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By Ming-Kao Yen

A considerable amount of work has been reported in the literature in regard to the texture and earing behavior of copper strip. The rolling texture of copper has been confirmed as (110) [112] and (112) [111], which yields ears of a drawn cup at the position 45" from the rolling direction.1-3 The recrystallization texture has been established as the cubic or (100) [001] texture, where the earing positions are at 0" and 90" to the rolling direction.4-8 It has also been reported that in the development of cubically aligned grains of copper strips, the percentage of this cubic texture increased with an increase of final reduction and final annealing temperature.8,9 A comprehensive study on H.C. copper (British commercial copper of high-conductivity quality = Cu 99.95 pct, O2 0.03 pct, Ag 0.003 pct, Fe 0.005 pct and Pb < 0.001 pct) was made by Cook and Richards.6 They concluded that the recrystallization textures could be described as one or more of the following textures: (1) a single texture (100) 10011, (2) a twin texture (110) [112] and (3) a random orientation, depending upon the previous history of the specimen concerned. The effect of various alloying additions in copper was reported by Dahl and Pawlek.10 They found that certain alloying additions, such as 5 pct Zn, 1 pct Sn, 4 pct Al, 0.5 pct Be, 0.5 pct Cd, or 0.05 pct P suppressed the formation of cubic texture. Brick, Martin and Angierll reported that the cold rolled textures due to various additions fitted a rather simple pattern. However, the recrystallization textures were subject to very considerable variations. In the discussion of this paper, Baldwin stated that deoxidized copper containing 0.02 pct P gave a complicated recrystallization texture at lower temperature. When this copper was annealed at high temperature, a single texture appeared which was described as (110) [ill] but. according to a pri- vate communication from Baldwin, this orientation reported was in error and should have been reported as (110)[112]. He also reported that the earing positions of drawn cups were at 60" to the rolling direction.12 Recently, Howald, in his discussion on the paper by Hibbard and Yen,13 reported that the rolling texture of phosphorus deoxidized copper, containing from 0.006 to 0.020 pct phosphorus, was of the pure copper type. When these coppers were annealed at lower temperatures, they exhibited a random orientation, and when they were annealed at higher temperatures they had a mixed (111)[110] and (100)[001] texture, depending on the severity of the final reduction and annealing temperature. However, the specific influence of phosphorus and other impurities on the recrystallization textures and the deep drawing properties of copper strip has not been thoroughly reported. Therefore, an attempt has been made in the present work to determine the rolling and recrystallization textures and also the earing behavior of five types of commercial copper and thereby to evaluate the effect of phosphorus and some other significant impurities on the development of texture for cold reductions of about 87 to 89 pct. Materials Used The five types of copper employed in the present investigation were two phosphorus deoxidized coppers of different phosphorus content (0.007 and 0.013 pct P), an oxygen-free copper (OFHC), an electrolytic tough-pitch copper, and a fire-refined tough-pitch copper. These materials were subjected to a thorough spectroscopic and chemical analysis. The designations and the chemical compositions were as shown in Table 1. The coppers, FA1, FA2 and FA3. were hot-forged from 3-in. billets into a ½ X 6-in. plate and cold rolled to the ready-to-finish gauge indicated below. FA4 and FA5 were hot rolled and scalped to ready-to-finish gauge. The grain size of all the materials in the ready-to-finish condition was about 0.030 to 0.045 mm. Table 2 shows the last stage of the production schedule for each copper strip used. Experimental Procedure ANNEALING, GRAIN SIZE AND HARDNESS DETERMINATIONS Specimens of each type of copper were finally annealed in air for periods of one hour at temperatures ranging from 300 to 1600°F and were subsequently cooled in air. The average grain diameter of the annealed specimen was estimated by comparing with a standard grain size chart. Hardness was determined on the Rockwell 15 T scale. CUPPING TESTS Cups were made in a blanking and drawing set, in which blanks of 2-in. diam were drawn to a cup of 1.25-in. diam with an average depth of about 0.75 in. The clearance between the punch and die was about 0.032 in. The ears of the cup were measured with a special fixture which read the height of ears to one-thousandth of an inch on every ten-degree interval along the circumference of the cup. POLE FIGURES The usual transmission diffraction method with unfiltered copper radiation was employed to determine the pole-figures of the specimens cold-rolled or annealed at 900°F. All the pole-figures were derived from the positions of intensity maxima on 111 diffraction rings of the X ray photo-grams taken at 10 rotation of a

Jan 1, 1950

By Bai Shiwie, Li. Guangyu

This paper presents the study in situ on stress field of rock mass in a large dam site. By means of two different measure instruments and the method of stress relief, a lot of measure in situ has been done, including stress measurement of three dimensions at ten points and two deep-hole stress measurements in the perpendicular boreholes which are 59.4m and 53m deep seperately, and the basic accordant results corresponding two methods have been got. In the process of the deep-borehole stress measurement we got the stress value in critical state in which cylindrical core would become core-disking in the high stress area, which was first got in the world. The maximum principal stress was up to 650 kg/cm2. The stress value obtained by test and the thickness of rock disks all basically accord to the analysis by mechanical mechanism of core-disking The plane linear elastic finite element analysis has been completed. Results of inverse calculation all ac- cord to the measurement results in four different positions. The whole outline of the stress field of dam site was delineated clearly.

Jan 1, 1982

By H. P. Greenwald

IN the year just passed the Coal Division&apos;s Committee on Rock-Dusting reviewed the status of this safety measure in American coal mines and prepared a paper thereon which will be presented at the February meeting of the Institute. This paper supplements one appearing in Vol. 139 of the "Transactions," page 87 (1940). Because that paper will be issued soon, only a summary is given herein.

