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By K. A. Jackson, J. D. Hunt

A general theory for the growth of lamellar and rod eutectics is presented. These modes of growth depend on the interplay between the diffusion required for phase separation and the formation of interphase boundaries. The present analysis of these factors provides a justification for earlier approximate theovies. The conditions for stability of rod and Lanlellar structures are consitleved in terms of the mechanisms by which the structure can change. The mechanisms considered include both small adjustments to the lnnzellar spacing due to the motion of lamellar faults, and catastrophic changes due to instabilities. It is concluded that stable growth occurs at or near the minimum interface undevcooling for a gizierz growth rate. The conseqrlences of the existence of a diffusion boundary layer at the interface are discussed. The experimental results for the variation of growth rate, undercooling, and Lanzellar spacing are cornpared with the theory. We believe that the theory presented in this paper provides an adequate basis for understanding the complex phenomena of lanzellar and rod eutectic growth. The growth of lamellar eutectics has been the subject of several theoretical and many experimental studies. The foundations for the theoretical work were laid by zenerl and Brandt2 in their analyses of the growth of pearlite. Zener estimated the effect cf diffusion, and took into account the surface energy of the lamellar structure. He found that the lamellar structure could grow in a range of growth rates at a given undercooling provided the lamellar spacing was appropriate for the growth rate. Since pearlite grows with only one growth rate and one lamellar spacing at a given undercooling, there is clearly an ambiguity in the theory. Zener removed this ambiguity by postulating that the growth rate was the maximum possible at the given undercooling. He predicted then that the product of the growth velocity v and the square of the lamellar spacing A should be constant, i.e., A2v = const. Brandt2 started out by assuming that the interface between the lamellae and austenite was sinusoidal. Because of this, the ambiguity encountered by Zener did not arise. Brandt was able to obtain an approximate solution to the diffusion equation, but, since he did not take into account the surface energy, his considerations are incomplete. Tiller3 applied some of these ideas to the growth of eutectics, and proposed a minimum undercooling condition to replace the maximum velocity condition used by Zener. These conditions are formally identical. Hillert4 extended the work of Zener. He found a solution to the diffusion equation assuming the interface to be plane. Taking surface energy into account, and applying Zener's maximum condition, he was able to calculate an approximate shape of the interface. Jackson et al.5 used an iterative method employing an electric analog to the diffusion problem to refine the calculation of interface shape. It was found that the interface shape calculated from a plane-interface solution to the diffusion equation was negligibly different from the exact solution. The method provided an analog only for eutectics for which the volumes of the two phases are equal, growing from a melt of exactly eu-tectic composition. There has also been considerable experimental work on eutectics, Several experimenters8-10 found that A2v is constant as predicted by Zener.1 Hunt and chilton10 demonstrated that ?T/v1/2 is also a constant for the Pb-Sn system as predicted. Lemkey et al.11have recently found A2v to be constant for a rod eutectic. In the present paper, we present the steady-state solution for the diffusion equation for a lamellar eutectic growing with a plane interface, for the general case, that is, with no restriction on the relative volumes of the two phases, and with the melt on or off eutectic composition. A similar solution is also found for a rod-type eutectic. Expressions are obtained for the average composition at the interface and the average curvature of the interface. These equations for the average composition and curvature are similar in form to those derived by Zener1 and Tiller,3 and provide a justification for some of the approximations made by these authors. The mechanisms by which the spacing in a lamellar structure can change are considered. The important mechanism for small changes in lamellar spacing involves a lamellar fault. Examination of the stability of lamellar faults leads to the conclusion that the growth occurs at or near the extremum.* The insta- bilities which can develop in a rodlike structure are also discussed, resulting in the conclusion that this structure also grows at or near the extremum. Comparison of the conditions for rod and lamellar growth permits a prediction of the surface-energy anisotropy required to produce rods or lamellae for various volume-fraction ratios. The diffusion equation predicts the existence of a diffusion boundary layer at the eutectic interface unless the eutectic has 0.5 volume fraction of each phase and is growing into a liquid of eutectic composition. This boundary layer is such as to make the composition in the liquid at the interface approximately equal to the eutectic composition. This boundary layer permits changes in composition during the zone refining of eutectics. Photographs of the eutectic interface of a growing transparent organic eutectic system have been made. Both the components of this eutectic are transparent organic compounds that freeze as metals do.12 The in-

