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LYONS* HARVEY an investigation of the phenomenon of fr c ttin g 4wear and attendant parametric EFFECTS TOWARDS DEVELOPMENT OF FAILURE PREDICTION CRITERIA.

THE OHIO STATE UNIVERSITY* PH.D.* 1976

©

Copyright by

Harvey Lyons 1978 AN INVESTIGATION OF THE PHENOMENON OF FRETTING-WEAR

AND ATTENDANT PARAMETRIC EFFECTS TOWARDS

DEVELOPMENT OF FAILURE PREDICTION CRITERIA

DISSERTATION

Presented in Partial Fulfillment of the Requirements for

the Degree Doctor of Philosophy in the Graduate

School of The Ohio State University

hy

Harvey Lyons, B.S.E., M.E., P.E.

The Ohio State University 1978

Reading Committee: Approved By

J. A. Collins T. G. Foster W. L. Starkey

Department of Mechanical Engineering ACKNOWLEDGMENTS

The author wishes to express his sincere appreciation to Professor Jack A. Collins, of the Department of Mech­ anical Engineering, for the advice and encouragement given throughout the course of this Dissertation.

A special word of thanks is certainly due the following individuals:

Mr. Dwight L. Moseley and Mr. Howard E. Hawley, machine shop personnel of the Mechanical Engineering De­ partment, for providing quality test specimens and valuable assistance.

Mr. Cecil L. Rhodes, of the Mechanical Engineering

Department, whose technical assistance was a significant factor throughout the developmental period of research.

Professor Donald R. Kibbey, of the Department of

Industrial and Systems Engineering, for assisting in the surface measurement studies.

Mr. Roland V. Farrar, of the Department of Metallur­ gical Engineering, for generously assisting in the metallography and microscopy phases of research.

ii «

VITA

September 26, 1931 Born - New York City, New York 1952 ...Certificate, Industrial Design, Pratt Institute, New York City. 1952 - 1954...... U.S. Army - Korea. 1951 - 1972...... Project and Design Engineering Positions in the Metallurgical, Mining, Process, Materials-Handling, and Water Treatment Industries. 1962...... B.S. (Engineering), The Cooper Union, New York City. 197 1...... M.E. (in Mechanical Engineering) , The Cooper Union, New York City. 197 2...... Professional Engineering License, New York State. 1972 - 1978...... Research Associate, Teaching Associate, The Ohio State University, Columbus, Ohio.

iii TABLE OP CONTENTS

Page ACKNOWLEDGMENTS...... ii VITA...... iii LIST OP TABLES...... viii

LIST OF FIGURES...... * Chapter I. INTRODUCTION...... 1 Development of Thesis ...... 1 Technological Overview...... 2 Significance of Fretting-Wear ...... 3 II. DEFINITIONS ...... 5 The Fretting Phenomenon ...... 5 Fretting-Wear Failure ...... 6

III. PURPOSE OF RESEARCH ...... 8 S c o p e ...... 8 Objectives...... 9 IV. HISTORICAL BACKGROUND AND RESEARCH EFFORTS. . 13 Introduction...... 13 Early W o r k s ...... 14 Recent Efforts...... 15 V. THE NATURE OF SURFACES AND CONTACT STRESSES . 41 Introduction...... 41 Definitions .and Parameters...... 42 Hertzian Stresses ...... 50 Superposition of Tangential Stresses. . . 60

iv Page

. Chapter VI. MODEL DEVELOPMENT FOR WEAR WITHIN THE FRETTING ZONE...... 64 Fretting-Wear Mechanisms and Related Phenomena ...... 64 Modeling Parameters...... 74 Review of Potential Fretting-Wear Models. 77 Development of a Model for Prediction of Fretting-Wear ...... 86 The Physical Model...... 87 The Statistical Model ...... 92 VII. EXPERIMENTAL APPROACH...... 100 Introduction...... 100 Test P l a n ...... 101 Experimental Apparatus...... 110 Test Procedures and Monitoring Devices. . 120 Data Handling...... 123 Profilometry...... 124 Metallography ...... 125 Scanning Electron Microscopy...... 130 VIII. EXPERIMENTAL RESULTS...... 133 Introduction...... 133 Summary of Results...... 134 Normal Approach - General Results . . i . 139 Normal Approach and Surface Roughness . . 156 Normal Approach and Normal Load or Pressure...... 165 Normal Approach and Axial Preload .... 178 The Physical Model. . 1 ...... 184 The Statistical Model ...... 188 Metallography ...... 200 Scanning Electron Microscopy...... 203 IX. CONCLUSIONS...... 220 Introduction...... 220 General Conclusions ...... 220 Specific Observations ...... 224 New Insights...... 228

v Page Chapter X. APPLICATION TO REAL SYSTEMS...... 232 Introduction...... 232 Experimental Program...... 234 Concluding Remarks...... 238 XI. SUGGESTIONS FOR FUTURE RESEARCH ...... 241 Introduction...... 241 Improvement o£ Test Program...... 242 New Methods...... 244

APPENDIXES A. Integrals of the Gaussian Distribution. . . . 247 B. Relationship Between Standard Deviation (a) and Root Mean Square (RMS)...... 250 C. Detail Drawings...... 253 D. Corrections to Normal Approach Raw Data . . . 265 E. Calibration Data...... 269 F. Fretting-Wear Test Procedure...... 278 G. Fretting-Wear Test Log...... 284 H. Recorder Printout Summary ...... 286 I. Multipoint Recorder Printout...... 288 J. Metallographic Specimen Preparation ...... 290 K. Electroplating of Specimen...... 293 L. Design D a t a ...... 295 M. Sample Calculations of Asperity Inter­ actions Based Upon Statistical Analysis and Hertzian Contact Stress Theory...... 302

vi *

Page APPENDIXES N. Sample Calculation of Specific Wear Rate. . . 308

LIST OF REFERENCES...... 310

vii LIST OP TABLES

Table Page 1. Test P l a n ...... 103 2. Specimens Chosen For Metallography and Microscopy » •...... 127 3. Normal Approach Due to Fretting-Wear vs. Normal Approach Computed from Statistical and Hertzian Theory...... 151 4. Normal Approach Due to Fretting-Wear vs. Percent Relative Humidity ...... 152 5. Normal Approach Due to Fretting-Wear in Test Type X: Average Value and Standard Deviation...... 153 6. Relative Roughness - All Tests...... 160 7. Normal Approach and Surface Roughness .... 161 8. Specific Wear Rates: 100,000 Cycles...... 162 9. Volumetric Wear Rates: 100,000 Cycles. . . . 162 10. Contact Pressure vs. Surface Roughness: Test Type I, SAE 1020 ...... 171 11. Apparent vs. Actual Normal Fretting Pressure: 100,000 Cycles...... 172 12. Bulk Temperature Effects Due to Fretting-Wear: Type I Tests...... 180 13. Standardized Separation Data...... 194 14. Development of Standardized Separation. . . . 195 15. Summary of Gaussian and Exponential Statistical Data. ...%...... 196

viii ft

Table Page 16. Experimental Research Surface Data Compared with Data From Other Sources .... 197 17. Integrals of the Gaussian Distribution. . . . 249 18. Specimen Axial Preload Load-Cell Calibration Data...... 270 19. Fretting-Shoe Force-Transducer Calibration Data...... 272 20. Motion-Measuring Transducer Calibration Data. 274 21. Normal Approach Transducer Calibration Data . 276

ix LIST OF FIGURES

f > Figure Page 1. Surface Roughness Profile ...... 43 2. Method of Deriving the Distribution Curve . . 47 3. Normal Distribution Curve ...... 48 4. Triangular Distribution Curve ...... 49 5. Hertzian Contact Between Two Spheres...... 52 6. The Point of Contact Between Two Spherical Bodies...... 53 7. Principal State of Stress at Any Point. .. . 55 8. Stress Distribution Along Load A x i s ...... 59 9. Asperity Interaction in Adhesive Wear. Formation of a Loose Wear Particle at a Single Asperity ...... 66 10. Contact Between a Smooth Plane and an Idealized Rough Surface ...... 93 11. Plane Sided Asperity Model...... 95 12. General Arrangement of Krouse Direct Stress Machine, Fretting Fixture and Instrumentation ...... 112 13. Schematic Diagram of Basic Fretting Fixture . 114 14. Assembly of Shoes, Specimens and Trans­ ducer Housings for Monitoring Cyclic Amplitude and Normal Approach ...... 115 15. Fretting-Wear Instrumentation Schematic . . . 118

x Figure Page 16. Oscilloscope Waveform of Fretting Slip Amplitude...... 122 17. Metallographic Sectioning Orientation: Transverse to Slip. This Orientation was Mot Adopted...... 128 18. Metallographic Sectioning Orientation: Parallel to Slip. This Orientation was Adopted for All Studies...... 128 19. Metallographic Study of Sectioned Specimen. . 129 20. Scanning Electron Microscope Study of Fretting-Wear Specimens ...... 132 21. Normal Approach: SAE 1020...... 154 22. Normal Approach: SAE 4340...... 154 23. Normal Approach: SAE 52100 ...... 154 24. Normal Approach: Type I Tests...... 155 25. Normal Approach vs. Surface Roughness: Test Type I ...... 163 26. True and Theoretical Normal Approach vs. Surface Roughness: Type 1...... 164 27. Normal Load vs. Fretting-Wear Cycles: Type 1...... 173 28. Normal Load: SAE 1020...... 174 29. Normal Load: SAE 4340...... 174 30. Normal Load: SAE 52100 ...... 174 31. Actual vs. Apparent Pressure: Type I Test. . 175 32. Roughness and Pressure vs. Cycles: SAE 1020. 176 33. Roughness and Pressure vs. Cycles: SAE 4340. 176

xi Figure Page 34. Roughness and Pressure vs. Cycles: SAE 52100 ...... 176 35. Pressure vs. Normal Approach: Type I Tests . 177 36. Axial Preload vs. Normal Approach: Test Type I - 500,000 Cycles...... 181 37. Axial Preload vs. Cycles of Operation: Test Type I ...... 182 38. Axial Preload: SAE 1020...... 183 39. Axial Preload: SAE 4340...... 183 40. Axial Preload: SAE 52100 ...... 183 41. Physical Model vs. Actual Fretting-Wear: SAE 1020 - Type I ...... 187 42. Idealized Asperity Interaction...... 188 43. Statistical Data: Gaussian Distribution. . . 198 44. Statistical Data: Exponential Distribution . 199 45. Specimen No. 1: SAE 1020, Type I, Metallograph, 300x...... 208 46. Specimen No. 1: SAE 1020, Type I, SEM, 1400x...... 208 47. Specimen No. 3: SAE 1020, Type I, Metallograph, 300x...... 209 48. Specimen No. 3: SAE 1020, Type I, SEM, 1400x...... 209 49. Specimen No. 5: SAE 1020, Type I, Metallograph, 300x...... 210 50. Specimen No. 5: SAE 1020, Type I, SEM, 1400x...... 210

xii Page 51. Specimen No. 9: SAB 1020, Type III, Metallograph, 300x...... 211 52. Specimen No. 9: SAB 1020, Type III, SEM, 14x...... 211 53. Specimen No. 13: SAE 4340, Type I, Metallograph, 300x...... 212 54. Specimen No. 13: SAE 4340, Type I, SEM, 1400x...... 212 55. Specimen No. 18: SAE 4340, Type I, Metallograph, 300x...... 213 56. Specimen No. 18: SAE 4340, Type I, SEM, 1400x...... 213 57. Specimen No. 19: SAE 4340, Type I, SEM, 140x...... 214 58. Specimen No. 19: SAE 4340, Type I, SEM, 1400x. Selected Field From Figure 57, as Indicated...... 214 59. Specimen No. 36: SAE 52100, Type VI, Metallograph, 300x...... 215 60. Specimen No. 36: SAE 52100, Type VI, SEM, 1400X...... 215 61. Specimen No. 5: SAE 1020, Test Type I. SEM Stereo Micrograph: 1400x 216 62. Specimen No. 24: SAE 4340', Test Type VI. SEM Stereo Micrograph: 700x...... 217 63. Specimen No. 36: SAE 52100, Test Type VI. SEM Stereo Micrograph: 70Ox...... 218 64. Scanning Electron Micrograph: Virgin Specimen...... 219 65. Parametric Interrelationships. SAE 1020, Type 1...... 229

xiii Figure Page 66. Parametric Interrelationships. SAE 52100, Type 1...... 230 67. Parametric Interrelationships. SAE 4340, Type V I ...... 231 68. Fretting-Wear Application: Pressurized Water Reactor Fuel R o d s ...... 239 69. Fretting-Wear Arrangement of Specimen and S h o e s ...... 240 70. Fretting Specimen ...... 255 71. Fretting S h o e ...... 256 72. Normal Approach LVDT Body C l a m p ...... 257 73. Normal Approach LVDT Core C l a m p ...... 258 74. Normal Approach LVDT Core Rod Holder...... 259 75. Slip Amplitude LVDT Body Clamp...... 260 76. Slip Amplitude LVDT Core Rod...... 261 77. Grooves For Fretting Shoes...... 262 78. Shoe Grooving Tool...... 263 79. Grooving Tool Holding Fixture ...... 264 80. Normal Approach Transducers ...... 266 81. Corrections to Normal Approach Transducer Raw D a t a ...... 268 82. Specimen Axial Preload Load Cell Calibration Curve ...... 271 83. Fretting-Shoe Force-Transducer Calibration Curve ...... 273 84. Motion-Measuring Transducer Calibration Curve ...... 275

xiv Figure Page • * 85. Normal Approach Transducer Calibration Curve ...... 277 86. Recorder Test No. 10. SAE 52100. 20,000 Cycles. Type I T e s t ...... 289 87. Schematic of Electroplating ...... 294 88. Design Data: Type 1...... 296 89. Design Data: Type IX ...... 297 90. Design Data: Type III...... 298 91. Design Data: Type IV ...... 299 92. Design Data: Type V ...... 300 93. Design Data: Type V I ...... 301

xv CHAPTER I

INTRODUCTION

Development of Thesis

The interest in this Dissertation originated in 1974 with a report (54)* prepared as a part of che writer's General Examinations. That study involved a comprehensive survey of publications associated with the significant failure mode fretting-wear in order to formulate research methodology for the development of a fretting-wear pre­ diction model. Fretting-wear is interfacial wear damage which may occur when the contacting surfaces of two solid bodies are subjected to a relative cyclic sliding motion, termed fretting. Several models were suggested at that time, based, in part, upon ideas of other researchers. These included: an all-inclusive model that would » methodically sum the wear damage accrued throughout a specified lifetime; a model based upon three stages of

*An Arabic numeral placed between the parentheses { ) refers to a reference in the "List of References".

1 2 fretting-wear proposed by Hurricks (41); a model patterned after the "Zero Wear" concept (55,63); a cumulative damage model proposed by Rabinowicz (73), similar to the linear damage rule applied to the process of fatigue of metals by Palmgren and Miner (62,66); and a model based on use of an accelerated statistical procedure involving "sequential analysis" (46). The fretting-wear model proposed in this Thesis is based upon experimental research data. It was designed to predict fretting-wear in terms of parameters significant to the influence of fretting.

Technological Overview

The accelerating pace of technological development places great demands on the designer. In many industrial applications, machinery is required to operate faster, be lighter in weight and more compact, sustain greater loads and last longer. Modem designs operate much closer to their limits; margins of safety have been decreased. Within this complex of systems, a myriad of mechanically- coupled parts or "pairs" reside; and these pairs are frequently subjected to an environment in which small, repetitive, relative displacements are induced between the mating parts. Whether or not such displacements are foreseen, their occurrence may produce an insidious form of wear— characterized as "fretting-wear." 3

Significance of Fretting-Wear

Fretting-wear damage may occur (87) whenever inter­ ference fits are used in machines; in bolted, keyed, splined or riveted joints; between wires in wire ropes and flexible shafts; in smal1-amplitude oscillating bearings; between leaves of springs. Fretting may either cause localized corrosion, wear, or microcracks which may drastically lower the fatigue strength of some materials. Fretting-wear is different from other types of wear in that it retains the majority of the debris brought about by the wear action within the contacting interface. Fretting may be present in any area of an aircraft structure where small, relative displacements are possible. Engines, primary structure and secondary structure are all candidates for this insidious failure mode. Though fretting frequently leads to potentially catastrophic results, it may also lead to high maintenance and inspection costs, increasing down-time and expensive retrofit requirements (1). Thus, durability and safety considerations may also relate to the presence of fretting. Researchers and Designers are now beginning to recognize the need to understand the phenomenon of fretting-wear and to measure such wear effects. There 4 is a growing awareness that fretting-wear is, in itself, a distinct and important failure mode. CHAPTER II

DEFINITIONS

The Fretting Phenomenon

FRETTING may be defined (18,87) as a combined mechanical-chemical action in which the contacting sur­ faces of two solid bodies are pressed together by a normal force and are’ caused to execute relative cyclic sliding motion, but where the magnitude of the normal force is large enough and the amplitude of the cyclic motion is small enough to significantly restrict the flow of fretting debris away from its site of origin. Fretting always gives rise to one of three additional phenomena. These are fretting-corrosion, fretting-wear and fretting-fatigue. i RETTING CORROSION and FRETTING- WEAR may be defined, respectively, as any corrosive action or wear damage which occurs as a direct result of fretting. FRETTING-FATIGUE may be defined as any fatigue damage directly attributable to fretting action.

5 6

Fretting-Wear Failure

"Failure," due to fretting wear, may be defined from a physical, chemical or metallurgical point of view, depending upon the specific situation being investigated. * In the context of this Thesis, failure is confined to the physical arena, and is further restricted to the occurrences whereby a mechanically-coupled joint is stated to be unable to perform its intended function due to loss of tolerance, misalignment, jamming, or excess friction. Failure, then, implies knowledge of the joint geometry, and the extent to which it may be permitted to wear before functional failure ensues. FRETTING-WEAR FAILURE may be defined as the inability of a mechanical joint to perform its intended function due to a change in the interfacial geometry of that joint, arising from the process of fretting. The "geometry change" refers to the magnitude of "normal approach" due to loss of interfacial material. NORMAL APPROACH is defined as the distance which points remote from the deformation zone on the two contacting bodies move together upon applica­ tion of a normal load. The designer may use the above definition of fretting-wear failure, in coordination with experimental data, to limit functional failure of a mechanical joint 7 affected by fretting. The development of fretting-wear * * does not preclude concurrent development of other fretting processes. Therefore, it is important that other fretting data be available so that a choice can be made of the significant failure mode..

I

i CHAPTER III

PURPOSE OF RESEARCH

Scope

The intent of this research has been to develop design data useful for predicting the functional life of a mechanically-coupled joint in a fretting-wear environment. The benefits of such research would be enhanced if a wear prediction model could be devised that would closely re-create the design data, and suc­ cessfully predict fretting-wear in all cases of general design practice. In support of this, it was decided to analyze the fretted surface per se in light of the burgeoning research activity employing statistical tech­ niques for analysis of surface interactions under con­ ditions of sliding wear. To gain some insight into the effectiveness of these techniques, fretting-wear tests were devised so that profilometric measurements could be analyzed statistically. Further, it was thought to be of qualitative interest to conduct metallographic surveys of the fretted specimens. Hence, sufficient

8 9 tests were planned and conducted to obtain the requisite metallographs. Finally, it was proposed to use the Scanning Electron Microscope to examine the actual fretting-wear damage in an ef£ort to more £ully under­ stand the nature of the wear phenomena.

Objectives

The following objectives were set for this disser­ tation effort:

A. Design Objectives 1. To measure, in situ, the normal approach due to fretting-wear, for each of three steel/steel combinations: SAE 1020 on 1020; SAE 4340 on 4340; SAE 52100 on 52100. 2. To compare the use of smooth versus textured fretting surfaces upon fretting-wear rate (i.e., rate of normal approach). 3. To compare the effects of tensile and compressive axial preloading upon crack propagation. 4. To perform tests in a manner and pattern that may offer clues to the "stages” of fretting- wear, particularly the "steady-state" stage of

wear. 10

I 5. To monitor all principal data continuously for use in comparative analyses. This may enable determination of whether changes in fretting pressure occurs coincidentally, or in sequence, with changes in normal approach; and whether the (presumed) cyclic action of normal approach has a significant effect upon the rate of micro/macro crack development. 6. To obtain data on volumetric wear rates and specific wear rates. 7. To apply the fretting wear data to actual design problems so that materials such as SAE 1020, SAE 4340, and SAE 52100 may be used to their fullest potential in applications where fretting- wear is a dominant failure mode.

B. Modeling and Statistical Objectives 1. To develop an analytical model that will predict

functional failure— in terms of cycles of operation— due to the net movement between two datum lines on the opposing joint faces under­ going fretting (i.e., to predict normal approach). 2. To select modeling parameters closely associated with fretting, and develop them into a general fretting-wear prediction model. 3. To employ profilometry for determining the manner in which the topography of a surface varies as fretting wear proceeds, and to obtain descrip­ tive statistical data such as the mean and standard deviation of surface roughness. 4. To determine whether statistical data might facilitate the design of surface texturing to expedite debris escape at the joint interface. 5. To use statistical methods for obtaining actual surface contact area at successive stages of normal approach; to compute the actual normal interfacial pressures at these stages; and to compare predicted wear rates with wear rates ob­ tained under actual operating conditions.

Metallography and Microscopy Objectives 1. To learn whether "stages" of fretting-wear may be delineated, particularly from observations on specimens subjected to unequal wear cycles.

« 2. To determine whether failure processes other than fretting-wear can be identified. 3. To make comparisons between fretting of surfaces with smooth and textured interfaces. 12

4. To study the surface and substrate appearance of specimens subjected to fretting-wear, and thereby further the qualitative understanding of such phenomena. CHAPTER IV

HISTORICAL BACKGROUND AND RESEARCH EFFORTS

* 4

Introduction

Attention has only recently been focused upon fretting-wear as a distinct failure mode. Historically, investigators have treated the phenomena of fretting and wear as relatively distinct topics; others have viewed fretting as a subordinate and rather specialized form of wear. It was thought conceivable, however, that earlier researchers may have delved into these phenomena, measured them, reviewed them, and perhaps reported them in an altogether different context. It was with this possibility in mind that the literature review was undertaken. To maintain historical and technical continuity, the review is presented chronologically, and includes sources that purport to deal with "fretting" or "wear" or "tribology" or "testing."

13 14

Early Works

• • Candy's (16) overview o£ the literature on fretting traces first mention of the phenomenon to a 1911 article by Eden, Rose, and Cunningham (25), in which fretting corrosion ("rust") was observed between the round test specimen and holder of a Wohler rotating-cantilever- type fatigue-testing machine. Nearly two decades later Tomlinson (99), in 1927, and again in 1939 (100), showed that relative motion between contacting surfaces was necessary for fretting to occur, and that the reciprocating nature of fretting motion was responsible for the major damage (26). Fink (28), in 1930, and Rosenberg and Jordan (76), in 1935, measured the relative effects of slip superposed on pure rolling. Investigating the fatigue strength of fitted shafts, Peterson and Wahl (67), in 1935, concluded that the fretting effect markedly de­ creased the shaft's endurance strength. Warlow-Davies (103), in 1941, developed the idea of first fretting and then fatiguing a test specimen to measure the fretting- fatigue damage; this same idea was used later by Starkey, Marco and Collins (87) in 1957 at The Ohio State Univer­ sity. 15

Recent Efforts

Campbell (13) 1953, summarized the state-of-the-art in fretting corrosion. Some of the reported fetors ' that were thought to influence fretting, and ttje prin­ cipal investigators are noted below.

a. Mason & White (57) 1952, showed,A forcombinat­ tion of spherical surfaces consisting of a mat orial of high shear strength rubbing against one of muciji lower shear strength that

, (2 - c)f o _ _ = ------(fr------8 / r (1 - o) where 6 « critical displacement for no gross slide N = normal load y,C“ the shear modulus of elasticity and roisson's ratio, respectively, of the softer material r <= radius of curvature of the surface f = coefficient of friction. • * b. Sackman and Rightmire (78), 1948, suggested that combinations of metals showing poor alloying ten­ dencies should be more resistant to fretting (^ind wear) than those which alloy readily. 16

c. Bowden and Tabor (10), 1950, showed that the relative hardness of the surface oxides compared to the underlying metal plays a primary part in determining the wear rate; and that a hard metal producing a soft oxide will resist wear, whereas a soft metal producing a hard oxide may produce serious wear.

d. Mason and White (57), 1952, and Gray and Jenny (30), 1944, indicated that a maximum shear strength com­ bined with a "maximum elastic strain limit" is the best combination for resisting fretting-wear.

e. Almen (3), 1937, stated that ambient temper­ ature and humidity seem to have some effect since "false brinelling" (fretting) of automobile wheel bearings during rail shipment is more severe in winter than in summer.

f. Bowden (10), 1950, Holm (40), 1946, and Merchant (59), 1940, discussed the fatigue failure of surface asperities with respect to amplitude of slip.

g. Dies (24), 1945, noted that the oxidation which accompanies fretting in air is accelerated by the local increase in temperature resulting from fretting-wear. 17

Uhlig (102), 1954, developed a quantitative ex­ pression for fretting-corrosion for relatively large values of load, frequency and slip. The total wear or metal loss corresponding to a total of C cycles is

W (total) ■ W (corrosion) + W (mechanical) or

W (total) « (k L*/a - k L) § + k 1 L C o l r 2 where W * specimen weight loss L a load C » number of cycles f a frequency 1 a slip amplitude

k , k , k » constants. 0 1 2

Polushkin (68), 1956, used the following terms to express the amount of wear in chromium steel ball bearing races:

a. Specific Wear Rate, which is defined as the loss of weight in grams x 10~6 per meter-kilo- gram of work expended.' 18

b. Wearing Strength, which is the reciprocal value of the specific wear rate, or the frictional work in meter-kilograms required to produce a loss in weight of 1 mg.

Starkey, et al. (87), 1957, found fretting-fatigue resistance to be substantially improved by either shot- peening or cold-rolling of the specimen. It was specu­ lated that other methods of producing residual surface compressive stresses, such as nitriding or flame plating, also should be beneficial in certain applications. Dewees (12), 1958, performed wear tests using nominal contact stresses ranging from 10 psi to 100,000 psi, with the majority of testing at a velocity of about 2 in/sec, and concluded:

a. The wear of materials under sliding conditions in test machines and in service can be reduced to a common basis for numerical comparison. The basis used is the specific wear rate de­ fined to be the depth of wear in microinches for a 1 lb load acting on one square inch of nominal wear area for one million inches of travel.

b., Conditions such as large nominal contact area * which promote trapping of a greater portion of the wear particles, produce higher wear rates.

Sciulli, et al. (12), 1958, noted that, at unit pressures up to 300,000 psi,

a. An exponential relationship exists between wear rate and stress.

b. At relatively high surface contact stresses the wear rate increases faster than at low surface contact stresses, but there is no sharp point of demarcation that could be termed a "critical stress."

Alley (2), 1960, listed some of the principal fretting parameters and their relative effects:

a. Uhlig's (102) 1954 expression indicating a linear weight loss with respect to slip amplitude.

b. Uhlig's (102) 1954 expression which predicted a parabolically increasing weight loss with increase in normal load.

c. Wright's (113) 1952 expression which predicted a linear increase in damage with respect to an increase in the number of reversals, where damage was defined as the volume of material removed. 20

d. McDowell's (58) 1958 work which indicated an approximately parabolic increase in fretting as the number of reversals is increased.

In 1963, (69), the following observations were noted:

a. If the asperities were hemispherical, the area of contact on any individual asperity carrying a load W would be proportional to

b. The true area of contact is proportional to the load and does not depend on the size of the contacting bodies.

Johnson (46), 1964, suggested a method of "sequential analysis" for_reducing testing time. The analysis allows researchers to estimate early in the test whether or not a desired improvement (in fatigue life, wear life, etc.) is likely to be realized. Collins (18), 1964, proposed a damage-factor that could be developed to provide an index to fretting- fatigue damage. Upon the premise that there were probably eight basic parameters of great importance in initiating and propagating fretting-fatigue, a damage factor was written as a function of these parameters: 21

D « G(A,P,S,N,M,F,T,E) where .. A = Amplitude of relative motion between the two surfaces being fretted P ** Magnitude and distribution of pressure between the two surfaces being fretted S « State-of-stress including magnitude, direction, and variation with respect to time, in the region of the surface of each of the two mem­ bers being fretted. N » Numbers of cycles of fretting M a Material of each of the two members being fretted, including surface condition F a cyclic frequency of relative motion between the two members being fretted. T a Temperature in the region of the two surfaces being fretted. E a Atmospheric environment surrounding the surfaces being fretted.

Kragelskii (52), 1965 text, discussed asperity interaction, such as: number of interacting asperities as a function of normal load; c*nd the real area of con­ tact as a function of normal load. Bowden and Tabor (11), 1967, noted the following: 22

a. Surface temperature rise increases with load and speed and becomes greater the lower the thermal conductivity of the bodies.

