THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING THE INFLUENCE OF SOME PHYSICAL PROPERTIES ON MACHINABILITY OF METALS Alexander Henkin A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan Department of Mechanical Engineering 1962 June, 1962 IP-572

Doctoral Committee: Associate Professor Joseph Datsko, Chairman Professor John Ao Clark Professor Samuel Ko Clark Professor Charles Lipson Professor Clarence Ao Siebert ii

ACKNOWLEDGEMENTS I wish to express my appreciation to: Professor J, Datsko, the Chairman of the Doctoral Committee, for his encouragement, critical suggestion and friendly counsel, Professors J. A. Clark, S. K, Clark, C. Lipson and Co A. Siebert, Members of the Doctoral Committee, for their advice and assistance during this investigation, Professor J. G. van Wylen, Chairman of the Mechanical Engineering Department for my staff appointment, and the H.T.I and Rackham School of Graduate Studies for the Predoctoral fellowships, The other members of the staff for their constructive commentso The National Science Foundation for its financial support of this study. The United Steel Corporation, the Bethlehem Steel Company, the Aluminum Company of America and the Climax Molybdenum Company of Michigan for the materials provided for this research. The Industry Program of the College of Engineering for its help in the reproduction of the dissertation, iii

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS o o o o... O O O O o O o O o o O O O o o o iii LIST OF TABLES. oooooooooooooo0000 o,0000 0000000000 000o0o 0o0000o. V LIST OF FIGURES o o o o ao o a e. o. * o o o a o a o o O, a O o O O O 0 9 vi I INTRODUCTION oooo................. o o.......... o o o o o 1 II REVIEW OF LITERATURE........... o o OOO............. o. 7 General..,,90.........99 9...9 7l Chip Formation o. o o O o..,, O o O O O. o. O. O O O o o o. o o o 8 Machinability and Physical Properties...............o oo0o000 17 III EXPERIMENTAL PROCEDURES AND RESULTS.........ooo0 0000000 20 Materials o..,... 0 o o o a o a o o o o o o o o a ao0.. 20 Tensile Tests.......................0000.0090.0000900........ 20 Tensile Tests o,,o.,o o 400 OO o oO3 o o e 0 o O O o O o o O O O O O O 20 Hardness Tests and Meyer Strain Hardening Indexo............. 23 Impact Tests,.O...o.o,,,,oooooooooooo.ooo ooo ooooooo ooo.o 28 Thermal Properties.... o...o.ooo.o.o.oo.ooo.ooooooooooo ooooo 33 Metallography......,,...,oooooooo..... 0 o o o o o oo o a 33 Microhardness Measurements of the Chip,.. ooooo oo............ 39 Machinability Tests.., o....oo... oo oooooo 40 Cutting Temperatures, o o o ~ ~... 51 Abr-asive Wear Testing.......0.........oooo9o9ooooo.ooo.o 59 Elevated Temperature Properties...................... 00.Oo 62 IV DIMENSIONAL ANALYSIS AND THE GENERAL MACHINABILITY EQUATION o 71 The Development of the General Machinability Equationo.oo..o 71 The Effect of the Size of Cut on the Cutting Velocity for Constant Tool Life o...............*o.o....0.oooo.oo9o9ooo. 87 Tool Life Velocity Relationship,,9 o9oooO,,o...o.o.ooooOOO. 94 V CONCLUSIONS,, O, o.Q o f o o o o 0 o o o. o. o 4,0, O O O 00000000000000000000000 00 95 V CONCLUSIONS,,........................................999. 9 5 APPENDICES A SAMPLE CALCULATION OF TOOL LIFE RELATIONSHIP FOR AISI 4340 STEELo o o 4, o o o o.... o o o.......o o o o. o o. o o o e. 97 B VERIFICATION OF THE POSTULATED EFFECT OF THE SIZE OF CUT ON BIBLIOGRAPHY o o o o o o o o o o o o o o o o o o o o 101 iv

LIST OF TABLES Table Page I CHEMICAL ANALYSIS OF THE MATERIALS..... 0............ o... 22 II STRESS STRAIN RELATION CONSTANTS, FLOW STRESS AND DEFORMATION ENERGY................................... o.. o 26 III TENSILE PROPERTIES OF TEST SPECIMENS........................ 27 IV BRINELL, MEYER AND ROCKWELL HARDNESS NUMBERS AND MEYER STRAIN HARDENING EXPONENT..o.............o..O...................... 29 V CHARPY IMPACT STRENGTH OF TEST SPECIMENS..oo..o oo0.....o.. 00 32 VI THERMAL PROPERTIES OF TEST SPECIMENS AT 77~F................. 34 VII PEARLTTE CONTENT OF THE STEELS............................... 40 VIII CUTTING SPEED TOOL LIFE CONSTANTS.... o...........0o o.o..0o 51 IX CUTTING TEMPERATURE CONSTANTS....................... 58 X ABRASIVE WEAR MAXIMUM PRESSURES AND NORMAL LOAD APPLIED...... 65 XI ABRASIVE WEAR TEST RESULTS...............*ooo........ 66 XII ELEVATED TEMPERATURE PROPERTIES OF MATERIALS TESTED IN THIS STUDY... o..o o o...... o e................... o. o o 68 XIII ELEVATED TEMPERATURE PROPERTIES OF MATERIALS USED TO VALIDATE THE GENERALIZED MACHINABILITY EQUATION...............o,.... 69 XIV VARIABLES FOR DIMENSION ANALYSIS.........................4o 74 XV PREDICTED MACHINABILITY VALUES..o...................0000 88 XVI RELATIONSHIP BETWEEN THE GEOMETRY OF CUT AND THE "CHARACTERISTIC LENGTH"............ o. OOO.O.O.. 92 v

LIST OF FIGURES Figure Page 1o The Three Basic Chip Types According to Ernst....,....... 3 2. Force Chip Geometry for an Idealized Two Dimensional Cut.. 4 3. Ideal Plastic Solution for Tool Point Stress Field in the Absence of a Built-Up Edge..............................o 15 4. Ideal Plastic Solution for Tool Point Stress Field in the Presence of a Built-Up Edge,.......................... o 15 5 Relation Between V60 and Mechanical Properties............ 15 60 Tensile Specimen.......................o....o. o 21 7. True Stress Strain Curves for Steels.................. 24 8. True Stress Strain Curves for Aluminum and Molybdenum.... 25 9. Meyer Relations for AISI 1020, 1045, and 4340 Steels..... 30 10. Meyer Relations for AISI 1212 Steel, Molybdenum, 1100-0 31 and 2024-T4 Aluminums................................. 11. AISI 1045 Steel, Hot Rolled (500 X, Nital Etch)........... 35 12. AISI 1045 Steel, Hot Rolled (100 X, Nital Etch)........... 35 135 AISI 4340 Steel, Hot Rolled (100 X, Nital Etch).......... 36 14. AISI 1020 Steel, Hot Rolled (100 X, Nital Etch).....o..,. 36 15. 2024-T4 Aluminum, Solution Heat Treated (100 X, Keller's Etch) Q..................o...o...........o.o oo 37 16. 1100-0 Aluminum (100 X, Keller's Etch),...o.............. 37 17. Molybdenum, Arc Cast and Extruded (100 X, 50% HN03 Etch).. 38 18. AISI 1020 Steel, Hot Rolled, Grid Superimposed for Point Count (100 X, Nital Etch)...............................o 41 19. AISI 1045 Steel, Hot Rolled, Grid Superimposed for Point Count (100 X, Nital Etch)............................... 41 20. Knoop Microhardness Measurements on an AISI 1020 Steel.... 42 vi

LIST OF FIGURES (CONT'D) Figure Page 21. ASA Single Point Tool Geometry and Designation............. 44 22, Typical Wear Curves. Material AISI 4340 Steel.,...Q00090 45 23. Cutting Speed Tool Life. AISI 1212, 1045 and 4340 Steelso. 48 24. Cutting Speed Tool Life. AISI 1020 and Molybdenum......... 49 25. Cutting Speed Tool Life, 2024-T4 Aluminum,,......00000.. 50 26. Duo Tool-Work Thermocouple for Measuring Cutting Temperature 53 27. Temperature EMF Characteristics of high Speed Steels vs Cast Nonferrous.,....... o.............. o o..o..... 54 28. Tool Chip Interface Temperature. AISI 1212, 1045 and 4340 Steels............................................ o o o o o o o o o o 55 29. Tool Chip Interface Temperature. AISI 1020 Steel and Molybdenum, o. a o...o 9 o..a e o o.a o e a o o e 9 0 0 a a O a. a.. o o o o o 56 30, Tool Chip Interface Temperature, 1100-0 and 2024-T4 Aluminums. e *........ 9... o o o o o oo o o o o o 57 31o Friction Wear Specimen,.,.,,,,oo o o o o o...... 60 32. Contact Geometry................ 63 335 Wear Patterns with Grid Superimposed (5.5X)..,,........... 64 34. Typical True Stress Strain Diagram........................ 77 35o The General Machinability Equation,.o,,.ooo o.oooo........... 84 36. Chip Formation in Molybdenum................... 85 37. Effect of Feed on Cutting Velocity for a Sixty Minute Tool Life o...........................0............0... 91 38. Effect of Depth on Cutting Velocity for a Sixty Minute Tool Life.,..,,.....,......,,....,..,,,...,,.,,,, 91 39- Chip Geometry Exponent t"a",.................,,,,,, o 93 40. Cutting Speed-Tool Life, AISI 1020 Steel,................. 100 vii

I. INTRODUCTION In response to the increased commercial interest in maching operations in the middle of the last century, the first scientific approach to the art of metal cutting was ir.itiated, Theory kept pace with practice up to the invention of the High Speed Steel by Taylor and White in 1898. With this discovery, the art of metal cutting entered an "Empirical Period', which was not brought to an end by any of the later scientific works. This latter period yielded empirical relationships between cutting conditions, tool life, cutting forces, power requirement and surface finish. Despite the large number of attempts to analyze the cutting process, basic relationships between the physical properties and the process variables are lacking. This is all the more disappointing as the behavior of the materials in other processes, like forming, welding and heat treatment is fairly well predictable, Though, strictly speaking, metal cuttting is a three dimensional operation, it approaches a two dimensional process for some particular cases. Most of the analytical studies of metal cutting were directed to study the idealized, orthogonal, two dimensional cut. With all its simplification, the prediction of the behavior of a metal, even in the two dimensional cut, has been beyond our present day's knowledge, This is not surprising, considering the state of the theory of plasticity, and the limited understanding of the friction and wear phenomena. The metal cutting researchers have further restricted their studies mainly to the formation of a continuous chip in the absence of a built-up-edge, -1

-2Figure 1 shows the three types of chips as classified by Ernst(1) It should be mentioned that the difference between them is not as distinct as the micrographs may suggesto Figure 2 demonstrates the force and chip geometry for the idealized two dimensional cutting process. An orthogonal cutting tool, with a rake angle 0(, is removing a layer of depth t and width w from a given work piece.' If t << w then the operation is essentially a plane strain process. The operation, a plastic forming process, is classically idealized by assuming shear to occur along a shear plane, defined by its shear angle 0. The force R acting on the tool could be resolved either into the cutting force FH and the feeding force Fv, or into the tangential component F and the normal component No The ratio between the last two components is defined as the coefficient of friction l; kt= F/N = tanp, where R is the friction angle. The reaction R', equal and opposite to R is resolved into a shearing force Fs, acting along the shearing plane, and a force Fn, acting normal to the shearing plane. To complete the description of Figure 2, we have to introduce the chip ratio r, defined as r = t/tc, where tc is the chip thickness, An innumerable number of attempts has been made to predict the shear angle, chip ratio, coefficient of friction, etc,, but unfortunately with very little success. Data obtained experimentally, could in many cases be correlated reasonably well for one set of conditions, but the relationships derived had no general validity. In any machinability study the researcher has always had to resort to measurement of some of the values mentioned above, and then compute the others from geometrical considerations,

-3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:iii-:::...... iii~~"~ ~~ i - R i ~ ~ —~~~~ ~Ii " *~~~~~~~~~~~~~~~~~~~~ ~~::~I-:::::::::J? ~I~::: I:: Figure~~~~ 1.~eTre Bai hp ~ps codigtoEnt()Tye1 ~:::i......~~~~~~~~~~~~~~~ Discontinuous or Segmental Chip; Ty~~~~~~~~~~~~~~~~~~pe 2 CntnosCi Wihu BitUpEg;an'ye ~CninosChpwt Built-Up Edge.