Jan 1, 1967

By Nicholas J. Grant, Joseph T. Blucher

High-purity aluminum and an Al-10 pet Zn alloy zvere tested in axial fatigue from 80" to 900oF, at struzn vales of 5 and 150 pct per min, at a strain amplitude of 1 pcl. Cycles to failure were recorded as well as the load per cycle during the entive test. Several grain sizes were examined in each material. Examination was made of modes of deformation, initiation and growlh of' cracks, and vecovery mechanisms such as srbgrain formation and boundary migration. Strain rate effects on cycles to failure are first observed ahoi'e 50O0F, the highev vate vesulting in longer lije. Crack initiclion at room temperature may be truns-or iutercrystalline but fructures are transcrystalline. Abore 600'F, crack iniliation and growth ave largely inlercvystalline. Boundary wzigratiotz to 45-deg positions is observed above 70Oo F, and fractrrves are a combination of grain bol~ndary voids and cvacks. It is only in recent years that studies of deformation and fracture which prevail in fatigue at elevated temperatures have attracted significant attention.' Of such studies considerably less attention was given to high strain-low strain rate fatigue. Moreover, the majority of high-temperature fatigue studies were performed at conventional machine speeds (1000 to 10,000 cpm). As it is well-demonstrated in uniaxial creep-rupture series, at high strain rates, even at high temperatures, metals undergo work hardening with little or no attendant recovery or recrystallization thus the nature of deformation and fracture which is observed is similar to that encountered at lower temperatures.'-" Thus, for example, fatigue testing of a stainless steel at 750°F does not involve high-temperature deformation processes,2 and might more correctly be termed "fatigue testing at an elevated temperature". It was the purpose of this work to study deformation and fracture in fatigue as a function of low strain rates and temperature, selecting conditions which would result in grain boundary sliding, migration, fold and subgrain formation, and intercrystalline cracking in high-purity aluminum and a high-purity A1- 10 pct Zn alloy. Grain size was an additional variable. Extensive studies of the deformation and fracture behavior of these aluminum materials in simple creep had been done in the authors' laboratory, and were to serve as a basis of comparison for the observed effects in fatigue:'-'' the range of the creep test temperatures was 80° to 1150oF. MATERIALS AND EXPERIMENTAL PROCEDURE The compositions of the 99.99 pct pure A1 and the A1-10 pct Zn alloy are shown in Table I. Button-head specimens, with a liberal fillet, of 0.20 in. diam and of gage length 0.40 in. were machined from wrought bar stock. The ratio of 2:l gage length to diameter was selected after preliminary tests showed that a shorter length gave a shorter life, probably due to end effects, and after evidence of buckling in longer gage length specimens. After machining, the specimens were chemically polished to remove the worked outer layer, and were subsequently heat-treated to stabilize the selected grain sizes. Both the high-purity aluminum and the A1-10 pct Zn alloy were heat-treated to produce grain diameters of approximately 0.5 and 2 mm in each case. These grain sizes are referred to in the text as fine and coarse grain, respectively. One lot of the high-purity aluminum was heat-treated to produce a still coarser grain size in which the cross section was occupied by 2 to 3 grains. This structure is referred to as very coarsegrained. After heat treatment, the specimens were again electropolished. To avoid complications of both stress and strain gradients in the cross section of the specimen, a hydraulic, axial fatigue machine was designed and built. A button-head specimen, 1/2 in. diam at the head, was firmly gripped in a split-type holder free of any play in the grips. The test temperatures varied from 80" to 900°F. The strain amplitude in all of the reported tests was 1 pct for a total strain amplitude of 2 pct. The strain range was set by precision micrometers and measured by a precision dial gage. Constant strain rates of 5 and 150 pct per min were selected so that high-temperature type deformation and fracture would occur in the higher-temperature tests5,6 The strains and strain rates must be regarded as nominal values because they are based on the original specimen dimensions, which changed significantly as a result of necking and crack propagation, as can be observed from Fig. 8. For the elevated-temperature tests, a thermocouple was inserted into a well in the head of the specimen; the selected temperatures could be maintained with less than ± 5oF fluctuation during the entire test. To avoid changes in grain size before the test, specimens were heated to the test temperature in less than 15 min; similarly, they were cooled to room temperature after fracture with an air blast to avoid or minimize recovery or recrystallization. During the fatigue tests, load vs strain curves were recorded by a strain gage load cell for each fatigue cycle. In addition, the maximum values of load amplitude were recorded for the entire test.