# * b. There is consistent evidence to show that, with clean surfaces, adhesion at the interface is a major cause of frictional resistance.

Bayer and Schumacher (6), 1968, noted that surface fatigue can be an important wear mechanism under sliding conditions, especially where contact stresses are low in comparison to the yield point strength of the material. Bethune and Waterhouse (7), 1968, investigated the adhesion that develops between like metals in contact, and concluded:

a. In air, the maximum adhesion developed between metal surfaces in fretting contact is much lower than in a protective atmosphere (nitrogen).

b. The coefficient of adhesion (i.e., the ratio of the load required to separate the surfaces to the normal load applied during the fretting), is independent of the applied load. This co­ efficient is related to the intrinsic hardness (i.e., the annealed or over-aged hardness) of the material by a logarithmic relationship. 23

c. In air, the fatiguing of the welded asperity junctions transforms to corrosion-fatigue, and the resulting fatigue strength is lower than it would be in a non-corrosive environment such as nitrogen.

d. There is evidence (104) that annealing and work-softening can occur during fretting, usually after a period of work-hardening.

Bethune and Waterhouse (8), 1968, investigated the « adhesion that develops between unlike metals in contact under fretting conditions, and concluded:

a. The coefficient of adhesion developed between mild steel against non-ferrous alloys is con­ siderably lower than the adhesion developed between the non-ferrous alloys against them­ selves .

b. The damage produced by fretting-fatigue is a result of the alternating shear stress induced in the specimen surface in and near the fretting region as a result of the adhesion between the two contacting surfaces. 24

The above authors used an expression developed by Liu, Corten and Sinclair (83), 1968, relating the alternating stress applied to the specimen to the alternating shear stress in the fretting region:

°alt " (4Tllt ” 1>04 x 10‘ -----^ ---7 ) alt alt 0.1S1 + 4y2 where aa^ « applied alternating direct stress « alternating shear stress in the fretting

region I* » coefficient of friction H « hardness of pad

Liu, et al. (83) developed the above equation on the assumption that the fatigue strength of the material in alternating shear is half that in alternating direct stress. Campbell (14), 1969, discussed the critical ampli­ tude to prpduce slip. In reviewing the force-time curves by Mason and White (57) it was stated that:

a. For amplitudes of relative motion below 0.000075 in., the force-time traces are perfect sine waves, indicating that the motion is all elastic. No measurable wear occurs at these amplitudes. 25

b. A slight distortion of the force-time trace is noticed at an amplitude of 0.000075 in., and the distortion becomes progressively more pronounced as more and more of the motion is inelastic slip, until at 0.0005 in. evidence of marked stick-slip appears.

Summers-Smith (94), 1969, discussed the simple wear relationship

V - k«W*S where V = wear volume W « load S « sliding distance k » constant

Dividing by the area of contact and replacing the sliding distance by velocity times time, it was shown that

rate of linear wear « pv

The linear wear rate is thus a function of pv, and for an assumed acceptable wear rate a limiting pv value can be determined for a particular material. Hurricks (26), 1970, reviewed the known facts con­ cerning the mechanism of fretting-wear in metals. He 26 divided the process into three stages:

(a) Initial adhesion and metal transfer (b) Production of debris in a normally oxidized state (c) Steady-state wear condition

For (a) the wear process disperses the protective oxide- metal surface layer, the ease of which depends on the oxide and metal hardness. For (b) the formation of a layer of reaction product acts to reduce metallic contact. For (c) a general disintegration and dispersal of the zones affected by the initial stages of the wear action occurs. Abrasion is probably not the significant factor in fretting-wear? fatigue microcracks probably promote most of the damage at this stage. Kostetskii (51)f 1970, proposed a physical model of the fretting process in which the major factors are the dynamic nature of the load and seizure (dynamic oxidation) of surfaces, together with special features of failure associated with the presence of wear products which do not escape from the friction zone.

Waterhouse and Taylor (105), 1971, investigated fatigue cracks caused by fretting. Cracks reportedly arise in the boundary between slip and non-slip areas in the contact region, relieving stress concentrations at this boundary. The conclusions were that even 27 extremely hard surfaces, which are unlikely to adhere and suffer fretting-wear, can still incur fretting- fatigue damage because of the stress concentration near the boundary between the slip and non-slip regions. Hence, the only way to mitigate the damage is to encourage slip over the whole contact area by increasing the ampli­ tude of slip or by reducing the coefficient of friction. Milestone and Janeczko (60), 1971, worked on the measurement of friction at fretting metal-to-metal con­ tacts. Values of the friction force obtained during a single fretting cycle suggest that the sliding is stick- slip. For the tests, sliding motion was 10.004 in., and nominal contact pressures were 1000 psi and 2500 psi. Friction increased 300-310% during the first 50 cycles; at 10** cycles the coefficient of friction exceeded the

* first cycle value by 180-240%. GSnsheimer and Friedrich (29), 1971, studied the mechanism of fretting-wear in order to develop lubricants which eliminate or reduce it. Tests indicated that;

a. A solid lubricant paste containing mineral oil

plus Mo S2 plus inorganic phosphates gave the best performance. 28

b. For the dry solid lubricating films, a bonded coating containing a combination of inorganic binders plus MoS2, showed the longest wear life.

Toth (101), 1972, noted that very little information is available for the prediction of the rate of fretting of steel. The author's study investigated the effects of oscillatory motion, surface pressure and surface hardness on the steady stage of dry fretting (without lubrication), and concluded the following for 1080 and 4340 steel:

a. Frictional force is at a maximum during the » first 50-100 cycles.

b. Value of frictional force is nearly constant after 200-1000 cycles.

c. Variation in amount of wear corresponds to the variation of frictional force. Rapid wear occurs during the first 200-1000 cycles.

d. Fretting-wear in its initial stage increases linearly with slip amplitude, i.e., the ampli­ tude of the vibratory motion. 29

e. At less than 0.002 in slip amplitude, exact measurement of the fretting-wear (under the experimental conditions) was not possible. Extrapolation indicates that measurable fretting* wear begins at around 0.001 in slip (under the conditions of surface pressure investigated, viz., 1280 psi, 3840 psi, 5120 psi).

f. Fretting-wear is greater at low frequencies and less at high frequencies, other conditions being equal.

g. For a soft steel (1018), an increase of fre­ quency to more than 20-30 cycles/sec does not significantly affect fretting.

Taylor and Waterhouse (97), 1972, used sprayed molybdenum coatings as a protection against fretting- fatigue. During the early stages of fretting damage, welds form, leading, in some cases, to considerable ad- hesion. The function of the coatings is to reduce ad­ hesion between the surfaces and to provide abrasion re­ sistance. The molybdenum coating tends to reduce the fatigue properties of the parent specimen, so the im­ provement in the fretting-fatigue strength is due to the fretting resistant properties of the coating and not to any effect it may have on the underlying material. 30

Collins and Tovey (19), 1972, investigated the effects of both the asperity-contact microcrack initiation mechanism and the abrasive pit-digging mechanism on fretting-fatigue. It was concluded the former effect predominated in these tests. It also was recognized that the direction of fretting motion relative to the direction of subsequent fatigue loading has a major in­ fluence on the fatigue strength. Thus, it was determined that, for fretting conditions reported, the effective stress concentration factor for specimens fatigue-loaded parallel to the direction of fretting was 4.2, while the stress concentration factor for specimens fatigue-loaded perpendicular to the direction of fretting was 1.7. These values are for fatigue strength at a life of 5x10** cycles. The seeming inconsistency in these stress concentration factors was explained by the orientation of micro cracks perpendicular to the direction of fretting motion. Wright and O'Connor (114), 1972, examined the inter­ relationship of fretting and geometric stress concentra­ tions, and concluded:

a. Fatigue strength was seen to be independent of slip amplitude.

b. Geometric stress relief improves the fatigue strength of assemblies even if fretting is not

eliminated. 31

Hurricks (42), 1972, investigated the temperature effects on fretting-wear, and concluded:

a. In the range of room temperature to 200°C (392°P), fretting damage on mild steel de­ creases with increasing temperature and reaches a constant value at 200°C.

b. A transition in fretting behavior occurs at a critical temperature for mild steels, the re­ duction in fretting damage starting to occur at 130°C. At 165°C wear is also sensitive to surface finish, while at 20°C it is not sensitive.

c. Microfatigue is a significant factor in the continuation of fretting-fatigue after the initial adhesion stage.

Stowers and Rabinowicz (90), 1972, reported that a wear coefficient, k, computed by Archard's equation (5), will enable fretting-wear to be analyzed in the manner of continuous sliding wear. The wear coefficient k is defined

k « 3PV/LX %

32 where P = indentation hardness of the softer material V ■ volume of material lost L « normal load X « total sliding distance, which in the fretting case is equal to 2aN where a « peak-to-peak sliding amplitude and N » number of cycles.

The wear coefficient was found to be proportional to the friction coefficient to the nth power where n is about 4,

k = Kfn and where K is a constant for each material combination *>4 with a typical value of 5x10 . Since K is a constant it could be considered a modified Archard wear coefficient defined as

K « 3PV/LXfn

The authors state that a value of k is generally about 0.2x10 and this applies to both mild and hardened steel. Also, the exponential relationship k ° Kfn is of the same form as for continuous sliding wear. Hurricks (43), 1973, presented a review of some metallurgical factors controlling the adhesive and abrasive wear resistance of steel. It was felt that a useful link 33 could be established between wear resistance and micro- structure. Some of the conclusions drawn are:

a. Adhesive wear, generally the starting point for a wear process, can be effectively reduced by * assuring contact over a large number of grains; hence a large grain size is undesirable. For ease of processing and use where impact condi­ tions are not severe, nitriding is preferred for high wear resistance on suitable steels.

b. Abrasive wear, which can arise from the pene­ tration and plowing out of material from a sur­ face by another body, will depend on material hardness, metal microstructure, work hardening properties, and the hardness, type and size of abrasive. The best abrasive wear resistance is generally found in an alloy steel with a structure of uniformly distributed fine carbide in a martensitic matrix containing some

residual austinite.

Kolozsvary (50), 1973, conducted an electron micro­ scopy study of surface fatigue in sliding wear and con­ cluded that: the presence of undissolved carbide is harm­ ful and that the optimum carbon content for good wear 34 resistance is about 0.80-0.85%; and that best results were obtained by low temperature carbonitriding following carburizing in a controlled atmosphere. With this ma­ terial, adhesive type wear occurred instead of surface fatigue. Suh (92), 1973, offered a new theory of wear called the delamination theory and a wear equation based on the adhesive wear model. He stated that Archard's (5) theory is weak because:

a. It completely ignores the physics and physical metallurgy of metal deformation.

b. Many of the assumptions employed in the mathe­ matical derivation are unreasonable and arbitrary.

c. The theory does not provide any insight to the wear of metals under different sliding conditions.

Bill (9), 1973, used electron microscopy to measure fretting-wear in Titanium, Monel-4Q0 and Cobalt-25% Molybdenum. Bill agrees with Hurricks* (16) suggestion that fretting does occur in a sequence of three stages, but not in the order proposed. He states the following order:

a. Initial adhesion 35

b. Fatigue in the contact region with the generation of "spall-like" pits.

c. The generation of oxidized debris in conjunction with a corrosion cracking mechanism. Abrasion by oxidized debris particles may also play a ■ role in the final stage.

Mordkowitz (63), 1974, predicted service life through use of the Zero Wear theory. Using a modified form of Palmgren's equation

max —< Ipooo n ,)VJ * Y Tr p sy where N » allowable number of passes to ensure zero wear

t = maximum shear stress max FSy ** yield point in shear

Y r » zero wear factor, referenced to N »2000 passes

Stockwell and Kannel (88), 1974, described an infra­ red technique for detecting subsurface voids in machine elements such as bearings and gears to determine if fatigue-induced subsurface flaws exist. The method is able to detect defects as deep as 17 times the radius of the void. 36

Hisakado (37), 1974, analyzed the physics of contact between two solids, considering the distribution of the radii of curvature of asperity peaks. Analytical results show that the mean radius of curvature of asperity peaks has a significant effect on the nature of the deformation of contacting asperities, i.e., whether the deformation is plastic or elastic. Also, the mean value of the radius of curvature has more effect on the real area of contact than the variance of the distribution of the radii of curvature. Conlon (21), 1974, proposed a method for measuring industrial wear. The method utilizes the thin layer activation technique by accelerating ions, and may be used in situ. It is claimed to have many advantages over other methods of wear measurement including neutron acti- vation. Its application to the study of the wear proper­ ties of machine tools and plastics is currently being investigated. Hoeppner and Goss (39), 1974, used metaliographic analysis of fretted specimens in cross-section, yielding useful information when investigating subsurface material changes and fretting-induced cracking. The conclusions were:

O 37

a. Large numbers of "secondary" cracks are produced In the fretted regions of laboratory fretting- fatigue specimens. "Secondary" cracks are associated with the fretting debris, while "primary" cracks occur in the specimen surface.

b. The observations lend further support to a fretting-fatigue damage concept related to mechan­ ical action between the contacting surfaces.

Waterhouse and Taylor (107), 1974, used scanning electron microscopy of fretted surfaces of 0.7 carbon steel, commercially pure titanium, and Al-Zn-Mg alloy, and found that loose wear particles are produced by the propagation of sub-surface cracks in similar manner to that postulated in the delamination theory of unidirectional wear (92). The authors' conclusions:

a. The production of loose wear particles by fretting of a sphere on a flat in a number of materials is by the spreading of sub-surface cracks leading to the detachment of platelike particles of oxide coated metal.

b. The thickness of the particles ranges from 1.3 to 3.5 ym. 38

c. Both of these observations are consistent with the delamination theory of wear.

Hurricks (44), 1974, in using the SEM to. examine mild steel surfaces fretted in argon, detected spherical debris as a characteristic feature of the wear process. The spherical particles are found at all temperatures up to 500°C, usually with a smooth but layered surface. Their formation and growth is a result of an alternating type of deformation occurring along a local interface. They appear to have the same metallographic structure and hardness as the surface material from which they form. Waterhouse (108), 1975, in a paper on the physics and metallurgy of fretting, noted that a situation which produces considerable fretting debris is usually not as serious from the fatigue point of view, since the debris may act as a lubricant between the surfaces and the abrasive process may wipe out crack nuclei in the surface before they have time to propagate; and that it is unwise to draw conclusions from observations of fretting-wear of a pair of materials on their possible behavior in fretting-fatigue. Suh, et al. (45), 1974, presented results of further investigations of the application of the delamination theory of wear to a composite metal surface sliding at low speeds; and stated the delamination theory of wear 39 provides the theoretical basis for reducing wear through the development of composite surfaces. Kirk and Swanson (49), 1975, used Scanning Electron Microscopy for observation of subsurface cracks in a copper sample, confirming predictions from the delamination theory of wear. Hailing (35), 1975, analyzed the fatigue mechanism of wear, (considered the primary wear mechanism by Kragelskii (52)); and indicated such mechanism should yield better appreciation of the effects of such factors as material constants and surface topographical features. Waterhouse (108), 1975, discussed three topics in­ volving fretting in hostile environments: nuclear reactor; diesel engine; and surgical transplant. These problems are all concerned with the slow attrition of surfaces by fretting; and they are likely to be of interest in the nineteen-eighties because of heightened usage. Waterhouse states that the main lines of such effort should be directed first, to improvement of Resign; second, to de­ velopment of new materials; and third, if this fails, to attempt to improve the surface performance of existing materials by considering surface treatments and coatings. AGARD Conference Proceedings No. 161 (1), 1975, dealt with fretting-wear in airframe components and power plant components. The topics covered the basic physics, 40 engineering data and approaches for solutions. The solutions offered included the nature of the mating surface materials, design factors, controlled alteration of the surfaces involved and lubrication techniques.

Rabinowicz (75), 1977, analyzed the formation of spherical wear particles, and found that:

a. Spherical particles are only to be anticipated in slow uniaxial sliding, in fretting and within cracks of a material being fatigued.

b. In unlubricated sliding systems spherical par­ ticles are likely to be found only with inert metals (e.g., silver or gold) or with non-metals. With metals like steel, they may be anticipated only in sliding systems which are lubricated or are in an inert atmosphere.

Figgis and Sarkar (27), 1977, proposed an asperity model capable of predicting the wear rate of brass; and that in the steady state the wear volume can be calculated from Talysurf traces. CHAPTER V

THE NATURE OF SURFACES AND CONTACT STRESSES

Introduction

The proper functioning (112) of a machine part is in many eases dependent on the quality of its surface. In its broader aspect, the term "surface quality" includes not only the dimensional qualities of the surface but also the material, hardness, color, luster and metallurgical structure. That dimensional quality having to do with the fine surface irregularities is known as the "roughness" of the surface. The development of surface measuring de­ vices of suitable sensitivity has made possible surface specifications to provide optimum wear resistance, paint adherence and fatigue strength. The surface finish (47) of a part may affect its fatigue strength in three ways: (1) by introducing stress concentrations resulting from surface roughness; (2) by altering the physical properties of the surface layer of the material (e.g., a decarburized surface in an as-forged part has diminished surface-layer strength); and (3) by introducing residual stresses (e.g., grinding operations 42 often leave the surface layer in residual tension and thereby reduce its ability to withstand fluctuating loads). To optimize performance (70,89), both surface finish and function need to be considered. The coordinated selection of materials with respect to lubrication, friction and wear is a relatively new science called Tribology.

Definitions and Parameters

The geometric texture (36,112) of ordinary surfaces is controlled by the characteristics of the finishing process by which they are produced, each process leaving its own imprint or pattern of irregularities. The pattern of surface irregularities is usually very complex, and it is of value to identify and describe some of the principal surface parameters.

1. ROUGHNESS. Relatively finely-spaced irregularities in the surface, of short wave­ lengths (microroughness), characterized by hills (asperities) and valleys of varying amp-

* litudes and spacings.

2. WAVINESS. Surface irregularities which are of greater spacing (i.e., longer wavelength) than the roughness, and often referred to as 43

macroroughness. In addition, the surface also contains undulations of very Ion? wavelengths caused by the vibration of the workpiece or tool, heat treatment, etc., during the prepara­ tion of the surface.

3. LAY. The direction of the dominant surface pattern.

4. PROFILE. The contour of any specified section through a surface, in a plane perpendicular to the surface.

5. MEASURED PROFILE. A representation of the pro­ file obtained by instruments or other means.

6. CENTER LINE. The line about which roughness is measured, such that the sums of the areas above and below the center line are equal as shown in Figure 1.

Profile

Center Line

FIGURE 1; Surface Roughness Profile. ROUGHNESS HEIGHT. The deviation, expressed in —6 microinches {one microinch « 10 in.), of the surface profile with respect to the Center Line. It may be computed in either of two ways:

Yi + y 2 + y, + ... + yn Arithmetic Average n n

5 I I *il ial

y? + y§ + y| + ... + y* RMS Average « J

n

(y*) t z i=l

Roughness measuring instruments calibrated for

RMS average will read approximately 117. higher for a given surface than those calibrated for arithmetic average. On most surfaces the total profile height of the surface roughness (peak- to-valley height) will be 3.5 to 4.5 times the measured average surface roughness in microinches. 45

8. FLAWS. Irregularities occurring at widely varying intervals in a surface, including such defects as cracks, blow holes, checks, ridges and scratches.

The surface layer of metals (36,70) consists of several zones having physico-chemical characteristics peculiar to the bulk material itself. It is bounded by the substrate or base material, and the gaseous environment in which the metal resides. Just above the substrate is a zone of work-hardened material (1 to 10 ym or 39.37 to 393.7 yin. thick), on top of which is a region of amorphous or micro-crystalline structure (approximately 3.94 yin. thick). The latter region is produced by the melting and surface flow, during machining, of molecular layers which are subsequently hardened by quenching as they are deposited on the cool underlying material. The surface layer con­ sists of a thin, often transparent, oxide film (0.394 to 3.94 yin. thick); it is usually contaminated by the products of chemical reactions with the atmosphere, and is covered by dust particles and molecular films deposited from the environment. Finally, the surface contains atoms of gas which have properties somewhat dissimilar to those of the gaseous environment. # It is important to obtain a clear quantitative assessment o£ the topographic features of a surface, since phenomena such as friction and wear depend greatly upon the real area of contact between surfaces. Several methods are used in the measurement of the micro/macro-geometrical features of surfaces. Among these are optical methods using electron interference or reflection microscopy and mechanical methods such as oblique sectioning and pro- filometry. The value of the profilometer is that it assesses a representative length of the surface providing high resolution of roughness in a plane normal to the surface. A major disadvantage is that it may misrepresent the whole surface texture, being restricted to a single- line sample. Further, the high vertical magnification may create a physical misconception of the actual surface profile, since most surfaces have asperities with gentle slopes rather than the jagged characteristics seen on profilometric traces. Finally, a surface-measuring in­ strument, such as a profilometer, does not provide any information about the slopes, shapes and sizes of the asperities, or about the frequency of their occurrence; hence, it is possible for surfaces of widely-differing profiles (e.g., sine wave, sawtooth wave, etc.) to give the same arithmetic average or RMS roughness value. 47

Surface profiles can be analyzed and discussed in terms more general than the limited terms provided by methods such as profilometry. Profiles of surfaces can be considered, statistically, as stationary random processes. Therefore, standard statistical methods may be used to analyze the surface properties and estimate pertinent statistical parameters. Many practical (i.e., "smooth") surfaces have an asperity height distribution that is nearly normal or gaussian. The method of deriving and illustrating such a distribution is shown in Figure 2 (36). A typical distribution curve is shown in more detail in Figure 3 (85).

Sampling Interval

£(Z)

Discrete All-Ordinate Interval Distribution Histogram

< FIGURE 2: Method of Deriving the Distribution Curve 48

f(Z)

0.135g 0.883g

O.Ollg

Standard Deviation

FIGURE 3: Normal Distribution Curve.

The cumulative distribution of the all-ordinate distribu­ tion curve is 00

F(Z) = / f (Z)dZ —00/■

The gaussian probability density function is

C(s, 3 ^ _ (2n)^ y

49 where x is the mean; and the height of any ordinate indi­ cates the probability of occurrence of that event in the total population. The gaussian shape (36) is near enough to the exponential distribution shape at the outermost decile of the distribution to lead to mathematical simpli­ fication. Elaboration of gaussian and exponential forms are given in Chapters VI and VIII. For completeness, consider a linear distribution of asperity peaks which is the case for "rough" surfaces. If the number of events varies linearly with height, then the distribution of events is said to be triangular or linear, as shown in Figure 4.

f(Z)

-Z -h +h +Z

FIGURE 4; Triangular Distribution Curve 50 where

hn /f(Z)dz = 1 -h and the triangular probability density function is

£(Z) - K — - — -— ; 0 < Z < (6)*c (6)*a 6o2

f(Z) = K— + Z ; -(6)*o < Z < 0 (6)*o 6o2

Hertzian Stresses

When two metallic bodies are pressed together, con­ tact stresses are caused by the pressure of one elastic solid on another at local areas of contact, viz., at or

4 near the crests of the contacting surface asperities. The same type of stress distribution exists whether we examine the contact stresses between a locomotive wheel and rail, a ball bearing and its race, or between two "smooth" curved contacting surfaces in a fretting environment. For each of these examples it may be noted that the members do not remain in fixed contact; they are subjected to 51 cyclic motions and repeated contact stresses leading, in some cases, to failure of the component. Within the fretting interface, asperities cyclically interact under loads both normal and tangent to the con­ tacting surfaces. The presence of tangential forces causes the maximum values of the resultant contact stresses in the two elastic bodies to be substantially larger them those produced by a normal force alone. In addition, the presence of tangential forces combined with normal forces causes changes in the state of stress. Two of the three principal stresses are, for this case, tensile stresses in the region immediately behind the area in traction. The maximum shearing stress therefore increases in magnitude and moves closer to the contacting surfaces. Many researchers (36,38,53,96) have assumed, for modeling purposes, that surface asperities are either hemispherical in shape or conical frustums with hemis­ pherical apexes. This discussion, therefore, will be limited to the interaction of spherical surfaces in static contact. Specifically, it will discuss the stress field at and near the point of contact between two solid spheres of different radii, subjected to a load P coinci­ dent with the vertical Z axis, and passing through the center of curvature of both bodies (79,81,84,98), as shown in Figure 5. 52

Hemispherical Contacting Surface^. Pressure Distribution

FIGURE 5: Hertzian Contact Between Two Spheres. 53

Initially, with no pressure between the bodies, point contact occurs at point 0, as shown in Figure 6.

Tangent Plane 2R Containing Point of Contact 2R

Before Application of Load P

After Application of Load P

FIGURE 6: The Point of Contact Between Two Spherical Bodies.

Under compression, points remote from the contact zone will move together by a distance 6, where

6 = 6j + 6 2 *» Normal Approach 54

Points which lie within the contact region (e.g., points M and N) move towards each other distance Z, where

Z *= Zj + z 2 and finally meet each other during the deformation process. Since in general Z < 6 (i.e., points in the contact region meet prior to completion of the normal approach), local deformation ensues. If w } and w^ represent the dis­ placements, due to local deformation, of each of the two bodies at any point within the contact region,

Sum of Deformations *= Wj + w 2 = 6 - z

The principal assumptions on which equations for contact stresses are based are:

a. Material is homogeneous, isotropic and elastic in accordance with Hooke's Law.

b. Contact zone has dimensions relatively small in comparison with the radii of curvature and dimensions of the bodies.

« The principal results of the Hertzian solution include: 55 a. The principal stresses (clf a2f a3), are com­ pressive stresses. b. The maximum shearing stress at any point is

^ amax ” amin^ * c. The maximum and minimum principal stresses at any point are, respectively, cra, and a2, as shown in Figure 7.

-a

FIGURE 7: Principal State of Stress at Any Point The contact surface is bounded by a circle of radius a.

+ V

1/Rj + 1/R,

1 - vj 1 - v* where: *» ; K2 =------nEj iie2

With Poisson's ratio v = 0.3, and Ej = E2 *= E, the contact boundary circle radius is

P / R,R, 1.109 E \ R, + R,

The normal approach between points remote from the contact zone is With Poisson's ratio v = 0.3, and E = E « E, 1 2 the normal approach is

The maximum pressure, pQ , exists at the center of the contact zone, at the surface, and its value is

where the maximum pressure is 1% times the average pressure across the interface.

With Poisson's ratio v « 0.3, and E t = E2 « E, the maximum pressure is 58 j. The other principal stresses at the surface are

0.8 pG when v ■ 0.3

k. The maximum tensile stress occurs at the circular boundary of the surface of contact. It acts in a radial direction and has the magnitude

= . p max 3 °

There is pure shear along the boundary of the surface of contact (where normal pressure on the surface becomes equal to zero). When Poisson's ratio v « 0.3,

o o 0.133 p( max

1. The maximum shear stress is on the Z axis, at a depth equal to about % of the radius of the surface of contact. With Poisson's ratio v = 0.3,

T » 0.31 p max *o 59 m. Figure 8 illustrates the relative magnitudes of the stress components below the surface as a function of the maximum pressure for contacting spheres (81).

1.0 o o. 0.8 a au 0.6 jjvi w radius of contact circle VM O 0.4 •Ho 4J 0.2

0 1.5a 2a 2.5a

Distance From Contact Surface

FIGURE 8i Stress Distribution Along Load Axis,

# 60

n. For completeness, the following expressions are included for a sphere pressed against a plane surface. With Poisson's ratio v « 0.3, E1»E2**E,

and 1/R2 “ 0,

Normal approach:

Contact circle radius:

Maximum surface pressure: PQ = 0.388

Superposition of Tangential Stresses

Surface fatigue failures are initiated by alter­ nating shear stresses, and these failures, variously known as pitting, spalling, shelling, etc. (47), occur on the surfaces of gears, bearings, cams, steel wheel rims, and other curved members in contact subjected to cyclic forces or deformations. 61

When a normal force acts alone to produce Hertzian contact stresses, the three principal stresses are cdm- pressive at every point in the body within the contact region. However, if the normal force is accompanied by a tangential (frictional) traction force in the contact area, the following is found to occur:

a. Two of the three principal stresses become tensile in the region immediately behind the traction zone.

b. If the coefficient of friction between the two surfaces of contact is sufficiently large, these tensile principal stresses are large. For example, the frictional force corresponding to a coefficient of friction of 1/3, increases the maximum principal stress by 40%, compared to stresses produced only by a normal force.

c. If these tensile nominal principal stresses are

* small, (as they probably are on well-lubricated surfaces, or on surfaces where the oxide itself acts as a lubricant), their actual values may be raised by stress concentrations resulting from surface irregularities or microscopic cracks which usually exist at and near the surface of real materials. (These tensile stresses, in 62

conjunction with many other factors such as wear, non-homogeneity of the material and type of lubrication, help to explain why a crack may develop and progressively spread across the surface of contact (79)), d. The combination of frictional forces and normal forces on the contact surface also causes changes in the shearing stress distribution in the region of contact* These changes include:

(1) The location of the point at which the maximum shearing stress occurs moves nearer the contact interface.