CHIP tC F R Fv _______ p- ZJ F ^ i-F Fs n F I TOOL WORK PIECE Figure 2. Force Chip Geometry for an Idealized Two Dimensional Cut.

-5By machinability the engineer invariably refers to the relative "ease" with which a material can be worked in a chip forming process, Among the extremely different criteria applied to evaluate machinability are: tool life, surface finish, forces, power consumlption and dimensional stability. The tool life as a criterion for machinability is of most general significance, though the other criteria may be of equal importance for some special conditions, The standard machinability ratings(2), referred to sometimes as machinability indexes, are comparisons of the relative cutting velocity of the work material with the cutting velocity of a standard material for some specific cutting conditions, Free machining steel, AISI 1112 or 1212, is used most often as the standard for ferrous materials, Because of its importance, the tool life criterion was adopted in this study. The factors affecting the machinability are the tool, the cutting conditions and the work material. All of these factors have attracted the attention of the metal cutting researchers for more than a hundred years. But, as Optiz(3) stated in 1960, "In spite of the abundance and diversity of the material, it is not possible up to the present to make positive predictions concerning tool life values of various materials." The objective of this investigation was to study both analytically and experimentally the effect of the physical properties of the work material on machinabilityo Among the physical properties studied were the stress strain relations, hardness, microstructure, abrasiveness and the thermal properties. A variety of materials, ferrous and non-ferrous, was selected to insure the largest possible variation in each one of the physical propertieso All of the variables except the work material and the speed-tool

-6life relationship for a set of standard cutting conditions were fixed for two reasons: first, it was not the intention of this investigation to study the effect of the tool and the cutting conditions on machinability, and secondly, sufficient experimental data is already available in the literature,

II. LITERATURE REVIEW General Whereas the machining process as such can be traced back to the earliest stages of civilization, the actual scientific approach to the art of metal cutting did not start until the turn of the nineteenth century. It was with Rumford(4), who presented in 1798 to the Royal Society of London his paper on an "Inquiry Concerning the Source of Heat Which is Excited by Friction," that this period started. Rumford attempted to show, by measuring the temperature rise in a canon boring process, that a change in heat capacity is associated with the formation of chips. Considering that fifty years were to pass before Joule introduced the concept of the "mechanical equivalent of heat," it is not at all surprising that Rumford could not successfully compute the work required for the chip formation from his temperature measurements, It was not until 1851 that any further significant studies in metal cutting were published. In that year Cocquilhat(5), who was the first to measure cutting forces, measured drilling torques. From the experimental data he very carefully computed the cutting pressures and the specific work per unit volume required in a metal removal process. From here on the number of publications in the area of machining has been steadily increasing until at the present time the total number exceeds several thousands. The effect of the cutting geometry on the efficiency of the cutting process was studied by Joessen. (6) His reports in the Austrian Engineering Journal in 1865 showed the studies of the drilling and the -T

-8turning operations. He concluded that a rake angle of 36~ in turning, and an included angle of 70~ in drilling minimized the cutting forces. The greatest influence on the development of the machining processes had undoubtedly the invention of the high speed steel by Taylor and White in 1898. The vast experimental work carried out by Taylor was summarized in his 1907 ASME presidential address: "On the "(7) Art of Metal Cutting."(7) This classical reference, a summary of a lifelong work by Taylor, is one of the most extensive machinability research projects ever undertaken by an individual. His most interesting conclusion, universally accepted today, is the exponential relationship between the cutting velocity V and the tool life TL, namely VT = C. In this equation, referred to as the Taylor relationship, C and n are constants the value of which depends on the cutting tool, the cutting conditions and the work material. Chip Formation The first attempts to explain the mechanics of chip formation are due to Timme(8'9'10) and Tresca(ll'l2) Tresca, who has developed many of the most basic concepts of the theory of plasticity, has contributed two classical articles to the field of metal cutting. In his 1873 paper "Planing of Metals" (11) and in his 1878 paper "On Further Applications of the Flow of Solids"(l2) he describes in detail the cutting process and the chip formation. Tresca considered the work material to be compressed in front of the to and thaen sheared in a plane parallel to the cutting direction. Though this observation is

-9incomplete, it seems to be partly true in the light of recent studies associated with this thesis made on polished and etched specimens and observed through a microscope during machiningO The second researcher, a contemporary of Tresca, who made some of the most basic contributions to the science of metal cutting was Timme. Timme was the first to recognize that the chip formation is the most basic aspect of metal cutting, He disagreed with Tresca on the mechanism of chip formationo Timme explained that the chip is formed by fracture along successive shear planes that are inclined to the direction of cutting. Though the writer disagrees with this explanation of the mechanics of the chip formation, credit should be given to Timme for his most excellent paper at such an early time of the development of both the theory of plasticity and the science of metal cutting, Mallock(13) in 1881 presented to the Royal Society of London an excellent paper on the subject of metal cutting. He examined polished and etched chips, and concluded that the deformation is restricted to clearly defined shear planes, which are inclined at an angle 0 to the cutting direction, Fracture occurs in these shear planes. Mallock was also the first to describe the chip formation in terms identical with the current "sliding deck of cards concept," that is often acknowledged as originating with Piispanen(14) in 1937 or Merchant(15) in 1945. He observed the effect of cutting fluids on friction but failed to note their effect on the shear angle. Hartig(l6) in 1873, Smith(l7)in 1882, and Haussner(l8) in 1892 were among the original contributors to the development of force and power measurement, so essential to the study of the metal flow, Though they all

-10measured only the component in the direction of the cutting velocity, Hausner already recognized that forces exist in other directions, Since these early investigations, force and power measurements became a standard procedure in machinability research, due in great part to Boston's work at the University of Michigan. A controversy was raised by Reuleaux(19,20) in 1900 by suggesting that a crack develops ahead of the tool. This was also observed by Kingsbury(21) who commented on the same phenomenon. The work by Kick(22) in 1901, Brooks(23) in 1905 and Rosenhain(2 ) in 1906 negated this concepto The writer himself has observed many cracks propagating in front of the tool for various ductile materials during current work being done on the same project that sponsored this thesis, Timme's work in Russia was followed by Briks(25) and Zvorikin(26) As early as 1893 Zvorikin, by minimizing the cutting force, came up with the shear angle relationship: 0 = 45 + i/2 - F/2 - 8 /2 (1) Where 0 is the shear angle, o( the rake angle f the friction angle between the chip and the tool, and i' the friction angle in the shear plane.. This relationship, for g' = 0 continued to appear as a new contribution, developed independently and sometimes on different postulates by various research workers for the past thirty years, Hermann(27) in the 1896 edition of the "Lehrbuch der Ingenieur und Maschinenmechanik" derived the relationship =0 45 +0 /2 - 3/2 (2)

-11on the premise that the shear plane is that plane in which the shearing stresses are maximum, Linder(28) in 1907, Piispanen in 1937(14) Ernest and Merchant(29) in 1941 and again Merchant(l5) in 1945 obtained the same relationship, and some of the aspects of their work will be discussed later. It will be appropriate at this stage to interrupt the discussion of the chip formation and mention, in their historical order, the development of some of the more important tools of the metal cutting researcher, as well as some of the more interesting observations, carried out during the 1920's and 1930's. The first persons to measure the chip temperature were Bruckenburg and Meyer(0) in 1911. Usacher(31) in 1915, was the first to actually measure the tool temperature by inserting thermocouples in the tool, But it was not until the middle of the twentites when Shore(32) Gottwein(33) and Herbert(34) published independently their work on tool chip interface temperature measurement by the tool-work thermocouple method. Extensive work in this area was carried out by Boston(5) and Schmidt(36), but it was not until the late 1940ts that the problem was attacked analytically by Chao and Bisacre(37) Chao(38), Loewen(39) and others. Coker(40'4 ) applied photoelasticity to the study of the stress distribution in the metal cutting process. Though it obviously could not reveal the stress distribution in the plastic region, it gave some interesting results about the nature of that region and the stresses around it. At the same time Schwerd(42 and Ishii 43 developed the techniques of photographing the cutting process in action, in contrast to the photomicrographs of the interrupted cut obtained earlier, Okochi and

-12(44,45,46) Okoshi were among the leaders of the metal cutting research in Japan, and employing some of the finest measuring and observation techniques they studied cutting forces, stress distributions, flow directions and the built-up edge problem, Both Okoshi( in Japan and Schwerd(7) in Germany, related the built-up edge to the cutting velocity, whereas Rapatz(48) attributed it to the cutting temperature, Rapatz claimed that velocity effects the builtup edge only indirectly by effecting the temperature, and this was supported by elevated temperature cutting tests by Ernest and Martellotti(49). During the same period Rosenhain and Sturney(50) have made their studies showing the built up edge to be part of the chip. In 1937 Piispanen(14) established the shear angle graphically by minimizing the power requirement. Recognizing the effect of the normal force on the shear plane he modified his analysis respectively. His paper "Theory of Formation of Metal Chips," that appears in the J. App. Phys. (51) in 1948 sums up the same work analytically, and adds a study of the discontinuous chip formation. Ernst and Merchant(29) obtained the expression for the average shearing stresses Z in the shear plane, referring to Figure 2 as: Fs F' cos ( +E8 -o)sin As A where As and A = wt are the area of the shear plane and the area of the cut respectively. Postulating that 7 is maximum, by taking a derivative with respect to (v they obtained for the shear angle 0 the same expression as in Equation (2), Obviously they assumed an independence between R' andf.

-15In 1945 Merchant(l5) repeated his analysis following the same reasoning as Zvorikin, minimizing the power P, or the cutting force FH given by FR rA cos ( - ) (4) sin0 cos (0 + B -c) The results were again those of Equation (2). Merchant further refined his solution by introducing the effect of the normal stress ~ on the shear stress 7. Z= Zo + Kg (5) where — 0 and K are constants. From Figure 2 it follows that O= Ztan (0 +? - ) (6) substituting Equation (6) in Equation (5) gives: z = ZO + K rtan (0 +' -d<) (7) substituting the value of C from Equation (7) into Equation (4) yields an expression for FH F H = sinC c'o A cos (p- (8) H sino cos (0 + -o ) - K sing sin (0 + -o<) Differentiating FH with respect to 0 as before, assuming the complete independence of the variables results in the shear angle relationship cot (20 + 3 -)) - K (9) or = -- j + C (10) where: C = arc cot K which Merchant called the "machining constant."

