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Viscoelastic effects in boundary lubrication Green, Marjorie Ann Carlson 1974

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VISCOELASTIC EFFECTS IN BOUNDARY LUBRICATION BY MARJORIE ANN CARLSON GREEN B.A.Sc, The U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B r i t i s h Columbia, 1967 M.A.Sc., The U n i v e r s i t y of B r i t i s h Columbia, Vancouver, B r i t i s h Columbia, 1971 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of Mechanical Engineering We accept t h i s t h e s i s as conforming to the re q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1974 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at The U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s representatives. I t i s understood that p u b l i c a -t i o n , i n part or i n whole, c r the copying of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Marjorie Ann Carlson Green Department of Mechanical Engineering The U n i v e r s i t y of B r i t i s h Columbia Vancouver, B.C. Date C|fwA I ( inC-ABSTRACT The static f r i c t i o n of steel under boundary lubricated con-ditions was investigated both experimentally and theoretically. The theoretical model was developed using the assumption that during the application of a tangential load to a f r i c t i o n couple, the real area of contact grows in a viscoelastic manner u n t i l a c r i t i c a l shear stress is reached. Using this model, i t was possible to d i s t i n -guish the effect of static and dynamic contact time on area growth and thus to show why the traditional "time dependence of static f r i c t i o n " theories have limited validity. The model predicts that u g , the static f r i c t i o n coefficient, i s a function of the rate parameter 0, and that a relaxation time can be assigned to a given interface. Subsequent experimental work using steel surfaces i n vacuum as well as steel surfaces lubricated by various surface films showed that surface conditions play a large role in determining the exact U G - 6 relationship for a given f r i c t i o n couple. Over the range of 9 investigated the static f r i c t i o n coefficient of steel is constant i f certain surface films are present; for other films the static f r i c t i o n coefficient vs 8 curve shows an upper and lower asymptote. In the latter case a relaxation time was assigned to each boundary lubricant. For given asymptotes these relaxation times can be used to predict whether the film w i l l be a useful lubricant at a particular 8. A subsequent investigation showed that the relaxation times are strongly affected by temperature. Since raising the substratum temperature results in smaller relaxation times, i t i s obvious that a particular lubricant may become ineffective as the substratum tempera-ture changes. i i i Both the experimental and t h e o r e t i c a l work c l e a r l y demonstrate that the s t a t i c f r i c t i o n of s t e e l can be s i g n i f i c a n t l y modified by the a p p l i c a t i o n of appropriate boundary lubricants. TABLE OF CONTENTS Page CHAPTER I . INTRODUCTION . . '. 1 CHAPTER I I . HISTORICAL BACKGROUND 5 CHAPTER I I I . THEORY . ' . . 16 3.1 I n t r o d u c t i o n 16 3.2 Models f o r S t a t i c F r i c t i o n 18 3.3 The Non-dimensional u v s T* P l o t 23 s 3.4 Changing the R e l a x a t i o n Time of an I n t e r f a c e 24 3.5 The E f f e c t of. Temperature on T Values 28 CHAPTER I V . EXPERIMENTAL APPARATUS AND EXPERIMENTAL PROCEDURE . 32 4 .1 Apparatus , . 3 2 4.2 P r e t e s t P r e p a r a t i o n of Samples 41 4.3 General Experimental Procedure 46 CHAPTER V . RESULTS AND DISCUSSION 47 5 .1 I n t r o d u c t i o n 47 5.2 Obta ining S t a t i c F r i c t i o n Informat ion f o r the S t e e l / S t e e l System 47 5.3 D i s c u s s i o n of u - 6 R e s u l t s 55 s 5.4 Dimensionless u ~ 6 Curves 64 s 5.5 E f f e c t of Temperature on S t a t i c F r i c t i o n . . . . . 65 Page CHAPTER VI. SUMMARY AND GENERAL DISCUSSION OF RESULTS 69 6.1 Summary 69 6.2 The Contact Area at S l i p 70 6.3 A p p l i c a b i l i t y of Results to Lubricant S e l e c t i o n 71 6.4 A Note on the Time-dependence of S t a t i c F r i c t i o n 73 CHAPTER VII. CONCLUSIONS 77 BIBLIOGRAPHY 80 APPENDIX I. THE VACUUM SYSTEM APPENDIX I I . PROPERTIES OF REAGENTS USED APPENDIX I I I 85 88 90 FIGURES 91 v i LIST OF TABLES Page TABLE I. Calculated Values of Relaxation Time, V i s c o s i t y , E l a s t i c Modulus and Shear Strength f o r the 2-Parameter Model 59 TABLE I I . E l a s t i c M o d u l i i and V i s c o s i t y Values as a Function of T /p f o r the 3-Parameter Model 62 o m TABLE I I I . V i s c o s i t i e s of Some Ma t e r i a l s 63 v i i LIST OF FIGURES Page FIGURE 1. V i s c o e l a s t i c Model of S t a t i c F r i c t i o n Developed by Johannes [19] . .... 91 FIGURE 2a. The Contact Area Between Two S o l i d Surfaces i s the Sum of the Small D i s c r e t e Areas of Contact Formed Where Opposing A s p e r i t i e s Meet 92 FIGURE 2b. The Area of Contact.and the Shear Strength as Functions of the Rate of A p p l i c a t i o n of the Tangential Shearing Force , 93 FIGURE 3. Tangential Loading During a S t a t i c F r i c t i o n Test .... 94 FIGURE 4. Models f o r S t a t i c F r i c t i o n ... 95 FIGURE 5. General Form of the u - 6 Curve 96 s FIGURE 6. Changing c Results i n a Family of y g -'6 Curves 97 FIGURE 7. The General S t a t i c F r i c t i o n Curve 98 FIGURE 8. General Arrangement of Vacuum System and Experimental Apparatus 99 FIGURE 9. Isometric Diagram of Experimental Apparatus , 100 FIGURE 10. Schematic of the Hydraulic Control System 101 FIGURE 11. Isometric Sketch of F r i c t i o n Couple 102 FIGURE 12, S t a t i c F r i c t i o n of C1020 St e e l i n Vacuum of 2 x 10" 8 t o r r at 20°C 103 FIGURE 13. S t a t i c F r i c t i o n of C1020 S t e e l i n Vacuum and A f t e r Exposure to Atmosphere 104 FIGURE 14. Comparison of S t a t i c F r i c t i o n of C1020 St e e l i n Vacuum 105 FIGURE 15. S t a t i c F r i c t i o n of C1020 S t e e l Covered with Oxide Films 106 FIGURE 16. Comparison of S t a t i c F r i c t i o n of.Oxide-covered C1020 Steel , 107 FIGURE 17. S t a t i c F r i c t i o n of C1020 St e e l A f t e r Abrading Surface Under S t e a r i c Acid-Hexane Solution 108 FIGURE 18. S t a t i c F r i c t i o n of C1020 St e e l Covered with a Monolayer of E i t h e r a Basic Iron Stearate or a Basic Iron Oleate 109 v i i i Page FIGURE 19. The E f f e c t of a C a ( S t ) 2 Monolayer on S t a t i c F r i c t i o n as Compared to the E f f e c t of an Fe(0H)2St Mono-laye r , ... 110 FIGURE 20. The E f f e c t of a C a ( 0 J 0 2 Monolayer on S t a t i c F r i c t i o n Compared to the E f f e c t of an Fe(0H)2 OZ Monolayer ... I l l FIGURE 21. Experimental Data and T h e o r e t i c a l y - 6 Curve f o r S t a t i c F r i c t i o n : Fe(0H) 2St Monolayer 112 FIGURE 22. Experimental Data and T h e o r e t i c a l y - 0 Curve f o r S t a t i c F r i c t i o n : C a ( S t ) 2 Monolayer 8 113 FIGURE 23. Experimental Data and T h e o r e t i c a l y - 8 Curve f o r S t a t i c F r i c t i o n : Fe(0H) 2 01 Monolayer 114 FIGURE 24. Experimental Data and T h e o r e t i c a l y - 0 Curve f o r S t a t i c F r i c t i o n : Ca(0&) 2 Monolayer 5 115 FIGURE 25. Experimental Data Collapses on General y - T * Curve Predicted from Mathematical Model 116 FIGURE 26. E f f e c t of Raising Surface Temperature to 35°C. Ca Stearate Soap Monolayer 117 FIGURE 27. E f f e c t of Raising Surface Temperature to 50°C. Ca Stearate Soap Monolayer . • 118 FIGURE 28. Log c vs 1/T f o r Calcium Stearate Soap Monolayers ... 119 FIGURE 29. y - 8 - T Surfaces f o r Various Conditions .......... 120 s FIGURE 30. y - T C h a r a c t e r i s t i c s of S t e e l Covered with Calcium stearate Monolayer 121 FIGURE 31. Experimental Temperature-Friction Data f o r Calcium Stearate Monolayer Covered Surface , 122 FIGURE 32. Loading H i s t o r y During Delayed S t i c k 123 FIGURE 33. Area Growth Due to Delay Time i f the System has a Relaxation Time of 40 Sees 124 ACKNOWLEDGEMENT iz The experimental part of t h i s program was c a r r i e d out i n the Tribology Laboratory of the Department of Mechanical Engineering at The U n i v e r s i t y of B r i t i s h Columbia. The author wishes to thank . Dr. C.A. Brockley f o r h i s advice and encouragement during the program. S p e c i a l thanks are due Dr. E.G. Hauptmann of the Department of Mechanical Engineering and Dr. J. Leja of the Department of Mineral Engineering f o r t h e i r suggestions and comments. F i n a n c i a l assistance was received through the N a t i o n a l Research Council of Canada and i s g r a t e f u l l y acknowledged. LIST OF SYMBOLS contact area at time t i n i t i a l contact area activation energy shearing force, tangential force rate of application of shearing force surface shear modulus creep compliance normal load shear stress c r i t i c a l shear stress of interface shear strength of l u b r i -cating films ^ shear strength of solid temperature shear strength of inter-face viscosity parameter i n mathematical model elastic parameter in mathematical model yield pressure of material time, time to failure a constant proportion of solid-solid contacts in an interface Units i n 2 i n 2 Kcal-gm-mole-1 lbs lbs-sec - 1 dynes-cm _ 1 dimensionless lbs .