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By F. J. Schuh

The drilling industry long has been plagued by failures in the bottom few joints of surface and intermediate casing strings. This paper presents an analysis of the various possible causes of failure and concludes that failures are caused by short-lived, high-energy torque impulses delivered from the drill string through the bit while drilling out the cementing plugs, cement and floating equipment. The magnitude of these torque impulses is shown to be a function of the rotational momentum of the drill string, and a method is derived to calculate the magnitude of these impulses. The available methods of strengthening the bottom joints are reviewed. It is concluded that, while present methods are ineffective, a combination of improved procedures for strengthening and minor restrictions on drillout practices will prevent failures. Introduction In most cases, failure in the bottom few joints of casing strings is not discovered until electric logs record that the bottom one, two or three joints have parted from the casing string and slipped down the hole. However, in some cases the parted section of casing uncovers a high-pressure or lost circulation zone, or shifts laterally restricting the passage of drilling equipment. In these instances extensive remedial work is required to realign the parted pieces and seal the exposed formations. Several methods used to strengthen the bottom joints of casing strings include locking set screws in the couplings, putting wedges in special collars, welding straps across the couplings, welding the couplings and, most recently, using epoxy resin-based, thread-locking compounds. Since none of these techniques has eliminated the problem, this study was initiated to find the cause of failures and to evaluate the available methods of prevention. Mechanics of Casing Failures An analysis of the various possible causes of failure indicates that the casing is unscrewed rather than broken and that therefore failure must occur before the shoe is drilled. Since there is no general agreement as to the causes of casing failure, some possible mechanisms were ATLANTIC RICHFIELD CO. DALLAS, TEX. considered in this analysis. Failure of the bottom joints of casing can occur by only one of three types of stress: tension, torsion or bending. The possible mechanisms of failure were evaluated by determining the forces required to cause casing failure by each of the stresses; and, where applicable, the possibility of failure by fatigue was considered. For casing to part under tension requires a downward load of more than the tensile strength of the casing. The lightest API weight H-40 grade casing requires a bit load on the bottom of the casing of 27,000 to 34,000 Ib per inch of bit diameter (Table 1). Since maximum drill collar weights seldom exceed 10,000 Ib per inch of bit diameter, it is apparent that casing strings cannot be parted by the downward load of the drill string. The second mechanism considered was failure by bending. This mechanism requires that the lowermost casing joints be free to be deflected laterally until the bending stress exceeds the strength of the pipe. To fail, the casing (at a height L above the shoe) requires a force and deflection' at the shoe of To deflect the casing shoe with the drill string obviously requires a dog-leg at the casing shoe. This dog-leg must have a rate of change equal to or greater than the change in curvature of the deflected casing, which is given by

Jan 1, 1969

By W. B. Mather

R. G. Wuerker (University of Illinois, Urbana)—Mr. Mather is to be congratulated for stressing the most urgent need for a program of testing the physical properties of rocks, as they are encountered by the petroleum engineers on their drilling jobs and by the miners on their excavating, roof control and mineral preparation tasks. Another valuable source of information is the Handbook of Physical Constants.22 It stresses the physicist's approach rather than the engineer's procedure. The study of hardness, and rock hardness in particular, is beset with many difficulties. There is no satisfactory definition of hardness yet, and the term hardness is used to describe a number of quite dif- ferent properties. Hardness tests are grouped into static and dynamic determinations. They should be expressed with reference to the mechanical action of the applied force, like indentation hardness, scratch hardness, abrasion hardness, rebound hardness. A discussion of all these various hardness tests and of the special difficulties encountered in hardness testing of such heterogeneous material as rocks is given in the U. S. Bureau of Mines' standard proposal. The more critical student may be referred to the book by D. Landau: Hardness, which is in my opinion the best existing treatise on this subject.

Jan 1, 1952

By R. L. Templin, D. A. Paul

The modulus of elasticity is defined as the ratio of stress within the proportional limit to corresponding strain. This property, as thus defined, is a constant for each kind of material; and in tension or compression is usually designated by the symbol E. The modulus of elasticity serves as an index of the stiffness of a material or a measure of its ability to resist change of shape under stresses not higher than the proportional limit. In view of the frequency with which the modulus of elasticity is used in engineering calculations, it is surprising to note the uncertainty that exists as to authentic values, and the marked lack of published information relating to the variation of the constant E within individual alloy systems. A value of 10,000,000 Ib. per sq. in. has been quoted as representative of aluminum and its alloys. This value has been found to be approximately corrcct for pure aluminum and aluminum alloys in which the total percentage of the alloying elements is low, but seriously in error in the case of alloys that contain relatively large amounts of the alloying elements. a National Metals Handbook. b Intcrnatiunal Critical Tables. '' Aluminum Co. of America. " Based on density of alurminum (2.70). c Smithsonian Pliysical Tables.

Jan 1, 1931

By Gen-Hua Shi, William Boyle, Richard E. Goodman

This keynote paper calls attention to two critically important issues relating to selecting supports for excavations in hard rock. The first is the proportion of the ultimate sliding volume that needs to be stabilized by the support system. Some excavations can be imagined to liberate very large rock volumes, whose weight can not be assigned to supports without severe economic penalty. Using the keyblock principle, it is argued that only the most critically oriented and finite blocks right on the periphery of the opening have to be supported; if these are retained by the support system, or by self resistance due to friction on the sliding faces, then the blocks behind will remain in place. As all concepts, this one has bounds and limits. Since the keyblock analysis for rock engineering is very new, these limits are not yet understood ... The second issue is the degree to which possibly stabilizing forces associated with the in-situ stress field ought to be accepted as support for potential keyblocks. It is shown that the initial stress can be effective in stabilizing rock wedges whose faces are nearly perpendicular to the excavation surface. It is too early to decide this issue but important to consider it.