Jan 1, 1944

By A. Gatti

A dispersion of AI2O3 was produced within chromium by the hydrogen reduction of a solid solution of Cr2U3-A1203. The yesulting powder. was compacted, extruded, and the material tested in tension at various temperatures and in creep at 1800°F. The material is ductile above 1200°F and is at least twice as strong as electrolytic chvomium at all temperatures. Its creep resistance, rupture strength, and ductility at 1800°F warrant further work to improve its Low -temperatutre properties. BECAUSE of its high melting point and excellent corrosion resistance, chromium has long been considered as a base for high-temperature alloys. Most chromium base alloys, however, are extremely brittle at low temperatures. Elements such as nickel and iron lower the melting point of chromium and thereby limit its high-temperature usefulness. Chromium-alumina materials made by othersl, 2 have shown good high-temperature creep resistance but poor ductility and thermal shock resistance. Pure ductile chromium3 is weak at high temperatures and reverts to a brittle state if exposed to nitrogenous atmospheres. In sintered aluminum powder (SAP)4 and internally oxidized alloys of silver, copper, and nickel, fine dispersions of oxide phases can control hardness, recrystallization, and yield stress. The possibility of formation of a ductile, high-strength material by precipitating dispersions of alumina in a chromium matrix appears worthy of investigation. MATERIAL Powder Production—Chromium oxide and alumina in amounts to produce a final alloy of Cr + 16 pct AI2O3 by weight were colloid milled, filtered, dried and high fired for 16 hr at 1600°C in air. The resulting solid solution of oxides was ball-milled to a fine powder and the chromium oxide reduced to chromium by heating in pure dry hydrogen for 64 hr at 1400°C. Final Materials Produced by Powder Metallurgy Techniques—-Chromium powder, containing a disper-sion of alumina, was pressed into 1 1/8-in. diam slugs at 25 tons per sq in. and sintered 16 hr at 1400° C in pure dry hydrogen. The sintered slugs were encased in a stainless steel can, 2 in. in diam, and extruded at 1200° C through a 1/2-in. die. The 16 to 1 extrusion ratio produced a final chromium-alumina rod 1/4 in. in diam about 30 in. long. Samples of the rod were plunge-ground to small rupture bars of 0.82-in. gage length with a 0.01-sq-in. cross section. RESULTS Microstructure Studies—Fig. 1 is the microstruc-ture of the material in the as-sintered condition while Fig. 2 is the microstructure of the material as-extruded. Comparison of the as-sintered and as-extruded micrographs show the redistribution and realignment of the alumina inclusions by the extrusion

Jan 1, 1961

By N. Tiner

In an article on magnesium and its alloys, Gann and Winston! stated that manganese has a limited solubility in the liquid state. W. Schmidt2 showed a diagram according to Joseph Ruhrmann indicating that the solubility of manganese in liquid magnesium falls from about 2.65 per cent at 790°C. to about 0.5 per cent at 675°C. The curve was extrapolated to show zero solubility at the melting point of pure magnesium (Fig. I). This work suggested that at the lowest manganese contents it was not possible to detect either a eutectic or the formation of a solid solution, so that manganese was stated to be present in the structure as large individual crystals. Two years after the presentation of, these results, Gann3 brought evidence to show that some manganese is capable of dissolving to form a solid solution, any excess of manganese present then assuming chiefly the form of small blue-gray particles scattered throughout the primary magnesium crystals, occasionally in clusters but seldom at the boundaries. He presented micrographs of cast alloys containing 0.1, 0.4 and 1.0 per cent manganese that show a small amount of coring around the individual particles due to solid solution, and indicate that the location of the manganese particles is closely associated with the original dendritic structure of the primary crystallization. He also pointed out that the amount of manganese that can be dissolved in magnesium depends on the amount of other alloying elements present, the effect of the second alloying element being to decrease the amount of manganese retained in the alloy. E. Schmid and G. Siebe14 have determined the solid solubility of manganese and its variation with temperature by means of precision X-ray diffraction measurements. They found that the solubility is 3.4 per cent at 645°C. and decreases to practically zero at 200°C. It is apparent that the X-ray diffraction measurements of Schmid and Siebel are not in agreement with the results of Ruhrmann as presented by Schmidt. This disagreement, and also the lack of data on magnesium-aluminum-manganese and magnesium-zinc-manganese systems, led the author to the present investigation, to determine accurately the liquid solubility of manganese and its variation with temperature. Experimental Method The experimental method for making solubility determinations consists of saturating the molten magnesium or the alloys with manganese at various temperatures and analyzing the dip samples taken from these melts. Melting is carried out in a cylindrical steel pot heated by an electric resistance furnace. The pot had a metallic outside coating to protect the steel against oxidation, and a graphite inside lining to prevent the contamination of the melt by prolonged contact with iron. The inside diameter of the pot was 4 in. and the depth 12 inches.