(2) If the coefficient of friction is 0.10 or greater, the point of maximum shear stress is essentially located at the contact surface. e. When the tangential traction is less than yP, (where y = coefficient of friction and P « normal load), macroscopic sliding does not occur. This happens (36) where friction is used as a mech­ anism for preventing slip between mating com­ ponents such as nuts and bolts, interference fits, and friction drives such as clutches. There may 63 be, however, local microscopic slipping in the contact zone. If such displacements occur cyclically, the phenomenon of fretting may be induced. This will be discussed more fully in Chapter VI. \

CHAPTER VI

MODEL DEVELOPMENT FOR WEAR WITHIN THE FRETTING ZONE

Fretting Wear Mechanisms And Related Phenomena

Fretting may occur whenever two interacting surfaces are pressed together and subjected to cyclic relative motion of limited amplitude. Each of the interacting surfaces contains a complex array of microscopic asperities, randomly distributed and superposed on a substrate having its own characteristic macroscopic distortions. Within this framework asperities interact and, depending upon the nature and severity of interaction, surface damage, i.e., wear, may ensue. Surfaces undergoing fretting may experience one or more wear mechanisms (20,35,36,43),* Among these, adhesive wear is probably predominant, but if adhesion is absent on a particular portion of the interface, other local surface interactions may occur there, including asperity interaction and macro-displacement. When asperities inter­ act or interlock, motion cannot take place without

64 deformation, which often leads to fracture of the as­ perities. Macro-displacement may occur if an asperity imbeds itself in a softer surface, causing displacement of that surface during relative motion. Abrasion, too, may play a destructive role, especially if the abrasion is due to metallic oxides created from asperity destruction. Other mechanisms, such as corrosive wear (in which a cor­ rosive atmosphere and wear combine their efforts), surface fatigue (in which cyclic Hertzian contact stresses cause alternating shear stresses below the surface), or galling (in which significant surface destruction such as welding, tearing, gouging, etc. takes place), also may contribute to wear. Fretting-wear is, in the initial stages, a form of adhesive wear, as shown in Figure 9, When virgin sur­ faces are pressed together under normal load, relatively few asperities are brought into contact. Hence, local pressures are high, the yield point stress is exceeded and the interacting asperities deform plastically until the real contact area has increased sufficiently to support the applied load without further plastic deformation. If these surfaces were in an oxygen-free atmosphere, adhesion would readily occur. In a typical environment of air, however, surface contaminants limit the adhesive effects. With the superposition of tangential motion, the surface films are partially removed, and cold welding of the 66

Traction T LoadI P Pressure B, jnimi Loose Wear Area A Particle

Traction T

FIGURE 9; Asperity Interaction in Adhesive Wear. Formation of a Loose Wear Particle at a Single Asperity.

contacting asperity junctions can take place, in effect strengthening the interfacial resistance to the tangential force. If the tangential motion is of a reciprocating nature, as occurs in fretting, the oscillatory motion will eventually cause the asperity junctions to be severed, though not necessarily at the original junction interface. Thus, small, loose wear particles are either deposited in the interstices of the metal/metal interface, or they re- adhere to one of the surfaces. For unlike materials of dissimilar hardness (72), it is the harder surface which is likely to become covered by the fragments of the softer

* 67 one. As the fretting-wear action progresses, new metallic oxides are formed, dispersed, and further fill the inter­ facial voids. The oxides (Fe2°3 and Fe3°4 for iron and steel alloys), in effect, inhibit asperity junctions from forming and contribute to the reduction of both friction and adhesive wear rate. Oxide debris (106) has a hardness equivalent to 500 VHN steel (i.e., Rockwell Hardness C-50), hence it has been considered a likely possibility that abrasive wear would also take place. The importance of the abrasive wear mechanism has, however, been minimized by some investigators. Rabinowicz and Mutis (71) have shown that small abrasive particles present between two sliding surfaces do not necessarily prevent adhesion from occurring especially when oxide particles are small com­ pared to virgin debris. Starkey and Collins (86) found that the weight loss during fretting almost doubled when oxide debris was removed from between the contacting surfaces. One characteristic of iron and steel oxides is that they are volumetrically larger than the parent metal (26), and their entrapment and buildup in the fretting zone leads to an increase in both the local and nominal interfacial pressures. For example, the high potential energy (29) stored in the surface during plastic deformation is released in the presence of reactive substances. In the «

68 oxidation o£ iron and oxygen

2 Fe + 1% 02 ----Fe2°3

This reaction produces 1.43 g ^2 ° 3 from 1 9 Fe, which, due to the lower density of iron oxide compared to iron, 3 3 produces 2.22 cm Fe^t^ from 1^ cm Fe. The volumetric ex­ pansion of trapped debris in the fretting zone and its * consequent effect on interfacial pressure can be indirectly deduced from the experimental data reported in Chapter VIZI of this dissertation. It was noted, for example, that a continual withdrawal of an external clamping vise was required to maintain a constant amplitude of fretting motion during a given fretting-wear test regime. This would indicate that interfacial pressures were increasing due to debris entrapment and, consequently, inhibiting fretting motion, a condition that could be corrected only by loosening the clamping vise. At the onset of this research, correspondence was initiated with several prominent researchers in the tri- bological field. One intent was to learn whether quanti­ tative measures were being developed to predict failure of clamped joints due to fretting-wear. Replies alluding to this question in the context of the present chapter are given below. R. B. Waterhouse (University of Nottingham, Great Britain) stated that in the early stages of fretting ". . . there undoubtedly seems to be adhesion occurring," and that a "delamination" mechanism occurs later in the process. Further, . the length of the adhesion stage seems to be related to the chemical nature and reactivi­ ty of the material and also the environment. With titanium, there seems to be very little adhesion and the process seems to be entirely delamination."

M. B. Peterson (Rensselaer Polytechnic Institute, New York) stated that "... adhesive wear is usually accompanied by severe welding, metal transfer, and galling. This leads to surface cracks which ultimately lead to fracture. The question is what happens first, failure due to wear or failure due to fracture.” Dr. Peterson also noted that ". . .in fretting-wear it would be important to catalog the different tjjpes of surface damage which result as the slip distance is increased." 70

c. J. Hailing (University of Salford, Great Britain) stated that ". . . i n normal contact asperities behave predominantly elastically with smooth surfaces and predominantly plastically with rough surfaces." Professor Hailing noted in his text on Tribology (36) that adhesive wear is the essential mechanism in fretting; however, he felt "... fatigue to be a very important reason for asperity failure. ..."

The delamination wear mechanism noted by Dr. Waterhouse was introduced in 1973 by N. P. Suh (92), and a recent special issue of Wear magazine (93) devoted the full issue to Dr. Suh's research in this area. In essence, due to surface traction and subsurface deformation, cracks nucleate and tend to propagate parallel to the surface at a depth governed by material properties and the coefficient of friction. The cracks finally shear to the surface at certain weak positions, producing long thin wear sheets. When cracks cannot propagate because of limited traction and deformation, crack nucleation becomes the wear rate controlling mechanism. The delamination theory is stated to be applicable to all materials in which subsurface crack nucleation and propagation mechanisms are operative. Finally, it purports to explain wear phenomena which 71 could not be explained by the adhesion theory, principally propounded by Archard (4). It was noted in Chapter V that surfaces in contact will not experience macroscopic relative motion if

T < pP (where T = tangential traction, p * coefficient of friction and P = normal load); but that local slip or microscopic sliding may occur within the contact inter­ face. Within the contact zone, when T < pP, two regions are noted: a central zone in which no slip occurs, and an outer zone which experiences microslip. If the contact interface is circular, as occurs between two spheres, the perimeter of the no-slip (i.e., "stick”) zone will be smaller than— and concentric with— the full contact circle. Stowers (91) cited the work of Mindlin (61) who reasoned that the addition of a tangential force, T, results in a shear stress singularity at the edge of the contact circle, and the shear stress singularity is relieved by the local sliding of the two surfaces. The expression for the radius, c, of the no-slip circle of contact is

c « a (1 - T/pP)l/ 3 where a = radius of the full contact circle T ■ tangential force . p = coefficient of friction P « normal load 72

As the tangential force, T, increases, the boundary of the stick-slip region moves radially inward, and slip con­ tinues until the force, T, is balanced by the sum of the local shear tractions in the slip region plus the shear traction in the no-slip region. Fatigue cracks originate at the boundary between the slip and no-slip areas, arising at this boundary because of stress concentration. When a crack is formed it relieves the stress concentration at that point, and the boundary between the slip and non­ slip areas moves inward, initiating new cracks (105). Normal approach may be defined as movement, along the normal load axis, of points remote from the contact zone. In the lateral direction (orthogonal to the load axis), there is a critical traction-induced displacement, 6 , below which only local sliding occurs (61):

4 „ _3»djl- c 8Ga

where G is the shear modulus given by E/2(l + v) and v = Poisson's ratio. The critical displacement is measured parallel to the traction T, and is the sum of distances the sphere centers are laterally displaced from the load axis upon application of the traction. Mindlin's elastic 73 model may be used to predict the critical amplitude below which only local slip occurs. For two flat surfaces in contact, however, Mindlin's theory does not appear to apply and the critical amplitude must be determined ex­ perimentally. Slip amplitude has been investigated by many re­ searchers in an effort to determine (a) the magnitude of slip at which fretting commences, and (b) the magnitude beyond which oscillatory sliding occurs. The lack of uniformity of opinion is probably due to a combination of the wide range of test parameters used for the applied loads, the nature of the interacting surfaces, and the environmental surroundings. Campbell (14) noted that evidence of marked stick-slip appears at an amplitude of 0.0005 in. Halliday and Hirst (34) stated that plastic flow leading to the formation of intermetallic junctions occurred at an amplitude of 2 microns (0.00008 in.), Ohmae and Tsukizoe (65) cited 70 microns (0.0028 in.) slip amplitude as the transition between*minor and major wear and surface deformation, and stated that, at slip ampli­ tudes greater than 300 microns (0.012 in.), the fretting mechanism becomes similar to wear behavior under recip­ rocating sliding. Waterhouse (106) suggested that the "upper limit" at which slip ceases to produce fretting and becomes conventional reciprocating sliding wear lies 74 between 25 microns (0.001 in.) and 130 microns (0.0052 in.). Suh (92) noted that the critical displacement for fretting wear should depend on the density and distribution of hard inclusions as well as surface topography. Finally, Stowers and Rabinowicz (90) stated that sliding amplitude is not a pertinent variable; that fretting-wear is simply proportional to the accumulated sliding distance, and independent of the amplitude or the number of reciprocating cycles which are necessary to reach that distance.

Modeling Parameters

The parameters to be included in a fretting-wear prediction model should be those which are significant in producing fretting-wear in a real engineering system. The variety and number of potential choices is staggering. If we were to group these potential parameters within a physical and statistical framework, the result might be as follows:

Mechanical Parameters

1. Coefficient of friction 2. Geometry, fit 3. Stress concentration 4. Vibration a. Amplitude (constant/variable) b. Frequency c. Cyclic duration «

75

5. Preloading, prestressing 6. Joint type a. Total constraint (pure mechanical inter­ lock; pure adhesion; mechanical interlock and adhesion) b. Total constraint, mechanical interlock c. Partial constraint, mechanical interlock 7. Load (constant/varying) 8. Pressure a . Magnitude b. Distribution 9. State of stress a. Magnitude b. Direction c. Variation with respect to time 10. Design features 11. Methods of manufacturing 12. Servicing

Environmental Parameters 1. Temperature (dry bulb; wet bulb) 2. Barometric pressure 3. Humidity 4. Density of air 5. Evaporative heat loss 6. Absorptivity or emissivity factor 7. Film or surface coefficient 8. Time.

Surface Parameters 1. Composition and heat treatment 2. Grain size 3. Inclusions and inhomogeneities 4. Structural surface conditions produced by heat treatment 5. Structural surface conditions produced by mechanical treatment 6. Structural changes relating to size of ■ test piece 7. Structural changes caused by preloading and prestressing 8. Anisotropy 9. Origin a. Ingot, bar, sheet b. Orientation in relation to rolling direction c. Batch/manufacturer 10. Specific wear rate 11. Stress corrosion effects

Clastic Parameters 1. Static proportional limit 2. Static yield limit 3. Apparent and true tensile strength 4. Dynamic proportional limit 5. Damping 6. Modulus of elasticity 7. Electrical resistance 8. Coefficient of thermal expansion 9. Surface activity of stressed material 10. Shear strength 11. Endurance limit

Preventive Parameters 1. Lubrication a. Rate b. Viscosity c. Consistency d. Oil separation rate e . Additives 2. Surface stressing a. Shot peening b. Cold rolling 3. Flame spraying 4. Polymeric films 5. Nitriding 6. Explosive hardening 7. Polishing 8. Grooves for debris runoff

Statistical Parameters 1. Sequential Analysis (46) utilizing a Weibull Distribution (109) 2. Height distribution of asperities (gaussian, exponential, etc.) 3. Asperity Distribution in the plane of the surface (uniform, random, etc.) 77

4. Probability of interaction with respect to: a. Choice of model (conical, hemispherical, etc.) b. Normal approach/surface separation c . Surface roughness d. Standard deviation of height distribution e. Asperity radius f. Surface density of asperities g. True area of interaction h. Hardness i. Loading spectrum j. Traction k. Types of deformation (elastic, plastic, elasto-plastic, etc.) 1. Sequence of surface destruction (run-in, steady-state, etc.) m. Surface films/lubrication. 5. Auto-correlation Function (In random signal analysis the auto-correlation function describes the general dependence of the values of random data at one time on the values at another time (80)).

The remaining portion of this Chapter will discuss several potential fretting-wear prediction models, the parameters chosen, and a recommended model for prediction of fretting-wear.

Review of Potential Fretting-Wear Models

Researchers have used a variety of approaches to develop models for predicting wear. While some of these were previously noted in Chapter IV, it should be of interest to briefly summarize the approaches used. 78 a. Models Based Upon Assumed Stages of Wear 1. Hurricks (26) stated the wear process might be divided into a 3-stage wear mechanism: (a) Wear due to initial adhesion and metal transfer (b) Wear due to debris production in a normally oxidized state (c) Wear at steady state b. Models Based Upon a Wear Statement 1. Uhlig (102) stated total wear to be the sum of wear due to chemical and mechanical means.

W (total) « (k6L% - kjL) + k2l L C

2. Summers-Smith (94) developed an expression for wear rate as a function of a limiting pv value.

rate of linear wear « pv

3* Stowers and Rabinowicz (90) developed a wear coefficient enabling wear to be analyzed in the manner of continuous sliding wear.

K *» 3PV/LXfn 79

4. Hurricks (42) developed an expression for wear volume while investigating the temper­ ature effects on fretting wear.

V » (A./2 + A a/2 + ✓ A.Aa ) 1»2 *

where V, = volume of layer of thickness * t2 y beneath areas A : and A2.

5. Bayer and Schumacher (6) demonstrated the relationship between surface fatigue and the amount of sliding, N, required to produce wear of the order of the surface finish.

N - 2 x 10*

where Yr is an empirical wear factor charac­ teristic of a given system. For systems with a low tendency for transfer, Yr « 0.54; for systems with a high tendency, Yr ® 0.2; Typ « yield point in shear; “ maximum shear stress. luaX 6. Suh (92) offered a new theory of wear, and stated wear rate is proportional to normal load and the distance slid.

W « kLS

where k is a wear factor given by

b k * +

where k 1# k2 ° constants which depend primarily on the surface topography v = Poisson's ratio b ** Burger's vector G a Shear modulus a^ » Friction stress S0 a Critical sliding distance

Models Based Upon Surface and Statistical Parameters 1. Greenwood and Williamson (31) developed relationships between contact deformation and topography based upon contact between a 81

plane and a nominally flat surface; assuming all asperity summits have same radius and have random height variations.

2. Greenwood and Tripp (32) show that results * of a two-rough-surface will predict same laws as a single-rough-surface model, assuming all asperity summits have same radius, and have a random height variation.

3. Yoshimoto and Tsukizoe (115) developed a contact model of conical asperities and an ideal flat surface, and deduced the number and size of the individual areas of contact; and the wear rate as a function of velocity and load.

4. Gupta and Cook (33) performed statistical analyses to empirically estimate real con­ tact area, density and size distribution of microcontacts.

5. Nuri and Hailing (64) used a theoretical model to simulate the contact between a smooth plane and a nominally flat surface with a large number of spherical asperities. All asperities had the same radius, and %

82

their heights varied randomly, it was learned that the normal approach, due to the deformation of the textured surface, is linearly related to the standard devia­ tion of the roughness.

6. Hailing (35) in examination of wear behavior prediction due to asperity interactions alone, stated that, in the two dimensional elastic model, the surface tractions, in many cases, do not affect the size of the contact zone for bodies having similar elastic constants; and that the surface tractions marginally increase the maximum strain value and reduce the subsurface depth at which it occurs.

7. Leibensperger and Brittain (53) analyzed an idealized model developed by Tallian (96) to measure the effect of surface roughness on shear stresses below the surface of an unlubricated Hertzian contact, using photo­ elastic techniques. To develop a fretting-wear prediction model it is necessary to decide which of the aforementioned parameters are significant. That is, a decision must be made whether to vary, modify, or hold constant one or several of the following:

a. Mechanical Parameters b. Environmental Parameters c. Surface Parameters d. Elastic Parameters e. Preventive Parameters f. Statistical Parameters

If one were to consider all of the above, a model could conceivably be stated in the following form:

Failure due to fretting-wear may be avoided if

Mechanical Environmental Surface Parameters Parameters Parameters

Preventive Parameters

Obviously, development of the above would be a monumental task. Alternatively, it might be possible to adapt this model to the stages of fretting-wear damage suggested by Hurricks (41). The proposed model might then take on the following form:

Failure due to fretting-wear may be avoided if

Wear Due To Wear Due to Debris Initial Adhesion Production in a Normally & Metal Transfer Oxidized State

^ f Wear at 1 . , n r» Steady State - 1,u

In attempting to further develop the Hurricks model it has been concluded that its principal drawback lies in the difficulty of selecting those parameters relevant to each stage of wear. Further, a large number of experimental constants must be developed to make the model useful for quantitative predictions. A model for wear has been developed at the IBM Endicott Laboratory (55) known as the "Zero Wear" model. The zero wear model states that wear can be held to a depth of wear scar of the order of one-half the peak-to- peak value of the surface finish for a particular number of passes, N, if the maximum shear stress, t__„» is JuaX smaller than or equal to a certain fraction, yr , of the shear yield point of the material, typ. The maximum number 85 o£ passes for zero wear may be written as

Y T N « 2 x 108 Tg yp Tmax

If, however, the actual wear exceeds the zero wear speci­ fications, a design procedure (55,63) for "non-zero wear" can be employed. The non-zero wear procedure is, however, more complicated, since there is no simple algebraic ex­ pression available for relating lifetime and design parameters for the general case, as there is for zero wear. Since it is entirely possible that the mechanisms of wear deterioration may be so complex that a mathematical model cannot be derived, Rabinowicz (73) offers a non- parametric approach based on the idea of linear cumulative damage, similar to the approach first applied to the process of fatigue of metals by Palmgren and Miner (22,56, 62,66). Here, accelerated testing procedures may be applied for estimating the wear life of a component, pro­ viding that the linear cumulative damage criterion is valid. The method involves selection of a "stress" which is used to extrapolate short-term test data to obtain a predicted life. Unfortunately,.the use of the term "stress" in this context may include temperature, amplitude of vi­ bration, etc. Such an imprecise definition of stress 86 may jeopardize or even nullify the usefulness of experi­ mental results obtained from tests of this type. Statistical methods (15,46) are often used to expedite decision making during extended testing programs. One method— sequential analysis— often enables a researcher to decide early the probability of realizing a desired improvement. Such a technique might be used to expedite the experimental validation of an analytical fretting-wear model.

Development of a Model For Prediction oi: Fretting-Wear

The model developed as a part of this dissertation depends upon certain statistical data gathered from ex­ perimental research in fretting-wear. It was first hypo­ thesized that asperity destruction might proceed in such a manner that surface topography would replicate periodical­ ly. Measurement of variations in surface-related statis­ tical parameters could provide data'such as volume of material eliminated from a joint, with respect to normal approach; and establishment of the time when debris could be expected to discharge steadily from the joint interface, i.e., the threshold of "steady-state" fretting- wear. Profilometrie measurements taken periodically on 87

surfaces exposed to fretting-wear, however, did not support the basic hypothesis of topographic replication. However, the statistical data were of value in describing surface conditions throughout the fretting-wear cycle. Hence, the decision was made to employ a statistical description of surface condition as part of the proposed model for predic­ tion of fretting-wear damage. This approach not only serves as a valuable input to the physical model by providing in­ formation not obtainable by deterministic measurements, such as the number of interacting asperities, but also serves to supplement basic understanding of the fretting-wear process.

The Physical Model

Selection of the most significant physical parameters in the fretting-wear process was made on the basis of data found in the literature, and from statements such as:

a. Hurricks (42) stated that adhesion has been shown to be amplitude-dependent, frequency- dependent, hardness-dependent, and in steels, dependent on carbon content.

b. Stowers and Rabinowicz (90) stated wear to be proportional to volume and hardness, and in­ versely proportional to normal load and total sliding distance. 88

c. Sachs and Horger (77), in their review of fretting theories, stated the important factors influencing fretting are duration of test, at­ mospheric conditions, normal load, frequency of slip and amplitude of relative motion.

Testing would be performed under controlled laboratory conditions; hence, environmental parameters were not in the model. Material and surface parameters would be in­ herently included in the model by virtue of a "specific wear rate" parameter, to be defined later. Neither lubri­ cation, surface coating, nor other wear preventives would be used; the contacting surfaces would be clean and dry. Finally, the model included the following measured test data;

a. Nominal Contact Area b. Normal Approach c. Frequency d. Normal Load e. Cyclic Amplitude

Within these guidelines, the following parameters were chosen for the model; Volume, V = (Nominal Contact Area)(Normal Ap- 3 proach), in. This relationship is reasonably valid when the normal approach exceeds the surface finish.

Total Slip per Cycle# A =* 2 (peak-to-peak slip), in.

Frequency of Oscillation, f, cycles second

Normal Load, N, pounds

3 Specific Wear Rate, SW =* in /in-lb, defined as the volume of material removed per unit length of sliding per unit normal load. It may be ob­ tained from test data by dividing wear volume (V) by the product of total fretting distance (L) and normal load (N), or may be obtained from reference (74) previously cited. Dewees (12) suggested that specific wear rate be used as a common basis for comparing the wear of materials under sliding conditions, and Kragelskii (52) employed the specific wear rate parameter to solve engineering problems in wear. Further, Rabinowicz and Stowers (74) developed a nomogram that enables determination of specific wear rate knowing, for example, wear volume, sliding 90

distance, and normal load. There is good agree­ ment between values obtained in the research of this dissertation and values obtained through use of the nomogram, as discussed in Chapter VIII. It is to be noted that "specific wear rate" is not a standard term and has been de­ fined in the literature in several different ways. For example, Dewees (12) defined specific wear rate to be the depth of wear in microinches for a 1 pound load acting on one square inch of nominal wear area for one million inches of travel. Polushkin (68) defined specific wear rate as the loss of weight per unit of work ex­ pended, employing the frictional coefficient in his definition. In this Thesis as in the Nomogram (74), specific wear rate is defined to be the fretting-wear volume divided by the product of total distance slid times normal load at the contact interface. Knowledge and use of the coefficient of friction is not re­ quired for the Nomogram (74). Refer to Appendix N for a sample calculation of specific wear rate.

6. Time to produce fretting-wear failure, T, seconds. Analogously, this parameter is the time to e££ect a value of normal approach that will render a mechanical joint functionally inoperable.

The interrelationships among the parameters are:

(1) Time, T

(Cycles of Operation Until Failure Occurs) a C Frequency ** f

(2) Total Fretting Distance, L « (Cycles of Operation)(Total Slip per Cycle) ** CA

C = L/A (3) Therefore, T

(4) Specific Wear Rate, SW

______(Wear Volume) ______V (Normal Load)(Total Fretting Distance) NL

(5) Therefore, T - -S S £ - - - M L 92

(7) Since Volume of Wear,

V *■ (Nominal Contact Area)(Normal Approach) and Total Slip per Cycle, A = 2 (peak-to-peak slip), the fretting wear prediction model is

(Nominal Contact Area)(Normal Approach) Time = ------2(peak-peak slip)(Frequency)(Normal Load)(SW Rate)

In conclusion, the fretting-wear prediction model shown above is an original formulation developed from parameters considered basic to fretting-wear, based on a study of the most pertinent data available in the litera­ ture, supplemented by data obtained as a part of this dissertation effort.

The Statistical Model

The statistical model is adapted from Hailing (36) who expanded the results of Greenwood and Williamson (31). The model is based upon the interaction between a smooth plane and an array of identical asperities as shown in Figure 10. 93

Smooth Surface

Reference Plane on Rough Surface

Normal Approach ■ (z - d)

FIGURE 10: Contact Between a Smooth Plane and an Idealized Rough Surface.

It has been previously noted that Greenwood and Tripp (32) examined models having either both surfaces rough or only one rough surface, and concluded that experimental findings give Indistinguishable results. Kragelskll (52), too, stated that the conclusions derived for the case of contact between a rough surface and a smooth one are applicable to the contact between two rough surfaces. The statistical model assumes each asperity to have a spherical summit and to be deformed equally under load. 94

Using Hertzian contact theory as a basis for evaluating normal load and contact area for each asperity summit, interaction between the idealized asperity surface and a smooth plane is developed from probabilistic theory. Upon selection of an asperity shape that will provide asperity radius and slope, the statistical model may be solved for data such as number of contacting asperities and total contact area. The asperity shape selected for the statistical model was developed by Tallian (96) and used by Liebensperger and Brittain (53) to suit the following criteria: (1) the Hertz contact area of the asperity will increase proportionately with its elastic deflection under load, (2) the shape is similar to asperity profiles found on surfaces having RMS roughness ranging from approxi­ mately 2 to 30 yin. The plane-sided asperity model shown in Figure 11 has a tip radius so selected that the tip extends over a small constant portion of the asperity height. 95

0 » RMS Surface Finish

6 « Asperity Slope

R - a/2(1 - cos0)

A ■ 2B/tan0

FIGURE 11: Plane Sided Asperity Model. The following is a summary of asperity interactions based upon statistical analysis (36):

a. Number of Interacting Asperities

1. Gaussian Distribution

N 1 1 F0 (h) n_ = 0.75 E' 6* "g1 Fjfh) 2

2. Exponential Distribution

N n e n*E' P a \ e

b. Total Contact Area 1. Gaussian Distribution

Nil $5 Fj (h) A = 0.75------9 E' a i P,(h) y 2

2. Exponential Distribution Using the statistical relationships (36) in coordi* nation with the Tallian model (96), the following may be obtained:

c. Contact Area per Asperity 1. Gaussian Distribution

A * A /n eg g g

2. Exponential Distribution

Ace “ V e

d. Diameter of Asperity at Contact Interface 1. Gaussian Distribution

Dg “ / 4ftcg/n

2. Exponential Distribution 98 e. Asperity Deformation (Normal Approach) 1. Gaussian Distribution

H « %D Tan 0 g g

2. Exponential Distribution

H e « %D e Tan e

where:

N » Normal Load

1 1 - vj 1 - vj E' E, E*

or, E' « % (E/1 - v 2) for the same material.

F0(h), FA (h), Fj(h) are integrals of the t gaussian distribution (32), and are given in Appendix A.

a » Standard Deviation = RMS roughness of surface from profilometry. See Appendix B.

ag “ (°? + “ o/'Y~ for the same materials in the gaussian distribution.

•

cr0 ■ standard deviation for the ex­ ponential distribution. 99

3 * Asperity radius, obtained from the Tallian model (96) and used by Leibensperger and Brittain (53).

a /7~ 3g ■ '" 2 (i-co's 9 ) for the 9aussian distribution

3 fi « 3 (1 -cos 9 ) ^or t*ie exPonent^a^ distribution

where 6 = 1 0 ° (slope of asperity) in the Tallian model (96). Refer to Figure 11.