Jan 1, 1982

By A. E. Gorum, I. Cornet

Fatigrle of ionic crystals has been studied primarily in magnesinm oxide. under cyclic stress dislocations move irrreversibly; they multiply; slip bands form and grow; cracks mucleate and propagnte, and failure occurs. The use of ionic crystals such as MgO is advantageorus in such investigations because they are optically transparent. Individual dislocation Intersections with {100} surfaces may be observed with a standard microscope, using etch-pit techniques. Slip, deformation, crack .formation, and fracture in MgO crystals under cyclic stress are compared with cotrresponditzg processes in metals. ThE effect of cyclic loading in metals has been studied for many years. The appearance of slip lines is readily observed and the ensuing fracture may also be seen. From these observations it is possible to predict the behavior of a material and make an educated guess as to what is happening internally, but the actual changes taking place within the structure are not readily apparent. If one could obtain a material in which the individual glide components could be observed, it would be invaluable in determining the actual slip distribution resulting from cyclic loading as well as the distribution of slip in the neighborhood of a growing crack. Such a material is magnesium oxide. Dislocation arrays may be observed by means of etch pits

Jan 1, 1961

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

The hardness dependence on grain size for polycrys-talline cartridge brass and a leaded brass has been measured by Brine11 and Rockwell B testing. In each case, the hardness, H, depends on the average grain diameter, 1, according to: H =Ho + kHl-1/2 where Ho and kH are experimental constants. Diamond pyramid hardness values have also been measured as a function of the indentation size and grain size to give additional information on the nature of the hardness test and the dependence of hardness on micro-structure. The hardness of polycrystalline brass depends on its grain size. Bassett and Davis' demonstrated this as early as 1919 by making Brinell hardness measurements on cartridge brass. Since then, the hardness of this type of material has been measured as a function of grain size by making Rockwell,2'3 Vickers,4 and Brinell5 tests. he hardness dependence on grain size has also been measured for other materials. Angus and summers6 investigated the grain size dependence of the Brinell hardness of polycrystalline copper and a Cu-4.5 pct Sn bronze. In other studies, nickel,? Armco iron,Big an Fe-0.07 pct C alloy,I0 and an 0.39 pct C-12.45 pct Cr stainless steel" have been investigated. In some of the preceding cases, the hardness results have been analyzed to show that the hardness varies with the average grain diameter, 1, according to an l-l\4, l-1/4 or I-2 dependence,11-13 The studies of the influence of grain size on hardness have not been based on any theoretical model. This may be because the hardness of a material is itself a complicated property. However, attempts have been made to correlate, experimentally and theoretically, the hardness of a material with its unidirectional stress-strain behavior.14-l6 On this basis, Hall" proposed that the polycrystal hardness dependence on grain size might follow directly from the Hall-Petch18,19 relation for the grain size dependence of the yield stress. Thus, the hardness-grain size relation was given as: H = Ho + kHl-1/2 [1] where Ho and kH were taken as experimental constants. The relation was applied to the measurements on brass,' copper,6 bronze,= and Armco iron.' More recently, this relation was shown by Armstrong and jindal20 to adequately describe the measurements on cartridge brass made by Bassett and Davis' and Babyak and Rhines.5 In this case, the relationship was taken a step further by independently relating the values of Ho and kH to the values of oyand ky, previously reported by Armstrong, Codd, Douthwaite, and petch21 from measurements of the yield stress dependence on grain size for this type of material. In the present investigation, new Brinell and Rockwell B hardness measurements have been made as a function of grain size for a cartridge brass and a leaded brass. In addition, diamond pyramid hardness values were measured as a function of the indentation size. All these results are applied to a further analysis of the hardness dependence on grain size. MATERIALS AND EXPERIMENTAL METHODS Cartridge brass and a leaded brass were selected for this investigation for two main reasons: it was anticipated 1) that these materials could be cold-worked and recrystallized to a wide range in grain size and 2) that the results to be obtained on these typical industrial materials could be usefully compared with previous investigations. The chemical analyses of the actual materials which were employed are given in Table I. The as-received 1/2- and 3/4-in.-thick plates were given various reductions in thickness by cold rolling. The rolled material was heat-treated at various temperatures between 330" and 850°C for differing time periods from 5 min to 9 hr to achieve a variation in the average grain diameter between 0.0339 and 0.000543 cm.22 During heat treatment, the brass was protected from zinc loss by packing it in chips or foils of the same composition material. Reasonably equi-axed grain structures were obtained in each case. The metallurgical grain sizes of the specimens were determined from measurements of the average linear intercept on a random line. Annealing twin interfaces were not counted along with grain boundaries. The

Jan 1, 1970

E. A. H. Tays, San Blas, Sinaloa, Mex. (communication to the Secretary*):—The results obtained by Messrs. Hofman and Hayward in their experiments, proving that a low percentage of copper sulphate with a variable percentage of salt, depending on the ore, gives the best results, confirm practical mill-work which I did in 1895. I have none of my notes, taken at the time, to refer to, so have to rely solely on memory, which precludes the conciseness that is alway desirable. In 1894 I took charge of the plant of the San Rafael Company, near Chinipas, Chihuahua, Mex., which at that time was treating a very refractory ore carrying about $15 in gold and from 20 to 25 oz. of silver per ton, the bullion being about 300 fine in gold. The silver in the ore was in the form of a sulphide. Although carrying an average of 0.75 oz. of gold per ton, free gold could rarely be seen by panning, but upon roasting a sample of the ore the gold became visible at once—a result which was discovered by chance and used to advantage later. In order to utilize the old mill to the best advantage, it was decided to use pan-amalgamation after roasting. The roasting, done in a lime-kiln, was similar to the ordinary " burning " operation. The roasted ore was trammed to the mill-bins and crushed by 10 stamps to pass a 30-mesh screen. The pulp was de-watered and fed to four 1-ton pans. My recollection is that upon starting the mill-work, the charge contained 1.5 lb. of copper sulphate and 5 per cent. of salt per ton. From the start the extraction was unsatisfactory and the loss of quicksilver was very large. Experiments were then carried out on a working scale. First, the quantity of copper sulphate was increased 4 oz. at a time; then it was reduced