-14At a later date Merchant and Field(52) returned to study the mechanics of the discontinuous chip. Stabler(5) on purely geometrical considerations obtained in 1951 the expression: 0 = 45 - + c/2(11) Lee and Shaffer(54) applied the methods of analyzing the stress and strain distributions in the plane plastic flow of an ideally plastic material to the problem of machining. Figure 3 shows the slip line field associated with the appropriate boundary conditions, and the corresponding Mohr circle diagram. The region ABC is plastically rigid and under a uniform state of stress. If we substituted our notation for his, to say w - At2\~~ =~~ f~ ~(12) we obtain for the shear angle: 0 4 - + o (13) It further follows that the shear stress (t) and the normal stress (G) on this shear plane are equal. This conclusion disagrees with experimental evidence, and Lee postulated that this is due to the presence of the builtup edge. Figure 4 shows the analysis taking the built up edge into consideration, Again, using our notation, he obtained a modified expression for the shearing angle: 0 = 45+?-_ +0 (14)

.15-, $ (a) Slip Line Field (b) Mohr Circle Diagram Figure 3. Ideal Plastic Solution for Tool Point Stress Field in the Absence of a Built-Up Edge (Lee and Shaffer 54). (a) Slip Line Field (b) Mohn Circle Diagram Figure 4. Ideal Plastic Solution for Tool Point Stress Field in the Presence of a Built-Up Edge (Lee and Shaffer 54). i ~, a VIELD teTsS EAlTO Figure 5. Relationship Between V60 and Mechanical Properties. (Janitzky 72).

-16where r is a measure of the size of the built up edge. Physically 3t>o and it follows from Mohr's circle that C)> C. Lee returned further to study the chip formation mechanism in his paper "The Theory of Discontinuous Machining."(55) In 1952 Hucks(557) published the results of an extensive investigation of shear angle relationship. It led to a relation which is basically not different from the others, In 1953 Shaw(58) et al. studied the various aspects of the relation between friction and the shear angle in metal cutting, and a year later they published their paper on "Discontinuous Chip Formation."(59 Hill(60) in 1954 explored the possible range of inclinations of the shear plane, by "excluding configurations that imply overstressing of material at the singularities of stress." Okushima and Hitomi(6162), in their very fine 1957 and 1958 papers investigated, both analytically and experimentally, the orthogonal cutting mechanism, by studying the transitional deformation range, the "flow region." In 1959 Lamm(63) presented his "Hydrodynamic Theory" of chip formation, essentially descriptive and following his 1940 publication in the Soviet Union.(6) Colding(65) in 1960 attempted with limited success to consider the unisotropy in the development of the shear angle. Among the contributors to the theory of chip formation that were not discussed here for physical limitations are: Bastien, Kurrein, Leyensetter, Loladze(66), Opitz, Thomson, Weisz, Wallichs, Zorev(67) and others,

-17Machinability and Physical Properties Since the extensive work by F. W. Taylor(7), practically every metal cutting researcher has devoted some of his time to study various aspects of machinabilityo The amount of work involved in evaluating machinability experimentally is very often objectionable. Millions of dollars have been spent by the United States Air Force in the early 1950's to evaluate the machinability of titanium and other alloys, Researchers recognized that the long tool life wear tests have to be replaced, either by shorter tests, or by an analytical method to predict machinability on the basis of the physical properties of the material, Among the many tests that were suggested during these past fifty years to lower the testing time and expense, three deserve some attention. The first is the "constant pressure lathe" test, the second is the radioactive testing; and the third is the measurement of tangential cutting forces as a means to evaluate machinability. By using the "constant pressure lathe" an attempt was made to "evaluate the materials on the basis of the feed resulting from fixed horizontal tool pressure,"(68) Merchant(69), among others, in 1953 tried to use radioactive means to measure what he called an "instanteous rate of tool wear," His technique consisted of using tools "rendered radioactive by neutron irradiation in a nuclear reactor, collecting the resulting chips, and measuring their radioactivity due to the particles abraded from the tool during a few seconds of cut." This method in essence attempts to take the results of a very short time wear test and project the results on the long time wear process of the tool.

-18Schlesinger(70) was among those who believed that the tangential component of cutting force is a good criterion of machinability. He claimed further that the method actually compensates for the difference in the abrasiveness of the various materials. Unfortunately none of these methods was adequate for an arbitrary chosen material and short time machinability tests are still lacking. The ability to predict machinability from physical properties has always been challenging, Janitzky(71), in 1938, related the machinability of steels to their Brinell Hardness (HB) and their area reduction (Ar), as obtained in a standard tensile test. He expressed the functional relationship between the cutting velocity for a sixty minute tool life (V60) and those variables as: C v60 1.63 1.01 (15) HB Ar (15) Where C is a constant depending on the cutting conditions. Janitzky further claimed that "variation in chemical composition does not influence machinability provided that the steels may be heat treated to have the same mechanical properties," In 1944 Janitzky(72) took a new look at the same problem. This time he correlated machinability with the tensile strength (9T) and the ratio of the yield strength (y7) to the tensile strength (y/GT). The relationship obtained is given by Equations (16) and (17): V60- =or ~ V60 =- LT 2 -o-0.5)]2 for.o,5 (17)

-19where C1 is a constant depending on the cutting conditions. Figure 5 is a graphical representation of these two expressions for one set of cutting conditions. () Unfortunately the mechanical properties are not the only physical properties affecting machinability, and therefore no generally valid solution should have been expected from Janitzky's studies. As to the hardness, it should be mentioned that Boston and Colwell(7) and Schlesinger(75) were among those to state that hardness alone is by no means a measure of machinability, As a great part of the metal cutting research was devoted primarily to machinability of steels, attempts were made to correlate machinability with composition and with microstructure. The SAE Technical Report(7) on the effect of composition on machinability, and the United (77) States Air Force Machinability Report No. 2(77) on the effect of microstructure on machinability seem to be the summary of the most extensive work in the respective areas, It is evident that further study of the effect of physical properties on machiniability is necessary. This study is intended to fulfill part of that necessity,

IIIo EXPERIMENTAL PROCEDURES AND RESULTS In this section the testing procedures used to determine the physical properties of the material are described first followed by those procedures used to evaluate their machinabilityo Materials The materials used in this investigation are steel, aluminum and molybdenum; their composition is given in Table Io They were all used in their "as received conditions" which are as follows: steel, hot rolled; 1100 aluminum hot forged and annealed; 2024 aluminum hot forged and precipitation hardened; molybdenum, arc-cast and extruded. Test specimens were taken from different parts of the-bar stock to verify the uniformity of the material according to the following pattern: discs for hardness traverses were cut from both ends as well as from the half length of each bar; tensile, impact and wear specimens were cut from near the half length of the bar and specimens were made from several radial locations, Tensile Tests Tensile properties and true stress strain relations were determined on a Southwark Emery 60,000 lbso hydraulic tensile testing machine. Three specimens with reduced sections, as shown in Figure 6 were tested of each material. The reduction in cross section had no noticeable effect on the true stress strain relations, and was introduced to facilitate measurement of the instantaneous circumference of the cross section- The -20

" 3 5I ~I ~- -Iu 8 8 0.479 0.500 0. 50'0 I~~~~~~~~~~. I I 50 -10 THD. Figure 6. Tensile Specimen.

TABLE I CHEMICAL ANALYSIS OF THE MATERIALS Material C Mn P S Si Ni Cr Mo Fe Cu Mg Ti Zn Al 1 AISI 1020 0.19 0.50 0O022 0o026 0.170 - - - Bal 2 AISI 1212 0o o6 0 89 0.100 0,200 oo006 - - - Bal 3 AISI 1045 0o48 0.75 0,015 0,038 - - -- Bal 4 AISI 4340 o, 41 0,74 0.011 0.020 0.350 1.77 0.80 0.27 Bal -- -- -- 5 Al 1100-0 - 001 -- - - - 0.09 56 0.13 0.01 0.01 - Bal 6 Al 2024-T4 -- 0.62 -- o 010 -- 0.01 -- o 27 4 70 1.50 012 Bal 7 Molybdenum 0.028 -- -- -- -- Bal --

-23area was computed from the circumference of the cross section, measured with a wire attached to a dial indicator, A relationship of the form G (= T was found to be valid in the plastic region as shown in Figures 7 and 8,where (C is the true stress in psi, E the true strain, and C and m are material constants, values of which are tabulated in Table II. The stress strain relations, corrected after necking began according to Bridgman(78) are given in Figures 7 and 8. Yield strength (Gy) at 0,2% offset, tensile strength (T ), fracture stress (Gax), fracture strain (Emax) and reduction in area (Ar) were determined and are tabulated in Table IIIo The flow stress (rF) was determined as the intersection of the plastic stress relation, =6; 6, with the elastic stress strain relation Q= eE, where E is Young's Modulus. This yields for the flow stress the value of OF = 1 Deformation energy (W) was computed to first approximation as: W =fgd G croT-; cJ 7 (1f6i' (18) o0 The values of W and (GF are given in Table II, Because of flaws in the molybdenum specimens they had to be tested in compression, and the data was modified to be compatible with the results of the tensile tests. Hardness Tests and Meyer Strain Hardening Index Several different hardness tests were conducted because no one scale is commonly used for the large range of hardness values of the materials under consideration.

300 --- 000 A I a. 1 50 0 0 wJ ____________ _ _ __ _ ~^ _______________ ______ C)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~R 0 b 100 H _ _ _ _ _^ 3 ^ _ _ __ _ _ (n 60 w _ _ _ _ _ _ tz:~~~~\z H 40 -— _______AISI 1212________________ 20 0.01 0.02 0.03 0.04 0.05 0.1 0.2 0.3 0.4 0.5 1.0 TRUE STRAIN c (in/in) Figure 7. True Stress Strain Curves for Steels,

400 2024-T4 6L -= 10) 50 0 I MOLYBDENUM I I I 11 200 80 C, 30 1 2 R I0 340 —- --------- --.... - or 6 - - ---------- - - - _ —------- - - _ —--- 0.01 0.02 0.03 0.04 0.05 0.1 0.2 0.3 0.4 0.5 1.0 TRUE STRAIN, c (in/in) Figure 8. True Stress Strain Curves for Aluminum and Molybdenum.

-26TABLE II STRESS STRAIN RELATION CONSTANTS, FLOW STRESS AND DEFORMATION ENERGY Flow Deformation Material Constants1 Stress2 Energy3 Material m E o (7F psi - psi in-lbs/in3 1. AISI 1020 110,000 0.211 24,500 75,600 2. AISI 1212 110,000 0.235 20,000 73,800 3. AISI 1045 160,000 0.134 72,000 47,000 4, AISI 4340 210,000 0.088 118,000 80,700 5. Al 1100-0 22,900 0.203 5,000 27,800 6. Al 2024-T4 100,000 0.165 39,000 8,300 7. Molybdenum 105,000 0.129 41,000 31,300 3. W-J-f To

TABLE III TENSILE PROPERTIES OF TEST SPECIMENS Yield Tensile Fracture Fracture Reduction Modulus of Strength Strength Stress Strain in Area Elasticity Material G(7 (T (a A E UyvT ^max ^-max r psi psi psi psi 1. AISI 1020 32,500 64,000 110,000 0.854 57.5 29 x 106 2. AISI 1212 28,000 61,000 105,000 0.855 57.5 29 x 106 3. AISI 1045 78,000 106,000 140,000ooo 0.577 51.5 29 x 106 4. AISI 454o 155,000 155,000 195,000 0.446 56.0 29 x 10 5. Al 1100-0 6,900 goo 15,500 28,000 1.542 74.0 10 x 10 6. Al 2024-T4 43,000 64,000 72,000 0.15 12.5 10.6 x 106 7. Molybdenum 49,500 80,500 91,000 0.588 52.0 54 x 106 1At 0.2% offset.