Jan 1, 1945

By M. L. Brashears

IN the last 15 years industrial use of ground water has more than doubled, and in 1951 amounted to 5 billion gallons per day. A similar sharp increase in the utilization of ground water for irrigation and public-water supply occurred in the same period. In many areas rapid increase in withdrawal from wells has taken place almost entirely unhampered by regulatory control and with little or no integration of effort. As might be expected, the chief interest in many regions has been maximum production rather than sustained perennial yield. As a result, widespread depletion of underground reservoirs and deterioration of the quality of the water stored in them has taken place in many areas, even though total pumpage in the United States is far below ultimate potential. Of even more concern is the fact that excessive withdrawal has drawn salt water into the reservoirs beneath many heavily populated centers along the Atlantic, Gulf, and Pacific coasts, causing costly abandonment of pumping plants.&apos; Many hydrologists expect that consumption of water will rise rapidly in the near future, and some predict that industrial requirements will more than double in the next decade.2,3 Thus it appears likely that the draft on many already heavily pumped underground reservoirs will be greatly increased and the search for additional sources of usable ground water intensified in years to come. In view of this, industry as a whole will be forced more and more to recognize the potentialities and limitations of ground-water reservoirs and to utilize them more effectively to prevent costly water shortages and disruption of production. Through painful experience, some industries are already well aware of the need for effective water utilization, and have managed individually or through joint effort to check trends threatening to deplete underground reservoirs completely or to impair the quality of the water. Various remedial measures have been used to bring about successful management of local or regional ground-water resources. Of these, replen-ishment of aquifers by recharge wells or basins has played an important role in overcoming some ground water problems. Artificial recharge of underground reservoirs by water spreading has been practiced successfully in the United States for many years. In the West it has become an important method of salvaging flood run-off for irrigation of crops and maintenance of public water-supply reserves, and it is used to some extent in parts of the East. Artificial recharge by means of wells, on the other hand, is a relatively new development. Until recently it was employed in only a few areas, principally along the East coast. For the last few years, in the ever increasing search for additional water supplies, industry has had greater recourse to this method. Utilization of recharge wells to control the temperature and quality of underground water supplies is also being considered seriously. Operation of recharge wells, like water spreading, is governed largely by local conditions. It requires water relatively low in turbidity, whereas in some areas water spreading has been used successfully with water of high turbidity and silt content. However, water spreading must be employed in large areas and can be carried on effectively only where aquifers crop out at the surface. Recharge wells can be used in limited space. Recharge wells are similar to production wells except that the water flows in the opposite direction. Thus any water-bearing bed that will yield water to wells may be recharged by wells. Often, however, the water available for recharge is of a different character and temperature from that existing in the ground-water reservoir and if transmitted directly underground from a recharge well to a production well might require expensive or difficult treatment before it could be used. Fortunately the physical characteristics of reservoir beds, which control the movement and behavior of ground water, are generally not homogeneous. Moreover, the movement of ground water is very slow because of the frictional resistance of the reservoir beds. By taking full advantage of hydrologic and geologic conditions, it is therefore possible in many instances to bring about favorable changes of temperature and dilution as the water moves from the recharge wells underground to the production wells. Furthermore, if the natural quality or temperature of ground water is unfavorable for industrial purposes, recharge wells may be used to introduce water of more favorable quality or temperature into the ground-water reservoir. When water is discharged into a recharge well, the head in the well is increased. Because of this, a cone of elevation is produced on the water table or the artesian pressure surface in the area surrounding the well. The cone of elevation is similar to the cone of depression produced around a pumping well except that the apex of the cone is above the water table or artesian pressure surface. Thus if a recharge well and a production well tapping the same water-bearing bed are close together, as would be the case at many industrial plants, some of the water discharged from the recharge well would be drawn into the production well within a short time. Under such conditions it is apparent that water of unfavorable temperature and chemical characteristics should not be used for recharging. The more important ground-water reservoirs in the United States often consist of alternating layers of impermeable beds and porous material that will yield water readily to wells. Physical characteristics of individual beds in a ground-water reservoir may not persist over great distances, the impermeable layers grading into beds that will yield large quantities of water. Thus the water-yielding material in underground reservoirs, whether large or small,