-• . l b - i n "2 l b - i n " 2 l b s - i n - 2 l b s - i n - 2 °K l b s - i n " 2 in-sec-lb _ 1 l b - i n _ 1 l b s - i n " 2 sec dimensionless dimensionless Symbol U n i t s e(t) s t r a i n m per i n c(t) s t r e s s l b s - i n " 2 8 r a t i o of r a t e of a p p l i c a - sec 1 t i o n of shearing f o r c e , F to the normal load, N. n ,n ,n. surface v i s c o s i t y gm/sec s o i IT surface pressure dynes/cm U ,U , U s t a t i c f r i c t i o n c o e f f i c i e n t s dimensionless s s s . max. mm. r e l a x a t i o n time sec I. INTRODUCTION Given the long h i s t o r y of f r i c t i o n - o r i e n t e d research, to the casual observer i t might appear that f r i c t i o n and l u b r i c a t i o n are w e l l understood. C e r t a i n l y there i s ample evidence to show that even e a r l y c i v i l i z a t i o n s were aware of f r i c t i o n and knew enough about i t to pour l u b r i c a t i n g l i q u i d s i n f r o n t of sledges and to use r o l l e r s to move heavy loads. This same observer might a l s o point to the extensive 18th Century work of a number of European s c i e n t i s t s i n c l u d i n g Coulomb and Amontons. The three "fundamental laws of f r i c t i o n " — f r i c t i o n i s p r o p o r t i o n a l to load but independent of area and s l i d i n g v e l o c i t y — arose from t h i s work. Unfortunately, f r i c t i o n i s not the simple phenomenon that these laws would suggest and i n c e r t a i n s i t u a t i o n s the laws are not v a l i d . Thus f r i c t i o n studies s t i l l continue, not j u s t to d e f i n e the exceptions to Amontons' laws, but because modem basic research seeks a much b e t t e r understanding of the mechanisms of f r i c t i o n and i t s a l l i e d phenomena, l u b r i c a t i o n , wear and adhesion than e i t h e r these "laws" or the previous research can provide. One reason why f r i c t i o n research has progressed so slowly i s that s u i t a b l e research t o o l s have been developed only l a t e l y . I n s t r u -ments such as the e l e c t r o n microscope and surface roughness i n d i c a t o r s have aided f r i c t i o n research immensely i n the short time they have been a v a i l a b l e . In a d d i t i o n , the recent demand for s o p h i s t i c a t e d machinery capable of operating i n space, at high temperatures, at high speeds or 2 i n adverse environments, has stimulated f r i c t i o n research. Although some of the research has been of an ad hoc type, c a r r i e d out to provide immediate design data on d i f f e r e n t material combinations, systematic s c i e n t i f i c work was also funded. The lack of design data pointed out the most serious shortcoming of f r i c t i o n research: an i n a b i l i t y to pre-d i c t f r i c t i o n values. This problem i s p a r t i c u l a r l y acute f o r systems operating under boundary lu b r i c a t e d conditions. One p a r t i c u l a r aspect of boundary l u b r i c a t i o n , the s t a t i c f r i c t i o n of metals coated with t h i n f i l m s , was examined i n the present study. Unlike hydrodynamic l u b r i c a t i o n where the s l i d i n g surfaces are f u l l y separated by a f l u i d f i l m and the f r i c t i o n losses i n the system are due to the v i s c o s i t y of the f l u i d , boundary l u b r i c a t i o n occurs when the separating f i l m i s only a few molecules thick. Slow s l i d i n g speeds and high loads may cause l u b r i c a t i o n to be of the boundary l u b r i c a t i o n type. In any case, the important fact i s that the f r i c t i o n i s determined by both the properties of the f i l m and by the chemical and ph y s i c a l nature of the s o l i d s i n contact. When discussing boundary l u b r i c a t i o n , i t i s usual to recognize two kinds of boundary f r i c t i o n •— s t a t i c f r i c t i o n and k i n e t i c f r i c t i o n . S t a t i c f r i c t i o n i s defined as the force required to cause one of the contacting surfaces to begin to s l i d e over the other. K i n e t i c f r i c t i o n i s the force required to keep.the surfaces s l i d i n g with a constant v e l o c i t y . Besides the usual s l i d i n g t e s t s , s t a t i c and k i n e t i c f r i c t i o n can be studied using a type of friction--induced v i b r a t i o n c a l l e d r e l a x a -t i o n o s c i l l a t i o n s . From data obtained i n t h i s way, and from s l i d i n g t e s t s , i t was generally believed that s t a t i c f r i c t i o n was time-dependent and that 3 k i n e t i c f r i c t i o n was v e l o c i t y dependent. The explanation of the time-dependency of s t a t i c f r i c t i o n centered around the assumption that the ac t u a l contact area between the surfaces increased during the " s t a t i c " loading time that preceeded gross s l i p . The contact area was thought to be increased by the creep induced by the normal load. On c r i t i c a l l y examining the previous work, e s p e c i a l l y that of Johannes [19], i t becomes obvious that the "time-dependent" explanation has some severe l i m i t a t i o n s . By i n t e r r u p t i n g a f r i c t i o n t e s t f o r a given period of time, then r e s t a r t i n g the t e s t Johannes demonstrated that the e f f e c t of creep time on s t a t i c f r i c t i o n was minimal. No s i g n i f i c a n t increases i n s t a t i c f r i c t i o n were noted.' This observation encouraged him to r e j e c t the older explanation and to consider a s i n g l e a s p e r i t y as a v i s c o e l a s t i c body so that the increase i n contact area i s due to the load r a t e s e n s i t i v e deformation of that body when the shearing f o r c e i s a p p l i e d . Obviously, time i s involved i n t h i s model too, since the s t r a i n of a v i s c o e l a s t i c body i s completely determined by i t s loading h i s t o r y , but i t i s also obvious that equal amounts of loading time and creep time cannot have the same e f f e c t on the contact area. This approach to s t a t i c f r i c t i o n i s very promising. The use of the loading r a t e parameter, . * e = r a t e of a p p l i c a t i o n of shearing force normal load immensely s i m p l i f i e s r e p o r t i n g f r i c t i o n r e s u l t s . The use of e l a s t i c and viscous parameters i n d i c a t e s which pro p e r t i e s of a f r i c t i o n couple might a f f e c t s t a t i c f r i c t i o n . Under boundary l u b r i c a t i o n conditions, the f r i c t i o n i s d e t e r -mined by the prop e r t i e s of the l u b r i c a t i n g f i l m and by the p h y s i c a l and chemical p r o p e r t i e s of the underlying s o l i d . For a given s o l i d , i t i s 4 w e l l known that surface f i l m s of both organic and inorganic compounds can markedly a f f e c t i t s f r i c t i o n c h a r a c t e r i s t i c s . The aim of the present work i s to expand the t h e o r e t i c a l base and to i d e n t i f y the o r i g i n s of the observed v i s c o e l a s t i c e f f e c t s i n s t a t i c f r i c t i o n . 5 I I . HISTORICAL BACKGROUND Although f r i c t i o n phenomena have been studied f o r a long time, i t i s only during the l a s t 60 years that r e a l advances have been made i n . our understanding of the fundamental p h y s i c a l and chemical processes involved i n f r i c t i o n and l u b r i c a t i o n . A comprehensive review of every c o n t r i b u t i o n would be impossible because of the volume of. m a t e r i a l generated and unnecessary because several good reviews [22] already e x i s t . Because of t h i s and because published papers can vary g r e a t l y , both i n q u a l i t y and a p p l i c a b i l i t y to a s p e c i f i c problem, t h i s survey w i l l be l i m i t e d to a s e l e c t i o n of papers considered to be most s i g n i f i c a n t c o n t r i b u t i o n s to s t a t i c f r i c t i o n research. Most s t a t i c f r i c t i o n research would f a l l i n t o one of two general categories. In the f i r s t category, are studies concerned with the chemical and p h y s i c a l p r o p e r t i e s of surfaces. Research i n t h i s category i s p r i m a r i l y concerned with the e f f e c t s of surface f i l m s , both n a t u r a l l y occurring and d e l i b e r a t e l y applied, on f r i c t i o n . The e x p e r i -mental r e s u l t s of t h i s research are used mainly f o r d e s c r i p t i v e purposes. They tend to be more u s e f u l i n p r e d i c t i n g trends than i n p r e d i c t i n g a c t u a l boundary f r i c t i o n values. Because of e f f o r t s i n t h i s d i r e c t i o n , however, the boundary-lubricating q u a l i t i e s of various organic and inorganic compounds have been widely recognized and s u c c e s s f u l l y a p p l i e d . At the same time, c e r t a i n aspects of s o l i d - s t a t e and f r i c t i o n welding and other processes which require high f r i c t i o n values, were c l a r i f i e d by t h i s research. In the second category, the research tends to be orie n t e d towards the mathematical modelling of s t a t i c f r i c t i o n . Placed i n t h i s category, i s the large volume of published work dealing with the var i o u s aspects of f r i c t i o n - i n d u c e d o s c i l l a t i o n s , time-dependent s t a t i c f r i c t i o n and several attempts at modelling s t a t i c f r i c t i o n . One of the goals of t h i s type of research, besides a better understanding of f r i c t i o n , i s to f i n d a way to p r e d i c t q u a n t i t a t i v e l y boundary f r i c t i o n values. The study of boundary l u b r i c a t i o n was pioneered