In conclusion, the statistical data and asperity shape suggested in this Thesis provides a probabilistic basis for measurement of asperity interactions at a contact interface. CHAPTER VII

EXPERIMENTAL APPROACH

Introduction

To measure fretting-wear accurately, a basic require­ ment is to produce fretting-wear in an assemblage of com­ ponents that is both reliable and consistent in behavior. Of equal importance, is to effect all wear measurements in situ. With respect to the former requirement, this research effort had access to a fretting fixture developed by Collins (17), and used successfully by other investi­ gators, principally in fatigue and fretting-fatigue re­ search. For the latter requirement, modifications were required to permit accurate wear measurements. Later por­ tions of this chapter will discuss these modifications in greater detail. This chapter elaborates on all aspects of the ex­ perimental program— originating with the research proposal, and culminating with the collection of raw test data, a period comprising 15 months. In addition, profilometer

100

fa 101 measurements and specimen preparation procedures for metallographic and microscopic examinations are described. Titles of the sub-sections of this chapter are listed below. * A. Test Plan B. Experimental Apparatus C. Test Procedures and Monitoring Devices D. Data Handling E. Profilometry

F. Metallography G. Scanning Electron Microscopy

A. Test Plan

1. Types and Numbers of Tests. Initially, the Test Plan called for fretting-wear tests using smooth-faced shoes with the specimen having a compressive axial preload. Subsequently it was decided to test textured (grooved) shoes under the same preloading conditions. Early in the testing program it was decided to again extend the scope of testing to include tensile axial preloading, and to investigate the effects of the shoes' groove orientation upon fretting-wear in the specimen. Tests conducted on compressively preloaded specimens, fretted with smooth-faced shoes, were run using 102 test durations ranging from 10,000 to 500,000 cycles. * These tests were designed to gather data on progressive wear, both quantitatively and qualitatively. All other tests were conducted at the 100,000 cycle level, only, this being the "standard" test duration selected for com­ paring wear behavior of all specimen/shoe/load configura­ tions. In the final Test Plan, eight types of tests were included, as listed in Table 1. "Vertical-grooved" shoe in Table 1 denotes shoe grooves were parallel to slip direction. "Transverse- grooved” shoe denotes shoe grooves were perpendicular to slip direction. Axial preload refers to the state of stress induced in the specimen at the onset of test run .and maintained throughout the test. Test types I through VI produced reasonably consistent data. Test types VII and VIII (no slip control) ran very erratically and gave inconclusive data, and have not received further analysis. Thirty-six tests were planned for each material, to accommodate test types I through VI. Therefore, a total of 108 tests was projected. Evaluating test scatter at the conclusion of these tests, it was decided to add 6 more data points: 3 tests using 1020 steel and 3 tests . using 52100 steel specimens. Thus, a grand total of 114 tests was completed to provide the research data presented in this Thesis. %

103

TABLE 1 TEST PLAN

Test Type Description

I Non-grooved shoe, compressive axial pre­ load. Test durations: 10K, 20K, 50K, 70K, 100K, 200K and 500K cycles. II Non-grooved shoe, tensile axial preload. Test duration: 100K cycles. III Vertical-grooved shoe, compressive axial preload. Test duration: 100K cycles. IV Vertical-grooved shoe, tensile axial preload. Test duration: 100K cycles. V Transverse-grooved shoe, compressive axial preload. Test duration: 100 K cycles. VI Transverse-grooved shoe, tensile axial preload. Test duration: 100K cycles. VII Non-grooved shoe, compressive axial preload. Test duration: 100K cycles. No Slip Control. VIII Non-grooved shoe, tensile axial preload. Test duration: 100K cycles. No Slip Control.

* 104

2. Test Parameters a. Test Parameters Held Constant During the Entire Testing Program: (1) Frequency: 30 Hz (2) Amplitude of Slip: 0.00375 in. (3) Normal Load at shoe specimen inter­ face: 500 lb. (10,000 psi nominal, con­ tact pressure)

b. Test Parameters Varied During the Testing Program: (1) Axial Preload: (a) 500 lb. (10,000 psi) compression in specimen (b) 500 lb. (10,000 psi) tension in specimen (2) Duration: (a) Varied from 10,000 to 500,000 cycles for tests on axially-compressed specimens having smooth-faced shoe- pairs (b) Maintained at 100,000 cycles for all other test types 105

(3) Shoe Surface: (a) Smooth-faced (b) Vertical grooves (grooves parallel

t o B l i p )

(c) Transverse grooves (grooves per­ pendicular to slip)

3. Test Environment All testing was performed in an ambient laboratory air environment. The ambient conditions were not con­ trolled but were recorded prior to each test run as sum­ marized below. The values indicated represent the range and mean values observed over the entire testing program.

a. Dry Bulb Temperature: 78°P Avg. 72°P Min. 85°P Max. b. Relative Humidity: 67% Avg. 61% Min. 73% Max. 106

4. Specimen Materials Three steels were selected for fretting-wear testing and analysis. These include: SAE 1020, SAE 4340, and SAE 52100. Their chemical analyses and heat treatments follow.

SAE 1020 .— Selected from a single heat of hot-rolled 3/4 in. solid round bar stock having the following certified composition.

c Mn P S Fe

0.20 0.45 0.04 0.05 Balance

The 1020 material for both specimens and shoes have a yield strength of approximately 36,000 psi and an ultimate strength of 50,000 psi.

SAE 4340.— Selected from a single heat of 3/4 in. solid round bar stock having the following certified com­ position. 107

c Mn P S Si Cr Ni Mo Fe

0.51 0.66 0.012 0.018 0.30 0.77 1.78 0.22 Balance

The 4340 material for both specimens and shoes was heat treated as a single batch according to the following heat treating procedures.

1. Normalize in atmosphere at 1600°F for IS minutes. 2. Austenitize in atmosphere at 1550°F for 15 minutes. 3. Quench in agitated oil at 120-140°F. 4. Temper in air draw at 1100°F for 45 minutes.

The heat treatment produced a Rockwell hardness of approxi­ mately C-35, a yield strength of approximately 158,000 psi, and an ultimate strength of 168,000 psi.

SAE 52100.— Selected from a single heat of hot- rolled 0.813 in. solid round bar stock having the following certified composition. 108

C Mn P S Si Cr Ni Ho Cu

1.0 0.30 0.025 0.025 0.25 1.5 0.25 0.08 0.35

The 52100 material for both specimens and shoes was heat treated as a single batch according to the following heat treating procedures.

1. Austenitize one hour at 1550°F. 2. Endothermic atmosphere to maintain 0.90/1.0 points of carbon. 3. Oil quench at 120-150°F. 4. Temper 2-3 hours at 350°F,

This heat treatment produced a Rockwell hardness of approxi­ mately C-60. In order to develop a workable method for machining, heat-treating and polishing SAE 52100 specimens, a preliminary sample of thirteen were pre-machined to within approximately 2-4 mils of final dimension and then heat- treated to Rockwell C-60. Examination following heat treatment showed "bowing" of up to 50 mils. It was de­ cided to fully-anneal the bars, straighten them, partially finish to final size, re-heat treat to Rockwell C-60, and finally, polish to desired surface finish. This procedure 109 produced satisfactory results. The balance of the 52100 bars were thereupon stress relieved, machined, partially finished, heat treated and polished--in that order. All specimens and shoes were carefully machined by the same machinist, using the same sequence of operations. Specimens were hand-held during polishing while using a linen buffing wheel, lathe mounted. Polishing was effected using progressively smaller grit sizes. Final polishing used jeweler's rouge to produce a surface finish of less than 10 microinches RMS roughness. All final polishing marks were approximately parallel to the longi­ tudinal axis of the specimen.

5. Specimen and Shoe Geometry The test specimens were fabricated from a solid cylin­ drical rod machined to produce a final test section of rectangular cross-section. This provided flat surfaces to be sandwiched between a shoe-pair to produce simultaneous fretting action on both sides of the specimen. The specimen has the same configuration as used by Collins (17). Refer to Appendix C. The test shoe configuration is similar to that used by Collins, but were extended and modified to permit in­ stallation of two parallel transducers for measuring normal approach, as well as a modified core-holder assembly for measuring amplitude of slip. Refer to Appendix C. 110

For tests requiring textured shoes, parallel grooves were cut in each shoe by using a conically-ground carbolloy tool bit mounted in a vertical milling machine. Appendix * C illustrates the grooving pattern used in the fretting shoes. The tool bit was previously designed by Syed (95) in an investigation of the effectiveness of surface grooving as a fretting-fatigue mitigation agent at steel- steel joints. Syed documented the effectiveness of a grooving tool vs. the expense and/or other attributes of other grooving methods such as: hand filing, photoetching, and electro-static discharge machining. The groove geometry used in these fretting-wear tests was a compro­ mise between a geometry that would theoretically permit all debris to freely discharge from the joint interface, and the practical limitations of both tool bit and surface response such as burring and distortion. By a trial and error approach, a geometry was selected to provide the practical maximum number, width and depth of grooves.

B. Experimental Apparatus * 1. Fretting Fixture All fretting-wear tests were performed on a Krouse

a Direct - Stress Fatigue Testing Machine, a part of the laboratory facilities of the Department of Mechanical Ill

Engineering at The Ohio State University. The fretting fixture was designed by Collins (17) to be clamped onto the columns of the Krouse machine, allowing fixture and machine to produce fretting pressures up to 40,000 psi, and longitudinal (axial) stresses in the specimen up to • 100,000 psi (compression or tension). The adjustable eccentric drive of the Krouse machine provided the required relative cyclic motion to produce fretting on the specimen. Refer to Figure 12, which shows the general arrangement of the Krouse machine, fretting fixture, and instrumenta­ tion used in this research. The fretting fixture consists of the following prin­ cipal elements:

a. A static stress preloading frame and load cell that fastens to the cyclic loading column of the Krouse machine to produce and measure axial preloading of the specimen.

b. A calibrated shoe-loading'device that produces and measures fretting pressures between the specimen and its shoe-pair.

c. Upper and lower mounting blocks which clamp onto the columns of the Krouse machine, support the shoe-loading device, and guide the pre- loading frame. FIGURE 12; General Arrangement of Krouse Direct Stress Machine, Fretting Fixture and Instrumentation. 113

Refer to Figure 13, which schematically illustrates the basic fretting fixture setup. The basic fretting fixture was designed (17) to accommodate, in addition to the static load cell and cali- brated shoe-loading device, transducers that monitor slip amplitude. The original brackets for mounting these transducers and, accordingly, the original shoe profile, required modification to provide clearance for the new transducers for continuous monitoring of normal approach due to fretting-wear. Refer to Figure 14, which shows the modified slip amplitude transducer bracket, the normal approach transducer housing, and the specimen and shoe-pair in situ. Refer to Appendix C for details of transducer brackets. 114

Static Stress Preload Frame a

Load Screw Load Cell

Shoes Specimen

Calibrated Shoe-Loading Device

Mounting Block--- Cyclic Motion Input Krouse Machine

FIGURE 13; Schematic Diagram of Basic Fretting Fixture 115

Normal Approach LVDT Core

Shoe Specimen

Slip LVDT Normal Load \ Body Bracket Cell Diaphragm Shoe

Normal Approach LVDT Body

SECTIONAL PLAN Scale: Full Size

FIGURE 14: Assembly of Shoes, Specimens and Transducer Housings for 'Monitoring Cyclic Amplitude and Normal Approach. *

116

2. Ins trumentation Transducers, instrumentation, circuitry and recording devices were designed and selected principally to permit continuous/sequential recording o£ the four parameters of interest:

a. Cyclic amplitude of motion (slip amplitude) b. Axial preload of specimen c. Normal load at shoe/specimen interface d. Normal approach due to fretting-wear

Cyclic slip amplitude was monitored at the fretting inter­ face by means of a Linear Variable Differential Trans­ former, or LVDT. A Schaevitz type 100 MHR AC-LVDT with linear range of ±0.100 in. was selected for this application. Axial preload of each specimen was monitored at the static stress preload frame by means of a load cell using Micro- Measurements type EA-06-125 TA-120, option W strain gages. Normal load at the shoe/specimen interface was monitored by means of a load cell utilizing Micro-Measurements type EA-06-125 AD-120, option E strain gages. The normal ap­ proach was monitored in Bitu by means of an LVDT. A Schaevitz type 010 MHR AC-LVDT with linear range of ±0.010 in. was selected for this application. All transducer circuits, following amplification, were fed to a central control station. Here, the amplified 117 signal could be: (1) selectively monitored on a digital voltmeter (DVM); (2) viewed on an oscilloscope; or (3) fed, en masse or selectively, to a multipoint recorder. Refer to Figure 15 for a schematic of the instrumentation. A carrier amplifier (Consolidated Engineering Cor­ poration type 1-127) employed four channels to amplify, respectively, axial preload load-cell; normal load load­ cell and one active and one standby LVDT for cyclic amplitude measurement. A demodulator/amplifier (ATC type 6101-E-2-X) was used for each of the two Normal Approach LVDT's. A B & K Electronic Voltmeter (Brtiel & Kjar type 2409/2416) was placed in the cyclic amplitude circuit be­ tween the control station and recorder. Its purpose was to "filter" peak values of slip by sampling the levels of a varying signal during a given time interval, trans­ mitting half the peak-to-peak value, averaged over several cycles, to the recorder. A Leeds & Northrup type W "Speedomax" 12-point Recorder operated continuously throughout each test run, to record'sequential values of slip, preload, normal load and normal approach. The chart speed was 30 inches per hour. The timing motor printed a data point every 6 seconds. The 5 transducer signals were fed to the recorder so that each transducer was recorded twice during every rotation %

118

Axial Normal Normal Preload . Load Approach

O t «s

Source of Data

Terminal Board

ATC Carrier Demodulator Amplifier^ cn •a

I—

Central Control Station

Scope (Standby) Peak Metei

Multipoint Recorder

FIGURE 15: Fretting-Wear Instrumentation Schematic. 119 of the printer wheel. A test run of 100,000 cycles, for example, lasted 55.5 minutes. Each transducer signal was printed every 36 seconds. Hence, a specific data point appeared approximately 92 times during the test. During the "debugging" period, several trial test runs were recorded. A subsequent plot of normal approach vs. number of cycles displayed a rather erratic "wear" pattern. Analysis indicated that a very slight misalignment within the fretting fixture could occur, and although it had no discernible effect on other test parameters, the misalignment could influence the displacement measurement indicated by the LVDT body/core system. However, if both normal approach LVDT's simultaneously monitored and recorded the displacement data, the erratic wear pattern could be readily corrected during data tabulation. For further details on these corrections to normal approach raw data, refer to Appendix D. Mechanical disconnects were liberally located through­ out the circuitry to protect the several transducers, simplify specimen setup time, enable rapid repairs, and assist in calibration. All instrumentation was subjected to calibration checks at frequent intervals. The strain gage load cells for measuring axial preload and normal load were calibrated on an Instron Tensile-Testing Machine. The LVDT's used for measuring slip and normal approach 120 were calibrated using a fixture designed by Syed (109), and modified to suit the revised and added instrumentation. For calibration data see Appendix E.

C. Testing Procedures and Monitoring Devices

1. Organized Procedures

A systematic plan was developed at the beginning of the testing program, and followed on a daily basis as described in "Fretting Wear Test Procedure," Appendix F. Included in the testing procedure were checks of the ampli­ fication equipment and peak meter; and, on days when the cumulative number of test cycles exceeded 100,000, all equipment was subjected to a recheck. Briefly, the experimental testing of each specimen and shoe-pair involved the following procedures:

a. Pre-test Equipment Check. Qualitative/quanti­ tative monitoring of Amplifier, Demodulator, Peak Meter; restoration of null position; re­ cording of ambient conditions. b. Specimen Test Setup. Step-by-step procedure for mounting all test equipment/apparatus. c. Prior to Test Run. Establishment of test parameters & initial recording of same. 121

d* Test* Activities accompanying the actual fretting wear test. e. Post Run. Activities accompanying the completion of a test run. f. Miscellaneous. Periodic calibration check of instruments; periodic check of tightness of fretting fixture.

2. Auxiliary Monitoring A source of concern during the pre-testing phase of this research was the inconsistent performance of the amplification network. Therefore, in order to check the quality of amplification prior to each test run, de­ vices were developed and calibrated to produce a known response in each amplifier and demodulator channel. The output of such devices were duly recorded before each test run; deviations and trends were noted and subsequently adjusted. For strain gage circuits amplified in the carrier amplifier, the carrier amplifier's internal shunt resistors were used under no-load conditions to check amplifier gain. For LVDT circuits amplified in the carrier amplifier, a dummy bridge was developed to check the gain. For LVDT circuits amplified in the ATC demodulators, an "incremental gain" device monitored the stability of amplification. 122

An oscilloscope was used on a continuing basis to "spot check" the magnitude of cyclic slip amplitude. This also served as a rough check on data being simultaneously printed by the L&N recorder. Refer to Figure 16 for a typical slip waveform. Monitoring of the null point of each transducer was performed daily, and repeated, if testing on a par­ ticular day exceeded 100,000 cycles. A record was kept of all null adjustments to keep abreast of any and all trends.

FIGURE 16: Oscilloscope Waveform of Fretting Slip Amplitude. 123

D. Data Handling

Raw data were monitored and recorded in three ways:

1. A Test Log was developed for comprehensively recording all basic data, including date, test number, material, and mark number, as well as initial and final transducer data as read from the DVM. Refer to Appendix G.

2. A Recorder Printout Summary was used to list data taken from the multipoint recorder at startup and completion of each test, as well as the net change of each transducer as seen by the recorder. Refer to Appendix H.

3. A Multipoint Recorder Printout was made for each test run. Common transducer points were connected and the chart was subdivided into 10,000 cycle increments for later graphing. Refer to Appendix I.

After the recorded printout was divided into 10,000 cycle segments, the magnitude of each transducers' data was written on the printout at the point where the data line intersected the 10,000 cycle line. The data were then transferred to a chart which listed, at 10,000 cycle points, the magnitude indicated by each transducer. This format provided the following advantages: 124

1. It offered a rapid, comparative check of data at any given 10,000 cycle location in the fretting-wear cycle.

2. It simplified identification of unreasonable excursions in test data with respect to ex­ pected values based on other similar tests.

3. It simplified the graphing of results on an individual or collective basis. Thus, the average of a particular column of data, associ­ ated with a particular time in the fretting- wear cycle, was readily computed,

E. Profilometry

The profiles of both surfaces of every specimen were measured, before and after testing. The measuring instru­ ment used was a Type 'Q' Profilometer Amplimeter, Model 11, with a Mototrace Type V trace having a 5 nun. stroke. The instrument was manufactured by Physicists Research Company. Profilometry measurements were taken in the Department of Industrial and Systems Engineering of The Ohio State University. Each 1/4 inch diameter fretted zone was measured at S locations to assure representative data. Data were %

125 averaged with and without including the central portion o£ the fretted region. In some cases, the geometric center of a fretted region appeared to be more severely worked than the outlying portion (i.e., the stick/slip transition). Hence, data were partitioned accordingly. Each "data line" has a maximum and minimum value, due to the stroke length of the stylus. Data were handled in the following manner:

a. An average was computed for each data line.

b. An average of all data lines was computed with, and without, center values.

c. Cumulative averages were computed for specimens having the same test duration with, and without, center values.

F. Metallography

One specimen of each material for each of the VI test types was prepared for metallographic examination, a total of 36 specimens. Table 2 lists the specimens selected. Two possibilities for specimen sectioning were con­ sidered, as illustrated in Figures 17 and 18. Figure 17 126 is orthogonal to the slip path; and there is a high proba­ bility the most critical region would be lost in sectioning and subsequent metallographic preparation. The specimen orientation shown in Figure 18 was selected for sectioning since such orientation will display the fretted region along its entire slip length. Following sectioning, using a silicon carbide metal­ lurgical saw, each specimen was electroplated, mounted, ground, polished and etched. Refer to Appendixes J and K for details, respectively, of metallographic specimen preparation and electroplating. All studies were made on a Bausch and Lomb Research Metallograph at 300x magni­ fication, using #4154 Kodak Contrast Process Ortho 4x5 cut film. The metallographic studies employed a standard orientation so that the slip direction was always uniquely positioned, as shown in Figure 19. The B6L metallograph and all equipment necessary for metallographic preparation of specimens are located in the Department of Metallurgy of The Ohio State University. 127

TABLE 2

SPECIMENS CHOSEN FOR METALLOGRAPHY AND MICROSCOPY

Test Assigned No. & Actual Test Nos. Test Duration Type Cycles 1020 4340 52100

I 10,000 *1 **(46) t(49) 13 (47) (50) 25 (51) (48)

I 20,000 2 (24) (8) 14 (9) (25) 26 (10) (26)

I 50,000 3 (5) (21) 15 (6) (22) 27 (23) (7)

I 70,000 4 (11) (17) 16 (12) (19) 28 (20) (13)

I 100,000 5 m (14) 17 (44) (41) 29 (45) (16)

I 200,000 6 (27) (30) 18 (31) (28) 30 (32) (29)

I 500,000 7 (39) (33) 19 (34) (37) 31 (35) (38)

II 100,000 8 (55) (52) 20 (62) (53) 32 (60) (57)

III 100,000 9 (104) (76) 21 (77) (71) 33 (78) (75)

IV 100,000 io' (106) (85) 22 (86) (80) 34 (105) (81)

V 100,000 11 (91) (88) 23 (89) (95) 35 (93) (90)

VI 100,000 12 (103) (100) 24 (101) (98) 36 (99) (102)

Assigned No.

Actual test no. used for Metallography ^Actual test no. uBed for SEM %

128

View % Die. Fretted Region

Slip

Axis of Specimen Specimen -J L 4x4

Fretted Region

FIGURE 17: Metallographic Sectioning Orientation: Trans­ verse to Slip. This Orientation Was Not Adopted.

•_ Slip VI '

-- U

Specimen

FIGURE 18: Metallographic Sectioning Orientation: Parallel to Slip. This Orientation was Adopted for all Studies. 129

% Dla. Fretted Surface

Studies taken at cross-section of specimen, normal to sectioned surface, adjacent to fretted area.

FIGURE 19; Metallographic Study of Sectioned Specimen. 130

G. Scanning Electron Microscopy

As with metallography, one specimen of each material for each of the VI test types was prepared for SEM exami­ nation, a total of 36 specimens. Table 2 lists the specimens selected. Prior to SEM investigation, low-magnification (13x) metallographic surface studies were taken on a Unitron Series N Metallograph with a 35 mm camera attachment, using Kodak 35 mm TRI-X Pan film. These low-magnification studies provided a qualitative overview of the fretted specimens, and gave a clearer assessment of surface fretted with both smooth and grooved shoes. All specimen surfaces (prior to low-magnification metallograph and SEM viewing), were cleaned to remove accumulated oxides, dirt and debris in the following manner:

1. Place acetone on cellulose nitrate tape (replicating tape). 2. Place tape onto fretted surface. Keep in place 3-5 minutes. 3. Remove tape carefully so that oxides and foreign material are transferred to the tape. 4. Final clean specimens with acetone in ultra­ sonic cleaner. 131

Microscopic studies were made on an International Scientific Instrument Super II Scanning Electron Micro­ scope at 1400x magnification, typically, using Polaroid Type 55/Positive-Negative Land film. SEM views were taken at or near the geometric center of the fretted region. Selected stereo-photomicrographs were made of each of the 3 materials, both virgin and as-fretted. The scanning electron micrographs are oriented so that the slip direction is uniquely positioned, as shown in Figure 20. The Unitron Metallograph and the SEM are located in the Department of Metallurgy of The Ohio State University. 132

r"

Specimen

hi Die. Fretted Surface

FIGURE 20: Scanning Electron Microscope Study of Fretting-Wear Specimens. CHAPTER VIII

EXPERIMENTAL RESULTS

Introduction

Fretting-wear, in this Thesis, is measured by "normal approach," the net displacement toward each other of the two parts of a joint subjected to fretting-wear. Although normal approach is the key parameter in assess­ ment of fretting-wear, other parameters are also of interest. The design engineer must be aware of the in­ fluence of changes in loading, pressure, surface topography, bulk temperature and crack nucleation, since any of these may be significant in service-life prediction. Each important parameter is assessed in terms of its effect upon normal approach due to fretting-wear. i Additional supporting data are included in the Appendixes * of this Thesis. The subsections of this chapter include:

A. Summary of Results 6. Normal Approach - General Results C. Normal Approach and Surface Roughness D. Normal Approach and Normal Load or Pressure

133 134

E. Normal Approach and Axial Preload F. The Physical Model G. The Statistical Model H. Metallography I. Scanning Electron Microscopy

A. Summary of Results

1. Normal approach due to fretting-wear between smooth-faced shoe/specimen pairs was approxi­ mately one-half the normal approach due to fretting-wear between the same type of specimen and a grooved shoe. This was true for SAE 1020, 4340 and 52100 steel specimens under both com­ pressive and tensile axial preloads. The ex­ perimentally-obtained values of specific and volumetric wear rates confirmed this observation.

2. The "softer" steels produced, in most instances, greater fretting-wear under the same conditions than did a "harder" steel. However, normal approach due to fretting-wear between SAE 52100 grooved shoe/specimen pairs was approximately equivalent to normal approach between SAE 1020 smooth shoe/specimen pairs, over a period of 100,000 cycles. 135

3. The higher wear rates found for all grooved shoe combinations were probably due to the groove geometry which assisted in the removal of loosened debris and oxides. Shoe grooves oriented transversely to slip direction pro­ moted faster removal of loosened interfacial material.

4. Normal approach due to fretting-wear between smooth-faced shoes and specimens can be closely approximated as a linear function of cycles from origin to test endpoint. This was true for all materials and for both compressive or tensile preloads.

5. The correlation between relative humidity and rate of fretting-wear was not conclusive. There* was some tendency for increased fretting-wear at higher humidity values for SAE 1020 steel in test type I at the 100,000 cycle level, but this tendency was not observed for SAE 4340 nor 52100 steel.

6. Specific wear rates, at the 100,000 cycle level,

were in close agreement with those obtained from the Rabinowicz-Stowers Nomogram (74) for all materials and test types. 136

7. Normal approach was computed from theoretical sources and compared with normal approach de­ veloped from actual fretting-wear tests on SAE 1020, 4340 and 52100 steels. One basis of comparison was the rate of normal approach with respect to surface roughness. During the initial 10,000 cycles of fretting-wear, the normal approach of SAE-1020 steel was approxi­ mately the same as normal approach computed theoretically. Beyond 10,000 cycles, the normal approach of SAE 1020 steel, as well as that of SAE 4340 and 52100 steels, exceeded the normal approach computed from theoretical sources.

8. There was a diminution of interfacial pressure during the early stage of each test run, and cyclic interfacial pressure changes throughout each fretting-wear test. The initial pressure decrease was associated with a sharp,increase in profilometric surface roughness, but pro- filometric measurements remained relatively constant thereafter.

9* Estimated actual contact pressure at the shoe/ specimen interface was approximately 2 orders of magnitude greater than the apparent or 137

nominal pressure. This is based upon data developed from the statistical model and Hertzian contact theory.

10. A graph of actual vs. apparent contact pressure for a given test type was found to be a linear function. The slope was approximately equal to the ratio of apparent to actual contact area.

11. Frictional heating at the fretting interface increased the bulk temperature of the specimen enough to produce a significant static load increase in compressively-loaded specimens, and % - - - ' 1 a significant decrease in tensilely-loaded specimens.

12. There was good agreement between the physical model and experimental data for about 50% of the 18 material/test variations. In general, the model predicted that a given value of normal approach would occur in fewer fretting-wear cycles than actually did occur in fretting-wear tests.

13. From the statistical model, the quantity of interacting asperities was found to number initially in the tens of thousands; and to 138

diminish rapidly to a few hundred or thousand

at the conclusion of a typical 100,000 cycle test. The actual contact area, however, remained constant, even though a continually rougher surface was factored into the model.

14. Metallographic studies clearly showed, in SAE 1020 steel specimens, that surface oxides and a deformed substrate microstructure extended from the original surface. There was less sub­ strate deformation in the harder steels (i.e., SAE 4340 and 52100). Crack formation, dis- cernable in SEM studies, was not clearly apparent. Metallographic preparation procedures and microstructural deformation may have obscured these cracks.

15. SEM surface photomicrographs recorded cracks transverse to the slip direction in many of the SAE 1020 specimens, in several of the SAE 4340 specimens, and in very few of the SAE 52100 specimens. Sequential views of SAE 1020 speci­ mens developed for type I tests suggested pro-

* gressive crack propagation by virtue of in- creasingly-wider fissures in the fretted sur­ faces. Specimens preloaded in compression, and 139

fretted with smooth shoe-pairs, Indicated a greater tendency for crack formation than did other configurations.

B. Normal Approach— General Results

Each of the six test types produced a different rate of wear within each family of steels tested. There was, however, a common pattern of fretting-wear rate. Within a specific alloy-family, a smooth-faced shoe produced a normal approach due to fretting-wear approximately one- half that of a grooved-faced shoe with all other conditions being the same. Examining the wear rates using smooth­ faced shoes, compressively-preloaded SAE 1020 specimens (test type 1) were found to wear about 1/3 faster than their tensilely preloaded counterparts (test type II). However, the preload sense had no discernable effect on SAE 4340 or 52100 steel specimens, the wear rates being nearly equally in magnitude for both compressively or ten- silely-preloaded specimens. Normal approach,due to fretting-wear with groove­ faced shoes, found SAE 1020 and 4340 specimens to exhibit similar patterns of fretting-wear. In order of increasing normal approach due to fretting-wear for SAE 1020 and 4340 specimens under any given set of test conditions: 140

a. The smallest wear rate developed with shoes having grooves parallel to slip, and com­ press ively-loaded specimens (test type III). b. The next higher wear rate occurred with the same groove orientation and tensilely-loaded specimens (test type IV), c. The next higher wear rate was observed with shoes having transverse grooves and compressively- loaded specimens (test type V). d. The highest wear was observed for transversely- grooved shoes and tensilely-loaded specimens (test type VI).

