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By Fritz F. Prugger, Peter R. Jones

This paper considers some of the main aspects of underground mining in the flat, rich, but deep lying deposits of Saskatchewan. It briefly describes the pertinent geological features as they relate to mining and the practical de-stressing techniques used to allow productive extraction in the high stress environment present in many of the province’s mines. Mining layouts, materials handling, and the evolution of some of the world's largest mining equipment are examined.

Jan 1, 1983

By Abbas Ali Daneshy

A study of the mechanics of hydraulic fracturing shows the fracture initiation pressure to be a function of the in-situ principal stresses, the formation and fluid properties, and how the wellbore has been completed. The orientation of the hydraulic fracture is perpendicular to the least in-situ principal stress. The geometry of the induced fracture depends on the treatment fluid properties, the injection rate and volume, fluid leak-off and formation properties.

Jan 1, 1974

By T. W. Turk, S. A. Sass

The engineering design features of the Mercur Gold Project crushing, grinding, carbon-in-leach, bullion, reagent, and tailings disposal areas will be discussed in this paper. It presents a project overview and flowsheet along with selected design alternatives. During the engineering phase, major equipment and other features were selected to optimize design within site location and environmental constraints. The project team organization and procedures were adopted to accommodate multiple optimization studies while maintaining a tight engineering schedule.

Jan 1, 1985

By W. R. Clough, M. E. Shank

IT has been noted in a study of the flow and fracture of nodular cast iron under biaxial stress conditions (complete results of which will be published later) that when this metal is subjected to stress it may undergo a striking density change. Such behavior was first determined by strain gage measurements made on tensile test specimens, and has since been substantiated by other types of measurement. The chemical analyses and mechanical properties of several nodular irons to be discussed here are given in Tables I and 11. Tensile data for iron A was obtained from a hollow cylindrical combined stress specimen of the same dimension as those used by L. F. Coffin, Jr.1 in his investigation of gray iron properties. Standard 0.505 in. solid tensile-test bars were used for irons B and C. On each specimen type, A-8 wire resistance strain gages were used—two diametrically opposing gages in the axial direction, two in the tangential or hoop direction. By subtracting elastic strains from the measured strains, the plastic strains could be calculated. By assuming that radial and tangential strains are numerically equal, a measure of permanent volume change can be obtained by summing the plastic strains. This appears to be a good assumption, since the metal either fractured, iron A, or readings were discontinued, irons B and C, long before necking took place. This calculated variation of volume increase with stress is given for irons A and B in Fig. 1. Data for iron C is almost identical with that for iron B. The volume change indicated by Fig. 1 has been substantiated by a more direct type of density measurement. A method developed by S. G. Fletcher and' Morris Cohen,' and completely described in the discussion of their article, has been used. The accuracy of specific volume measurement has been estimated as 0.00002 cu cm per gram. Essentially the method consists of weighing a sample in air and then immersed in water. Measurements were made before and after straining the material. The results shown in Table I11 were obtained by means of half-size (0.252 in. diameter, 1 in. gage length, 3/8-16 threads) tensile specimens. Initial measurements were made on the whole specimen before stressing. After stress-

Jan 1, 1955

Jan 1, 1967

By C. L. Sainsbury

Lode and placer tin deposits of the western Seward Peninsula, Alaska, have produced more than 2200 tons of metallic tin and constitute the only known domestic deposits of economic grade and size. The lode deposits consist of quartz-topaz greisens containing cassiterite and wolframite as well as numerous base-metal sulfide minerals, and most are in or near altered biotite-granite that forms isolated stocks or in rhyolitic dikes near granite. Within the main lode-producing area in the central York Mountains, nonpegmatite beryllium deposits, consisting principally of fluorite, chrysoberyl, diaspore, tourmaline, and white mica, with minor euclase, bertrandite, phenakite, hematite, and todorokite, are distributed zonally around the tin deposits and locally are transitional with them. All the known beryllium deposits are replacement lodes in carbonate rocks. In the area discussed, both tin and beryllium deposits are localized in a structural belt striking N70° to N85°E across the central York Mountains. The belt is characterized by numerous normal faults, which cut extensive thrust sheets, and by dikes of rhyolite, rhyolite porphyry, and lamprophyre that were injected along the faults. Ore deposits are localized where the dikes intrude brecciated rocks beneath thrusts and, although complex in detail, form tabular lodes that tend to lie along the thrusts. The granites contain abnormal amounts of tin, beryllium, lithium, and boron, and the tin and beryllium lodes are believed to be genetically associated with these enriched granites