Jan 1, 1968

By AIME AIME

A new Index of the Transactions, Volumes I. to XXXV., is now being prepared, and will probably be ready for distribution during the coming summer. The Index will be about the size of the average volume of the Transactions, and will be bound in cloth and in half morocco. The price of the cloth-bound copy is $5, expressage prepaid. Half morocco binding will cost $1 extra. It is very desirable that all who wish to purchase this Index will notify the Secretary's office promptly, sending a check, money-order or draft, made payable to the American Institute of Mining Engineers.

May 1, 1907

PROFESSOR CECIL H. DESCH of Sheffield Univer-sity is to give the sixth annual Institute of Metals lecture in connection with the A. I. M. E. meeting in February. Professor Desch is well known to metallur-gists in this country not only from his books on metal-lography, intermetallic compounds, the physicist in metallurgy, and the chemistry and testing of cement, but also by his many published papers in the technical journals. Professor Desch is the third distinguished foreigner to lecture before the. Institute of Metals under its pro-gram which calls for an annual lecture by a distin-

Jan 1, 1927

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

B. F. TILLSON,* Franklin, N. J.-A preliminary study of this paper did not, in my case, succeed in checking with the shovel dimensions of one of the large shovel manufacturers. I therefore raise a question as to there being some difference in standards used by different manufacturers in regard to the dimensions of the shovels for similar sizes and styles, so it may be rather confusing to some of us when we attempt to use the table in this paper and classify the capacity of the shovels as given here with some that are on the market.

Jan 4, 1919

"Salt Lake City was founded July 24, 1847, by Mormons under the leadership of Brigham Young. It had a population of 118,110, according to the United States census of 1920, and of 151,968, according to a civic survey, January 1, 1925. The Salt Lake metropolitan district is estimated to have 180,079 inhabitants.The city's area is 51.8 square miles. Its altitude is 4,354 feet. It has 514 miles of streets, of which 91 miles are paved. The streets in the main portion of the city are 132 feet wide and the blocks are 660 feet long. It has 144 miles of street railway and 2,200 electric street lights. It has fifteen parks and playgrounds, forty public schools and six private schools. It has eighty-nine church edifices, of which forty-nine are devoted to denominations other than the Mormon Church.It is the capital of the state, the headquarters of the Mormon Church and the headquarters of most of the mining companies and many other business institutions of the state and adjacent territory.The State University, the State School of Mines and the Inter-Mountain Experiment Station of the U. S. Bureau of Mines are in the eastern part of the city. Fort Douglas is east of the University the country clubs are in the southeastern portion of the city. The State Fair Grounds are in the northwestern portion.The city is the center of a trade area about 700 miles in diameter and is in almost the exact center of a circle that embraces the principal western mining areas. It is the home of several widely-known mining supply companies and all the other leading concerns in that line are represented by agency or branch house."

Jan 1, 1925

As already said Pattin's map and the later one of Evans' showed coal in several places in Ohio as early as 1750, and possibly 1748; the reference on the latter map was' to an exposure near Bolivar, in Tuscarawas County, as well as along the Hocking River. So far. as now known, it 'was not mined in either place until 1810. George Croghan, in descending the Ohio with his party in 1765, mentions an "Alum Hill" which they saw near the present site of Pomeroy, probably an exposure of saline deposits, but does not mention coal. As settlement north of the Ohio River was prohibited until 1787, no coal was mined until long after that date. In 1785 a survey of seven ranges in the Ohio country was made, the line running west from a point on the north bank of 'the Ohio River, due north of the western termination of the southern boundary of Pennsylvania. The surveyors noted, "from hence to Stoney Brook between two very steep and high Ridges; it is eight yards wide, its bottom is of Slate and Sand Stone, and in many parts of it are large pieces of excellent Coal washed by, the Rains from the Neighboring Hills."' This was the present Yellow Creek, and the coal was from some of the lower measures. The Scioto Company published a pamphlet in French in 1787, to promote the sale of their lands and emigration to them, in which was said,