-28Rockwell and Brinell hardness tests were conducted on a Wilson Rockwell Hardness Tester and a Steel City Testing Laby Brinell Hardness Tester respectively. The Brinell machine was also used to determine the Meyer hardness number and the Meyer(79) strain hardening index n. Meyer's law expresses the relation between the load and the size of the indentation of a spherical indenter. The equation is exponential and is expressed as L = Kd, where L is the load, d the chordal diameter of the remaining indentation, K and n are material constants. The latter is the Meyer index or the strain hardening exponent, The average hardness values and Meyer's exponents are tabulated in Table IV. Meyer's relation is expressed graphically in Figures 9 and 10, Impact Tests A standard v-notch Charpy specimen, 0.394 x 0.394 x 2,165 inches was used for the impact tests. All notches were machined with the same new cutter. A Sonntag Universal Charpy Impact Machine of 240 foot-pounds was used for the. tests. Precautions were taken to ensure proper contact of the pendulum tup with the specimen surface opposite the notch. In each test, excluding the 1100-0 aluminum the anvil swung cleanly through the specimen without jamming the specimen in the machine. The aluminum 1100-0 specimens were bent but did not fracture, Four specimens were tested of each material at a room temperature of 75~F, and the results are recorded in Table V.

TABLE IV BRINELL, MEYER AND ROCKWELL HARDNESS NUMBERS AND MEYER STRAIN HARDENING EXPONENT Brinell Hardness Meyer Hardness Meyer Material Rockwell Number Number Constants 1 Hardness Material 500 kg 3000 Kg 500 Kg 3000 Kg K n B C Load Load Load Load Kg/mm2 Kg/mm2 Kg/mm2 Kg/mm2 * * * * 1. AISI 1020 110 137 112 147 74.5 2.28 69.0 * 2. AISI 1212 114 126 116 136 74.0 2.23 63.0 * 3. AISI 1045 175 212 177 222 112,5 2.31 92.5 * 4. AISI 4340 271 323 272 332 200.0 2.26 * 31.5 5, Al 1100-0 28.4 * 30.0 14.9 2.24 * * 6 Al 2024-T4 134 149 136 159 74.0 2.35 * 7 Molybdenum 175 195 177 205 109.0 2.28 87.5 1Constants in the relation L = Kdn.

3000 4340 2000 1.045 o /-1020 < 1000 500 I 2 4 6 8 10 INDETATION DIAMETER -mm Figure 9. Meyer Relations for AISI 1020, 1045 and 4340 Steels,

2024 -T 4I 3000 _ _ _ _ 4 1 MOLYBDENUM 2000 1212 0 ^ ________ ___ — 1/-^ _ _ __ _ ^ N-~1100-0 -J~~~~~ *000 === = = 500 1 2 4 6 8 10 IDENTATION DIAMETER, mm. Figure 10. Meyer Relations for AISI 1212 Steel, Molybdenum, 1100-0 and 2024-T4 Alurainuris.

-52TABLE V CHARPY IMPACT STRENGTH OF TEST SPECIMENS IMPACT STRENGTH Average Material Value Minimum Maximum Ft-lbs Ft-lbs Ft-lbs 1. AISI 1020 24.6 24.0 25.5 2. AISI 1212 8.9 8.0 9.8 3. AISI 1045 15.3 14.5 16.5 4. AISI 4340 5.6 4.0 7.5 5. Al 1100-0 54.91 5.5 55.5 6. Al 2024-T4 5.1 5.0 5.2 7. Molybdenum 1 0 1.0 1.0 1Specimens did not break,

-335 Thermal Properties Thermal conductivity was determined by the "split block" comparative method, the standard for comparison being Armco Iron. Two measurements were conducted, below and above room temperature respectively, and room temperature values were obtained by interpolation. The tests were carried out at the Heat and Mass Transfer Laboratory, Armour Research Foundation of Illinous Institute of Technology. Specific heat values were taken from the data compiled by Armour Research Foundation. Density was determined by weighing cylindrical specimens of known dimensions on an analytical scale. The above properties and the associated values computed from them are given in Table VIo Metallography A metallographic examination was conducted on all the materials under investigation, The samples were mechanically polished through the 0, 00, and 000 dry papers. Final mechanical polish was perfonred on wet cloth with Linde A powder, The specimens were then etched and lightly repolished. The etching reagents used were Nital 2o for the steel, Keller's Reagent for the aluminum and 50% Nitric Acid for the molybdenum. The micrographs are given in Figures 11 to 17. For the purpose of conducting a point count, a grid was superimposed photographically on the print of the microstructure. (80,81 This was achieved by exposing the printing paper first to the negative of the structure and then to the negative of the grid before developing it, Two

-34-. TABLE VI THERMAL PROPERTIES OF TEST SPECIMENS AT 77~F Density Specific Volume Thermal Thermal Heat Specific Conductivy Difusivity Diffusivity Material Heat c QC K of lb/ft3 Btu/lb-~F Btu/ft3-~F Btu/hr-ft-~F Ft2/hr 1. AISI 1020 488.3 0,120 58 6 30.3 0 52 2. AISI 1212 486, 4 0.120 58.4 54 5 0. 59 34 AISI 1045 487,4 0,120 58.5 25.1, 43 4, AISI 434o 488.3 0 120 58.6 19.3 0o33 5. Al 1100-0 168.6, 230 38,8 121.0 3, 12 6. Al 2024-T4 175.7 0.250 40.0 71,2 1.78 7. Molybdenum 65707 0,065 42,1 69.6 1,65

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-38X.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~s ~~~~~~~~~ a~~~~~~~~~~~~~M:x-.-'..'....... —.N..... X'l.'~...,s v t A....... X Xg::""A'-''0::"'X'.N~i-g.''""'''; -' A;;ijlllli~~?~".;''' l;;;';;;;'S - ~~::-:^:;;; E;;;;,',;;;, <.;..;; 1;; asxCi.1...w S;...... A d a Fig ure. 17.............0 Et..........~~ ~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:::-:::::::~~8.............. -:_::__ -:_: A K..........................-iiii —i-i~iii~i~:iiii —i...........................~:,::, ii i~'iiiiiil iiilli iil i~. II1 Illllljl llll ~lllill i lljl............. ~ ~ ~ ~ ~ ~ ~ ii~:~ ~:il::::~:iii:::::-: —::::::~::::-: —-:::::-:::::::A:::::::::::::::::::Figure 17. Molybdenum,,Axc Cast and Extruded (100 X, 50% HN03 Etch),

-59examples are shown in:Figures 18 and 19 and the results are tabulated in Table VII. The percent of ferrite and pearlite in the microstructure was also computed on the basis of the chemical analysis. (82) The analysis and the comparison with the results of the point count are given in Table VII. The analytical method is considered more reliable than the point counting for various reasons. First, it is less influenced by the subjective impressions of the investigator. Secondly, finely dispersed microconstituents require a high magnification for the point counting, resulting in a highly localized picture, which is in most instances not representative of the sample. And thirdly, the portion of the second phase being at the grain boundaries cannot be counted, Microhardness Measurements of the Chip As Herbert(91) has already suggested that the hardness of the chip could be a measure of machinability, it was considered appropiate to investigate this statement further, Cuts were conducted at various speeds, the chips were mounted, polished and etched, and Knoop microhardness measurements were taken. Figure 20 shows an AISI 1020 steel chip with the hardness reading superimposed on it. Similar microhardness tests were conducted on all the materials studied. It is seen clearly that the strain hardening of various grains is extremely different, and that in general, as expected, the softer phase, the ferrite, deformed more than the harder phase, the pearlite. It was impossible to draw any conclusions about the machinability of the work material, neither from

-40TABLE VII PEARLITE CONTENT OF THE STEELS Carbon Carbon PEARLITE CONTENT Content Content of Computed Point Eutectoid Count MATERIAL % 1. 1020 AISI 0.19 0.750 25.3 21.5 2. 1212 AISI 0oo6 0.755 7.9 3.6 3. 1045 AISI 0.48 0.735 65.3 74.4 4. 4340 AISI o.41 0.425 96.5 100.0 1. C = A x 100 B the maximum, nor from the average hardness of the chips. The problem was further complicated on examining the effect of the depth of cut on chip hardness, Hardness of the chip is by no means a property of the material, though it is obviously dependent on the material's properties. It would have been justified to use it, if it gave a clear cut quantitative indication of the machinability of the work material. It did not, and Herbert's statement is considered to be an oversimplification of the problem. Machinability Tests Single point tool life tests in which progressive wear was measured were conducted on all the experimental materials,

-419~' s'' t *6 j ja~~~~~~~~~~~~~~~~~~~~~~~t)..f^~~~~~~~~~~~........S 44 ~ t. 000: 000 0 000 - 000 0 00.. -... 0.Xi000-0000is..i00000000000 st~~~~~~~~~~~~~~~t-.00v. w-. ~.Se.......thiit ioP 1* <^ A o #xiiid Figure 18. A-TSI 1020 Steel, Hot Rolled., Grid Superimposed f or Point Count (lO0 X, Nital Etch). iS::::fi if figi~i, 5 i i i~i:. i7|;'''-iii:::':::7:::0::.:': -::.:::::-,''-:':d:i:V:.:MIT!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:'S iS-''''-'t-~~~~~~~~~~:~''''"''''';:,:'v''-'''''''''''''~ii~i srii~~iiii:' iEiiiai''"'''' S",'," Xg Siiii X t W.. z:'' " R:>.....t.' 000000000000000000 000000 t0000; X W..~~~~~~~........ ll;~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~itles ev::::::::::<;::::i::: aiisiiiii~iei~i~i~i:::ii:~i~~i6 Figure:, 1 AISI 1045 Steel, Hot Rolled, Grid Superimposed for Point Count (100 Xo Nital Etch),~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~::::e~li:Ii~i

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Commonly used standard T-l high speed steel tool material was selected in order to minimize the testing time and the material requirement s As no one tool geometry is optimum for all the materials that could be encountered, the simplest geometry, ASA designation 0, 0, 7, 7, 7,, 0 0 was chosen. The details of the tool geometry and nomenclature are given in Figure 21, The tools were ground on a Cincinnati Tool Grinder to a 12-15 RMS surface finish, all with the same 48A80-H5-V8 grinding wheel. The machinability tests were conducted on a 14" swing American Pacemaker engine lathe with a variable speed drive. Turning cuts, with a constant depth of 0.050 inch a constant feed of 0,0057 inch/revolution were carried out at various speeds. Cutting speeds were selected to give a tool life between one and one hundred and twenty minutes, preferably between 10 and 60 minutes, All tests were conducted dry. In the first set of tests, the cuts were interrupted periodically to inspect the wear of the cutting edge. Flank wear, crater wear, and end wear, if present, were measured and recorded with the aid of a toolmaker's microscope, Figure 22 shows typical wear curves obtained for the different materials in this investigation, Machining time corresponding to a flank wear of Oo100 inch was defined as "tool life" for the purpose of this study, which is a standard procedure. In the second set, the tests were conducted continuously to complete destruction of the cutting edge.

-44END CUTTING EDGE ANGLE NOSE RADIUS i\ C SIDE CUTTING EDGE ANGLE SIDE RAKE ANGLE XL! i- C - a — a BACK RAKE ANGLE SIDE RELIEF ANGLE — 8 END RELIEF ANGLE a Back Rake Angle Side Rake Angle Y End Relief Angle 8 Side Relief Angle E End Cutting Edge Angle'? Side Cutting Edge Angle Nose Radius Figure 21. ASA Single Point Tool Geometry and Designation.