Jan 1, 1954

By Fred C. Bond

MOST investigators are aware of the present unsatisfactory state of information concerning the fundamentals of crushing and grinding. Considerable scattered empirical data exist, which are useful for predicting machine performance and give, acceptable accuracy when the installations and materials compared are quite similar. However, there is no widely accepted unifying principle or theory that can explain satisfactorily the actual energy input necessary in commercial installations, or can greatly extend the range of empirical comparisons. Two mutually contradictory theories have long existed&apos; in the literature, the Rittinger and Kick. They were derived from different viewpoints and logically lead to different results. The Rittinger theory is the older and more widely accepted. In its first form, as stated by P. R. Rittinger, it postulates that the useful work done in crushing and grinding is directly proportional to the new surface area produced and hence inversely proportional to the product diameter. In its second form it has been amplified and enlarged to include .the concept of surface energy; in this form it was precisely stated by A. M. Gaudin2 as follows: "The efficiency of a comminution operation is the ratio of the surface energy produced to the kinetic energy expended. According to the theory in its second form, measurements of the surface areas of the feed and product and determinations of the surface energy per unit of new surface area produced give the useful work accomplished. Computations using the best values of surface energy obtainable indicate that perhaps, 99 pct of the work input in crushing and grinding is wasted. However, no method of comminution has yet been devised which results in a reasonably high mechanical efficiency under this definition. Laboratory tests have been reported&apos; that support the theory in its first form by indicating that the new surface produced in. different grinds is proportional to the work input. However, most of these tests employ an unnatural feed consisting either of screened particles of one sieve size or a scalped feed which has had the fines removed. In these cases the proportion of work" done on. the finer product particles is greatly increased and distorted beyond that to be expected with a normal feed containing the natural fines. Tests on pure crystallized quartz are likely to be misleading since it does not follow the regular breakage pattern of most materials but is relatively harder to grind at the finer sizes, as will be shown later. This theory appears to be indefensible mathematically, since work is the product of force multiplied by distance, and the distance factor (particle deformation before breakage) is ignored. The Kick theory&apos; is based primarily upon the stress-strain diagram of cubes under compression, or the deformation factor. It states that the work required is proportional to the reduction in volume of the particles concerned. Where F represents the diameter of the feed particles and P is the diameter of the product particles, the reduction ratio Rr is F/P, and according to Kick the work input required for reduction to different sizes is proportional to log Rr/log 2.5 The Kick theory is mathematically more tenable than the Rittinger when cubes under compression are considered, but it obviously fails to assign a sufficient proportion of the total work in. reduction to the production of fine particles. According to the Rittinger theory as demonstrated by the theoretical breakage of cubes the new surface produced, and consequently the useful work input, is proportional to Rr-1.5 If a given reduction takes place in two or more stages, the overall reduction ratio is the product of the Rr values for each stage, and the sum of the work accomplished in all stages is proportional to the sum of each Rr-1 value multiplied by the relative surface area before each reduction stage. It appears that neither the Rittinger theory, which is concerned only with surface, nor the Kick theory, which is concerned only with volume, can be completely correct. Crushing and grinding are concerned both with surface and volume; the absorption of evenly applied stresses is proportional to the volume concerned, but breakage starts with a crack tip, usually on the surface, and the concentration of stresses on the surface motivates the formation of the crack tips. The evaluation of grinding results in terms of surface tons per kw-hr, based upon screen analysis, involves an assumption of the surface area of the subsieve product, which may cause important errors. The&apos;evaluation in terms of kw-hr per net ton of 200 mesh produced often leads to erroneous results when grinds of appreciably different fineness are compared, since the amount of -200 mesh material produced varies with the size distribution characteristics of the feed. This paper is concerned primarily with the development, proof, and application of a new Third Theory, which should eliminate the objections to the two old theories and serve as a practical unifying principle for comminution in all size ranges. Both of the old theories have been remarkably barren of practical results when applied to actual crushing and grinding installations. The need for a new satisfactory theory is more acute than those not directly concerned, with crushing and grinding calculations can realize. In developing a new theory it is first necessary to re-examine critically the assumptions underlying

Jan 1, 1952

By Robert W. Zimmerman

POROUS SOLID COMPRESSIBILITIES There are four different compressibilities associated with porous solids, each relating the fractional change in either bulk volume or pore volume with the change in either pore pressure or confining pressure. These will be referred to as Cbc, Cbp, Cpc, and Cpp, with the first subscript denoting the relevant volume, and the second subscript denoting the relevant pressure. They are defined as: [ ] Note that minus signs are included in two of the definitions so that each of the compressibilities will always have a positive value. In general, each compressibility depends on the elastic moduli of the matrix material, the porosity, and the exact geometry of the pores. Taking the latter factor into account calls for separate analysis for each different pore shape, which of course can only be attempted for a few relatively simple cases. But lower bounds for each of the four compressibilities can be found, independant of pore structure, in terms of only the porosity (0) and the elastic moduli of the matrix material (any pair chosen from K, E, G and V). The first step is to find relationships between the four compressibilities, starting with the following observation: If a porous solid made of a linear elastic, isotropic and homogeneous matrix material is subjected to uniform hydrostatic pressure of magnitude P on its external and all of its internal (pore) surfaces, the state of stress in the solid will be exactly the same as that which would occur

Jan 1, 1982

By J. R. Cahoon, W. V. Youdelis

In a recent publication by Flemings and Nereo, equations for the calculation of the solute distribution in castings were developed, and the solute distributions for unidirectionally solidified A1-4.5 pct Cu ingots cast under various thermal conditions were calculated. The equations derived by Flemings and Nereo for the dendrite "expansion" and "steady-state" zones are essentially equivalent to those previously published by Kirkaldy and Youdelis, 16 for, although the flow velocity cooling rate, and temperature gradients appear in the fundamental differential equations, calculation of the solute distribution requires that the above be explicitly related to the assumed or measured solid-liquid mass distributions during solidification. In the treatment of Kirkaldy and Y-oudelis the mass distributions are simply assumed or measured without any prior and explicit association of the mass distributions to a velocity parameter. The treatment of Flemings and Nereo permits solidification conditions more complicated than the simple unidirectional case to be considered (although in principle the treatment of Kirkaldy and Youdelis could also be extended to include the more general solidification case); however, we note some limitations in the treatment of Flemings and Nereo, and the purpose of this discussion is to point these out and also to indicate those points of similarity in the mass distribution models used which make the two treatments equivalent. Both the Kirkaldy-Youdelis and Flemings-Nereo treatments consider a zone of dendrite "expansion" followed by a "steady-state" zone. However, Flemings and Nereo have failed to consider a zone of "collapse" which begins at the base of the first dendrites to reach the top of the ingot. The omission of this zone of "collapse" results in too high a value for the solute concentration in the latter portion of the ingot to solidify and the conservation of total solute is not possible. In the zone of "collapse" the solute concentration rapidly decreases, which may be accounted for as follows: consider a mushy zone of length X,, shown schematically in Fig. 11 (a), which develops at the chill face and then moves as a steady-state configuration along the length of a solidifying ingot. The solute distribution in this zone, when it first attains the steady state, is shown qualitatively in Fig. 11(b). The segregation is positive (above Co) in the region ab because this region contains primary dendritic solid, ranging from kco to kcE in composition (where k is the partition coefficient and CE is the composition of the eutectic liquid), and liquid metal near eutectic composition. The segregation is negative (below Co) in the region bc because it contains primary dendritic solid only slightly above kco in average composition and liquid metal only slightly above Co in composition. As the zone X, moves as a steady state

