found in its native state. Twenty-five of the more important potash minerals are listed in Table 1. The properties of the five potash minerals most common in Permian salt formations follow: Sylvite is isometric; has a hardness of 2, a specific gravity of 1.98, vitreous luster, and cubic cleavage; and ranges in color from clear to brick red. In taste it is similar to halite but has a sharper taste and a cooling effect on the tongue. It is very plastic under pressure. Langbeinite is isometric; has a hardness of 4, a specific gravity of 2.82, vitreous luster, conchoidal fracture, and no cleavage; and ranges in color from clear to gray. It is taste- [ ] less, somewhat granular, and slowly soluble in water. Polyhalite is triclinic; has a hardness of 3, a specific gravity of 2.77, and dull luster; and

Jan 1, 1960

By Arnulf Muan, Klaus Schwerdtfeger

Activity-composition relations in Pt-Cr and Pd-Cr alloys of low chromium concentrations UCr < 0.3) have been determined in order to ascertain quantitatively the extent of reactions to be expected between Cr2O3-containing oxide phases and platinum or palladium crucibles used as containers in studies of oxide equilibria at low oxygen pressures. This work is a continuation of similar work previously

Jan 1, 1965

By Margaret Dienes, Karl L. Fetters

IT is recognized that ingot structure is important in determining the quality of finished steel. Such elements of ingot structure as the size, shape and distribution of primary crystals; the size, shape and distribution of shrinkage cavities; the degree and kind of segregation (both macro and micro); the distribution of nonmetallic impurities and gas cavities are each the result of solidification phenomena. These structural features vary with variations in ingot practice: Their control requires a knowledge of their correlation with the variables of ingot practice. The structures of full-sized commercial steel ingots have been studied extensively by the Steel Ingots Committee of the Iron and Steel Institute.1 This work has contributed much to our knowledge of ingot structure and the factors that control it. These investigations of necessity have been limited in scope because of their costliness and the great amount of time required. Studies of the structure of small steel ingots have not been very satisfactory because of the rapid rate of freezing of the ingots. Their structures are thus difficult to resolve and to interpret. Medium sizes of steel ingots in the ranges of 150 to 500 lb. do offer opportunity for study, but their cost also becomes greater and their use less expeditious. Experimental models for the study of steel-ingot structure have been made of nonferrous metals. Gathmann2 used lead-tin alloys and reported that they were satisfactory for determination of the location of the major shrinkage cavities and the "planes of weakness" resulting from the pattern of crystallization. Certain features of mold design have been illustrated by these results. Bezdenezhnihk3 has used copper and aluminum ingots similarly and has shown the effect of mold-wall thickness on the depth of columnar grains. These studies of nonferrous models have been useful, but their results have been limited because the analogy with steel ingots obviously is not a close one. Model wax ingots have also been useful in pointing out important features of mold design. Gathmann4 watched the solidification of wax ingots, through a glass-walled mold, and has reported the effects of mold type on the location of the shrinkage cavities. Segregation was simulated by using a mixture of paraffin and stearine and adding a red dye that on freezing segregated preferentially to the stearine. Brearley5 also used wax models to determine .the effects of some of the principal features of mold design. Carlsson and Hultgren6 used stearic acid to show that the columnar crystals of ingots tend to slope upward progressively from the mold wall toward the center of the ingot. As with the nonferrous ingots, the wax ingots have

Jan 1, 1943

By W. B. Mather

GEOLOGICAL studies have revealed the occurrence of hundreds of pegmatite dikes in north- east Brazil, Fig. 1, in the three states of Rio Grande do Norte, Paraiba, and Ceara. Heretofore data have not been available on the possible production of lithium minerals from these areas, and in March, April, and May 1953 the author undertook a reconnaissance survey covering a cross-section of the pegmatites. Sixty-one pegmatites were examined. The pegmatites of Rio Grande do Norte and Paraiba are located in an arid region (Seratao), and except in the most southerly portion there is a mini- mum of vegetation and overburden. The region is easily prospected and relatively accessible by jeep or truck. The pegmatites examined in Ceara are in an area of lush vegetation along the flanks of the Jaqueribe River valley. It is therefore more difficult to prospect, and the dirt roads, as a means of access, leave much to be desired. For all practical purposes rail transportation, except in Ceara, is not available. The rocks of the area1-4 are composed of Pre-Cambrian schist, gneiss, quartzite, and marbles. They have been intruded by granites, monzonites, and diorites and cut by quartz veins and pegmatites.