Jan 1, 1968

By AIME AIME

AT FOUR O'CLOCK members gathered in the auditorium for the annual business meeting of the Institute which, according to its charter, must be held on the third Tuesday of February each year. President Turner presided and after the usual formal action on minutes announced that he would create a precedent by transferring the President's annual address (which by tradition has always been delivered at the banquet on Wednesday evening) to the business meeting, and, furthermore, would only present a brief abstract of it. Since it appears in full on pages 127-131 of this issue it can be followed with the careful attention its thoughtful analysis of current conditions deserves.

Jan 1, 1933

By J. F. Wolff

CARL ZAPFFE, Brainerd, Minn. (communication to the Secretary*).¬Unless one has actually directed explorations for iron ore, it is doubtful whether the importance of Mr. Wolff's paper, the value of the information contained, and the large amount of detail work involved in what is set forth can be fully appreciated. It is indeed rare to get such a com-

Jan 3, 1917

By A. C. Butterworth

M OST operators of open-pit mines in the Lake Superior iron ore district are quite familiar with the use of fuel oil in the heavy-duty Diesel engines commonly used in truck-haulage service but some operators, including my own company, Pickands Mather, have had butane-engine trucks in service for several years, and less is known of their operation. One of the first installations of trucks for iron-ore haulage was in 1939 at a deep open-pit mine on the Cuyuna Range. These superseded standard-gauge steam haulage. Trucks then obtainable were equipped with 150-hp Diesel engines, and the speed of these units on an 8 % grade would have been so slow, considering the depth of the pit, that plans for an all-truck haul out of the pit were rejected. About this time one of the engine manufacturers brought out an auto-

Jan 1, 1948

By C. Y. Clayton

In connection with certain cooperative work carried on between the Ordnance Department of the U. S. Army, the U. S. Bureau of Mines, and the U. S. Geological Survey during the year 1918, it was the writers' privilege to make metallographic examinations of a great many test bars and other pieces of nickel-steel gun forgings. The material studied came from many different steel plants throughout the country and consisted both of forgings that had been accepted by the Ordnance Department and those that had failed to pass the specified physical tests. In general, these tests require a minimum tensile strength of 95,000 lb. (42,091 kg.)! an elastic limit of 65,000 lb. (29,483 kg.), an 18 per cent, elongation, and a 30 per cent. reduction in area. An average chemical composition of the steel studied is 0.38 per cent. carbon and 2.9 per cent. nickel. The steel was of both basic electric and basic open-hearth manufacture. The object of the metallographic work was twofold: to assist in detecting defects in the steel and, if possible, to suggest remedies for the same; and to obtain as much information as possible in regard to the relation of the microstructure of the metal to its physical properties. The grcatcr part of the investigation was devoted to defective metal that failed to pass the ordnance specifications. Many types and kinds of more or less serious defects thus came under observation, but most of these were due to the attempts by the manufacturer to meet the enormous demand for ordnance steel with more or less inadequate equipment, and were soon remedied. Two defects, the so-called "flakes" or "snowflakes" and a certain "fibrous" or "woody" fracture, were encountered so frequently and were so disastrous to the steel that the greater part of the study was devoted to them. As a result much information as to their nature and their effects upon the steel and something in regard to some of the conditions that favor their development has been obtained. The purpose of the present