Jan 1, 1910

By L. A. Panek

During the past three years, USBM has developed an apparatus and technique for direct measurement of existing pressure and change of pressure in mine rock. This relatively simple and inexpensive monitor is reliable for months after being installed. It is used to determine shift of ground pressure created by different sequences of mining, to ascertain the cause of rock failures, and to evaluate the need for artificial support. The technique has been employed to measure pressures in limestone, greywacke, concrete, diabase, and soft iron ore. When rock is subjected to a load it is deformed. Ordinarily this is observed in a mine as the displacement of one point with respect to another—the deflection of the roof, which may be observed as a convergence between roof and floor; or the extrusion of material from the rib, which may be observed as a decrease of the distance between the rib and the post of a timber set. The effect of excessive pressure may be a rockburst if the rock is strong, or it may be squeezing ground if the rock is soft. Some desirable effects of high stress (high in relation to strength) are the caving of roof in a longwall mining operation, the caving of ore in block caving, and the decrease in mechanical energy required to break down the mineral seam in a retreating pillar-robbing operation. In any case, whether the observable effect of rock load is desirable or undesirable, it is a displacement, and depends on the following four factors: 1) The structure—the size and shape of openings, pillars, and linings, the geologic bedding and jointing. 2) The mechanical properties of the rock—prin-cipally the strength, modulus of elasticity, and flow characteristics. 3) The load or applied stress—primary sources are the weight of superincumbent rock, which increases with depth, and unrelieved tectonic stresses; secondary sources are redistributed pressures caused by other nearby openings, especially large mined out zones (rock pressure depends partly on the rock structure created by mining). 4) Duration of load, related to the length of time the opening is exposed. CONTROL OF ROCK DISPLACEMENT Rock displacement can be controlled by control of these four factors. Consider now the means of exercising such control over these factors. Control of the structural features is obviously possible to a great extent, as such control is exercised largely by choosing the method of mining and the methods of natural and artificial support. Rock properties vary, even within a particular mine, but they are controllable only in the limited sense that control may be exercised by choosing the beds or zones to be mined so that rocks with undesirable properties will not occupy critical positions within the rock structure created by mining. Rock pressure is the most complex of the four factors through which ground control can be achieved because it is invisible, difficult to measure, and poorly understood. Rock pressure is controllable only to the extent that control is exercised on the rock structure created by mining. Considering openings within a particular mine, time of exposure varies, and is readily controllable because it is easily measured and easily understood — the longer an opening stands, the greater the likelihood of failure or excessive convergence. Control is exercised by choice of an appropriate sequence of driving openings of different classes, such as haul-ageways and rooms, which are required to remain well supported for different lengths of time under different conditions. Again, control is exercised through the method of mining. All controllable factors can be controlled by proper design of the mining method. The orientation and relative positions of the mine workings and the sequence of their excavation are likely to be much more important to ground control than is the design of artificial support. This implies that the major decisions in regard to ground control are made, knowingly or not, at the time the mining method is chosen. WHY MEASURE ROCK PRESSURE In addition to restrictions on the several factors, control implies the measurement of these factors in some sense, whether only qualitatively by visual observation, or by actual quantitative determination with a measuring instrument. Rock pressure is the most difficult of these factors to measure, largely because of the interaction between the measuring device and the rock. Nevertheless, the quantitative

Jan 1, 1961

By I. A. Goddard

INTRODUCTION This paper deals with the development of the sublevel open stoping (SLOS) method in lead orebodies at the Isa Mine of Mount Isa Mines Limited, during the last ten years. Open stoping in different forms has been used at the Isa Mine for many years. Prior to the period under review, stopes were small, pillars were not always recovered, and scrapers extracted the ore. By the end of the sixties, the use of load-haul-dump units was becoming more widespread. Wagner ST5's were the mucking units for the lead cut and fill stopes. Some of the open stopes in 5 orebody above 13 level had 100 kW slushers, but the more southerly stopes were the sites for the introduction of diesel front-end loaders for extraction. In the early seventies, new methods were used in the block of six stopes in 2 and 5 orebodies between 8 level and 13 level and a trial stoping project was undertaken in 7 orebody between 11 level and 13 level to determine possible stope dimensions for the extraction of the Racecourse orebodies below 13 level. By the mid-19701s, stoping was well underway in 5, 7 and 8 orebodies between 13 level and 15 level, using the 'triplet' system, incorporating cemented hydraulic fill to allow greater pillar recovery. As the eighties were entered, development of the Racecourse orebodies below 15 level commenced, as did preparations for 1 orebody in the upper levels of the north end of the mine. In both cases, the pillar recovery method has been changed to reduce the amount of cemented fill required for pillar recovery. GEOLOGY Most of the lead orebodies at Isa Mine lie chiefly to the north of the central shaft complex. They are bedded sulphide deposits in a host rock called Urquhart Shale, which dips at roughly 650 to the west. The main minerals are galena and sphalerite, with the silver mineral, freibergite, being contained in the galena. To the hangingwall of the sequence are the Black Star orebodies (1, 2 and 5) which are relatively wide, pyritic and with low to above average grade lead. The Racecourse orebodies (6 to 16) lie to the footwall, and have a large variation in width, low to high grade lead, and gradation in the lead to zinc ratio from north to south. Stope outlines are often determined by economic or engineering considerations rather than geological. The published extraction reserves are 56 million tonnes of primary ore, containing 150 grams of silver per tonne, 6.4% lead and 6.5% zinc. Traditionally, it has been regarded as lead ore, although the dominant revenue earner varies from time to time. In the Black Star orebodies, the ore and hangingwalls are more competent and open stoping has long been used. The major Racecourse orebodies which have been open stoped are 7 and 8 orebodies. This has been where the orebodies are wider (to the south) and where hangingwall conditions allow. This latter aspect has been greatly influenced by the presence of 'silica dolomite1. This tough, relatively homogeneous, non-bedded rock is, in fact, the host rock for the copper mineralisation at Mount Isa, and provides a competent hangingwall for some of the lead stopes. While the shale's bedding and jointing has a major influence on the ground conditions, there is a major fault system which causes local problems. The principal virgin stress direction is perpendicular to the bedding, but the local stress situation is complicated because of shielding by filled stopes in the hangingwall copper orebodies and because of the interaction between orebodies being extracted to the footwall. Most development on strike is mined with a 'shanty-back’, with the back being as close to normal to the bedding as possible. This is near parallel to most jointing and the principal stress direction. Figure 1 is a plan view of 14 level north, which provides a representative horizontal section through the orebodies. A typical cross section is shown in Figure 2. The narrow, parallel footwall orebodies can be seen to differ from the wider hangingwall orebodies.