by Hardy [23] during the period 1918-1932. By 1920, both Hardy and Langmuir [56], a chemist, had recognized that small amounts of c e r t a i n organic compounds were capable of reducing s t a t i c f r i c t i o n . Langmuir was the f i r s t to demonstrate that even a s i n g l e monolayer could l u b r i c a t e a surface while Hardy was the f i r s t to prove that the molecular x<reight of an organic compound was an important f a c t o r i n reducing s t a t i c f r i c t i o n . H i s systematic i n v e s t i g a t i o n of a s e r i e s of organic a c i d s , a l c o h o l s , and s t r a i g h t chain p a r a f f i n s , showed that i n c r e a s i n g the chain length of an organic compound p r o g r e s s i v e l y decreased the s t a t i c f r i c t i o n c o e f f i c i e n t . Hardy went on to develop a theory of boundary l u b r i c a t i o n i n which adsorbed f i l m s of hydrocarbons played a major r o l e . He v i s u a l i z e d the opposing surfaces as being completely separated by adsorbed monolayer of the surf a c t a n t . His theory f u r t h e r s p e c i f i e d that there was no s o l i d - s o l i d con-t a c t over any part of the i n t e r f a c e between the s l i d i n g s o l i d s and that the f r i c t i o n a l r e s i s t a n c e was s o l e l y due to the s l i d i n g of one boundary l a y e r over the other. The work of Hardy and Langmuir stimulated f u r t h e r research i n boundary l u b r i c a t i o n and i n surfactant adsorption on s o l i d surfaces. Their work generated an i n t e r e s t i n the chemistry of adsorption, the structure and mechanical properties of surface f i l m s , the r e a c t i v i t y and. topography of s o l i d surfaces and the mechanics of surface-surface i n t e r -7 a c t i o n that continues today. During the course of l a t e r research on boundary f r i c t i o n , Hardy's o r i g i n a l theory was considered to be an o v e r - s i m p l i f i c a t i o n of a c t u a l f r i c t i o n conditions and i t was subsequently modified. The current t h e o r i e s of boundary f r i c t i o n and l u b r i c a t i o n accept Hardy's idea that s u r f a c e - a c t i v e substance can adsorb onto surfaces to form low shear strength f i l m s but they also s p e c i f y that a c e r t a i n amount of s o l i d -s o l i d contact must be expected. This m o d i f i c a t i o n was l a r g e l y the r e s u l t of s e v e r a l studies of wear p a r t i c l e s , surface damage and m a t e r i a l t r a n s -f e r generated during s l i d i n g under boundary l u b r i c a t e d c o n d i t i o n s [20] . Although the amount of wear i s d r a s t i c a l l y reduced by the a d d i t i o n of s u r f a c t a n t s , the f a c t that i t s t i l l occurs strongly supports the argument that there i s s o l i d - s o l i d contact through the f i l m . The modified boundary l u b r i c a t i o n theory a t t r i b u t e s the f r i c t i o n force to the combined r e s i s t a n c e of the s o l i d - s o l i d and f i l m - f i l m contact areas i n the f o l l o w i n g way. I f a Q represents the proportion of s o l i d - s o l i d contacts i n an i n t e r f a c e having a t o t a l contact area A, then the f r i c t i o n f o r c e i s F = A Ta S + (1 - a )Sn~], where S and S„ are the shear strengths of the [_os o Zj • s I s o l i d and the l u b r i c a t i n g f i l m r e s p e c t i v e l y . Assigning an exact value to S. i s d i f f i c u l t because the mechanical pro p e r t i e s of l u b r i c a t i n g f i l m s Xr • are d i f f i c u l t to measure. Akhmatov [17] , B a i l e y and Courtney-Pratt [58] and Scruton [47] have been able t o determine a number of p r o p e r t i e s , such as the shear modulus and the y i e l d s t r e s s , of the f i l m s . Scruton's recent work on m e t a l l i c soaps i s p a r t i c u l a r l y a p p l i c a b l e to boundary f r i c t i o n because i t shows that the shear strength of metal stearates i s not a constant value but that i t i s strongly a f f e c t e d by the contact 8 pressure. At 1 Kg/mm2, f o r example, the shear strength of calcium stearate i s .2 Kg/mm2, but when the contact pressure i s 200 Kg/mm2, the shear strength i s increased by a f a c t o r of 50, to 10 Kg/mm2. Another i n t e r e s t i n g aspect of boundary f r i c t i o n involves the chemistry of s u r f a c t a n t - s o l i d r e a c t i o n s . Some organic compounds are much more e f f e c t i v e as l u b r i c a n t s than others and, on the other hand, some metals are more " r e a c t i v e " than others. Bowden and Leben [16], G r e e n h i l l [46], Schulman et a l . [24] and many other i n v e s t i g a t o r s have used a v a r i e t y of techniques to study the formation and e f f e c t i v e n e s s of boundary f i l m s . The general conclusions ( s p e c i f i c a l l y a p p l i c a b l e to the present study) to be drawn from t h e i r work are: 1) Organic compounds can form oriented, h i g h l y s t r u c t u r e d f i l m s on metal surfaces. These f i l m s w i l l reduce f r i c t i o n and wear. Depending on the metal involved, the surfactant can be chemically or p h y s i c a l l y adsorbed onto the surface. With s p e c i f i c reference to f a t t y acids, a p a r t i c u l a r f a t t y a c i d may react with the substrata to form a m e t a l l i c soap or i t may only be p h y s i c a l l y adsorbed. Also, depending on the surfactant concentration and the time of exposure, the surface may be covered with a p a r t i a l monolayer, a monolayer or m u l t i l a y e r s of adsorbed species. 2) The e f f e c t of heating the substrata i s to change the s t r u c -ture of the f i l m [20]. Over a c r i t i c a l temperature range, the s t a t i c f r i c t i o n c o e f f i c i e n t w i l l increase markedly. Upon co o l i n g , the e f f e c t i s r e v e r s i b l e [20]. For some metals, the c r i t i c a l temperature i s approximately equal to the bulk melting point of the f a t t y a c i d ; for others, the temperature corresponds to the bulk melting point of the appropriate organometallic soap. 3) The mechanical d i s r u p t i o n of the surface during a f r i c t i o n t e s t can have two e f f e c t s . I f the surfactant i s no longer a v a i l a b l e to the surface, then the l u b r i c a n t l a y e r s are worn away by repeated t e s t i n g and higher s t a t i c f r i c t i o n values x j i l l r e s u l t [16] . In some s i t u a t i o n s , however, mechanical d i s r u p t i o n of the surface a s s i s t s i n the formation of chemisorbed f i l m s of metal soaps [53]. Besides making f r e s h metal a v a i l a b l e to the surfactant, the d i s r u p t i o n may cause the surfaces to be "mechanically a c t i v a t e d " . This i s known as the Kramer e f f e c t and i t enhances the chemical r e a c t i v i t y of a surface. Smith and A l l a n [52] and Smith and M c G i l l [53] i n v e s t i g a t e d t h i s e f f e c t f o r a s e r i e s of metals using n-nonadecanoic a c i d as the surf a c t a n t . They estimated that the Kramer e f f e c t energy can supply about 23 K cal/mole so that metal-acid r e a c t i o n s that would not proceed spontaneously under normal circumstances may occur i f the surface i s disrupted while i n contact with the surfactant. Therefore, r e p e t i t i v e runs across a surface might decrease the s t a t i c f r i c t i o n c o e f f i c i e n t . A l t e r n a t e l y , machining a metal surface under a s o l u -t i o n containing a surfactant would be a reasonable way of depositing a monolayer of m e t a l l i c soap on that surface. A f a v o r i t e method of studying the l u b r i c a t i n g e f f e c t of va r i o u s organic a c i d monolayers and m u l t i l a y e r s i s to deposit them on a s o l i d surface using the Langmuir-Blodgett technique. Many i n v e s t i g a t o r s have 10 used t h i s technique to study the e f f e c t s of molecular weight, substrata temperature, contact pressure, etc., on f i l m d u r a b i l i t y and on boundary f r i c t i o n . Because of extensive research on monolayers, i t i s now recog-nized that the pH and metal i o n content of the water substrata determine the chemical composition and p h y s i c a l p r o p e r t i e s of the monolayer formed on i t s surface [32], [34], [41]. In view of the f a c t that these develop-ments i n monolayer science occurred a f t e r 1950, i t i s probably wise to i n t e r p r e t the e a r l i e r work on the f r i c t i o n of Langmuir-Blodgett mono-l a y e r s with care. P r i o r to 1950, i n v e s t i g a t o r s could not have been f u l l y aware of the e f f e c t s that pH or small amounts of s t r a y metal ions can produce. For example, i t i s p o s s i b l e that a monolayer designated as a s t e a r i c a c i d monolayer may i n f a c t be a calcium s t e a r a t e or copper stear ate soap monolayer as these m e t a l l i c ions are common i m p u r i t i e s i n water. In the foregoing d i s c u s s i o n of the chemical aspects of boundary f r i c t i o n , the d i s t i n c t i o n between s t a t i c and k i n e t i c f r i c t i o n has not been stressed. A c t u a l l y there i s a growing f e e l i n g that the d i s t i n c -t i o n between them i s a r t i f i c i a l [2], [59]. I t i s generally, agreed that a very s e n s i t i v e v e l o c i t y or displacement transducer, set up to measure any r e l a t i v e movement between two surfaces, would show t h a t , beginning, with the