Search Documents

By James K. Kindig

Hazen Research, Inc., has developed a new process for removing pyritic sulfur and ash from coal. Feed coal is contacted with iron carbonyl vapors, Fe(CO)5, at 190°C which puts a thin skin of magnetic material on the pyrite and ash, but does not affect the coal. Thus, low intensity magnetic separators yield a nonmagnetic coal, low in sulfur and ash, and a magnetic refuse, high in sulfur and ash. Results are given for clean coal produced by this method. A comparison is made between results of the magnetic process and the U. S. Bureau of Mines two-stage flotation process cleaning identical samples of Pittsburgh Coal. Capital and operating costs of the two cleaning methods are discussed.

Jan 1, 1976

By R. J. Yan

There was a plant equipped with a 32000t Hydraulic Press to be built, under which a box foundation of 22.5m x 15m x 14.25m (depth) with a base slab of, varying thickness was proposed. The subgrade reactions, bending moments and settlements needed to be determined by means of in-situ model test. A model of the same materials as the prototype scaled to l/10 was embedded in-situ with simulated depth in the bedrock. A lot of data obtained from 39 bench marks, 32 elongation measuring points, 30 couples of electric resistance strain gauges and 24 pressure cells attached to the model foundation enables all the quantities required to be found out. Since it was put into operation, the settlements measured has reasonably agreed with the test results and the foundation has been in good condition.

Jan 1, 2010

By I T. Tshabalala

In typical conventional narrow vein stoping operations, the use of temporary support components to offer some support to workers, whilst the permanent and generally more elaborate support system gets installed or constructed, still results in injuries to people. The authors wishes to explore the probability and practicality of making use of new generation support products to make the support operations safer as well as enhance productivity in the stope face. This paper will examine the use of Autorock Drills as a means to drill roof support holes and install appropriate support components into these holes, as well as the application of ?Thin Spray Liners?, commonly called TSL?s as an additional means of creating a safer operating environment. The installation of netting as a means of roof protection and other support aspects such as cemented roof-bolts will also be explored. These proposed items are envisaged to improve the safety of our people and reduce production down time and increase production and productivity.

Jan 1, 2008

By John J. Sammarco

Miners depend most heavily on visual cues to recognize underground mining hazards; consequently, illumination plays a critical role in miners? safety. Some hazards are located in the miners? peripheral field-of-view (10 degrees to about 60 degrees off-axis) or on-axis (0 degrees). The objective of this research was to determine if there were visual performance improvements when using solid-state cap lamps with light-emitting diodes (LEDs) as compared to incandescent light bulbs commonly used in miner cap lamps. Recent research has indicated that an increased short-wavelength content of the spectral power distribution of LEDs relative to incandescent lamps improves peripheral visual performance for low-light (mesopic) conditions. The visual performances of nine subjects were quantified by measuring the subjects? speed and accuracy in detecting floor objects located on axis and at ±20 degrees off axis. The objects were located near field (1.83 meters) and far field (3.66 meters). Upon presentation of the objects, subjects would count and point to each object using a red-laser pointer. The object detection response time and number of missed objects were recorded. The results of the visual performance comparison for an LED, a prototype LED, and an incandescent cap lamp are presented. There we no missed objects when subjects used the LED-based cap lamps but, there were three missed object occurrences when subjects used the incandescent cap lamp. The mean detection time when using the incandescent cap lamp was 55.3% greater than the prototype LED cap lamp and 43.5% greater than the LED cap lamp. It can be inferred from this data that the spectral distribution of LED-based cap lamps could enable significant visual performance improvements as compared to incandescent cap lamps1.

Jan 1, 2007

By Bauer Young

Ante la crítica realidad económica de los países subdesarrollados, se plantea la propuesta de que si estos países puedan liberarse de la pobreza, no será a través de sus aportes financieros, sino por sus sacrificios en la escala esconómica. Para ello, se revisa el modelo de círculo vicioso de la pobreza (tasa cero), los testimonios en contra, las relaciones entre capital y desarrollo, ahorro e ingresos, y por último, se realiza el análisis económico y las plataformas económicas.