Jan 1, 1920

By R. S. McCaffery, D. E. Krause

There has been some discussion among blast-furnace operators regarding the relative merits of tuyeres of the converging type and tuyeres designed in an attempt to produce a diverging jet of air. An article1 on Progress in German Blast Furnace Practice indicates the interest in this subject abroad. This article illustrates a diverging type of tuyere which is shown here in Fig. 1A. The design appears to be rather poor as regards known properties of air flow. The adoption of this tuyere, the arlicle states, resulted in a decrease of blast pressure of about 4 Ib. per sq. in. and an increase of the output of the furnace. If the improvements mentioned are due entirely to the change in tuyere design, the subject of tuyere design seemed worthy of investigation and this paper is a report of such work. Because of the gain in efficiency brought about by the use of a diverging tuyere in the German plant, it was thought desirable to investigate the shape of the air streams issuing from various types of tuyeres to ascertain whether the gain was due to the tuyere itself or to the distribution of the air in the furnace. Since it is difficult to do experimental work on a full-sized furnace, or even on full-sized tuyeres, and because of the equipment available for the work, it was decided to carry out the work on scale models of tuyeres. Therefore, in this work, single tuyeres were used and the blast discharged into the atmosphere. The shape of the air stream was determined by means of a Pitot tube suitably supported in the air stream at various positions. The air was furnished by a Roots blower driven by a 10-hp. direct-current motor having field control, and capable of discharging 250 cu. ft. per min. with a pressure on the discharge of 4 in. of mercury. A modern blast furnace with 21-ft. hearth requires about 50,000 cu. ft. per min. of free air at from 16 to 23 Ib. per sq. in. pressure, depending upon the type of burden. This pressure is the total pressure required to force the air through the burden and through the tuyeres. Upon computation the pressure drop through the tuyeres is about 1 to 2 lb. per sq. in. By making the tuyeres to a one-fifth scale, and by using a pressure of 1.5 in. of mercury, the shape of the air streams should be

Jan 1, 1931

Discussion of the paper of Ralph Hayden, presented at the Butte meeting,. August, 1913, and printed in Bulletin No. 80, August, 1913, pp. 1443 to 1467. JOHN V. N. Done, Denver, Colo.:-Mr. Hayden has placed the metallurgical profession greatly in his debt .for this valuable paper. The importance of such a complete description of the research work on which is based the building of a plant to add at least 10,000,000 lb. of copper per year to the production of the Anaconda Copper Mining Co., at small expense, will be appreciated by all our members, and especially those who are facing similar problems. The information given in regard to the treatment methods discarded will be a great help to many workers, as it is often of as much importance to know what ? not to do" as what method to adopt. I Some further comment on the tests of the Dorr thickener may be of interest, as they have led to developments which I believe will prove of great importance. Before the Dorr thickener was installed, I had shown Mr. Laist reports from the Steptoe Valley concentrator, in which it was stated that one thickener 17 ft. in diameter was the equivalent in settling capacity of twelve 8-ft. cones, although the latter-contained double the surface area.. Mr. Laist, had made careful tests on the settling capacity of in 8-ft. cone on Anaconda slime, and we naturally expected the thickener would show a much higher capacity for equivalent area. When, is Mr. Hayden stated, the tests showed no increase, I realized that we were comparing it with a cone under test conditions, while the Steptoe results were based on operative conditions, find the explanation given by Mr. Waddell for the great difference had been, that " there is only one unit to watch instead of twelve, without the constant result of feed to twelve cones becoming unbalanced. Also the one 1 1/8-in. spigot used on the Dow requires no attention compared with the dozen 3/8-in. spigots of the cones.' I realized also as a. result of the tests that the total settling area required to handle the immense tonnage of the Anaconda company would be enormous, and very expensive in view of the housing required by Montana climatic conditions. After studying the matter over, I told Mr. Laist that I believed a thickener operating in a much shallower tank would have nearly the same capacity. I asked him to test it out in the same tank filled 3 ft. deep, and stated that if my idea

