. .7 _ . “V . . u .0.” .1..." ”RV“ ““ _w,““““> ,, .. A ‘ , v , .s , 4 ' Ay _ . V . » T ‘ ' - h H - A ‘ ‘; 3 BANDING AND ITS INFLUENCE.“ ;;i-»~;1«;;;§ :~~._,_; é - THE IMPACT AND FATIGUE PIRDPE " i ' * ' ‘ :1 .REN'GTH ' .340 ST EL {1'5 .i ' Dissertation for the Degree To? Ph. D: _. MlCHlGAN STATE umvsasm * ‘ ANTL vmmmo 1973 'r:: . v.-.v.- .n "T. ,n.~.., . . ,.,' our" hruuy—f’. -,,. ’41-;;-”.._,_','," >‘ as- ' .w'. l' , " I" .'.2'.‘."' , J." 5:, .' . r,.".~v.1..r ,, r_ «.n¢' v r. (.3!) - v ' «Fm: EM ' LIBRARY Banding and Its Influence on the Impact and Fatigue Properties of High Strength SAE 4340 Steel presented by Anil Venkat Rao has been accepted towards fulfillment of the requirements for __1’h-_D_-_degree in Metal lurgx W/M Major professor A) ‘ ‘ ‘ LIIM 1"»61.~’lligan State L":1iversity BIN DEM IPIIIIPIIY. Illlllll, . Fullllln: . ABSTRACT BANDING AND ITS INFLUENCE ON THE IMPACT AND FATIGUE PROPERTIES OF HIGH-STRENGTH SAE 4340 STEEL by Anil Venkat Rao An investigation was undertaken to study the phenomena of handing and its influence on the impact and fatigue properties of two high- strength SAE 4340 steels which differed in their inclusion ratings. In both the as-received and the quenched-and-drawn conditions, the materials exhibited banding which, upon analysis, showed a segregation of phos- phorus, manganese, chromium, nickel, and molybdenum.in the bands. Upon a high-temperature homogenization treatment at 2350°F for 20 hours, the segregation was reduced to a sufficient degree to eliminate banding. Comparison of the properties of the homogenized and the banded specimens in the tempered martensitic state showed that the elimination of banding resulted in significant improvements in both the impact and fatigue strength. An explanation is given to account for this behavior. BANDING AND ITS INFLUENCE ON THE IMPACT AND FATIGUE PROPERTIES OF HIGH STRENGTH SAE 4340 STEEL By Anil Venkat Rao A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Metallurgy, Mechanics, and.Materials Science 1973 Dedicated to my dear parents, who have been an endless source of love, kindness and inspiration throughout my entire life. ii ACKNOWLEDGMENTS I wish to express my gratitude to Professor Howard L. Womochel for his invaluable guidance and counsel throughout this research. It was both a pleasure and privilege working with him during my stay here, and I shall be always indebted to him.for building a basis for my profes- sional career. My special thanks are due to Professor Donald J. Montgomery for giving encouragement and assistance whenever I needed it. I also wish to express my thanks to Professors Austen J. Smith, William N. Sharpe, Paul H. Rasmussen, Robert W. Summitt, and Rolland T. Hinkle, who served on my guidance committee; and to Mr. Donald Childs and associates, Mr. Vivian Shull and Mr. Robert Rose, for their help in the experimental work. Thanks are also due to the General Motors Spectrographic Committee for supplying the standards which were used in the electron microprobe analysis. And last but not the least, thanks are due to Mrs. Thelma Liszewski for the care and patience that she displayed in typing this manuscript. iii TABLE OF CONTENTS LIST OF TABLES o o o a o o o o a s o o o o o o o o o o o 0 LIST OF FIGURES o a o o o o o o a o o o o o o o o o o o o 0 CHAPTER I. INTRODUCTION . . . . . . . . . . . . . . . . . . CHAPTER II. ON BANDING: A HISTORICAL REVIEW . . . . . . . 2.1 Its Origin . . . . . . . . . . . . . . . . . . . . . 2.2 Different Theories on Banding . . . . . . . . . . 2.3 Homogenizing as a Way to Eliminate Banding . 2.4 Effect of Banding on Mechanical Properties . . . . CHAPTER III. EXPERIMENTAL TECHNIQUE USED AND RESULTS OBTAINED 3.1 a Heat Treatment of the First Group of Steels . . . Impact Properties of the First Group of Steels . Fatigue Properties of the First Group of Steels . Heat Treatment of the Second Group of Steels . . Impact Properties of the Second Group of Steels . Fatigue Properties of the Second Group of Steels - Heat Treatment of the Third Group of Steels - - Impact Properties of the Third Group of Steels - - Fatigue Properties of the Third Group of Steels . 3.2 3.3 00'“ DVD 00" CHAPTER IV. DISCUSSION . . . . . . . . . . . . . . . . . . 4.1 Discussion on Banding . . . . . . . . . . . . 4.2 Influence of Banding on the Impact Properties . . 4.3 Influence of Banding on the Fatigue Properties . . OMB v. concws IONS O O C O O O O C C . C C O O O O C O 0 APPENDIX A. CALCULATION OF THE TEMPERATURE REQUIRED TO REMOVE Em INC 0 O O C C O O O C O C O O O O O O O O O 0 APPENDIX B. CALCULATION OF THE MAXIMUM TENSILE STRESS ON THE FATIGUE SPECIMENS . . . . . . . . . . . . . . . iv Page vi viii 18 21 27 29 31 36 41 45 46 54 54 57 63 63 95 109 119 121 123 APPENDIX C. APPENDIX D. APPENDIX E. MICROHARDNESS TESTS FOR THE 1 OD AND 4 HNQD SPECIMENS CALCULATION OF THE STANDARD DEVIATION 07. FOR NICKEL, MANGANESE, CHROMIUM, AND MOLYBDENUM . . . . . . . . CALCULATION OF THE LOAD (FORCE) UNITS FROM THE LOAD- TIME CURVE o e o o s a o o o o a o o o o s o o o o BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . Page 125 127 128 129 Number 2.1 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 4.1 4.2 4.3 LIST OF TABLES Melting-point Lowering and Solid- -1iquid Distribution of Some Elements in Iron from Phase Diagrams (J. Chipman1 ) , Impact Strength in Foot Pounds at Various Heat Treatments (QD, NQD, mQ D) O O O O O O O O O O O O O O O O I O O 0 Analysis of Variance Table for Impact Strength (QD, NQD, IMD). C C I C C O O O O O O I O O O O O O O O O O O O I 0 Number of Cycles at Various Heat Treatments (QD, NQD, HNQD). Analysis of Variance Table for Number of Cycles (QD, NQD, 1mQD) C O O O O C O C O O O O O O O O O O O O O O O O O O 0 Values of Impact at Different Heat Treatments (1 QD, 2 NQD, 3 MD, 4 mQD) o o o o o o o o o o o o o o a o o o o o o 0 Analysis of Variance Table for Impact Strength (1QD, 2 NQD, 3 “QB, 4 mQD) o o o a c o o o o o o o o c o o o o o o o o a Number of Cycles at Various Heat Treatments (1 QD, 2 NQD, 3 “QD, 4 IINQD) O O O O O O O O O O O O O O O O O O O O O O 0 Analysis of Variance Table for Number of Cycles ( 1 QD, 2 MD ’ 3 INQD ’ 4 MD) 0 O I O O O O O O O O O O O O O O 0 Analysis of Variance Table for Impact Strength (1 QD, 2 NQD) Impact Strength in Foot Pounds at Various Heat Treatments (5 QD, 6 MD) 0 O O O O O O O O O O C O O O O O O O O I O 0 Analysis of Variance Table for Impact Strength (5 QD, 6 ImQD) O O O C O O O O O O O C O O O O O O O I O O I O O O 0 Number of Cycles at Various Heat Treatments (5 QD, 6 HNQD) . Analysis of Variance Table for Number of Cycles (5 QD, 6 mqn) O O O I O O O C O O O O O O O O O O O O O O O O O 0 Specifications of the Electron Microprobe . . . . . . . . . Number of Counts for the Standards . . . . . . . . . . . . . Number of Counts for the Banded Specimen (1 QB). . . . . . . vi Page 35 39 41 45 46 48 50 53 55 56 59 61 79 80 81 Number 4.4 4.5 4.6 Number of Counts for the Homogenized Specimen Reduction in Segregation Due to Homogenization Standard Deviation for the Different Elements vii Number 1.1 2.1 2.2 2.3 2.4 2.5 2.6 2.7 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 LIST OF FIGURES SAE 8640 Automotive Forging Showing a Marked Fibrous Structure . . . . . . . . . . . . . . . . . . . . . Diagram Showing Conditions for Eventual Migration of Carbon [P. Bastien2 '2 ] Effect of Addition of Silicon on the Ar3 Lines for Plain Carbon Steels [J. Kirkaldy et a12°24] , , , , , , , , Effect of Addition of Manganese 3n zhe Ar3 Lines for Plain Carbon Steels [J. Kirkaldy et a1 ' ] . . . . . . . . . . . Effect of Addition of Chromium on the Ar3 Lines for Plain Carbon Steels [J. Kirkaldy et a12'24 ]. . . . . . . . . Effect of Addition of Phosphorus on the Ar3 Lines for Plain Carbon Steels [J. Kirkaldy et a12°24] . , , , , , , . , , Effect of Addition of Nickel on the Ar3 Lines for Plain Carbon Steels [J. Kirkaldy et a12°24] , , , , , , , , , Diagram Showing the Assumed Sinusoidal Variation of Concen- tration through the Steel . . . . . . . . . . . . . . Heat-treating Electric Furnaces (Sentry on the Left and bye 8 on the Right ) O C O O O C O O O O O O O O O O 0 Schematic Diagram Showing the Positions of the Impact and Fatigue Specimens in the Test Bar. . . , . , , , , , , , . The Instrumented Charpy Impact Tester. . . . . . . . . . . The Dimensions of the Charpy Impact Specimen , . . . . . , A Fixture to Polish Fatigue Specimens. . . . . . . . . . . A Magnified View of the Above . . . . . . . . . . . . Moor's Fatigue Testing Machine . . . . . . . . . . . . . Plot of 8&N Curves for the First Group of Steels (QD, NQD, mQD) o o o o o 0 a o o o o c o o o o o o a o o o o o a o 0 Plot of Impact Strength versus Temperature for the Second Group of Steels (l QD, 2 NQD, 3 HNQD, 4 HNQD). . . . . . . viii Page 14 16 17 17 17 17 18 28 32 33 34 37 37 38 42 47 Number Page 3.10 Plot of S-N Curves for the Second Group of Steels (1 QD, 3 IINQD, 4 WQD) a o O o o o o 0 o o o o o o o o o o o o o o 52 3.11 Plot of Impact Strength versus Temperature for the Third Group Of Steel 8 (5 QD ’ 6 mQD) . O C C O O O O O O O O O O O S 8 3.12 Plot of S-N Curves for the Third Group of Steels (5 QD, 6 mQD) o o o o o o o o o a o o o o o a o o a o o o c c o o 62 4.1 Portion of Equilibrium giagram of Iron and Iron Carbide [D. Clark and W. Varney '1] . . . . . . . . . . . . . . . . 64 4.2 Microstructure of the As-received Steel Showing Bands of Ferrite (white) and Pearlite (dark) (x 100) , , , , , , , , 66 4.3 A Magnified View of the Above (x 500) . . . . . . . . . . . 66 4.4 Microstructure of the Steel in the Quenched Condition Showing Bands of Martensite (white), Retained Austenite (white), and Tempered Martensite (dark). The Tempering Took Place During the Polishing Operation (x 100) . , , , , 68 4.5 Microstructure of the Steel in the Quenched and Drawn Condition (1 OD). The bands in the Tempered Martensite Are Due to the Coalescence of Carbides on the Segregated AlloyinsElements(x100)................. 68 4.6 Microstructure of the Steel in the Normalized and Quenched Conditions Showing Bands of Martensite, Retained Austenite, and Tempered Martensite (x 100) , , , . , , . , , , , , , , 69 4.7 Microstructure of the Steel in the Normalized, Quenched, and Drawn Condition (2 NQD) Showing Bands of Tempered mrten81te (x 100) O I C O O O O O O C O O O O O O C O O O 69 4.8 Microstructure Showing the Accentuation of Banding in the 1 OD on Annealing (x 175) . . . . . . . . . . . . . . . . . 71 4.9 Microstructure Showing the Accentuation of Banding in the 3 “QB on mneal 1ng (x 1 75 ) I O O O O O C C O O O O O C O O 7 1 4.10 Microstructure Obtained after Homogenizing at 2350°F for 20 Hrs. and Slow Cooling. The Coarse Ferrite and Pearlite Were Prior to Transformation, Large Austenite Grains (x 100) 72 4.11 Microstructure of the 4 HNQD specimen. Note the Uniform Tempered Martensitic Structure. The High Temperature Homo- genization has Resulted in the Elimination of Banding (x 100) o o o o o o o o o o o o a o o o a o o o a o o o c o 72 ix Number 4.12 4.13 4.14 4.15 4.16 4.17 4.18 4.19 4.20 4.21 4.22 4.23 4024 4.25 4.26 4.27 4.28: 4.29 Microstructure of the 4 HNQD after Annealing. Unlike 1 QD, 2 NQD and 3 HNQD, Banding Does Not Reappear on Slow Cooling in.the 4 HNQD as is Evident from the Uniform Distribution of Ferrite and Pearlite (x 175) . . . . . . Microstructure of the 4 HNQD after Normalizing. Note the Uniform Tempered Martensitic Structure (x 175) . . . . . Calibration Graph for Molybdenmm . . . . . . . . . . . . . Calibration Graph for Nickel . . . . . . . . . Calibration Graph for Manganese . . . . . . . . . . . . Calibration Graph for Chromium - . . . . . . . . Concentration Variations across the 1 OD as Obtained by Electron Beam.Scanning . . . , , , , Concentration Variations across the 4 HNQD as Obtained by Electron Beam Scanning Shows Segregation of Phosphorus in the 1 OD . . . . . . . Shows Uniform Distribution of Phosphorus in the 4 HNQD (x 175) C O O O O O O O O O O O O O O I O O O O O O O O O O Sulphur Print Indicating the Distribution of the sulphides in the 4 HNQD (bottom), and 1 QD (top) spec mus (x 2) O O O O O C O O O O O C O O O O O 0 O O Microstructure of the As-received Specimen Showing the Sul- phide Inclusion (light grey) in the Pearlite Band (x 175) . Microstructure of the As-received Specimen Showing the Silicate Inclusion (dark) in the Ferrite Band (x 175) . . Distribution of Inclusions in the Polished 1 OD Specimen (x 175) O O O O C C O C O O O O C O O O O C O O O O O O O 0 Distribution of Inclusions in the Polished 4 HNQD Specimen (x 175) O O O O O C O O O I O O I O O O O O O O O O O O O 0 Distribution of Inclusions in the Polished 5 QB Specimen (x 175) C O C O C . C C O O O O O O O O C O O O O O O O O 0 Distribution of Inclusions in the Polished 6 HNQD Specimen (x 175) O O C O O O O C O O O O O O O O O O O O O O O O O O Fracture Surface of the 5 OD Specimen Tested at -210°C. Measured Charpy Impact Energy = 7 ft.lbs. (x 6.5) . . . . . X Page 73 73 75 76 77 78 87 88 89 89 91 92 92 93 93 94 94 96 Number Page 4.30 Fracture Surface of the 5 QD Specimen Tested at -56°C. Measured Charpy Impact Energy = 28 ft.lbs. (x 6.5) . . . . . 