Jan 1, 1981

By J. R. Cahoon, H. W. Paxton

The possibility of using unidirectionally solidified, two-phase alloys as an approximation to fiber composite materials is investigated. The short-term me.chanical properties and failure modes of unidirectionully solidified A1 (rich)-Cu alloys containing ap -Proximately 0, 17.5, and 27.7 vol pct of 0 phase 'fibers" are determined at temperatures from 25" to 500" and compared with those obtained for conventionul SAP alloys. In a previous publication,' hereafter referred to as I, the possibility of understanding some of the room-temperature mechanical properties of unidirectionally solidified castings was explored. For Al(rich)-Cu and Al(rich)-Mg two-phase alloys over a substantial range of compositions, the yield and ultimate strengths and common ductility measures were very adequately predicted from the principles of fiber strengthening4 and the analysis of ductility outlined by Gurland and Plateau." The results obtained in I suggest the possibility of using unidirectionally solidified, two-phase alloys to simulate fiber composite materials where the inter-dendritic second phase or constituent acts as the reinforcing material. Recent attempts concerning the fabrication of fiber conlposites have concentrated on producing composites with a good bond between fiber and matrix and with very long fibers so that their maximum contribution to the strength of the composite may be realized. However, these objectives are difficult to attain in practice and present fabrication processes are either extremely laborious or costly.13 The slow, unidirectional solidification of eutectics has received considerable attention as a method for producing composite materials. 5,6 This method can fulfill both of the above objectives but it is currently laborious, expensive, and has the additional disadvantage that the volume fraction of reinforcing phase cannot be easily varied. On the other hand, unidirectionally solidified, two-phase alloys, also with a good bond between the phases, are relatively easy to make and the volume fraction of reinforcing "fibers" can be easily varied by changing the average composition of the alloy. The disadvantage of the cast alloys is that the mechanical effectiveness of the "elongated interdendritic reinforcements" (EIR)* may be reduced due to their rela- tively short lengths, the w factor in Eq. [2] of I. However, if the EIR have a high strength their contribution can be considerable. For composite materials containing discontinuous cylindrical fibers of various lengths the ultimate strength is given by1 where it is assumed that the composite fractures when the fibers fail. In Eq. [I], a, is the stress in the matrix just prior to failure of the composite, Vf is the total volume fraction of fiber reinforcing constituent, Vf(l+) is the volume fraction of fibers whose lengths exceed the critical length, I,, which is defined as the shortest length of fiber in which the stress can build up sufficiently to break the fiber. af is the fracture strength of the fiber material, w is a factor accounting for the discontinuity of those fibers whose lengths exceed I,, 1-/d is the average aspect ratio of those fibers whose lengths are shorter than I,, and t is the shear stress in the matrix at the fiber-matrix interface. The factor w is dependent on the length of the fibers and also on whether deformation of the matrix occurs plastically or elastically. However, for a given length of fiber, w is smaller when elastic deformation of the matrix is assumed.' It is of interest to consider the properties of simple unidirectionally solidified, two-phase alloys at elevated temperatures in view of the possibility of using suitable modifications for high temperature service. Knowledge of the creep behavior of these materials is still rudimentary (although under active investigation) and the present paper concerns itself with short time tensile properties of some alloys similar to those investigated in I (i.e., unidirectionally solidified Al(rich)-Cu alloys). Unidirectionally solidified alloys containing 5.6, 17, and 23 wt pct Cu were tested parallel to the direction of solidification at temperatures from 25" to 500°C. In the present investigation, the alloys were homogenized for 2 days at 535°C giving a matrix of homogeneous a phase (5.2 wt pct Cu) and an interdendritic constituent (EIR) which was completely Q phase (53 wt pct Cu). EXPERIMENTAL Alloys of nominal composition 5.6, 17, and 23 wt pct Cu (containing approximately 0, 17.5, and 27.7 vol pct 8 phase, respectively, after homogenization at 535°C) were prepared by melting 1200 g of A1 (99.99 pct) in a high purity graphite crucible and adding the appropriate amount of freshly cleaned copper chips (99.9 pct). The molten alloy (at 700°C) was poured into a preheated graphite mold (also at 700°C) and the ingot unidirectionally solidified by impinging water on the steel baseplate of the mold. The alloy was degassed immediately

