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By W. C. Schroeder

PRACTICAL experience has shown that at elevated temperatures solu-tions containing sodium hydroxide may attack stressed steel in a manner that cannot be explained in terms of ordinary corrosion. Because the ductility of the metal has been greatly reduced during the reaction, the entire phenomenon is usually called "embrittlement." Thus, after several years of operation caustic evaporators have been so badly embrittled that rivets could be cracked off with the blow of a hammer. Since fine intergranular cracks are almost always present in the zone of fracture, it has often been assumed that a process of selective corrosion in grain boundaries was responsible for the failure, although this has not been clearly proved experimentally. Concentrations of sodium hydroxide below those necessary for the uniform, rapid attack of the steel surface are reported to be most effective in producing embrittlement2,3. In the operation of steam boilers a similar type of failure has been found, mainly in riveted seams or other capillary spaces where the solu-tion may concentrate and where high stresses may also exist. It is believed that in such localized areas the dissolved solids may reach a value many times the few hundred parts per million prevalent in the body of the boiler. While this type of boiler failure has been the subject of investigation for a period of 20 years', an understanding of its mecha-

Jan 1, 1936

By L. C. Graton, Joseph Murdoch

I. Introduction......................... 26 1. The Relations of Scale in Geologic Work........ 26 2. General Characteristics of Copper Sulphide Ores..... 29 3. Scope of Present Study................. 31 11. Description of the Important Minerals............ 36 1. Pyrite....................... 36 2. Pyrrhotite....................... 41 3. Chalcopyrite...................... 41 4. Bornite........................ 40 5. Covellite....................... 50 6. Chalcocite....................... 52 7. Enargite...................... 59 8. Tetrahedrite and Tennantite.............. 61 III. Conclusions.......................... 62 I. Introduction. The Relations of Scale in Geologic Work. Many features of human accomplishment rest upon the possibility of representing natural objects on a scale of different magnitude from the actual one. Most drawings, for example, are of very different scale from that of the object depicted, and indeed are useful mainly 011 this account. More important than the question of mere convenience, however, is that of meeting the physical limitations of vision.' Thus, a mural

Jan 1, 1914

By H. M. Howe

A Discussion of the paper of Professor Howe, presented at the London Meeting, July, 1906, and printed in Bi-Monthly Bulletin, No. 14, March, 1907, pp. 169 to 274. SECRETARY'S NOTE.-M. Beutter's introductory remarks, being simply a resume of Prof. Howe's paper, with a disclaimer of the intention to criticise it, have been omitted, and the remainder of this contribution has been somewhat condensed, without omitting any essential statements. M. BEUTTER, St. Etienne* (communication to the Secretary-+):-Professor Howe observes in paragraph 47 of his paper that the fluid-compression of steel. diminishes piping by forcing the liquid and viscous metal, while the pipe is forming, or after it has formed, into the space so produced, and proceeds to study the different systems of compression, alluding to the four principal ones: Whitworth, Illingworth, Williams, and Harmet. Having now for many years had in use the last-named process, that of M. Henri Harmet, I shall attempt to explain the difference between it and the three other processes named. The Harmet process does not diminish or close the pipe after it has formed, but prevents it from forming; and I may add that it is the only one of the four which produces this result. It is true that the Whitworth process diminishes the interior hollow by localizing it around the central axis of the ingot, which is afterwards removed by trepanning the hollow forgings for which this process has been, I believe, always exclusively used. The Illingworth and Williams processes, which, in my opinion, are applicable only to small ingots, of necessity allow the pipe to form, or (to use the expression of Professor Howe) they allow the surface of the lake of liquid steel to sink into the interior of the ingot, since they involve waiting a certain time before compression, so that (in the case of the Williams process) the ingot-mold can be opened without dan¬ger, or (in the case of the Illingworth process) so as to avoid the risk that the steel may enter the grooves produced by the removal of the distance-bars. During the time required for

Jul 1, 1907

Apr. 9, AIME, Chicago Section, Chicago Bar Assn., 29 S. La Salle St., Chicago. Apr. 11-12, Geological Society of America, Cordilleran Section, annual meeting, University of Arizona, Tucson. Apr. 15, AIME, Morenci Subsection, Longfellow Inn, Morenci, Ariz. Apr. 15-17, AIME, South West district meeting, Jefferson Hotel, St. Louis, Mo. Apr. 17, AIME, Utah Section, New House Hotel; Salt Lake City. Apr. 21-22, American Zinc Institute, annual meeting, Hotel Statler, St. Louis. , Apr. 21-23, Chemical, Metallurgical, and Mining Society, and Diamond Drilling Research Laboratory, symposium on diamond drilling, Johannesburg, South Africa. Apr. 22, Assn. of Consulting Chemists & Chemical Engineers, Inc., general symposium, Hotel Belmont Plaza, New York. Apr. 25-26, AIME, New England Regional Conference, Kenmore Hotel, Boston. Apr. 26-May 11, Liege International Fair, Liege, Belgium. May 4-8, Electrochemical Society, Inc., Spring meeting, Benjamin Franklin Hotel, Philadelphia.