Jul 1, 1961

By P. Klaus

"KfW IPEX-Bank is the commercial arm of KfW Bankengruppe, responsible for international project and export finance.KfW was one of the first banks in Germany to promulgate environmental guidelines for its commercial business activities. These guidelines were first made public in 2000 and updated for the second time in 2004. They now include specific reference not only to environmental but also to social concerns. The guidelines specify the procedures to be followed in assessing credit risks related to environmental or social hazards.The bank considers sustainability as an interdependent framework of economic, ecological and social factors. In its efforts to contribute to sustainable development worldwide the bank uses its influence as far as possible to improve a project’s performance if such improvement is deemed necessary."

Jan 1, 2005

Removal of Thiocyanate from Solutions by Precipitation

Sep 13, 2010

A model has been developed as part of the AMIRA P420 Gold Processing Technology Project to simulate the recovery of gold by centrifugal gravity devices. The model (which is available online) uses the simulation methodology developed by Laplante et al (1995) to predict gravity recoverable gold (GRG) recovery under varying operating conditions and circuit configurations. In addition to predicting GRG recovery, the model also predicts the GRG content and size distribution of the cyclone overflow and underflow. The predicted overflow GRG content and size distribution can be used as inputs for a leaching model in which size dependent leaching rates are applied for each size class of GRG and non-gravity recoverable gold (non-GRG) in the cyclone overflow, allowing size-by-size leach recoveries to be determined for GRG and non-GRG. The application of the gravity model and leaching model are demonstrated using a case study. The simulated gravity recovery and leaching performance showed excellent agreement with the measured values. The developed models can be used to assess the sensitivity of gravity gold and leach recoveries to varying feed GRG content, GRG size distribution, gravity circuit feed rate, classifier performance and leach residence time. The described methods can be used to optimise new and existing gravity and leaching circuits.

Aug 1, 2010

By Donald E. Buck

In 1988, Albania's centrally planned economy continued to decline. The country's officially published yearend economic report did not contain concrete results such as the growth of national income or industrial output. 2 The shortfall for central budget earnings for 1988 amounted to 9% below the planned target. Losses in industry were attributed to poor management and organization, as well as to low technical standards and excessive consumption of fuels and raw materials. The construction, energy, and mining sectors of industry did not meet their annual production plans. As in 1987, within these sectors, the chromite and petroleum extracting and processing industries continued to lag in output. Both chromite and petroleum remained Albania's chief sources of foreign exchange; the production downturn of these commodities continued to negatively affect the country's foreign trade position, especially in view of constitutional prohibitions against using foreign credit to finance trade. The chief events in the minerals industry in 1988 included the construction startup of the first of four planned new concentrators at the Bulquize chromite mine, as well as the construction startup of new ferrochromium capacities at Elbasan. Also, the copper mining industry reported the completion of facility expansion at the Perlat mine in the Mid-rite district. Albania began new facility construction at the Dinamo heavy-equipment enterprise at Tirana to maximize self-sufficiency in mining equipment production. Upon completion, the new factory would double the out-put of mining equipment at the enterprise and would introduce new designs for electric trucks and pneumatic drills for the mining industry. The new facility would also increase the production of new machinery and equipment for the country's beneficiation plants.

Jan 1, 1990

By Steven J. Schatzel, Robert B. Krog

Frictional ignitions are defined as the ignition of a flammable mixture of methane and air that is initiated by frictional heating. Ignitions created through the addition of energy from open flames and exposed electrical circuits are not included in this analysis. Energy released in a roof fall that creates a spark and ignites a methane mixture would be considered a frictional ignition. Frictional ignitions represent the majority of all ignitions in underground coal mines. Over the study period of 1983 to 2005, a total of 1993 ignitions were reported in underground bituminous coal mines in the United States, of which 1589 were frictional ignitions. Reportable ignitions to the Mine Safety and Health Administration (MSHA) are any unintentional occurrences of flame underground regardless of duration. Frictional ignitions were reported in 155 mines and 13 states. Continuous miners represented the largest source for frictional ignitions with 1090 (68.6% of all frictional ignitions). Longwall mining operations represented the highest concentration of frictional ignitions during this study period with 1365 frictional ignitions (85.9% of all frictional ignitions). The 17 mines with the most frictional ignitions were all longwall mining operations and had 1130 frictional ignitions (307 from the shearer) that represented 71.1% of the total. In 1983, mines with frictional ignitions represented 6.9% of operating underground mines and 36.6% of total underground coal production. The percentage of operating underground mines with frictional ignitions and their total production has increased steadily and in 2005 represented 9.8% of active mines and 46.2% of underground coal production. The three coalbeds with the highest number of frictional ignitions (Blue Creek, Pittsburgh No 8, and Pocahontas No 3) had 1049 ignitions that represented 66.0% of all frictional ignitions. The three states with the highest number of frictional ignitions were Alabama (710), Virginia (247), and Pennsylvania (242) that represented 75.5% of the total. Frictional ignitions peaked in 1991 with a high of 114. In 2005, only 34 frictional ignitions were reported. If only frictional ignitions that occur at the face are considered, there have been no fatalities since 1983. Since this time, there were 33 ignitions that caused 53 workers to lose a total of 2912 working days. When including ground falls, then there have been four frictional ignitions with one incident causing two fatalities and injuring eight workers. From 1983-1991, underground productivity and the number of frictional ignitions increased. However, productivity continued to increase from 1991-2000 while total frictional ignitions fell, thereby disproving this connection between productivity and frequency of frictional ignitions. Ninety percent of all frictional ignitions occurred in underground coal mines that liberated more than 393 L/s (1.2 MMcfd million cubic feet per day) of methane through the main ventilation system. Although methane production is not the determining factor for the occurrence of frictional ignitions, it is a good indicator of the anticipated frequency.