f i r s t a p p l i c a t i o n of ta n g e n t i a l f o r c e , there i s always a small amount of displacement (of the order of micro-inches) between the sur-faces. Thus, the surfaces are never i n a true " s t a t i c " contact s i t u a -t i o n . Recognizing t h i s f a c t , some researchers [59] argue that the " s t a t i c f r i c t i o n c o e f f i c i e n t i s merely the l o c a l maximum on the " k i n e t i c " f r i c t i o n curve. On the other hand, the term s t a t i c f r i c t i o n i s u s e f u l because i t does d i s t i n g u i s h the force needed to get an object moving from r e s t 11 from the f o r c e needed to keep i t moving at a constant r a t e . Also, i f one observes s t i c k - s l i p o s c i l l a t i o n s , then the d i f f e r e n c e between s t a t i c and k i n e t i c f r i c t i o n becomes quite d i s t i n c t : the s l i d e r appears to remain s t a t i o n a r y f o r a period of time, then i t i s suddenly released as the e l a s t i c forces i n the system overcome the " s t a t i c " f r i c t i o n a l f o r c e s at the i n t e r f a c e . With regard to the present study, i t i s recognized, 1) that small displacements " m i c r o s l i p s " take place p r i o r to gross s l i d i n g and 2) that i t i s d i f f i c u l t to define exactly when the " s t a t i c " p e r i o d ends. However, the terms s t a t i c and k i n e t i c f r i c t i o n w i l l s t i l l be used. In the second part of t h i s review of s t a t i c f r i c t i o n research, a t t e n t i o n w i l l be focussed on the theories of s t a t i c f r i c t i o n . The simplest model, o u t l i n e d by Bowden and Tabor [3] i n c l u d e s the e f f e c t of boundary f i l m s i n the f o l l o w i n g way. Using a p l a s t i c flow c r i t e r i o n to describe the area growth of : a contact region of o r i g i n a l area A q, that i s subjected to a normal load N and t a n g e n t i a l force F g i v e s : N 2 F 2 N ... + a •A A A o 2 where A i s the instantaneous area of contact. The normal pressure p, at any i n s t a n t i s p = N/A and the shear s t r e s s i s S = F/A so t h a t : p 2 + aS 2 = p 2 . o This i s the equation f o r j u n c t i o n growth [3]. Values of a have been determined f o r various metals [3]. S e l e c t i n g a = 9 as a reasonable value, then: p 2 4- 9S2 = p 2 . o However, t h i s equation does.not p r e d i c t when j u n c t i o n growth w i l l end. Bowden and Tabor a r r i v e at a condi t i o n f o r macroscopic s l i d i n g of l u b r i c a t e d contacts by considering the i n t e r f a c i a l m a t e r i a l to have a c r i t i c a l shear s t r e s s , S., which i s l e s s than S„, the c r i t i c a l shear x M st r e s s of the metal. Therefore, i f S. = Y s„,, then the f a i l u r e c o n d i t i o n x M i s : p 2 + 9 y 2 S M 2 = p 2 . M o The y i e l d pressure p^ i s r e l a t e d to the c r i t i c a l shear s t r e s s of metal: P Q = 3S^ [3]. Therefore, gross s l i d i n g occurs when: p 2 + 9 S . 2 = 9 S . 2 Y" 2 x x or V : '• i " ' 3(Y - 2 - D 1 ' and the c o e f f i c i e n t of s t a t i c f r i c t i o n i s : F S i A 1 V = W p A 3(y- 2 - 1 ) 1 / 2 Considering y to be a measure of the " c l e a n l i n e s s " of the surfaces leads to the f o l l o w i n g conclusions: 1) i f y = 1 (for " p e r f e c t l y clean" surfaces where = S ) , then u = 0 0 and j u n c t i o n growth continues i n d e f i n i t e l y ; 2) i f Y = 0 . 8 , y = 0 . 4 5 so that a small decrease i n i n t e r f a c i a l shear strength markedly a f f e c t s the s t a t i c f r i c t i o n . Although Bowden and Tabor's explanation c l e a r l y shows the c r i t i c a l i n f l u e n c e of i n t e r f a c i a l strength on the s t a t i c f r i c t i o n c o e f f i c i e n t , i t f a i l s to ex p l a i n how the s t a t i c f r i c t i o n c o e f f i c i e n t could be influenced by the loading h i s t o r y . From studies of s t i c k - s l i p type 13 v i b r a t i o n s , a number of i n v e s t i g a t o r s have concluded that s t a t i c f r i c t i o n i s time dependent because creep takes place during the period before f a i l u r e — that i s during "the s t a t i c contact time". At l e a s t f i v e d i f f e r e n t groups have inve s t i g a t e d t h i s s t a t i c f r i c t i o n - t i m e phenomenon and three d i f f e r e n t r e l a t i o n s h i p s have been proposed: 1 _ , C <"s Derjaguin, Push and T o l s t o i P s y k d + t c (1957) [61]. 2 - ^s = \ + - c t -i s 1 - e Howe et a l (1955) [62] and Kos t e r i n and K r a g e l s k i i (1962) [63]. 3. y = u + at b Rabinowicz (1940 [64] and s "k s Brockley and Davis (1965) [12]. These semi-empirical r e l a t i o n s h i p s share two assumptions: (1) that at zero time of s t i c k (t = 0), the s t a t i c c o e f f i c i e n t of f r i c t i o n u i s equivalent to the k i n e t i c c o e f f i c i e n t , u, > and (2) most important — that the normal f o r c e , not t a n g e n t i a l loading f o r c e , i s the c o n t r o l l i n g f a c t o r i n i n c r e a s i n g the s t a t i c f r i c t i o n c o e f f i c i e n t . Results of model studie s by Spurr [65] and Moore and Tabor [66] supported a "junction-growth by creep" explanation of increased s t a t i c f r i c t i o n with i n c r e a s i n g s t a t i c contact time. The common consensus was that the contact area increased with time under the a c t i o n of the nor-: mal load. Hardness-time (the geometry of the indenter-surface i n t e r a c t i o n i s s i m i l a r to the a s p e r i t y - s u r f a c e i n t e r a c t i o n ) and hardness-temperature experiments also supported the argument that the j u n c t i o n growth was due to creep: Atkins, S i l v e r i o and Tabor [67], Mulhearn and Tabor [68]. However, Johannes [19] c o n c l u s i v e l y demonstrated that the creep explana-t i o n had l i m i t e d v a l i d i t y . By i n t e r r u p t i n g a s t a t i c f r i c t i o n t e s t 14 during the s t a t i c contact period and holding the f r i c t i o n couple under a constant normal and tangential load for various periods of time, he was able to show that no appreciable increase i n s t a t i c f r i c t i o n force occurred. From t h i s , he concluded that the contact area growth due to creep was minimal.' Further examination of the. parameters involved i n s t a t i c f r i c t i o n t e s t s led him to consider that a v i s c o e l a s t i c model of area growth would be more appropriate and that the tangential loading rate i s an important parameter i n determining s t a t i c f r i c t i o n . Of course, time i s involved i n any v i s c o e l a s t i c model, but the equations of v i s c o e l a s t i c deformation c l e a r l y show that creep times and loading times are not equivalent i n terms of the s t r a i n s they produce. Using the K e l v i n -Voigt v i s c o e l a s t i c model to explain area growth, Johannes was able to derive a mathematical model for s t a t i c f r i c t i o n that f i t t e d h i s experi-mental r e s u l t s reasonably w e l l . This model w i l l be discussed i n greater d e t a i l i n Chapter I I I . Although Johannes was the f i r s t to apply a v i s c o e l a s t i c defor-mation model to s t a t i c f r i c t i o n , a number of people had suggested that the contact area could grow i n a v i s c o e l a s t i c fashion. Schredrov [30] and Seireg and Welter [57], for example, were interested i n the micro-s l i p that precedes gross s l i p p i n g . Schredrov developed a mathematical model for m i c r o s l i p which assumed that the i n t e r f a c e could be considered as a v i s c o e l a s t i c body. Unfortunately, he did not present any experi-mental proof of h i s theory. Seireg and Weiter used very s e n s i t i v e d i s -placement transducers to monitor the h o r i z o n t a l creep which occurred when they applied a constant tangential force to the i n t e r f a c e for given periods of time. They found that a 3-parameter (Boltzmann) v i s c o e l a s t i c model described t h e i r r e s u l t s . I t i s i n t e r e s t i n g to consider further why s t a t i c f r i c t i o n might show a v i s c o e l a s t i c type of behaviour. With s p e c i f i c reference to mild s t e e l , there i s some evidence that the s t r a i n r a t e can a f f e c t the deformation p r o p e r t i e s ( f r a c t u r e strength and d u c t i l i t y ) of s t e e l s [69]. A rough c a l c u l a t i o n would show, however, that the net e f f e c t on s t a t i c f r i c t i o n xrould be quite small — at low s t r a i n r a t e s where the d u c t i l i t y i s maximum, the f r a c t u r e strength i s at a minimum and v i c e versa. When considering s t a t i c f r i c t i o n s t u d i e s , i t i s a l s o i n t e r e s t i n to note that a l l t e s t s i n which r a t e - e f f e c t s were reported were conducted under boundary l u b r i c a t e d conditions. From previous i n v e s t i g a t i o n s [16] i t i s known that organic compounds have a profound i n f l u e n c e on s t a t i c f r i c t i o n — adding c e r t a i n s u r f a c t a n t s can even suppress s t i c k - s l i p o s c i l l a t i o n s . I d e n t i f y i n g the source of the v i s c o e l a s t i c behaviour could prove u s e f u l both i n l u b r i c a n t s e l e c t i o n or i n pressure welding and adhesion where maximum surface contact i s d e s i r e d . Thus, part of the present study i s a study of s t a t i c f r i c t i o n under vacuum conditions (the best way of determining i f the s t a t i c f r i c t i o n of " c l e a n " s t e e l was r a t e dependent) and a study of the e f f e c t of oxides on m e t a l l i c soap monolayers on s t a t i c f r i c t i o n . The t h e o r e t i -c a l base was also expanded. 