Jan 1, 1942

By William Laird

The predominent method of coal mining in the United States for years has been room-and-pillar mining. The reason for this has been the advantages of room-and- pillar method which is a relatively flexible system and its capital investment. The room-and-pillar method permits some selectivity in mining, especially where gas wells, faults and possible coal quality may be a factor. The mobility of continuous and conventional mining equipment used to develop entries may also be used for retreat mining of rooms and pillars. Longwall mining of coal takes place along a long straight face, or wall, blocked out between two butt or panel entries. The long faces or walls are normally projected in lengths of 61 to 183 m (200 to 600 ft) in this country. The longwall method of mining had its beginning in the United States during the 1800's. During that period, pack wall and wood posts were used for roof support. The longwall face was mined by miners using picks to undercut the coal. To keep the coal face from turning over, short wood posts called sprags were set in a slant position as the coal face was undercut to the depth of two to three feet. When the under-cutting cycle was completed, the sprags were removed to permit the coal to fall from the roof pressure. The longwall mining of coal did not take a firm hold during the 18009s, and room-and-pillar prevailed. In the early 19009s, steel jacks were introduced, and along with it, the modified caving theory. In March of 1950, a retreat longwall mining system, utilizing a plow, manually operated props, wood cribs and chock releases, was installed in one of Eastern Associated Coal Corp.'s mines.

Jan 1, 1981

The key-note of good writing, as of good manners, is B natural. Sincerity is the first requisite for effective writing. When a man says what he knows or believes, he is likely to be interesting, because each human being possesses an individuality, a point of view, or a range of sympathy that makes him different from his fellows. To say or to write what you do not think, for the mere sake of talking or writing, is a verbal exercise that must be performed with extraordinary skill if it is to be attractive. Affectations are rarely attractive, rarely effective. To be natural is to be yourself, not a poseur; to give the reader the best of yourself, instead of re-warming the baked meats of yesterday. Quotations-which are second-hand thoughts-will serve occasionally when the thing you want to say has been said so well by another that it would be waste of energy to try to say it better; gut, as a rule, the utterance of the writer himself is more interesting than the quotation, because the writer brings something of himself to bear on the subject, and for the moment is more in touch with the reader than any dear departed author. Therefore, say things as best you can in your own way, neither in borrowed words nor in the phraseology that mimics another. Write as if you were speaking to a person whom you desire to persuade or convince. You will then write better than you speak, because, in the first place, you can be more deliberate, and, secondly, you can revise what you have written. Speaking and writing are similar mental acts, with a difference: the difference between eating food raw and eating it cooked. Some kinds of food gain nothing by being cooked; likewise some kinds of utterance are not bettered by being written down first; but most expressions of thought, especially

Jan 1, 1931

By Sandford S. Cole

Manganese compounds occur in many mineral forms widely distributed throughout the crust of the earth. The most important of these commercially are the oxides which are usually found as irregular masses, but in some places (notably U.S.S.R.) occur as extensive beds of varying thickness and purity. The principal sources of ore have been U.S.S.R., Ghana (the Gold Coast of Africa), India, Union of South Africa, Belgian Congo, French Morocco, Cuba, Brazil, and Mexico. New developments of ore are being conducted in Brazil, British Guiana, French Equatorial Africa, and Northern Rhodesia. The production of the United States normally meets less than 10 pct of domestic manganese consumption. Manganese ore (35 pct or more Mn) is used principally by the ferrous metallurgy industry for production of manganese metal, ferromanganese, and other manganese alloys for use in production of steel ingots and castings. Some manganese is used in the nonferrous industry as an alloying element and cleanser in aluminum alloys, aluminum bronze, constantan, manganese bronze, Monel, Everdur, nickel-chromium resistance alloys, and nickel-silver. The metallurgical uses consume about 97 pct of the total manganese ore requirements of the United States. The balance goes principally for the manufacture of dry cells and for chemicals, with limited amounts for ceramic products, plastics, welding rods and varnish. The Materials Survey on Manganese, compiled in 1952 for Materials Office National Security Resources Board by the Bureau of Mines and Geological Survey, provides an excellent review of resources, reserves, specifications, uses, mining, beneficiation, metallurgical processes and deposits, and is worth referring to for greater details. Mineralogy and Geology The more common manganese minerals with typical characteristics are listed in Table 1 in order of importance. [ ]

Jan 1, 1960

By William P. Blake

Postscript to the paper read by Prof. William P. Blake at the Lake Superior meeting, September, 1904. POSTSCRIPT.*-Since the publication of my paper upon the blackening of the surface of rocks in desert regions, I have noted that similar views of the origin of superficial discoloration in the case of certain rocks from the Salt Lake basin of Utah have been expressed by Prof. George P. Merrill. In the pamphlet, he described the brown-coated weathered boulders from Tooele county, reaching the conclusion that the discoloration was due to the solution of the manganese and iron compounds 'in the interior of the boulder, while they were in the water, and the gradual bringing of this material to the surface through capillarity and its oxidation when exposed.