The SAE 52100 alloy differed in grooved-shoe wear in that the highest and lowest wear rates were interchanged with respect to the softer steels. That is, the lowest wear rates were observed for transversely-grooved shoes and tensilely-loaded specimens, while the highest wear rates were observed for grooves parallel to slip and com- pressively-loaded specimens. Therefore, in order of in­ creasing wear rate due to grooved shoes, SAE 52100 per­ formed as follows: Test types VI, IV, V and III, respec­ tively. Refer to Figures 21, 22, and 23 for comparative normal approach in each material type, for a fretting-wear period of 100,000 cycles. Figure 21 shows SAE 1020 having the greatest divergence of wear rate at 100,000 cycles X41

(20.5 x 10~4 in); and Figure 23 shows SAE 52100 to have the least divergence (9.8 x 10~4 in). Comparing wear rates among families of steels, normal approach due to grooved-shoe fretting-wear in the SAE 4340 and 52100 steels equalled or exceeded that of smooth-faced shoes in SAE 1020 steel, at 100,000 cycles. In terms of wear rate, therefore, a "softer" steel such as SAE 1020 may under some conditions be "equal" in fretting- wear resistance to a "harder" steel such as SAE 4340 or 52100. The grooves served as an escape conduit for debris and oxide particles that might have otherwise been (in a smooth-faced joint) trapped interstitially. The interfacial pressures changed somewhat during each test configuration as the result of a continuing manual effort to maintain constant cyclic slip amplitude of motion. The amplitude of slip was monitored continu­ ously, and its magnitude was maintained constant as follows: as slip tended to decrease, normal pressure was decreased; as slip tended to increase, normal pressure was increased. Researchers have reported that the majority of sur­ face damage occurs in the initial stages of fretting-wear, and that the interfacial buildup of oxides and debris accommodates the relative motion as shear within its layers,

» 142 effecting a reduction in actual cyclic slip amplitude (41). Such effects were noted in the fretting-wear tests in this Thesis. Both smooth and grooved-faced shoes re­ quired reduction of normal pressure at the onset of each test, suggesting a rapid ch'ange in surface character and buildup of interfacial material with consequent effect on cyclic slip amplitude. Grooved shoes produced higher wear rates than did smooth shoes, but specimens experienced lower interfacial pressures from grooved shoes than they did from smooth shoes. The fact that smooth-faced shoes did not exhibit the high fretting-wear rates produced by groove-faced shoes, does not preclude the possibility that effects other than pressure reduction and debris dis­ charge did occur. Debris entrapment, at generally higher normal loading in the contact zone of smooth-faced shoes, may cause substrate deformation leading, perhaps, to crack nucleation and propagation. Such effects were, in fact, noted more clearly in specimens subjected to smooth­ faced shoes, and this will be discussed later in this chapter. Type 1 tests developed fretting-wear data, both in­ crementally and continuously, to 500,000 cycles. These tests used smooth-faced shoes and compressively-preloaded specimens and were designed for progressive fretting-wear investigation at levels of 10K, 20K, 50K, 70K, 100K, 200K 143 and 500K fretting cycles. Refer to Figure 24 for the com­ parative* normal approach data from the three materials used in Type X tests. It may be noted, in Figure 24, that a straight line has been superimposed on each of the three graphs, drawn from origin to the 500,000 cycle endpoint. Actual test data deviates only slightly from the super­ imposed line. Data in test type IX, as well, displayed a nearly straight-line graph as shown in Figures 21, 22, and 23. Thus, linear design graphs or equations may con­ ceivably be employed for prediction of fretting-wear life as a function of allowable normal approach if smooth/smooth surfaces under compressive or tensile preloading are being used. Normal approach, in this research, was measured by two LVDT transducers in tandem, as illustrated in Figure 14. The measured fretting-wear produced between a given specimen and its shoe-pair during a fretting-wear cycle was found to be approximately one order of magnitude greater than normal approach computed either from statistical or Hertzian theory. "Normal approach" is a general termi­ nology also used to describe deformation that occurs due to contact between two spherical bodies under static load with no cyclic slip, including the case of static load induced deformation between asperities whose number and contact area distributions may be described only on a statistical basis. It is emphasized that neither Hertzian theory nor statistical descriptions include the cumulative effects of cyclic interaction of asperities, such as ad-

* hesion, macro-displacement, surface fatigue and abrasion. Neither do these theories include a consideration of the "running-in" period during which the "high spots" are re­ moved by adhesive wear and plastic deformation, nor tem­ perature effects, which can cause significant variations in wear rates. Refer to Table 3 which compares normal approach due to fretting-wear with normal approach com­ puted from statistical and Hertzian theory. Normal approach -4 due to fretting-wear averaged 17 x 10 inch for all test types' at 100,000 cycles, ranging from a minimum of 5.2 x 10”4 in (SAE 52100, test type I), to a maximum of 32.9 x 10*"4 in (SAE 1020, test type VI). See Appendix M for a sample calculation of normal approach for both statistical and Hertzian theory. Relative humidity was computed just prior to each test run. Sufficient test data were not accumulated to clearly correlate percent relative humidity with wear rate. There was a slight indication that higher wear rates developed in SAE 1020 steel specimens concurrently with higher relative humidities (test type I). This weak cor­ relation did not, however, seem to apply to other families of steels. Better control of ambient conditions would be «

145 required to investigate the effects of humidity on wear rate. Some researchers (36,41,102) have reported that less fretting-wear occurs in high-humidity air than in dry air. Refer to Table 4 for a summary of fretting-wear vs. percent relative humidity observed during the course of this dissertation. The data presented in this Chapter were obtained from instrumentation that was carefully monitored and ad­ justed as required to provide reliable test data. Particu­ lar care was taken to minimize uncertainties in equipment performance and to maximize repeatibility of data. As noted in Chapter VII, in the Section on "Testing Procedures and Monitoring Devices," and as further detailed in Appendix F, organized and systematized procedures were followed prior to, during and after each test run. Those procedures included monitoring and adjusting the null point of each transducer prior to each test and monitoring con­ sistency of gain in all amplifier channels. Those measures, performed on a methodical basis, were taken to minimize some inconsistencies found in the initial assemblage of test components. Normal load data account for the largest error among all data collected due to the continuous need to monitor and manually adjust normal load between shoe and specimen to maintain a constant cyclic amplitude of slip. (The need and desirability for an automatic slip "feedback” 146

system is noted in Chapter XI: "Suggestions for Future Research.") The best indicator of the careful and con­ tinuous attention given to the manual normal load adjust­ ments in this research can be found in the recorder print­ out data in which slip amplitude is shown to be nearly constant throughout a given test run. An example of the generally constant value of slip may be seen in Figure 86 of Appendix I. Representative of the test data found in this re­ search are the data shown in Table 5 for normal approach due to fretting-wear in test type I. The average values and standard deviations are given at 100,000 cycle incre­ ments. Data scatter at these 100K cycle increments are shown in Figure 24. Overall accuracy of test data is a function of the individual accuracy of each component within the measure­ ment system. From Figure 15, the measurement system re­ ferred to is the chain of components between data source and data recording. The recorded data, R, is a function of the n independent variables Uj, u2, u#, . . . , un# where the u's represent the component outputs

R « f(ut, ua, u jf . . .,un) 147

If the component errors are denoted ±Aulf ±Au2, ±Au3, . . . , ±Aun # the absolute error, AR, due to a chain of components, is

9f 3f 3f AR Au, 3Uj Au . + Au,n 3u * 9u. n

The functional relationship that exists between data source and recorded data may be developed from a two-com­ ponent system as follows. Let the two-component system consist of an amplifier in series with a transducer, and having the following designation for components whose in­ accuracies are mutually-exclusive.

E = output I « parametric input as the transducer u} = efficiency of transducer u2 « efficiency of amplifier AUj = transducer component error Au2 ** amplifier component error

Then E «= (I) (u,) (u2) X48

Therefore 4R - 4u, 357 + 4U* 3*7

AR » Au,(lu2) + Au 2 (Xu ,) and the absolute error, AR, may be computed knowing com­ ponent error, Au, and efficiency of transmission, u.

(1) For the axial preload load cell transducer: I «= 500 pounds u, « u2 ■ u3 « 0.98 Au, * 0.2% error in load cell

Au 2 » 3.0% error in amplifier Au, = 0.3% error in recorder

E = Iu,u2u9 AR = Au,(Iu.u.) + Au,(Iu,u.) + Au (lu u ) 1 * 5 213 312 AR «* .002(500) (- 98)2 + .03 (500) (.98)2 + .003 (500) (.98)2 AR - 500(.98)2(.002 + .03 .003) AR « 17 lb.

Uncertainty of axial preload data = 500 ±17 lb. 149 (2) For the normal-load load cell transducer: I * 500 pounds

ut " Uj “ u, 8 0.98 Au, - 0.2% error in load cell Au2 » 3.0% error in amplifier Au, ■ 0.3% error in recorder Since these data are identical to data for the axial-preload load cell, Uncertainty of normal load data « 500 ± 17 lb.

(3) For the slip amplitude LVDT transducer: I ■ 0.00375 in peak-to-peak slip amplitude Uj ■ u2 ■ u, ■ u% ■ 0.98 Au, * 1.25% error in LVDT Au2 •* 3.0% error in amplifier Au, « 2.0% error in peak meter Au^ ** 0.3% error in recorder

E = Iu,u2u,ul|

AR - Au, (IUjU jU^) + Au2 (IUjU jU^) + Au, (Iulu2ui>) +

A u ^ ( I U j U j U,)

AR ■ 0.00375(.98)5{.0125 + .03 + .02 + .003) AR ** 0.00023 in

*

Uncertainty of slip amplitude data - 0.00375 ± 0.00023 in 150

(4) For the normal approach LVDT transducer: I *> 0.010 in full-scale displacement

u,1 2 u„ = u 3 =* 0.98 AUj a 1.25% error in LVDT

Au2 “ 0.75% error in demodulator Au, 0.3% error in recorder

E a Xu u u i 2 3 AR » Au,(Iu2u,) + Au2(Xutu9) + Au,(Iu,u2) AR - 0.010(.98)2(.0125 + .0075 + .003) AR a 0.00022 in

Uncertainty of normal approach data n 0.010 ± 0.00022 in 151 TABLE 3

NORMAL APPROACH DUE TO FRETTING-WEAR VS. NORMAL APPROACH COMPUTED FROM STATISTICAL AND HERTZIAN THEORY

r Normal Ap proach** Statistical Hertzian Type Material RMS* Actual Gauss. Expon. Sph/Sph Sph/Plane

I 1020 150 16. 1.41 1.51 1.38 1.09 I 4340 102 9.3 0.94 1.01 0.93 0.74 I 52100 31 5.2 0.28 0.30 0.27 0.21

II 1020 136 12.3 1.28 1.37 1.14 0.90 II 4340 105 9.8 0.99 1.06 0.70 0.56 II 52100 30 5.6 0.28 0.30 0.19 0.15

III 1020 400 28.6 3.84 4.01 2.38 1.89 III 4340 231 13.9 2.20 2.33 1.45 1.14 III 52100 140 15.0 1.32 1.41 0.95 0.74

IV 1020 385 30.3 3.69 3.87 2.30 1.83 IV 4340 245 15.9 2.34 2.47 1.90 1.50 IV 52100 142 12.3 1.34 1.43 0.92 0.73

V 1020 181 32.2 1.71 1.82 1.57 1.25 V 4340 87 17.0 0.82 0.89 0.44 0.35 V 52100 48 13.1 0.42 0.45 0.33 0.27

VI 1020 160 32.9 1.51 1.61 1.19 0.94 VI 4340 111 26.2 1.05 1.12 0.73 0.58 VI 52100 33 11.5 0.30 0.32 0.21 0.17

*RMS surface roughness values are In. x 10~^

**Normal Approach evaluated at 100,000 cycles of fretting-wear. Units are in. x 10”^. 152

TABLE 4 NORMAL APPROACH DUE TO FRETTING-WEAR VS. PERCENT RELATIVE HUMIDITY*

1020 4340 52100 Type Norm App** % RH Norm App % RH Norm App % RH

I 16.1 63.5 9.3 64.0 5.2 63.8 II 12.3 67.3 9.7 71.8 5.6 70.3 III 28.6 67.3 13.9 67.3 15.0 67.7 IV 30.3 69.3 15.9 60.5 12.3 66.0 V 32.2 68.5 34.0 69.7 13.1 73.3 VI 32.9 72.0 26.2 63.0 11.5 63.0

*Test Period: 20 May 1977 through 8 August 1977.

hit Normal Approach evaluated at 100,000 cycles of fretting- wear. Units are in x 10~4. 153

TABLE 5 NORMAL APPROACH DUE TO FRETTING-WEAR IN TEST TYPE I: AVERAGE VALUE • AND STANDARD DEVIATION

Cycles of Average Value Fretting- of Material Wear Normal Approach Standard Deviation

100K 16.1 x 10"4 in 3.31 x 10”4 in 200 34.7 5.6 1020 8.7 steel 300 55.7 400 71.2 13.2 500 87.8 17.0

100 7.3 2.7 200 19.3 3.2 4340 300 31.7 0.66 steel 400 40.7 0.36 500 49.8 0.0

100 5.2 1.3 200 9.6 0.7 52100 300 12.4 0.9 steel 400 15.9 1.1 500 18.9 1.1 0 10 20 30 40 50 60 70 80 90 100 No. of Cycles, Thousands FIGURE 21: Normal Approach: SAE 1020.

VI

III

Str. Line

FIGURE 22; Normal Approach: SAE 4340

30* III

VI

Str. Line

FIGURE 23: Normal Approach: SAE 52100, 100 Legend

O : SAE 1020 87.8 & : SAE 4340 O : SAE 52100

SAE 1020

Avg. Value for All Tests (Typical).

SAE 4340

< 4 0

SAE 52100 18.9

0 20 50 70 100 200 300 400 500 No. of Cycles, Thousands in FIGURE 24 Normal Approach: Type I Tests. in 156

C. Normal Approach and Surface Roughness

Normal approach exceeded the RMS surface roughness by approximately one order of magnitude at the 100,000 cycle level. Longer test durations showed higher ratios between normal approach and roughness. For example, in * test type X, at 100,000 cycles, the normal approach of SAE 1020 steel was 16.1 x 10“4 in; and the corresponding RMS roughness was 1.5 x 10~4 in. Hence, the normal approach/RMS ratio was 10.7 to 1; that ratio increased to 46.5:1 at 500,000 cycles. Table 6 lists the average sur­ face finish of each specimen at the 100,000 cycle level; and Table 7 gives a full listing of normal approach vs. surface roughness (NA/RMS) at 100,000 cycles of fretting- wear. Surface roughness (as measured progressively in test type I) increased quite sharply within the initial 10,000 to 20,000 cycles of operation, and thereafter climbed at a moderate rate. Refer to Figure 25 for an overview of surface roughness relative to normal approach and cycles of fretting-wear over a period of 500,000 cycles of fretting-wear. Because of the relatively high ratio of normal ap­ proach to surface roughness (NA/RMS), and the relatively constant profilometric values of the roughened fretted surface beyond the 100,000 cycle level, it appears that X57 the volume of material displaced at the surface could be closely approximated by the product of normal approach and nominal contact area. This procedure was followed in computing volumetric and specific wear rates. The results are in good agreement with estimates given by a Nomogram developed by Rabinowicz and Stowers (74). Refer to Tables 8 and 9 for comparative values of specific wear rate and volumetric wear rate, respectively, at the 100,000 cycle level. In the previous section on "General Results," Table 3 compared actual with computed theoretical normal approach at the 100,000 cycle wear level. The computed data was based partly on profilometrie measurements and statistical theory. A more graphic illustration of the order-of- magnitude discrepancy between true and theoretical normal approach is given in Figure 26. This Figure shows a rather shallow increase in normal approach with respect to surface roughness for both statistical and Hertzian theories. It is noted that the normal approach for SAE 1020 steel parallels the statistical and Hertzian values of normal approach through the 10,000 cycle level. However, SAE 1020, as with S/VE 4340 and 52100, has a marked rise in normal approach beyond the 10,000 cycle locus.

Surface profilometric measurements are shown in Table 6. These were taken at the conclusion of a 100,000 *

158 cycle test. The pattern of measurements was designed to obtain a representative roughness range for the fretted surface. Many of the specimen surfaces fretted with grooved * shoes developed a mixture of oxide and metal debris that partially obscured the "ridges" produced by the shoes. This obscurement was additionally complicated by a pro- filometer stylus stroke of 5 mm (0.2 in) which gave rough­ ness values that reflected, in part, stylus traversal across both the fretted and some portions of non-fretted surface. Grooving, in the virgin shoe, produced a net decrease in nominal shoe contact area of 15%, and such loss could produce, theoretically, a nominal pressure increase of 17.5%. Comparing grooved and smooth-faced shoes, there was increased opportunity for loose debris and oxides to escape from a grooved interface. With shoe grooves oriented transversely to slip direction, the slip amplitude assisted in collection of loose debris, because each groove width was dynamically increased by the added factor of slip. Thus, shoes having transversely-oriented grooves of width 0.005 in found their effective groove width, due to slip, to be increased to 0.00875 in, a 75% enlargement. Slip amplitude was not sufficient, however, to displace the grooves such that all debris could (theoretically) be collected; a "dead" space of 0.0213 in remained between each groove. In Chapter VII, it was noted that the original concept for a grooving geometry was to assure full coverage of debris from the specimen, but practical considerations prevented the achievement of this goal. Summarizing, grooved shoes permitted greater flow of loose material than did non-grooved shoes. However, the rate of discharge apparently exceeded the volumetric capacity of the shoes' grooves, thereby increasing interfacial pressures locally which, in turn, reduced slip amplitude. In order to maintain a constant cyclic slip amplitude, contact pressure was constantly monitored and manually reduced as necessary. Pressure reduction was necessary in all fretting-wear tests employing grooved-shoes as well as smooth shoes. Such pressure reductions were required in the initial stages of each fretting-wear test. Shoe grooves oriented transversely to the slip direction permitted greater volumetric flow of debris and oxides away from the fretting interface than did grooves parallel to the slip direction. This may be attributed to the greater effective groove width of the transverse grooves as a result of slip, as described above. 160

TABLE 6 RELATIVE ROUGHNESS— ALL TESTS

Test 1020 4340 52100 Type Virgin Center Virgin Center Virgin Center

I 9.2 148/152 9.8 104/99 9.6 31/31 II 9.2 138/134 11.0 105/106 8.3 30/31 III 19.0 406/391 8.5 231/231 10.4 141/140 IV 12.7 394/375 9.0 244/246 9.3 143/141 V 13.1 182/181 10.3 88/87 9.8 48/48 VI 15.8 159/161 9.9 110/113 7.6 33/34

Note: 1. Values at "Center" averaged over 100,000 cycles* Units are RMS microinches (in x 10“6). 2. Center value on L.H. side of slash includes center of specimen's fretted surface. 3. Center value on R.H. side of slash does not include center of specimen's fretted surface.

Type I: Smooth/Smooth; Compression Preload; 10K, 20K, 50K, 7OK, 100K, 200K and 500K Cycles Type II: Smooth/Smooth; Tension; 100K Cycles Type III: Vertical Grooves; Compression; 100K Cycles Type IV: Vertical Grooves; Tension; 100K Cycles Type V: Transverse Grooves; Compression; 100K Cycles Type VI: Transverse Grooves; Tension; 100K Cycles 161

TABLE 7 NORMAL APPROACH AND SURFACE ROUGHNESS

1020 4340 52100 Type RMS NA NA/RMS RMS NA NA/RMS RMS NA NA/RMS

I 1.5 16.1 10.7 1.0 9.3 9.1 0.3 5.2 16.8 II 1.4 12.3 9.1 1.1 9.8 9.3 0.3 5.6 18.7 III 4.1 28.6 7.1 2.3 13.9 6.0 1.4 15.0 10.6 IV 3.9 30.3 7.8 2.4 15.9 6.5 1.4 12.3 8.6 V 1.8 32.2 17.7 0.9 17.0 20.0 0.5 13.1 27.3 VI 1.6 32.9 20.7 1.1 26.2 23.8 0.3 11.5 35.0

Note: 1. Normal Approach (NA) and RMS surface roughness evaluated @100,000 cycles. -4 2. Units are in x 10 162 TABLE 8

SPECIFIC WEAR RATES: 100,000 CYCLES*

10 20 4340 52100 Type Thesis Ref (74) Thesis Ref (74) Thesis Ref (74)

I 22.0 29.5 13.0 14.1 7.5 7.0 II 17.8 17.6 19.8 21.0 11.9 10.6 III 51.0 56.0 34.0 35.0 37.0 39.6 IV 55.0 63.0 29.0 35.0 34.0 35.0 V 55.0 63.0 60.0 77.0 27.0 28.0 VI 70.0 77.0 65.0 70.0 30.0 35.0

Units are in3/in-lb x lO"’*'*'.

TABLE 9

VOLUMETRIC WEAR RATES: 100,000 CYCLES

1020 4340 52100 Type A* B** A B AB

I 1.46 8.1 0.85 4.7 0.47 2.6 II 1.12 6.2 0.88 4.9 0.50 2.8 III 2.6 14.0 1.2 6.9 1.4 7,5 IV 2.7 15.0 1.4 7.9 1.1 6.2 V 2.9 16.0 1.5 8.5 1.2 6.6 VI 3.0 16.0 2.4 13.0 1.1 5.8

*A - in3/min x 10“6 **B ■ in3/cycle x 10"^ 200

SAE 1020 (87.8,1850

160 CM iO x (49.8,145)

• 120 a aia 0 l> 0 £ 0U 0 h 0 tfi w (18.9,62)

40 SAE 52100

0 10 20 30 40 50 60 7080 90 100 Normal Approach, In. x 1 0 " ^

FIGURE 25; Normal Approach vs. Surface Roughness: Test Type I. 163 210

Hertz (Sphere/Plane) Exponential Distribution

180 Hertz (Sphere/Sphere) Gaussian Distribution

1020

150

K 120 at ata *| 90 9 <§ O at 4a

52100 10

i - 6 ,-5 10 10 Normal Approach, Inches FIGURE 26: True and Theoretical Normal Approach vs. Surface Roughness: Type I. ot 165

D. Normal Approach and Normal Load or Pressure

All specimens experienced a rapid diminution of normal load at the contact interface within, approximately, the first 10,000 cycles of fretting-wear; fluctuations pre­ vailed thereafter. Specimens fretted with smooth-faced shoes experienced higher peak contact loading than did similar specimens matched with grooved shoes. Figure 27 is a graphical record of normal contact load variations for each of the materials over a period of 500,000 cycles (test type I). Figures 28, 29 and 30 show the variation in normal load, within each material type, for a period of 100,000 cycles. Recall that the variations in normal load occurred because it was thought to be essential to maintain a constant slip amplitude throughout each test. To do this, manual adjustment of normal contact load was necessary. SAE 4340 steel experienced the widest divergence of normal load adjustment within 100,000 cycles: 289 pounds. The smallest divergence over the same test duration was indicated by SAE 1020 steel: 177 pounds. Normal load was continuously recorded for each fretting-wear test. Normal load was converted to contact pressure through use of statistical descriptions of surface profile and Hertzian contact stress theory. If the contact ft

166 interface of shoe and specimen had been ideally flat, smooth-faced shoes would have developed nominal fretting pressures of 10,000 psi at startup, and groove-faced shoes would have produced an initial contact pressure of 11,750 psi, a 17.5% increase over smooth shoes. With real sur­ faces, however, actual area of contact can be much smaller than the nominal contact area, and such surfaces in contact will develop correspondingly higher local pressures. Using statistical surface descriptions and Hertzian con­ tact stress theory, pressures in the fretting zone were found to be approximately 2 orders of magnitude greater than nominal pressures. A summary of the pressure ranges developed from each of these contact theories, for all tests, is as follows:

a. Nominal 1. Smooth-faced shoe: 10,000 psi 2. Groove-faced shoe: 11,750 psi b. Hertzian Theory 1. Sphere/Sphere; 1,500,000-2,200,000 psi

2. Sphere/Plane: 1,000,000-1,400,000 psi c. Statistical Theory 1. Gaussian Distribution: 850,000-1,200,000 psi 2. Exponential Distribution: 1,400,000-1,900,000 psi 167

It was observed that as fretting-wear progressed, the specimen surface roughened and radii of asperities increased. "Actual" contact area, however, remained essen­ tially constant based on statistically-described surfaces, and nominally constant on surfaces modeled by Hertzian contact theory. Summarizing, for all surfaces analyzed:

a. Nominal Contact Area 2 1. Smooth-faced shoe: 0.0490 in 2 2. Groove-faced shoe: 0.0415 in

b. Hertzian Model of Actual Contact Area _4 2 1. Sphere/Sphere: 1.40 - 3.20 x 10 in -4 2 2. Sphere/Plane: 2.80 - 5.80 x 10 in c. Statistical Model of Actual Contact Area -4 2 1. Gaussian Distribution: 4.81 x 10 in -4 2 2. Exponential Distribution: 3.00 x 10 in

For the statistical model, actual contact area estimates were based on an assumed distribution of asperities, either gaussian or exponential. To apply Hertzian contact stress theory to a nominally-flat interface, use was made of a statistical approach for obtaining the number of interacting asperities. Further, a statistical estimate of asperity radius was obtained from the Tallian model (96), shown in Figure 11 of Chapter VI. It is to be noted that (a) number of interacting asperities, and (b) radius of the asperities, 168 are both a function of surface roughness. During the course of a 500,000 cycle type I test on SAE 1020 steel, —6 surface roughness varied from 10 x 10 in RMS to approxi­ mately 210 x 10‘6 in RMS. This range of roughness is given, with associated contact pressures, in Table 10. A full listing of nominal and "actual" fretting pressures for each material, at the 100,000 cycle level, is given in Table 11. "Actual" contact areas were nearly constant for statistically-described surfaces. Therefore, they were a nearly constant multiplicative function of the nominal contact area. In terms of pressure, too, "actual" contact pressures were a linear function of nominal contact pressure. These relationships are illustrated in Figure 31. Surface roughness was measured by Frofilometer at seven test durations in type I: 10K, 20K, 50K, 70K, 100K, 200K, and 500K cycles. Those durations were selected on the basis of a literature survey that suggested stages of wear in terms of fretting cycles. For purposes of this Thesis, the following assumed fretting-wear stages are proposed as a guide for progressive fretting-wear measure­ ments : 169

a. 10,000 cycles...... Wearing In b. 10,000-20,000 cycles... 1st Stage (Varying Coeff. of Friction) c. 20,000-50,000 cycles... 2nd Stage (Constant Coeff. of Friction) d. 50,000-100,000 cycles... 3rd Stage (Steady-State Fretting Wear)

Although coefficients of friction were not measured, Figure 25 indicates that the assumed stages of fretting-wear did develop within the initial 100,000 cycles of testing. Further, although cyclic replication of surface roughness was not apparent, some type of replication may possibly f be reflected in pressure fluctuations over the course of a fretting-wear test. Refer to Figures 32, 33, and 34 which compare variation in surface roughness with pressure over 500,000 cycles of fretting-wear. Fluctuating pressure, which resulted from continuous adjustment to maintain a constant slip amplitude, is probably due to debris buildup and dispersal. It is reasonable to hypothesize that the several maxima and minima along the.pressure locus reflect the effects of significant volumetric changes in debris entrapped at the fretted interface. To test this hypo­ thesis, more selective surface measurements need to be taken in future research, using the pressure locus as a guide. 170

The variation in pressure, with respect to normal approach, indicates some commonality among the three steels tested in type I tests. Refer to Figure 35, where it is noted that each material exhibits a major normal pressure fluctuation, followed by several smaller pressure fluctuations. There is a possibility that Figure 35, * as well as Figures 32, 33, and 34 could assist in future selection of test intervals that would provide a clearer determination of fretting-wear stages. TABLE 10

CONTACT PRESSURES VS. SURFACE ROUGHNESS: TEST TYPE I, SAE 1020

RMS Normal Total Number Asperities Actual Press .: psi. millions Roughness, Load in Contact, thousands Statistical Hertzian Nominal Press., microinches lb Gaussian Exponential Gauss. Expon. Sph/Sph Sph/Plane psi

10 457 53. 29. .951 1.525 2.02 1.29 9150

30 456 5.9 3.2 .950 1.520 2.02 1.29 9140

60 440 1.47 0.8 .915 1.465 2.06 1.31 8800

90 432 0.65 0.36 .899 1.440 2.00 1.27 8640

120 . 430 0.37 0.20 .895 1.435 1.99 1.27 8600

150 462 .0.24 0.13 .960 1.540 2.03 1.30 9240

180 498 0.16 0.09 1.040 1.660 2.14 1.37 9960

210 (500 0.12 0.07 1.040 1.660 2.10 1.34 10000 (approx.) TABLE 11 APPARENT VS. ACTUAL NORMAL FRETTING PRESSURE: 100,000 CYCLES

Normal RMS Actual Press.: psi, millions Test Type Material Load, Roughness, Statistical Hertzian Nominal Press., lb microinches ' Gauss. Expon. Sph/Sph Sph/Plane psi

I 1020 490 150 1.020 1.63 2.08 1.33 9800 T 4340 479 102 .995 1.60 2.07 1.32 9600 I 52100 462 31 .980 1.54 2.04 1.30 9250

II 1020 463 136 .960 1.54 1.78 1.27 9250 II 4340 330 105 .685 1.10 1.79 1.14 6600 II 52100 315 30 .655 1.05 1.74 1.11 6300

III 1020 375 400 .915 1.47 1.70 1.10 8850 III 4340 268 231 .655 1.05 1.73 1.10 6300 III 52100 272 140 .655 1.07 1.80 1.15 6400

IV 1020 368 385 .900 1.44 1.70 1.08 8650 IV 4340 368 245 .900 1.44 1.92 1.22 8650 IV ' 52100 247 142 .605 .970 1.77 1.12 5800

V 1020 388 181 .945 1.52 2.08 1.34 9150 V 4340 190 87 .465 .745 1.56 1.00 4500 V 52100 330 48 .805 1.30 1.83 1.17 7750

VI 1020 313 160 .765 1.23 1.91 1.21 7350 VI 4340 270 111 .670 1.06 1.80 1.14 6350 VI 52100 255 33 .620 1.00 1.77 1.12 6000 600

1020

550

4340 515 500

478

52100 438

400 Too 200 300 400 500 No. of Cycles, Thousands

FIGORE 27; Normal Load vs. Fretting-Wear Cycles: Type I. 173 Normal Load, Founds 450 550 550 150 150 250 450 250 150 350 350 250 450 550 350 0 0 I VI III 10 FIGURE 29: Normal Load: SAE 4340. SAE NormalLoad: FIGURE29: IUE2: omlLa: SAE1020. NormalLoad: FIGURE28: IUE3: omlLa: SAE52100 NormalLoad: 30:FIGURE 20 06 08 90 80 70 60 30 N. fCce, Thousands Cycles, of ■ No. 40 50 VI VI III I IV III

100 174 Actual Pressure, psi, Thousands 1100 1000 1050 950 900 850 8 IUE3: Actualvs. Apparent Pressure:FIGURE31:TypeI Test. paetPesr, s, Thousands psi, Pressure, Apparent SAE 1020 9 slope SAE 52100 area 102:1 actual apparent ' ; SAE 4340 481 x 10 049 inAREA

10“3 in'10“3 175 13 176 200 RMS Roughness

K 150 11

2 100

Pressure Actual Actual Pressure, psi x 10^ 100 200 300 500 No. of Cycles, Thousands FIGURE 32; Roughness and Pressure vs. Cycles: SAE 1020.