Jan 11, 1913

By Waldemar Dyrssen

I CANNOT agree with the results obtained by the committee. The gas obtained per pound of coal is too high in calorific value and the amount of gas is too large. It should require about 190 cu. ft. of oxygen per 1000 cu. ft. of gas and not 75.14 cu. ft. as is given on page 35 of the report, or about 2.5 as much. Calculating the calorific value per pound of coal from the coal analysis given on page 34, according to Dulong's formula, the gross and net calorific heat are about 12,890 and 12,430 B.t.u., respectively, which is about 18,600 and 17,900 B.t.u., respectively, per pound of carbon in the coal. This is an unusually high figure, as ordinary bituminous coal has less than 18,000 gross B.t.u. per pound of carbon. Assuming, however, that the calorific values calculated are correct, the following results are obtained. On page 35, the net calorific heat in the gas per pound of coal is given as 12,856 B.t.u. and calculation for the gross value shows it to be about 13,950; in other words, the gas contains (13,950 - 12,890) ÷ 12,890 = 8.2 per cent. more heat than the coal on a gross basis and (12,856 - 12,430) ÷ 12,430 = 3.4 per cent. more on a net basis. The calculated amount of carbon in this gas per pound of coal gasified is about 0.688 lb., or nearly the same as in the coal (0.6972) and the gross and net calorific heat per pound of carbon in the gas are 20,300 and 18,710 B.t.u. which are 9.1 and 4.5 per cent. more than for the carbon in the coal. These calculations show that the results given in the report cannot be correct. There must always be some heat losses in the gasification of coal, in radiation from the producer, and in sensible heat in the gas; there must be some loss of carbon in ashes and in soot, and there are always tarry vapors in the gases that are condensed and do not appear in the fixed gases. From the excessive heat in gas per pound of carbon contained therein, it can also be concluded that the percentage of hydrogen in the gas is too high, from which it follows that the moisture decomposed is too high and that more free oxygen must be used.

Jan 11, 1924

By William Kent

William Kent, Pi.~t~bIJrQh, Pa.: The steel rnanufac.tnret of this country nlust ever he grateful to Dr. Dudley for his painstaking and conscientious endeavor to estaldish the relation between the chemical analysis and the wearing capcity of steel rails. They tnust thank him for the vast array of $acts he presents, and for having given them sixty-four analyses with which to combat his own conclusions and to establish their own, which are entirely opposite to his. In Dr. Duclley" discussion of his former investigation, at the Pittsburgh meeting, he said, "If you do not like my conclusions, draw your own conclusions." I have studied his last paper as thoroughly as the limited time since I received it would adruit, and have drawn some concluvions which I will first state, and then attempt to demonstrate. Briefly stated, my conclusions are: lst, That as far as these 64 analyses reveal anything of service to railmakers and cotsumera, it is that within the following chemical and physical limits, viz., Carbon,..0.20 to 0.60 Pisovphorue ,..0.026 to 0.146 Silicon,.. 0015 to 0.480 BInnganese.......0.262 to 0 880 Phosl~horus un~ts,..20.3 to 6.72 Bending weight,. 2270 lbs. to 4260 Ibs. Drfl~ctinn,.. 13O to 190° or in other words within the limits of rienrly the whole range of the chenlical and bending testa of these 6-2 mils: the wearing capacity bears no relation at all to mrbon, to phosphorus, to silicon, to mnnganese, to phosphorus units, to bending weight or to deflection or if there is any relation between the wearing capacity and thest! six or sr!ven variables, it is so obscured by the action of other cause or variat~les not yet known, that such relation cannot be expressed by any practical formula. 2d. That the difference in wearing capacity of these 64 rails was not due to unrbon, to phosphorus, to silicou, to manganese, or to anj combinntion of these four elements, but that it was due to some other cause or cornbination of causes, of which Dr. Dudley's whole iuvestigtion furnishes 11s no clue whatever. A few of the nlarry possible causes I lnay name : sulphur, copper, oxide of iron inclossl air or other gases, orerblowing, underblowing, oyrhaiting, undcrIreatinp, too hot-finishing, too cold-finishing, cold-straightening, toc great or too litkle rductiun hlu the rail to the ingot, or the portion

Jan 1, 1881

By W. E. Field

In the Coast Mountains approximately 110 miles north of Vancouver, the gold mine of Bralorne- Pioneer Mines Ltd. lies at an elevation of 3500 ft. The deepest or 41 level in the mine is at an elevation of 1400 ft below sea level, and the rock temperature on this level is 122.5°F. The thermal gradient is 1 "F increase in temperature for each 67.5 ft increase in depth. The mine produces between 500 and 600 tons per clay, utilizing an adit two internal shafts, and one service shaft from surface. The Queen shaft, extending from the 26 to the 41 level, IS the deepest, and most production now comes from this area. Stoping in by cut and fill using mill tailing hydraulic backfill.