Mar 1, 1905

By Lucius W. Mayer

WHILE the mind of the financier does not normally run along channels similar to those of his technical adviser, engineers, because of their exactness, are ever more called upon to manage affairs where financial matters are involved. It is, true, not a relatively large number have thus far functioned in this capacity. It is also true that the essentially financial mind could not serve in a responsible engineering position; for to be a successful engineer one requires precise thinking, making due allowance for factors of safety. To be a financier seems to require less aptitude for exact thinking than of enthusiasm and confidence in capitalizing prospective possibilities. Both require imagination, the engineer being, more conscious of the limitations of natural conditions. It is to be regretted that the engineer' stands so far aloof from financial matters. Many consider them- selves successful, as did Steinmetz, as long as their reward is the consciousness that they are giving supreme service to mankind. They are 'generally happy in their work and, like our honored brothers who are teachers, gain their greatest satisfaction, not in the amount of their remuneration so much as in the service rendered society and in the excellence of results achieved. Indeed, these sentiments bespeak character and command respect.

Jan 1, 1924

By S. Terry, W. Callender, R. J. Cornelius

When a dry ball-mill grinding circuit was in- stalled at the pellet plant of Hamersley Iron Pty. Ltd., it was something of a pioneering venture, since this was one of the first instances where such a circuit had been applied to iron ore on a major scale. The Hamersley pellet plant is located in Dampier on the coast of Western Australia. The feed for it consists of -8mm fines produced as a screened product at the Mt. Tom Price mine 186 miles inland from Dampier. It was these fines that encouraged the choice of a dry grinding facility for the plant. At the outset, tests had shown that the fines could not be filtered satisfactorily with a wet grinding system. At the pelletizing plant, the fines are stockpiled, reclaimed, dry ground in ball mills, formed into pellets on balling discs, hardened on an indurating line, and stockpiled for shipment overseas. These operations are shown in Fig. 1.

Jan 7, 1969

By R. G. Hudson, L. Yang

In electrochemical separation of metals, it is necessary to control the potential applied between the electrodes so that only the desired electrode reactions can occur. A knowledge of the minimum potential needed for a given electrode reaction to take place continuously is therefore pertinent to the success of the process. In molten chloride systems at high temperatures, activation polarization is believed to be small,1,2 so the minimum potential needed for the electrolytic decomposition of a molten metal chloride MC1n (n = valence of the metal ion) is therefore essentially the equilibrium electrode potential E of the metal-chlorine galvanic cell in the solution. If the decomposition products are pure M and chlorine at a pressure of p atm, E*Eo-rt/nf in [i] Since EO (the standard electrode potential of MCln) is a constant at a given temperature and R (the gas constant), and F (the Faraday's constant) are all constants, the variation of E with the electrolytic bath conditions is largely determined by the effect of the latter on the activity of the metal chloride amcln (standard state = pure MC1,). Measurement of E and study of how amCin varies with temperature and concentration, the nature of the solvent, and that of the coexisting solutes are therefore pertinent in the selection of optimum operating conditions for the electrochemical separation of metals. Because of its low melting point, high decomposition potentials of its components, and the low solubility of heavier metals in it, the LiC1-KC1 eutectic melt is a useful solvent and has been used in the electrodeposition of Mo,3Ce,4 and u5 metals. Senderoff and Brenner3 measured the potentials of Zn/Zn++, Fe/Fe++, Cu/Cu+, Mo/Mo+++, and Ag/Ag+ against an Ag/AgCl (pure) reference electrode at 600°C and a concentration of 4.1 mole pct of each chloride and came to the conclusion that complex ion formation occurred in some of the melts. Laitinen and LiUe gave an electromotive force series at 450°C for a number of {Metal/Metal ions (unit activity)) electrodes in LiC1-KC1 eutectic melt, the {pt/pt++ (unit activity)) electrode being chosen as the reference. Walker and Danly7 studied the ther-modynamic properties of NiC12 in LiC1-KC1 eutectic melt over a wide range of temperatures and concentrations by measuring the electrode potential between a nickel electrode and a chlorine electrode in the melt. Since potential measurements made by using the chlorine reference electrode are of more direct significance both in the study of electrochemical separation and in the evaluation of the thermodynamic properties of the melt, it is therefore decided to measure the electrode potentials of cells of the type {M/MCin (mole fraction = N) in LiC1-KC1 eutectic melt/Cl2 over a range of N values and temperature for a number of metal chlorides. The results should indicate the order by which the various metals plate out on the cathode and how this order is affected by temperature and the concentration of the metal chloride in the solu-