Jan 9, 1954

By T. B. Gyles

Zinc is made by the National Smelting Co. and its associates by both the horizontal retort process and the vertical retort process developed by the New Jersey Zinc Co. This paper deals only with the horizontal retort practice at Avonmouth. That the horizontal retort process does survive in all countries in some form or other is due to at least partial success in overcoming some of the inherent difficulties of the process. The horizontal retort furnaces ran into considerable difficulties when the product of the selective flotation of mixed lead and zinc ores became the normal material for treatment. It is necessary, therefore, to make some reference in connection with the process to the preliminary treatment of the ore prior to distillation.. Therefore we include some small reference to this aspect in our description. Furnace Design and Structure Of the types of furnaces in operation at the company&apos;s various works, those at Avonmouth are perhaps more typical of the trend to utilize large units, with a subsequent saving in costs, such as heating and supervision.

Jan 1, 1937

By C. J. Bise, E. K. Albert

Mathematical modeling and computer simulation are the two primary techniques used for production analysis of underground coal mine layouts. Oftentimes, however, the selection between these two techniques is not based on an awareness of the level of effort needed for input formulation versus the suitability of the desired output. This paper will review mathematical modeling and two of the more prominent simulators (Virginia Tech&apos;s FACESIM and Penn State&apos;s UGMHS) used in underground coal mine production analysis. A hypothetical section will be analyzed by these programs and, based on the results of the aforementioned study, their advantages and disadvantages will be discussed.

Jan 1, 1985

By D. W. Brunton

The maps of our large mines are usually prepared with the greatest care; and it is somewhat singular that, in compari~on with the great amount of time and money spent in surveying and platting, 80 little actual use is made of them. Almost the only purpose for which a completed survey-map is afterwards consulted, is the determination of the relative position of the different workings to each other, and to the boundary-lines of the property. After the completion of such a map, it should be made the beginning of another, and in most cases a far more important undertaking, namely, its utilization as a starting-point for a complete inventory of the company&apos;s underground possessions. The ordinary mine-survey map, being nothing but a record of what has been done, is, in one sense, only ancient history. To increase its value, such additions should be made as will render it a complete statement of the amount and value of ore in sight at any particular time, and a guide for future development. Comparatively little extra labor is involved in this undertaking, since the larger and most expensive part of the work has already been completed when the mine has been surveyed and mapped. The necessary additions consist in working out and platting on the maps, the geology of the mine as exposed in the workings, in such a manner that the geological survey may be of daily use in the development and operation of the mine. The first step towards the production of a geological map consists in tracing individual level-sheets from the general or composite map. The area to be included, outside of the property in question, will depend very much on local conditions; but, for geological, legal and commercial reasons, it should be extended as far as reasonably practicable. The scale to be