16 I I I . THEORY 3.1 Introduction As discussed i n Chapter I I , the time dependency of s t a t i c f r i c t i o n has been a subject for a c e r t a i n amount of experimental and t h e o r e t i c a l work. Besides the s t a t i c f r i c t i o n measurements themselves, other independent experimental evidence substantiates claims that the s t a t i c f r i c t i o n c o e f f i c i e n t f o r a given f r i c t i o n couple i s not neces-s a r i l y a constant. D i f f e r e n t values for i d e n t i c a l samples may be obtained because the breakaway force (and thus the s t a t i c f r i c t i o n c o e f f i c i e n t ) i s determined by parameters which involve rate, or the duration of the p r e - s l i p test period. For example, i t i s well known that a small amount of h o r i z o n t a l displacement or " m i c r o s l i p " of the order of 40 micro inches takes place during the " s t a t i c " contact period which precedes s l i p . This m i c r o s l i p r e f l e c t s the junction growth occurring at the i n t e r f a c e . Shchedrov pointed out that the amount of m i c r o s l i p v a r i e s from one test to another and i n h i s 1957 paper [30], he derived a function which predicted the amount of m i c r o s l i p . His d e r i -v ation, involving s p e c i f i c contact pressure, tangential load and time of tangential loading was based on the assumption that the deforming zone behaved l i k e a Kelvin-Voigt s o l i d a f t e r i t s e l a s t i c l i m i t was reached. More recent l y , measurements of the e l e c t r i c a l resistance of the i n t e r f a c e have shown that the m e t a l l i c contact area i s not a uni-valued function of the applied tangential load but for given normal and tangential loads, i t i s larger i f the tangential load has been applied at a slower rate [15]. As might be expected, the s t a t i c f r i c t i o n values p a r a l l e l e d t h i s increase i n m e t a l l i c contact area Of the various mathematical models that have been postulated 17 to explain the observed u g behaviour, models which incorporate the well established concept of contact area growth and the idea that t h i s area growth occurs because the i n t e r f a c e deforms i n a manner consistent with the deformation of a l i n e a r v i s c o e l a s t i c body seem to be the most promising. There i s ample evidence that other, people besides Shchedrov [30], Ahkmatov [17] and Seireg and Welter [57] for example, recognized that the i n t e r f a c e between contacting bodies might be capable of d i s -playing v i s c o e l a s t i c behaviour. Also, as noted i n the preceding sec-tion s , the e f f e c t of v i s c o e l a s t i c i t y on the f r i c t i o n of elastomeric materials has been well established [27] by experimental and t h e o r e t i c a l work over the l a s t 20 years. However, Johannes [19] was the f i r s t to apply t h i s idea to the s t a t i c f r i c t i o n of s t e e l and to show that the appropriate v a r i a b l e involving time was 8, where: rate of a p p l i c a t i o n of shearing force, F normal load, N The goal of the present work was to expand the t h e o r e t i c a l base and to i d e n t i f y the o r i g i n s of the observed v i s c o e l a s t i c e f f e c t s i n s t a t i c f r i c t i o n . Johannes did not assign e l a s t i c or viscous properties to any s p e c i f i c components of the i n t e r f a c e but instead viewed i t as a unit undergoing deformation because of the shearing force, F. This unit responds to the shear s t r e s s as a l i n e a r , 2-parameter v i s c o e l a s t i c sub-stance (a Kelvin-Voigt s o l i d ) which has an ultimate shear strength per unit area represented by a Prandtl-type element. The model he used i s shown i n Figure 1. While a Kelvin-Voigt model i s the simplest mechani-c a l model which describes s o l i d - l i k e behaviour and i t represents some substances (cork and rubber) reasonably w e l l , a 3-parameter model has been found to provide a much better approximation to the behaviour of 18 most materials. I t i s regarded as the "general l i n e a r s o l i d " model. The Kelvin-Voigt model i s a s p e c i a l case of t h i s general l i n e a r s o l i d model. In the absence of any other information such as creep test or rel a x a t i o n t e s t data (materials of the general l i n e a r s o l i d type show li m i t e d stress r e l a x a t i o n behaviour during long loading times whereas Kelvin-Voigt s o l i d s do not), choosing which model best represents the v i s c o e l a s t i c properties of the in t e r f a c e s considered here i s d i f f i c u l t . When the experimental data are analyzed and numerical values are assigned to each of the e l a s t i c and viscous components of the i n t e r f a c e , the choice between models w i l l be easier. In the interim, both models were considered. 3.2 Models for S t a t i c F r i c t i o n When the 2 samples are f i r s t placed together, N establishes the i n i t i a l contact area A /between the surfaces so that A = (N/p ) o o m where p , the l o c a l p l a s t i c y i e l d pressure, has a value of about 3 m times the y i e l d stress [3]. This area i s made up of the numerous small, d i s c r e t e areas where opposing a s p e r i t i e s meet, see Figure 2(a). F i s applied perpendicular to N, and at t = 0, F = 0. F i s applied at a constant rate, F, so that F ( t ) = Ft . The corresponding stress on the in t e r f a c e i s a(t) = (Ft/A Q) as shown i n Figure 3. The e f f e c t of F on each d i s c r e t e area i s to cause that area to grow, increasing the o r i g i n a l length i n the d i r e c t i o n of F. The extent of the area growth i s . determined by the appropriate v i s c o e l a s t i c deformation law • defining A ( t ) . For a given normal load N over a range of rates F, the area growth at f a i l u r e would resemble that shown i n Figure 2(b). F i s applied at a constant rate F u n t i l the shear strength 19 per unit area, T , of the i n t e r f a c e i s reached and f a i l u r e (gross movement) r e s u l t s at time t ^ . Note that i n t h i s model i t i s assumed that T q does not change with F, so that the shear strength per unit area remains constant across the f u l l range of F as shown i n Figure 2(b). Therefore, any increase i n the s t a t i c f r i c t i o n c o e f f i c i e n t would be due only to increases i n the contact area. Thus, the problem i s to determine U g i n terms of 6 given the type of v i s c o e l a s t i c deformation expected. The following d e f i n i t i o n s and functions are used for both the Kelvin-Voigt and general l i n e a r s o l i d models: A - J L ° Pm • F F f i n a l h f y s N N a ( t ) = f t = X o f F Ft a = _ l i n a l = _ f f A A o o o T q = shear strength per unit area of the i n t e r f a c e .... (1) The c r i t e r i o n for f a i l u r e (gross s l i p p i n g ) i s : T A (1 + e(t,)) = Ft .... (2) o o t r For a l i n e a r v i s c o e l a s t i c body under general loading, e(t) i s found using an hereditary i n t e g r a l i n the following form [31]: 2 0 e(t) = a(t) J(O) + f d J ( t - t ' )  a ( t > d ( t - t ' ) •'O dt' (3) where J ( t ) , the creep compliance, i s the s t r a i n per unit area due to the applied applied unit s t r e s s . I t describes completely the s t r e s s - s t r a i n behaviour of a given material up to the f a i l u r e point. 3.2.1 Kelvin-Voigt Body For a 2-parameter s o l i d , where the v i s c o e l a s t i c i t y i s represented by a spring and dashpot, i f k i s the e l a s t i c modulus of the spring member and c i s the v i s c o s i t y of the dashpot, the creep compliance i s : k J ( t ) = 1 - e ... (4) The r a t i o c/k i s c a l l e d the retardation time f or a Kelvin-Voigt body. After s u b s t i t u t i n g equation (4) into equation (3) and i n t e g r a t i n g , i t i s found that the increased area at s l i p i s : k A Q e ( t f ) = t , k z I-kt^ - c + ce c fcf (5) From the f a i l u r e condition i n equation ( 2 ) and the i d e n t i t i e s i n (1), u g i s obtained as a function of 0 and the phys i c a l properties T , p of the i n t e r f a c e : o m — + e £ pm k k y s 1 - e + - 1 u s = 0 (6) In examining equation (6) further, i t i s found that: 1) the u - 0 curve e x h i b i t s upper and lower asymptotes s 21 corresponding to very small and very l a r g e values of 6 r e s p e c t i v e l y . The upper asymptote i s : T r o Pm k - T o y s max. while the lower asymptote i s y . = (T /p ) . These s mm. o m values are independent of the v i s c o s i t y parameter c. 2) i f c changes, the r e t a r d a t i o n time, c/k, changes and the y s vs 0 curve may be s h i f t e d to the r i g h t or to the l e f t , but i t remains between the boundaries described by the upper and lower asymptotes: T o lower asymptote: — = y . p s mm. and k T upper asymptote: — — r r — ^ r y = Vc T n o v p (.k — i ; s max m " 3) i f there i s no v i s c o s i t y c/k -> 0 and the y g vs 9 curve becomes a s t r a i g h t l i n e l y i n g on the upper asymptote. From ( 5 ) , the growth i n area i s A q e(t) = (a^/k) = (T /k) i n t h i s case. The general form of the y vs 0 o s curve which t h i s model p r e d i c t s f o r a value of c/k > 0 i s shown i n Figure 5. 