Jan 1, 1969

By Fred C. Bond

MOST investigators are aware of the present unsatisfactory investigatorsstate of information concerning the fundamentals of crushing and grinding. Considerable scattered empirical data exist, which andare useful for predicting machine performance and give acceptable accuracy when the installations and materials compared are quite similar. However, there is no widely accepted unifying principle or theory that can explain satisfactorily the actual energy input necessary canexplain commercial installations, or can greatly extend the range of empirical comparisons. Two mutually contradictory theories have long existed in the literature, the Rittinger and Kick. They were derived from different viewpoints and logically lead to different results. The Rittinger theory is the older and more widely accepted.&apos;TheRittinger In its first form, as stated by P. R. Ritted.&apos;tinger, it postulates that the useful work done in crushing and grinding is directly proportional to the new surface area produced and hence inversely proportional to the product diameter. In its second form it has been amplified and enlarged to include the concept of surface energy; in this form it was precisely stated by A. M. Gaudin&apos; as follows: "The efficiency of a comminution operation is the ratio of the surface energy produced to the kinetic energy expended." According to the theory in its second form, measurements of the surface areas of the feed and product and determinations of the surface energy per unit of new surface area produced give the useful work accomplished. Computations using the best values of surface energy obtainable indicate that perhaps 99 pct of the work input in crushing and grinding is wasted. However, no method of comminution has yet been devised which results in a reasonably high mechanical efficiency under this definition. Laboratory tests have been reported- hat support the theory in its first form by indicating that the new surface produced in different grinds is proportional to the work input. However, most of these tests employ an unnatural feed consisting either of screened particles of one sieve size or a scalped feed which has had the fines removed. In these cases the proportion of work done on the finer product particles is greatly increased and distorted beyond that to be expected with a normal feed containing the natural fines. Tests on pure crystallized quartz are likely to be misleading, since it does not follow the regular breakage pattern of most materials but is regularrelativelybreakage harder to grind patternat the finer sizes, as will be shown later. This theory appears to be indefensible mathematically, since work is the product of force multiplied by distance, and the distance factor (particle deformation before breakage) is ignored. The Kick theory4 is based primarily upon the stress-strain diagram of cubes under compression, or the deformation factor. It states that the work required is proportional to the reduction in volume of the particles concerned. Where F represents the diameter of the feed particles and P is the diameter of the product particles, the reduction ratio Rr is F/P, and according to Kick the work input required for reduction to different sizes is proportional to log Rr /log 2." The Kick theory is mathematically more tenable than the Rittinger when cubes under compression are considered, but it obviously fails to assign a sufficient proportion of the total work in reduction to the production of fine particles. According to the Rittinger theory as demonstrated by the theoretical breakage of cubes the new surface produced, and consequently the useful work input, is proportional to Rr-l.V f a given reduction takes place in two or more stages, the overall reduction ratio is the product of the Rr values for each stage, and the sum of the work accomplished in all stages is proportional to the sum of each Rr-1 value multiplied by the relative surface area before each reduction stage. It appears that neither the Rittinger theory, which is concerned only with surface, nor the Kick theory, which is concerned only with volume, can be completely correct. Crushing and grinding are concerned both with surface and volume; the absorption of evenly applied stresses is proportional to the volume concerned, but breakage starts with a crack tip, usually on the surface, and the concentration of stresses on the surface motivates the formation of the crack tips. The evaluation of grinding results in terms of surface tons per kw-hr, based upon screen analysis, involves an assumption of the surface area of the subsieve product, which may cause important errors. The evaluation in terms of kw-hr per net ton of —200 mesh produced often leads to erroneous results when grinds of appreciably different fineness are compared, since the amount of —200 mesh material produced varies with the size distribution characteristics of the feed. This paper is concerned primarily with the development, proof, and application of a new Third Theory, which should eliminate the objections to the two old theories and serve as a practical unifying principle for comminution in all size ranges. Both of the old theories have been remarkably barren of practical results when applied to actual crushing and grinding installations. The need for a new satisfactory theory is more acute than those not directly concerned with crushing and grinding calculations can realize. In developing a new theory it is first necessary to re-examine critically the assumptions underlying