Jan 1, 1970

By Yoichi Ishida, Ching-Yao Cheng, John E. Dorn

Tile creep behavior of a iron was investigated over the range of temperatures from 375° to 1150°K. Apparent activation energies for creep, obtained by the effect of sudden changes in temperature on the creep rate, revealed the presence of- four distinguishable regions. The creep behavior of a iron in Regions II (480° to 774°K) and 111 (775° to 1045°K) was found to correlate well with a model where the creep rate is controlled by the nonconsevualive motion. of jogged screw dislocations. An anomalous increase in the apparent activation energy fur creep in Region III was found to be in harmony with the known decrease in the free activation energy for self-diffusion over the Curie transformation range. Furthermore, the creep rates in Regions II and III were found to increase with stress due not only to the effect of stress on the activation energy but also to an increase in density of mobile dislocations. The evidence suggests that pipe diffusion along moving dislocations could be a significant factor over the lower temperatures of Region II. ALTHOUGH the creep properties of iron and steel have been of interest to metallurgists for some time and an extensive literature is now available, most of the published information has not produced much toward understanding the fundamental dislocation processes controlling the creep behavior of these materials. Whereas the activation energy for high-temperature creep of metals usually agrees well with that for self-diffusion, Sherby, Orr, and Dorn1 deduced from the data of Tapsell -and c1enshaw2 that the activation energy for creep of Armco iron is about 78,000 cal per mole and more recently Lytton and sherby3 reviewed the data of Jenkins and Mellor4 and found an activation energy for creep of a iron of 80,000 cal per mole. Both values are substantially greater than the activation energy for self-diffusion in a iron. Because of the limited data suitable for purposes of identifying the controlling dislocation mechanisms of creep and the unusually high activation energies for creep quoted above, it was considered desirable to reinvestigate in detail the creep of a iron by more reliable techniques which would provide sufficient data for determination of the creep mechanisms. EXPERIMENTAL TECHNIQUE Creep specimens were prepared from 3/8 by 4 in. iron bar stock of the following composition by weight percent: 0.001 C, 0.0120 0, 0.001 N, 0.004 S, and 0.003 P. The as-received bars were cold-rolled to a thickness of 0.100 in., annealed under argon for 30 min at 1113°K, cold-rolled to a final thickness of 0.063 in., and machined into tensile specimens having gage section 0.250 in. wide and 1.70 in. long. Finally they were recrystallized under argon at 1113°K. Specimens to be crept above 1060°K were recrystallized at 1173°K. Both recrystallization treatments gave the same reproducible equiaxed ASTM No. 4 grain size. Creep testing was conducted in machines fitted with Andrade-Chalmers arms that maintained a constant stress to within ±0.2 pct of the reported values. Deformation over the specimen gage section was sensed with a linear differential transformer and recorded auto-graphically as a function of time. The strains deduced from these measurements were sensitive to ±5 x 10-5. During creep the specimens were contained in an argon-filled chamber which was immersed in a temperature-controlled molten tin bath. Creep temperatures, as measured by thermocouples attached to the specimen, were maintained to within ±10.25°K of the reported values. For activation-energy determinations rapid changes in temperature of about 12°K were obtained within 30 sec by direct resistance heating of the creep specimen, and maintained to ±1°K of the reported values. Observations of structural details of specimens before and after creep tests were made by electrolytic polishing and etching in acqueous ammonium persulfate. EXPERIMENTAL RESULTS A typical example of the determination of apparent activation energies, Q, by the effect of small changes in temperature is illustrated in Fig. 1. Q is defined by

Jan 1, 1967

By Paul H. Price

The history of the salt industry in West Virginia dates back nearly two hundred years; however, the history of salt as an important raw material for the chemical industry is much more recent. The earliest record of West Virginia salt was in 1753, when a raiding party of Shawnee Indians attacked frontier settlements in Virginia taking captive a number of the pioneers. One of these, who later escaped and returned to her friends, described how the Indians camped at a salt spring on the banks of the Kanawha River and evaporated the water to obtain a supply of salt to take back to Ohio with them. Settlement of the Kanawha Valley began in 1774, that same year the Battle of Point Pleasant ended the Indian's power in the Ohio Valley; and settlement of the Kanawha Valley progressed rapidly with a consequent increase in the importance of the Kanawha Licks as a source of salt. In those days the evaporation of the brine was a family matter for which the family wash-kettle was commandeered.

Jan 1, 1949

By S. R. Goodman, Hsun Hu

A detailed study of texture developmenf in poly crystalline copper atzd 70-30 brass has been completed. Textural changes as a function of deformation are shoum by pole jigmres and by intensity measurements oF- various rejlectiotzs from the rolling plane and the rolling direction. These examinations were accompanied by measurements of stacking fault frequency, hardness changes, and microstructure. Some of the results were briefly presented earlier. Additional results reported here are consistent with the idea that deformation faulting or slip by partial dislocations is of primary importance in the formation of deformation textures in fcc metals. lo examine the idea that deformation faulting is of primary importance in determining whether the texture is the copper type or the brass type an extensive study of the development of polycrystalline textures in copper and 70-30 brass was initiated. Besides the determination of complete pole figures, the intensities of the various reflections from both the rolling plane and the plane perpendicular to the rolling direction, the peak shifts due to deformation stacking faults, and the hardness of the rolled specimens were examined at various reductions from 10 to 99 or 99.5 pct. Mi-crostructures were examined by transmission electron microscopy. Some of the results were briefly presented in an earlier publication.' Since then, additional information has been obtained. This is given in the present paper. EXPERIMENTAL PROCEDURE Material and Specimen Preparation. The material used was a commercial electrolytic copper bar 1i in. wide and 2 in. thick and a 70-30 brass bar la in. wide and 1i in. thick. Chemical analysis indicated a purity of 99.97 pct for the copper, with 0.025 pct 0 as the major impurity. The 70-30 brass was of higher purity with 0.0016 pct 0 as the major impurity. Extreme care was taken in the preparation of the starting material to insure uniformly fine grains with a nearly random initial texture. The two bars were first cold-forged and then annealed to eliminate any original texture. The grains were then refined by several cold rolling (approx 30 pct reduction) and annealing treatments. The + -hr anneals were carried out in a salt bath at 390" to 440°C for copper and at 490°C for brass. The resulting penultimate grain size was 0.06 mm for copper and 0.03 mm for brass, and both showed very little preferred orientation. The number of prior cold rolling and annealing cycles was such that the final thickness after various final reductions of 10 to 95 (for brass) or 99 (for copper) pct was the same (0.020 in.). These annealed strips were rolled in two directions by reversing end for end between passes according to the following schedule: 0.006 in. per pass to 0.100 in., 0.003 in. per pass to 0.050 in., 0.002 in. per pass to 0.025 in., 0.001 in. per pass to 0.020 in. Texture Determination. The development of rolling textures was studied by examining complete pole figures determined from the (111) reflection. Specimens thinned from one face of the strip to half thickness (0.010 in.) were used to obtain the central portion of the pole figures, while specimens thinned from both faces to 0.003 in. were used to obtain the peripheral portion. The reflection and transmission techniques have been described previously. In addition to X-rav pole figures, texture development was also studied b; examining the intensity variation of the (Ill), (200), (2201, (311), (331), (420), and (442) reflections from the rolling plane and from the plane normal to the rolling direction, as a function of deformation. The same specimens used for the central portion of the pole figures were used for the intensity measurements of the various reflections from the rolling plane. For intensity measurements from the plane normal to the rolling direction, composite specimens were prepared by mounting sections cut parallel to the transverse direction of the strip. An epoxy resin was used to bond these sections together, and the entire composite was then mounted in a cold-setting resin to facilitate subsequent polishing and etching to remove distorted metal at the cut. The intensities were expressed in units of the integrated intensities measured from an annealed copper specimen having almost no preferred orientation. Stacking Fault Frequency Determination. Following the analysis of Warren: the stacking fault frequency, a, was determined from the change in the peak separation (A%) of two neighboring reflections of a deformed specimen, as compared with the normal peak separations of a fully annealed specimen. To obtain sufficient intensities for the second-order reflections, (222) and (400), composite specimens were prepared from parallel sections cut from the strip at 30 deg to the rolling direction for copper and 25 deg for the brass.* From texture data, these sections are known to contain a large population of both (111) and (200) planes. Since residual stresses can also cause X-ray line shifts (the direction of line shifts depends upon the sign of the stress), the use of composite specimens consisting of sectioned planes should help compensate for these effects as the residual stresses change sign from the surface to the central section of a rolled strip. Since the amount of peak shift is almost un-measurable in brass rolled 15 pct and in copper rolled