96 4.31 Fracture Surface of the 5 QD Specimen Tested at 100°C. Measured Charpy Impact Energy = 38 ft.lbs. (x 6.5) . . . . . 97 4.32 Fracture Surface of the 6 HNQD Specimen Tested at -210°C. Measured Charpy Impact Energy = 16 ft.lbs. (x 6.5) . . . . . 97 4.33 Fracture Surface of the 6 HNQD Specimen Tested at -56°C. Measured Charpy Impact Energy = 30 ft.lbs. (x 6.5) . . . . . 98 4.34 Fracture Surface of the 6 HNQD Specimen Tested at 100°C. Measured Charpy Impact Energy = 43 ft.lbs. (x 6.5) . . . . . 98 4.35 Photograph Indicating the Position of the Strain Gauge on the Mr had I I I I I I I I I I I I I I I I I I I I I I 1 00 4.36 Schematic Diagram of the Instrumentation for the Force-time masuremnt 8 I I I I I I I I I I I I I I I I I I I I I I I I 1 00 4.37 Force (Load) -time Curve for the 6 HNQD Specimen Tested at -210°C. Measured Charpy Impact Energy = 16 ft.lbs. . . . . 101 4.38 Force (Load) -time Curve for the 5 OD Specimen Tested at Room Temperature. Measured Charpy Impact Energy = 36 ft.lbs. 101 4.39 Force (Load) -time Curve for the 6 HNQD Specimen Tested at Room Temperature. Measured Charpy Impact Energy = 40 ft.lbs. 102 4.40 Idealized Force (Load) -disp1acement Curve . . . . . . . . . 103 4.41 Initiation of the Crack at the Root of the Notch (x 1.25). . 105 4.42 Lateral Growth of the Crack in the 5 QD (above) and the 6 HNQD (below) Specimens. Note the Jagged Appearance of Fracture in the Non-homogenized Specimen (x 1.25). . . . . . 105 4.43 Crack Extending Down the Sides in the 5 QD (above) and the 6 HNQD Specimens. Note the Difference in the Direction of the Travel Paths (x 1.25) . . . . . . . . . . . . . . . . . 107 4.44 Nonrmetallic Inclusions Aid in the Propagation of Crack (x 175) I I I I I I I I I I I I I I I I I I I I I I I I I I 107 4.45 Charpy Impact Fracture Surface of 5 OD Tested at Room Temperature Showing Sharp Banded Ridges (x 12) . . . . . . . 108 4.46 Charpy Impact Fracture Surface of 6 HNQD Tested at Room Temperature Showing a Reduction in Ridges (x 12) . . . . . . 108 xi Number Page 4.47 SEM Photograph at Center of 5 QB Tested at Room Temperature Showing Sharp Bands (x 200). . . . . . . . . . . . . . . . . 110 4.48 SEM Photograph at Center of 6 HNQD Tested at Room Tempera- ture Showing Bands Dispersed at Random (x 200) . . . . . . . 110 4.49 Schematic Diagram of the Model to Explain Fatigue Failure . 111 4.50 SEM Photograph Showing the Inclusion Acting as a Nucleating Site for Fatigue Fracture in the 1 QD (x 200). . . . . . . . 113 4.51 SEM Photograph Indicating the’Band as a Nucleating Site for Fatigue Fracture in the 1 OD (x 200) . . . . . . . . . . . . 113 4.52 SEM Photograph Indicating the Crack Propagating along a String of Non-metallic Inclusions in the 1 QD (x 200). . . . 115 4.53 SEM Photograph Indicating the Crack Moving from Right to Left across the Bands and through a Path of Non-metallic Inclusions in the 1 QD (x 200) . . . . . . . . . . . . . . . 115 4.54 SEM Photograph Indicating the End of Stage 2, and the Onset of Fracture (going from left to right) (x 200) . . . . 117 4.55 Fatigue Fracture Surface of the 1 OD at a Low Magnifi- cation (x 6) I I I I I I I I I I I I I I I I I I I I I I I I 118 4.56 Fatigue Fracture Surface of the 4 HNQD at a Low Magnifi- cation (x 6) I I I I I I I I I I I I I I I I I I I I I I I I 118 3.1 Calculation of the Maximum Tensile Stress on the Fatigue SpeCimns I I I I I I I I I I I I I I I I I I I I I I I I I I 124 C.1 Plot of Rockwell Hardness (Rc) vs. the Distance across the Spec 1mn I I I I I I I I I I I I I I I I I I I I I I I I I I 126 xii I. INTRODUCTION Lack of homogeneity is one of the very common sources of weakness in metals or indeed of materials in general. However scientifically the engineer may design his machinery or structural material with a view to uniform distribution of stresses when the piece is in service, the maximum strength qualities will not result unless the material composing the piece possesses uniformity of stress resistance. Therefore, extra- ordinary efforts are made to manufacture the structural material in such a way as to minimize heterogeneity of structure or composition. In the case of alloys, including all varieties of steel, complete homogeneity is an impossibility. Any steel, whether carbon or alloy, loses its homogeneous character as soon as it cools past a temperature of saturation for any phase, and thereafter it is by nature a segregated system. The segregation in ingots give rise after hot working to a fibrous (banded) structure having alternatively higher and lower degrees of the segregated elements. Fig. 1.1 shows this marked fibrous structure in a 4-inch SAE 8640 automotive forging. It is now generally accepted that banding is due mainly to the microsegregates of various elements. Such segregates influence the carbon distribution, and form mainly during the original solidification of the ingot. Different workers have variously ascribed the nature of these microsegregates to phosphorus, arsenic, oxygen, sulphur, manganese, nickel, and other elements. Fig. 1.1 SAE 8640 Automotive Forging Showing a Marked Fibrous Structure. It is not yet known, with any degree of certainty, if banding causes any significant changes in the mechanical properties, especially the dynamic mechanical properties like impact and fatigue. To quote R. L. Cairns and J. A. Charlesl, "Studies of banding in steel have not shown unequivocally that this phenomenon (of banding) has deleterious effects. It causes differences between the longitudinal and transverse mechanical properties, but a measure of any effect on the longitudinal tensile strength and transverse impact strength has not been determined." To mention just a couple of discrepancies -- Schwartzbart2 showed that in 0.21%C, 1.47% Mn steel, the transverse tensile strength in quench and tempered states improved by up to 10% and the elongation 2.5 to 8.5 times, if the material was homogenized before quenching. Jatczak3 con- cluded, however, that homogenization causes very little alteration in longitudinal mechanical properties, and only slight, commercially insig- nificant, improvements in the transverse ductility and impact strength. The impact strength and the fatigue strength in the transverse direction are found to be appreciably lower than that in the longitudinal direction. This behavior has been previously attributed to nonrmetallic inclusions. But in high-strength steels like SAE 4340, the non-metallic inclusions are not present in sufficient amounts to account for the large differences in the transverse properties. Could the reason, in addition to nonrmetallic inclusions, be banding? If so, could the removal of banding bring about an improvement in the impact and fatigue properties? This question is of paramount interest in industry, since the transverse mechanical prOperties sometime become the controlling factor for many types of high-stress service like pressure vessels, highepressure pipings, gun tubes, generator rotors, crankshafts, torsion shafts, coil springs, diaphragms, and welded-plate structures. In the aircraft and space industry, even a slight degree of improvement is significant, as the factor of safety must necessarily be kept low to cut down the weight. 11. ON BANDING: A HISTORICAL REVIEW 2.1 Its Origin Any steel, whether carbon or alloy, loses its homogeneous character as soon as it cools past a temperature of saturation for any phase, and thereafter it is by nature a segregated system. Segregation in steel is due to the low diffusivity of the solute and to the distance between the solidus and liquidus line on the phase diagram (the solidification range). As in general the element dissolved in steel lowers the melting point of iron, crystallization leads to a partial rejection of the solute, which progressively enriches the part that remains liquid. This segregation takes place both on a grain scale (micro- or dendritic segregation) and also on the scale of the cast piece or ingot (macro-segregation). Macro- segregation is due to a mass effect and is hence of a different character from microsegregation, but the two phenomena are nevertheless interdepen- dent, since the segregated liquid thrown out by the crystals has to reappear somewhere in the ingot. The microsegregation in ingots gives rise after hot working to a fibrous structure having alternatively higher and lower degrees of the segregated elements (P, Mn, Si, Ni, Cr, Mo, etc.). This fibrous struc- ture is known as a primary banded structure. During solidification carbon, like the other elements, segregates to the interdendritic spaces. After complete solidification, however, 6 the carbon rapidly becomes homogenized, as opposed to the other elements which undergo practically no diffusion. After the passage through the transformation zone (between the Ar3 and Arl) the secondary structure appears, which is usually ferrite and pearlite. The ferrite and pearlite appear in alternate bands with the same frequency and the same disposition as the primary segregated bands. This layered arrangement is known as a secondary banded structure. Not all elements segregate to the same extent in steel, and hence their contributions to the banding phenomenon are different. If the distribution coefficient of an element L in iron is denoted as k, then by definition k = Concentration of element L in solid Concentration of element L in liquid A measure of the segregation tendency of the element is the quantity (1 - k). Chipman1 has shown that if both the solid and liquid obey Raoult's law, then the segregation coefficient "1-k“ is proportional to the lowering of freezing point brought about by dissolving the element L, ‘i.e., l-k = M.A T/lOOO X , where M is the atomic weight of the element and AT is the lowering of freezing point due to XI of the element in solution. Values of (l-k) and of K, the freezing-point lowering caused by one percent addition of several alloying elements, are summarized in Table 2.1. Very little accurate information is available on k for gamma iron. Estimates of the segregation coefficient for gamma iron are indicated in parentheses. Table 2.1 Melting-point Lowering and Solid-liquid Distribution of Some Elements in Iron from Phase Diagrams (J. Chipmanl) -AT (in 6 Fe) Element Atomic Wt. for 1% Segr. Coeff. (l-k) K b-Fe y-Fc Carbon 12.01 90 0.80 0.70 Manganese 54.94 1.7 0.10 0.25 Phosphorus 30.98 28 0.87 0.94 Sulphur 32.07 40 0.98 (0.95) Silicon 28.09 6.2 0.17 (0.5) Nickel 58.71 2.9 0.17 0.05 Chromium 52.01 1.8 0.09 (0.15) Molybdenum 95.95 1.5 0.14 (0.4) The impurities in steel (P and S) suffer a very pronounced segrega- tion. They also increase the A3 point appreciably. In case of low alloy or plain carbon steels, these impurities play eur essential part in the formation of the banded structure. Oxygen also is seen to have a high value of l—k. However, since oxygen has no effect on the Ar3 transformation temperature andhag only a very limited solubility in iron, it plays only a small part in the banding phenomenon. The alloying elements Ni, Cr, and Mo, and also Si, Mn, and Cu, suffer much less segregation than the impurities. However, since 'metallic elements can readily be added in relatively large amounts, their segregation, although small in proportion, may nevertheless be appreciable in absolute terms. 