Jan 1, 1952

By Frederick G. Coqueron, Joseph E. Pogue

FOR a number of years, the Department of Petroleum Economics of The Chase National Bank has been conducting a study of the capital employed in the petroleum industry. The technique followed is that of combining and summarizing the available financial and operating data for a group of thirty representative oil companies, doing about two thirds of the domestic business of the entire industry. This paper presents the results of the findings for the year 1943, and supplements the survey, "Sources, Disposition, and Characteristics of the Capital Employed by Thirty Oil Companies During the Nine-Year Period, 1934-1942," presented before the Petroleum Division of the American Institute of Mining and Metallurgical Engineers on Feb. 24, 1944, and also published as a pamphlet by The Chase National Bank.

Jan 1, 1944

By AIME AIME

THE 122d meeting of the Institute was held in the Lake. Superior Copper and Iron Country Aug. 20 to Sept. 3, 1920 with an approximate registration of 1100 members and guests. This is the 'first visit of, the Institute to this vicinity since 1904 although previously it held meetings there every six or, seven years. 'The eastern party assembled at Buffalo and sailed on the S. S. "Tionesta ". on Friday morning, Aug. 20, arriving at Houghton, Mich., Monday, Aug. 23. En route stops were made at Detroit, where sightseeing auto trips were taken, and at Mackinac Island, where a short stop permitted a visit to the picturesque and historic Fort Mackinac.

Jan 1, 1920

By B. C. Mariacher, I. Hoffman

In 1952, beneficiated phosphate ore first began to move from the Oron plant of Negev Phosphates Ltd. in the Negev Desert to the super-phosphate plant at Haifa, Israel. Since that time this company has continually sought to overcome its natural handicaps affecting the operating efficiency and quality of the product in an effort to bolster the agricultural program of Israel and the development of an exportable commodity. The most serious deterrent to the development of a beneficiation process was the total absence of water. The Oron plant lies approximately 30 miles south of the irrigated regions of Israel with the nearest producing water well located about 10 miles to the northwest. The urgency of early phosphate production made it necessary to consider only dry processes in the initial operation. Fortunately, the ore was amenable to a dry process which yielded a usable concentrate assaying about 28.5 pct P2O5; but phosphate recovery was low. A description of the characteristics of the Negev ore should help to clarify the principles upon which the dry concentration is based.

Jan 5, 1961

By E. Morgan Massey

Located in virgin coal acreage near Gilbert, W. Va., Massey Coal Mining Co.'s Ben Creek No. 2 mine afforded the company's engineers the opportunity of designing and laying out the entire mining operation from the mine faces to the railroading loading site. However, the topography of this region posed difficult problems in haulage of coal for, in this extremely rugged terrain the uppermost coal seams lay in the mountain-top ridges, approximately 1400 ft above the valley floor. The decision for mining equipment naturally leaned to the new high-capacity continuous miners where seam conditions permitted: otherwise, to the new super-high capacity conventional cutting and loading machines. Since the coal seams lay in ridges and points of considerable outcropping, the decision was to keep the transportation on the surface and mine the coal with multiple entries into the outcrop. This way, the major problems of underground haulage, drainage, and ventilation are eliminated, and the opportunity to take advantage of a-c underground power becomes a much simpler proposition.