Jan 1, 1969

By B. H. Kear, B. J. Piearcey

The orientation and temperature dependence of the tensile and creep propevties oj Mav-M200 crystals halle been determined. Crystals oriented for single slip exhibit ,maximum ductility, minimum work hardening, and least creep resistance, whereas crystals in multiple slip orientations show nzinimu~n ductility, strongest work hardening, and greatest creep resistance. At 1400" and 1600°F there is a marked improzlenzent in creep strength for orientations approaching [001] and [111], indicating that interactions between dislocations gliding in intersecting octahedral slip systems play an important role in creep resistance. At 1800°F the creep strength is much less dependent on orientation, which is rationalized in terms of slip in cube planes as well as octahedral A frequent mode of failure in high-strength cast nickel-base superalloys is by intergranular fracture, particularly along those grain boundaries oriented transverse to the major stress axis. VerSnyder and ~uard' demonstrated that this problem could be overcome by eliminating transverse grain boundaries through unidirectional solidification. Piearcey and versnyder2 made use of this principle in the development of unidirectionally solidified gas turbine blades and vanes, where the growth direction of the columnar grain structure coincides with the axis of principal stress under operating conditions. The present investigation was undertaken to determine if further improvement in properties may be obtained by eliminating grain boundaries altogether, so as to take advantage of the well-known dependence of mechanical properties of single crystals upon the orientation. 1) EXPERIMENTAL PROCEDURE Single crystals of Mar-M200* were grown from the melt under vacuum by a modified Bridgman method. The melt was poured into a preheated alumina mold, and crystal growth was promoted from one end by appropriate gradient cooling. Tensile and creep specimens (2 in. diam by $ in. gage length) were prepared by a series of operations involving electrical discharge machining, precision grinding, and electropolishing. The orientations of the specimens were determined by the Laue X-ray back-reflection method. Tensile tests were carried out in aWiedemann machine with furnace attachment, using a strain rate planes. In all orientations imzpvouement in the strength charactevistics of the material can be induced by heat treatment. Creep ad stress rupture data for (001) oriented crystals are compared with similar data obtailted previously joy random polycvystalline material, and also columnar grained material having a prejevved (001) orientation. The single-crystal )material exhibits both longer rupture life and lower minimum creep rate at all temperatuves, and the rupture elongation is comparable with that in the columnar grained material. From these results it is concluded that single crystals should and useful application in gas-turbine blades and tanes. The optimum orientation for a blade is considered to be with its axis of principal stvess parallel to (001) ou (111). of 0.0001 sec-'. Load and extension were recorded directly on an X-Y recorder. The strain measuring device consisted of extension arms attached to the grips at one end and leading out of the furnace to an LVDT (linear variable differential transformer) at the other. Creep tests were performed using a standard constant load creep frame. 2) DISCUSSION OF RESULTS 2.1) Structure of Alloy. The structure and segregation in as-cast and heat-treated Mar-M200 has been described in detail else where.~ The main features are as follows: the as-cast material is heavily cored, due to pronounced dendritic segregation during solidification; the dendrites are rich in tungsten and cobalt whereas the interdendritic regions are rich in chromium, titanium, nickel, and carbon. The structure consists of -60 vol pct coherent precipitate of y', basically Ni3(A1,Ti), in a matrix of y (nickel-base solid solution), interspersed in the interdendritic regions with minor MC carbides and -y' eutectic. The y' particles, and y-y' eutectic, contain more titanium, aluminum, and nickel, and less tungsten, cobalt, and chromium than the y matrix. Heat treatment partially removes segregation, eliminates the eutectic, refines the y' dispersion in y, and gives additional partially coherent M23Cs carbide. An as-cast crystal, therefore, is composed primarily of two oriented phases (y + y'), whereas the normally heat-treated crystal consists of three oriented phases (y + y' + MZ3Cs). Typical electron transmission micrographs of the y + y' structure are shown in Fig. 1. Crystals grown in the (100) orientation develop a simple unidirectional dendritic structure, Fig. 2, since (100) happens to be the preferred direction of growth for dendrites in this material. Crystals grown in the {110) and (111) orientations, however, tend to promote equal growth, generally in separate colonies, in the two and three geometrically favored (100) growth directions, respectively. In other orientations of growth, a single (100) dendrite direction generally pre-

