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By Mohan K. Wali

This report, the first in a series of 13 reports, provides a summary of 11 major topics on which individual reports have been prepared. These major topics are: (a) Nature of coal mine spoils, topsoils, and unmined soils; (b) influence of macro- and microclimate on (c) plant production on spoils and topsoils; (d) prediction of aboveground biomass from plant cover; (c) mineral composition of plants; (f) controlled environment studies on plant growth response; (g) microbial communities (h) water chemistry and organism diversity of catchbasins; (i) vegetation and soil development on abandoned, and (j) topsoiled sites; and (k) viability and diversity of seed bank. Based on these investigations, general conclusions and some recommendations are presented.

Jan 1, 1982

Jan 1, 1897

By J. C. Norman

Jan 1, 1985

By Robin E. Goad

?Located 160 Km northwest of Yellowknife, NWT, Canada Current winter road access ?New all-weather road planned ?Power within 22 km ?Hwy to Edmonton 80 km south Close to existing infrastructure

May 1, 2006

By Pan Gao, Songyang Yin, Zhibiao Guo, Jinglin You, Yuhui Li

Under the geological conditions of the interaction of upper goafs and lower working face in deep mining, coal seam mining causes a large stress concentration, which may lead to large deformation of the surrounding rock and rock burst risk. The research reported herein is aimed to utilize the FLAC3D software to establish a three-dimensional numerical model and analyze the law of the surrounding rock stress evolution during coal mining under complex geological conditions. The simulation results reveal that the peak abutment stress reaches its maximum value at 20–30 m in front of the working face, about 1.8–4.3 times the original rock stress, and the peak stress is larger in the stable mining stage. Along the dip of the working face, the peak stress occurs about 8–10 m away from the roadway side. The upper barrier coal pillar and the interval coal pillar in order exhibit stress concentration areas of 142 m and 88 m. According to the law of the deflection stress distribution of the surrounding rock in the presence of various widths of the coal pillar, a 10-m coal pillar between the roadway and the adjacent goaf could enhance the stability of the roadway. For the stress concentration area, drilling holes with a depth of 20–25 m are utilized to reduce the pressure, and anti-impact supports are installed in the middle of the roadway. Due to the varying stresses of the rocks around the roadway, partition prevention and control countermeasures are capable of efficiently preventing the instability of the surrounding rock.

Mar 22, 2023

By Manoj Khandelwal, Minghui Liu, Jian Zhou, Kun Du

The waste rock and tailings backfill into the mined-out areas are the most effective method for solving the environmental pollution and surface disasters for nonferrous metals mines. In practice, the success and availability of backfill operations are dependent on the slurry fluidity and the strength properties of cement backfill. The transport of the slurry through the pipeline to the designated backfilling area relies on its eximious flow properties, while the appropriate strength of the filling body ensures the safe operation of the stope. In this paper, the effects of cement and aggregate types on the slurry fluidity and strength characteristics of cemented backfill are studied in detail, which are often ignored in other pieces of literature. Diffusivity is used as an indicator to evaluate the slurry fluidity. Various slurries whose concentrations ranging from 70%, 73%, 75%, 78%, and 80% are made with different aggregate ratios and cement-sand ratios are tested. It has been shown that slurry fluidity is inversely related to its concentration, but 78% is the “stopping point” for the deterioration of fluidity. The addition of rod-milled sand improves or worsens the cemented backfill (CB) strength depending on the amount of rob-milled sand. The uniaxial compression experiment results on 216 CB specimens produced by different combinations of influencing variables showed that CB specimens made from cement with superior mechanical properties have a higher uniaxial compressive strength (σucs). It has been also found that the effect of aggregate ratio on the CB strength is not singular, but works in conjunction with the curing time and the cement-sand ratio. The longer the curing time and the higher the cement content, the higher the CB’s σucs. To avoid the time-consuming and costly problem of obtaining the strength of the CB from indoor experiments, an SVR model capable of predicting the uniaxial compression strength of CB specimens is proposed, which is optimized by genetic algorithm (GA) and particle swarm optimization (PSO) algorithm. The results of the three performance indexes (MAPE, MSE, and R2) show the superior performance of the GA-SVR and PSO-SVR models and the agreement of the predicted results with the experimental results, which indicate that these two models can accurately predict the σucs of CB.