Jan 1, 1960

By Aloys H. Wohlrab

[THE conditions that govern the selection of a suitable type of detachable bit for the small isolated mine, for rock work and tunnel contracting and for the large mine are quite dissimilar, therefore intelligent recommendation of a particular make of detachable bit must involve consideration of many factors. Small, isolated mines may find advantageous a detachable bit that a larger mine cannot afford to use, because of more efficient conventional steel sharpening and steel-distribution practice, but a small mine may of be able to adopt the practice of larger mines because of necessary capital expendites for equipment for detachable-bit sharpening and shanking. The perfect detachable bit, suitable for all conditions, has n yet been developed. CONVENTIONAL DRILL BIT IN USE That drilling speed increases as the hit gauge decreases is well known, but since small-hole drilling is the exception rather than the rule the rate of such increase is probably not so generally recognized. Tests married out by Holman Brothers Limited1 with 7/8-in. show that when bit sizes are reduced from. 1 ½ in. 1 3/8 in., and 1 3/16 in., to 1 3/8 in., 1¼ in., and it' in., respectively, the volume of the hole is15 per cent less and the drilling speed 4q per cent higher. Recent tests by the United States Bureau of Mines2,3in hard, uniform basalt showed that a reduction in average gauge from 2.077 to 1.826 in., a difference of 0.251 in., gave an increased drilling speed of 65 per cent. The limits to which a drill hole may be extended depend upon the loss in gauge. Since the conventional bit with 5° and 14° clearances did not possess sufficient reaming edge to permit the smaller gauge changes that were required for small-hole drilling, experiments were made in bit construction with a view to correcting this deficiency. This resulted in the adoption of the full reaming cross bit (having full Carr characteristics) by some mines.4 In order to drill holes having a minimum taper from the collar to the bottom of the hole, full reaming center-hole cross bits with 90° cutting angles, 5° and I4° wing tapers, forged on 7/8-in. quarter-octagon drill rods, are used in the conventional drill-steel practice at Hollinger. In the steel shop close attention is given to the condition of the dies and dollies, which, combined with a rigid inspection of the finished bit, ensures as nearly a perfect bit as can be forged economically. Shop practices and costs have been discussed in earlier papers.5,6 The method by which the radii for the special dies used for forging bits of different gauge diameter are obtained so that the points and reaming edges cut circles of the same diameter has been discussed by Hibbert.7 REQUIREMENTS FOR DETACHABLE BIT FOR HOLLINGER Under these circumstances, it was apparent that it would be difficult to introduce a detachable bit that could successfully compete with the conventional bit already in]

Jan 1, 1942

By C. Zener, J. H. Hollomon

IT Is commonly recognized that a given material may be described as ductile or brittle only with reference to the conditions of test. Thus under the usual test conditions quartz is brittle, but under high pressures it is ductile. Salts that are brittle at room temperature become ductile at elevated temperatures. Pitch, brittle with respect o rapid loads, flows at low rates of loading. Pearlitic steel, ductile under the usual conditions of test, may be embrittled under the proper conditions of combined stresses, temperature, and rate of loading. EARLIER INVESTIGATIONS A clear analysis of the conditions necessary for plastic flow and for fracture was first given by Ludwik,1 who introduced two types of stress, the "flow stress" and the "stress at fracture." These stresses may refer to tensile or to shear stresses, or, in fact, to any type of stress. Ludwik considered these two stresses to be independent of one another, functions of the conditions of test and of the prior history of the material. For the purpose of analysis, both a flow stress and a stress at fracture can be envisaged as functions of strain over the entire range from zero to infinite strain. Thus, the material is brittle if the stress at fracture is less than the flow stress and ductile if the reverse is true. According to Ludwik's analysis, the problem of determining the effects of combined stresses, of temperature and of strain rate upon the behavior of metals reduces to a problem of determining the effect of these variables upon the flow stress and upon the stress at fracture. In the present paper, methods are described for determining the effects of two of these variables, temperature and strain rate, and examples are given of the dependence or now stress and stress at fracture, upon these two variables. The effect of combined stresses will be discussed in a succeeding paper. The flow stress may be determined from a load-diameter curve. Load-diameter curves were obtained over a wide range of temperature and over the limited range of strain rates obtainable with the lever-type Riehle machine used. The. curves were then converted to an extremely wide range of strain rate by making use of the equivalence of the effects of changes in strain rate and changes in temperature, previously proposed2 and demonstrated' by the authors. According to this principle of equivalence, strain rate E and temperature T affect the flow stress only through a single parameter p of the form: p = EeQ/RT [I] In this equation, R is the gas constant (2 cal. per gram mol per deg. C.), and Q is a heat of activation, which varies from material to material, and may depend upon the strain, but not upon the strain rate or the temperature. There is associated with every value of p a flow-stress curve. Combinations of strain rate and of temperature that give the same p have the same flow-stress curve. Therefore, merely by changing the temperature of test, the effect of changing the strain rate may be obtained. Thus, under isothermal conditions, the material will behave the same at