0 V, = 60 FPM 0.10 V3 ___A___ A V,=65FPM 13 V3t 70FPM U) 0.08 I 13 0.06 0.04 0.02 -- 0 10 20 30 40 50 60 70 80 90 100 TIME - MINUTES Figure 22. Typical Wear Curves. Material AISI 4340 Steel.

.46The tool life curves were found to agree with, for the common range of velocities shown in Table VIII,the Taylor relationship VTL = C, where TL is the tool life in minutes, V the cutting velocity in FPM, and C and n are constants depending on the cutting conditions and the materials machined. C is the cutting velocity that yields a one minute tool life, and n is the slope of the above plot in a log-log coordinate system, The method of least squares, the general analysis of which follows, was applied to determine the tool life relationship from the experimental data. The following is the analysis carried out to evaluate the constants C and n in the tool life equation VTL = (19) rewrittn in logarithmic form in V = in C - n In TL (20) ln V = y Set in TL = x (21) Set in C = a -n = b y = a + bx (22) Sum over all equations N: N N N y = a + b x (23) 1 1 1 N Note that Z a = Na 1 N N.. Z y = Na + b x (24) 1 1

-47Multiply Equation (22) by x: xy = ax + bx2 (25) Sum all equations N: N N N x y + a x + b x2 (26) 1 1 1 Solving Equations (24) and (26) for a and b will yield the following solutions: Zx xy- x y (27) ZxZx-NZx2 x X X N xy Lx, x - N xy Zx~x-NEx where the summation is over all values No Substituting back the values from Equation (21) gives the final answer for the two constants C and n: Z (In V) Z (In TL)2 - Z (n TL) Z (ln TL) (ln V ) n C =N E (In TL - (In TL) (n TL) (29) n = Z (ln V) Z (ln TL) - N Z (In V)(ln TL) (30) N (n TL) - Z (ln TL) Z (n TL) The values of the constants C and n, and the range of validity of the tool life equations are tabulated in Table VII and a sample computation is given in Appendix A. The results of the machinability tests are presented in Figures 23, 24, and 25~ The excellent machinability of 1100-0 aluminum prevented us from obtaining the actual tool life cutting velocity relationship. We could neither reach cutting velocities above 4400 fpm to measure tool chip

500 400 300 200 —2 10 W 100 z 70 3CCL~~A --- -- 50 40 30 20 ----.... I 1.0 3 6 10 30 60 100 200 TOOL LIFE-MINUTES Figure 23. Cutting Speed - Tool Life. AISI 1212, 1045 and 4340.

300 200 _1020.L 00 o 4C 3C 2C 1.0 3 6 10 30 60 100 200 TOOL LIFE-MINUTES Figure 24. Cutting Speed - Tool Life. AISI 1020 and Molybdenum.

Q.-. T 6000 ~~~~(9D~~~~~~~~~~~ 5.CtigSedTo fe2044Aln.0 z BO0 3000,..._ 0 I 3 6 10 30 60 100 300 TOOL LIFE-MINUTES Figure 25. Cutting Speed Tool Life. 2024-T4 Aluminum.

-51interface temperatures, nor fail the tool because of material limitations, With a cutting speed of 4000 fpm the tool showed only 0.016 inches of flank wear after thirty minutes of cutting. Therefore we had to extrapolate the wear curves, and predict a cutting velocity of about 8500 fpm for a sixty minute tool life, TABLE VIII CUTTING SPEED - TOOL LIFE CONSTANTS Constants1 Cutting Speed Range of Validity Material C n V2 V L u F-PM FPM AISA 1020 225 0o081 150 230 AISA 1212 270 0Oo85 180 270 AISA 1045 156 o0o66 120 160 AISA 4340 82 0o078 55 85 Al 1100-0 * * * * Al 2024-T4 8450 03.00 2000 4000 Molybdenum 137 0.158 90 140 1. VTn = C L 2o V lower limit 35 V - upper limit 4. No Taylor relationship obtained, Cutting Temperatures Cutting temperatures, being indicative of the cutting process, were determined for all materials under investigation,

-52The tool chip interface temperatures were measured by using two tool-work thermocouples, described schematically in Figure 26. The method (33, 83) due to Gottwein and Reichel) is, despite its limitations, an acceptable way to evaluate cutting temperatures. It is definitely the simplest, as it is independent of the work material, and therefore requires only one calibration for the set of tools used in the experiment. For the purpose of this investigation, one tool was the high speed steel tool used in the machinability tests, and the other a cast non-ferrous, Crobalt No. 2. The temperature - EMF characteristics were determined by inserting the two tools into a metallic bath of known temperature, and measuring the generated EMF with a Sanborn Low Level Preamplifier. Precautions were taken to keep the cold junction at room temperature. The calibration curve is given in Figure 27, The tools were then used to evaluate the cutting temperatures for the different materials under the same conditions that the machinability tests were conducted, A newly ground tool was used for each test. The temperature velocity relationship was found to be of the exponential form Q = AVa, where ~ is the tool chip interface temperature in ~F, V the cutting velocity in FPM, and A and "a" are constants depending on the cutting condition and the material tested. Table IX gives the valus of the constants and the carange of velocities within which the temperature velocity relationship is valid. The cutting temperature plots are given in Figures 28, 29, and 30.

-WORK PIECE I I / I I \ ^ H.S.S I | TOOL CNFTOOL mV METER Figure 26. Duo Tool-Work Thermocouple for Measuring Cutting Temperature,

6.0 _ —----- 5.0 4.0.J 3.0 0 uL. 2.0 Lii 1.0 - 0 200 400 600 800 1000 1200 1400 1600 DEGREES F ABOVE REFERENCE JUNCTION Figure 27. Temperature EME Characteristics of High Speed Steel vs. Cast Nonferrous Tools.

3000 U. o 200 00 w cr -4340 1 1500 -- 4 w 1000 _ z i8aoor - — _ 1 600 C) 400 -- 10 20 40 60 80 100 150 200 300 CUTTING VELOCITY, FPM Figure 28. Tool Chip Interface Temperature. AISI 1212, 1045 and 4540 Steels.

3000 3o 2000 w D 1500 XCr { lF )MOLYBDENUM a.: 1000 I I I I I I' 800 Z ____ _ ___ ~s 1020o H 600 -_ 400 10 20 40 60 80 100 150 200 CUTTING VELOCITY, FPM Figure 29. Tool Chip Interface Temperature. AISI 1020 Steel and Molybdenum.

2000 U. - 1500 LJ a: I —?~~~~~~~~ ~~2024 -T4 n 1000: 800 o 600 " —I O0 — 0 400 2 00. 500 1000 2000 4'000 8000 CUTTING VELOCITY, FPM Figure 30. Tool Chip Interface Temperature. 1100-0 and 2024-T4 Aluminums.

-58TABLE IX CUTTING TEMPERATURE CONSTANTS Velocity Constants Validity Range Material A a V V3 L u OF FPM FPM AISI 1020 154 0.36 20 180 AISI 1212 105 o,43 50 200 AISI 1045 116 0.48 4o 150 AISI 4540 144 0.47 20 120 Al 1100-0 118 0,22 500 5000 Al 2024-T4 275 0o16 300 5000 Molybdenum 71 0o61 20 120 1.o = AVa 2. V - lower limit V upper imit 5o V - upper limit U

-59Abrasive Wear Testing Wear tests were conducted to examine the abrasiveness of the materials under study, The University of Michigan Friction Wear Machine(84) used in these tests, is described in detail in the above mentioned reference, The machine is basically a drill press, modified for the purpose of friction wear testing, Many different geometries of wear specimens may be used, A combination of a sphere and a plane was chosen for this investigation since it facilitates obtaining the desired stresses without overloading the machine and essentially elminates alignment difficulties, The test specimen, a spherical segment of the work material ground to 12 - 15 RMS surface finish, is described in Figure 31. The mating plane is a portion of the high speed steel tool bits used for the machinability tests, polished to facilitate wear measurements, (85,86,87) The contact stresses were computed according to Hertz, and the results are given below. The maximum compressive stress is given by p = 3N (31) max 2ra2 a = 34 (K1 + K2)/ (32) Substituting into Equation (31) the value of "a" from Equation (32), and the numerical values p1 = =2 = 1/3 and R = 5/8, we obtain; 2/3 p _ 3N12 1 E2 E2 max =2 5N (E2/E1 + 1) =.856 N1/3 E21 ] (33) N -= e594 rx E2/E1 + 12 _- *594 (34)

-600.125 12 - 15RMS - 0.2501 Figure 1. Wear Specimen. Figure 31. Wear Specimen.

-6lIntroducing the value E2 = 29 x 106 we get the final expression _ - ^/ rPP3 -E2 N = 1896 [max + 1 (35) 105 ilO91 iE1 NOMENCLATURE a = radius of contact area E = modulus of elasticity K = - E N = normal load P = compressive stress R = radius of spherical speciman J = Poisson's ratio Subscripts 1 = spherical specimen 2 = plane specimen max = maximum

-62The values of the normal loads applied in the friction wear tests corresponded to an initial fictitious stress level of one and one half times the stress for a strain of 0.002 ino/ino They are listed in Table Xo The friction wear tests were conducted dry, for periods of one (1), two (2) and thirty (30) minutes, at a nominal surface spued of 100 fpm. The wear patterns on the high speed steel tool bits were photographed with a grid superimposed upon them photographically. The area of the wear pattern was measured, and the volume of the wear products computed. This volume, as shown in Figure 32, is approximately proportional to the square of the area, Results are listed in Table XI. A sample of wear patterns is given in Figure 33. Though it was thought, at the beginning of this study, that any attempt to predict machinability would require consideration of the abrasiveness of the work material, we have concluded later to the contrary. It is generally considered that the size, shape, amoult and distribution of the second phase determines the mechanical properties as well as the abrasiveness of the material. From the tests conducted in this study, it appears that the effect of the second phase is taken care of sufficiently well by the mechanical properties. Elevated Temperature Properties Toward the end of this study it became obvious that it would be necessary to obtain high temperature properties of the work materials in order to be able to correlate the machinability with those properties, The room temperature properties, that we had obtained experimentally,

-63I 1-i L _ I __ (R-h)2+ a. R2 h<< o 02 * h a2 VOLUME: V = Th(3a2+hh 7T a2h T -a AREA:A = 7Ta2.'. A Figre Contact Geo Figure 32. Contact Geometry.

-641 min. 2 min. H 2 min. H 2 min. 30 min...H....... (a) (b) Figure 33. Wear patterns, with grid superimposed (5.5x) (a) AISI 4340 steel (b) AISI 1045 steel

-65TABLE X ABRASIVE WEAR MAXIMUM PRESSURES AND NORMAL LOAD APPLIED Maximum Normal Normal Load Pressure Applied Material Pax N psi lbs 1. AISI 1020 45 x 103 0,69 2, AISI 1212 37 5 x 103 0,40 3. AISI 1045 105 x 10 8.78 4, AISI 4340 180 x 103 44,23 5. Al 1100-0 9,8 x 103 0o03 6, Al 2024-T4 54,8 x 103 4355 7. Molybdenum 70,5 x 103 1,57

-66TABLE XI ABRASIVE WEAR TEST RESULTS 1 2 30 Wear Time Minute Minutes Minutes Material Aea 1 ea0 i Aea 2 10-in 10 in 10 in 1. AISI 1020 Steel 12.4 4.1 - 12.4 43.0 2. AISI 1212 Steel 13.3 1.2 - 8.3 41.4 3. AISI 1045 Steel 39.8 29.0 - 36.5 172.2 4. AISI 4340 Steel 33.2 89.4 - 96.1 202 0 5. Al - 1100-0 6.6(2) (3) 90.5(2) 6, Al - 2024-T4 4.1 1.7 - 5.0 303 7. Molybdenum 7.5 5.0 - 11.6 77,8 (1) Range for three tests. (2) Excessive vibrations increase contact area. (3) No two minute tests conducted.