Jan 10, 1960

Jan 1, 1967

By Harold S. Morgan

INTRODUCTION The Waste Isolation Pilot Plant (WIPP) is being developed in southeastern New Mexico by the United States Department of Energy as a research and development (R&D) facility to demonstrate the safe disposal in salt of radioactive wastes resulting from defense activities. As part of the WIPP R&D program, a series of in situ tests will be performed to determine the behavior of drifts and storage rooms in the creeping salt medium (Matalucci, et al. 1982). Data obtained in these tests will be used to evaluate and improve numerical models used to compute the structural response of these drifts and rooms. Stress has been proposed as one of the parameters to be measured in the tests, and borehole inclusion stressmeters have been included in the instrumentation package. Cages of this type provide an indirect measurement of stress change in that they actually monitor borehole displacements which are then related to changes in the in situ stress away from the borehole. The relationship between stress and displacement is highly dependent upon the constitutive behavior of the rock in which the gage is emplaced. This relationship is well understood for rocks with linear stress-strain behavior (Fossum, et al, 1976), but, for creeping rocks like salt, the relationship has yet to be determined. Thus, inclusion gage response in salt must be investigated fully before stress measurements from the WIPP in situ tests can be used for comparisons with computed stresses The calculations presented in this paper were performed as part of an investigation of inclusion stressmeter performance in salt. They focus on the strain gaged stressmeter (SGS) (Cook and Ames, 1979) and on a hypothetical solid cylindrical inclusion with variable stiffness Issues addressed include the effects of creep and the effects of gage stiffness on stressmeter output for various loading conditions. The

Jan 1, 1984

By A. E. Harnsberger

IT is obvious that details such as the physical and chemical properties and methods of heat-treating of the materials mentioned must be omitted in a paper on the subject of materials used in oil-refinery pumps1. Only sufficient identification is given to enable the reader to find additional information from already published data. Also, the subject covers many operating conditions, but only the most important services can be discussed here. To the oil refiner, the pumping equipment is of vital interest. Practi-cally every refinery operation, from the charging of crude oil to a dis-tillation unit to the shipping of refined products, involves some form of pumping machinery. Intermediate refining stages involve a great variety of pumping machinery to carry out successfully the aims of the refinery technologist. Temperatures at which oils are handled vary from -50° F. to 900° F. Pressure may vary from subatmospheric to 2000 lb. per, sq. inch. The selection of the proper materials involves a careful consideration of the conditions under which the particular pump must operate. The four most important considerations are temperature, pressure, corrosion, and abrasion or wear. Consideration of temperature may be divided into three parts: (1) extremely low temperatures of the order of -50° F.; (2) temperatures at atmospheric or slightly above; (3) temperatures from 200° to 900° F. Pressures fall into two groups: (1) pressures reached by ordinary trade pumps of the order of 200 lb. per sq. in., (2) extreme pressure conditions involving pressures as high as 2000 lb. Noncorrosive and corrosive oils can be treated differently. Under the latter falls corrosion in the presence of water, which will occur up to 250° F. The second type of corrosion occurs in high-temperature pump-ing equipment, with temperatures from 450° to 900° F., largely caused by sulfur compounds. There are also other corrosive conditions met with

Jan 1, 1935

By F. C. Wagner, E. P. Klier, D. E. Nulk

The presence or absence of plastic strain at a cleavarage surface is a question of much importance, and upon its answer depends future possible theoretical work. To investigate this question back-reflectinn X ray patterns were obained on the cleavage facets of ferrite grains. The test set-up consisting of FeK colli- mated radiation, single grain material and stationary cassette and specimen will not lead to a diffraction pattern, in general, but is an ideal arrangement for the exami-nation of surface effects. A pattern taken on hydrogen purified

Jan 1, 1949

By F. B. Plummer, R. B. Newcome

The practice of introducing acid into oil wells to increase production of oil and gas has been in use since 1894, when it was first used in the Pennsylvania oil fields30.‡ It is only since 1928 that it has been used to any extent in the Mid-Continent18. The process has proved successful in increasing production, at least temporarily, in depleted oil fields where the producing formation is highly calcareous and where water drive is not too pronounced. In the Zwolle field in Louisiana, where the producing horizon is a chalk, increases of 100 per cent have been recorded25. In north-central Texas, where the oil is produced from the Marble Falls limestone, equally pronounced increases have resulted3. The production also in some fields yielding oil from quartz sand cemented with calcitc has been benefited. The evidence of actual increase in total recovery of oil, however, has been questioned by some engineers18. It has been pointed out that the results of the treatment of a well in a now district, where the process has never been tried out, can never be predicted with certainty, since other factors besides percentage of calcareous content of the oil sand play a large part in determining the success of the method. Numerous articles have been published on acid treatment and on the effects of acid on limestone1-35, yet very little has been written concerning experimental work on the actual effect of acid on capillary pores and larger oil-coated voids of oil sands. This is due partly to difficulties in duplicating field conditions in a laboratory and partly to the fact that the process has been carried out largely by contracting companies that have been unwilling to publish details of their results for fear of loss of business to competitors. The authors, using equipment developed to measure the radial permeability of oil-sand cores2', have developed a method of investigating the results of acid treatment which has enabled them to test numerous cores and to study in some detail the action of acid on the different types of rocks, particularly fine-grained rocks.