Feb 3, 2022

By G. B. Shea

In the search for possible future sources of petroleum products, the recovery and utilization of bitumens from the large outcropping deposits of bituminous sandstones in the United States have been under study by the Bureau of Mines for the past several years. The results of laboratory research in the adaptation of the hot-water separation process to recovery of bitumen from bituminous sandstones were reported in an earlier publication, on the Edna deposits near San Luis Obispo, Calif. This publication included analytical data on the cracked products and asphalts obtained from the extracted bitumen and on the cracking and distillation of the bitumen. Comparable hot-water separation tests have been run in the San Francisco, Calif., laboratory of the Bureau of Mines on quarry samples from the large deposits of bituminous sandstones near Vernal and Sunnyside, Utah. The bitumens were isolated from the extracts of the separation plant and analyzed at the Petroleum and Oil-Shale Experiment Station of the Bureau of Mines, Laramie, Wyo. Part I of this report summarizes the general characteristics of the Vernal and Sunnyside deposits and discusses the hot-water separation process as applied to those bituminous sandstones and the results obtained. The separation tests showed that these bituminous sandstones also respond to treatment by the hotwater method of separation. The bitumen in the Vernal sandstone was extracted more readily by the action of hot water than was the Edna bitumen, which greatly simplified plant operation. The Vernal sandstone contains no water-soluble iron compounds, such as were found in the Edna sandstone, and, therefore, required no preliminary water washing. Recovery of bitumen from the Vernal sandstone was about 96 percent.

Jan 1, 1952

By A. B. Needham

A number of the pegmatites in the southern Black Hills of western South Dakota contain sheet mica; and as the demand increased during World War II the area became an important producer of strategic qualities of mica. During this period of maximum activity, the U. S.. Geological Survey made detailed studies of the geological structural control, the mineralogical associations, and the production Of many pegmatites in the Black Hills. On the basis of results of this study, and at the suggestion of the Geological Survey, several of the pegmatites were examined by the Bureau of Mines, and a few were selected for further investigation. Accordingly, the White Bear, Silver Dollar, Buster Dike, and Hot Shot mines were diamond-core-drilled in 1947. The Hot Shot mine was investigated further by deepening the shaft and crosscutting the pegmatite in 1948. The mica-bearing deposits occur in lenticular intrusions of pegmatite in schists of various mineral composition. Eleven diamond-drill holes, totaling 2,111.4 feet in length, were completed on the four deposits. The shaft on the Hot Shot deposit was deepened 44 feet to the 112-foot level, and crosscuts were driven from the bottom of the shaft to the hanging Wall and foot wall of the pegmatite. This publication briefly describes the location, ownership, and history of the deposits and gives details of the work done by the Bureau of Mines and the Geological Survey.

Jan 1, 1950

By Kari Niiranen

LKAB (Luossavaara-Kiirunavaara AB) is operating iron ore mines, concentration plants and pelletizing plants in Northern Sweden. The largest of the apatite magnetite deposits and the mines are Kiirunavaara with annual production rate of approximately 27 Mt crude ore underground. LKAB produces two varieties of pellets: blast furnace pellets and direct reduction pellets (LKAB DR Oxide Pellets). Meanwhile the concentration process in a sequence of the low intensity magnetic separation (LIMS) and flotation at the concentration plant. In spring 2007 there were noticed great fluctuations of SiO2 grade in the crude ore. The high SiO2 grade is particularly problematic in the case of direct reduction pellets. In consequence, a project was started (called Silica in the Mine) to define exactly the problem related with silica and to find out, if possible, the reason for the great fluctuation of SiO2 grade in the crude ore going to the processing plant. A further target of this project was to develop a simplified method at the laboratory scale, to predict SiO2 grade in the magnetite concentrate in the future, but also predict the physical properties of the ore with respect to mineral processing. The essential stage of systematic characterization of the ore body for mineral processing properties is the estimation and simulation of different parameters from the laboratory scale to the large scale at the concentration plants using empirical data collected at the mineral processing by LKAB in Kiruna. Further a target was also to find useful physical parameters for mineral processing and implant those parameters into the existing geological 3D-model of the deposit. This information will be used for making prognosis of the future mining and the quality of the crude ore. It will also give better control and improve the production planning in the mine and the performance at the concentration plant in Kiruna concerning the decrease of the SiO2 grade of the magnetite concentrate.