2.2 Theories on Banding Let us briefly examine the theories that have been put forward to explain the phenomenon of banding in steels. (1) The Inclusion Theory. This hypothesis proposed by Brearley2 states that the real cause of banding lies in the small globules or specks of slag already existing in the ingot. These inclusions act as nuclei on which the ferrite is first precipitated when the material cools down through the Ar3 point. Since in hot rolled steels these inclu- sions are elongated in the direction of the work, the ferrite shells formed around them.are of similar shape. As further deposition takes place on the already existing ferrite, the remaining austenite becomes enriched in carbon, and finally, at the Ar1 temperature, it is con- verted into pearlite interleaved between the bands of ferrite. Mahin3, on quenching steels between the Ar and Ar temperatures, 3 1 found the first formed ferrite to be associated with the inclusions. The ferrite thus formed controlled the subsequent deposition of ferrite at slow rates of cooling. Attempts have been made by several workers to bring about precipita- tion of ferrite upon artificially produced inclusions. Brearleya, Mahin and Hartwigs, and Hatfield6 showed that artificially introduced inclu- sions of sand were associated with ferrite if the material was suffi- ciently worked to produce intimate contact between the sand and the metal. Benedicks and Lufquist7 proposed that silicate inclusions rich in oxygen could act as nuclei for ferrite. Oberhoffer and Hartmann8 shoved that electrolytic iron which has been melted and carburized, and 9 that had received an addition of manganese sulphide, showed a banded structure, whereas a similar melt without the sulphide addition was free from banding. In support of the inclusions theory, are two well-documented facts. (1) In normal hypo-eutectoid steels the inclusions are almost invariably to be found in the ferrite, a fact which is true in both castings and worked products, and (2) a clean steel is, in most cases, distinctly freer from banding than is one unusually rich in inclusions. However, there are several reasons which demonstrate equally con- vincingly that the Inclusion hypothesis cannot describe the whole truth. One reason is the fact that if a small sample of a steel with a banded structure is annealed at a sufficiently high temperature (about 2100- 23000F) for a few hours, the banding can be entirely eliminated. This temperature is certainly not high enough to bring about any observable difference in the amount or distribution of the slag or sulphide inclu- sions. Furthermore, McCance9 and Whiteley10 have shown that the banded structure, once removed by the high-temperature anneal, is not re-formed by subsequent normalizing. The inclusions now occur in ferrite and pearlite indiscriminately, instead of existing entirely in the former. Moreover, if a normal banded steel is heated up above the Ac3 point and quenched, banding is still present, despite the fact that since fer- rite is now no longer present, no influence of the inclusions upon it can be responsible for such an effect. (2) The Phosphorus Theory. Stead11 was the first to state that phosphorus caused banding in steels. He contended that the dendrite heterogeneity was due to phosphorus, because of its resistance to dif- fusion. Phosphorus that is segregated in the interdendritic spaces 10 causes the rejection of the C atoms from the interdendritic spaces into the dendritic axis, thereby increasing chemical dendritic heterogeneity. Phosphorus lowers the solubility of carbon in austenite and raises the Ar3 transformation temperature, both factors leading to ferrite being associated with the phosphorus-rich regions. If these regions are them- selves oriented, as a result of the influence of the working on an originally cored solid solution in a parallel fashion, a banded structure will result. J. Whiteley's12 work showed, however, that before phos- phorus can cause migration of carbon in steel, a difference of at least 0.07% is needed between adjacent regions, and the mean phosphorus content should be greater than 0.13%. Sauveur and Krivobok13 in their research concluded that phosphorus in the substantial absence of any other elements may cause persistent den- dritic segregation and the presence of both carbon and phosphorus results in a more intense and persistent dendritic segregation. On an alloy containing 0.39%P and 0.17%C, they found the carbon to be completely driven from the interdendritic spaces into the axis, resulting in den- drites consisting of pearlitic axis and of ferritic "fillings." The main evidence on which the phosphorus hypothesis rests is that the phosphorus content of the ferrite bands of a banded steel is distinctly higher from that of the material as a whole. Also, Oberhoffer and Hartmann8 showed that addition of phosphorus to electrolytic iron resulted in banding,while an identical specimen in which phosphorus was not added showed no banding. The theory that ferrite banding is caused by phosphorus segregation, however, has not been always fully accepted. Several researchers have, 11 for example, found pronounced ferrite banding in very low-phosphorus steels. Sauveur14 reported ferrite banding in steel containing only 0.004% phosphorus. Also, according to Whiteleylo, the solubility of phosphorus in ferrite is appreciably higher than that in austenite at the same tempera- ture. As a steel cools, therefore, and precipitates ferrite, phosphorus tends to diffuse outwards from the austenite into the ferrite, in which the phosphorus content is raised above that of the residual austenite. The Characteristic variations of phosphorus in a normal rolled mild steel may therefore be the result of the banding of ferrite and not the cause. Another objection to the phosphorus theory is that banding can recur after heat treatment of sufficient duration to homogenize the phosphorus present. (3) The Segregated Elements Theory. Mahin.and Wilson15 examined the effects of silicon, phosphorus, titanium, chromium, nickel, aluminum, and copper on the premature separation of cementite in steel. They con- cluded that all these elements singly or jointly are effective in causing premature cementite separation, if they are themselves segregated in steel. Prohoroff16 studied the effect of elements which showed persistent dendritic segregation, notably silicon, manganese, nickel, and titanium, on the distribution of carbon, and proposed that banding could be prevented by "balancing" steels. By balancing he meant the formulation of steel compositions such that the overall effect of segregated elements on carbon could be equalized throughout an ingot. 12 H. L. Geiger17 studied the banding phenomenon in SAE 3100 gear steels. He concluded that ferrite has higher solubility for nickel than does cementite. On slow cooling, this causes the carbon to be rejected to areas of slightly lower nickel concentration, producing the banding effect. Furthermore the nickel migrates very slowly, and the fundamental structure responsible for banding was found not to be broken up by any of the ordinary practical heat-treating methods. Sauveur and Reed18 found that ingots having as little as 0.04% carbon (9.8% nickel) exhibited a pronounced dendritic structure in the cast and annealed section from which they inferred that nickel causes the observed segregation. Peter and Finkler19 stated that sulphur segregation was the chief cause of bending in many plain carbon steels. In the sulphur-rich zones the steel is depleted of manganese, which is bound as manganese sulphide. The result is that the sulphide-rich portions have a higher Afa point than the sulphide poor. Ferrite, therefore, is nucleated first in the mmnganese-sulphide-rich portions. Cameron and Waterhousezo, in studies of steel containing 0.2% As, concluded that arsenic segregates, producing in general, a banded struc- ture which persists throughout all heat treatments applied. This banding was attributed to two factors: (1) Arsenic has very low diffusi- vity in austenite; (2) Arsenic tends to eject carbon from solution in the austenite giving rise to bands of arsenic-rich ferrite and arsenic-poor pearlite. (4) Other Theories. (Thompson and Willows21 proposed that banding was due to oxygen dissolved in the iron. Differential oxygen concentrations were presumed to be set up during solidification, forming iron oxide on l3 cooling. These oxide-oxygen segregates were elongated during working and influenced the carbon distribution. Benedicks and Lofquist7 set up a dynamic segregation theory according to which the banding arises in rolling through the confluence of soft portions into "flow channels', the harder portions being pushed aside and forming longitudinal bands at the side of the "flow channels." Both the oxygen theory and Benedick's and Lofquist's dynamic-segregation theory are today chiefly of historical interest. (5) Recent'Theoriegron-Banding Essentially two theoretical views have been expressed to explain the phenomenon of banding. (l) C. Jatczak, D. Girardi, and E. Rowland22 regarded the banding as primarily due to the chemical heterogeneity present in steel. The carbide-forming elements like manganese, chromium, and molybdemum.tend to increase carbon concentration in their vicinity, while solution-type elements like nickel tend to decrease carbon concentration in their neighborhood. Therefore, in single alloyed steels, the degree of carbon segregation and the location of high and low carbon areas depend solely on the amount and distribution of that particular alloying element. In multi-alloyed steels, however, the banded conditions depend upon a balanced influence as determined by alloy types, amounts and distribu- tions. Jatczak et al therefore attribute the banding to the pre- segregation of the alloying elements above the Ar3 line in the iron— carbon diagram. 23 (2) Bastien , on the other hand, emphasizes the role of the consti- tutional effect of the alloying elements in shifting the Ar line, 3 14 resulting in premature or delayed nucleation of pro-eutectoid ferrite. In the case of phosphorus segregation, for example, since the phosphorus- rich regions have a higher Ar3 temperature, the pro-eutectoid reaction will begin in these regions, rejecting carbon to the phosphorus-poor regions and delaying the beginning of transformation there even further. Consequently, the final microstructure consists of ferrite in phosphorus- rich regions and pearlite in phosphorus-poor regions. In addition, Bastien stresses the effect of cooling rate on banding in case of hypo- eutectoid carbon and low-alloy steels with appreciable amount of phos- phorus present. Figure 2.1 shows the TTT curves for two steels with different phosphorus contents. A Slow cooling Curve of deposition of proeutectold ferrite .i;—_- _59 \ 2.High phosphorus content Quicker ——- cooling \\I. Low phosphwhs—Eomcnt (b) TEMPERATURE F._'-.--——-|—""' I l I l I I J (b) LOG TIME (0) Fig. 2.1 Diagram Showing Conditibns for Eventual Migration of Carbon [P. Bastien2°23]. Since phosphorus increases the hardenability as well as raises the Ac3 transformation temperature, the curves representing the start of the austenite transformation in steels of different phosphorus content must 15 intersect (Fig. 2.1). The two curves would apply not only to two dif- ferent steels, but also to two different regions of the same steel. If cooling takes place slowly (curve a), the cooling curve would intersect curve 2 at M; and curve 1 at N at a lower temperature. Ferrite will therefore be deposited in regions with a higher phosphorus content, resulting in concentration of carbon in the remaining austenite. If cooling takes place at a faster rate, the corresponding cooling curve (b) intersects the transformation curves (1) and (2) at N’ and M}. The austenite transformation now begins in regions with a low phosphorus content and tends to produce a concentration of the carbon in areas rich in phosphorus. The normal carbon displacements away from the phosphorus- rich regions may thus be inverted. J. S. Kirkaldy24et a1 conducted an experiment to assess the relative importance of these two theories. They studied the banding behavior in ternary systemo Fe-Si-C, Fe-Mn-C, Fe-Ni-C, Fe-Cr-C, and Fe-P-C. They concluded that above the Ar: temperature, the segregates affect 3 the thermodynamic-activity of carbon. Holding at austenitic temperatures equalizes the activity of carbon. Thus, where the segregating element raises this activity, as in the case of phosphorus, nickel, and silicon, the carbon is rejected. And in regions rich in manganese and chromium, where the activity of carbon is lowered, carbon begins to collect. The magnitude of the presegregation is always a small fraction of the mean concentration, but its presence has an effect on the Ar3 tem- peratures at different points and influences the sequence of ferrite nucleation.. For example, a 1.5% Si alloy (Fig. 2.2) will not only raise the Ar line but also, as a result of the presegregation, the silicon 3 16 will be associated with lesser carbon, moving it from a point To to a point T1. This increases the difference in nucleation temperature from AT' for a band of uniform carbon content to AT, resulting in a more intense form of banding. 