Jan 1, 1936

By F. B. Plummer, R. B. Newcome

The practice of introducing acid into oil wells to increase production of oil and gas has been in use since 1894, when it was first used in the Pennsylvania oil fields30.‡ It is only since 1928 that it has been used to any extent in the Mid-Continent18. The process has proved successful in increasing production, at least temporarily, in depleted oil fields where the producing formation is highly calcareous and where water drive is not too pronounced. In the Zwolle field in Louisiana, where the producing horizon is a chalk, increases of 100 per cent have been recorded25. In north-central Texas, where the oil is produced from the Marble Falls limestone, equally pronounced increases have resulted3. The production also in some fields yielding oil from quartz sand cemented with calcitc has been benefited. The evidence of actual increase in total recovery of oil, however, has been questioned by some engineers18. It has been pointed out that the results of the treatment of a well in a now district, where the process has never been tried out, can never be predicted with certainty, since other factors besides percentage of calcareous content of the oil sand play a large part in determining the success of the method. Numerous articles have been published on acid treatment and on the effects of acid on limestone1-35, yet very little has been written concerning experimental work on the actual effect of acid on capillary pores and larger oil-coated voids of oil sands. This is due partly to difficulties in duplicating field conditions in a laboratory and partly to the fact that the process has been carried out largely by contracting companies that have been unwilling to publish details of their results for fear of loss of business to competitors. The authors, using equipment developed to measure the radial permeability of oil-sand cores2', have developed a method of investigating the results of acid treatment which has enabled them to test numerous cores and to study in some detail the action of acid on the different types of rocks, particularly fine-grained rocks.

Jan 1, 1936

By J. J. Jakosky

THE fundamental hydrodynamic principles governing the production of oil from wells have been carefully studied and evaluated by many investigators. These prior studies are quite complete and cover virtually the entire field of oil production and recovery.1 One of the most impor-tant measurements in production studies is that of the bottom-hole pressure at various rates of production.2 It is the purpose of this paper to outline the technique and economics of fluid-level measurements as applied to pumping wells and to review briefly other methods for obtain-ing bottom-hole data. The applications of bottom-hole pressure or fluid-level measure-ments are based on simple hydrodynamic principles. Under equilib-rium conditions, pbh = hd + pg + pch [ l] when pbh = bottom-hole pressure, lb. per sq. in. absolute, h = height of fluid in well, ft., d = average fluid density, lb. per sq. in. per foot, pg = weight of section of gas column 1 in. square from fluid level to casing head, pch = casing-head pressure, lb. per sq. in. absolute. In words, equation 1 states that the bottom-hole pressure is equal to the weight hd of the column of fluid plus the weight of the column of gas between the fluid and the casing head plus the casing-head pressure. At moderate rates of flow, the rate of production is approximately proportional to the difference between the reservoir, or static bottom-hole, pressure and the flowing or producing pressure; i.e.: Q = c(pr - pbh) [2] pr = the reservoir pressure, c = the constant of proportionality. However, at production rates approaching zero and also at high rates the proportionality may break down. By combining equations 1 and 2 the

Jan 1, 1939

By E. A. Anderson

THIS seems to be the year for superlatives in A.I.M.E. meetings. The programs of the various Divisions and Institute committees offered an abundance of interesting and valuable information in the form of technical papers, symposia. and lectures to large and interested audiences. The Institute of Metals Division may hold up its head with pride for its own program. With six technical sessions, three full-day symposia, and the annual I.M.D. dinner, four meeting days were not enough and many simultaneous sessions were required. The quantity and quality of the paper were equaled by the numbers and interest of those attending.