200 12 RMS 150 N. Roughness

100 ■

Pressure

0

FIGURE 33s Roughness and Pressure vs. Cycles: SAE 4340.

200

150 Pressure

100 RMS ✓ Roughness

0

FIGURE 34: Roughness and Pressure vs. Cycles: SAE 52100. Actual Pressure, psi, millions 0.8 0.9 1.0 1.1 1.2 0 (18.0,1.07) V_' 020 10 FIGURE 35: Pressure vs. Normal Approach: Type I TypeTests. Pressure vs.Normal Approach:FIGURE35: SAE 52100 SAE 040 30 Normal Approach, In. x 10“* x In. Approach, Normal 50 SAE 1020 SAE (49.8,0.9) 070 60 090 80 (87.8,1.0)

100 177 178

E. Normal Approach and Axial Preload

All test specimens were statically preloaded along their longitudinal axis, either in compression or tension. The static preload was nominally 500 pounds (10,000 psi). Within the initial 10,000 to 20,000 cycles of fretting- wear, recorded data showed a marked change from the preset value. Specimens preloaded in compression showed an increase in loading; specimens loaded in tension experienced a decrease in preload. It was assumed, among other possi­ bilities, that such changes were principally caused by an increase in the specimen's bulk temperature, due to frictional heat generated at the fretting interface, where the average velocity of sliding was 0.019 ft/sec. Thermocouples were placed on specimens of each of the 3 test materials during a typical 100,000 cycle test run. Results of the 3 temperature investigations are shown.in Table 12. To confirm the findings given in Table 12, the specimen in test no. 14 was not removed from its fretting fixture until a period of 24 hours had elapsed. The load change of the previous .day's test had fully disappeared, confirming that bulk temperature increase was responsible for changes in axial loading during the course of a test run. Figure 36 illustrates the variation in normal approach with respect to axial preload over 500,000 cycles. These tests are redrawn in Figure 37 to show cyclic variations in 179 load. Figures 38, 39, and 40 show axial preload as a func­ tion of cycles of operation for all tests in each family of steels. The aforementioned load change due to preload sense and bulk temperature rise is evident in Figures 38, 39 and 40. Collins (17), in his work on fretting-fatigue, em­ phasizing stress-field effects, found that a static com­ pressive stress in the specimen during fretting will pro­ duce fatigue deunage greater than in a specimen subjected to static tensile stress. In this research, either static compression or tension was induced at the shoe/specimen interface in order to measure its effect on fretting-wear (i.e., normal approach). Earlier in this chapter, it was noted that smooth-faced shoes produced nearly equal wear in specimens statically preloaded in compression or tension. An exception occurred with SAE 1020 steel for which static compression produced about 30% greater wear. Fretting-wear data in specimens subjected to grooved-shoes were less conclusive; no pattern of wear, on the basis of preload sense, is evident. Normal approach, due to fretting-wear using grooved shoes, was found to be a function of groove orientation rather than static preload. 180

TABLE 12 BULK TEMPERATURE EFFECTS DUE TO FRETTING-WEAR: TYPE I TESTS

Net Temp., Load Length Test Test No. of Dry Bulk Incr.t Increase, Number Type Material Cycles Bulb AT lb. microinch

14 I 1 0 2 0 100K 77°F +15.5 280 230

15 I 4340 100K 75°F +1 0 . 0 150 123

16 I 52100 100K 75°F +1 0 . 0 205 170 FIGURE36; 500,000AxialPreload vs.Cycles. Normal Approach:Test TypeI— Axial Preload, Pounds 600 550 650 750 800 900 700 850 0 52100 10 4340 20 (18.9,865) 30 omlApoc, n x10”^ x In. Approach, Normal 40 060 50 (49.8,855) 1020 8070 (87.8,805) 90 100 900

SAE 52100 865(52100) 850 856(4340)

805(1020) 800 SAE 1020

750

SAE 4340 700

650

600

550

500 50 100 200 300 400 500 No. of Cycles, Thousands 182 FIGURE 37: Axial Preload vs. Cycles of Operation: Test Type I. a

400 500 Axial Preload, lbs 300 600 800 700 400 500 600 300 800 700 300 500 600 800 900 700 IUE4: Axial SAE52100Preload: 40:FIGURE IUE3: AxialPreload: SAE4340. 39:FIGURE IUE3; AxialPreload: SAE1020. 38;FIGURE II o o Cce, Thousands Cycles, of No. III III III VI II 100 183 184

F. The Physical Model

A physical model for fretting-wear prediction was proposed in Chapter VI. Its form and parameter choices grew out of a study of other wear models and an effort to achieve both accuracy and simplicity. The proposed model was:

T " “F" " (A) (fMN) (SW) where: T ** time to develop a specified normal approach, seconds

C 8 number of cycles of operation

f 8 frequency, cycles per second

V 8 volume 8 (nominal contact area)(normal 3 approach), in t A 8 total slip per cycle, inch

N 8 normal load, pounds 3 SW 8 specific wear rate, in /in-lb

It is convenient to rearrange the equation so that a clear comparison can be made with recorded data. Actual data, in its most direct form, is displayed as normal approach vs. cycles of operation. Rearranging the equation, then, cycles of operation to produce a specified normal approach may be expressed as Total slip per cycle, A, and specific wear rate, SW, are constants for each'test type within each family of steels, therefore

Cm “ ~N~ ; K (A)(SW)

To compare cycles of fretting-wear to produce a given normal approach as predicted by the model, Cm , with actual cycles of operation to obtain the same normal approach, C £1 , a graph of normal approach vs. actual cycles was developed for each of the 18 test configurations. This arrangement is shown in Figure 41 for SAE 1020 steel, test type I. The number of cycles of fretting-wear predicted by the model (Cm) was less than the actual number of cycles of fretting-wear (CB) found to produce a specified value cl of normal approach. On the average, the model predicted that normal approach due to fretting-wear would be achieved in 34% fewer cycles of fretting than actually occurred in testing. The discrepancy between the model and experimental data may be due to the following:

1. Model-predicted fretting-wear (Cm) is linear with respect to number of fretting cycles. Actual fretting-wear (C_) is, in most cases, non-linear. CL 186

2. The value of normal load (N) used in the model was 500 pounds, this being the normal load es­ tablished at the startup of each test. However, from experimental data, the normal load, in nearly all of the fretting-wear tests, decreased on the average by approximately 35% as shown in Figures 28, 29 and 30. Use of a smaller value of normal load in the’ fretting-wear pre­ diction model could help to minimize the dis­ crepancy between the model and experimental data.

Refer to Appendix L for a full tabulation of actual design data, C& , and superimposed model-predicted data, Cm - IUE4i Physical TypeModelI. vs.ActualFretting-Wear:FIGURE 41i SAE1020—

Normal Approach, mils 0 1 5 2 3 4 6 8 9 7 0 oe rdce er C Wear, Predicted Model 100 (A) (N) (SW) o o yls Thousands Cycles, of No. 200 9

culWa. C Wear. Actual 4 300 9 i 395 400 500

8.78 187 188

G. The Statistical Model

In Chapter VI it was noted that contact between a smooth plane and an idealized rough surface gives ah in­ distinguishable difference in asperity distribution as compared to the asperity distribution associated with interaction between two rough surfaces. In Figure 42 the interaction between a smooth plane and rough surface is shown schematically.

2a to 3o

z-d

mean

Actual Idealized

Peak to Valley Normal Approach ■ z-d

Undeformed Asperity Height - d

FIGURE 42: Idealized Asperity Interaction. 189

The relationship between the undeformed asperity height, d, and standard deviation of asperity heights, a, is fundamental to this discussion. That relationship (36) is:

h « -g— « Standardized Separation

Further, probabilistic, or statistical, estimates of contact between gaussian surfaces produces expressions for values of contact area and values for number of contact spots per unit area. In determining each of these values an integral is constructed (32,36). Using standardized vari­ ables such as h = d/a and probability density scaled to give a unit standard deviation, "Integrals of the Gaussian Distribution," Fm (h), are formed. Several integral types recur throughout the statistical development, each being a function of d/o and a. Refer to Appendix A for these Integrals.

The values of h, d, a, and Fmm (h) that are of most interest in this Thesis are given in Table 13. There is initial need, then, to select the value (or values) of h most pertinent to this Thesis. Referring to Figure 42, it is noted that the %(peak-to-valley) value is dimensioned as 2a to 3a. Various sources (53,96,112) state maximum peak-to-valley heights range from 4a to 6 a. The lower 190 value applies to average, well-finished steel surfaces; the higher value is for the asperity model shown in

Figure 11. Examining peak-to-valley heights of 4a and 6 a, it was concluded that a good characteristic value is h * d/a a 1 .5 . These data are given in Table 14. The resultant value for h implies that the characteristic undeformed height of asperity, above the centerline (or mean), is 1.5 times the standard deviation of surface roughness, a. Using h a 1.5, the statistical interactions (listed in Chapter VI) can be computed. Refer to Table 15 for gaussian data as a function of h = 1.5. Exponential data are also given; these data are not a function of h. The statistical summary in Table 15 indicates that for characteristic values of surface parameters (standard deviation, asperity radius, standardized separation), normal load, and modulus of elasticity, the magnitude of several parameters based on interactions between statically- loaded surfaces may be computed. The asperity radii was evaluated using the Tallian model (96) shown in Figure 11. These statistical interactions are graphically summarized in Figures 43 and 44 as functions of h and a. Some of the more recent literature has furnished surface data that may be compared with the statistical data developed in this Thesis for all tests. Refer to 191

Table 16 which compares data in this Thesis with data com­ piled from other sources. In the formative development of this Thesis, a model for fretting-wear, employing grooved shoes, was developed based, in part, upon surface interactions proposed by Rabinowicz (72). The objective was to combine estimates for the number and diameter of randomly-distributed as­ perities with a grooved-shoe geometry designed to collect 80% to 100% of asperity debris. It was hypothesized that such grooves would convert the fretting-wear to the equiva­ lent of oscillating-wear. Briefly, the model was developed in the following manner: a. Applied Normal Load, L = PAr

where: A_r = real area of contact P b material penetration hardness, which is approximately 3 times the yield strength in uniaxial compression (72) b. The total number of junctions, n, of diameter, d, present at any instant, is given by 4A 4 n ■ ---— = — --- (L/P) nd2 nd2 where junction diameter, d, was obtained from reference (72). 192

It was assumed that if the interacting asperities were randomly distributed and large in number, the asperity interactions would be approximately equidistant from one another. Therefore, a junction matrix evolved, in the form of equilateral triangles. Examining the spacing, b, of junctions expected in a triangular matrix on a circular plan of diameter, D, it was found that:

b * W D 2/n (1/2 / T )]*

Applying the above development to the asperity inter­ action of a k in. diameter shoe of SAE 4340 steel under 10,000 psi nominal contact pressure:

i) Shoe Diameter: % in ii) Shoe Area: 0.049 in^ iii) Junction Diameter, d = 4 x 10~*4 in 4 iv) Number of Junctions: 10 v) Spacing of Junctions, b = 75 x 10-4 in

From the above, it is noted the ratio of junction spacing to junction diameter is approximately 19:1. In the sub­ sequent development of grooving geometry that would collect the randomly-oriented asperity debris, the following ter­ minology evolved: %

193

vi) The "land" portion between consecutive grooves = 2b. vii) The groove width = 2b + 2d.

Using the above, the following theoretical groove efficiency of collection was found to be:

viii) d < slip < b: Efficiency » 80% ix) Slip b: Efficiency = 100%

Summarizing, the above model was of value for gaining greater understanding of asperity sizes and numbers. There is a limitation, at the outset, in that "material pene­ tration hardness" is a parameter upon which subsequent computations such as number of junctions and junction spacing depends. Material temperatures at the fretting interface may be high enough to modify material properties. For example, Waterhouse (106), in fretting-wear experiments on bright drawn mild steel, showed that recrystallization of the ferrite occurred in the surface, extending to a _3 depth of approximately 4 x 10 in. Such recrystallization indicated that the surface had experienced a temperature increase of approximately 850°F to 930°F. Thus, the above­ noted model would seem to be limited to static loading, and would require modification before it could be successfully used for fretting-wear predictions. ft

194

TABLE 13 STANDARDIZED SEPARATION DATA

F0(h) Fj (h) d - (h)(0), mlcrolnches h " 0 * F*(h) F*0i) 0 - 1 0 30 60 90 120 150 180 210

0.0 1.16 0.93 0 0 0 0 0 0 0 0 0.5 1.58 1.01 5 15 30 45 60 75 90 105 1.0 2.11 1.11 10 30 60 90 120 150 180 210 1.5 2.75 1.21 15 45 90 135 180 225 270 315 2.0 3.67 1.33 20 60 120 180 240 300 360 420 2.5 6.00 2.00 25 75 150 225 300 375 450 525 X95

ZABLE 14 DEVELOPMENT OF STANDARDIZED SEPARATION

GAUSSIAN EXPONENTIAL

*dG- dG" *dE “ dE " 3a-(z-d) RMS*=0 3a-(z-d) hG 2a-(z-d) hG hE 2a-(z-d) hE

10 18.8 2.0 9.8 1.0 19.9 2.0 9.9 1.0 30 59.5 2.0 29.5 1.0 59.7 2.0 29.7 1.0 60 119.1 2.0 59.1 1.0 119.4 2.0 59.4 1.0 90 178.0 2.0 88.0 1.0 179.1 2.0 89.9 1.0 120 239.0 2.0 119.0 1.0 239.0 2.0 119.0 1.0 150 297.5 2.0 247.5 1.0 299.0 2.0 149.0 1.0 180 357.0 2.0 177.0 1.0 358.0 2.0 178.0 1.0 210 417.0 2.0 207.0 1.0 418.0 2.0 208.0 1.0

*RMS and d ■ mlcrolnches (In. x 10"**) TABLE 15

SUMMARY OF GAUSSIAN AND EXPONENTIAL STATISTICAL DATA

a - 10 30 60 90 120 150 180 210

(a) Nunber of Interacting Asperities Gl* .53 .059 .015 .0065 .0037 .0024 .0016 .0012 X 105

El** .29 .032 .008 .0036 .0019 .0013 .0009 .0007 X lo5

(b) Total Asperity Contact Area, sq. Inch. G2 .481 X 10~3

E2 .300 X 10“ 3

(c) Contact Area Per Asperity, sq. Inch. G3 . .0091 .0818 .328 .736 1.308 2.04 2.94 4.0 X 10“6

E3 .0103 .0930 .372 .837 1.500 2.32 3.35 4.6 X 10"6

(d) Diameter of Asperity at Contact Interface , Inch. G4 .109 .322 .645 .970 1.29 1.61 1.94 2.26 X 10"3

E4 .115 .344 .690 1.03 1.38 1.72 2.06 2.41 X 10~3

(e) Normal Approach or Asperity Deformation, (z-d), Inch. G5 .095 .284 .569 .854 1.14 1.41 1.71 2.00 X 10~4

E5 .101 .303 .606 .909 1.21 1.51 1.82 2.12 X 10“4

(f) Asperity Radius, Inch. G6 4.7 14. 27. 42. 56. 70. 82. 98. X 10“4

E6 3.3 9.9 19. 30. 40. 50. 58. 69. X 10“4 196

*G ■ Gaussian; **E ■ Exponential. TABLE 16

EXPERIMENTAL RESEARCH SURFACE DATA COMPARED WITH DATA FROM OTHER SOURCES

Dlaaeter of Standard Ho. of Asperity at Deviation Interacting Radius of Contact of Surface Asperity Asperity Source Material Asperities Asperities Interface Roughness Slope Height

SAE 1020t a) Gaussian. a) Causalan a) Caussian O - 10xl0‘6ln. e-io* 40 to 60 0.120x10 to 4.7x10"* in. 1.09xl0“*in. to peak-to SAE 4340, to 0.530xl05 to L valley; Thesis 187x10“* In. 42.9xlO“*ln. a - 400xl0“6in. (Refer SAE 52100 to Figs. 5a avg. b) Exponential b) Exponential b) Exponential (o = RMS surface 11 A 42) (Refer 0.066x10s to 3.3xl0“*in. 1.15xl0“*in. steel to roughness) to Figs. 0.290x10s 11 A 42) 132 x 10“*in. 45.8xl0r*in.

Cupta A 1018 15x10”* In. to o ■ 6x10“® In. Cook steel ------t o A (33) 48x10“* In. a - 19x10“® in.

Creeowood a)Polished a) 2xl0“2 In. a)a- 0.4x10“®in. & Mild Steel * Wllllaason b)l laDis. b) 59x10”* In. b)o-lxl0"6in. ---- (31) Steel Roller « Bearing Nurl 6 Mild 2.4x10”* In. o - 6x10”* in. ------Hailing Steel to t0 6 (64) 6.3x10-* In. a- 125xlOT*in. Vllllaason Steel 4xl0~*in. to 6-5*-10* 10xl0*®ln. (ill) 8xl0"*in. to

300xl0“%n. 197 198

.8 h - 2.5

o .7

.6

i h - 2.0 t 10 .5 h ■ 1.5 h ■ 1.0

.4 h - 0.5 0.0

.3

.2

-L. -L. 0 30 60 90 120 150 180 210 0 30 60 90 120 150 180 210 Standard Deviation, a a

* u o.o U9 1 P

10

a a FIGURE 43: Statistical Data: Gaussian Distribution. 199

10 o

CM «rt$ 10

6010

U

10 0 30 60 90 120 ISO 180 210 120 150 180 210 Standard Deviation, a

a 10

o 10

0 30 60 90 120 150 180 210 0 30 60 90 120 150 180 210 0 a FIGURE 44; Statistical Data: Exponential Distribution. 200

H. Metallography

A metallographic survey of a representative specimen from each test configuration was performed. Table 2, in Chapter VII, identifies the specimens chosen. A total of 36 studies was completed, each study viewed in accordance with Figures 18 and 19 of Chapter VII. Microstructural deformation at, and extending from, the surface was clearly evident in SAE 1020 steel specimens. Less evident was substrate deformation in the harder steels: SAE 4340 and 52100. Metallographs of SAE 1020 specimens are shown in Figures 45, 47, 49 and 51; SAE 4340 specimens are shown- in Figures 53 and 55; an SAE 52100 specimen is shown in Figure 59. Some evidence of crack propagation to surface and/or delamination was noted in the following:

a. Figure 47: Type I, SAE 1020, smooth/smooth, compression preload, 50,000 cycles. b. Figure 53: Type I, SAE 4340, smooth/smooth, compression preload, 10,000 cycles. c. Figure 55: Type I, SAE 4340, smooth/smooth, compression preload, 200,000 cycles.

There are a number of possibilities for the lack of further evidence of crack nucleation and propagation. 201

These may Include one or several of the following:

a. Metallographic preparation such as sectioning, grinding, polishing and etching may have ob­ scured many of the cracks. b. Surface deformation may have made cracks less definable at, or near, the point of maximum shear stress.

c. Coefficient: of friction may have been of suf­ ficiently high value to cause the maximum shear stress to be located in the contact zone, where obscurement is heightened. d. The number of fretting-wear cycles may have reached the point at which oxides, debris and other factors had become more significant than local effects such as crack nucleation and propagation. e. Magnification may have been a limiting factor; but a balance was chosen between achieving a 4 representative view of oxide, substrate, etc., and a magnification which, if excessive, could have obscured the crack patterns. f. Sectioning planes other than the one used could have possibly enhanced clarity of crack de­ velopment . 202

g. Multiple-specimen investigation, rather than single specimens under each loading configuration might have given further insight.

h. In accordance with comments made earlier in this Chapter, it might have been of value to select specimens at test durations where contact pressure changes were quite evident. At such points, debris and oxides would presumably have been discharged; and the effects of diminished compressive stress, accompanied by some amount of elastic restoration, might have temporarily altered crack development patterns.

In his overview of the delamination theory of wear, Suh (93) noted that the depth of the plastic deformation zone depends upon the actual surface traction; and that none of the major difficulties encountered in predicting analytically the deformation of the surface layer is the inability to measure or derive the exact magnitude of the » normal and tangential loads exerted by the hard asperities and the actual area of asperity contact.” Metallography, in this Thesis, was used to assist in the qualitative overview of surface response in fretting- wear. However, these metallographic surveys may also further the understanding of surface damage caused by cyclic collection and dispersal of oxides and debris. 203

This concept will be discussed further in the following section on scanning electron microscopy.

I. Scanning Electron Microscopy

« Scanning electron micrographs of a representative specimen from each test configuration were taken. Table 2, in Chapter VII, identifies the specimens chosen. A total of 36 specimens were viewed, each study in accordance with Figure 20 of Chapter VII, whereby the slip line runs from left-to-right in all micrograph studies. Micrographs of SAE 1020 steel specimens are shown in Figures 46, 48, 50, 52, 61 and 64; SAE 4340 steel specimens are shown in Figures 54, 56, 58, 62 and 64; SAE 52100 steel specimens.are shown in Figures 60, 63 and 64. There was evidence of progressive crack propagation in SAE 1020 steel. Increasingly wider surface fissures at fretting-wear test durations of 10,000, 50,000 and 100,000 cycles are noted in, respectively, Figures 46, 48 and 50. Generally less-evident in the harder steels, some cracks were noted in SAE 4340 as shown in Figures 54 and 56, and in SAE 52100 as shown Figure 60. Direction of crack propagation is typically orthogonal to slip direction. The wider fissure in Figure 50 may be compared to its pre­ sumed origination in Figures 46 and 48 in the following manner. It is noted that the metallographic study of

r-"i *

204

Figure 45 indicates a relatively large volume of oxides

* and debris compared with the progressively smaller quanti­ ties in Figures 47 and 49, respectively. This tends to support the possibility that crack development occurs with concurrent diminution of interfacial pressure, as evidenced by oxide and debris reduction. The preceding remarks are, however, somewhat speculative, since Figures 46, 48 and 50 are micrographs of progressively fretted specimens of the same material and load configuration, but not of the same specimen. Referring to Figure 27, it may be noted that the curve which depicts the variation in normal load vs. number of cycles, does indicate a decided pressure drop at the 10,000 cycle level, and an inflection point at 100,000 cycles. These data may lend further support to the speculation that there is an inter­ relationship among debris volume, contact pressure and crack propagation. The stereo micrographs in Figures 61, 62 and 63 pro­ vide greater appreciation of the surface damage inflicted under fretting-wear. Figure 61 gives further insight to specimen no. 5, previously shown in Figure 50. Figure 62 is of a specimen that was preloaded in tension, and fretted with shoes having grooves transverse to slip di­ rection. Figure 63 has the same load configuration as Figure 62; and the vertical band seen in Figure 63 is 205 that portion of the specimen which faced a groove and did not undergo fretting-wear. Figure 52 is a micrograph of a 1020 steel specimen that was compressively preloaded and fretted with shoes having grooves parallel to the slip line. Test duration was 100,000 cycles. Figure 58 is a magnified view of a portion of Figure 57. Crack propagation is suggested but, as with many other specimens studied but not displayed in this Thesis, oxides and debris may be responsible for much of the visual obscurement. Figure 64 is an SEM study of the typical virgin specimen surface. Clearly noted are the polishing marks parallel to the intended line of slip. The SAE 4340 and 52100 surfaces are relatively clean and smooth, whereas SAE 1020 is cluttered with inclusions and debris. The mechanics of crack propagation is beyond the intended scope of this Thesis, but the SEM results invite consideration of other researchers* views.

a. Juvinall (47), in considering the reasons for absence of a well-defined surface fatigue limit, noted that M. . . crack propagation is believed to result predominantly from the maximum tensile stresses which are present." Further, tensile stresses occur notably from tangential 206

loading due to sliding; and residual stresses caused by yielding. b. Collins (17) reasoned that, when microcracks are nucleated in a static-compressive environ­ ment, a localized high tensile stress is caused to exist at the tip of the microcrack. The latter effect would occur after the fretting treatment has been completed, and the stored, elastic energy has returned the specimen to its original dimension. c. Jahanmir and Suh (93) noted that void formation occurs very readily around subsurface hard par­ ticles, but that crack propagation occurs very slowly. For metals of medium tensile strength and high fracture toughness (such as 1020 steel), where void nucleation can occur easily, crack propagation may be the rate controlling mechanism. On the other hand, easier crack propagation (and more difficult void nucleation), could arise for metals of high tensile strength and low fracture toughness. d. Fleming and Suh (93) noted that, due to large compressive stresses, the faces of a crack near the surface of a specimen lock together and transmit shear stresses. The stress field, in 207 sliding, contains a region of zero stress, perpendicular to the line of action of the applied force. Stresses on either side of the zero stress region are tensile or com­ pressive. Cracks, which in ductile materials are essentially parallel to the surface, can therefore propagate only when the crack and the asperity contact are so situated that part of the crack is in the tensile region. FIGURE 45: Specimen No. 1: SAE 1020, Type I, Metallo graph, 300 x.

A ' ’ / ; ( . ^

/ /

FIGURE 46; Specimen No. 1: SAE 1020, Type I, SEM, 1400x. 209

FIGURE 47; Specimen Mo. 3i SAE 1020, Type I, Metallo- graph, 300x.

FIGURE 48: Specimen No. 3: SAE 1020, Type I, SEM, 1400x. FIGURE 49: Specimen No. 5: SAE 1020, Type I, Metallo graph, 300x.

FIGURE 50; Specimen No. 5: SAE 1020, Type I, SEM, 1400x. 211

FIGURE 51i Specimen No. 9: SAE 1020, Type III, Metallo- graph, 300x.

FIGURE 52: Specimen No. 9: SAE 1020, Type III, SEM, 14x. 212

FIGURE 53; Specimen No. 13: SAE 4340, Type I, Metallo- graph, 300x.

FIGURE 54: Specimen No. 13: SAE 4340, Type I, SEM, 1400x. «

213

FIGURE 55: Specimen No. 18: SAE 4340, Type I, Metallo graph, 30Ox.

FIGURE 56: Specimen No. 18: SAE 4340, Type I, SEM, 1400x. FIGURE 57: Specimen No. 19: SAE 4340, Type I, SEM, 140x.

FIGURE 58: Specimen No. 19: SAE 4340, Type I, SEM, 1400x. Selected Field From Figure 57, as Indicated. 215

FIGURE 59; Specimen No. 36: SAE 52100, Type VI, Metallo- graph, 300x.