By João Paulo Sousa Coelho

A sedimentação consiste em uma operação unitária de separação entre sólidos e líquido, realizada em tanques denominados sedimentadores, que se baseia na ação do campo gravitacional sobre as partículas para decantá-las e removê-las da água. Sua eficácia é extremamente dependente do tamanho das partículas, tendo em vista que a velocidade de sedimentação é diretamente proporcional ao tamanho delas. Dessa forma, no espessamento das lamas, é imprescindível a utilização de reagentes químicos (coagulante e floculante) que possibilitem a formação de agregados de maior tamanho. Neste contexto, realizou-se esse trabalho para investigar o efeito da dosagem desses reagentes sobre a sedimentação de lamas de minério de ferro. Para isso, empregou-se o Planejamento Fatorial, por meio do qual se planejou uma série de ensaios de sedimentação, variando-se as dosagens desses reagentes. As variáveis resposta monitoradas foram: a área unitária de sedimentação, o índice de turbidez do líquido sobrenadante e o percentual de sólido do material sedimentado. Baseado nos resultados experimentais, concluiu-se que os menores valores de área unitária de espessamento foram obtidos em dosagens maiores de coagulante e floculante, ao passo que dosagens excessivas desses reagentes, especialmente de floculante, provocaram um aumento do índice de turbidez do líquido sobrenadante e uma redução do grau de adensamento da polpa espessada.

Oct 30, 2017

By Stephen Hodgson, Ken Brouwer

September 2005, Northern Dynasty Mines announced the discovery of a new, high-grade deposit at its Pebble project in southwest Alaska. The product of insightful geological investigation, Pebble East, as it is now known, is quickly growing into one of the most significant copper deposits in the world. Preliminary analysis shows it could reduce the U.S. copper supply deficit by a third. The new deposit has also altered Northern Dynasty’s view of how Pebble should be developed. This article describes the Pebble project as it is currently understood and outlines the work planned for the next several years.