-.67 served as a guide in the proper selection of the elevated temperature properties. Table XII gives the tensile strength, area reduction and thermal conductivity of the experimental materials at 6000F, the average temperature of the cutting zone. The Brinell Hardness was computed from the tensile strength by using experimental relationships. Table XIII gives the same properties for eighteen additional materials which were used to varify the general machinability equation.

-68TABLE XII ELEVATED TEMPERATURE PROPERTIES OF MATERIALS TESTED IN THIS STUDY(1) Tensile Area Thermlal Brinell Material Strength Reduction Conduct ivty Hardness7) GT Ar K HB psi %Btu/Hr-Ft-~F Kg/mm2 1. AISI 1020 Steel 58,000(2) 60 25.5(4) 116 2. AISI 1212 Steel 53,000(3) 60(3) 28.0(4) 106 3. AISI 1045 Steel 90,000(3) 35(3) 22.0(4) 180 4. AISI 4340 Steel 135,000 4o 8.5(4) 270 5. Al-100-0 2,800(5) 90(5) 115,0(3) 4.9 6. A1-2024-T4 15,700(5) 65(5) 80.0(3) 27.5 7. Molybdenum 85,000(6) 75(6) 66,0(6) 170 1o All properties at 600~F. 2. Whenever the reference is not given the data was taken from the Metals Handbook, 8th edition, ASM, 1961. 35 Estimated values from published data, 4, Austin, J. B., The Flow of Heat in Metals, ASM, 1942. 5. The Elevated Temperature Properties of Aluminum and Magnesium Alloys, ASTM, 1960. 6. Molybdenum Metal, Climax Molybdenum Company, 1960. 7. Brinell Hardness was computed from the Tensile Strength. For steel and molybdenum G = 500 HB For aluminum GT = 575 HB

TABLE XIII ELEVATED TEMPERATURE PROPERTIES OF THE MATERIALS USED TO VALIDATE THE GENERALIZED MACHINABILITY EQUATION(1) 2 ^ ~Tensile Area Thermal Brinell(l5) Material(2) Strength Reduction Conductivity Hardness T \Ar K HB psi% Btu/Hr-Ft-~F Kg/mm2 1. Rene 41 205,000(3) 15- 30(4) 8.6(3) 410 2. Ti-6 AL-4V 112,000(5) 62(5) 6.0(5) 224 3. Ti-155 - A 120,000(5) 48(5) 62(5) 240 4. Udimet 500 175,000(6) 15 8.5 350 5. Inconel X 155,000 34 11.9 310 6. 301 Stainless Steel 70,000(7) 40(4) 12.4 140 7. 303 Stainless Steel 72,000 53 11.9 144 8. 310 Stainless Steel 50,000(8) 55(8) 9.9(8) 100 9. 347 Stainless Steel 62,000(8) 2(8) 11.1(8) 124 10. 410 Stainless Steel 73,000 74 15.6 146 11. 430 Stainless Steel 64,000 75 1404 128 120 446 Stainless Steel 83,000 40 13.2 166 135 Fe-Cr-Mo Alloy 88,000(9) 60(4) 16.0(9) 176 14. Zirconium 30,000(10) 66(10) 10.7(10) 75 15. Armco Iron 32,000(4) 85(4) 32.0(10) 64 16. Gray Cast Iron * (12) 1-5(4) 32(14) 105(16) 17. Pearlitic Cast Iron * (12) 1-5(4) 26(4,13) 192(16) 18. Leaded Read Brass 29,000 15(4) 41 58

-70FOOTNOTES 1, All properties at 600~F. 2. Materials used to varify the validity of the General Machinability Equation, 35 Engineering data VM-107, Rene 41, General Electric Company (1958). 4. Estimated Values from published data, 5. Bulletins No, 1 and No. 5, Titanium Metal Corporation of America. (1957 and 1958), 6. Whenever the reference is not given the data was taken from the Metals Handbook, 8th Edition, ASM, 1961. 7. All Stainless Steel data, unless otherwise stated, is from Alleghany Ludlum Steel Corporation, Data Sheets, 1957. 8. Haynes Stellite Company, Data Sheet 1958, 9. Alloy Casting Institute, Data Sheets, 1957, 10. Zirconium Data File, Carborundum Metals Company, 11, Austin, J, B,, "The Flow of Heat in Metals," ASM, 1942, 12, No tensile strength value given. 135 McAdams, W. H., Heat Transmission, 14, Jakob, M., Heat Transfer, VI, 1956, 15. Brinell Hardness was computed from the Tensile Strength. All material except Zirconium CT = 500 HB for Zirconium CT = 400 HB 16. Measured values,

IV. DIMENTIONAL ANALYSIS AND THE GENERAL MACHINABILITY EQUATION This chapter is divided into three areas: the development of the general machinability equation; a study of the effect of the size of cut on the cutting velocity for a constant tool life; and a brief analysis of the cutting speed-tool life relationship, The Development of the General Machinability Equation Metal cutting is basically a plastic deformation process, where the material is locally deformed to fracture. It is accompanied by unavoidable high friction, both on the tool face between the tool and the chip, and on the flank between the tool and the machined surface, Both the deformation energy and the energy dissipated in friction is transformed into heat. Most of the heat is carried away by the chips, part is conducted to the work piece, and portions of lesser significance are conducted through the tool and carried away directly to the atmosphere. The process is essentially a steady state process within a few seconds after cutting (88) begins (88) The prediction of the behavior of a material in a cutting process, even under the idealized conditions of a two dimensional cut as shown in Figure 2 is a complex problem. It requires that the influencing physical properties of the material being cut be reliably known. Inasmuch as all materials are made to a specified range of physical properties, any machinability analysis therefore will be only as accurate as the physical property data on which it is based. This dissertation is concerned with the study of the effect of the physical properties of the work material on machinability, where -71

_72machinability is defined in terms of tool lifeo Obviously machinability is also a function of the tool material and geometry, the cutting conditions and the atmosphere in which the process is taking placeo To restrict the problem, as far as possible, the tool material and geometry, as well as the cutting atmosphere were fixed for this investigation. This does eliminate the variablesassociated with the tool and the surroundings as variables, and enables us to place all of our attention to the subject of our investigation: the effect of the work material properties on machinabilityo We further fixed the depth and width of cut to minimize experimental worko Sufficient data concerning the effect of the size of cut on tool life is already available in the literature to check any relationship under questiono The dimensional analysis(89) is a very powerful tobl to study the effect of the different independet variables effecting any physical phenomenon. It enables us to capitalize on partial knowledge of the physical situation. The nature of the fundamental laws which govern the system, and the boundary conditions have to be known and understood0 It is not necessary to be able to express them in the form of mathematical equations0 The Pi Theorem, or rephrased to express the "Principle of Dimensional Homogenity" as stated explicity by Eo Buckingham(90) in 1914 but used already implicitly by Baron Jean Baptiste Fourier is the basis of that analysiso The dimensional analysis as a tool simplifies appreciably the experiment, by reducing the actual number of variables in the test, and by giving more freedom in changing those variables that can be controlled most readily0 It provides a functional relationship between the variables

-73and helps to correlate the experimental data. As every other tool, it has its limitations. Firstly, all the independent variables affecting the process have to be known. Secondly, the analysis does not provide directly any explanation about the mechanisms involved in the phenomenon under study. And thirdly, there is a big flexibility in the choice of the dimensionless groups. It seems that the first of these limitations is generally true for any analysis, the second is true for any study using the phenomenological approach, and the third, rarely mentioned as a limitation, should be of most concern. Choosing the "right" groups may lead to the understanding of the process. Applying the Pi Theorem to the problem under consideration, a number of dimensionless groups are generated equal in number to the difference between the total number of variables and the number of arbitrarily chosen primary variables: Length (L), Time (T), Mass (M), and Temperature (e). The process is mechanical, undiscriminatory, and different dimensionless groups may be obtained, some of which are significant, others being completely meaningless, To which of the two classes any one dimensionless group belongs, can be determined only on physical grounds, by understanding the phenomenon. Table XIV lists seven independent variables, and the tool chip interface temperature e as a dependent variable. A discussion of the completeness of this list, the significance of the variables, and why other variables, seemingly influencing the process were not included would be appropriate at this time,

TABLE XIV VARIABLES FOR DIMENSIONAL ANALYSIS Variable Dimension Description HB ML-1 T-2 Brinell Hardness (Kg/mm2) Ar None Reduction in Area J C ML1 T-2 G-1 Volume Specific Heat (Btu/Ft3 -~F) K MLT-3G-1 Thermal Conductivity (Btu/Hr -Ft -~F) t L Depth of Cut (in) w L Width of Cut (in) V LT- Cutting Velocity (Ft/min) Gf G Tool Chip Interface Temperature (~F) -74

-75It appears to the writer that all of the parameters that characterize the metal cutting process, like cutting forces, coefficient of friction between the chip and the tool, "shear" angle, tool life, chip ratio, etc., are dependent variables. Some of them were considered as independent variables by previous researchers, others taken as dependent ones, None of these parameters may be predicted on the basis of todays theory, and most of them will have to be evaluated experimentally for many years to come. Further development of the theory of plasticity, and a better understanding of the chip forming mechanism, is a major prerequisite for any serious solution to the deformation problem in metal cuttingo Based on our studies it was found after investigating all of the mechanical properties that the hardness and the area reduction completely describe the plastic behavior of the metal for prediction of machinability. It is interesting to note that Herbert(91), in the 1920's, came to the conclusion that "the measure of the machinability is the hardness of the chip" Hardness "in general implies resistance to deformation", as Do Tabor states in the introduction to his book "Hardness of Metals"o(92) The range of elastic deformation for metals is relatively small, therefore the hardness is influenced primarily by the plastic properties of the material, the plastic modulus, C~o and the strain hardening index m in the equation 7= G0OC0 Figure 34 shows a typical stress strain diagram, Hardness as has been learned recently provides adequate information about the plastic portion of the stress-strain diagram but does not indicate its end point, To this extent it is equivalent to the "tensile strength" or the "compressive strength", and they could be interchanged in our analysiso

-76It is obvious from Figure 34, that to complete the information about the mechanical properties of the material, a variable describing the ductility of the material has to be introduced. This variable has to be descriptive of the maximum strain the material can endure, or as the metal cutting researcher prefers to look at it, the minimum strain required to cause fracture ~f o The relations between area reduction (A ), fracture strain Ef and the area ratio (Rf) are given below, so that any one of them may be used in our analysis freelyo A -A A = o f x 100 (36) r A f = n Ao/Af = In Rf (37) 100 Ar 1 100 Rf Where Ao is the original area of the cross section of a tensile specimen and Af the final area. To characterize the effect of the thermal properties on the metal cutting process the volume specific heat _JC (Btu/Ft3 -~F) and the thermal conductivity K, (Btu/Hr - Ft - ~F) should suffice. This statement is true, provided the heat transfer through the tool, and the heat conveyed to the surrounding is of second order importanceo Experimental evidence by Schmidt(93) Pahlitzsch(94) Danielian(95) and Vierrege(96) varify that assumption for dry cutting conditiono The cutting conditions, depth of cut t (in) 9 width of cut w (in) and cutting velocity V (ft/min) conclude the list of independent variableso

500 --- ---- | - - 500 1 - 1 max' i S ==:=or====~ ^ZZZ^ZZ^: — ^ ^'-"- IFRACTORE o 1 — -----: T SA - b _ - _ S _ _ UA) IIL 1.0 o4 o3 -2 TRUE STRAIN-E(in/in) Figure 534) Typical True Stress Strain Diagrari.