Jan 1, 1944

By Rossiter W. Raymond

(Canal Zone Meeting, November, 1910.) THE death of Professor Blake removes the oldest of American economic geologists and mining engineers, and deprives this Institute of one of its, earliest and most illustrious members. To many of us it brings a personal loss also, the loss of a friend. William Phipps Blake was born June 21, 1826, in New York City. -His father, Elihu Blake, was a surgeon-dentist of eminence, a direct descendant of William Blake, who settled in the Massachusetts Bay Colony about 1630. He was prepared for college at private schools in New York, and entered the Sheffield School of Yale, where he was graduated as Ph.B. in the chemical course, class of 1852, the first graduating-class of the institution. In the same year he became chemist and mineralogist of the New Jersey Zinc Co., and chemist of chemical works at Baltimore, Md. In 1853, lie started the Department of Mineralogy of the World's Fair at New York City. In 1854, 1855 and 1856, he was mineralogist and geologist of the United States Pacific Railroad Surveys of Williamson, Pope, and Whipple, and for the War Department at Washington. His writings, during this period comprise reports on the geology and mineralogy of California and other parts of the Southwest, and constitute well nigh the earliest scientific accounts of the regions described. One of them. was a translation of the Resume and Field Notes of Jules Marcou, of Whipple's expedition. From 1856 to 1859, he was engaged in explorations of the geology and mineral deposits of North Carolina, :and other parts of the country. In 1859, he became editor and proprietor of The Mining Magazine. This was a monthly periodical, founded in 1853 by W. J. Tenny, who conducted it until 1858, when it passed into the hands of Thomas McElrath, a New York publisher, and appeared in May of that year as The Mining and Statistic Magazine, with the name of

Sep 1, 1910

By J. E. Dorn, S. K. Mitra

The low -temperature tensile and creep behaviors of single crystals of copper were evaluated and analyzed in such a manner as to provide an estimate of the separate contributions of short-and long-range stress fields to strain-hardening. Furthermore, the average force-displacement diagram for thermally activated intep-section of two dislocations was estublished. This diagram plus a knowledge of the variation of dislocation spacing and the long-range back stresses with strain permits on accurate prediction of creep rates. The calculated activation energy for intersection under conditions of a constant strain rate increases linearly with the absolute tempevatus-e as required by theory. AN understanding of the detailed mechanisms for strain hardening constitutes one of the principal unsolved problems in dislocation theory. Two major models for strain hardening have been advanced in the past. The one that has received greatest attention assumes that strain hardening arises exclusively from long range interaction stresses between moving dislocations and piled-up arrays of blocked dislocations on the slip planes. This type of interaction was first announced by Taylor' who revealed that the back stress fields due to a simple uniform array of positive and negative dislocations entrapped in the deformed crystal would result in parabolic hardening. Shortly thereafter Andrade and Henderson" demonstrated that the strain hardening of fcc single crystals was not parabolic, as previously thought, and finally it was recognized that a typical stress-strain curve consisted of three successive stages of deformation, niz., the easy glide, Stage I, linear hardening, Stage 11, and the parabolic hardening, Stage 111, ranges. The objections to Taylor's somewhat na'ive model, which were presented so forcefully by cottrell; were largely removed by the more realistic details incorporated in Mott's analysis.5 But because Mott's theory for hardening via long range stress fields gave somewhat analogous results to that of Taylor's (inasmuch as it also predicted a parabolic rate of strain hardening whereas the observed rate of strain hardening in Stages I and I1 were linear), it was not widely accepted. Major consideration was therefore given to models, such as those which were advanced by Friedel and seegere that were formulated for the ad hoc purpose of yielding linear rates of strain hardening. The second major thought regarding strain hardening is based on the concept that it arises principally from short-range stress fields due to the interactions between intersecting dislocations. Cottrell and stokes7 showed, several years ago, that the constancy of the flow stress ratio at two temperatures regardless of the strain was inconsistent with the concept that strain hardening arose exclusively from long-range back stresses. The argument that strain hardening was primarily due to local interactions of intersecting dislocations was presented in considerable detail by asinski.' Extending Basinski's method of analysis of the intersection process, Mitra, Os-borne, and dorn recently demonstrated that indeed the strain hardening in aluminum single crystals arises principally from local effects coincident with intersection; however, these conclusions, too, must be modified, as will be shown later in this report. The present investigation, devoted principally to the low-temperature deformation of copper single crystals, was initiated in an attempt to ascertain whether or not the same conclusions arrived at for aluminum also apply to metals, such as copper, which have much wider stacking faults. It was soon observed that the strain hardening in copper could not be attributed exclusively to local effects between intersecting dislocations. Previously no analytical method for arriving at the possible simultaneous contributions of long-range stress fields and localized forces on intersecting dislocations was available; consequently, the separation of these two factors could not be readily accomplished. In the present report a method of estimating the separate contributions of each of these two factors to strain-hardening will be presented. The authors will show that both long-range stress fields of the type contemplated by Seeger and Friedel as well as short-range forces of the type considered by Basinski are responsible for strain hardening in fcc metals at low temperatures. This method of analysis also accounts for, in a satisfactory way, the effect of stress, temperature, and strain on the creep rate under constant stress. Furthermore, in the course of presenting their methods of analysis the authors will also reveal the rather complete agreement of their experimental data with the concepts of the theory for thermally activated intersection of dislocations. INTERSECTION MODEL As shown by seegerl0 the strain rate arising from thermally activated intersection of dislocations is given by