Jan 1, 2007

By T. C. M. Pillay, John Chipman

The Si-0 equilibrium in liquid iron was investigated in some detail by Gokcen and Chipman1 who reported equilibrium constants of the following reactions: In each case the thermodynamic equilibrium constant K was obtained by extrapolating K' to infinite dilution. Their results on reaction [I] were consistent with those of earlier observers, and there seems to be little doubt as to the approximate validity of the equilibrium product determined. On the other hand, the results on reactions [2] and [3] indicated unusual curvilinear relationships between the activity coefficients of silicon and of oxygen and the silicon concentration. Since a linear relation is observed in all other similar instances, it was concluded that some source of error had affected the gas-metal equilibrium relationships. Recently the authors undertook a restudy of these equilibria with the view especially to establishing the equilibrium constant of reaction [2]. Their experiments, however, were discontinued before a tbroughly satisfactory answer had been obtained and consequently have remained unpublished until the present time. Quite recently Matoba, Gunji, and Kuwana2 published the results of a very thorough study of these equilibria. It is the purpose of the present note to Compare these three sets of experimental data, a comparison which leads to Confirmation of the results of Matoba and coworkers. The experimental arrangements described by Dutilloy and Chipman were employed. A controlled mixture of Hz, H,0, and argon was led into the induction furnace over the surface of the Fe-Si melt contained in a silica crucible. On account of the slow approach to equilibrium, runs were continued for at least 8 hr and, in some cases, as much as 12 hr. Samples were taken by means of silica tubes at the start and during the final 4-hr period of each run. Out of twelve runs only seven appeared to have approached equilibrium with sufficient certainty to be reported here. The results of these experiments, all at 1600°c, are shown by the triangles in Fig. 1. Equilibrium was approached from both oxidizing and reducing conditions and the direction of approach is indicated by the shape of the triangle. Attempts to extend the study to higher silicon concentrations were unsuccessful on account of the transfer of silica from the metal bath to the upper portions of the crucible by means of a silicon-monoxide mechanism. Matoba, Gunji, and Kuwana used similar methods and approached equilibrium from both sides. Their results at three temperatures are shown by the solid lines of Fig. 1. A line corresponding to 1600 deg is interpolated from their equations and is shown by the dotted line. The results of Gokcen and Chipman at 1600 deg in the range 0.02 to 2.0 pct Si are also shown. At concentrations up to about 0.6 pct Si, these investigators approached equilibrium from both directions, and their results in this range appear to be trustworthy. Above 1 pct Si, however, all of their experiments involved oxidation only, as shown by a decrease in the silicon content of the bath. It now seems certain that they failed to reach equilibrium at these higher silicon concentrations and that the curvilinear relation shown by their results is incorrect. It is evident that their results in the lower silicon range are in good agreement with those of Matoba and coworkers. In fact, a straight line drawn through their results would parallel the dotted line and would differ from it by only 0.05 in log K. The new data also lie close to that line. It may thus be concluded that the three sets of data are in good agreement and that the equations proposed by Matoba and coworkers for reaction [2] are satisfactory . They take the limiting value of log K', at 0 pct Si as log K ,. The slope of each line gives the value

Jan 1, 1962

By J. Pinkley

DSI DYWI Rock Dust application is aiding in enhancing safety and productivity in underground coal mining. DSI DYWI Rock Dust combines wet dusting technology and polymers to allow for drying and lift characteristics for rock dusting. DSI DYWI Rock Dust typically dries within 24 to 48 hours depending upon the mine air velocity and humidity. The DSI DYWI Rock Dust Applicator Machine is a completely hydraulic unit. The DSI DYWI Rock Dust Applicator machine allows for batching of product and face spraying operations in permissible locations. The DSI DYWI Rock Dusting Applicator Machine fits in one half of a battery or diesel scoop bucket for ease of transport. It is completely hydraulically powered by the PTO circuit. The DSI DYWI Rock Dust Applicator unit requires a scoop operator, and a person to operate the spray wand, simple operation with two personnel. The first demonstration was at an underground continuous miner room and pillar coal mine which produced a pilot test period opportunity, which proved to be successful, and has now been in full launch mode with the US underground coal mining industry. A typical batch of operation allows for 250? of roof and rib (19? wide by 6? in height) coverage of DSI DYWI Rock Dust application. The DSI DYWI Rock Dust Applicator contains a hydraulic powered air compressor which allows for 30-50% more coverage per batch by improved dispersion of product via air assist spray nozzle. DSI DYWI Rock Dust will add approximately $0.02 to $0.04 per clean ton of coal cost to the mining operation over traditional rock dust cost depending upon mining height.

Jan 1, 2012

By D. D. Tannant

An experimental and numerical study was conducted on the geomechanical behaviour of oil sands during penetration tests in which a steel wedge with an apex angle of either 20 degrees or 30 degrees was forced into compacted oil sands. The boundary conditions simulated in the laboratory tests are similar to shovel penetration into oil sands. The objective of the laboratory tests was to measure the force required to push a steel wedge into compacted oil sands. A wedge penetration test differs from conventional triaxial tests in that much more shear is generated. The laboratory data was needed to improve calibration of micro-mechanical input parameters for a two-dimensional discrete element model of oil sands constructed with Particle Flow Code (PFC). Initial model calibration was performed with triaxial test data and then a PFC model of the wedge penetration test was constructed. The measured force-displacement behaviour of the steel wedge was compared with PFC modelling results. It was found that different combinations of PFC particle and bond parameters could equally well replicate the laboratory triaxial compression data for bitumen-rich oil sands. When the wedge model was run, it was found that the resulting force required to penetrate the wedge into the oil sands was about four to six times higher than that measured. This clearly indicates that further research is required to improve the predictive capability of PFC models of oil sands.