-78Other variables were considered and found, either to be dependent on variables already considered, or of second order signifance. For instance, it was assumed that consideration should be given to the presence of the second phase, in particular to its abrasive effect on the wear of the tool. Experimental work showed that this effect is well taken care of in the mechanical properties. After all, these properties are as much a function of the second phase as they are of the first phase. The coefficient of friction can serve as another example of a dependent variables, therefore should not be in our list. Moduli of Elasticity are considered of second order significance for reasons brought out above. Strain rate effects, are by far less significant than most metal researchers postulated(97)' (98) The analysis of the metal deformation, as being a shear phenomenon occurring in a very narrow region, led to the conclusion that the strain rates are extremely high. Our own work shows that the deformation happens in a much wider region, consequently yielding lowerstrain rates, and though they are still large their effect on the process is of second order. The average tool chip interface temperature Qf was chosen as the dependent variable. Based on our experimental work presented in Figures 28, 29, and 30, showing the cutting temperature versus the cutting velocity, this temperature was found to be 975 + 25~F for a cutting velocity V60, correspondint to a sixty minutes tool life. It will not be necessary therefore to have time in the generalized machinability relationship. The velocity for a sixty minute tool life will therefore be that velocity that gives an average tool chip interface temperature of 975~F,

-79On the basis of the above discussion we whould look for four dimensional groups. After much deliberation the following four were selected: (Vw/O); (w/t); (CpGf/HB) and Rf, where Rf was defined above as 100 - Ar 1 Rf = Ao/Af, or 100 R C0 is the thermal diffusivity defined as C = K/fC e K is the thermal conductivity, J is the density, and C is the specific heat. Before coming to this final conclusion we have considered many different variables, consequently we had many other dimensionless groups, some of which will be discussed here. The effect of the ratio between the yield strength ( Cy) and the tehnsile strength (GT) was examined. Though Janitsky(72) built his machinability index for steels on the ratio (Gy/ GT) it was not found to have general validity, (V 2/9 or fV2/ Gy), where (JV2) could be considered as an inertia stress is a dimensionless group, discussed by Drucker(99) and others was dropped, knowing that inertia forces are insignificant in convensional machining speeds(100) since V2 < Groups like (TLV/ T), of which Kronenberg(10l) makes use were dropped on the basis that the effect of the depth and of the feed are not interchangeable, though the area of the cross section (F) remains the same.

-80An attempt was made to make use of a group like (Q2 /HB KfC/Vt),. including (K C), which was claimed by Shaw et al(l102) to be very significant. Unfortunately the experimental data did not follow any specific pattern when plotted in this fashion. To conclude the discussion about those dimensionless groups that are included in this analysis, we would like to mention that many more groups were considered, some of them ratios or multiplication of others, physically they could not be interpreted, and experimentally they did not provide the expected correlation. The first group that was found to be significant is the thermal number (Vw/o) the importance of which was recognized by Bisacre(103) and Chao(37) and later by others(l14). The thermal number was interpreted as the ratio of the transit time over the relaxation time(103). More specifically to the metal cutting it governs the ratio of the heat conducted through the work to the heat convected by the moving chip. The second group or the area ratio R, becomes larger the higher the ductility of the material. The larger the ductility, keeping all other variables constant, the lower we would expect the machinability to be inasmuch as the ductility determines the area under the strstress sain curve which is a measure of the work done during machining. In the limit, when Ar = 100%, Rf = Oo, or in words, when the material can withstand an infinitely large strain, we should not be able to machine the material at all. The third group (CyGf/HB), where (C /HB) could represent a temperature raise, if all the heat is carried away with the chip, and none whatsoever is conducted away.

_81l The fourth group (w/t), where w is the width and t the thickness, represents the geometry of the cut and does not need any further elaboration. It follows that Vw/C = A(w/t)a (QCG/H)b (Rf) (39) or if t and w are constants V/o: = A (JCGf,/HB) (Rf) (40) To evaluate the constants in this equation the properties of the experimental materials as well as the corresponding velocity and temperatures were usedo In order to evaluate the machinability of the various materials it is necessary to select one set of standard conditions to serve as a basis. A very logical basis, one that has been very often used in the past, is the cutting speed that results in a 60 minute tool life, and is designated as V60o Experimental data on all of the materials studied in this project as well as some additional data found in the literature indicates that this also corresponds to one value of tool-chip interface temperature, which is about 1000~F for a 60 minute tool lifeo This limiting temperature is higher for a shorter tool life and is proportionally lower for tool lives in excess of 60 minutes. One further problem in this same category is the determination of the temperature at which the physical properties of the material should be evaluatedo After examining carefully movies of the metal deformation in the cutting zone, it is apparent that most of the deformation occurs in

-82a region where the temperature is about 600~F. On the basis of this observation, it was decided that all the physical properties of the material should be evaluated at 600~F, Using the properties of the material at 600~F, the cutting velocities corresponding to a sixty minute tool life, and the postulate that the temperature is for all practical purposes constant for these speeds, the numerical value of the exponents b and c are found to be 1,0 and -0.5, respectively. Substituting the values in Equation (40) and lumping all constants into one constant A2 we get: V/o( = A R -1/2 (41) 2H f B Where A =! 1150. V60 in FPM can be expressed explicitly as V60 A K (42) 60 2 HB Rf1/2 since oc= K/fC, and JC can be cancelled on both sides of the equation. Inasmuch as most handbooks list the area reduction rather than the more convenient area ratio, Equation (42) can be rewritten as = A2 K (l-Ar/100)1/2 (43) 6o 2 B substituting the value of A2 yields: V60 = 5 (1-Ar/100)/2 (44) B

-83This relationship enables us for the first time and by means of simple calculations, to orderly arrange the materials and predict their machinability on the basis of three of their physical properties; thermal conductivity K (Btu/Hr - Ft - ~F), area reduction A and Brinell Hardr ness HB (Kg/mm2). The constant A2 is computed from the various standard units used, Figure 35 shows this relationship graphically, with the experimental points on the graph. It is immediately obvious that the 2024-T4 aluminum and the molybdenum do not fit the curves. As a matter of fact, it would be strange if they did. For the 2024 aluminum, the melting range is 935 - 1180 ~F, and for a 1000~F interface temperature it would be expected that localized melting would occur at the grain boundaries, accompanied by a sharp decrease in the ductility and some reduction of the hardness, Therefore the machinability will obviously be better than predicted on the basis of the general machinability equation, As to the molybdenum, the micrograph of the chip, as shown in Figure 36, explains best why the material deviates from the expected behavior. Two observations can be made. First, the material fails through the grain boundaries with cracks forming in the material ahead of the tool, separating the metal being deformed by means of an insulting void space from the bulk of the work piece. Second, the material continues to undergo great deformation as the chip is formed. Most of the molybdenum carbides (Mo2C), the hardness of which is between 1400 and 1800 Vickers, are located at the grain boundaries, and consequently these hard carbides will be in contact with the tool.

1500 1000 - 800.. 600 400 - o 300 >0 K(I —-- --—, 0.04 0.06 0.08 0.1 0.2 0.4 0.6 0.8 1.0 I- Ar/1 I000) 200* TEST POINTS 100 -- ---------- -— J — 0.04 0.06 0.08 0.1 0.2 0.4 0.6 0. 8 1.0 ( I - Ar/1000) 96 94 92 90 80 60 40 20 0 Ar % Figure 35. The General Machinability Equation.

I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~........ i B 1 | | |. |~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~............... i ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~........ }'" 0 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...... i -- ii -- i l i;0 0 0 i t t -;; i if;5; 0; if i;; t i;; i x C l -; - 0;; t; - B; s::B~~~~..........';... 0 i; ig...:; f f! fS;:; t: i f:.00;; 0E 0:;;;;.".,.. iC: 0 f.............. D 0p t } \ <. C tl tt 0 * 0 A].A 0... } t) } t [ Ai.> 0. t hO:f; (:o ub. t..............................l );RR~~~~~~~~~~~~~~~~~~~~~~~~~~~ez~~~~~~~~~~....S....Q..

-86Their effect on the wear will be by far larger than their effect on the hardness of the work material. The cracks formed effectively insulate the cutting zone from the work material and consequently the effective thermal conductivity is much smaller, probably by a factor of three to four. As to the ductility on the small, the deformation in the chip shows that it was essentially not effected, If we sum up these factors, it is obvious why the actual sixty minute cutting velocity is so much lower than the predicted one, To validate the general machinability equation comparison is made with data published by different research institutes, technical societies and recommendation of the manufacturers, Table XV gives the predicted values of machinability in terms of V60 for a variety of materials. It verifies clearly the validity of the relationship for materials as different as cast iron, steel, aluminum, zirconium and titanium, as well as for nearly similar materials, as 1020, 1045, 4340 and 1212 steels or the stainless steels, The final machinability relationship stated above can be used with the following qualifications: 1. The predicted machinability values are no more accurate than the properties that are used to compute them, Exactly as the measured value of the area reduction may vary from one specimen to another of the same material by 50% or more so may the machability vary by as much as NF2, as any metal cutting researcher knows,

-872. The material should not have any critical transition temperature below 1000~F. If it does, it is necessary to go back to the first basic relation and select different temperatures and properties associated with them. 3. The hardness of the material should be at least 100 Brinell hardness numbers lower than that of the tool, 4. The numerical value of V6 is for a T-l high speed steel tool, with 0,0,7,77,70,0C tool designation, depth of cut t = 0.0057 in., width of cut w = 0.050 in., and cutting dry, The effect of variables other than the physical properties, such as the cutting conditions, are discussed in the following two sections. The Effect of the Size of Cut on the Cutting Velocity for Constant Tool Life Different approaches were used in the past to consider the effect of the dimensions of the cut on machinability. Woxen(5) introduced a "chip equivalent" q', defined as q' = t+w/wt, and considered the cutting velocity as some function Y of q'; V = t(C, q', TL), where C is a constant depending on the cutting conditions and the material cut. q' was considered to inadequately represent the effect of the dimensions of the cut, for the simple reason that interchanging the depth and the width, will have no effect on q', but have a remarkable effect on the cutting velocity for a constant tool life. Boston(l06) states on the basis of his experimental work that an exponential relationship of form VTL = Ct-X w-t exists, and describes