Jan 1, 1953

By Fred C. Bond

MOST investigators are aware of the present unsatisfactory investigatorsstate of information concerning the fundamentals of crushing and grinding. Considerable scattered empirical data exist, which andare useful for predicting machine performance and give acceptable accuracy when the installations and materials compared are quite similar. However, there is no widely accepted unifying principle or theory that can explain satisfactorily the actual energy input necessary canexplain commercial installations, or can greatly extend the range of empirical comparisons. Two mutually contradictory theories have long existed in the literature, the Rittinger and Kick. They were derived from different viewpoints and logically lead to different results. The Rittinger theory is the older and more widely accepted.&apos;TheRittinger In its first form, as stated by P. R. Ritted.&apos;tinger, it postulates that the useful work done in crushing and grinding is directly proportional to the new surface area produced and hence inversely proportional to the product diameter. In its second form it has been amplified and enlarged to include the concept of surface energy; in this form it was precisely stated by A. M. Gaudin&apos; as follows: "The efficiency of a comminution operation is the ratio of the surface energy produced to the kinetic energy expended." According to the theory in its second form, measurements of the surface areas of the feed and product and determinations of the surface energy per unit of new surface area produced give the useful work accomplished. Computations using the best values of surface energy obtainable indicate that perhaps 99 pct of the work input in crushing and grinding is wasted. However, no method of comminution has yet been devised which results in a reasonably high mechanical efficiency under this definition. Laboratory tests have been reported- hat support the theory in its first form by indicating that the new surface produced in different grinds is proportional to the work input. However, most of these tests employ an unnatural feed consisting either of screened particles of one sieve size or a scalped feed which has had the fines removed. In these cases the proportion of work done on the finer product particles is greatly increased and distorted beyond that to be expected with a normal feed containing the natural fines. Tests on pure crystallized quartz are likely to be misleading, since it does not follow the regular breakage pattern of most materials but is regularrelativelybreakage harder to grind patternat the finer sizes, as will be shown later. This theory appears to be indefensible mathematically, since work is the product of force multiplied by distance, and the distance factor (particle deformation before breakage) is ignored. The Kick theory4 is based primarily upon the stress-strain diagram of cubes under compression, or the deformation factor. It states that the work required is proportional to the reduction in volume of the particles concerned. Where F represents the diameter of the feed particles and P is the diameter of the product particles, the reduction ratio Rr is F/P, and according to Kick the work input required for reduction to different sizes is proportional to log Rr /log 2." The Kick theory is mathematically more tenable than the Rittinger when cubes under compression are considered, but it obviously fails to assign a sufficient proportion of the total work in reduction to the production of fine particles. According to the Rittinger theory as demonstrated by the theoretical breakage of cubes the new surface produced, and consequently the useful work input, is proportional to Rr-l.V f a given reduction takes place in two or more stages, the overall reduction ratio is the product of the Rr values for each stage, and the sum of the work accomplished in all stages is proportional to the sum of each Rr-1 value multiplied by the relative surface area before each reduction stage. It appears that neither the Rittinger theory, which is concerned only with surface, nor the Kick theory, which is concerned only with volume, can be completely correct. Crushing and grinding are concerned both with surface and volume; the absorption of evenly applied stresses is proportional to the volume concerned, but breakage starts with a crack tip, usually on the surface, and the concentration of stresses on the surface motivates the formation of the crack tips. The evaluation of grinding results in terms of surface tons per kw-hr, based upon screen analysis, involves an assumption of the surface area of the subsieve product, which may cause important errors. The evaluation in terms of kw-hr per net ton of —200 mesh produced often leads to erroneous results when grinds of appreciably different fineness are compared, since the amount of —200 mesh material produced varies with the size distribution characteristics of the feed. This paper is concerned primarily with the development, proof, and application of a new Third Theory, which should eliminate the objections to the two old theories and serve as a practical unifying principle for comminution in all size ranges. Both of the old theories have been remarkably barren of practical results when applied to actual crushing and grinding installations. The need for a new satisfactory theory is more acute than those not directly concerned with crushing and grinding calculations can realize. In developing a new theory it is first necessary to re-examine critically the assumptions underlying

Jan 1, 1953

By E. C. Pechin

AT the suggestion of some members of the Institute, attention is called to the record of the working of Dunbar Furnace during the twelve months ending in January, 1874. During this period, with a product of over eleven thousand gross tons, not a single ton of

Jan 1, 1874

By George C. Heikes

ALTHOUGH the application of light metals in war materiel increased during the year, based on the number of uses, the trend in aluminum and magnesium production in 1944 was characterized by a sharp decline in the production of both metals accompanied by a further accumulation of large Government reserve stocks. Several primary reduction plants were curtailed to prevent building excessive inventories. By the end of the year, however, a lively revival of war production took place when resistance stiffened on the western front in Europe. Production of primary aluminum ingot was reduced from over 90,000 tons per month at the start of the year to 45.000 tons per month by the end of the year.

Jan 1, 1945

By J. M. Seeman, R. A. Dodd

If some solution-quenched supersaturated aluminum solid solutions, e.g.., Al(Cu), are plastically deformed at room temperature and then aged at 200oC, the hardness may first decrease before increasing in the usual manner &apos; A similar transient softening is observed, even in the absence of plastic deformation, when a thin foil or small-diameter wire Al(Cu) specimen is rapidly quenched from the solution-treatment temperature and then aged.&apos; Also, some solution-quenched and neutron-irradiated alloys undergo an initial hardness decrease during subsequent aging.3 The usual explanation of the transient softening in the above examples involves the effect of vacancies introduced by plastic deformation, rapid quenching, and neutron irradiation, respectively However, the mechanism of softening is not unequivo-cably established. In the first-noted case, Gane and parkins&apos; observed that the softening was approximately proportional to the difference in the atomic diameters of solute and solvent, and it was argued that, if a large relative difference in atomic diameter promoted vacancy-assisted room-temperature solute diffusion to dislocations, dislocation climb occurring during subsequent aging at 200°C could cause transient softening. Some substantiation of this theory was offered by the additional observation that discontinuous yielding of solution-quenched polycrystalline Al(Cu) tensile specimens was suppressed by interrupting the test for a short aging treatment at 200°C. Of course, reversion (resolution of GPI) at 200°C would also cause softening, and Sil-cock4 expressed the opinion that the softening in the case of Al(Cu) must be partly associated with reversion. Also, Hirsch5 commented on the possibility that, if jogs cause hardening, an anneal at 200°C should straighten the jogged dislocations and result in softening. However, parkins&apos; has re-expressed his belief that these mechanisms are not entirely consistent with the observed serrated stress-strain curves. Experimental. New data has now been obtained for Al(Cu), Al(Ge), Al(Mg), and Al(Zn) primary solid-solution alloys. These alloys were prepared from metals exceeding 99.99 pct purity, and specimens 4 by 4 in. diam were solution-treated, quenched, deformed 10 pct in compression at room temperature, and aged at 200&apos;C in a cottonseed oil bath for various times. Generally, these operations could not be carried out in rapid succession, so the alloys were stored in a freezer between treatments to minimize aging. The variation in hardness with aging time, Figs. 1 to 4, was determined by microhardness testing with a 3.0-kg load. At least five readings were averaged to obtain each data point, and all measurements were taken about the center circumference of each cylinder (region of maximum deformation). Each specimen was used to obtain only one data point, i.e., specimens were not replaced in the aging bath after measurements were made. In