Jan 1, 1944

By R. I. Jaffee, C. M. Craighead, G. A. Lenning

The a-p type alloys are subject to a loss of tensile ductility with increasing hydrogen content. No hydride phase is visible in embrittled a-B type alloys. The embrittlement encountered appeared to be of the strain-aging type. Both compositional and structural factors are shown to influence the hydrogen tolerance of a-B type alloys. IN previous papers by the authors, the effects of hydrogen on the structure and mechanical properties of high-purity and commercial-purity titanium were described. It was shown that the presence of hydrogen in these materials results in a hydride phase having low solubility at room temperature. This insoluble phase had little effect on the room temperature tensile properties, but did decrease the notch-bar toughness to a large degree. The binary Ti-H systemz indicates that hydrogen is much more soluble in £ than in a-titanium. Hence, it is not expected that the embrittling effects of hydrogen in a-fi alloys will be similar to that found in a alloys. Materials of this type studied in the present investigation included two commercial a-/3 alloys, Ti-8Mn and Ti-4A1-4Mn; three high-purity Ti-Mn alloys containing 3, 6, and 9 pct Mn; and four high-purity Ti-Mo alloys, Ti-SMo, Ti-10.9M0, Ti-13.1 M0, and Ti-20M0, of the a-B and B types. Materials and Fabrication—The high-purity base alloys, composed of iodide titanium and high-purity metals, were prepared by double arc melting under argon in a water-cooled copper crucible, using a water-cooled tungsten electrode. Radiographic examination showed homogeneous Ti-Mo alloys. The analyses of the alloys used in this investigation and their as-fabricated hydrogen content, where determined, are listed in Table I. The two commercial alloys were 1/2 and % in. diam bar stock. No analyses other than hydrogen content were made. In order to maintain the a-B relationship existing in the two commercial alloys, vacuum annealing and hydrogenation were carried out in the B field prior to final fabrication. Fabrication then was done by The three high-purity Ti-Mn alloys were forged to 3/4 in. diam rods at 1600°F, and hot swaged to 1/2 in. diam at 1380°F. Machined and degreased bar stock was vacuum annealed or hydrogenated, fabricated to 1/8 in. diam rod by hot swaging, annealed in argon for 1 hr at 1380°F !75O°C), and water quenched. The six yz lb Ti-Mo ingots were forged to Wi in. diam rods at 1600°F and then hot swaged to % in. diam. Machined and degreased specimens were vacuum annealed or hydrogenated in the /3 field, prior to fabrication, by swaging to Y4 in. rod at 1400°F. After fabrication, the 5 and 10.9 pct Mo alloys were annealed in argon for 16 hr at 1290°F and water quenched to give equiaxed a-B structures. The higher molybdenum content alloys were argon annealed 4 hr at 1470°F and water quenched to give all £ structures.