06w § T YEIPERATURE 1 'C I . :— 799 L 1 II 02 04 II cousosmou (WEIGHT 1. CARBON) Fig. 2.2 Effect of Addition of Silicon on the A532kines for ]. Plain Carbon Steels [J. Kirkaldy et a1 The behavior of the Fe-C-Mn couple (Fig. 23) is an exact counter- part to the Fe-C-Si one. Manganese lowers both the Ar3 line and the activity of carbon in austenite while silicon raises both of them. The Fe-C-Cr (Fig. 2.4) couples are identical to the Fe-C-Mn couples when the carbon is low enough. However at higher carbon concentrations, the Ar3 lines cross over because of the closed v loop present in the iron- chromium constitution diagram. This could eliminate or even reverse the banding direction in higher carbon alloys. The behavior of phosphorus (Fig. 2.5) is identical to that of silicon and apposite to manganese. Only aflsmall amount of phosphorus is needed to shift the Ar3 a large amount. This effect is due to the very tight v loop in the iron-phosphorus phase diagram. 1‘6) TMMWRE l7 s-C-C%Cl TEMPERATURE 1°C) 00°F " o-c-ssss- . l 1 no” (:2 01-4 as we” 92 °‘ °‘ comesmou (View as CAM) COMPOSITION (WEIGHT'bW’ Fig. 2.3 Effect of Addition Of Fig. 2.4 Effect of Addition Of Manganese on Ar3 Lines for Plain Chromium on Ar Lines for Plain Carbon Steels[J.Kirkaldy et a12'24] Carbon Steels IJ. Kirkaldy et a12 24] The Fe-C-Ni couples (Fig. 6) are unique in that the direction of pre- segregation does not aid transegregation. (This is because nickel, like silicon, raises the activity of carbon in iron but, like manganese, lowers the Ar3 line. Hence AT is less than AT'. Nonetheless AT is still sufficient to insure prior nucleation in the nickel—free regions leading to the manganese-like transegregation. This demonstrates the dominant influence Of constitution in determining bending behavior. “or F's-C - O-I'LP TEMPE NATURE 1 'C) TEMPEWWE ('C) l 1 $00 OI! . O“ II o 02 04 as COMPOSITION (when 15 canon) COMPOSITION (WEIGHT % CARBON, Fig. 2.5 Effect of Addition of Fig. 2.6 Effection of Addition Of Phosphorus on the Ar Lines for Nickel on the Ar3 Lines for Plain Plain Carbon Steels IRirkaldy2 '24 ] Carbon Steels [J.Kirkaldy et a12-24] 18 2.3 Homogenizing As a way to Elimingte Banding Segregation can be eliminated to a great extent by holding the steel at a high temperature in the austenitic range for several hours to facili- tate diffusion of the alloying elements. This process is called homo- genizing. The homogenizing temperature should be chosen as high as possible so as to accelerate diffusion, but nevertheless below the temperature corres- ponding to the theoretical solidus to avoid remelting of the most segregated regions. Too high a temperature during these anneals can cause other problems such as deformation of the pieces, a high cost of production, and mainly decarburization. Lavender and Jones25 calculated the temperature required to remove banding assuming that the concentration varies sinusoidally through the steel as shown in Figure 2.7. Fig. 2.7 Diagram Showing the Assumed Sinusoidal Variation of Concentration through the Steel. If Cm is the average concentration, the variation from the average concentration at any point is given by C . Cm sin ii" a (1) where 21 is the "wavelength" between the bands. 19 After high-temperature homogenization, the concentration at any point is given by 2 2 C - Cm.sin (fix/16).;1T Dt/L (2) where D is the diffusion coefficient of the segregated element and t is the time of homogenization. It can be shown that Equation (2) satisfies the differential equa- tion 2 he. . Db—C bt bx2 with C = 0 at x = 0 and x = I for all values of t, and - 2 2 e n Dt/L a Cm. when c = Cm sin.nx/L when t - 0. At x = L/Z, c = Cm t - 0. The amplitude of the bands is thus a fraction l/f of its original amplitude when - 1/f (3) It is apparent therefore that the degree of homogenizing that can be achieved will be greater, the greater the rate of diffusion of the alloying element, the longer the holding time at high temperature and the smaller the distance that the alloying element has to diffuse (dendritic dimensions). Taking logarithms of both sides of Equation (3), we have 2 0.4343‘1—25 - log r ‘2 10 It is estimated from the micro-radiographszs, that banding will not be 20 observed when it is reduced to 1/10 of its original amplitude. Putting f - 10, we have 2% . -—-—1 2 = 0.233 . (4) 1 0.4343n The diffusion coefficient D is given by the equation Ae-Q/ RT D a: (5) where R,- gas Constant 8 2 Cal/g, T = absolute temperature and A and Q are constants obtained from diffusion measurements. Taking logarithms of both sides of equation (5), we have _ ‘ = 0.4343 9 logloA logloD RT T = - -0.4343 9 (6) R(1og10A - logloD) Putting the value of D from Equation (4) into Equation (6) yields 0.4343 Q 2 _ W R[1ogloA log10 t ] T. Kattamis and M.’Flemings26 calculated the homogenization kinetics of a low-alloy steel, based on a sheetlike model of dendritemorphology and on an assumption that there is no mass transfer along the columnar growth directions; diffusion being perpendicular to the columnar growth direction and normal to the family of cylindrical isoconcentration surfaces. They arrived at the following solution: Q Q C(x,y,e) - z 2 Km Cos(¥)COs(ul;¥ x n-O‘mPO 2 2 2 2 2 e’(n/1o+m/£)TTDO+E 21 where C(x,y,9) is the solute concentration at the point (x,y) and at time 9, D is the diffusion coefficient of the element, L',£' are one-half the primary dendritic—arm spacing in the x and y directions respectively, and O is the average solute concentration. They found that the values obtained from the equation agreed pretty close to the experimental results for isothermal treatments up to 80 hrs. at 2200°F. 2.4 Effect of Banding on Mechanical Properties Since the banded material is heterogeneous from both a chemical (primary bands) and a structural (secondary bands) viewpoint, its mechan- ical properties are affected in consequence. Several experimental studies have been made of the effect Of pearlite-ferrite banding on mechanical properties, but the results are ambiguous. The non-fatigue mechanical properties (tensile strength, ductility, and impact) are considered first and then the fatigue proper- ties are dealt with. 2.4.1 Effect of Banding on the Non-fatigue Mechanical Properties. Pearlite/ ferrite banding has been suspected of causing several detrimental effects in steel. H. Schwartzbart27 investigated the mechan- ical properties Of a 0.21% carbon, 1.47%wmanganese steel which exhibited severe banding due to manganese segregation. He showed that the trans- verse tensile strength in quenched and tempered states improved by up to 10% and the elongation 2.5 to 8.5 times, if the material was homogenized before quenching. The manganese inhomogeneities and resultant pretrans- formation segregation of carbon, led to the production of martensite with 22' a periodic variation in mechanical properties. The improvement in trans- verse mechanical properties was attributed tO the removal of this varia- tion. However, working on a heavily banded 0.6% carbon steel, C. Jatczak, D. Girardi, and S. Rowland28 concluded that homogenization causes very little alteration in longitudinal mechanical properties, and only slight, commercially insignificant, improvements in the transverse ductility and impact strength. Matton-Sjobergzg, investigating the possible role of banding in the fracture of mild steel, concluded that the cracking process always started in the ferrite, with the cracks running at or near the center of the ferrite bands. In finely banded structures, the pearlite bands with their greater elastic limit and ultimate strength, prevented the plastic deformation of the soft ferrite layers. This caused a severe stress system within the ferrite, resulting in a brittle fracture. In more coarsely banded structures, however, the ferrite layers are thicker. Hence the primary cracking occurred after a considerable amount of plastic flow in the ferrite. A coarsely banded structure, therefore, gave a higher energy absorption value than a finely banded structure. Owen et 8130,31 also showed that cleavage fracture occurred within ferrite but initiated at the ferrite/ferrite grain boundaries, or ferrite/pearlite interfaces. They concluded that the fracture was dependent on the ferrite grain size or primary austenite grain size, being a function of submicrostructural factofs within the ferrite, and that the pearlite volume fraction or band spacing .was only of secondary importance. They noted a lowering of both transverse and longitudinal 23 impact energy absorption with banding, but found no associated lowering of the transition temperature. Mantio and Boulger32 concluded that a banded microstructure is less resistant to brittle fracture than a unform unbanded structure. In sup- port of this statement, they quoted the work of Sims, Banta and Waters33 who compared high-tensile steel plates rolled from slabs of the same ingot, one slab being given an intermediate homogenizing treatment for ten hours at 2350°F. Homogenizing the slab lowered the 10 ft-lb Charpy V-notch transition temperature of the plate by about 60°F. Kazinczy34 investigated the effect of homogenizing annealing on the strength in the thickness direction of clean, semikilled shipbuilding steel. He found that a normalizing treatment followed by fairly quick cooling removed the ferrite banding, but that, after correction for reduced grain size, this treatment had practically no effect on the fracture anisotropy. Annealing for 24 hrs. at 900-12500C reduced the anisotropy both through a slight lowering of the strength in the longitu- dinal direction and a slight increase in the transverse direction. However, some anisotropy still persisted. Hultgren et al35 studied the influence of the banded structure on the mechanical properties of a tool steel, a ball-bearing steel, and a quenched and tempered steel. The properties parallel and transverse to the fiber direction were studied in forged steel with dendritic and globular primary structure. They found a lower impact strength in the transverse than in the longitudinal direction. They conceded that the difference may have been caused by banding. 24 Malinochka and Kovalchik36 found the mechanical properties to be similar, but the ductility and impact strength lower, in the transverse than in the longitudinal direction in rolled spring-steel strip. They attributed this difference to the segregation of silicon and sulphide stringers. R. A. Grange37 studied the tensile and notch-impact properties in a severely banded wrought steel containing 0.25%C and 1.5%Mn. He concluded that both microstructural banding and elongated inclusions cause aniso- tropy in.mechanical properties. In steel with very few elongated inclu- sions, anisotropy was markedly reduced by elimination of banding. On the other hand, elimination of banding resulted in only slight improvement of anisotropy in a steel containing many elongated inclusions. Banding did not significantly affect the tensile strength, yield strength, or elonga- tion in the tensile test, but did reduce the reduction of area, notch toughness, and the energy for ductile fracture. F. A. Heiser and R. W. Hertzburg38 studied the fracture anisotropy of a banded low carbon steel of low hardenability. The ductility and impact-resistance anisotropy was controlled by the delaminations which occurred by inclusion/matrix interface separation in the mechanically fibred material. When these delaminations occurred normal to the crack direction, they were found to be beneficial; however, when they occurred in the crack direction, on the fracture plane, they were detrimental since this resulted in additional crack extension. They concluded that homogeneization, which did not alter the inclusions, did not affect the anisotropy. 25 It is significant to note that most of these mechanical properties were determined in the ferrite-pearlite banding which are prominent in low-carbon steel. However, the medium carbon machine steels are almost invariably quenched and tempered for critical stress applications. This may result in bands of tempered martensite having alternate layers of low and high alloy concentrations. It would be interesting to know how this banded tempered martensitic structure affects the impact properties. 