Sep 1, 2012

By Ronald B. Stone

This paper describes a proposed solution to the problem of mining a 315 foot diameter unsupported sphere at a depth of 2700 feet in a salt dome by conventional mining methods. The proposed solution utilizes many of the varied technologies available to the mining engineer for solving mining and underground construction problems. The following are reviewed in the paper: A. The location of the sphere within the dome as required by construction criteria. B. The relation of the location of the access shafts to the sphere. C. The rock mechanics theory in relation to the salt dome and large size of the excavation. D. The proposed "honeycomb" method of mining which will be a partial answer to rock mechanics stability requirements. E. The equipment which it is recommended be utilized to accomplish the construction. F. The rock mechanics measuring instruments proposed. G. The methods of disposal of the mined salt. Conclusions and areas of further study are outlined in the final statement.

Jan 1, 1968

By B. Mishra, Q. Shi

Numerical simulations have been used to investigate roof fall in the past decades. Comparing to the continuum based methods, the discrete element method has been well recognized for its excellent performance in simulating large strain problems and fracturing processes in the rock mass. However, the discrete element method has its limitations. When simulating a large-scale problem, a large number of particles are required, which consumes significant computational resources. In the present study, a 3D numerical model coupled with the finite-difference method (FDM) and the discreteelement method (DEM) was created to simulate the laminated roof failure in an eastern coal mine in the US. In the FDM-DEM coupled model, the laminated roof of the entry is represented by an assembly of bonded particles using PFC3D. The laminated roof is simulated by adding parallel discontinuities. The discontinuities are given certain stiffness and strength in the model. The ribs, floor, and far-field surrounding rock are represented by continuum zones using FLAC3D. The strength of the discontinuities is varied sequentially and the fracturing of the laminated roof was analyzed with respect to entry advance. The results showed that the laminated roof fractures along the discontinuities while an intact roof fractures in a dome shape. Increasing the strength of discontinuity could enlarge the tensile zone inside the laminated roof and hence change the crack distribution. In addition, the crack quantity in the laminated roof behind the advancing face decreases with the increment of discontinuity strength while this trend is not occurring ahead of the advancing face. The simulation demonstrated that coupled method using PFC3D/FLAC3D can reproduce the laminated roof failure in underground coal mines.

Mar 2, 2022

By AIME AIME

N EARLY 1300 members and guests crowded the halls of the Engineering Societies Building during the winter meeting of the Institute just closed, and more than 600 attended the banquet. In variety of program, quality of papers, interest in discussion, and brilliance of social features, the meeting maintained the high reputation of the past. Nothing elaborate in the way of excursions was attempted, experience having proved that February weather in New York is much too uncertain to warrant extensive field trips. A sight-seeing journey up the Hudson to the Bear Mountain bridge was, however, made despite the snows of the week before and the week after. The annual business meeting, while attended by a minority of the members in the building, was marked by the display of keen interest in the work and called out several interesting discussions. The excellent reports of the committees that had organized their work and directed it along definite lines, emphasized the need of funds with which to support assistants or Fellows who shall correlate and put to the highest use the facilities of the Institute in research along technical lines. This thought was developed at the banquet by the retiring president, J. V. W. Reynders, and it is expected that the Directors will take early steps to collect a fund for this purpose. The number of the individual sessions was too great and the papers and discussions too numerous to permit mention here of all the features of inter- est. A general review only follows. The papers and detailed discussions will be printed and sent to members as promptly as possible.

Jan 1, 1926

By John L. White

The vibro driver/extractor is a machine that grips to a pile and vibrates it up and down. When the vibrating pile is lowered into the ground, all soil around the pile begins to vibrate. A vibrating pile breaks the friction between the pile and the soil, thus allowing it to penetrate the ground. A vibro is usually operated by hoisting it into the air with a crane and then placing it onto the pile. The vibro has hydraulic gripping jaws that are controlled from the ground. Once the operator has successfully lowered the vibro onto the pile, the jaws are closed and locked onto the pile and operations can begin. Please see the drawing below: [ ]