Jan 1, 1906

By W. L. Mamme, G. Y. Chin

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain was analyzed by Taylor and by Bishop and Hill in terms of a minimum (internal) and a maximum (external) work criterion, respectively. These two criteria have now been generalized to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (noncrystallographic) pencil glide. The generalized treatment also takes into account the possibility of a Bauschinger effect and of unequal hardening among the shear systems, which were considered in the Bishop and Hill work. Optimization techniques of linear and nonlinear programming are shown to be applicable for the numerical calculation of the minimum or maximum work. In the case of crystallographic shear, the constraint functions are linear and hence the optimal work is obtained as the saddle value of the lagrangian function Wi(y) e minimum and W,(u) + (a) for the maximum, where Wi is the (internal) work, We is the (external) work, Y is the crystallographic shear strain, u is the applied stress, and and are constraints. It is shown that the Lagrangians are functionally the same and the saddle value of one problem is identical to the saddle value of the other, proving that the two analyses are completely equivalent. In the case of pencil glide, although the constraint functions are nonlinear and neither convex nor concave, the equivalence of the optimal values to the saddle value of the Lagrangian (which is again identical for both problems) is still valid. WHEN a crystal deforms plastically by crystallographic shear, five independent shears are generally required to accommodate five independent strain components specifying the deformation. Assuming slip as the only shear mechanism, Taylor1 in 1938 analyzed the deformation in terms of a minimum work criterion. He hypothesized that of all combinations of five slip systems which are capable of accommodating the deformation, the active combination is that one for which the internal work C is a minimum, where 1 TI is the critical resolved shear stress for slip on the 1-th slip system and is the corresponding simple shear. By further assuming equal 72 for all equivalent slip systems and no Bauschinger effect, Taylor re- duced the minimum work problem to one of minimum and applied the analysis to the case of axisym- Metric flow by {111}(110) slip in fcc crystals. However, he did not consider the question of whether the resolved shear stress has in fact attained the critical value for slip on the newly found active systems without exceeding it on the inactive systems. In 1951 Bishop and ill&apos; put forth the maximum work analysis in which slip is again assumed as the only deformation mechanism. In this analysis, the work o1 done in a given strain ij by a stress ujj not violating the yield condition is maximized. In addition, the analysis takes into account the possibility that the critical resolved shear stress for slip may not be equal among the slip systems and that the slip behavior may exhibit the Bauschinger effect. As with Taylor, a single set of slip systems—{111)(110) — was analyzed numerically. It thus appears that the Bishop and Hill treatment is on a more sound physical basis than the Taylor treatment. However, Bishop and Hill showed that where there is equal hardening among all slip systems and when there is no Bauschinger effect, Eq. [11 ] of Ref. 2, as assumed by Taylor, the results of their maximum work analysis are the same as those of Taylor&apos;s minimum work analysis. Hence at least under those conditions there is an implication that the Taylor analysis does lead to a critical resolved shear stress for slip on the predicted active systems without violating the yield condition on the inactive systems. Recently, the Taylor analysis was applied for numerical solutions of the axisymmetric flow problem, for slip on {110}(111), {112}(111). {123)(111) systems as well as a mixture of all three sets of svstems."1 Computational techniques based on the optimization theories of linear and nonlinear programming4 were employed in these solutions. The same techniques were employed in the solutions of an axisymmetric flow problem of deformation by slip on (111) (110) systems and twinning on (111)(112) systems5 which had been considered theoretically from a modified Taylor approach. The utilization of these techniques has led to the realization that the solutions of Taylor&apos;s minimum work problem imply the solutions of Bishop and Hill&apos;s maximum work problem. The two problems turn out to be dual problems in the well known sense of mathematical programming. It is thus the purpose of this paper to first generalize the minimum and maximum work analyses to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (non-crystallographic) pencil glide, as well as the possibility of a Bauschinger effect and of unequal hardening

Jan 1, 1970

By Charles C. Russell

Pressures developed by the coal during the coking process have been responsible for serious trouble to many companies that operate or build by-product coke ovens. The insidious nature of this trouble is indicated by the fact that oven operators, unless they have ascertained the characteristics of the coals they use, cannot determine the existence of dangerous pressures until after the damage has been done. A rather popular misconception is that ease of pushing of the charge at the completion of the coking period indicates that no dangerous pressure has been developed, but this is far from the truth; pressures developed during the coking period are often completely dissipated by the shrinkage of the charge in the completion of coking, and so any criterion based on the ease of pushing is futile. However, methods of testing coals are available that will definitely distinguish the dangerous coals from those that are safe, and such methods have been brought to a high degree of certainty. The operator should take no risk that involves either a lack of knowledge of the behavior of coals during coking or the failure to believe that certain of the coals or coal mixtures can cause damage to the oven structure. This merely tends to minimize the problem and leads to claims that coking coals of all kinds may be carbonized with no danger of damage to the oven structure provided some particular kind of byproduct oven is used. This lack of appreciation of the true situation is in itself one of the main factors leading to damage of coke-oven structures. Coals that develop more than a certain safe pressure cannot be used in by-product coke ovens without causing damage to the side flue walls. The following paper presents a highly certain method for the measurement of the pressures developed during the carbonization of coal—a method that is the culmination of many years of work on the problem in which a number of methods for the purpose were investigated and used. While actual pressures found may appear to be small when expressed in pounds per square inch, the number of square inches in each oven wall is so large that the total pressure on the oven wall becomes an enormous load.

Jan 1, 1940