2.4.2 Effect of Banding on Fatigue If banding does have an influence on the fatigue properties, then this must be evident in the transverse fatigue properties. However, very little information is available in the literature on transverse fatigue properties. The fact that the fatigue strength transverse to the forging fiber may be appreciably less than the fatigue strength parallel to it, has been largely overlooked. Until a.few years ago, the literature was inconclusive on the exis- tence of isotropy or anisotropy in the fatigue properties of forgings in general. For example, Aitchison39 remarked that the fatigue strength ought to be related in part to the ductility properties and therefore ought to show anisotropy. However, in a subsequent investigation of several steels and irons, Aitchison and Johnson“0 found little or no ani- sotropy. Hensel and Hengstenberg41 and Moore and Wishart42 studied the anisotropy of fatigue strengths in wrought iron and found the fatigue and tensile properties very erratic. M. Schmidt43 studied the effect of forging reduction on the anisotropy of several properties including the farigue strength and claimed to find a 15 percent decrease in transverse endurance limit.at higher forging reductions. 26 More recently some authors have attributed the poorer fatigue prOper- ties in the transverse direction to the presence of non-metallic inclu- 44’45 found that the inclusion-free SAE 4340 sions. J. T. Ransom et a1 steel showed a 50% higher transverse fatigue limit than a similar steel with non-metallic inclusions. They attributed this to the fact that fatigue cracks initiated at the non-metallic inclusions in the trans- verse direction. The stress-concentrating effect of an elongated inclusion is high for stresses perpendicular to its length but practi- cally nil for stresses parallel to its length. The elimination of the inclusions should therefore have little effect on the longitudinal fatigue strength but should raise the transverse fatigue limit to the longitudinal. However, some anisotropy in fatigue still remained. This indicated that inclusions were not the only cause of anisotropy, but banding also plays a part. G. E. Deiter et al46 conducted a research into the factors affecting ductility and fatigue in forgings. They found that non-metallic inclusions adversely affected both longitudinal and transverse fatigue limits. The longitudinal fatigue limit was controlled by the size and not the number of non-metallic inclusions; however, they were not clear as to what con- trolled the transverse fatigue limit. They concluded that "while the non-metallic inclusions and the steelmaking variables are important factors in determining the transverse fatigue limit, their relative importance is not clear; apparently there are some unknown factors which can exert strong influences." III. EXPERIMENTAL TECHNIQUES USED AND RESULTS OBTAINED Because of the importance of SAE 4340 steel in the critical high strength applications, it was selected for the research project. Two high-strength steels were chosen. They had almost the same chemical com- position, but they differed in the amount of inclusions present. The steel which was vacuum degassed had a lower inclusion rating than the one which was not. The following are their specifications: Non-Vacuumedegassed Vacuumpdegassed Steel - A Steel - B SAE Specification SAE 4340 SAE 4340 Carbon 0.38 0.39 Manganese 0.78 0.78 Phosphorus 0.015 0.012 Sulphur 0.012 0.013 Silicon 0.29 0.29 Nickel 1.65 1.72 Chromium. 0.82 0.81 Molybdenum 0.24 0.26 Grain Size No. 7 7 Size 4" dia., 8' long 4" dia., 4' long 27 28 Fig. 3.1 Heat-treating Electric Furnaces (Sentry on the Left and Hayes on the Right) 29 3.1:g; Hag; Treggment of the First Groupgof Steels Steel A will be considered first. After an extensive literature survey, the following temperatures and times were chosen for homogenization: (a) 2200°F for 6 hours, (b) 22500F for 10 hours, (c) 2350°F for 20 hours Homogenization at 2350°F for 20 hours should bring about complete homogenization for all elements except nickel (See Appendix A). Nickel requires a temperature of higher than 2517OF. At this high a tempera- ture, there is a danger of re-melting, decarburization, and deformation of the piece. Besides, it is not economically feasible. Hence the upper limit of homogenization was taken at 2350°F. A lower limit of 2200°F was arbitrarily taken to see if the improve- ment in mechanical properties can be achieved economically. This low temperature homogenizing treatment will be considered first. A.9 inch chunk of specimen was cut from the steel bar, and heated in a Sentry furnace (Fig. 3.1). A carbon block and muffle was used to pro- tect the specimen from decarburization. As a further deterrent against decarburization, pieces of graphite were introduced in the furnace. Sample drillings were taken at layers of 1/8" from the surface. Chemical analysis on these drillings gave the following results: 1/8" from 2/8" from 3/8" from 4/8" from 5/8" from Surface Layer Surface Surface Surface Surface 07. by wt. .13 .28 .33 .35 .35 30 Decarburization was found to be present to a depth of 3/8" from the specimen surface. However, as the fatigue and impact specimens are located beyond this depth, the problem of decarburization is overcome. The temperature in the furnace was measured by the rayo tube which was attached to the back of the furnace. Periodically a Platinum— Platinum Rhodium couple was introduced from the front end as another check on the temperature. The two temperature readings agreed fairly consis- tently. After the homogenizing treatment, the furnace was shut off and the specimen was allowed to cool in the furnace. The 9" specimen was then removed from the furnace and cut into 3/4" slabs. The slabs in the front and the rear end were discarded and the rest were then: a) Normalized at 1700°F for l l/2 hours (followed by air cooling) to refine the coarse grains of the homogenizing treatment. The normalizing was done in the Electric Hayes furnace (Fig. 311); b) Aus- tenized at 1575°F for 1 1/2 hours and oil quenched; and c) Tempered (drawn) at 1050°F for 1 1/2 hours. These specimens were then designated as HNQD which meant Homogenized, Normalized, Quenched,and Drawn. A second batch of samples consisting of 3/4 inch thick slabs was normalized at 17000F, quenched from 15750F, and tempered at lOSOOF. This batch was designated as NQD which meant Normalized, Quenched, and Drawn. A third batch of samples consisting of 3/4 inch thick slabs was quenched from 1575°F and tempered at 10500F. This batch was designated as QD which meant Quenched and Drawn. All the specimens, therefore, ended up in the tempered martensitic state. They differed, however, in the extent to which segregation (banding) was present. 31 The selection of batches HNQD and OD for the study of the effect of banding on the mechanical properties is obvious. The NQD batch was taken to insure against concluding that the effect of the HNQD on the mechanical prOperty is due to the homogenizing, when it may be due to normalizing. The impact and fatigue specimens were machined from the 3/4 inch slabs (Fig. 3.2). All the specimens were therefore in the transverse directions relative to the original steel bar. 3.l.b Impact Properties of the First Group of Steels The Charpy impact specimens were tested on the impact testing machine which is equipped with a heavy pendulum hammer pivoted about a horizontal axis (Fig. 3.3). The hammer is made to strike the Charpy bar behind the notch (Fig. 3.4). Since the specimen is supported on its two ends, it breaks as a simple beam with the notch on the tension side. The energy required to break the sample is the difference in potential energy of the hammer at the beginning and at the end of its swing. This absorbed energy, expressed in ft. lbs., is a measure of the materials'toughness, and is automatically recorded on the impact tester. The table below indicates the impact strength in foot pounds obtained for the different heat treatments. The impact testing was done at room temperature. 32 Fig. 3.2 Schematic Diagram Showing the Positions of the Impact and Fatigue Specimens in the Test Bar. 33 Fig. 3.3 The Instrumented Charpy ImpactTester. Fig. 3.4 The Dimensions of the Charpy ImpactSpecimen. 6mm. (as/5'9 _i_..___._ ‘ ,_ J 0.2501”). A l— A __ :1 (0505ng WWW . N —- j 9 * L12 " l.__(;jg’;:,- _J {J L’OW- 4.; L '(0394') afar 34 Table 3.1 Impact Strength in Foot Pounds at Various Heat Treatments (QD, NQD, HNQD) Obs. No. QD NQD HNQD 1 26.5 22.5 23.5 2 25.0 25.5 23.0 3 28.0 24.0 28.0 4 22.5 26.0 27.0 5 21.0 23.0 26.0 6 24.0 33.0 24.0 7 22.0 31.0 32.0 8 21.5 33.0 30.5 9 25.5 24.5 28.0 10 25.0 28.0 33.0 11 28.0 28.0 (23.0 12 34.0 26.0 24.5 13 26.5 25.0 33.0 14 26.0 35.0 32.5 15 32.0 33.0 16 25.5 30.5 17 26.0 30.0 18 25.5 33.0 19 30.0 20 31.0 Total 464.5 572.0 388.0 Average 25.8 28.6 27.7 35 To find out statistically whether the heat treatments had any 1 . effect on the impact values, the F test was used. Computational Procedure (1) Totals for each treatment: 464.5, 572.0, 388.0. (2) Overall total = 1,424.5 (3) Crude total sum of squares = (26.5)2 + (25.0)2 + . + (32.5)2 = 39,762.75 (4) Crude sum of squares between treatments = $fl§%§213 + iélgaglz- + $§§§13 = 39,099.02 20 14 (5) Correction factor due to mean = (1’4gg'512 = 39,023.0817 (6) Sum of squares between treatments = (4) - (5) = 75.9383 (7) Total sum of squares = (3) - (5) = 739.6683 (8) Sum of squares within treatments = (7) - (6) = 663.73 Table 3.2 Analysis of Variance Table for Impact-Strength (QD, NQD, HNQD) Sum Degree Source of Squares of Freedom Mean Squares F Test Between Treatments 75.9383 2 37.9691 F a 2.8030 Within Treatments 663.7300 49 13.5455 Total 739.6683 51 14.5033 At a 5% significance level, the critical value of F 3.23. o.os,2,49 3 Since F«< F it is concluded that the means do not differ signi- critical’ ficantly. Hence the homogenizing process at 2200°F did not significantly alter the impact properties. 36 3.1.c Fatigue Properties of the First Group of Steels Prior to testing, the fatigue specimens were polished in a special fixture (Fig. 3.5, Fig. 3.6) designed for polishing. Strips of polishing papers were attached on the aluminum disc which was rotated against the specimen mounted on the turning lathe. The specimen was polished to the 000 grade and then buffed, giving a fine mirror polish. Polishing is essential, to eliminate the scratches on the specimen surface which may act as nuclei for the initiation of fatigue cracks. The fatigue specimens were tested on a Moore rotating beam fatigue machine (Fig. 3.7). This type of testing produces on the specimen one principal stress (alternately tension or compression), the other two principal stresses being zero. The fatigue fractures usually occur along planes of maximum tensile stress. The maximum stress acting on the specimen is given by om = 20.38 1L ax d3 (See Appendix B) where W Weight of hanger + weights loaded on it, and d Diameter of the specimen. The table given below indicates the number of cycles the specimens withstood, for the different values of stresses. If the specimen with- stood more than 107 cycles, it was concluded that the specimen could withstand an indefinite number of cycles without failure at that parti- cular stress. On this premise, the machine was stopped at an arbitrary value beyond 107 cycles. Values below 107 cycles indicate the number of cycles the specimen ran before it failed. The fatigue testing was done at room temperature. 37 Fig. 3.5 A Fixture to Polish Fatigue Specimens. Fig. 3.6 A Magnified View of the Above. 38 Fig. 3.7 Moor's Fatigue Testing Machine. 39 Amaabaoo soao.oom moHo.moH momH.moH maqm.ooH mo asmw o maoo.¢o mqmm.HN om¢o.- omn~.- ~mom.m How Hwflm.n wow oqmn.n Nam ooo.~o mwo¢.m «am mxHH.m amp Humm.m «mm weom.m «an o¢oo.n mos Naom.n me mmam.m omm oasm.m «mm seam.m 5mm wemm.ma mmwm.m~ mmao.mu NQNH.¢N awm~.m was ammo.x m¢~.~a Name.“ Hoo.~H ooo.oo mq~o.m qu moma.m man nawo.m “we omwo.a moH.NH oHHx.m qu oomq.m «on oxmo.x mm~.NH ammo.“ mx~.NH oumw.m «on HmmN.Hm «Ham.am ouam.x~ Homm.ou mama.x aeo.~H mooH.a mam.~H mmoa.o mm¢.H ooo.mn mama.“ osm.mH same.“ mm~.~H Hmom.m com wwH~.o mmo.H q¢¢~.o onn.fl nose.“ Boo.~H name.“ Hoo.NH mnmo.~ aNH.~H ammo.~ nma.~H axqa.mw aoom.m~ «amm.w~ ¢~m¢.w~ Hayes HHoo memo.“ N¢~.NH omno.~ ¢¢N.~H ¢o¢H.h oam.ma ooo.om saxo.a moo.~H HNOH.~ mqo.~H memo.“ mmo.NH memo.“ o¢H.NH ammo.n mo~.- ammo.~ ~m~.~H omaa.m mma.~a «Hmo.~ moo.~H mNNH.x nn~.nH muw mm oh .wo moaomo mo no as .wo moaomo no no 0% .wo v moaoho wo anon Amsom mo Edmv H o A mucumaonh H o A mvammaonh A H o A mvndmsosh um maze aaz no mucoaumoua use: maowua> um mmaomo mo nonabz m.m mgm<9 40 ']3<> find out statistically whether the heat treatments had any effect on the fatigue properties, the F test was used. Comput ationgl Procedure (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11 ) (12 ) (13 ) (14 ) Row totals = 85.1477, 81.2591, 75.3278, 64.9618. Column totals = 100.5492, 103.1363, 103.0109. Within combination totals = 28.4324, 28.3544, .... 