Jan 1, 1990

By S. Luszcz, R. W. Vook, Fred Witt

In situ X-ray investigations were made on polycrys-talline silver films deposited by vacuum evaporation on (111) CaF2 and (100) NaCl single-crystal substrates at 80°K. The films were evaporated and annealed in an X-ray diffractometer attachment having a residual gas pressure of 2 x lo-' Torr. All measurements were made without exposing the films to the atmosphere. Measurements were made on the films in the as-deposited state and after various annealing treatments. The intrinsic stacking and twin fault densities, the magnitudes of the uniform and nonuniform strains, and the crystallite sizes were determined. In addition the textures in the films were measured qualitatively. The results obtained for the as-deposited films on single-crystal substrates are in substantial agreement with previously reported results for silver films deposited on glass. Intrinsic stacking and twin faults, as well as uniform and nonuniform strains, were present in these films. During the various annealing treatments (up to 350°C) the faults and nonuniform strains annealed out. Considerable grain growth and texture changes occurred also. The effects were much greater for the NaCl substrate than for the CaFz substrate. The relative magnitudes of the grain growth in the variously oriented grains could be explained qualitatively in terms of the thermal strains and strain energies introduced into the differently oriented grains during the initial, irreversible anneal. These strains were due to the different thermal expansion coefficients of the film and substrate. X-RAY diffraction measurements on evaporated films deposited on substrates at low temperature have the advantage that many of the imperfections introduced into the film during deposition are "frozen in". Thus, the influence of a very important experimental variable, substrate temperature, on the imperfection structure of evaporated metal films may be studied. Moreover, the effects of annealing such films makes possible the study of thermally activated recovery processes in these films. The present study was designed to determine the influence of single-crystal substrates on the resultant film structure relative to the previous results obtained using glass substrates.' To this end great care was taken to keep the experimental variables the same in the two cases. Different experimental conditions would, of course, result in films having different physical properties. Again the initial substrate temperature was in the neighborhood of 80°K and the films were subsequently annealed to 350°C. The pure metal silver was chosen for evaporation, primarily because of its relatively low stacking fault energy and consequent high fault density in the as-deposited state. The silver films were formed by evaporation onto air-cleaved {ill} CaF, and (100) NaCl surfaces cooled to 80°K in an X-ray diffractometer attachment2 having a base residual gas pressure of 2 X l0-' Torr. The films were not exposed to the atmosphere until all of the X-ray data had been recorded. In this way one of the most important experimental variables, environment, could be well-controlled and reproduced. X-ray measurements were made at the temperature of deposition and included determinations of the diffraction line peak positions, line shapes, and integrated intensities. The peak position measurements were used to determine the intrinsic stacking fault densities and the average uniform strain in the film. The shapes of the diffraction lines provided information on the twin fault density, true crystallite size, and average nonuniform strain. The preferred orientation in the film was determined qualitatively from the integrated intensities. I) EXPERIMENTAL PROCEDURE The evaporator attachmentZ was charged with 99.999 pct Ag pellets positioned in a tantalum filament which had been outgassed previously at l0-8 Torr. The CaFz and NaCl single crystals were cleaved in air and then placed in position in the chamber so that their cleavage surfaces were on the diffractometer axis. The chamber was prepumped using a sorption pump, sealed off, and then baked at 150°C for 24 hr. The ion pump operated during the bakeout cycle. The substrate was then heated to 500° C by means of an auxiliary heater and kept hot until the rest of the chamber was cooled slowly to room temperature. This bakeout procedure consistently resulted in an ultimate pressure in the low lo-' Torr range. The substrate was then cooled down on 80°K. Its temperature was monitored by a thermocouple wedged into the rear of the copper substrate holder. The diffracted intensity and peak position of the 111, 222, and 333 CaF, lines were measured prior to evaporation. Nickel-filtered, pulse-height-discriminated copper radiation was used. Similar measurements were made for the 200 and 400 lines from NaC1. These measurements were used as a lattice parameter check and to determine the thickness of the evaporated silver films from the attenuation of the substrate lines. The evaporation rates were approximately 3A per sec for both films while the maximum pressures during evaporation were 3 x lo- ' and 7 x 10"8 Torr for the CaF, and NaCl cases, respectively. The film thickness was measured by the attenuation of the CaF, and NaCl substrate lines and by at optical interference method. Values of 1700 and 1500A, respectively, were obtained for the silver