Jan 12, 1963

By R. W. Armstrong, P. C. Jindal

WE should like to point out that Hu and cline.1 in their study of the recrystallization of titanium, have obtained data which appear very important for accurately determining the dependence of hardness on grain size for this material. It has been proposed2,3 that the macrohardness. H. of a poly crystalline material should depend on its average grain diameter, l. in accordance with the relationship: H =H0 + kHl-1/2 [1] where Ho and kH are experimental constants. This relationship follows from the hardness dependence on yield stress or flow stress4 and. thence. the Hall-Petch stress-grain size relations.5'6 Fig. 1 shows the Diamond Pyramid Hardness. Dph. values vs the reciprocal square root of the average diameter of the recrystallized grains, taken from the titanium data reported by Hu and Cline. The data in this figure give a linear relationship for the hardness over a wider range of grain diameters than anyone has previously measured. The data are not linear, for example. on an I-1 or l-1/3 scale. At the very large grain sizes the data are in reasonable agreement with measurements earlier reported by Holden, Ogden, and Jaffee.7 For the grain sizes smaller than 1 µ, which correspond in Fig. 1 to hardness values greater than 150, the material was reported as not being completely recrystallized and, therefore, these data appear less meaningful as far as the hardness dependence on grain size is concerned. However. it has been suggested by other investigators that deformed materials exhibit strengthening due to an effective grain size refinement even in the unrecrys-tallized condition.8-10 Also. Hu and Cline have shown that a change in texture occurs for titanium during the recrystallization process and. especially. following it. The influence of this texture change on the hardness-grain size relation would be expected to be less than that reflected in the unidirectional stress-strain behavior, even for an hcp material. because of the actual combined stress system which applies for the hardness test. For, at least, certain combined stresses, average values of the orientation factors should still occur in the stress-grain size analysis of a material exhibiting a preferred orientation.' We previously suggested3 that the experimental constants. H0 and kH. from the Meyer hardness-grain size relation should be correlated with the Hall-Petch constants, uoy and ky.5,6 Our recent study" of the Hall-Petch relation and the hardness-grain size results which obtain for a number of polycrystalline materials shows that: The inequality [2] is explained by noting that the hardness should be correlated. perhaps, with the flow stress at some value of strain, as suggested by Dugdale,12 and. also, that the influence of strain on the Hall-Petch relation is to increase uo and not change k very much." Normally. Dph values and Brinell hardness values are nearly equivalent to each other and to the Meyer hardness number. For the case of titanium, then. the inequality [2] may be evaluated using the experimental values of ao = 8.0 kg per sq mm and ky = 1.3 kg per mm3/2 obtained from the experiment of Guard.6,13 Thus, (Ho/uo) = 12 and (kH/k3) = 1.3. This research has been supported at the University of Maryland through the Center of Materials Research by the Advanced Research Projects Agency of the U.S. Government.