21.5548. Overall total = 306.6964. Crude sum of squares = (7.1223)2 + (7.0894)2 + .... + (5.3032)2 1987.4610. Crude sum of squares between columns g;00.5492)2 + (103.1363)2 + (103.010213 16 Crude sum of squares between rows (85.1477)2 + (81.2591)2 + (75.3278)2 + (64.96l§)2 = 1,959.9052. 12 = 1,978.9570. Crude sum of squares between combinations (28.4324)2 + (28.3544): + .... + (21.5548)2 = 1979.5987. Correction factor due to mean = $§Q§;%%§élg, = 1,959.6392. Sum of squares between heat treatments = (6) — (9) = 0.2660. Sum of squares between stresses = (7) - (9) = 19.3178 Sum of squares for the Within Combination effect = (5) - (8) = 7.8623. Total sum.of squares = (5) - (9) = 27.8218. Sum of squares for the Interaction effect = (13) - (12) - (11) - (10) = 0.3757. 41 Table 3.4 Analysis of Variance Table for No. of Cycles (QD, NQD, HNQD) Sum Degree Source of Squares of Freedom Mean Squares Test Between Heat 0.266 2 0.1330 F = 0.6092 Treatment Between Stresses 19.3178 3 6.4392 F = 29.4970 Interaction 0.3757 6 0.0626 F = 0.2867 Within Combination 7.8623 36 0.2183 Total 27.8218 47 0.5919 At a 5% Significance Level, the critical values of F are F0.05,2.36 3'26 F0.05,3,36 2'87 F0.05,6,36 2'36 The F values in the table for interaction and heat treatment are well below the critical 5% value of F. On the other hand, the F test for the between stresses effect is significant. Hence only the stresses and not the heat treatments affect the number of cycles to failure. A plot of S-N curves for the HNQD, NQD and QD (Fig. 3.8) shows that there is no improvement in the fatigue properties due to homogenizing. 3.2.a Hegt Treatment of the Second Group of Steels Since 2200°F did not have any marked influence either on the impact values or on the endurance limit, the next step that was taken was to increase the homogenizing temperature. The homogenizing temperatures chosen for the second group of steels were: (1) 2250°F for 10 hours, and (2) 2350°F for 20 hours. 42 Fig. 3.8 Plot of S-N Curves for the First Group of Steels (QD, NQD, HNQD) . NOH OOH me _ \q n-nw —.q _.d _ q _ u d — q d - u d u A _ on Aoamom onv nufioau Mo .0; I 902m .902 .no Ila Ilium S n M II 8 1? u d l s I. a a I no rub .ATAIU Ill co 1 oozmnd 32-0 no-0 l .L 034 000 0 .13 43 Nine inch chunks of the original steel bar A were homogenized at the above temperatures in the Sentry furnace. To find the extent of decarburization, sample drillings were taken from the center of the bar at the front end, the middle, and the back end. They gave the following results: Location of Homog. at 2250°F Homog. at 2350°F Sample Drillings for 10 hrs. for 20 hrs. Front end 0.36% C 0.33% C Back end 0.36% C 0.36% C Middle 0.36% C 0.36% C The results show that the front end of the bar treated at 2350°F was decarburized. After cutting off half an inch of the bar, an analysis was made again. The sample drillings now showed carbon to be 0.36%. It was concluded that the rest of the bar underwent no decarburization. These specimens were then cut into slabs of 3/4 inch thick, the ends were discarded and the remainder was normalized at 1700°F, quenched from 1575°F and tempered to 1125°F. The specimens that were homogenized at 2250°F for 10 hours were designated as 3 HNQD and those which underwent homogenization at 2350°F were designated as 4 HNQD. A second batch of samples was normalized at 1700°F, quenched from 1575°F and tempered to 1125°F. These were designated as 2 NQD. A third batch of samples was quenched from 1575°F and tempered to 1125°F. These were designated as 1 QB. The impact and fatigue specimens were machined from the 3/4 inch slabs (Fig. 3.2). All specimens were in the transverse direction rela- tive to the original bar. 44 Table 3.5 lists the impact strength in foot pounds for the dif- ferent heat treatments. The impact testing was done from -56°C to + 60°C. To find out statistically whether the heat treatments had any effect on the impact values, the F test was used. Computgtional Procedure (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) Row Totals = 364.5, 419.5, 437, 465.5, 479.5. Column Totals = 517.0, 514.0, 538.5, 596.5. Within Combination Totals 88.5, 96.0, .... 129.0. Overall Total = 2166.0 Crude Total Sum of Squares (30.0)2 + (29.5)2 + ...... + (43.0)2 = 79,312.0. Crude Sum of Squares between Columns (517)2 + (514)2 + (538.5)2 + (596.5)2 15 Crude Sum of Squares between Rows (364.5)2 + (419.5)2 + (437.012 + (465.5)2 + (479.512 12 78,485.30. 8 78,868.33. Crude Sum.of Squares between Combinations (88.512 + (96.012 + .... + (129.0)2 3 79,205.33. 2 Correction factor due to mean = 2123 = 78,192.60. Sum of squares between heat-treatment = (6) - (9) = 292.70. Sum of squares between temperature - (7) - (9) = 675.73. Sum of squares within combinations = (5) - (8) = 106.67. Sum.of squares total - (5) - (9) 1,119.40. Sum of squares interaction = (13) (12) - (11) - (10) = 44.30. 45 3.2.b Impact Properties of the Second Group of Steels Hooch o.oo- m.omm m.mmm o.oHn o.aan _ga=Hou n.oeo o.o- n.5HH n.NHH m.o~H o.mo o.mm o.mm o.oo oooo o.~o o.oo o.mm o.Ho .oaoa awn: o.oo m.om m.om m.om m.moo o.a~H o.oHH n.oHH o.ooH m.Ho m.oo m.om m.~m comm m.mo m.om 0.5m o.wm .oaoa aoom o.~o o.om o.om m.mm o.amo m.mNH m.ooH o.ooH o.moH m.mo o.om o.om o.om coo o.Ho m.mm o.mm o.om ooooz o ooH o.om 0.5m o.mm o.mm m.oHo o.oHH m.m03 o.HoH o.oo o.om n.om m.mm o.~m ooo o.mm o.om o.om o.mm ooH .ooo o.xm o.om n.mm o.o~ m.oom o.moH 0.xw o.om «.mm oaoooa HHoo o.om o.o~ o.m~ o.o~ coon- o.mm 0.0m o.om n.o~ ooH sun o.om o.Hm o.m~ o.on H38. 3oz ooze o maze m 32 N no H 9.383509 mucoauooue one: uaouowman us uoogan mo mooao> m.m mqm um moHoho mo quEbZ n.m MAmncentration,is equalizedz. Thus, where the segregating element raises this activity, as in the case of phosphorus and nickel, then at austeernitic remperatures the phosphorus-rich regions will have a lower conceerntration of carbon than the rest of the material; and where the allqywing element lowers the carbon activity, (Cr, Mn, M0), the reverse is the case. The carbon segregation, therefore, will depend upon a balanced influence of these two types of elements. For the given SAE 4£340 steel, the phosphorus accounts for only a small percentage, and nickeil, though present in appreciable quantities, has a low segregation coeffiicient in austenite (see Table 2.1). Therefore, in the given steel, one «mould expect the inter-dendritic spaces containing the carbide- formilig elements, Cr, Mn and Mo, to be rich in carbon. The magnitude of.tkris presegregation is only a small fraction of the mean concentration, but its presence has an effect on the Ar3 temperature at different pOints and influences the sequence of ferrite nucleationz. Mn, Cr, Mo, and Ni all lower the Ar3 transformation temperature. Hence on cooling from the austenite, the ferrite first forms on the iron-rich dendrites. These dendrites due to hot working are present in the form of bands. Ferrite continues to form with decreasing temperature until point e is reached. At this temperature the remaining austenite will transform into pearlite. Thus at room temperature the structure appears as bands of iron-rich ferrite and impurity-rich pearlite. This is the condition in which the experimental steel bar SAE 4340 was obtained (Fig. 4.2, 4.3). Let us now study the effect of different heat treatments on banding. On reheating the SAE 4340 steel above the AC3 temperature, austenite reappears. If the temperature of holding in austenite is low enough 66 Fig. 4.2 Microstructure of the As-received Steel Showing Bands of Ferrite (white) and Pearlite (dark) (x 100). Fig. 4.3 A Magnified View of the Above (x 500). 67 (below 18000F.), as is the case for the quenching and normalizing heat treatments, the diffusion of the alloying elements is not fast enough to cause any change in their distribution in the austenite. The primary banded structure should therefore remain intact. If the steel is now cooled faster than the critical cooling rate, martensite is obtained. There is no premature separation of ferrite at the Ar temperature in 3 this case. On tempering, therefore, one would expect a uniform tempered martensitic structure free from secondary banding. However, as can be seen from Fig. 4.4 - 4.7, banding is still apparent. This is explained by the coalescence of the carbides during tempering3. The carbides dissolve in places where they are least stable, and grow in places where they are most stable. The stability of the carbides is increased in the bands of high alloy concentration if the alloying element is a carbide-former like manganese, chromium, and molybdenum. The stability of the carbides is decreased if the alloying element (like silicon and phosphorus) preferentially dissolves in the ferrite. For the given SAE 4340 steel, the carbide-formers dominate and hence the coalescence of the carbides take place in their vicinity. As these carbide-formers are drawn into bands in the interdendritic spaces, the coalescence of carbides show a banded structure. This was verified by microhardness tests (see Appendix C). Microhardness readings gave a value of 32 Re on the dark bands and a value of 27.5 Rc on the light bands for the 1 OD. The secondary banding of Fig. 4.4-4.7 appears to be attenuated, in comparison with the secondary banding of Fig. 4.2, 4.3. The primary banding, however, has changed little, if any at all. This is because the difference in cooling rate from the austenite has affected only the carbon migration but not the interdendritic alloy segregation. This 68 Fig. 4.4 Microstructure of the Steel in the Quenched Condition Showing Bands of Martensite (white), Retained Austenite (white), and Tempered Martensite (dark). The Tempering Took Place During the Polishing Operation (x 100). Fig. 4.5 Microstructure of the Steel in the Quenched and Darwn Condition (1 OD). The bands in the Tempered Martensite Are Due to the CoalescencecH5Carbides on the Segregated Alloying Elements (x 100). 69 Fig. 4.6 Microstructure of the Steel in the Normalized and Quenched Conditions Showing Bands of Martensite, Retained Austenite, and Tempered Martensite (x 100). Fig. 4.7 Microstructure of the Steel in the Normalized, Quenched, and Drawn Condition (2 NQD) Showing Bands of Tempered Martensite (x 100). 70 was verified by reheating the OD and the NQD specimens to austenite and cooling slowly. Fig. 4.8 shows the return of pronounced banding when the QD specimen was annealed. Even the 3 HNQD specimen which was homo- genized at 22500F for 10 hours shows a return to banding on annealing (Fig. 4.9), indicating that the temperature of homogenization wasn't high enough to bring about the removal of segregation of the alloying elements. The higher temperature homogenization (23500F for 20 hours), how- ever, presents a different story. At this high a temperature, the elements diffuse rapidly enough to equalize the concentration in the austenite. The primary banding which is a result of the dendritic segre- gation is therefore eliminated. In addition to increasing the diffu- sivity, the high temperature also coarsens the austenite (Fig. 4.10). This coarsening of the austenite grains to dimensions greater than the . . . . . 4 segregation distances aid in the removal of secondary banding . Once the primary banding is removed, the secondary banding (which depends on the primary) is automatically removed, as is evident in the 4 HNQD specimen (Fig. 4.11). Also the banding once removed by this high temperature homogenizing treatment will not reappear on subsequent heat treatments. Figs. 4.12 and 4.13 show that the 4 HNQD, upon annealing, exhibits a uniform dispersion of ferrite and pearlite and upon normal- izing gives a non-banded tempered martensite. In the discussion so far, all the alloying elements were clustered as a group and the differences in the microstrctures were explained on the basis of the migration of the carbon atom. Let us now examine each of the alloy elements in detail and see how they play a part in banding. 71 Fig. 4.8 Microstructure Showing the Accentuation of Banding in the 1 OD on Annealing (x 175). Fig. 4.9 Microstructure Showing the Accentuation of Banding in the 3 HNQD on Annealing (x 175). 72 Fig. 4.10 Microstructure Obtained after Homogenizing at 2350°F for 20 Hrs. and Slow Cooling. The Coarse Ferrite and Pearlite Were Prior to Transformation, Large Austenite Grains (x 100). Fig. 4.11 Microstructure of the 4 HNQD specimen. Note the Uniform Tempered Martensitic Structure. The High Temperature Homogenization has Resulted in the Elimination of Banding (x 100). ..glx \J 73 Fig. 4.12 Microstructure of the 4 HNQD after Annealing. Unlike 1 QD, 2 NQD and 3 HNQD, Banding Does not Reappear on Slow Cooling in the 4 HNQD as is Evident from the Uniform Distribution of Ferrite and Pearlite (x 175). Fig. 4.13 Microstructure of the 4 HNQD after Normalizing. Note the Uniform Tempered Martensitic Structure (x 175). 