Jan 1, 1969

By F. V. Lenel

Two years ago in Chicago a seminar was held on the theory of sintering of pure metal powders. As an introduction to this seminar D,.. Rhines1 gave an excellent survey of the literature on this subject, His method of presentatioll was to summarize the experimental observations on sintering and from them to develop a composite theory of sintering in which he combined all the important contributions to the theory into one organic whole. In contrast to the mechanism of sintering of pure metal powders, which, of course, al\vays takes place in the solid phase, sintering j,, the presence of a liquid phase, cannot be treated as one unified mechanism, such as the sintering mechanism of pure metals. The reason is that there are really several mechanisms depending upon the type of alloy system which is sintered and the field of its con. stitutional diagram ill which the sintering takes place, Two mechanisms have heen investigated and will be reviewed in this paper. Ill the first lnechanism the liquid is presellt during the entire time while the compacts are at the sintering temperature, In other words they are sintered between the liquidus and the solidus of the alloy system and are ~e~erogelleous during the entire sintering cycle. The second mechallism applies to alloys in which the liquid phase is formed during the sintering process, but disappears before the sintering process is completed through diffusion and formation of a solid solution. These alloys are therefore homogeneous at the end of the sintering cycle. This second mechanism is more complicated because of the two stages of sintering, the liquid and the solid, as they may be called. It is therefore not surprising that the few detailed investigations of sintering in the presence of a liquid phase have been concerned with heterogeneous sintered alloys, namely the tungsten-nickel-sinter ing which is the so-called "heavy alloy," and the cemented carbides. The mechanism of sintering of these systems is characterized by the fact that theoretical or near theoretical density is attained during sintering, while simultaneously a distinct grain growth takes place through solution of the smallest grains of the solid phase in the liquid phase and reprecipitation on the larger grains. In the first part of the survey this sintering mechanism which is called for short the heavy alloy mechanism is treated in detail. In the second part Of the survey experimental observations for the sintering of homogeneous sintered alloys where the liquid phase disappears before the completion of sintering are discussed. Much less systematic work has been done on these alloys to which the conlmercially important Porous bronzes and the iron-nickel-aluminum permanent magnet alloys belong. Emphasis will be laid throughout this survey upon the microstructural and density changes during sintcring because the Sintering mechanism can usually be described directly by these changes. Other

Jan 1, 1949

By H. B. Aaron

DIFFRACTION micrography provides a useful tool for studying complex strain fields. Newkirk1 observed an X-ray diffraction effect due to strain interactions at the intersection of slip lines in LiF and attributed this effect to a reduction of primary extinction due to strain-gradients. It is the object of the current study to correlate the observations and rationalize the appearance of the strain fields around intersecting slip planes in x-ray extinction contrast studies by a semiempirical method. Fig. 1 shows typical strain patterns observed by Newkirk on (200) reflections in LiF using chromium radiation and a variation of the Berg-Barrett (B-B) technique. In other reflections (e.g., {220}) the strain patterns are absent. If one defines a vector 3 along the striations from the more to the less dense portion, and a vector v in the direction of the X-ray beam parallel to the reflecting plane, such that both 3 and v lie in the reflecting plane of the crystal, Fig. 1, then the positions of the striations on (200) reflections appear to be confined such that where is the angle between v and 3, Fig. 1. It will be seen later that 3 is the projection of Sb on the reflecting planes. In some instances the strain effects are observed only above the slip plane, Fig. l(C), in others only below, Fig. l(D). Where the strains appear to be both above and below the slip line, Fig. l(E), one sees that there are actually two slip lines present, Fig. 1(F) and (G). Furthermore, the strain patterns are observed in the vicinity of the intersection of emergent edge dislocations (diagonal lines on the micrograph) with emergent screw dislocations (horizontal lines on the micrograph), e.g., Fig. l(HJ) and (MN), but not in the vicinity of the intersection of two emergent edge dislocation arrays, Fig. l(HJ) and (KL). However, in the latter case the contrast of the dislocation array itself is reduced along (KL) and increased along (HJ). Line (AB) in Fig. 1 is the edge of the crystal, and the material to the left of (AB) is the side of the sample. Any empirical correlation will have to include most, if not all of the aforementioned observations. Lang2 and Newkirk1 determined that the condition for contrast is given by g-b#0 [2] where b is the Burgers' vector and g the diffraction vector (normal to the reflecting planes). If one assumes that the direction of the observed strain fields is given by the vector sum of the slip vectors (Sb1) of the intersecting slip planes, then Eq. [2] may be generalized to g-S#0 [3]