3.2.2 3-parameter General Linear S o l i d For a 3-parameter s o l i d where k^, k^  are the e l a s t i c para-meters, and c i s the v i s c o s i t y parameter (see. Figure 4 ( b ) ) , the creep compliance i s [31]: 22 J ( t ) = k 1 + k 2 r k i k 2 i _t r k i k 2 i _t _ k l + k 2 . c + 1 k-, _ 1 - e \ + . k 2 c (7) The r a t i o k l + k2  k l k2 c i s known as the r e l a x a t i o n time. A f t e r sub-s t i t u t i n g equation (7) into (2), the f a i l u r e condition, and using the i d e n t i t i e s given i n (1), the U g vs 0 curve has the form: m where: k 1 + k 2 1 - e s + - 1 (8) T = k l + k2  k l k2 This U g vs 0 curve also has an upper and lower asymptote for • • • 0 << 1 and 0 » 1. Also, i t has the same general shape as the y g vs 0 curve f o r the 2-parameter Kelvin-Voigt s o l i d shown i n Figure 5. In th i s model, the upper asymptote i s determined by k^, T q and p^ as follows: from (8) for 0 « 1: s max. m k, - T 1 o The lower asymptote, u . i s also found from (8) for J r "s min. » 1: s mm. m k 1 + k 2 k1 + k 9 ~ T „ 1 2 o Note that i f k„ » T , then y 2 o s min. 23 3.3 The Non-dimensional y vs T * Plot . s Consideration of the r o l e of c and k^, k^ i n determining the U g - 8 curve leads to the formation of a more general p r e d i c t i o n of s t a t i c f r i c t i o n r e s u l t s . If the upper and lower asymptotes were fi x e d and c was varied independently, a family of u g vs 0 curves would r e s u l t for both models. This i s i l l u s t r a t e d i n Figure 6. I t i s now obvious that by making the abscissa, 0, dimensionless the family of curves w i l l collapse onto a s i n g l e general curve, u vs x *. I f t h i s reasoning i s applied S j to the present study, i t i s obvious that i f the test i n t e r f a c e s do • follow one of the v i s c o e l a s t i c laws of deformation, and the u - 0 s curves a l l have the same upper and lower asymptotes but d i f f e r e n t relaxa-t i o n times, then the experimentally determined u g - 0 values must f a l l on t h i s general curve. If the upper and lower asymptotes are set at the general values x and y r e s p e c t i v e l y , then equation (6) becomes: for the Kelvin-Voigt-Prandtl s o l i d : a + 1 - e k ^s c e + b u = 0 s (9) and equation (8) becomes f o r the general l i n e a r s o l i d - P r a n d t l model: y „ a + 0T 1 - e s 8x I + b u = 0 J s . (10) where: T = k l + k2  k l k2 From (9) and (10), i t i s obvious that a family of y g vs 24 curves r e s u l t s given d i f f e r e n t c values (and therefore d i f f e r e n t x and c/k r a t i o s ) . Furthermore, t h i s family of curves collapses to a s i n g l e general y^ - x^* curve by: 1) m u l t i p l y i n g 9 by c/k for the Kelvin-Voigt-Prandtl s o l i d ; 2) m u l t i p l y i n g 0 i n the general l i n e a r s o l i d - P r a n d t l model case by x. Then, for example, i n the general l i n e a r s o l i d case, a l l data for i n t e r f a c e s having the same asymptotes x and y but d i f f e r e n t X values should collapse i f the data are p l o t t e d , not on the usual • * y ,6 axes but on y , x„* axes where x~* = X0 as shown i n Figure 7. r s ^s 3 3 3.4 Changing the Relaxation Time of an Interface The question now a r i s e s as to whether or not the properties of an i n t e r f a c e can be changed so as to change i t s r e l a x a t i o n or r e t a r -dation time. Very l i t t l e i s known about how organic compounds a f f e c t the rheology of the a i r / s o l i d i n t e r f a c e . In contrast, the e f f e c t of these compounds on the surface v i s c o s i t y of the air/water i n t e r f a c e i s well known. A great deal of experimental data has been published along with a l i m i t e d amount of t h e o r e t i c a l work [47]. Although the a v a i l a b l e data must be interpreted with care because of c e r t a i n experi-mental v a r i a t i o n s i n the surface v i s c o s i t y measurements and because' extrapolating information gained by studying air/water systems to a i r / s o l i d systems has l i m i t e d v a l i d i t y , i t i s possible to draw several general conclusions from t h i s work. Considering only carboxylic acids and t h e i r m e t a l l i c soaps: a) The surface v i s c o s i t i e s of carboxylic acid monolayers 25 such as s t e a r i c a c i d and o l e i c a c i d are only approximately Newtonian. They have been shown to e x h i b i t a small amount of v i s c o e l a s t i c i t y at surface pressures greater than 20 dynes per cm [45]. Kimizuka [32] found that s t e a r i c a c i d spread on an a c i d i c subphase (T = 20°C, area per molecule o 20.5 A 2) behaved as a Voight s o l i d having an apparent sur-face v i s c o s i t y , n g , of 0.13 gm per second, and a surface -3 shear modulus, G, of 8.4 x 10 dynes per cm. The surface rheology i s s e n s i t i v e to surface pressure, temperature, pH and the ca t i o n content of the substrate as we l l as shear .rate. I f these v a r i a b l e s are kept constant and the chain length of the organic species i s increased, then the surface v i s c o s i t y , (as one measure of f i l m p r o p e r t i e s ) would be expected to i n c r e a s e because of increased i n t e r c h a i n cohesion. Experimental data from Gaines [45] supports t h i s statement. P a l m i t i c a c i d _3 (C^^ H^^ COOH) has a surface v i s c o s i t y of 1.8 x 10 gm per second, (25°C, ir = 15 dynes per cm, 0.01 N acid) while i t s C^Q homologue, C^g H^^ COOH ( a r a c h i d i c a c i d ) , -2 has a surface v i s c o s i t y 15 times as l a r g e (3 x 10 gm per second) at the same temperature and surface pressure. The e f f e c t of the double [ - c = c - ] bond or of side chains would be to decrease the surface v i s c o s i t y . O l e i c a c i d , f o r example (TT = 15 dynes per cm, 17°C, -4 pH = 2.0) has n = 1.43 x 10 gm per second compared -3 to 1.5 x 10 gm per second f o r s t e a r i c a c i d under s i m i l a r c o n d i t i o n s . The presence of the eis-double bond 26 i s responsible f o r the s i g n i f i c a n t l y decreased v i s c o s i t y . b) More i n t e r e s t i n g to t h i s study i s the e f f e c t of metal ions on surface rheology at the water/air i n t e r f a c e . Depending on pH of the substrate and the metal ion con-3+ tent, the e f f e c t can be marked. Adding A l to an a c i d i c substrate at pH = 5.5 (T = 35°C) causes s t e a r i c a c i d films to assume ne a r - s o l i d properties. Their response to shear stresses has been analyzed i n terms of a 4-parameter v i s -c o e l a s t i c model [40] by Motomura and Matuura. I f the o area per molecule i s kept at approximately 33 A, the measured values of the Burger's body are of the order of n^, n^ = 5 x 10^ gm per second, = 500 gm per second, G^ = 100 gm per second, where n^, G^ are the parameters of the Voigt element of t h i s 4-parameter model. At appropriate pH values, other ions such as Ca , Ba give metal stearate f i l m s which are known to behave as K e l v i n -3"f I | j | Voight bodies while Fe , Cu , Ca give stearate f i l m s which have the c h a r a c t e r i s t i c s of Maxwell bodies. Some ions, Na +, K +, NH^+ do not form s o l i d i f i e d f i l m s with f a t t y acids under these conditions [47]. A further complication of soap formation i n monolayers i s that the a b i l i t y of metal ion to form a viscous s o l i d i f i e d f i l m with an organic acid i s dependent on s t e r i c f a c t o r s [35]. O l e i c a c i d , f o r example, has nearly the same molecular weight and chain length as s t e a r i c a c i d but the presence of the double bond at the C Q p o s i t i o n prevents Ca ions from forming a complex network with the o l e i c acid molecules. Thus, i t would be expected that, unlike s t e a r i c a c i d , 27 which w i l l form a hig h l y structured s o l i d - l i k e soap f i l m with Ca i o n s , the v i s c o s i t y of o l e i c a c i d monolayers would be r e l a t i v e l y u n a f fected -H-by Ca ions even though soap formation s t i l l takes place. The work of Deamer and Cornwell [ 3 6 ] confirms t h i s expectation. E a r l i e r work by Durham [ 3 5 ] shows that e t h y l groups i n the a - p o s i t i o n s of branched chain f a t t y a cids may also provide enough s t e r i c hindrance to impair f i l m s o l i d i f i c a t i o n by Ca ions. I t i s d i f f i c u l t to apply these observations d i r e c t l y to the present s i t u a t i o n where monolayers of m e t a l l i c soaps are deposited on the s o l i d surface and then tested f o r f r i c t i o n p r o p e r t i e s . However, i t i s p o s s i b l e to draw some general conclusions since i t i s expected t h a t -the deposited monolayers w i l l r e t a i n the same i n t e r n a l s t r u c t u r e as they possessed at the air/water i n t e r f a c e . Therefore, i t i s to be expected that the y^ - 6 curve f o r the l e s s viscous Ca-oleate f i l m w i l l l i e to the r i g h t of the corresponding curves f o r Ca-stearate because the r e l a x a t i o n time f o r a Ca-oleate monolayer should be smaller than that of Ca-stearate. P r e d i c t i n g the r e l a t i v e p o s i t i o n s of the f i l m s of the s t e a r i c and o l e i c a c i d soaps deposited at pH 4 i s more d i f f i c u l t as r e l e v a n t r h e o l o g i c a l information i s scarce. Spink and Sanders [41] have shown that at low pH values (pH = 2.7) basic i r o n hydroxide ions i n the aqueous substrata w i l l form s o l i d i f i e d f i l m s with f a t t y a c i d s . In the present work, the source of i r o n contamination i s the specimen i t s e l f as no Fe ions were d e l i b e r a t e l y added. Unfortunately, no d e t a i l e d information on surface rheology f o r e i t h e r of the basic i r o n soaps was a v a i l a b l e so that i t was not pos s i b l e to p r e d i c t the s t a t i c f r i c t i o n r e s u l t s . 