TABLE XV PREDICTED MACHINABILITY VALUES Material Predicted Corrected Experimental Cutting Conditions V6o () V6 (2) V60(3) FPM FPM FPM 1. AISI 1020 Steel 158 160 160 Actual Test Value 2. AISI 1212 Steel 190 190 190 Actual Test Value 3. AISI 1045 Steel 113 120 120 Actual Test Value 4. AISI 4340 Steel 61 60 60 Actual Test Value 5. Al-ll00-0 8650 8500 8500 Extrapolated Test Values 6. A1-2024-T4 1960(4) 2600 2600 Actual Test Values 7. Molybdenum 220(5) 60 60 Actual Test Values 8. Rene 41 20 17-20 50-60(6) t=0.005; w=1/52; Carbide Tools(7) 30-40 t=0.010; w=1/161/8; Carbide Tools 9. Ti-6 AL-4V 19 15-30 30-60(8) HSS Tools, 15~ Rake(9) Coolant(10), size of cut not specified 10. Ti-155-A 21 15-30 30-60(8) HSS Tools, 15~ Rake, coolant, size of cut not specified 11. Udimet 500 26 25 15(11) t=0.009; w=0.100; 15~ Rake, 48 minute tool life, 0.060 wear land; coolant 12. Inconel X 36 38 38 20% of V60 for AISI B1112 steel 13. 301 Stainless Steel 78 80 80(12) Same conditions 14. 303 Stainless Steel 64 55-70 70-90(13) Rough'Positive Rake(14), coolant, size 80-130(13) Finish of cut not specified 15. 310 Stainless Steel 76 60-80 60-90 Rough 100-120 Finish 16. 347 Stainless Steel 84 75-95 60-90 Rough 100-120 Finish 17. 410 Stainless Steel 62 55-75 80-100 Rough 100-130 Finish 18. 430 Stainless Steel 64 55-75 80-100 Rough 100-130 Finish 19. 446 Stainless Steel 70 60-80 60-90 Rough 90-120 Finish 20. Fe-Cr-Mo Alloy 66 55-75 80-100(15) Finish cut, positive rake, coolant, size cut not specified 21. Zirconium 94 80-100 100-150(16) t=0.0050.010; w=0.010-0.040; positive rake, coolant 22. Armco Iron 220 225 225 Actual Test Value 23. Grey Cast Iron 340 350 270(17) t=0.006; w=0.100 24. Pearlitic Cast Iron 150 155 120(17) t=o.006; w=0.100 25. Leaded Red Brass 745 500-1000 585+1150(18) 150-600% of V60 for AISI B1112 Steel -88

FOOTNOTES 1. From the general machinability equation 1150 K (1-Ar/OO 1/2 V60 = (l-Ar/100) HB applying the data of Tables XII and XIII. 2. Cutting velocity corrected to our condition from values in (3). 35 Cutting velocities as recommended by industry and research institutions, and cutting conditions as specified by the source. 4. Prediction too low owing to localized melting in grain boundaries as explained in text. 5. Prediction too high owing to failure in grain boundaries, exposures of the molybdenum carbides, and effective insulation of the chip. 6. Engineering data VM-107, Rene 41, General Electric Company 1958, 7. Cutting velocity for one hour tool life is about three times as large for carbide tools as for high speed tools. 8. Bulletin No, 1 and No, 5 Titanium Metal Corporation of America (1957 and 1958). 9. Positive rake has a large effect on machinability of ductile material and negligible effect on machinability of brittle materials. 10. Coolant reduces the cutting temperature, in turn increasing the cutting velocity for any one tool life, 11. Metal Progress Data Sheet, 98 B, August 1961. 12. Titanium Reports, University of Michigan, 1953. 135 All stainless steel data taken from Metals Handbook, 8th edition, 1961. 14. Cutting conditions for all stainless steels are the same. 15. Alloy Casting Institute, Data Sheets, 1957. 16. Zirconium data file, Carborundum Metals Company. 17 Previous experimental work of Professor Datsko. -89

-90adequately the effect of the dimension of the cut on the cutting velocity for any tool life TL. He cites the following particular relationships: For steel: V = C t061 w-6 (45) For cast iron: Vg9 = C2 t053 w0'23 (46) Where C1 and C2 are constant of different values for the different steels and cast irons. (107) Merchant and Ernst, in the Tool Engineers Handbook, state that in general V = Ct*077 w0-37. The data compiled by the ASME Research Committee on Metal Cutting is reproduced in Figures 57 and 38. The curves show the correction factors for the velocity of a sixty minute tool life, as affected by a change in the dimensions of the cut. The curves represent all the data in the Manual on Cutting of Metals(l08) The exponents in this case are 0.62 and 0.36 for t and w respectively. To consider the effect of the size of cut it is necessary to look at the two groups (Vw/o ) and (t/w)a containing the dimensions of the cut; the depth t and the width w. We may introduce a "Characteristic Length" q, which will include the effect of t and w in the following manner: (Vw/D ) (t/w)a =(V/) w-a ta =(V/*)q (47) where q = wl-a ta (48)

10 2- 1.0 v 5.0 0 62 ^ so __- -I__ 1 KI.0 ( —-)50- d 0.36_ f --:Kd =1.0o( —~ I- --- -- - -- - ^s. __ - _I _ _ __-If K d_ _1-0- j__ 0o 0 g~2.O -_- _fo 0.0101 d =_._I0 o o 0 0 W.0 I 1.0 "O 1 10/ oIrVliyoaSxyiuTollcyf I I n T i0f.ie >- 0.5 w w > 0.25 0. I I I 0.1 0.1 1.0 10 0.1 1.0 10 FEED RATIO - FEED /STANDARD FEED DEPTH RATIO =DEPTH/STANDARD DEPTH Figure 37. Effect of Feed of Cut on Cutting Figure 38. Effect of Depth of Cut on Cutting Velocity for a Sixty Minute Tool Velocity for a Sixty Minute Tool Life. Life.

-92Based on all the experimental evidence mentioned above we can conclude that "a" is about two third (a = 2/3) for 0.1 < t/w < 0.2, and therefore: q = wl/3 t2/3 (49) From physical considerations and experimental results we know that "a" is not a constant, but varies with the ratio of the depth of cut to the width of the cut (t/w). When t = w, or their ratio is equal to unity, obviously the effect of both sould be alike, "a" will be equal to one half (a= 1/2) and q = wl/2 tl/2. But when the ratio (t/w) goes to zero, the limit of "a" should be unity. Mathematically expressed: lim a = 1 (t/w)* o (50) from which it follows: lim q = t (t/w)4o (51) Table XVI, sums up the corresponding values of "a" and "q" for different (t/w) ratio. Figure 39- supplements this table, TABLE XVI RELATIONSHIP BETWEEN THE GEOMETRY OF CUT AND THE "CHARACTERISTIC LENGTH" t/w a q in O 1 t 0.15 2/3 t2/3 w1/3 1 1/2 tl/2 wl/2

1.0 0.8 0 LI0 a. 0.4 — 0.2 0 0.2 0.4 0.6 0.8 1.0 DEPTH WIDTH RATIOt/w Figure 39, Chip Geometry Exponent "a"

.94Appendix B shows the results of a test conducted with a different depth of cut t and width of cut w to verify the above concept. It shows the validity of the postulated effect of q on V60. Tool Life Velocity Relationship In general the tool life cutting velocity follows the exponential Taylor(7) relationship, VTn = C where n and C are constants depending on the tool, the cutting conditions and the material machined. The relationship is valid over the range of cutting velocities, which yield practical tool lives. For high speed steel tools, in general 0.05< n <015, though it may vary over wider ranges. Taking an average of n = 0,10, will give reasonably good predictions for the cutting velocity for tool lives different from sixty minutes. The error in predicted cutting velocity is smaller than 5.5% if tool life is between 20 minutes and three (3) hours. The error is still less than 11% if the tool life range is extended to eight (8) hours. It should be mentioned that the smaller the value of n, the more sensitive is the tool life to the cutting velocity. In the extreme cases, for very small values of n, any error is objectionable, and it is necessary to resort to measuring the tool life.

V. CONCLUSIONS 1o A functional relationship was developed between the physical properties and machinabilityo 2. The Brinell Hardness (HB) and area reduction (Ar) were found to describe adequately the effect of the mechanical properties on machinabilityo 3o The thermal conductivity (K) was found to describe adequately the effect of the thermal properties on machinabilityo 4. All material properties should be evaluated at the average temperature in the cutting zone. 5o The effect of the abrasiveness of the second phase on machinability is well taken care of by considering the mechanical properties of the material, 60 Abrasive wear tests could not be used to improve the prediction of the machinability of a material. 7. No relationship could be established between machinability and eithe impact strength, deformatin energy or the strainhardening exponents, 8, No relationship could be established between the chip hardness and machinabilityo 9. For a sixty minute tool life with a T-1 tool material the average tool chip interface temperature is 975+ 250~F and the average temperature of the cutting zone is about 600~ Fo -95

10. The cutting velocity (V60) for a sixty minute tool life is given by: 1150 K (A/(521/2 V6 = B ( Ar/l00oo)/ (52) Cutting conditions are: T-l High Speed Steel Tool, having the ASA shape 0,0,7,7,7,0,0, Depth of cut t = 0.0057 in. Width of cut w = 0.050 in, Cutting Fluid - air The machinability relationship is valid provided that: a) The work material has no critical transition temperatures below the tool chip interface temperature. b) The hardness of the work material is at least 100 Brinell Hardness numbers below the hardness of the tool,

APPENDIX A SAMPLE CALCULATION OF TOOL LIFE RELATIONSHIP FOR AISI 4340 STEEL Cutting Tool Velocity Life ln V ln T (ln T) (ln T)(ln V) V FPM TL min. y x x xy 1 70.0 2.8 4.24850 1.02962 1. 06012 4.37434 2 60.0 34.0 4 09435 3.52637 12.43529 14.43819 3 65.0 19.6 4,17439 2.97553 8,85578 12.42102 4 70.0 1.75 4.24850 0.55962 0,31317 2.37755 5 80,0 1,3 4.38203 0.26236. 06883 1.14967 6 75.0 1.6 4.31749 0. 47000 0.22090 2.02922 7 55.0 27.5 4.00734 3.31419 10.98386 13.28109 8 85.0 0.75 4,44266 -0.28769 0 08277 -1.27811 9 60.5 106.0 4.10265 4,66344 21.74767 19.13246 10 653. 53.0 4.17900 3.97030 15.76332 16.59188 11 67,5 9.4 4,21213 2.24071 5,02078 9.43816 12 70.5 8.3 4.25562 2.11626 4.47856 9.00600 13 70.5 12.4 4.25562 2.51770 6.33884 10.71442 14 75.0 4 3 4, 31749 1.45862 2, 12757 6.29758 15 85.0 2,5 4.44266 0.91629 0.83959 4.07076 16 95 0 0.7 4,55388 -0,35318 0.12447 -1.60834 Summation 68,23431 29.38014 90.45952 122. 43589 -97

-98( x2) (Zy) = 6172.4 (Zx) (Z xy) = 3597.2 (Z x) (Z y) = 2004.7 N xy = 1959.0 N x2 = 1447.4 ( x) ( x) = 548.2 in C = (Z x2) (E y) - (Z x) (Z xy) 6172.4 - 3597.2 2575.2 4.481 N x 2 - (Z x) (Z x) 1447.4 - 863.2 584.2 C = 82.1! 82.0 n = ( x) ) - N xy _ 2004.7 - 1959.0 45.7 0.0782 n = (Ex...... N Z x2 - (x)(Zx) 584.2 584.2 n = 0.078 and the tool life relationship for the material is: VT 0.078 = 82 VL

APPEND IX B VERIFICATION OF THE POSTULATED EFFECT OF THE SIZE OF THE CUT ON V60 To verify that under the same cutting conditions, changing the size of the cut only: V60a = 60 w1/3 t2/3 = constant, A set of tool life tests were conducted on an AISI 1020 steel. The cutting velocity V60, for t = 0.0057 in.and w = 0,050 in, was measured and predicted to be 160 fpm. Consequently for t = 0,.0113 inand w = 0.100 in the predicted V60 should be 80 fpm, Figure 40 is a plot of the actual machining data for the heavier cuts. From this data the experimental value of V60 is found to be 85 fpm. The variation between the calculated and the experimental value of V60 is within the range expected due to experimental errors. -99

200 a 15o 10 ________ —---- ----- ---- ---- - _ UI- -- 700 0 20 - 1.0 3 6 10 30 60 00 TOOL LIFE-MINUTES Figure 40. Cutting Speed Tool Life. AISI 1020 Steel.

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