Jan 1, 1963

By Yassine Lahmadi, Edoardo Trivellato, Christian Chereau, Bénédicte Robert

Within the framework of the adaptation of the South-East European Technicentre (Technicentre Sud-Est Européen TSEE), SNCF Voyageurs appointed Pini with the project management mission (MOE) for the design and construction monitoring of a road tunnel. This investment has a dual function: during the site transformation phase, it facilitates the work logistics (and shorten traffic flows); and in the operating phase, it is intended to ease all movements on the site over the long term. This is a limited-length gallery (50 meters) to be performed in conventional excavation below Poniatowski Avenue (Paris 12e). The excavation, crossing the entire width of the boulevard, constitutes a major challenge, given the very low coverage (less than 5.5 m), and the surrounding main infrastructures. The same project mis- sion includes the design of the tunnel accesses, via reinforced-concrete frame structures. The targeted design questions several aspects of its execution framework, and particularly, continuous operation must be guaranteed to the neighboring networks during the works. The installation of an umbrella- pipe all along the excavation profile, the progression in divided sub-sections, and the implementation of a complex monitoring system are hence key elements for limiting and controlling any deformation. An exhaustive 3D finite element modelling was performed, taking into account the detailed phasing of construction (pre-support, excavation in divided section, preliminary support and definitive lining), to dimen- sion the structures, and, overall, to analyze the impacts on the neighboring structures and facilities. During the execution phase (planned for mid-2024), monitoring activities with back-analyses as close as possible to the works are planned.

Jun 23, 2024

By Ximeng Li

The entries that are subjected to dynamic pressure are much more difficult to maintain due to repeated disturbance. A case study of an entry stress distribution was performed using the FLAC3D program. By analyzing the distribution of stress field around the entries, this paper provides guidelines for entry support design in the lower (#16) seam subjected to the repeated disturbance from longwall mining in the immediate overlying (#17) seam, 72ft (22 m) above. The results showed that there was stress superposition inside the barrier pillar in the lower seam, 15ft (5m) to 45ft (15m) deep, during development. The influence zone of the front abutment pressure in the upper (#16) seam was about 100ft (30m) outby the faceline. The stress-relieved zone was from 0 to 100ft (30m) inby the face. The area further inby the face (i.e., 230 ft (70 m) inby the face) was within the gob compaction zone. Along the face advancing direction, the affected zones of the entries in the lower (#17) seam that were subjected to the dynamic pressure from longwall mining of the immediate overlying seam could be divided into four stages: pillar development stress stage, front abutment pressure stage, unstable gob stage, and stable gob stage. Those entries within an area from 100ft (30m) outby to 100ft (30m) to 230ft (70m) inby the faceline should be reinforced with special supports. The numerical modelling matched the monitoring results well.

Jan 1, 2013

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' 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'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's minimum work problem imply the solutions of Bishop and Hill'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 H. C. Fiedler

A high degree of cuhe-on-edge grain orientation and good magnetic properties were obtained in Si-Fe strip processed from laboratory heats containing vanadium nitride inclusions. The higher the nitrogen content the greater was the restraint on normal grain growth and the greater was the ability to undergo secondary recrystal-lization. The degree of restraint in a heat containing magnanese sulfide inclusions was slightly greater than that in the lowest nitrogen vanadium nitride heat. The high rate of diffusion of nitrogen in the temperature range in which the texture is developed makes it necessary to retard the loss of the inclusions until the texture has been developed. MAY and Turnbulll have shown that to develop the cube-on-edge secondary recrystallization texture in Si-Fe it is necessary that inclusions, such as manganese sulfide, be present to prevent normal grain growth. They showed that the driving force for the growth of the secondary grains is inversely proportional to the diameter of the matrix grains, and that the function of the inclusions is to maintain a small matrix grain size. Fast3has developed cube-on- edge texture in Si-Fe by nitriding the hot rolled band. The silicon nitride thereby formed promotes secondary recrystallization during the anneal of the final gage strip. To obtain the best magnetic properties, the inclusions must be removed from the strip after the grain orientation has been developed. Nitride inclusions have an inherent advantage over sulfide inclusions in that the greater diffusivity of nitrogen as comared to sulfur permits the use of shorter times and or lower temperatures for the purification heat treatment. The purpose of the work to be described was to examine the usefulness of vanadium nitride inclusions in developing the cube-on-edge texture and to determine the magnetic properties of oriented strip made from heats containing these inclusions. A comparison is made with a heat having had iden-

Jan 1, 1962