Jan 1, 1968

By H. R. Ogden, E. S. Bartlett, A. G. Imgram

Unmodified disilicide coatirigs were applied to sheet-tensile specimens ofCb-Dg3 and Mo-TZM veJractovy- metal alloys. Coating thickness, degree of coating-substrate interdiffusion, and specimen geonzetry (notched and plain were included in the variables studied. Tensile tests were made to determine the ductile-lo-brittle transition temperature. The disilicide coating modestly increased the transition temperatlre of TZM, but had no effect on 043. Neither material condition (recrystallized or stress-velieved) nor specimen geometry (notched or unnotched) significantly altered the effects of coatings on the transilion temperatures of. the alloys. Cracks in the brittle coatings did not propagate into the substrate, and fracture modes appeared to be the same for both un-coated and coated specimens. MOST potential structural applications for refractory metals and alloys involve exposures to oxidizing environments at elevated temperatures. The general lack of oxidation resistance of these metals will require protective coatings to allow fulfillment of their potential. Currently preferred coatings for the oxidation protection of refractory metals are brittle intermetallic aluminides or silicides. These are typically formed on the surface of the refractory-metal substrate by a diffusion reaction between the substrate and a gaseous or liquid medium that is rich in aluminum or silicon. Because of the brittleness of these coatings, they will sustain no plastic deformation at low temperatures. They are frequently cracked by cooling from the coating temperature because of the thermal-expansion mismatch with the substrate alloy. Even if they survive cooling intact, they crack rather than sustain deformation under load at low temperatures. Thus, when a coated refractory metal is strained beyond the elastic limit of the coating at low temperatures, the mechanical environment of the substrate would include both static and dynamic cracks. These might be expected to influence the flow and fracture behavior of the substrate. This could be manifested in an altered fracture mode and/or an increase in the normal ductile-to-brittle transition temperature of the refractory-metal substrate. This paper presents the results of a research program that was conducted to determine the influence of the presence of a brittle surface coating on the low-strain-rate tensile behavior of typical refractory metals at low temperatures. EXPERIMENTAL PROCEDURES Material Preparation. Thirty-mil-thick sheets of molybdenum TZM alloy (Mo-0.5Ti-O.1Zr) and colum-bium D43 alloy (Cb-IOW-1Zr-O.1C) were obtained commercially. These alloys were selected as substrate materials representing two classes of materials important in current refractory-metal technology. The TZM was in the stress-relieved condition, and exhibited a heavily fibered grain structure. The D43 had been processed by the duPont "optimum" fabrication schedule,' and exhibited slightly elongated grains typical of this process. Tensile specimens of two geometries were prepared from these materials: 1) plain specimens with 0.2-in.-wide 1.0-in.-long gage sections; 2) specimens similar to above, but with a 0.06-in.-diam hole drilled in the center of the gage section, providing a stress concentration factor, Kt, of 2.5. The "notch" geometry was selected to represent a typical condition of a rivet hole or other geometric discontinuities as might be encountered in various applications. Machined specimens were degreased, with a final rinse in acetone, prior to the application of coatings. Specimens of each substrate and configuration were pack-siliconizedin a particulate mixture of 80 pct A1203, 17 pct Si, and 3 pct NaF. Specimens were embedded in this mix (contained in graphite retorts) and coated in an electrically heated argon-atmosphere furnace under time-temperature conditions to effect nominal 1- and 3-mil-thick silicide coatings: Coating Thickness, mils Thermal Treatment 0.6 to 1.4 24 hr at 982°C 2.4 to 3.2 48 hr at 1093°C Coating kinetics were similar for both the TZM and D43 substrates. These treatments had little or no visible effect on the substrate microstructure as determined by optical metallography. The coatings on TZM were essentially single-phase unmodified disilicides, while those on D43 showed substantial evidence of modification by proportionate reaction with the respective substrate elements or phases, as shown in Fig. 1. It was recognized that these coatings might not be particularly desirable regarding protective capability. However, it was desired to circumvent possible inter -ferring chemical interaction with the substrate by pack additives such as chromium, titanium, boron, aluminum, and other elements that typify the better protective coatings for these materials.' Thus, the results presented apply specifically to the simple silicide coatings investigated. They may not be rep-

Jan 1, 1967

By P. Greenfield, C. C. Smith, A. M. Taylor

The Mg-Zr alloy ZA and Mg-Mn alloy AM503(S) are shown to have a markedly improved resistance to creep deformation after suitable heat treatments. This improvement makes them suitable for certain stress-bearing fuel element components in nuclear reactors. The extent of strengthening is described and an explanation of the behavior of both materials is given, based on a combination of strain-aging and grain growth. The increase in operating temperatures of fuel element components in Calder Hall type nuclear reactors has necessitated the development of magnesium base alloys with a very high resistance to creep at temperatures up to 500°C. Such alloys are not required for fuel element cans, which require high-creep ductility rather than strength, but for can supporting and stabilizing components, which are needed to support the imposed loads without deforming more than about 1 pct in times of up to 40,000 hr. The amount and type of alloying addition made to magnesium for these parts is limited by the necessity of keeping the cross-section to thermal neutrons as low as possible. The alloys must also possess a high resistance to oxidation in CO2. Alloys which have been developed for this application include ZA, an alloy of magnesium with 0.5 to 0.7 pct Zr and AM503(S), an alloy of magnesium with 0.5 to 0.75 pct Mn. In the as-extruded condition these alloys are very weak and ductile in creep but it has been found that they can be strengthened to a significant extent by heat treatment. This paper describes the method of developing a high-creep resistance in ZA and AM503(S), the extent of the strengthening produced and discusses the probable mechanisms of strengthening. TEST MATERIALS Specimens were taken from typical casts of ZA and AM503(S) alloys extruded into 2 1/4-in.-diam bars, supplied by Magnesium Elektron Ltd. Typical analyses of the bars were as follows: The as-extruded mean grain diameter was 0.001 to 0.002 in. for the ZA alloy and 0.003 in. for the AM503(S) alloy. EXPERIMENTAL METHODS Extruded bars of ZA alloy, 2 1/4 in. in diameter and 9 in. long, were heat treated in electrical resistance furnaces in an atmosphere of flowing CO2 containing 50 to 300 ppm water, thereby reducing the extent of oxidation compared with that which would have occurred in air. Heat treatments were carried out at 600oc for times of 8, 24, 48, 72, and 96 hr and material was subsequently both furnace cooled and water quenched. In order to measure the effect of time of heat treatment, specimens were creep tested at 400°C and 336 psi for about 1000 hr. Subsequently, the behavior of material heat treated for 96 hr at 600°C and furnace cooled was tested at a variety of stresses from 200° to 500°C. Tests were also conducted at 200o and 400°C on material in the as-extruded condition for comparative purposes. With the AM503(S) alloy, only the effect of heat treatment at 565°C for 4 hr was examined. It has been shown1 that such a heat treatment produces marked strengthening in this alloy. Tests on this material were conducted at a variety of stresses at 200°, 300°, and 400oc with comparative tests on as-extruded material at 200o and 400°C. The creep tests were carried out on machines using dead-weight loading and direct micrometer strain measurements on specimens 5 in. long and 0.357 in. diameter. At temperatures of 400° C and below, the creep tests were conducted in air, but at higher temperatures an atmosphere of CO2 was used. Grain size measurements were made on ZA in the extruded and heat treated states and on each specimen after creep testing. This was done by a line count of a minimum of 20 grains in two or three random fields in the longitudinal and transverse directions. The same method was used for measuring the grain size of as-extruded AM503(S), but the grain size of the heat treated material was so large that this method could not be employed. For heat-treated AM503(S) the large grained characteristics (between 0.1 and 1 in.) were confirmed by the measurement of individual grains. In the case of the ZA alloy, specimens taken from various stages in the program were analysed for hydrogen by a combustion method. Material in various states was also analysed for the soluble and insoluble zirconium content by dissolving in dilute hydrochloric acid. This technique has been useda for the determination of amounts of zirconium present