FIGURE 60; Specimen No. 36: SAE 52100, Type VI, SEM, 1400x. FIGURE 61; Specimen No. 5: SAE 1020, Test Type I SEM Stereo Micrograph: 1400x. FIGURE 62; Specimen No. 24: SAE 4340, Test Type VI. SEM Stereo Micrograph: 700x. FIGURE 63: Specimen No. 36: SAE 52100, Test Type VI. SEM Stereo Micrograph: 700x. 219

SAE 1020: SEM 500x

SAE 4340: SEM 500x

SAE 52100: SEM 500x FIGURE 64: Scanning Electron Micrograph: Virgin Specimen. %

CHAPTER XX

CONCLUSIONS

Introduction

The work of this Thesis is concluded by integrating the parametric relationships of Chapter VIII with the re­ search objectives stated in Chapter III. Developments not foreseen at the commencement of this research, but significant to the results, are also noted. The subsec­ tions of this Chapter include:

A. General Conclusions B. Specific Observations C. New Insights

A. General Conclusions

The conclusions cited below may be better understood by referring to the following Figures:

i. Figure 65. SAE 1020 steel, Type I test, 500,000 fretting cycles, smooth shoes, com­ pressive preload.

220 221

11. Figure 6 6 . SAE 52100 steel, Type I test, 500.000 fretting cycles, smooth shoes, com- presalve preload. ill. Figure 67. SAE 4340 steel, Type VI test,

1 0 0 . 0 0 0 fretting cycles, grooved shoes transverse to slip, tensile preload.

1. Normal Approach due to fretting-wear developed smoothly over the full test duration, unaffected by the sharp changes noted in other parameters, particularly at the onset of the fretting-wear test. (Refer to Figures 21, 22, 23 and 24.) Between 100,000 and 500,000 fretting- wear cycles for smooth/smooth surfaces under either com­ pressive or tensile preloading, the normal approach in­ creases linearly with fretting cycles.

2. Surface Roughness measurements displayed a characteristically sharp rise within the initial 1 0 , 0 0 0 to 2 0 , 0 0 0 fretting cycles, followed by a slight decrease in the 50,000 to 100,000 cycle interval, and a steady, moderate increase thereafter for Type I tests. These con­ clusions are based on measurements made progressively during the fretting-wear test at 10K, 20K, 50K, 70K, 100K, 200K and 500K cycles. For all other test types, surface measurements were taken only at the conclusion of 100,000 fretting-wear cycles. Due to the relatively 222 high value of surface roughness found in tests II through

VI (shown in Table 6 ), and the fact that these high sur­ face roughness values developed over the rather brief interval of 100r000 cycles (55.5 minutes), it is hypo­ thesized that the roughness profile of all test types would be similar to those displayed in Type I.

3. Normal Load was continuously monitored, and adjusted as required, to maintain constant cyclic slip amplitude throughout each test. During the initial stages (41) of a test, surface interactions produce unoxidized debris. In this research, the debris apparently filled the interstices, then oxidized, causing increased inter­ facial pressures which in turn inhibited slip. This necessitated a manual reduction in normal load to restore the desired slip amplitude. It was shown in Chapter VI that iron oxides have a volume more than twice that of the virgin metal. Cyclic buildup and discharge of debris and oxides continued throughout the*test. These cyclic variations were more noticeable with smooth/smooth shoe/specimen pairs. Specimens fretted with grooved shoes were apparently able to discharge the wear debris more rapidly. For grooved shoes, the normal load reduction initially required was more pronounced, as shown in Figures 28, 29 and 30, but only slight adjustments were 223

' needed to maintain constant slip amplitude during the balance of a typical fretting-wear test.

4. Axial Preload was sensitive to bulk temperature changes due to frictional heat generation in the fretting zone. A relatively moderate bulk temperature rise of 10° to 15°F caused significant changes in specimen length, as shown in Figures 38, 39 and 40, and in Table 12.

5. Volumetric Wear may be expressed as the product of normal approach and nominal or apparent contact area, if the ratio of normal approach to surface roughness is sufficiently high, and the value of roughness remains relatively stable. (Refer to Table 7.) Using the ex­ perimental data of this Thesis, the calculated values of specific wear rate were in close agreement with published values. ,i

6 . The Number of Asperity Interactions, based on statistical estimates, was primarily dependent upon sur­ face roughness, as shown in Table 10, Other parameters upon which asperity interaction is dependent include normal load and elastic modulus. Normal load, which fluctuated cyclically during each fretting-wear test, did not vary greatly in magnitude, however. Plastic «

224 deformation undoubtedly occurred locally at the tips of

* higher asperities, but elastic constraint was provided by the surrounding bulk material. With surface roughness in the 10 microinch range, approximately 53,000 asperity interactions were estimated in the virgin specimen as indicated in Table 15. These data support use of a smooth, high-hardness metal if a minimum of surface damage and maximum fretting-wear life is desired. For example: SAE 52100 steel, with a Rockwell hardness of C-60, never exceeded a surface roughness of 31 microinches RMS over 500,000 fretting-wear cycles, and its normal approach was only 22% and 38% of the SAE 1020 and 4340 steels, respec­ tively .

7. Actual local Normal Pressure exceeded the nominal, or apparent, normal contact pressure by approximately two orders of magnitude. Based solely upon changes in sur­ face roughness, actual normal contact pressures increased 5% to 10% during a typical wear test as shown in Table 10*

B. Specific Observations

1. Shoe Grooving. The grooved shoes used in this research produced a wear rate approximately twice that of shoes not grooved, as noted in Figures 21, 22 and 23. Grooves oriented transverse to the slip direction produced 225 higher wear rates than did grooves parallel to slip. The relatively higher rates may be traced to the effect of slip amplitude which effectively increased the grooves' width by 75%. Groove capacity, which was, in effect, continually decreasing as fretting-wear developed, was apparently inadequate to fully accommodate wear debris discharge. With respect to preload sense, SAE 1020 and 4340 steels developed higher wear rates with a tensilely- loaded grooved specimen, either transverse or parallel to slip; SAE 52100 steel showed quite the contrary. It is not known, on the basis of the aforementioned (non­ destructive) testing, whether wear grooves, while ex­ pediting volumetric wear, minimize the more insidious types of wear (e.g., void and crack nucleation). Syed (95) found grooves oriented parallel to slip to be more effective in fretting-fatigue than grooves transverse to slip direction; and that the fatigue endurance limit may be improved by as much as 2 0 % by using "properly grooved shoes."

2. Preload Sense. Static preload, both tension and compression, was significantly altered by bulk temperature rise. There was, therefore, insufficient experimental evidence to clearly ascertain whether static compression or tension would produce greater wear rate under all six loading configurations for all three families of materials. 226

More specimens were fretted under static compression than tension, because it was expected that, due to elastic restoration, crack propagation might be more serious. This did seem to be the case, but mainly for smooth-faced shoes of SAE 1020 steel. Static preload may not be solely responsible for crack propagation, however, since interfacial pressures were also higher in smooth-faced shoe/specimen pairs. To determine whether fretting-wear, as for fretting-fatigue, is more serious under compressive than tensile preload, additional investigations would be necessary.

3. Stages of Fretting-Wear. Fretting-wear has been postulated to occur in several stages, the final stage being steady-state wear. Hurrick (41) suggested 3 stages as noted in Chapter VI. This Thesis research indicated that at least three stages can be discerned as follows. If "stability" of surface texture or roughness is an indicator of steady-state wear, then steady-state fretting- wear would appear to occur at approximately 1 0 0 , 0 0 0 cycles, as evidenced by the progressive surface roughness measure­ ments taken for test type I, The sharp decrease in normal load, matched with the equally sharp increase in surface roughness, during the initial 1 0 , 0 0 0 to 2 0 , 0 0 0 cycles of fretting-wear, could identify the initial 227 fretting-wear stage, characterized by wearing-in, varying coefficient of friction and initial adhesion and metal transfer. The Intermediate fretting-wear stage, then, would lay between 20,000 and 100,000 cycles. Supplementary measurements, e.g., the coefficient of friction, might be useful in further definition of these fretting-wear stages. These stages, and accompanying pressure variations caused by debris buildup and dispersal, may be also assessed in terms of progressive crack propagation as noted in SEM micrographs at the 10,000, 50,000 and 100,000 cycle levels of fretting-wear shown in Figures 46, 48 and 50.

4. The Fretting-Wear Prediction Model was developed from parameters considered basic to fretting-wear. Using experimental data, the model predicted that normal approach due to fretting-wear would occur in fewer cycles of fretting than actually did occur in tests. Discrepancy between the model and experimental data could be minimized by modifying the value of normal load that is used for model prediction. 228

C. New Insights

During the early stages of this research, it was felt that changes in fretting pressure required to main­ tain constant fretting amplitude occurred either coinci­ dentally with— or in sequence with— changes in normal approach; and that these cyclic excursions might have an important effect on the rate of microscopic crack develop­ ment in the fretting interface. Unexpectedly, normal approach due to fretting-wear was found to be, apparently, independent of the parametric interactions which led to rapid increase in surface roughness, rapid decrease in nominal interfacial pressure, bulk temperature effects that significantly altered static preload, rapid diminu­ tion in number of asperity contacts and effects of grooving and groove orientation. These results were, to some extent, forecast in Chapter VI based on a quotation by Stowers and Rabinowicz (90) stating that fretting- wear is simply proportional to the accumulated sliding distance and independent of amplitude and number of cycles to reach that distance. Fretting-wear is a phenomenon that may, with care, be measured accurately. Such measurements can prove useful in service-life prediction. The parametric data, which was evolved together with normal approach data, may ultimately offer the designer both insight and the basis for design predictions. 87.8

x 45

1. Normal Approach Due to Fretting-Wear

190 »H K 100

2. Surface Roughness

w600 •o §500

3. Normal Load To Maintain Constant Slip 900 m800 •o 805 §700 c-600 500 A j Axial Preload

8.8

Volumetric Wear Rate

5.3 x 10

1.5x10

6. Humber of Asperity Interactions

>10.0

7. Normal Pressure (Gaussian)

FIGURE 65; Parametric Interrelationships. SAE 1020r Type I. 230 ««r b 20' 18.9 h 1 5 . * 10

1. Normal Approach Due to Frettlng-Wear H 601- K *°‘ * 20,

2. Surface Roughness

§«o' 400L 3. Normal Load to Maintain Constant Slip 900' 865 0980° ■ *3 700' 1 600' 500- Axial Preload s

1.9

5. Volumetric Wear Rate

5.3x10*

6. Number of Aeperlty Interactions

m i*1 10.7 S 1.0,

7. Normal Pressure (Gaussian)

FIGURE 66: Parametric Interrelationships. SAE 52100, Type I. 231

26.15

1. Normal Approach Due to Frettlng-Wear ? 120 112. (approximate)

2. Surface Roughness

« 500 ^ g 4 0 0 ‘ £ 300 270 200L 3. Normal Load To Maintain Constant Slip 600 5 500 1 400 343 300 Axial Preload

13. n Volumetric Hear Rate

5.3x10 4.6x10

6. Number of Asperity Interactions

o.h 12 • k 10. •gs.o a 6.6 6.0 7. Normal Pressure (Gaussian) 0 10 20 30 40 50 60 70 80 90 100K Cy. FIGURE 67; Parametric Interrelationships. SAE 4340, Type VI. CHAPTER X

APPLICATION TO REAL SYSTEMS

Introduction

The fretting-wear methods and data developed in this Thesis could be used to investigate a fretting-wear situ­ ation sometimes found in fuel rod assemblies in nuclear power systems. The light-water cooled pressurized water reactor (PWR), one of two types of power generating systems fully commercial in the United States, produces steam from water heated under pressure by the flux of neutrons generated in a nuclear core (82). The steam is generated in a secondary heat exchanger or steam generator and then piped to a turbine generator for the production of electricity. PWR's are made largely of low alloy steels (reactor vessel, nozzles), stainless steels (internals) and zir­ conium alloys (fuel assembly, control rod, guide tube). The fuel rods are bound together in an "egg-crate" arrangement to form a fuel assembly of approximately

232 233

15 inches square; and each assembly, or cell# contains about 225 fuel rod tubes. The fuel assemblies form a tubular column 1 2 feet in length# laterally supported at 7 levels. The reactors' transverse section can typically house 100 to 200 fuel assemblies. As many as 241 fuel assemblies are used to form the core for a 1300 mega- watt-electron PWR (82). A fuel rod is typically constrained at six contact points at each lateral support# resulting in a total of 42 points of contact on each of the rods. Assuming use of 2 0 0 fuel assemblies# 1 2 feet in length# each containing 5 225 fuel rods# there are approximately 2.7 x 10 points of contact on the fuel rods in a PWR. Within each fuel rod are UO2 fuel pellets; helium is inserted in the gap between pellet and rod so as to permit soft contact (be­ tween fuel and tube) at peak operating temperature. In operation# pressurized demineralized water flows at a high rate through the core region resulting in vibration of each fuel assembly. Flow-induced cyclic 5 displacements are caused to occur at each of the 2.7 x 10 points of contact. Thus, a potentially serious fretting- wear problem evolves. Fuel rod tubes are often made of Zircaloy 4 because of the material's low neutron ab­ sorption cross-section and its excellent corrosion re­ sistance in the demineralized water coolant. The fuel 234 rods have a design life of about 3 years. About one-third of the rods are replaced or rotated every year. While other failure modes must also be carefully investigated, this discussion refers only to the effects of cyclic straining between fuel rods and constraint grids which leads to fretting-wear.

Experimental Program

Given the above design problem, the following pro­ cedures might be undertaken in light of the experimental work described in this Thesis. Refer to Figure 6 8 for a schematic diagram of the PWR and fuel rod cells.

1. Known Parameters and Data a. Fuel Rod Tube Material: Zircaloy 4 Outside Diameter: 0.4-0.5 inch Wall Thickness: 0.02-0,03 inch Overall Length: 12 ft. Lateral Support: Approximately 20 in centers (at constraints) b. Water Influx Type: Demineralized water Temperature: 600°F (mean) 5 Rate: 2 X 10 gph

Pressure: 2000 psi 235

c. Contact Zone Normal Load: 25 pounds • Contact Area: 0.06 in. x 0.03 in. Contact Pressure: 14,000 psi Cyclic Frequency: 50-100 Hz. at constraint Cyclic Amplitude: 0.0002 inch (peak-to-peak) Static Preload: 1000 pounds

2. Experimental Program (Refer to Figure 69) a. Normal Load: 25 pounds b. Frequency: 50-100 Hz. c. Slip Amplitude: 0.0002 inch (peak-to-peak) d. Static Preload: 1000 pounds e. Environment: (1) Tube Internals: Simulated Fuel Pellets & Helium (2) Tube Externals: Silicone-Shrouded Heat Element f. Duration: Maximum number of cycles equivalent to, say, 1 day of operation

e.g., 5 0 °y°^e8 x 8'6Xj°yS0c - 4.32 x 106 cycles

g. Specimen: Zircaloy 4, filled with simulated fuel pellets and helium. Sealed ends as per

Figure 69. h. Shoes: Wedge-ended to provide contact surface of 0.06 in x 0.03 in as per Figure 69. 236

3. Test Program a. Environment. Estimate wattage in silicone heat blanket to attain 600°F at steady-state. Use Variac to modify wattage as required. Monitor skin temper­ ature of specimen with thermocouple. b . Duration Run tests at varying cycle durations so as to enable examination of fretted surface at incre­ mental fretting-wear levels. c. Specimen Design specimen and "separable" end caps to be 6% inch long as shown in Figure 69. This will permit use in same fretting fixture used in this Thesis' research.

4. Model Prediction The fretting-wear prediction model may be used to predict the number of cycles of•fretting to produce a specified value of wall penetration, i.e., normal approach, in a fuel rod. For example, if reactor specifications allowed a maximum wall penetration of 50% of the fuel rods' wall, the fretting-wear prediction model could be used to predict the number of fretting cycles, C^, 237 to produce the allowable wall penetration in the following manner.

Cm “ (A) (nT (SW)

______(nominal contact area)(normal approach) (2 peak-peak slip)(normal load)(specific wear rate) where: nominal contact area « 0.06 in x 0.03 in normal approach ** 0.010 in 2 (peak-peak slip) » 2(0.0002 in) normal load » 25 pounds specific wear rate » from published values or experimentally evalu­ ated. For purposes of this example, assume the specific wear rate to be 13 x 10**11 in3/in-lb, which is the value for SAE 4340 steel for test type I as shown in Table 8.

Therefore: (0.06 in x 0.03 in)(0.010 in) Q s ------m 2(0.0002 in) (25 lb) (13 x 10*11 in3/in-lb)

C a 14 x 106 cycles of fretting-wear to produce a normal approach of 0.010 in 238

At the conclusion of the test program, the number of cycles predicted by the model, Cm , may be compared with the actual number of fretting cycles, Ca , that is required to develop a normal approach of 0.010 inch.

Concluding Remarks

The proposed Test Program has been designed to enable use of the' fretting fixture and instrumentation used in the fretting-wear research for this Thesis, The testing - simulates, but does not duplicate, the environmental con­ ditions in a PWR. However, it is felt the Program will provide valuable insight of the phenomena associated with fretting-wear in a hostile environment. 239

Reactor Vessel

•o £ rH HO IM Outlet Inlet 4J Q aa

0 *H0 0100 06 u0) CJo Fuel Assembly.

Fuel Rod JL Hard Stop f c ±

W

it Fuel Rod-' '-Spring Stop View 1A-A* Detail of Cell Bundle Detail

FIGURE 68: Fretting-Wear Application: Pressurized Water Reactor Fuel Rods. 240

Shoe Pair

Fuel Rod Tube Sect. 'A-A* X

Separable End Cap •Wrap-Around With Spherical Seat Heat Element

Separable End Cap •Fuel Rod Tube With With Key Seat Fuel Pellets & Helium

FIGURE 69; Fretting-Wear Arrangement of Specimen & Shoes. CHAPTER XI

SUGGESTIONS FOR FUTURE RESEARCH

Introduction

The foregoing research effort was directed towards a functional approach to "failure prediction" and greater awareness of the interdependencies among the variables in a fretting-wear environment. Other experimental and analytical methods might offer additional insights. A two-part program of future study is suggested. This might take the following form:

A. Improvement of Test Program Select, vary, control and measure the parameters discussed below. B. New Methods Consider supplemental experimental methods currently being employed in tribological research, as noted below.

241 242

A. Improvement of Test Program

1. Environment. Monitor the effects of environment on fretting-wear, with respect to surface films and oxides, by conducting tests in a fully-controlled environment. Hailing (36) noted that ", . . the high wear experienced under vacuo is now a problem of practical significance in high-flying aircraft, missiles and spacecraft." In Hurricks* (41) review of the mechanisms of fretting, he stated that Wright (113) found oxidized debris first occurring at a threshold air pressure of between 1 and 10 mm Hg.

2. Pressure. Use the normal load (or pressure) locus to determine test milestones for measurement of crack propagation and surface damage. Assess fretting- wear at relative maxima and minima, based upon the pressure locus of typical test runs. Location of maxima and minima might represent cyclic buildup and dispersal of inter­ facial debris.

3. Slip Maintenance. Develop a feedback system that would automatically maintain constant slip amplitude, thereby eliminating the need for continual monitoring and manual control. 243

4. Test Duration. Evaluate 'the effects of (a) extended, and (b) intermittent wear tests. Extended tests, having durations of several million cycles, and aided by the slip "feedback" system noted above, would provide valuable long term data for failure prediction and model validation. Intermittent tests would simulate systems that operate in a non-continuous manner, e.g., aircraft and certain manufacturing facilities.

5. Temperature. Measure bulk temperature near the fretting zone. Sensors might be located (a) at the interior surface of a hollowed-out fretting shoe near the fretting interface or (b) in the specimen, embedded midway between the two fretting surfaces. Other sensors might be mounted on the specimen body. Such temperature measurements would enable the determination of whether the recrystallization temperature had been exceeded. Kragelskii (52) noted that residual stresses often develop in the surface layer when the bulk material cools down. The residual stresses may lead to a gradual loosening of material near the fretting interface and fatigue failure owing to the formation of microcracks. Thus, temperature monitoring might assist in the analysis of fretting-wear behavior, particularly for tests subjected to intermittent operation as noted above. %

244

6. Traction. Friction measurements, in a controlled environment, might provide further understanding of the I role oxides and surface films play in fretting-wear. These measurements might also assist in determining the effects of temperature on traction. Kragelskii (52) noted that, in practical terms, cyclic frequency affects the coefficient of friction. Suh (93) stated that one of the consequences of sliding speed is a temperature rise which results in ". . . the formation of different oxide layers on the surface, which changes the surface traction. . . ."

B. New Methods

Materials. Use of dissimilar materials, or materials having a particular crystal structure, might reduce wear and surface damage. Rabinowicz (72) noted that, as a general rule, n. . . it is found that severe frictional behavior is found when the two sliding surfaces consist of the same metal, or when they consist of closely similar metals, as shown by the ability of the two metals to form alloys, or by the substantial solubility of atoms of one of the metals in a lattice of the other. ..." Suh (93) stated that, for effective wear control, ". . . all that is necessary is to design the microstructure 245 of materials to reduce the friction coefficient and to raise the hardness and toughness of materials. Unfortunate-

> ly, it is not possible to achieve both high hardness and toughness with a single microstructure."

2. Surface Coatings and/or Treatment. Many processes (23) that may extend the wear life of a metal part are commercially available. Techniques for hardening metal surfaces include laser and electron-beam hardening, flame spraying, plasma spraying, detonation spraying, vacuum evaporation, chemical vapor deposition, sputtering, electron plating and ion plating. For steel, the most common and commercially available techniques are carburizing, carbonitriding, conventional nitriding and boronizing. Fluorocarbon coatings, which reduce friction, can be applied to metal substrates by fluidized-bed or electro­ static spray methods. Anti-wear coatings and solid lubri­ cating coatings such as graphite or MoSj have been com­ bined to synergistically provide improved hardness and semi-permanent lubrication. Jahanmir, Suh et al. (45) have found that wear can sometimes be reduced by reducing the coating thickness. For example, by using a cadmium coating of less than 1 urn on AISX 1018 steel, the wear rate was reduced by three orders of magnitude. 246

3. Design Optimization. A recent methodology, called probabilistic design (48), originated in aerospace t engineering and is now being used in the consumer products industry. Compared to the "traditional" design approach, which uses safety factors, the probabilistic approach employs the alternative concept of reliability. Using this approach at the design stage, the designer must statistically define all the design variables and parameters, and then follow prescribed probabilistic procedures that culminate in the optimization of system reliability. The probabilistic design approach might suggest fretting-wear model development based upon a statistical description of normal approach due to the fretting-wear process. I

APPENDIX A

INTEGRALS OF THE GAUSSIAN DISTRIBUTION

247 APPENDIX A

INTEGRALS OF THE GAUSSIAN DISTRIBUTION, (32)

0 0

F (h) = — -— f t s - h)m e”s*/2 ds m r r r J h

For h large and positive,

F (h) * - H i - h'm e-h>/2 1 - (nttl) (m+2) + m /2TT 2h2

For h large and negative,

Pm (h) (-h)m

The recurrence relation Fm+i(h) ® “ hFm ^ can be used to build up the higher functions, as shown in

Table 17.

248 249

TABLE 17 9

INTEGRALS OF THE GAUSSIAN DISTRIBUTION

h F0(h) F i(h) (h)

0.0 0.500 00 0.398 94 0.430 02 o in

• 0.308 54 0.197 80. 0.195 20 1.0 0.158 65 0.083 32 0.075 67 1.5 0.066 81 0.029 31 0.024 64 2.0 0.022 75 0.008 49 0.006 65 2.5 0.006 21 0.002 00 0.001 47 3.0 0.001 35 0.000 38 0.000 26 3.5 0.000 23 0.000 06 0.000 04

4.0 0.000 03 0.000 01 0.000 00 $

APPENDIX B

RELATIONSHIP BETWEEN STANDARD DEVIATION (a) AND ROOT MEAN SQUARE (RMS)

250 I

APPENDIX B

RELATIONSHIP BETWEEN STANDARD DEVIATION (

. . . i J 2 E ® : j-i * N Xj- + X 2 + Xj + ... +x, CN Y" where x » Arithmetic Mean = ------= / x^/N N

N

RMS »

j = l N

N

Oa * /[L

N

Na2 « JZ ^xj2 “ 2xjx + x*)

251 252 N N N N0S - Y_ -2x J _ Xj + Y_ 3? 3-1 3=1 3=1

N Na2 = N(RMS)2 - 2x ^ + Nx2 j-1

Solving for (RMS)2, N N

(RMS) 2 a a2 - x2 + 2x ( ^ Xj/N ) ? but ( T x^/N) = x j=l jal

« a2 - x2 + 2x2

(RMS)2 a a2 + x2 or,

(RMS) « IJ a2 + X 2

But x a o in Profilometry,

The re fore, RMS = a APPENDIX C

DETAIL DRAWINGS

253 APPENDIX C

DETAIL DRAWINGS

List of Detail Drawings

Figure No. Drawing No. Title

70 1000 Fretting Specimen 71 1001 Fretting Shoe 72 1002 Normal Approach LVDT Body Clamp 73 1003 Normal Approach LVDT Core Clamp 74 1004 Normal Approach LVDT Core Rod Holder 75 1005 Slip Amplitude LVDT Body Clamp 76 1006 Slip Amplitude LVDT Core Rod 77 1007 Grooves for Fretting Shoes 78 1008 Shoe Grooving Tool 79 1009 Grooving Tool Holding Fixture

254 »

-0.12.5 - 0*00 ' pO. 4-000 (Ref)

« . — t o.oo5 f t In L 0.100 I?. t^Rod - 0.501 O O S e c N o te A 0.498 IIo o 0.437 10005 in 11 Rad. O

0.375*°*001 0 .3 3 7 10005 (R ef.)

FIGURE 70 ■ N o t e s 5 0 1 -A Fretting - Specimen 5AE 1 0 1 0 - L A.O.IOO Rod. Fillet must 5 0 5AE 4 3 4 0 HEAT TnATSiNGkC meet shoulder enact* i - B Fretting Specimen ^-£>. * 6 1" I. B a t c h t o s c -SS ly tangent with no 5AE 5 1 1 0 0 Heat treat ^ikicuE discontinuity ,and 5 0 1-C Fretting Specimen « 5f-L MATCH To «C- GO leave a o.oso flat OUAN. PART No. PART NAME MATERIAL ROUGH size REMARKS s h o u ld e r. — TOLERANCES — THE OHIO STATE UNIVERSITY B.AIt surfaces (nqrKed (nan u mams) MECHANICAL ENGINEERING DEPARTMENT — COLUMBUS. OHIO shall be polished rMCnsMi...... a /i+ d e c im a l ...... i o . o i o SCALE REP. ASSY. NO. with LEA compound, INOUIAR ..a ....**...*.. 4k pnOJCCTNa. DlSSeiTT. I" With final polish mqrlfCs TITLE DWG. NO. OWN. BY lUsDAS 3-J3-16 parallel to long Gk i O F r e t t i n g S p e c i m e m 1 of specimen CKO. BY o o o ro tn ui No. 3 Prill «ifc Deep i - 2 8 N F - 2 0 . 3 I I o*?48 0 .0 62

3 2 R (Not, More) (T y p .)