28 3.5 The E f f e c t of Temperature on T Values From pressure-area (IT - A) curves and from the surface v i s -c o s i t y studies of numerous monolayers, i t i s w e l l known that tempera-ture changes dr a m a t i c a l l y a f f e c t the s t r u c t u r e and the r h e o l o g i c a l p r o p e r t i e s of monolayers at the air/water i n t e r f a c e . Furthermore, e a r l y work i n the f r i c t i o n and wear area c l e a r l y i n d i c a t e d that increases i n temperature s e r i o u s l y impair the e f f e c t i v e n e s s of monolayers as l u b r i c a n t s . At c e r t a i n c h a r a c t e r i s t i c temperatures, l u b r i c a t i o n breaks down completely [3]. D i r e c t information on the s t r u c t u r e of deposited f i l m s has been obtained by e l e c t r o n microscopy and e l e c t r o n d i f f r a c t i o n s t u d i e s [49]. Films of f a t t y a c i d soaps have a d e f i n i t e s t r u c t u r e and the e f f e c t of r a i s i n g the temperature i s to destroy the order i n the f i l m . For example, e l e c t r o n d i f f r a c t i o n patterns w i l l fade as the tempera-ture of the sample i s r a i s e d because the molecules become d i s o r i e n t e d (the monolayer "melts") and because some v a p o r i z a t i o n occurs. More extensive studies of surface d i f f u s i o n have shown that molecules of a deposited f i l m are capable of moving over a s o l i d sub-s t r a t a i f the temperature i s high enough. Molecules of s t e a r i c a c i d from s t e a r i c a c i d f i l m s deposited on mica sheets [48] can d i f f u s e over the surface even at room temperature and at higher tempera-tures they w i l l move with r e l a t i v e freedom across the surface. The a c t i v a t i o n energy f o r the surface d i f f u s i o n has been measured at 8.6 K cal/gm atom compared to a value of 21 K cal/gm atom f o r desorption of s t e a r i c a c i d from platinum. One r e s u l t of surface d i f f u s i o n at higher temperatures i s i l l u s t r a t e d by an experiment i n which a mica surface, covered with a 29 s t e a r i c a c i d monolayer, was heated to 35°C and held at that temperature f o r 30 minutes [48]. The increased thermal a g i t a t i o n coupled with the elapsed time, enabled a s i g n i f i c a n t number of molecules to leave t h e i r o r i g i n a l p o s i t i o n s i n the f i l m and to migrate across the surface and accumulate i n shallow scratches i n the surface. How would small increases i n surface temperature a f f e c t the U g - 9 curves f o r monolayer covered s t e e l surfaces? Considering equations (9) and (10), p^, the mean y i e l d pressure of the i n t e r f a c e i s es t a b l i s h e d by the substratum and i s approximately equal to 3Y, where Y i s the y i e l d point of the substratum. The hardness of mild s t e e l i s a f f e c t e d by high temperature but remains constant up to at l e a s t 200°C, so that p^ would be unaffected by small temperature changes. T , the shear strength of the i n t e r f a c e , which i s r e l a t e d to p m > would also remain at approximately i t s room temperature value f o r small temperature increases. The r e l a x a t i o n or r e t a r d a t i o n time, T, of a v i s c o e l a s t i c m a t e r i a l i s , however, strongly influenced by temperature so that T = x(T ) . Generally, x decreases with i n c r e a s i n g temperature. E x p e r i -mental work [27] has shown that the r e l a x a t i o n time of v i s c o e l a s t i c m a t e r i a l s obeys: l o g x(T) = - 3T + a (11) so that, J L x(T) = a e B T (12) Further t h e o r e t i c a l work [47] has indic a t e d that: E • a RT X(T) = Ae (13) 30 where E i s a c h a r a c t e r i s t i c a c t i v a t i o n energy and R i s the gas constant a approximately, 2 cal/mole. Therefore, equations (9) and (10) can be modified using (13) to give a general u - 6 - T r e l a t i o n s h i p . T h i s r e l a t i o n s h i p w i l l be v a l i d only f o r a l i m i t e d temperature range because of phase changes i n the monolayer and desorption. Unfortunately, most observations of the fr i c t i o n - t e m p e r a t u r e r e l a t i o n s h i p y i e l d very l i t t l e q u a n t i t a t i v e information that can be extended to cover s p e c i f i c f r i c t i o n couples but some general e f f e c t s are known: (1) I f the m e t a l l i c substratum i s s u f f i c i e n t l y r e a c t i v e , then a m e t a l l i c soap w i l l be formed when the monolayer i s deposited. As the temperature i s r a i s e d , the f r i c t i o n c o e f f i c i e n t remains reasonably constant u n t i l the s u b s t r a -tum reaches a temperature which i s approximately equal to the bulk melting point of the m e t a l l i c soap. At t h i s p o i n t , the f r i c t i o n c o e f f i c i e n t w i l l increase by a f a c t o r of about 10 and there i s a corresponding increase i n surface damage. This i n d i c a t e s a phase change i n the monolayer and thus would i n d i c a t e that the v i s c o e l a s t i c model may no longer be v a l i d . (2) I f the substratum i s unreactive or a monolayer of a m e t a l l i c soap i s deposited without strong adhesion, then the f r i c t i o n c o e f f i c i e n t shows a very large increase when the temperature of the substratum reaches the bulk melting point of the a c i d or the deposited m e t a l l i c soap. Bowden also reports that temperature e f f e c t s i n t h i s temperature range are r e v e r s i b l e . This i n d i c a t e s a phase change i n 3 1 the monolayer and not decomposition. At higher tempera-tures, though, desorption of the monolayer occurs and the f r i c t i o n c o e f f i c i e n t w i l l remain high even i f the temperature i s lowered. Obviously then the - 6 - T r e l a t i o n s h i p developed i s a p p l i c a b l e only to temperature ranges below the melting point of the monolayer. 32 IV. EXPERIMENTAL APPARATUS AND EXPERIMENTAL PROCEDURE 4 . 1 Apparatus Three main pieces of equipment were required f o r the i n v e s t i -gation. The f i r s t item i s a device which measures the s t a t i c f r i c t i o n over a range of B values, the second piece of equipment i s the vacuum system and the t h i r d i s the equipment needed f o r applying monolayers of organic acids to the t e s t specimens by the abrasion technique and by the Langmuir-Blodgett technique. The vacuum system and f r i c t i o n measuring apparatus i s shown i n the photograph i n Figure 8. 4 . 1 . 1 Measuring the S t a t i c F r i c t i o n as a Function of 0 The apparatus f o r measuring y s and 9 i s r e l a t i v e l y simple. A u n i t was required which could apply, measure and record 3 parameters: N , the normal f o r c e ; F, the shearing ( l a t e r a l or ta n g e n t i a l ) f o r c e and F the r a t e of a p p l i c a t i o n of the shearing force. N and F were ap p l i e d separately by Bimba h y d r a u l i c c y l i n d e r s , and x^ere measured by recording the displacement of c a l i b r a t e d s t r a i n rings on a dual channel Brush chart recorder. The design of the complete u n i t was complicated by the r e s t r i c -t i o n that some of the f r i c t i o n t e s t s had to be conducted i n vacuum. The f i n a l design i s shown i n Figure 9. This design was chosen p a r t l y because i t requires only one bellows feedthrough u n i t , B, i n t o the vacuum system. This bellows feedthrough, a 4" diameter, 6" d i s p l a c e -ment l i n e a r u n i t was s p e c i a l l y constructed so that the feedthrough shaft moves f r e e l y through a 1-1/4" opening i n the mounting flange. Unlike conventional feedthrough u n i t s , there was no f r i c t i o n a l r e s i s -tance due to rubbing of the shaft against the inner wall of the mounting flange, or against a p o s i t i o n i n g sleeve. 