Jan 1, 1969

By J. W. Spretnak, H. R. Ogden, A. G. Imgram

The effect of working reduction, stress-relief annealing, and recrystallized grain size on the tensile and notch-tensile properties of molybdenum and Mo-0.5 Ti was studied. It was found that increasing the amount of working reduction increased the strength and reduced the tendencies toward brittle behavior. Stress -relief annealing did not alter the strength but lowered the transition temperature. Increasing the recrystallized grain size lowered the strength and raised the transition temperature. The notch -unnotch strength ratio began to decrease with decreasing temperature at temperatures below those at which the notched ductility fell to zero for all of the micro structural conditions investigated. BEING bcc metals, the refractory metals in Groups Va and VIa (V, Cb, Ta, and Cr, Mo, W) undergo a ductile-to-brittle transition and exhibit brittle fractures at low temperatures. Previous research has shown that molybdenum and tungsten not only have higher transition temperatures than columbium and tantalum but show a marked sensitivity of transition temperature to structure as well.' Recrystallized materials become brittle at considerably higher temperatures than is the case with material having a worked or fibered micro-structure. Evidence of structure sensitivity has also been detected in columbium- and tantalum-base alloys containing appreciable amounts of molybdenum or tungsten such as F-48 (Cb-15W-5Mo-1Zr) and Ta-10w.2 This paper describes the results of research conducted to further evaluate the effects of metal. lurgical structure on the low-temperature tensile and notch-tensile properties of molybdenum and Mo-0.5Ti. The effects of rolling reduction, stress-relief annealing temperature, and recrystallized grain size were studied. Considerable progress has been made in explaining the fundamental mechanisms of the flow and fracture characteristics of bcc metals. Several of these concepts are helpful in interpreting the data obtained in this study. Brittle fractures occur when the highly temperature-sensitive yield strength equals, or exceeds, the temperature-insensitive brittle cleavage fracture stress.3 The rapid increase in yield strength with decreasing temperature, characteristic of all bcc metals, is therefore of primary concern. petch4 has described the yield strength, ay, (stress required to initiate plastic flow) of bcc metals by the expression where ai is the frictional resistance to slip, Ky is a constant numerically equal to the slope of a a vs curve, and 2d is the average grain diamefer. The oi term itself is thought to be composed of a temperature-insensitive component dependent on impurity content and second-phase particles and a temperature-sensitive component dependent on the Pierls-Nabarro force.5 This equation has also been demonstrated to hold for the flow stress (stress required to maintain continued plastic flow).' Brittle-crack nucleation is thought to occur by the coalescence of dislocations piled up in slip planes at sessile dislocations or twin and grain boundaries.7,8 These proposed mechanisms require that a large number of dislocations be released into the active slip planes so that sufficiently large stress concentrations are produced at the dislocation pile-ups to enable coalescence into a micro-crack. Therefore, at least a microscopic amount of slip must occur in some grains to facilitate initial crack formation. Cottrell 7 has predicted that brittle fracture, nucleated by slip, should occur when where ty is the shear yield strength, ß = 1 in un- notched xension, u is the shear modulus, and y is the effective surface energy. This equation incorporates the Griffith concept of fracture that a crack will propagate if the decrease in strain energy equals or exceeds the increase in surface energy.

Jan 1, 1964

By W. A. Backofen, D. Lee

Titanium of commercial purity (RC-70) and two all-a (hcp) alloys (4Al-1/4O2 and 5Al-2.5Sn) were tested in sheet form under conditions of combined-stress loading. Plane-strain compression and plane -strain tension together with uniaxial compression and tension provided information for constructing the tension-tension and compression-compression quadvants of the plane-stress yield locus. Coordinate values were obtained from yield-strength measurements; the slope at each point was based on a plastic-strain ratio. The materials represented a wide range of plastic anisotropy, which was reflected in correspondingly varied departures of the yield locus from that for iso-tropy. The tension-tension and compression-compression quadrants were not identical. If the uniaxial yield strength is insensitive to direction and the sign of the applied stress, the Mises or perhaps the Tresca criterion is adequate for predicting the onset of yielding under combined-stress loading. The prediction is not so straightforward in plastically anisotropic material. Depending upon details of texture, combined-stress yielding resistance may be substantially different from that indicated by the usual criteria.' However. a continuum theory of yielding under such conditions is available for reasonably direct application.2,3 Whether or not it can be used successfully must, of course, depend upon how closely the conditions of the theory are satisfied in the material in question. In its present form the theory contains no provision for Bauschinger-type effects, nor does it allow for the consequences that might grow out of deformation by more than one mechanism, e.g., by slip and twinning.4 With those limitations, more importance must be attached to experimental information about the yield surface for anisotropic materials. Studies of the yield surface have generally been confined to states of plane stress (tension-tension and tension-compression) established in thin-wall tubes by externally applied forces and internal pressure. That approach would be entirely suitable for anisotropic materials if they were available in tube form or in sufficient bulk to be machined into test specimens. 6-9 It would not serve for the textured and anisotropic sheets of much current engineering interest, unless sheet could be formed into high-pressure tubing without structural change. Since there would seem to be little chance of the latter, practical alternatives are needed. One such alternative is the subject of this paper. It involves the use of a few selected but relatively simple uniaxial loading tests on sheet specimens. The underlying idea is presented here with some details relating to application and a few results bearing on how well it has worked. THE BASIS OF TESTING Conventional Measurements. Yielding for a general case of anisotropy is described by the plane-stress locus in Fig. 1. Reference directions in the sheet specimen are related to the stress coordinates as shown with the insert: x is the rolling direction, y the transverse direction, and z the through-thickness direction. The four reference-direction yield strengths (t, tension; c, compression), Xt, Xc, Yt, and Yc, are all different. Nine paths that can be followed in uniaxial loading experiments are identified. Paths 1, 2, 3, and 4 represent conventional tension and compression testing to establish Xt, Yt,.Xc, and Yc. Useful information also comes from the ratio of the transverse plastic-strain components associated with yielding and flow in conventional tension or compression. A condition to be satisfied in locus construction is that the plastic-strain vector be everywhere normal to the locus.10 The projection of the vector which would