74 To facilitate such a study, Cr, Mo, Mn andltiwere analyzed in the elec- tron microprobe for both the 1 OD and the 4 HNQD conditions. The speci- fications of the electron microprobe are given in Table 4.1. Initially calibration graphs were plotted for molybdenum, nickel, manganese and chromium (Fig. 4.L4-4.l7) from a set of standards of known alloy contents (Table 4.2). These standards were obtained by courtesy of the General Motors Spectrographic Committee. Each point on the calibration graph represents the difference in counts between the average peak and the average background for a particular concentration. As the 1 OD specimens showed banding, there was no problem in selecting the area for microanalysis. Two determinations were made each on the dark and light bands. In the case of the 4 HNQD, however, since no bands were visible, three points were taken at distances approxi- mately a third of the wavelength of bands apart (80 u). Tables 4.3 and 4.4 show the respective readings for the 1 OD and the 4 HNQD specimens. Table 4.5 incorporates the maximum and minimum averages of the previous two tables, and correlates them to the concen- tration from the calibration graphs. Table 4.5 indicates that chromium homogenized the most, reducing in amplitude to about a fifth of its original value, while nickel homogenized the least. This is to be expected from the respective diffusion coefficients for chromium and nickel (see Appendix A). Table 4.6 represents a statistical analysis of the results. The calculations done in obtaining these values are indicated in Appendix D. Table 4.6 indicates that for elements nickel, chromium, and manganese, the difference between the maximum and minimum counts exceeds the 3 o 75 Fig. 4.14 Calibration Graph for Molybdenum. 76 Fig. 4.15 Calibration Graph for Nickel. _ . 1 a ,. n .ILIILI-I...1.P.-!.I|F 77 Fig. 4.16 Calibration Graph for Manganese. 78 Fig. 4.17 Calibration Graph for Chromium. 79 TABLE 4.1 Specifications of the Electron Microprobe Voltage = 25 RV Sample Current = 0.02 ua Magnification = 280 X Area under View = 600 u Resolution = 2 u Duration of measurement of counts = 20 seconds The counts were measured at the following wavelengths for the different elements: Elements Peak 1(Ao) Background 1(Ao) Chromium 2.2925 2.3675 Nickel 1.6580 1.7330 Manganese 2.1030 2.1730 Molybdenum 2.0410 2.1110 .w>waoonwxomm 80 .m>o.oooo coo cco ooo coo ooo ooo coo coo ooo coo ooo ooo coo ooo coo coo ..... .mmm. .mmm. .mmm. ..... ..... .mmm. .mmm. ..... ..... ..... ..... ..... ..... ..... ..... ooo ooo oco ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo coo ooo coo coo ooo oco ooo ooo ooo ooo ooo oco oco oesouwxoom ooo ooo coo ooo coo oco ooo oco coo ooo ooo ooo ooo ooo coo ooo ooo ooo coo ooo ooo ooo ooo ooo ooo coo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo ooo oco ooo ooo ooo ooo ooo ooo ooo coo ooo ooo .o sooooo oooo oeeo eooo ooo ooo oooe ccoo coo cooo oooo oooo ooo cooo oooo oooo coo .... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... ..... .mmmm ..... ..... .mmm. occo ooo coo cooo oco oooo ooeo oooo ooo coo oooo ooo ecoo oooo oooo oco oooo .oooo ooo oooo oooo oooo eooo oco ooo eooo eeoo ooo oooo oceo ocoo coo cooo cooo oooo ooo oooo oooo oeoo ooo ooo oooe cooo ooo oooo oceo eooo oco cooo oeoo oooo ooo oooo oooo cooo ooo ooo oooe oeoo oco cooo oooo oooo ooo oooo oooo oooo ooo coco cooo oooo ooo ooo oooe eooo ooo oooo oooo eooo ooo ooeo oooo ocoo ooo no as «z 02 no oz oz 02 no oz «2 o: no oz Hz ooo oo.o oo.c oo.o ooc. ooo. oo.o coo. oec. ooo. ooo. ooo. ooo. ooo. coo. coo. ooo.o Tm 7N min «A e» cooo ooo—«comm mnm< .w>< .oooo - oooo . ooouo>< oo.oooo oeoo oo.oooo ooo Home oo.cooo oooo oo.ooo .m>< ossooooooo ooo oo.ooo o.oco o.ooo ooo ooo o.coo oo.ooo ooo ooo ooo ooo ooo oco ooo ooo ooo ooo ooo coo ooo ooo ooo ooo vcnouwxoom ooo oco ooo oco ooo ooo ooo ooo ooo ooo ooo ooo ooo coo ooo ooo .w>< oooo oo.oooo oo.oooo oo.eoco o.oeo cooo oo.oooo o.oooo ooo cooo oooo coco ooo cooo oooo ooeo coo oooo oeoo oooo oeoo ooo oooo oooo oooo ooo ooco some cooo ooo oooo cooo oooo ooo ocoo cooo oooo ooo oeoo oeoo oooo ooo uc oz oz oz uo oz oz oz oooo ooooo oooo xuoo Aoo oo zozocooo.oooz< .m>¢ oooo - oooo . ooouo>< o.oooo o.oeoo o.oooe oo.ooo o.oooo o.ooeo oo.oooo oo.ooo .w>< oesooooooo o.coo oo.ooo oo.ooo o.ooo ooo oo.oco o.coo o.oeo ooo oco oco ooo ooo oco ooo ooo coo ooo ooo ooo ooo ooo ooo ooo ocoouwxomm ooo ooo oco coo ooo coo ooo coo ooo ooo ooo coo coo ooo ooo ooo .w>< zooo ooco oo.oooo oo.ooco oo.ooo o.oooo oo.oooo oo.oooo oo.ooo ocoo cooo oooo ooo ocoo cooo oooo ooo coco oooo ooco ooo oooo oooo oooo coo mm o o ooco oooo ocoo ooo oooo oooo oooo ooo ooco oooo ooco ooo oooo oooo cooo ooo oc s.z oz oz no oz oz oz oouo ooooo cooo xuoo zoo Ho zmzocooo ooozoo ooo oco oozooo oc zoozoz Aooocooooco o.e ooooo 83 . w>< . w>< .oooo.. zooo . ooouoeo oeoo o.oooo o.oooo o.ooo oo.oooo c.eoeo o.cooe c.ooo o.oeoo o.oooo cooo o.coo .o sooosooooooo ooo ooo ooo coo o.ooo o.cco o.oco o.ooo o.ooo o.ooo ooo o.ooo ooo ooo coo coo oco ooo ooo ooo ooo ooo coo ooo oesouwxoom ooo ooo ooo coo ooo oco ooo coo ooo oco ooo ooo ooooo ooco o.ceoo o.ooco o.ooo oo.oooo o.oooo ocoo o.ooo ooco cooo oooo ooo ooco oooo occo ooo ooco oooo eooo ooo ooco oooo oooo ooo ooco cooo oooo ooo cooo oooo oooo ooo coco oooo ocoo ooo Q” o o ooco oooo ooco ooo cooo cooo oooo ooo ooco cooo cooo ooo ooco cooo ooco ooo cooo oooo oooo ooo ooco oooo oooo ooo 8 oz oz oz uc oz oz oz 8 oz oz oz zmzHommm QMNHzmuozom mus mom mHZDDU mo mumZDz ¢.o mAnMQ nm¢dz ll FF = Fracture Region Fig. 4.40 Idealized Force1(Load) -disp1acement Curve. The initial rise of the curve corresponds to the elastic part of the deformation. A represents the upper yield point and B the lower yield point. This is followed by plastic deformation giving rise to work har- dening. The next step of the deformation, which is shown as the flattened part is the initiation of breakage. This is followed by a descending curve which represents the growing of the crack. From Fig. 4.37 it is seen that at low temperatures, the crack, once formed, propagates rapidly and in a brittle manner. This is because at 104 low temperatures the critical shear stress for slip is increased, so that the fracture stress is reached before the flow stress. Figs. 4.38 and 4.39 indicate that at room temperature both the homo- genized and the non-homogenized specimens exhibit ductile propagation of cracks. However, the homogenized specimen is seen to have a greater resistance to crack initiation. This is indicated by a higher load and a greater "flattened portion" in Fig. 4.39 for the homogenized specimen in comparison with the quenched and drawn specimen in Fig. 4.38. This higher resistance to crack initiation results in greater impact values for the homogenized specimen. To get further insight into the mechanism of fracture, an inter- rupted impact test was performed. In this case the hammer was swung from a point just beyond the specimen, but not high enough to completely fracture the specimen. The first evidence of the crack was observed at the root of the notch near the midpoint (Fig. 4.41). This corresponds to approximately point C on the curve in Fig. 4.40. The crack then grows laterally until at the maximum load a crescent-shaped crack extends completely across the speci- men (Fig. 4.42). Note also that the 5 QD, as compared to the 6 HNQD specimen, is jagged in appearance, indicating many nucleating sites for fracture and easy lateral growth. This corresponds approximately to point C' on the curve in Fig. 4.40. The deflection up to this point is associated with bending strain in a relatively large volume of metal extending to as much as a quarter inch from the notch. The crack then deepens while extending down the sides of the specimen (Fig. 4.43). Here the deflection is achieved through a tearing-like 105 Fig. 4.41 Initiation of the Crack at the Root of the Notch (x 1.25). Fig. 4.42 Lateral Growth of the Crack in the 5 QD (above) and the 6 HNQD (below) Specimens. Note the Jagged Appearance of Fracture in the Non-homogenized Specimen (x 1.25) 5 QD, the 6 indie inclu forms of po speci: re spe. non-h. Carbi- first (day. gated be We. aid 11 5an fl" fared 599C131 106 mechanism.which causes an intensification of the strain in the metal immediately adjacent to the fracture. This corresponds to the region C'D on the curve in Fig. 4.40. From Fig. 4.43 it is seen that in case of the 5 QD, the crack propagates almost vertically down, while in the case of the 6 HNQD the crack travels at an angle of 450 from the root of the notch, indicating a more ductile propagation of the crack. The non-metallic inclusions also aid in the propagation of the crack as is seen in Fig. 4.44. At point D, the slope begins to decrease rapidly and the curve forms a tail terminating in fracture at a very low load, well to the right of point D. A possible explanation for the superior properties of the homogenized specimen compared to the non-homogenized specimen can be traced to their respective microstructures. As was mentioned earlier, the bands in the non-homogenized specimens differ in hardness due to the segregation of the carbides. Under impact, the bands with the higher hardness will fracture first. In the case of the homogenized specimen, however, the fracture is delayed since the mean hardness is lower than the hardness of the segre- gated carbide bands of the non-homogenized specimen. Another explanation could be that in case of the 5 OD, the interface between the bands may act as possible nucleating sites for the crack and aid its propagation. Figs. 4.45 and 4.46 show the sharp ridges of the 5 OD compared to the more diffused macrostructure of the 6 HNQD. Scanning electron micrographs at the centers of the specimens frac- tured at room temperature indicate a dimpled rupture fracture in each specimen. However, the 5 OD reveals long, narrow, aligned ridges which 107 Fig. 4.43 Crack Extending Down the Sides in the 5 OD (above) and the 6 HNQD Specimens. Note the Difference in the Direction of the Travel Paths (x 1.25). Fig. 4.44 Non-metallic Inclusions Aid in the Propagation of Crack (x 175). 108 Fig. 4.45 Charpy Impact Fracture Surface of 5 OD Tested at Room Temperature Showing Sharp Banded Ridges (x 12). Fig. 4.46 Charpy Impact Fracture Surface of 6 HNQD Tested at Room Temperature Showing a Reduction in Ridges (x 12). ‘1) (7‘, .3 J 109 act as stress concentration factors, whereas the 6 HNQD shows these ridges to be small and dispersed at random. (Fig. 4.47, 4.48.) But it is very difficult to formulate any empirical equations with accuracy to correlate the influence of the banded structures on the susceptibility to brittle fractures. The bands are discontinuous and do not occur at fixed intervals. When these bands are subjected to bending stresses, foliated fractures may appear for a number of reasons. These can include a primary banded segregation in the presence of a homo- geneous secondary structure, primary and secondary segregation, or alignments of inclusions with a more or less marked primary segregation. These metallurgical factors, combined both with the particular notch sensitivity and resistance to crack propagation of each band, and also the conditions of stressing, render the problem extremely complex. 4.3 Effect of Banding on Fatigue Fatigue failure occurs under dynamic loading when a metal subjected to a repetitive or fluctuating stress fails at a stress much lower than that required to cause fracture on a single application of load. The importance of fatigue lies in the fact that it accounts for at least 90% of all service failures due to mechanical causes. A fatigue fracture is particularly insidious because it occurs without any warning. Fatigue results in a brittle fracture, with no gross deformation of the fracture. .Fatigue failures are caused by three basic factors: a) a maximum tensile stress of sufficiently high value, b) a large enough variation or fluctuations in the applied stress, and c) a sufficiently large number of cycles of the applied stress. 110 Fig. 4.47 SEM Photograph at Center of 5 OD Tested at Room Temperature Showing Sharp Bands (x 200). Fig. 4.48 SEM Photograph at Center of 6 HNQD Tested at Room Temperature Showing Bands Dispersed at Random (x 200). v 0‘. 