Jan 1, 2002

By Eric Sitorus, Septian Prahastudhi, Roy William, Wieda Azani

In July 2020, massive slope failure occurred in the southeast corner Grasberg open pit. This was the final episode in the breakthrough of Production Block 2 South (PB2S) of the Grasberg Block Cave to connect to the surface. This breakthrough had been rapidly evolving during the first half of 2020 and occurred as expected with no adverse impacts to safety or operations. To manage and safeguard the exposure to the workforce and operations, numerous hazards were identified and anticipated. The failure of the sill pillar between the open pit and PB2S cave was identified as the main area of interest and was closely watched during the failure process. This paper reviews the systematic approach developed to convert monitoring data into information around the collapse of the GBC PB2S cave sill pillar. The data that was interpreted consisted of micro-seismic, piezometric, ground-based radar and observational inspections. Geological structures on the boundary of the PB2S cave were clearly involved in the breakthrough process. As the cave propagation reached these structures and triggered instability, the resulting acceleration and breakdown were clearly shown by IBIS radar units associated with high movement in the slope. The focus of this paper is on the evolution of changes seen in the micro-seismic data and how it was used to understand the rapidly changing conditions of the sill pillar. The seismic parameters evaluated were event distribution, Es/Ep value, and the seismic moment tensor inversion. The changes of breakthrough indication seen in these parameters were substantiated by Shear Wave Splitting (SWS) analysis that showed a close correlation with the fractured zone above the PB2S cave as indicated by the increasing anisotropy.

Jan 1, 2022

The Steering Committee for Minerals and Mining Policy convened two workshops during March 1996 to address the following topics: Business Environment- National and Provincial Powers, Administration and Regulation, Mineral Marketing, Beneficiation, Research and Development, Environmental Issues, Mining Impact on Surface Usage, Southern Africa Regional Issues. Human Resources: Elementary Residual Racism, Housing, Downscaling, Migrant Labour and Human Resource Development. Mineral Tenure: Mineral Rights, System of Access to Mineral Rights, Access to Exploration information, optimal Exploration, Trust Lands. Small-scale Mining. Development of Small-scale Mining, Artisanal Mining.

Jan 1, 1996

By Diego de Araujo Santana

O tamanho médio dos grãos é um parâmetro estrutural frequentemente estimado quando se está avaliando, principalmente, as propriedades mecânicas dos materiais metálicos. A American Society for Testing and Materials (ASTM) estabelece, nas normas ASTM E112 e ASTM E1382, metodologias para estimar o tamanho médio dos cristais de maneira manual e semiautomática/automática, respectivamente. O presente trabalho propõe, além de uma nova metodologia semiautomática, duas metodologias automáticas para estimar o tamanhão médio de grão em materiais metálicos policristalinos monofásicos, assim como um parâmetro para avaliar a morfologia dos grãos. O tamanho de grão G ASTM encontrado utilizando os novos procedimentos testados se apresentou muito próximo aos valores obtidos pelos métodos padronizados, que também foram aplicados e usados como referência para avaliação da representatividade das medidas. Desse modo, os métodos propostos se apresentam como uma alternativa viável para estimar o referido parâmetro estrutural dos materiais metálicos.

Aug 17, 2017

By C. B. Webber, W. A. Grell

"Sherritt Gordon's Ruttan Mine is a copper-zinc operation located approximately 600 miles north-west of Winnipeg. Open pit mining began in 1973 at 10,000 Tpd., with a change over to underground mining in 1981 producing 7,500 Tpd. Ore is crushed to -3/4"" followed by rod and ball mill grinding (two ball mills in series), differential copper-zinc flotation, and dewatering. The copper and zinc concentrates are trucked 75 miles to Lynn Lake, where they are shipped by rail to the HBM&S smelter at Flin Flon.This paper describes a method used to predict the effect of grind particle size on metallurgical performance, as well as details on the copper and zinc metallurgical performance due to fine grinding in actual plant operation.Initial statistical studies on historical data (including ore source, head gr3de, grind, etc.) indicated that copper and zinc recoveries increased with fineness of grind, in the range of 50 to 65% -200 mesh.In order to extrapolate beyond 65% -200 mesh, and to develop expected nonlinear relations between grind, Cu concentrate grade, and recovery, the assays of screen fractions of copper concentrate and tailing were used to determin8 the relation between net smelter return (a function of grade and recovery) and grinding cost. The optimum economic grind would be that grind at which the net smelter return less grinding cost reached a maximum."