Jan 1, 1967

By D. R. de Fontaine

By computing the values of the resolved shear stress for a great many orientations of the tensile axis on all 12 (111) <110> slip systems, Taylor and Elam&apos; were able to map out a stereogram of slip systems, given here, Fig. 1, in Diehl&apos;s notation (see, for example Hauser and Jackson&apos;). The purpose of the present note is to derive such a stereogram by mathematical reasoning and to give a simple method of defining the system with highest resolved shear stress for any direction of the tensile axis, thereby eliminating tedious computation of the Schmid factor. Let the tensile axis, of direction cosines [xyz], make the angles 0 and relative to the slip plane normal [HKL] and the slip direction [hkl] respectively. Fig. 2 shows a simple cubic cell whose edges define a Cartesian coordinate system. Let A be a unit vector of origin 0 supported by the tensile axis. Its end point [xyz] then lies on a sphere of unit radius, on the positive hemisphere of which the planes z = 0, x = y, y = z limit the so called primitive triangle of a standard [loo] stereographic projection. For any point of this triangle, the following hold: 0«2 «y *sx « 1 [l] Now, for given [xpz], the most highly stressed system will be the one for which the following expression of the Schmid factor has the largest possible value: (HKL) belonging to the form (111) and [hkl] to the form <110>, the denominator on the right hand side of Eq. [2] is equal to 1.fi.a. The unknowns H, ... h, . . . can now be determined by correctly distributing +1 and -1 to H, K, L, and +1, -1,O to h,k, 1 giving the numerator of Eq. [2] its greatest positive value (the angles 0 and cpare chosen acute) subject to the condition: Hh+Kk+Ll = 0 [3] since the slip direction must lie in the slip plane. Condition [3] can be satisfied only by having one of its terms vanish and the other two equal to +1 and -1. Taking the case of the tensile axis lying in the primitive triangle, x2y, z and therefore Hh will be chosen equal to +1 with H = h = +1 in order to retain a maximum of + signs. There remain two alternatives: either 1 = 0 or k = 0. 1) take 2 = 0 Then Kk = -1 and the numerator of [2] becomes: Retaining a maximum of + signs gives L = k = +1 and becomes: 2) take k = 0 Then L1 = -1and, likewise, the numerator of [2] becomes: xz - z2 + xy + yz [5] But the difference [5] - [4] can be written: (y - z)(x+y +z) [6] positive or zero by virtue of [I]. If [6] is positive (y > z), then the largest possible value for the numerator of [2] for any xyz inside the primitive triangle is given by [5], i.e., for: That is to say, the active slip system corresponding to an orientat:~on of the tensile axis inside the primitive triangle is:

Jan 1, 1962

By R. E. Reed-Hill

Recently Levine applied the Conrad-Wiedersich17 equation where H is the activation enthalpy, v the activation volume, T* the effective shear flow stress, T the absolute temperature, and ? the strain rate, to an analysis of titanium single-crystal data. The activation energy as a function of testing temperaturs obtained from specimens oriented for single (1010) prismatic slip is shown in Fig. 12. This diagram indicates a different linear dependence of H on T in the temperature interval from 220° to 300°K than from 0° to 220°K. Levine interpreted the break in this curve as indicating a change in the thermally activated mechanism controlling the flow stress. The purpose of this communication is to point out that the data in Fig. 1 is not consistent with the concept of a flow stress controlled by a simple thermally activated mechanism between 220° and 300°K. The Conrad-Wiedersich relation assumed that the strain rate can be expressed by:

Jan 1, 1968