N O T E S S e c t i o n ^ “A * ^,5urfQce mqrked ^ Shall be polished with LEA compound- FIGURE 71 Final polish marks 50 pr. 2-A Fretting Shoe S A E 1 0 2 . 0 |/fe Lg shall be parallel' M tAI T«IAT ('MQ l C 50 pr 2-B rretting Shoe SA E 4 3 4 0 % ® * I Ks Lg. Ba TCM T O K - i S B. For 5AE 52100 only : m i a t t X* a i s i m q u 50 pr 2 -C Fretting Shoe SAE 5 2 1 0 0 patcm TO kc- Ao The surface shall be OUAN. PART HO. PART NAMC MATKAIAL ROUGH sac HCMARK9 given a finish of \? — TOLCRANCES— THE OHIO STATE UNIVERSITY ( n a n u inarat) m before heat treatment PRACTIOMAV..It MECHANICAL ENGINEERING DEPARTMENT — COLUMBUS. OHIO Menu ...... **• 1 O»ow to RC-(>0. Allow approx. RCP.ASS*V.NO. ANOUtAO...... ± '/l * p r o j c c t n o . p 13 S e R T - s c a l c FULL '2-4 mils mahscial to TITLK o w g . n o . OWN. BY H. Ltjons 6-14-76 permit final finish of ~fo s p e c i w e n -Size. CKO. BY B. Lyons 6-IS-76 F r e t t i n g S h o e tool 256 V4o. 43 D rill, -C h am fer Allen Head Cop Scrgujs. ^4-40 pas-f 3 I0 + Ho.3| Drill + 0 clo t’ ^Transducer &odu F o u r * 4 '4 ONC *£* full *thd. No. 9 C.6.* 4 Deq (4 Hole*) * n?ef.) One ^3*4© NC * ^"full thd.

ikR (ryp)5 ?

si. * ® ° £ ' Half Se ctiON A-A each side 1.312

1 D rill T h ru 7 * Drill Thru

FIGURE 72

Ho. D rill Th ru ONE ---- Trans. Bodcf Cl

slot {Transducer 0.406 0 4 0 6 ( R e f ) 0.405 1.312 1.312

No.3 Drill +hfU i-28NF —v D e t a i I (2Holes)--- \ Scale : 2 -1 REFERENCE 1. Allen Head Cap Screws Retj. One ^3*4flNC * till thread Two * 2-56 NC - £*£u H t hreqd

*«oreJ 2. LvPT Core Rod Holder No. 50 Drill, No, 47 Drill thru,#3-48 past s lo t See Pw g* N o» 1004 * 2 - 5 6 NC No- 57 Drill to slot, KJo. 17 C.&. * £*deep. FIGURE 73 No. 25 C.6.“ 0.156 deep o n e Trons.Core Clamp St pin. St (2 Holes} OUAN, PAST NO, PART NAME MATERIAL ROUSH sac REMARKS — TOLERANCES— THE OHIO STATE UNIVERSITY fcsecrr as ineme) ...... i /fc* MECHANICAL ENGINEERING DEPARTMENT — COLUMBUS. OHIO sccmai...... ± OMto « m v u i ...... ± — PROJECT NO. DI S S E R T SCALE FULL REP. ASST. NO. ----- OWN. RY N.L^onS TITLE o w o .n o . N O R M A L APF > R O * C h CKO. BY H. Lyorts 3-14*74 L V P T C O R IE C L A M P 1 003 258 R E P t R E M C E

Work. with 1003. 0.3 7 5 D 0 .5 0 D C h o n o -fe r

No. 53 Dr.'ll ■r -2SNF 1-72 N F - 2 B 0.2 SO

S ection *A~A'

Solder w*+h No, iSV Eutoc rod. 1-72 NF-2B - 9/th Qrtd grind -flush. Core R o d (By Others) Transducer Core Clamp (See Dwg.No. 100 3) Assemble! With LVPT Core Screw FIGURE 74

TWO Core Rod Holder StqiA. S-Ll. QUAN. p a r t No. PADT NAMC MATCRU'. fioaoii m e USMARKS — TOLERANCE* — ( n a n n incin«t> THE OHIO STATE UNIVERSITY FUACTWKM ...... 7 6 4 MECHANICAL ENGINEERING DEPARTMENT - COLUMOUS. OHIO acm.t ....i o,o*o PROJECT No. d i s s e r t : | KCALS 2" = I’ DV.AU7.NO. Tine CWO.NO. own. b y H- L^ons 3*0*74 N O R M A L APPROACH CKO. BV H «Ly o nS 3*14*74 LVPT CORE ROD HOLDER 1004 259 N o . 4-7 Drill# 1 ""^Chamfer # 3 - 4-8 NC past & I No.37 Drill to slot 0.137 N o . 17 df*

No,4-3 t>rill thru #4-40NC F.S. H i; No.3l Drill to sloflV^f* No.9 C.&.* 0.125 (A Holes) 2 £(**£! 32 s lo t . R E F C R E N C f t e a c h s id e . A llen Head Cop ScreuJs Re^. t One ^ 3 * ^ 8WC»^ -full tliread Foqr ^ 4 ‘40 NC * ^ ft*II thread & D r ill-T i FIGURE 75 ______Trans. 5odtj Clomp 7o75 Alum. (Z Holes)- QUAN. NO, PART NAMEPART r o u g h sac I REMARKS — TOLERANCES — THE OHIO STATE UNIVERSITY ( n a n as arcanto) nunoML,...... ± /U MECHANICAL ENGINEERING DEPARTMENT — COLUMBUS. OHIO OCCMM...... ± 0.010 REP. ASSY. NO. ANOIIIM ...... d b 111 PROJECT No. DI S S E R T . CCALK FULL OWN. BY H.Lljon* 3 *13 *7* TfTLK ewe. n o . SLIP AMPLITUDE CKO. BY 3-U-7* LVDT BOPV CLAMP 1005 260 I* 3 3 4* /6 L_ 1 J| • ______

3 1-72 N P 32 2-56 NC

FIGURE 76 5. 8 C ore R o d 308 S.Stf. 32 * *2 QUAN. PANT NO. PAirr KAHt MATERIAL p o u c h sac REMARKS — TOLERANCES— THE OHIO STATE UNIVERSITY (nccrr u inann) ., fractional...... & /&* MECHANICAL ENGINEERING DEPARTMENT - COLUMBUS. OHIO OCCIMAL A O .O IO M*«UI ..... ± /x° PROJECT No. DiaseciT. SCALE 2' * I* REP. AS ST. NO. OWN. BY TITLE OWC.NO IT-iS-Tt SLIP a m p l it u d e CKO. BY M.l 3 LVDT CORE ROD I 006 7842 tu o X- 0 0 5 GROOVE WIDTH V) u 0 .7 5 0 p. hi .055 ¥ U <® .0 3 0 | 6 K O O V6 DEPTH

G r o o v e D e t a il

FIGURE 77

16 FRETTING SHOE 1020 COT GROOVES

16 f r e t t i n g s h o e 4-340 COT GROOVES 16 FRETTING SHOE S'2.100 COT GROOVES OUAM. PART NO. HATERIAI. HOUGH sots REMARKS — TOLERANCES— THE OHIO STATE UNtVERStTY (m m as snancs> RRACYIOMALi /l.^ MECHANICAL ENGINEERING DEPARTMENT — COLUMBUS. OHIO •KCWAL » O lO •CALC w*l’ n o AN9IKAV PROJECT No. DISSERT. 4 REP.ASST. TITLE DVTO.NO. OWN. BY H.LYOOS 7-t*T7 GROOVES FOR CKO. BY 7-6-77 FRETTING SHOES 1007 262 &D I A. 26.S

16

CAR.50C0 V FIGURE 78 OtfAH. PART N*. MAT NAMC MATERIAL ROUGH IfZI !R REMARKS — TOLERANCE*— THE OHIO STATE UNIVERSITY (neat a* in o m ) r u o t o K A i ...... ft yi«. MECHANICAL ENGINEERING DEPARTMENT - COLUMBUS. OHIO decimal ...... ft .oio ARiUlAR ...... ft project no . d i s s e r t . (CALC 'Z* I* REP. ASC*T. Hat. DWG. NO. BWH.tr J.lVonS 7*t*n TITLE SHOE GROOVING TOOL 1008 CKO. AV M.LYo m S 263 ■i D R ILL x *6 TO MATCH TOOL D»A DRILL UP TO 3 1 SLOT

mko

371

.TAP 10-32*

FIGURE 79

OUAN.| PART No. | FART NAME | IfATCRIAL | ROUGH SI2C | RCMARKS — 1 rOLCRANCtS— THE OHIO STATE UNIVERSITY Cocirr as inann! rMACTIQMAl MECHANICAL ENGINEERING DEPARTMENT - COLUMBUS. OHIO OCCIMAV ANAULAN .. FROJECTNo. PlSOftET SCALE FULL rcf.a s r t .n o . — OWN. BY TITLC _ DWG, NO. H. LVorJS 7-fe-77 QROO V I N < 5 T O O t - c k o . ar H.LVorJS 7-fa-T» MOlDtMG PICTURE 100 9 APPENDIX D

CORRECTIONS TO NORMAL APPROACH RAW DATA

265 APPENDIX D

CORRECTIONS TO NORMAL APPROACH RAW DATA

Zero Wear Line

LVDT Core Specimen LVDT Body

FIGURE 80: Normal Approach Transducers.

Problem: During operation, misalignment may occur between LVDT body and core. This can lead to unequal transducer movements. Misalignment possibilities and solutions are shown in Figure 81.

The following procedure was used to tabulate normal approach raw data for identification of unequal trans-. ducer movements.

266 267

1. At the conclusion of a fretting-wear test, the multipoint recorder printout was divided into 10,000 cycle increments.

2. The magnitude of normal approach was noted on the recorder printout at the intersection of a 10,000 cycle increment and the normal approach loci.

3. Normal approach data were transferred to a "worksheet" as follows. a. The change in magnitude of each transducer for each 10,000 cycle increment was listed in columnar form. b. Transducer data that increased in magnitude with respect to 10,000 cycles of fretting were termed positive normal approach. c. Transducer data that decreased in magnitude with respect to 10,000 cycles of fretting were termed negative normal approach.

4. The magnitude and sense of changes in normal approach for each of the two transducers were compared at each 10,000 cycle level. 5. The net normal approach at a given 10,000 cycle increment was computed in accordance with the "corrections" shown in Figure 81. «

268

6. The total normal approach due to fretting-wear for a full test run is the sum of the incremental values of normal approach evaluated at the 10,000 cycle increments as described above.

LVDT WEAR SITUATION CORRECTIONS TO RAW DATA

Specimen . Core Core

Wear “ %m,

Jammed Core

■ n

Unequal Positive

Wear - Zero (pos.) (neg [Equal Neg. & Pos.

Wear - %(m2 - m :) (pos.) (neg.) Unequal Neg. & Pos.

FIGURE 81: Corrections to Normal Approach Transducer Raw Data. APPENDIX E

CALIBRATION DATA

269 APPENDIX E

CALIBRATION DATA

TABLE 18 SPECIMEN AXIAL PRELOAD LOAD-CELL CALIBRATION DATA The specimen load-cell was calibrated on an Instron Tensile- Testing machine (OSU 483295). A carrier amplifier of Consolidated Engineering Corporation, type 1-118 (OSU 246300), was used in conjunction with a Fluke 8000A Digital Multimeter (OSU 731126). Strain was read on the Multimeter in millivolts. Values shown are an average of three runs with increasing load and three with decreasing load.

Load (lb) Indicated Strain (mv)

-1000 34.0 - 750 25,5 - 500 17.1 - 250 8.7 0 0.0 250 8.6 500 17.0 750 25.3 1000 33.9

270 271

Tension

20 Indicated Strain Indicated Strain (millivolts)

250 500 750 1000 -1000 -750 -500 -250 0 Load (Pounds)

FIGURE 82s Specimen Axial Preload Load Cell Calibration Curve. TABLE 19 FRETTING-SHOE FORCE-TRANSDUCER CALIBRATION DATA

The force-transducer was calibrated on an Instron Tensile- Testing machine (OSU 483295). A carrier amplifier of Consolidated Engineering Corporation, type 1-118 (OSU 246300), was used in conjunction with a Fluke 8000A Digital Multimeter (OSU 731126). Values shown are an average of three runs. Compensation gages were permanently installed within the transducer for temperature compensation.

Load (lb) Indicated Strain (mv) 0 0.0 200 7.8 400 13.2 600 20.0 800 25.5 1000 30.8

272 273

40

30

20 Indicated Strain Indicated Strain (millivolts) 10

0 200 I 600 800 1000 Load (pounds)

FIGURE 83: Fretting-Shoe Force-Transducer Calibration Curve. TABLE 20 MOTION-MEASURING TRANSDUCER CALIBRATION DATA

The motion-measuring transducer consisted of a linear variable differential transformer (LVDT). The calibration fixture used the spindle of a micrometer caliper to drive the transducer, whose mechanical and electrical displace­ ments were read, respectively, on a dial gage and, via carrier amplifier, on a Digital Multimeter. Values shown are an average of five runs.

Actual Amplitude Measured by An Indicated Accurate Dial Gage (in) Displacement (mv)

0.000 0. 0.001 23.5 0.002 47.4 0.003 71.0 0.004 94.5 0.005 118.0

274 p

275

120 Indicated Indicated Displacement (millivolts)

0 0.001 0.002 0.003 0.005 Displacement (inches)

FIGURE 84: Motion-Measuring Transducer Calibration Curve. TABLE 21 NORMAL APPROACH TRANSDUCER CALIBRATION DATA

The motion measuring transducer consisted of a linear variable differential transformer {LVDT). The calibration fixture used the spindle of a micrometer caliper to drive the transducer, whose mechanical displacement was read on a dial gage; and whose electrical displacement was fed to an ATC demodulator/amplifier and read on a Digital -2 Multimeter (OSU 731126). A 3.3 x 10 microfarad capacitor, placed across the demodulator's primary and secondary terminals, doubled transducer output from 0.010 in (at 50 mv) to 0.020 in (at 100 mv). Values shown are an average of.five runs.

Actual Amplitude Measured by An Indicated Accurate Dial Gage (in) Displacement (mv) 0.000 0. 0.004 20.1 0.008 40.0 0.012 59.8 0.016 80.1 0.020 100.0

276 277

100 Indicated Displacement Indicated (millivolts)

0.004 0.008 0.012 0.016 0.020

Displacement (inches)

FIGURE 85: Normal Approach Transducer Calibration Curve. APPENDIX F

FRETTING-WEAR TEST PROCEDURE

278 APPENDIX F

FRETTING-WEAR TEST PROCEDURE

A. Pre-Test Equipment Check 1- Amplification Equipment a. Carrier Amplifier (1) Adjust oscillator (full-scale). (2) Remove all inputs. (3) Insert test devices in input receptacle to measure consistency of gain. (One device for channels 1 and 4; other device for channels 2 and 3.) (4) Restore inputs. b. ATC Demodulator (1) Temporarily hook-up Normal Approach LVDT's. (2) Use test device on each Demodulator to measure consistency of gain. c . Peak Meter (1) Set at "RMS" and "REF". (2) Calibrate to setting no. 8.

279 280

2. Null Instruments

a. Hook-up all instruments under no-load condition. b. Adjust "Resistive Balance" on Amplifier until null is achieved.

3. Preliminary Data a. Using Sling Psychrometer, obtain DBT and WBT and determine Relative Humidity. b. Record Mark No.'s of Specimen and Shoes. c. Obtain Profilometer data of specimen surface.

B. Specimen Test Setup (Note: N.S. « Near Side; F.S. *= Far Side.) 1. Clean and degrease specimens and shoes (using 1,1,1,Trichloroethane). 2. Mount shoes in N.S. and F.S. Fretting Blocks. 3. Mount specimen in loading column of test machine. Monitor Axial Preload to assure specimen is butted against upper pressure plate before fully-tightening bolts. 4. Set axial preload value on specimen and lock. 5. Mount F.S. Fretting Block and square with specimen face. 6. Attach Slip LVDT body bracket to F.S. Block. Do not lock. 281

7. Attach Normal Approach LVDT body bracket to F.S. Block. 8. Obtain Imprint of F.S. shoe on specimen using onion skin and carbon paper. Adjust until full' shoe print is obtained. 9. Bolt F.S. Fretting Block to horizontal support plates. 10. Attach Slip LVDT core bracket. Rotate eccentric manually to assure smooth functioning. 11. Lock Slip LVDT body bracket. 12. Insert Normal Load compression rod assembly in F.S. Block. (This partial assembly includes the 4 rods and their mating block.) 13. Mount N.S. Fretting Block and, using onion skin and carbon paper, square face with specimen. 14. Remove N.S. Fretting Block and fasten to it the Normal Approach LVDT core bracket. 15. Re-mount N.S. Fretting Block. 16. Adjust Normal Approach LVDT.core rods. Do not lock. 17. Lock set screw of Normal Approach LVDT core rod bracket. 18. Bolt N.S. Fretting Block to horizontal support

plates. 19. Re-check position of Normal Approach LVDT core rods; lock. 282

20. Mount N.S. compression plate on compression rods. 21. Retain shoe imprints for record. 22. Set Peak Meter at "PEAK" and ”0.1" (100 mv full- scale) .

C. Prior to Test Run 1. Check and record (static) values for Slip, Normal Load, Axial Preload, Normal Approach. 2. Set up eccentricity for Slip amplitude. 3. Partially compress Normal Load transducer. 4. Turn on fretting-wear drive system; quickly assess slip amplitude vs. normal pressure. Adjust eccentric as required to obtain desired values of Slip and Normal Load. 5. Set Counter.

D. Test Run 1. Turn on Multipoint Recorder. 2. Turn on fretting-wear drive*system. 3. Continuously monitor Slip (using B&K Peak Meter, and Scope), and manually modify Normal Load to maintain constant Slip amplitude. 4. Photograph Slip curve oi> Scope. Post Run 1. Record (static) values for Slip, Normal Load, Axial Preload, Normal Approach. 2. Dismantle test setup. 3. Mark appropriate faces of specimen "N.S." and "F.S."; mark shoes similarly. 4. Obtain Profilometer data. 5. Obtain SEM data.

Miscellaneous 1. Periodically check calibration of instruments. 2. Periodically check tightness of fretting fixture. «

APPENDIX G

FRETTING-WEAR TEST LOG

284 APPENDIX G FRETTING-WEAR TEST LOG

Date Test No. Material 1020 4340 52100 1020 4340 52100 Specimen Bar Marking Shoe Shoe Yes Grooving No Equipment Ampl'r. Check Demod. Profil* r. Start (RMS) End No! of Cycles Frequency Preload Start Lbs. End Norm Load Start Lbs. End Slip Amplitude Peak Meter Setting Scope Check Normal Start App. (mv) End SEM Yes • Record No Dry Bulb, °F , Wet Bulb, °F Relative Humidity Hardness Notes

285 APPENDIX H

RECORDER PRINTOUT SUMMARY

286 APPENDIX H

RECORDER PRINTOUT SUMMARY

Start Value End Value Parameter Trans'r Net Change Remarks Number mv unit mv unit + or -

Preload

Normal Load Slip Normal Approach

287 APPENDIX I

MULTIPOINT RECORDER PRINTOUT

288 Stop 20K

Normal Axial Approach Preload

10K

Normal Normal Slip Approach Load

Start

80 Millivolts 289 FIGURE 86; Recorder Test No. 10. SAE 52100. 20,000 Cycles. Type I Test. «

APPENDIX J

METALLOGRAPHIC SPECIMEN PREPARATION

290 APPENDIX J

METALLOGRAPHIC SPECIMEN PREPARATION

A. Electroplating 1. Spotweld stainless steel wire to specimen. 2. Clean with Acetone. 3. Air dry. 4. Suspend in plating bath. 5. Develop approximately 5 mils plating per face. 6. Clean with distilled water.

B. Mounting 1. Place desired surface face-down in silicone cap.

Silicone Cajr Resin

.Specimen Desired Surface

2. Mix resin: 2 parts powder to 1 part "Quickmount,"

by volume. 3. Stir 90 seconds. ' 4. Allow 30 minutes setup time.

291 292

C. Grinding 1. Coarse: 120 grit belt, with water. 2. Graduated fine: 8" disc, with water. a. 240 grit b. 320 grit c. 400 grit d. 600 grit 3. Clean with methanol or ethyl alcohol.

D. Polishing 1. Rough a. One micron diamond paste and kerosene. b. Mount specimen in holder with 1/8 in proj. c. Polish 1-3 hours. d. Clean with ethyl alcohol. e. Clean with detergent and water. f. Water rinse. g. Air dry. 2. Fine a. 0.05 micron alumina and distilled water. b. Mount specimen in holder. c. Polish 1-3 hours. d. Clean with detergent and water. e. Water rinse. f. Air dry. Note: Use different cloth pairb for diamond and alumina.

E. Etching Use 5% Nitric acid in methanol or ethyl alcohol solution. APPENDIX K

ELECTROPLATING OP SPECIMEN

293 APPENDIX K

ELECTROPLATING OF SPECIMEN

Specimen (Cathode) Electrolyte

Resistance Box Anodi Milliameter Power Supply Thermometer Asbestos Pad

FIGURE 87: Schematic of Electroplating.

Operation 1. Heat electrolyte to 40-60°C. 2. Maintain temperature. 3. Set polarity switch on power supply to "Normal". 4. Turn on power supply. 5. Adjust output control to 25 ma. 6. Increase to 50 ma after % hour. 7. Develop approximately 5 mils plating per surface.

294 APPENDIX L

DESIGN DATA

295 296 100 (395,87.8) [WO, »T9] 1020

Model, C

Actual, C

100

MlOO 52100

a 50

(360,18.9)

100 200 300 No. Cycles, Thousands

FIGURE 88: Design Data: Type I. Normal Approach. In. x 10 10 - IUE8: DesignData: II. Type FIGURE89: Model, G Model, No. Cycles, Thousands Cycles,No. 52100 4340 1020 (62.8,5.6) (65.6,9.8) cul C Actual, ( 9 2 . 2 , 1 2 . 3 ) 100 297 298

1020

Model, C

Actual, C

4340

52100

20

100 No. Cycles, Thousands

FIGURE 90: Design Data: Type III. 299

1020 (72.8,30.3)

Model, C

Actual, C

(73.0,15.9)

S 40 52100

3 20

CL (64.2,12.3) (100,11. l)

100 No. Cycles, Thousands

FIGURE 91: Design Data: Type IV. 1020 (77.3,32.2) 30- Model, C

2 0 " Actual,9 C i

10 -

30-

(37.4,17.)

1 0 -

52100

(64.2,13.1)

1 0 -

100 No. Cycles, Thousands

FIGURE 92: Design Data: Type V. 301

1020 (62.5.32.9) Model, C

20 -

Actual, C

4340

(53.7,26.2)

52100 •rt

'40 60 100 No. Cycles, Thousands

FIGURE 93i Design Data: Type VI APPENDIX M

SAMPLE CALCULATIONS OF ASPERITY INTERACTIONS BASED UPON STATISTICAL ANALYSIS AND HERTZIAN CONTACT STRESS THEORY

302 APPENDIX M

SAMPLE CALCULATIONS OF ASPERITY INTERACTIONS BASED UPON STATISTICAL ANALYSIS AND HERTZIAN CONTACT STRESS THEORY

1. Sample Calculation of Asperity Interactions Using Statistical Data for a Gaussian Distribution of Asperities. a. Number of Interacting Asperities

N 1 1 f 0 (h) n_ = 0.75 B9% V h) b. Total Asperity Contact Area

Nn B-% F,

where: N = 500 pounds E'= % (E/l-v2)»%(30xl06psi/l-(.33)2)»17xl0*psi

Let: a = 10x10*"* in; 6 = 10°; h « 1.5

303 304

Then: a = a/ 2 = 10xl0”V 2 = 14.14x10”* in 9

0g = a/”2/2 (1-cos 6) = 10xl0“€/27(.0304)=4.66xl0"',in

F0(h)/FK (h) = 2.75

F x (h)/F^ (h) = 1.21

Therefore: 500 1 1 2.75 n « 0.75------r—r — g 17x10* (4.66x10” )* (14.14x10)

ng « 53,000 interacting asperities for RMS roughness of 10 microinches

(500)(3.14) (4.66x10"")^ A_Q = 0.75 ------1.21 17x10* (14.14x10”*)*

Ag =0.481x10”5 in2 total asperity contact area for RMS roughness of 10 microinches

Using the statistical values shown above with the Tallian Model (96) for the asperity profile, the following data are evaluated. Contact Area per Asperity

A » A /n eg g g

« 0.481x10** 3/53 x10 3

eg = 0.908x10"* in2

Diameter of Asperity at Contact Interface

D g -

/4 (0.908x10"*)/3.14

Dg « 1.09x10"" in

Asperity Deformation (Normal Approach)

H » %D„ Tan 0 g g

%(1.09x10“")(Tan 10°)

H = 0.950xl0-5 in 9 306

2. Sample Calculation of Asperity Interactions Using Hertzian Contact Stress Theory.

The following calculations apply to the contact between two spherical bodies. a. Normal Approach

6 « 1.23

b. Maximum Contact Pressure

p„o « 0.388

Let: Normal load, N « 500 pounds Number of interacting asperities = 53x10s (from statistical sample calculation). Standard deviation, a = lOxlO-6 in

Then: P * 500/53x103 = 0.0095 lb/asperity

R,i ■ R, z = B„ g * 4.66xl0-1* in (from statistical sample calculation). .

E* = % (E/1 - v2) = 17x106 psi (from statistical sample calculation) Therefore:

3/ (9.5xlO"V (9.32x10"*) 6 = 1.23 (17x10®)2 (4.66xlO"*V

— s 6 = 1.35x10 in normal approach

3 I (9.5xl0“3)(17x10®)2(9.32x10"")2 Po = °-388 / -- * xl (4.66x10 )*

pQ = 1.45x10® psi maximum contact pressure APPENDIX N

SAMPLE CALCULATION OF SPECIFIC WEAR RATE

308 APPENDIX N

SAMPLE CALCULATION OF SPECIFIC WEAR RATE

Sample Calculation of Specific Wear Rate for SAE 1020 Steel, Type I Test.

Specific Wear Rate = (Normal LoadMTotalGliding Distance)

At 100,000 cycles of fretting wear: Wear Volume = (Nominal Contact Area)(Normal Approach) = (0.05 in2) (16.1 x 10"1* in) « 8.1 x 10"s in3 Normal Load = 490 lb at 100,000 cycles Total Sliding Distance = 7.5 x 102 in

Therefore: 8.1 x 10-5 SW (490)(7.5xl02)

SW = 22 x 10"11 in3/in-lb .

If specific wear rate is computed at, say, 20,000 cycle in­ crements, the average of these incremental values over 100,000 cycles of fretting-wear is 23xlO- M in*/in-lb. This may be further compared with the' Nomogram (74) value of 29.5x10™11 in3/in-lb using the above values of volume, load and distance. «

LIST OF REFERENCES

1. AGARD Conference Proceedings No. 161, Specialists Meeting on Fretting in Aircraft Systems, Technical Editing and Reproduction, Ltd., London, 1975. 2. Alley, T. L., "An Investigation of the Basic Mechanism Whereby Fretting Induces Fatigue Failure of Metals," M.Sc. Thesis, The Ohio State University, Columbus, Ohio, 1960. 3. Almen, J. O., "Lubricants and False Brinelling of Ball and Roller Bearings," Mechanical Engineering, Vol. 59, 1937, p. 415. 4. Archard, J. F., "Contact and Rubbing of Flat Surfaces," J. Appl. Phys., Vol. 24, No. 8, Aug. 1953. 5. Archard, J. F. and Hirst, W., "The Wear of Metals Under Unlubricated Conditions," Proceedings of the Royal Society of London, A, 236, 1956, pp. 397-410. 6. Bayer, R. G. and Schumacher, R. A., "On the Signifi­ cance of Surface Fatigue in Slidinq Wear," Wear, Vol. 12, 1968. 7. Bethune, B. and Waterhouse, R. B., "Adhesion of Metal Surfaces Under Fretting Conditions: I. Like Metals in Contact," Wear, Vol. 12, 1968, pp. 289-296. 8. Bethune, B. and Waterhouse, R. B., "Adhesion of Metal Surfaces Under Fretting Conditions: II. Unlike Metals in Contact," Wear, Vol. 12, 1968, pp. 369-374. 9. Bill, R. C., "Study of Fretting Wear in Titanium, Monel-400, and Cobalt-25 Percent Molybdenum Using Scanning Electron Microscopy," ASLE Transactions, Vol. 16, 1973. 10. Bowden, F. P. and Tabor, D., The Friction and Lubri- cation of Solids, Oxford University Press, Chap. 14, 1950, pp. 290-295.

310 311

11. Bowden, P. P. and Tabor, D.r Friction and Lubrication, Methuen and Co., Ltd., London, 1967. 12. Boyd, J., (ed.). Lubrication Science and Technology, Vol. 1, No. 2, Pergamon Press, New York, 1958, pp. 312-328. 13. Campbell, W. E., "The Current Status of Fretting Cor­ rosion," Symposium on Fretting Corrosion, ASTM Special Publication No. 144, 1953, p. 2. 14. Campbell, W. E., "Fretting," in Boundary Lubrication— An Appraisal of World Literature, ASME Research Committee on Lubrication, 1969, pp. 119-131. 15. Cary, H. and Thomas, R. E., "Accelerated Testing as a Problem of Modeling," Proceedings, Sixth National Symposium on Reliability and Quality Control in Electronics, Washington, D.C., Jan. 11-13, 1960. 16. Caudy, D. W., "The Design and Development of a New Research Facility Capable of Performing Fretting- Fatigue Studies Using a Simplified Specimen Shape," M.Sc. Thesis, The Ohio State University, Columbus, Ohio, 1968. 17. Collins, J. A., "A Study of the Phenomenon of Fretting- Fatigue with Emphasis on Stress-Field Effects," Ph.D. Dissertation, The Ohio State University, Colun&us, Ohio, 1963. 18. Collins, J. A., "Fretting-Fatigue Damage-Factor Determination," ASME Paper No. 64-WA/MD-10, 1964. 19. Collins, J. A., and Tovey, F. M., "Fretting-Fatigue Mechanisms and the Effect of Direction of. Fretting Motion on Fatigue Strength," Journal of Materials, Vol. 7, No. 4, December, 1972. 20. Collins, J. A., "Failure Prevention Analysis in Mechanical Design," The Ohio State University, Columbus, Ohio, 1972. 21. Conlon, T. W., "Thin Layer Activation by Accelerated Ions— Application to Measurement of Industrial Wear," Wear, Vol. 29, 1974. %

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