Jan 1, 1962

By M. J. Sinnot, J. C. Shyne

Low-frequency mechanical damping measurements were made to investigate internal friction in Fe-A1 alloys. The atomic ordering of the Fe-A1 system strongly influenced the stress-induced ordering internal friction. Magnetoelastic damping was also encounteyed and was shown to be reduced by the application of a static stress. THIS paper describes some damping experiments made on alloys of Fe and Al. Stress-induced ordering internal friction was measured with samples containing from 9.8 to 31.3 at. pct Al. Aluminum is soluble in a-Fe to about 50 at. pct and forms at least two long-range ordered structures, Fe3Al and Feu.' Stress-induced ordering internal friction is known to occur in many substitutional solid solutions, but few measurements of this damping effect have been made with alloy systems that have pronounced ordering tendencies. LeClair and Lomer developed expressions relating the relaxation strength of the damping process to the degree of atomic ordering and predicted that stress-induced ordering internal friction would be zero with complete ordering.' This concept was confirmed experimentally by Lulay and Wert using the system cd-Mg It is also consistent with the weak stress-induced ordering peaks observed in P -brass by Artman and in 16 wt pct Al Fe-Al by bert.' It was expected, therefore that the ordering characteristics of the system Fe-Al would strongly influence the stress-induced ordering internal friction exhibited by the experimental alloys. SAMPLE PREPARATION The alloys used in this investigation were induction melted under vacuum using high-purity melting stock. The iron was electrolytically refined Plastiron 101 which contained 99.85 wt pct Fe. The aluminum was a special 99.95 pct pure grade supplied by Alcoa. The only other raw material was spectrographically pure graphite which was used in small quantities as a deoxidant. The amount of carbon used was slightly in excess of the amount required to completely deoxidize the melt; this resulted in residual carbon contents of 0.01 to 0.02 pct in the finished alloys. The vacuum cast 2 1/2-in. diam ingots were hot rolled to 5/8-in. diam round bars. Portions of these bars were hot swaged and hot drawn to 0.050-in. diam wire. Straight pieces of the hot drawn wire were slowly heated to a temperature of 1300°C in a He atmosphere. After holding for 4 hr, the samples were allowed to cool in the furnace. This annealing treatment resulted in grain growth in the samples, the final grain size being about the same as the wire diameter. The grain boundaries were oriented perpendicularly to the wire axis, giving a bamboo grain structure. The existence of a preferred orientation could not be detected in these coarse grained samples. If the samples had a fiber structure, this probably would have been the same in all samples because of similar processing, thus the influence of crystal orientation on the relaxation strength would have been similar in all samples. The aluminum contents of the alloys are listed in Table I. EQUIPMENT The principle of the torsion pendulum was used for the internal friction measuring device. The

Jan 1, 1961

By L. G. Margolin

INTRODUCTION In this paper we derive an expression to predict the onset of growth of a crack in a quasibrittle material. We employ an energy criterion, which was first proposed by Griffith (1920), and is essentially equivalent to the first two laws of thermodynamics. The criterion is applied to the elastic-plastic crack of Olesiak and Wnuk (1968), which is a three-dimensional generalization of the Dugdale (1960) crack. Our expression for the onset of growth differs in several respects from a criterion based on a crack in a brittle material (i.e., using linear elastic fracture mechanics) . Furthermore, the new features are in qualitative agreement with the experimental data. Among these new features are 1) the dependence of the apparent surface energy, or critical strain energy release rate on crack size (the shape of the R-curve); 2) the effect of in-plane stresses (i.e., the stresses that do not lead to any traction on the crack faces) on crack growth; and 3) a brittle-ductile transition. The energy criterion, as a necessary condition for crack growth, rests on a firm theoretical basis. However, its role as a sufficient condition is less secure. Several alternate criteria have been proposed as necessary and sufficient conditions for the onset of crack growth. We will contrast several of these, including critical strain (Olesiak and Wnuk, 1968; Goodier and Field, 1963) and crack opening displacement ("COD", Burdekin and Stone, 1966) with the energy criterion. We will show that these alternate approaches are inconsistent with the energy criterion, in the sense of being necessary conditions, and so should be rejected as criteria for growth--at least for the elastic-plastic crack.

Jan 1, 1984