Jan 1, 1957

By John H. Hollomon, C. Zener

It is commonly recognized that a given material may be described as ductile or brittle only with reference to the conditions of test. Thus under the usual test conditions quartz is brittle, but under high pressures it is ductile. Salts that are brittle at room temperature become ductile at elevated temperatures. Pitch, brittle with respect to rapid loads, flows at low rates of loading. Pearlitic steel, ductile under the usual conditions of test, may be embrittled under the proper conditions of combined stresses, temperature, and rate of loading. Earlier Investigations A clear analysis of the conditions necessary for plastic flow and for fracture was first given by LudwikI1 who introduced two types of stress, the "flow stress" and the "stress at fracture." These stresses may refer to tensile or to shear stresses, or, in fact, to any type of stress. Ludwik considered these two stresses to be independent of one another, functions of the conditions of test and of the prior history of the material. For the purpose of analysis. both a Flow stress and a stress at fracture can be envisaged as functions of strain over the entire range from zero to infinite strain. Thus, the material is brittle if the stress at fracturc is less than the flow stress and ductile if the reverse is true. According to Ludwik's analysis, the problem of determining the effects of combined stresses, of temperature and of strain rate upon the behavior of metals reduces to a problem of determining the effect of these variables upon the flow stress and upon the stress at fracture. In the present paper, methods are described for determining the effects of two of these variables, temperature and strain rate, and examples are given of the dependence of tlow stress and stress at fracture, upon these two variables. The effect of combined stresses will be discussed in a succeeding paper. The flow stress may be determined from a load-diameter curve. Load-diameter curves were obtained over a wide range of temperature and over the limited range of strain rates obtainable with the lever-type Riehle machine used. The curves were then converted to an extremely wide range of strain rate by making use of the equivalence of the effects of changes in strain rate and changes in temperature, previously proposed2 and demonstrated3 by the authors. According to this principle of equivalence, strain rate e and temperature T affect the flow stress only through a single parameter-p of the form: p = eeQ/RT 111 In this equation, R is the gas constant (2 cal. per gram mol per deg. C.), and Q is a heat of activation, which varies from material to material, and may depend upon the strain, but not upon the strain rate or the temperature. There is associated with every value of p a flow-stress curve. article of strain rate and of temperature that give the same p have the same flow-stress curve. Therefore, merely by changing the temperature of test, the effect of changing the strain rate may be obtained. Thus, under isothermal conditions, the material will behave the same at

Jan 1, 1944

By C. Zener, John H. Hollomon

It is commonly recognized that a given material may be described as ductile or brittle only with reference to the conditions of test. Thus under the usual test conditions quartz is brittle, but under high pressures it is ductile. Salts that are brittle at room temperature become ductile at elevated temperatures. Pitch, brittle with respect to rapid loads, flows at low rates of loading. Pearlitic steel, ductile under the usual conditions of test, may be embrittled under the proper conditions of combined stresses, temperature, and rate of loading. Earlier Investigations A clear analysis of the conditions necessary for plastic flow and for fracture was first given by LudwikI1 who introduced two types of stress, the "flow stress" and the "stress at fracture." These stresses may refer to tensile or to shear stresses, or, in fact, to any type of stress. Ludwik considered these two stresses to be independent of one another, functions of the conditions of test and of the prior history of the material. For the purpose of analysis. both a Flow stress and a stress at fracture can be envisaged as functions of strain over the entire range from zero to infinite strain. Thus, the material is brittle if the stress at fracturc is less than the flow stress and ductile if the reverse is true. According to Ludwik's analysis, the problem of determining the effects of combined stresses, of temperature and of strain rate upon the behavior of metals reduces to a problem of determining the effect of these variables upon the flow stress and upon the stress at fracture. In the present paper, methods are described for determining the effects of two of these variables, temperature and strain rate, and examples are given of the dependence of tlow stress and stress at fracture, upon these two variables. The effect of combined stresses will be discussed in a succeeding paper. The flow stress may be determined from a load-diameter curve. Load-diameter curves were obtained over a wide range of temperature and over the limited range of strain rates obtainable with the lever-type Riehle machine used. The curves were then converted to an extremely wide range of strain rate by making use of the equivalence of the effects of changes in strain rate and changes in temperature, previously proposed2 and demonstrated3 by the authors. According to this principle of equivalence, strain rate e and temperature T affect the flow stress only through a single parameter-p of the form: p = eeQ/RT 111 In this equation, R is the gas constant (2 cal. per gram mol per deg. C.), and Q is a heat of activation, which varies from material to material, and may depend upon the strain, but not upon the strain rate or the temperature. There is associated with every value of p a flow-stress curve. article of strain rate and of temperature that give the same p have the same flow-stress curve. Therefore, merely by changing the temperature of test, the effect of changing the strain rate may be obtained. Thus, under isothermal conditions, the material will behave the same at

Jan 1, 1944