111 Fatigue properties in the transverse direction are known to be inferior to those in the longitudinal direction. As was mentioned pre- viously (Chapter 2), most of the authors attribute the low fatigue proper- ties in the transverse direction to the presence of non-metallic inclu- sions. Undoubtedly the inclusions play a role in improving the fatigue properties, as is evident when steel A and B are compared. However, inclusions are not the only reason for poor transverse fatigue properties. Since high temperature homogenization brought about a significant effect on both the impact and fatigue properties, by the elimination of banding without any changes in the size, shape, or distribution of inclusions (Figs. 4.25, 4.26, 4.27, 4.28), it is obvious that the effect of banding is equally important. Moreover the vacuum-degassed steel B is suffi- ciently free of inclusions to attribute the changes in the mechanical property to the changes in inclusions on heat treatment. A possible explanation of the poor fatigue properties will be given on the basis of a model. Fig. 4.49 indicates a schematic model for the banded specimen, showing exaggerated uniform bands. Ff °\ |Tensio C) - Light band ‘9 - Dark band ”1 v - Inclusions Fig. 4.49 Schematic Diagram.of the Model to Explain Fatigue Failure. 112 It is generally accepted that crack initiation in smooth specimens of ductile crystalline solid occur in slip bands or other regions of strain localization. The development of such cracks usually involves the slow, continuous development of a "peak-valley" surface topography on the rapid development after some cycling of slip band extrusions and intrusions. It is believed8 that these submicroscopic cracks are initiated at a rela- tively early stage of the fatigue life. Any factor which brings about an increase in the stress concentration will enhance the probability of such cracks. It is postulated that both inclusions and bands act as microscopic stress raisers. In banded steel, then, there is a greater probability of initiating the crack. As shown in Fig. 4.49, the cracks can either start at a non-metallic inclusion or at one of the weaker bands. The weaker band is the one that is depleted of the alloying elements and carbon and hence exhibits a lower yield and ultimate strength. Another explanation of the weakness may be due to the presence of mixed microstructures of tempered martensite and bainite, instead of a uniform dispersion of 100% tempered martensite. A 100% tempered marten- sitic structure is known to be superior to any other type of structure9-11. Fig. 4.50 indicates the initiation of the crack adjacent to the inclusion in the 1 OD. Note the lines radiating from the "hole" which was occupied by the inclusion. Fig. 4.51 does not indicate such convergence of lines. Hence the cracks started at a less notch-sensitive area, maybe a band, and propa- gated in a waverlike manner. 113 Fig. 4.50 SEM Photograph Showing the Inclusion Acting as a Nucleating Site for Fatigue Fracture in the 1 OD (x 200). Fig. 4.51 SEM Photograph Indicating the Band as a Nucleating Site for Fatigue Fracture in the l QD (x 200). 114 The crack growth can be classifiedlzu15 as stage I and stage II. The stage I is controlled by the resolved shear stresses on the slip plane. The crack here propagates at 45 degrees to the stress axis and may account for 0-90% of the number of cycles required for fracturels. Stage I fractures are often featureless except for rub marks that arise from contact of mating surfaces. The rates of crack propagation in stage I are of the order of angstroms per cycle. Hence it is extremely difficult to study this stage of fracture. The transition from stage I to stage 11 crack growth is usually attributed to the change of the shear stress to normal stress ratio that results from the crack tip growing away from a free surface into a region of greater constraint. In stage II, the plane of crack propagation is 90 degrees to the stress axis and the fracture surface is covered by stria- tions running parallel to the crack propagation front. The presence of fatigue fracture striations was first observed by Zappfe and Wordenlé. These striations are formed by reversal and locking of various slip systems and they represent the successive portions of the advancing crack front. Crack propagation rate in stage 11 growth can reach values of microns per cycle. The growth mechanism is fairly large and easy to observe. Hence most of the existing literature deals with this type of growth. Fig. 4.52 indicates the crack propagating along a string of non- metallic inclusions. Fig. 4.53 represents the crack moving from right to left across the bands and through a path of non-metallic inclusions. The striations in these figures are readily visible and hence they represent the stage II grewth of cracks. 115 Fig. 4.52 SEM Photograph Indicating the Crack Propagating along a String of Non-metallic Inclusions in the 1 OD (x 200). Fig. 4.53 SEM Photograph Indicating the Crack Moving from Right to Left across the Bands and through a Path of Non- Metallic Inclusions in the 1 OD (x 200). 116 Of the two stages of fracture, stage I is structure sensitive since it involves slip on crystallographic planes. Stage II fatigue fracture is less influenced by crystal structure or microstructure since it may be non-crystallographic and essentially controlled by the stress system, at least in its later stages. In addition to the nucleation of crack, the 'soft' bands of the 1 QD provides an easy path for crack propagation in stage I. In stage II the largerstress concentration associated with the longer crack dominates the structure at the crack tip and orients the path of crack propagation at 90 degrees to the stress axis. At the end of stage II, the cross-sectional area is sufficiently reduced, so the specimen is no longer able to withstand any more cycles, and fails in tension (Fig. 4.54). On a macro-scale, the difference in fracture appearance is apparent for the 1 QD and the 4 HNQD specimens (Fig. 4.55, 4.56). The crack starts on the right of the specimen, presumably on a 'soft' band or on an inclusion, and proceeds leftward. On comparison, the homogenized specimen is seen to be relatively free from bands. 117 Fig. 4.54 SEM Photograph Indicating the End of Stage 2, and the Onset of Fracture (going from left to right) (x 200). 118 4.55 Fatigue Fracture Surface of the 1 QD at a Low Magnification (x 6). Fig. 4.56 Fatigue Fracture Surface of the 4 HNQD at a Low Magnification (x 6). (1) (2) (3) (4) (5) (6) (7) (8) V. CONCLUSIONS For the given investigation, two high-strength SAE 4340 steels were chosen. These steels differed only in their inclusion rating, the vacuum degassed steel exhibiting a lower inclusion rating. Both the as-received and the quenched and drawn conditions exhibited banding which upon a micrOprobe analysis showed a segregation of manganese, chromium, nickel and molybdenum in the bands. Upon a high temperature homogenization treatment at 2350°F for 20 hours, the segregation was reduced to a sufficient degree to elimi- nate banding. Lower temperature homogenization at 22000F for six hours and 22500F for ten hours were found insufficient to remove banding. The banding once removed did not recur after subsequent heat treat- ments. The high temperature homogenization did not affect the size, shape or distribution of the non-metallic inclusions. Elimination of banding brought about an increase in impact strength at all temperatures. This was more pronounced at lower temperatures than at higher temperatures. The endurance limit was raised by about 8% by the removal of banding. The improvement in nmpact and fatigue properties due to the elimina- tion of banding is attributed to the fact that the bands act as 119 (9) 120 stress raisers for the nucleation of cracks in both the impact and fatigue specimens. Whether the degree of improvement brought about by the removal of banding is significant enough to justify the cost of heat treatment warrants some thought. For most commercial applications it is not. But in very special applications like the aircraft and space industry where the factor of safety must be kept low, even a slight degree of improvement may be merited. APPENDICES APPENDIX A CALCULATION OF THE TEMPERATURE.REQUIRED TO REMOVE BANDING The temperature required to remove banding is given byl: 0.4343 Q 0.23312 t ] R[log10A - log10 where T is the temperature in 0K; R = gas constant = 2 cal/g; A and Q are constants obtained from diffusion measurements; 2 is half the "wave- length" between the bands; and t is the time of homogenization in seconds. For the given SAE 4340 steel, the diffusion coefficients of the . 2 3 various alloy elements in austenite are ’ 0.945 e'994999 Dun = 2T 9N1 = 0.368 e'913%99 DCr = 1.0 e-§93%99 Dp = 28.3 e-§§§%99 0Mo = 0.091 e-ggaggg Let us take a reasonable time of homogenization, say 20 hours. Then, t 8 20 hrs. - 72,000 sec. From the photomicrographs it is seen that the "wavelength" of the bands of the given specimen is 2.54 x 10.2 cm. Therefore, 21 = 2.54 x 10-2. Hence L = 0.0125. 121 122 Then, to calculate, say, the temperature for homogenization of manganese, 0.4343 x 66,000 T = 2 0.233 x (0.125) 2[1og100.945 log10 72,000 ] 0.4343 x 66,000 = 15420K = 126900 = 23170F. 2[i.9754 - 1027037] Homogenizing temperatures can be similarly calculated for nickel, chromium, phosphorus, and molybdenum. They give the following values: Element Temperature needed for the removal of handing Manganese 2317°F Nickel 2517OF Chromium 2063°F Phosphorus 20430F Molybdenum 23340F APPENDIX B CALCULATION OF THE MAXIMUM TENSIEE STRESS ON THE FATIGUE SPECIMENS For the Moore rotating beam fatigue test, the stress acting on any element in the specimen is given by 0 = %€ (assuming pure bending) , where M is the bending moment, I is the moment of inertia about the horizontal axis, and c is the distance of the element from the neutral axis (specimen center in this case). Then, from the shape of the specimen, it is evident that the maximum stress occurs on the specimen surface at a point midway across the specimen length. Therefore, a _ w/2 (AB) d/2 max nd4/64 (see Fig. 3.1) where amax = maximum stress. It is compressive one half of the cycle and tensile the other half. AB = distance between two supports on the spindle, B 4" for the Moore machine; d = diameter of the specimen; and W 8 weight of hanger and weights loaded on it. amax = l€fié$l' = ggiig-H' where d is in inches. 123 124 Fig. B.l Calculation of the Maximum Tensile Stress on the Fatigue Specimens. A B C D BENDING MOMENT DIAGRAM APPENDIX C MICROHARDNESS TESTS FOR THE 1 QD AND 4 HNQD SPECIMENS The Lietz microhardness tester was used to determine the hardness of both the l QD and 4 HNQD specimens. Readings were taken at intervals of 130 um. The hardness was determined by producing an indentation with a pyramid shaped diamond, and optically measuring this indentation. The hardness thus obtained is called Vickers Hardness and is given by the formula 1854.4 P d2 Hv (kp/mmz) = where P = measuring force in Pond = 500 p and, d = mean value of the indentation diagonal in um. The following values were obtained for the hardness: 1 OD 4 HNQD Obs. No. Indentation Vickers Rockwell Indentation Vickers Rockwell Diagonal Hardness Hardness Diagonal Hardness Hardness d(um) Hv Re d(um) Hv Re 1 57.5 281 27.5 56 297 29.5 2 54.0 318 32.0 56 297 29.5 3 57.5 281 27.5 56 297 29.5 4 54.0 318 32.0 56 297 29.5 5 57.5 281 27.5 56 297 29.5 These values are plotted in Figure C.l. In the 1 QD, the dark bands have a higher hardness reading indicating the segregation of car- bon as carbides, whereas in the 4 HNQD where no hands are visible, a uniform hardness reading is obtained. 125 126 Fig. C.l Plot of Rockwell Hardness (RC) vs. the Distance across the Specimen. Scale: x:-axis 1 inch = 130 um y:-axis 1 inch = 1.5 RC Rockwell Hardness RC 33 32 a 31 d 304 29 4 28 . 27 (D 1 QB 13 4 HNQD l 1 A l w 130 260 390 520 650 Distance across the specimen (um) APPENDIX D CALCULATION OF THE STANDARD DEVIATION 0% FOR NICKEL, MANGANESE, CHROMIUM, AND MOLYBDENUM . . 1 . . . . . X-ray statistics give the standard dev1ation.oA for measuring the If N is the total number of line minus background intensity IL - IB. L counts measured at the line peak and NB is the total number measured at the background, then, % (NL + NB) NL ' NB ° 0% = 100 To calculate, say, the 0% for nickel, N 5633.25 (Table 4.3), L 860.5 . NB 100(5633.25 + 860.5)% 5633.25 - 860.5 1‘69% Therefore, 0% (0%)(Peak ) o for nickel = looJ—A" ' = (1°692193833'425 - 95.09 30 = 285.27 . Similarly, 30 values for the other elements are obtained. 127 APPENDIX E CALCULATION OF THE LOAD (FORCE) UNITS FROM THE LOAD-TIME CURVE The energy measured by the Charpy test is given by E = Y!P