Jan 1, 1982

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

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain has been analyzed by Taylor and by Bishop and Hill. The Taylor analysis is based on a principle of' virtual work, and involves finding, among numerous cotnbinalions of slip systems that satisfy the imposed strain, the combination in which the sum of the glide shears is a minimum. Previously, Taylor has treated the case of axisymmetric flow when slip occurs on (111)(110) (or {110)(111)) systems only. His analysis has now been extended by computer methods to the cases of slip on {112}(111) and {123)(111) systerns and of mixed slip on {110), {1 12), and (123) planes with a common (111) slip direction, all of which are important in the deformation of bcc crystals. The results are computer-plotted as contours of the ratio of the floe strength to the critical resolved slzea-r stress for slip, for axial orientations distributed throughout the standard stereographic triangle. Implications of the computer results to texture develop,merit, texture hardening, and dislocation theories oj work hardening are discussed. WhEN a single crystal is extended in the usual tension test, the lateral dimensions can change relatively freely. In this case, the glide shear produced by slip on a single slip system is sufficient to accommodate the (tensile) deformation. Since slip is governed by a critical resolved shear stress law (the Schmid law'), the single active slip system is one for which the stress, resolved on the slip plane and in the slip direction, is the highest among the several equivalent slip systems. This amounts to saying that a value M = U/t = y/~ is a minimum among the equivalent systems, where M is the inverse of the familiar Schmid factor (a and E refer to tensile stress and strain, and T and y refer to resolved shear stress and shear strain). A grain embedded in a polycrystalline aggregate, on the other hand, cannot freely change its shape due to constraint from its neighbors. In this case, slip from five independent slip systems (to accommodate five independent strains) is generally required.' Based on the principle of virtual work and assuming that the critical resolved shear stress for slip is the same for all systems, Taylor hypothesized that, among all combinations of (five) slip systems which are capable of accommodating the imposed strain, the active combination is that one for which the sum of the absolute values of the glide shears is a minimum. Again, this is equivalent to saying that the value of M = CjlyjI/ is a minimum, in analogy to the single slip case. Taylor aminimum,analyzed the case of {111)(110) slip for fcc metals, and applied the analysis to crystals undergoing axisymmetric flow, that is, the same macroscopic shape change as the poly crystalline aggregate under uniaxial tension (or compression). For the twelve equivalent {111}( 110) slip systems, there are 384 independent combinations of selecting five systems to satisfy the five independent linear equations of imposed strain.4 Taylor calculated the value of M for each combination* and obtained the active com- *A number of the independent combinations were omitted from consideration in Taylor's original work (see Ref. 5). bination (minimum M) for a number of axial orientations distributed throughout the standard stereographic triangle. Later work by Bishop and Hill*'8 showed that Taylor's least-shear hypothesis was equivalent to a maximum work principle which they advanced. Using the simplified Bishop and Hill method for {111)(110) slip, Hosford and Backofen' obtained detailed contours of constant minimum M for the same axisymmetric flow case. In contrast to {111}(110) slip in fcc metals, slip in bcc metals is generally described as occurring on {ll~)(lll), {112)(111), {123) (111) systems as well as mixed slip composed of all three. Since the direction cosines of the slip plane normal and the slip direction enter as a product in the Taylor analysis, the Taylor solutions of ,M for {110)(111) slip are identical to those for { 111} 110) slip. The other three cases of slip, however, have not been solved. In view of the numerous combinations of slip systems involved in the calculations, the Taylor analysis is clearly oriented toward computerized solutions. THE TAYLOR ANALYSIS In order to obtain the active combination of (five) slip systems by solving for the minimum value of M = we first express the (small) strain components E,, with respect to the cubic axes 1, 2, 3 ([loo], [010], [001], respectively) of the crystal, in terms of the sum of the glide shears yj from slip systems j: where n, and n,j refer to direction cosines of the slip plane normal, and dri and dsi to direction cosines of the slip direction, of slip system j, all referred to the cubic axes. In practice, the strain components are given with respect to the specimen axes X, y, 2. These components are readily converted to ers through the tensor transformation where irk and 1,~ are the direction cosines between the two sets of coordinate axes.

Jan 1, 1968