Jan 1, 1962

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.'TheRittinger In its first form, as stated by P. R. Ritted.'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' 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 Y. C. Liu, G. A. Alers

The effect of rolling reduction on the textures of Cu-A1 alloys has been investigated both by pole figure and by modulus methods. In alloys which exhibit complete copper or brass types of rolling texture, the rolling reduction has little effect on the texture except to increase the degree of preferred orientation. In alloys which exhibit a transition texture, however, increased rolling reduction increases the amount of brass-type texture at the expense of the copper-type texture. The present experimental results show that there is no one-to-one correspondence between the SFE and the rolling texture of fcc metals. Additional data taken from the literature for fcc metals also support this conclusion. On the other hand, the present and previous experimental results are shown to be in good agreement with the suggestion that the texture transition occurs at a critical value for the separation distance between two partial dislocations—a consequence of the "dislocation interaction" hypothesis for texture. formation. This critical separation occurs when the parameter .r/ub is 3.75 x 10'3. From this, a value for the SFE of 39 ergs per sq cm may be deduced for a Cu-2.85 at. pct A1 alloy. ThE correlation between the rolling texture of fcc metals and the stacking fault energy, SFE, was one of the first attempts to relate atomistic properties with the type of rolling texture.' This correlation gives a qualitative explanation for the experimental observation that the addition of alloying elements, which generally lower the SFE, changes the copper-type texture to a brass-type texture. The simplicity of this correlation had led to its general acceptance and even its quantitative use.' However, it is only a correlation and is largely based on descriptive features of pole figures, and on the poorly known SFE values in dilute alloys. Quantitative verification of this phenomenologi-cal correlation is, in fact, completely lacking. One purpose of the present study is to test this correlation. Another atomistic description for the formation of rolling texture is the "dislocation interaction" hypothesis of texture formation.3 In this hypothesis, the factor controlling the type of rolling texture depends on whether or not the separation distance between two partial dislocations exceeds a critical value. Materials having a separation of less than the critical value are supposed to exhibit a copper-type texture while those with a separation above the critical value are supposed to have a brass-type texture. At the critical value, it is expected that the material should show equal amounts of copper- arid brass-type orientations in their textures, i.e., a 50 pct transition texture. The SFE appears in this hypothesis as only one of several factors which determine the separation distance between partial dislocations. It is possible to test the validity of these two concepts by studying the rolling texture as a function of rolling reduction. Since the SFE per se is an intrinsic property of the metal, it should not, by definition, be influenced by local irregularities, such as variable stress conditions. Thus, no change in texture-type is expected to occur with changes in rolling reduction. On the other hand, according to the "dislocation interaction" hypothesis, any factor that effectively influences the separation distance of partial dislocations would be expected to change the rolling texture. Since the separation distance between partial dislocations is known to depend upon local stresses,4-6 it is anticipated that there would be an effect of the degree of reduction on the texture-type. Also, since applied stresses are more likely to increase, rather than to decrease, the separation between partials,4'5 the overall effect would be to increase the amount of material in the brass-type orientations as rolling reduction is increased. Furthermore, this reduction dependence would be most prominent in alloys exhibiting the transition texture since the distance between partials in those alloys is thought to be close to the critical value. Experimental data in the literature is insufficient to distinguish between these two alternatives. Haessner studied the effect of rolling reduction on textures in a series of Ni-Co alloys by means of the X-ray intensity-ratio technique,' and found that while one texture parameter indicated no reduction dependence the other indicated a slight dependence of the rolling texture on reduction in the range of 96 to 99 pct. As has been noticed previously, the intensity-ratio technique is a convenient but controversial method7 because there is no a priori reason to suggest which intensity-ratio would describe the texture most meaningfully. A more quantitative method of describing textures is found in terms of the orientation dependence of Young's modulus. Here, the type of modulus aniso-tropy associated with the copper-type texture is sufficiently different from that observed for the brass-type texture to allow the two types to be easily distinguishable and a quantitative measure of the amount of each can be deduced from the numerical results. This ability to provide quantitative data is particularly valuable when the two textures occur simultaneously in one alloy as is the case for the transition textures. In this paper the modulus method, supplemented by pole figure data, is used to look for an effect of roll: ing reduction the texture. Also by combining the texture measurements with recent determinations of the SFE in Cu-A1 alloys'0'" it should be possible to test for a relationship between the SFE and textures.

Jan 1, 1970

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' 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' 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' 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'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 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.'TheRittinger In its first form, as stated by P. R. Ritted.'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' 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