Jan 1, 1968

Jan 1, 1932

By A. D. Taylor

In recent years there has been an increasing effort to attract students into engineering. Obviously, the effort is necessary because young people find the image of the engineer unattractive. Some of the things they find unattractive are real, some are not, and part of the problem is too little knowledge of the field. First, I would like to comment on some of the ideas which appear to be justified. Engineering is a difficult course of study. True, and nothing can or should be done to change this. The education is continually being improved, but it is unlikely to be made easier.

Jan 1, 1970

Jan 1, 1902

By D. J. Schmatz, H. I. Aaronson, H. A. Domian

Diffusion kinetics in disordered hcp Cd-Mg alloys have been investigated by means of the Kirkendall effect and concentration-penetration curves determined with an electron-microprobe analyzer. Self-diffusion coefficients of both species were determined at the three marker compositions obtained, averaging 27.6, 46. 7, and 78.1 at. pct Mg, by means of the Darken analysis. These coefficients were then corrected for the unequal and concentration-dependent partial molar volumes of the two elements with the Balluffi analysis, and for the vacancy flux effect by the Manning analysis. The latter correction reduced the Balluffi correction produced larger changes in the self-diffusiv-ities; neither, however, produced statistically significant changes in the Do&apos;s or the H&apos;S. The most striking result of this investigation is that at all three compositions and at all temperatures studied both the uncorrected and corrected self-difjusivities of magnesium are higher than those of cadmium. The Cd-Mg system is the first one found in which the higher melting, lower vapor pressure element diffuses more rapidly. Both an empirical correlation due to Toth and Searcy and considerations of the atomic mechanism of diffusion indicate that this anomaly is probably due to a comparatively low value of the activation energy required for a magnesium atom and a vacancy to exchange sites, perhaps occasioned by the higher compressibility of magnesium atoms. KIRKENDALL effect studies have been previously reported for only two hcp solid solutions: the E phase of the Zn-Cu system1 and the a phase of the Cd-Hg system.&apos; In neither investigation were the marker-movement studies supplemented with the concentration-penetration curve determinations necessary to evaluate self-diffusivities by means of the atano and the Darken analyses. The present program was undertaken to obtain both types of data on a hexagonal solid solution in order to provide more detailed information relevant to the mechanism of diffusion in this type of lattice. The Cd-Mg system was chosen for this study because the disordered solid solution extends across the entire phase diagram at temperatures above 253"c5 and the substantial difference in the melting points of the component pure metals promised that marker movements would occur at reasonably rapid rates should the diffusivities of the two species be as unequal as might be anticipated. The experimental convenience of the relatively low melting points of cad-miun and magnesium and the availability of extensive and accurate activity data6 (required for application of the Darken analysis) were additional reasons for selecting this alloy system. Since the anisotropy of diffusion is not large in either pure cadmium7 or pure magnesium,&apos; the diffusion couples were prepared from polycrystalline components. The presence of a well-defined texture in the couples—the c axis of individual crystals tended to be normal to the diffusion direction— however, provides a fair degree of crystallographic definition to the data obtained. The principal (and entirely unexpected) finding of this investigation, that magnesium, the high-melting low-vapor pressure element, diffuses more rapidly than cadmium, in contradiction to a broad range of results in fcc and bcc alloys, as well as in the previously studied hcp alloys,172 makes the self-diffusivity determinations of immediate interest in understanding the origin of this anomalous result. EXPERIMENTAL PROCEDURE The cadmium (Belmont Smelting and Refining Co.) and magnesium (Dow Chemical Co.) used in this study were both of 99.99 pct purity. Alloys containing 51.0 and 65.6 at. pct Mg were prepared from these materials by melting under a MgC12-base flux in a high-purity graphite crucible. These alloys were subsequently hot-worked and then homogenized in a helium atmosphere at temperatures close to their solidus points. Sandwich-type diffusion couples of the type g/d/g were prepared from the pure metals by solid-state diffusion. Two-piece alloy couples of Mg/65.5 at. pct Mg (Mg/gCd) and Cd/51.0 at. pct Mg (Cd/CdMg) were welded by a liquation technique. The individual components of both types of couple were initially cylinders 1.27 cm in diam and in length; the ends of these cylinders were machined accurately flat and parallel. For both welding techniques, the pure cadmium cylinders and the alloys were chemically polished in a mixture of 40 pct ethyl alcohol, 40 pct hydrogen peroxide (30 pct conc), and 20 pct nitric acid,g while those of pure magnesium were polished in a solution of 10 pct nitric acid in ethyl alcohol.&apos; Immediately afterwards, both metals were rinsed in freshly distilled acetone, and then in similarly purified methanol.&apos; The Mg/Cd/g couples were assembled in a carefully cleaned stainless-steel welding fixture, in which a screw operating through a self-centering arrangement permitted a controlled pressure to be exerted upon a couple prior to welding.&apos;&apos; Tungsten marker wires 0.005 cm in diam were placed at the d:g interfaces of some of these couples, and imbedded in the couples during the application of pressure. As soon as a couple had been assembled, the welding fixture was inserted into a Pyrex capsule containing a packet of zirconium chips at each end. The capsule

Jan 1, 1967

By A. G. Preban, R. J. De Angelis, J. B. Cohen, P. Gordon, D. C. Brillhart

Changes in stored energy, resistivity, density, X-ray line broadening, and dislocation arrangements (from transmission electron microscopy) have been mensured on copper specimens shock-loaded at 75 to 435 kbars. The stored energy in shock-loaded copper and changes in density and resistivity are larger than those after conventional deformation. A high density of twins makes an appreciable contribution to all the measured quantities. Dislocation densities rise to values of 1011 lines per sq cm at the highest pressure. The resistivity, density, and X-ray In a study of the effects of shock loading on copper, changes in stored energy, resistivity, density, hardness, lattice parameter, line broadening, and dislocation structure have been examined after subsequent annealing of specimens shocked to various pressures. This paper presents certain aspects of the data, taken by two groups, one at the Illinois Institute of Technology, and the other at Northwestern University, and compares the changes in these properties, and what they indicate about the effects of shock deformation. measurements yield dislocation densities in substantial agreement at all pressures, after correcting for the effects due to the twins. At the higher pressures, electron microscopy yields dislocation densities that are lower by a factor of about 5 to 10. Dislocation densities from stored -energy measurements are high; this finding can be rationalized by the consideration that the deformation twin boundaries present are largely incoherent. There is no evidence for homogeneous dislocation nucleation during shock loading. Shock loading any metal or alloy, such as copper, causes a large increase in yield strength, with dimensional changes of the order of only a few percent."&apos; Other properties have not been extensively studied, but this result clearly indicates the importance of examining the substructure. Previous studies of the substructure of conventionally deformed specimens have been made using electron microscopy,3-6 X-ray diffraction,7,8 and etch pitting.9,10 The dislocation density can reach values of about 10" per sq cm; and the dislocations are arranged in cells approximately 0.15 in size. The substructure varies widely, however, from point to point in the specimen. The substructure of explosively loaded copper consists of cells of about the same dimensions6,11 but their size is more uniform.6 Profuse twinning occurs12,13 and the twins are often too small to be detected optically.6,13 The boundaries outlining these twins appear to be incoherent.14 There is now ample evidence 13-15 that twinning is a strengthening mechanism in fcc metals but this is only part of the strengthening effect in shock-loaded copper.* From the twinning systems which operate in shock-loaded single crystals,13 and from changes in texture on shock loading,17 it has been shown that both the

Jan 1, 1968

By J. E. Hanlon, S. R. Butler, R. J. Wasilewski

The temperature, orientation, and strain-rate dependence of tensile flow in single-crystal NiA1 of equiatomic composition have been investigated up to 800°C. Compression tests at room temperature have also been carried out. Optical and replica electron microscopy and X-ray diffraction methods were used to investigate the slip mechanisms. NiAl exhibits {110)(001) slip and cube slip {l00)(010) was also observed. This results in very high strength of single crystals in cube orientation. The implications of this slip mode, with the resultant small number of possible slip systems and three mutually perpendicular slip vectors, are discussed. ThE CsCl structure compounds represent a class related to the bcc elements, but their behavior is affected by three additional variables: composition (within the stability range of the compound), extent of long-range order perfection, and bonding energy. Very little data are available on the effects of these variables on mechanical properties. Rachinger and ~ottrell&apos; suggested slip to occur along (111) in compounds of low ordering energy; in compounds of higher bond strength (>0.06 ev), they observed (110) (001) slip. As pointed out by copley,&apos; only three in- dependent slip systems are available in the latter case; hence general deformation is impossible. Brown3 carried out a theoretical calculation of the yield-point variation with the degree of long-range order in the CsCl structure, based on the assumption of superdislocations. More general approaches, based on considerations of superlattice dislocations and antiphase domain boundaries in ordered structures, were carried out by Flinn~ and by Vidoz and Brown.&apos; These, however, give no information on changes in the slip structure—if any—between the ordered and the disordered compounds. This aspect was investigated experimentally and theoretically by Stoloff and Davies&apos; and by Marcinkowski and chessin7 in FeCo. The latter workers proposed the deformation behavior of the ordered FeCo to be essentially the same as that in many other bcc metals. Investigations of polycrystalline A~M~&apos;-&apos;O indicate considerable variation in mechanical properties with composition and test temperature. The existence of {123)(111) slip was reported in AgMg.&apos;9&apos;9&apos;0 (The formation energy of this compound, presumed to be ordered at all temperatures below melting, is 4.38 cal per g-atom," i.e., 0.024 ev per bond.) The yield strength has been reported as relatively independent of temperature below 0.45 T, (where T, is the absolute melting temperature). Tensile deformation of single-crystal AgMg was also investigated by Kurf-man," who observed marked tendency to single glide on{112}(111) and {110)(111). From observations of slip lines in deformed poly-crystalline NiA1, Westbrook et a1.I3 suggested the

Jan 1, 1968