33 The samples are and A^ (see Figure 9). A^ i s kept s t a t i o n a r y throughout a te s t as i t i s f i x e d to a s t a t i o n a r y support bar x-rtvich i s i t s e l f welded to the b e l l j a r . A^ has a r e s t r i c t e d amount of movement i n the x, y d i r e c t i o n f o r adjustment purposes. A^, the upper sample, i s mounted on the extension to the feedthrough s h a f t , S, and i s the moving specimen. The r e s t of the assembly i s mounted on a machine table which allows up to 10" of x and y movement f o r c o r r e c t l y p o s i t i o n i n g A^ on A^. The machine t a b l e i s f i x e d to a r i g i d support t a b l e which i s anchored to a concrete f l o o r . A^ and A^ are loaded together i n the normal d i r e c t i o n by applying an upward f o r c e W^  at Y with the hyd r a u l i c c y l i n d e r H^. Since the bar i s pivoted at X^, A^ i s force d onto A^. The magnitude, of t h i s normal f o r c e , N, i s known as W, i s measured by the c a l i b r a t e d s t r a i n r i n g and the dimensions of the bar are known. With t h i s arrangement, i t was p o s s i b l e to measure N to l e s s than 1/2 l b . Since N = 50 l b s . , then N could be measured to ± 1%. The h o r i z o n t a l f o r c e F was applied to the A^, A^ interface, by the hy d r a u l i c c y l i n d e r H^. The magnitude of F was consta n t l y monitored by recording the output of the s t r a i n r i n g against a time base using the Brush chart recorder. The r a t e of a p p l i c a t i o n of F, F, i s c o n t r o l l e d by r e s t r i c t i n g the flow of f l u i d from the h y d r a u l i c c y l i n d e r with a Nupro microvalve. F v a r i e d from .005 to 25 l b s . per sec. which was s u f f i c i e n t to cover 6 values from .0001 to 0.5 sec. The s t a t i c f r i c t i o n f o r c e , F , was found from the F-t chart by f i n d i n g the force at which F vs t was no longer a s t r a i g h t l i n e . When the F-t curve i s no longer a s t r a i g h t l i n e , then A^ i s s l i d i n g over A ?. I t i s we l l known that even at very small values of F -34 " m i c r o s l i p " - that i s s l i d i n g movements of the order of 10 micro inches or so - are taking place but F was defined as the force where sudden appreciable movement (of approximately 150 micro inches) of over A^ occurs. Since the minimum value of F measured was 10 l b s . and F could be measured to less than 1/4 l b . , the maximum error i n measuring F was ± 2.5%. The two s t r a i n rings used to measure N and F were used i n conjunction with two E l l i s Associates Model BAM-1 bridge a m p l i f i e r s . The output from the am p l i f i e r s was fed to a dual channel Brush recorder so that N, F, F could be constantly monitored during each t e s t . The c a l i b r a t i o n of the ring-amplifier-recorder system was checked before, a f t e r , and at 1 hour i n t e r v a l s during each set of runs. This was necessary because the BAM units are subject to a c e r t a i n amount of D.C. d r i f t over long periods of time. The hydraulic c i r c u i t used to con t r o l the two Bimba c y l i n -ders i s shown schematically i n Figure 10. The pump, accumulator, and rese r v o i r section of the hydraulic system was i d e n t i c a l to that used by Johannes [19]. The pressure was supplied by a t i l t e d axis piston-type constant displacement pump driven by an e l e c t r i c motor. A pressure r e l i e f valve regulated the output pressure of the pump. The pump was used i n t e r m i t t e n t l y to pressurize the accumulator which was used on the blow-down p r i n c i p l e thus providing a pulsation free source of constant pressure s u f f i c i e n t for several t e s t s . Since the accumula-tor pressure could be varied from approximately 600 to 1500 p s i , the range of flow rates through the micro valves was f a i r l y extensive. 35 4.1.2 Vacuum System One e s s e n t i a l part of t h i s i n v e s t i g a t i o n involved separating the f r i c t i o n c h a r a c t e r i s t i c s of the s t e e l i t s e l f from those of adsorbed f i l m s on the s t e e l . B a s i c a l l y , a u n i t s u i t a b l e f o r t h i s i n v e s t i g a t i o n would prevent o x i d a t i o n and general contamination f o r the duration of s e v e r a l runs. The system selected provided such an environment. I t also provided an a n a l y s i s of the environment i n the t e s t chamber i n terms of the concentration of gases remaining a f t e r the d e s i r e d vacuum has been .achieved. Another primary consideration was the preparation of s u i t a b l e t e s t specimens- The i n v e s t i g a t i o n thus r a i s e d the i n e v i t a b l e questions about "what i s a clean surface?" and "how can a clean surface be achieved?". These questions w i l l be discussed f u r t h e r i n the Proce-dures s e c t i o n during the d e s c r i p t i o n of sample preparations. The u l t r a - h i g h vacuum system used i n t h i s work was a bakeable a l l metal u n i t capable of reaching 5 x 10 ^ t o r r i n 15 hours with a 2 hour bake-out at 250°C. Since the rough pumping (atmosphere to 10 t o r r ) i s produced by cryogenic pumping and the high and u l t r a high vacuum i s produced by Titanium g e t t e r i n g and i o n pumping, there i s no p o s s i b i l i t y of organic contamination due to. back streaming of pumping o i l s . This i s an important consideration i n l u b r i c a t i o n - o r i e n t e d research. To determine which gases are present when the de s i r e d vacuum l e v e l i s reached a r e s i d u a l gas analyzer (RGA) (a quadrupole-type mass spectrometer) was purchased. ( T y p i c a l l y i n t e r e s t centres on the presence of any organic matter.) The probe s e c t i o n of the RGA xras mounted on a 2 1/2" flange between the sample and the i o n pump s e c t i o n . 36 The RGA has a mass range of 1-250 amu and a s e n s i t i v i t y of 1 x 10 t o r r p a r t i a l pressure f o r I t was also used as an accurate pressure gauge and as a very s e n s i t i v e leak detector. The d e t a i l e d s p e c i f i c a -t i o n s of the vacuum system and the RGA form Appendix I. 4.1.3 Deposition of Monolayers Part of the study required that monolayers of organic acids or t h e i r soaps be deposited on the s t e e l specimens. The two d i f f e r e n t methods of applying monolayers and the equipment required f o r each are described below. The f i r s t method used the Langmuir-Blodgett technique whereby a monolayer of an organic a c i d soap was f i r s t formed on an aqueous surface and then t r a n s f e r r e d to the s o l i d substrate. The second technique employed was an adaptation of a machining method used by Smith and M c G i l l [53]. The metal surface was machined under a d i l u t e s o l u t i o n of organic a c i d i n an i n a c t i v e (non-polar) solvent. As the f r e s h metal was exposed by the c u t t i n g t o o l , the organic a c i d chemisorbed onto the newly machined surface to give a monolayer coverage. (a) Langmuir-Blodgett Type Films The best known method of applying organic f i l m s to a s o l i d surface i s the Langmuir-Blodgett technique. This technique was used exte n s i v e l y i n e a r l y f r i c t i o n and wear research. Using t h i s method, i t i s p o s s i b l e to deposit monolayers and m u l t i l a y e r s of organic mole-cules onto s o l i d surfaces i n a c o n t r o l l e d fashion. The structure. of: these f i l m s , t h e i r p r o p e r t i e s , and t h e i r reactions with m e t a l l i c substrata have been studied i n t e n s i v e l y i n the l a s t 40 years [45] so that t h e i r c h a r a c t e r i s t i c s are w e l l known. The technique f o r monolayer 37 d e p o s i t i o n was described thoroughly by Blodgett i n her 1935 paper [42], Depositing monolayers by the Langmuir-Blodgett technique r e q u i r e s : (a) a shallow hydrophobic container f o r the l i q u i d s u b s t r a -tum (a "trough"); (b) hydrophobic b a r r i e r s to sweep the surface of the l i q u i d i n the trough; (c) a hand-windlass or lead screw arrangement to withdraw the sample smoothly at constant speed; (d) a camera and a planimeter to determine the t r a n s f e r r a t i o a f t e r d e p o s i t i o n i s complete (e) waxed thread to contain the monolayer; (f) a p i s t o n o i l to maintain a constant pressure on the monolayer during deposition; (g) reagents: acids and bases to c o n t r o l the pH of the water bath, s o l v e n t s , organic a c i d s , s o l u b l e metal s a l t s to provide m e t a l l i c ions i n s o l u t i o n ; and (h) thermometer, pH i n d i c a t o r papers. The p u r i t y s p e c i f i c a t i o n s of the reagents are given i n Appendix 2. A l l reagents were used as received from the s u p p l i e r . Attempts at f u r t h e r p u r i f i c a t i o n of small amounts of reagents often lead to greater contamination than o r i g i n a l l y e x i s t e d . The trough was a 6" x 10" x 2" deep pyrex container, coated, a f t e r a thorough cleaning with chromic a c i d and d i s t i l l e d water, with p a r a f f i n wax to make i t hydrophobic. The sweep b a r r i e r s were R P l e x i g l a s s . The l i q u i d substratum was d i s t i l l e d x^ater. The pH of the water was c o n t r o l l e d by adding s u i t a b l e amounts of HC1 or NH^OH. M e t a l l i c ions (e.g., Ca ) were provided when necessary by adding the -4 required amount of an appropriate m e t a l l i c s a l t (e.g., 10 M CaCO^)-C o n t r o l l i n g the pH was necessary because the f i l m composition i s af f e c t e d by pH. According to Gaines [45], a s t e a r i c a c i d monolayer formed on an aqueous substratum containing Ca ions i s 100% Ca stearate only when the pH exceeds 7.5. A f t e r the water surface was 3 8 cleaned thoroughly by sweeping i t with the b a r r i e r s , the sample was placed i n the trough below the water surface and the waxed cotton thread was c a r e f u l l y placed on the surface. A few drops of the 10 ^ M organic acid-n-hexane s o l u t i o n were then placed i n the thread-enclosed area. The n-hexane-organic a c i d s o l u t i o n spread r a p i d l y on the clean water surface and exerted a pressure against the c o n f i n i n g thread. Since the hexane was v o l a t i l e , i t evaporated i n a few minutes to leave a p a r t i a l monolayer f l o a t i n g on the surface. The a d d i t i o n of a p i s t o n o i l (such as o l e i c acid) placed outside the thread caused the f i l m to contract as the o i l compressed the thread enclosed area x^ith a constant pressure c h a r a c t e r i s t i c of each p i s t o n o i l (measured as 29.7 dynes per cm at pH = 4.0 f o r o l e i c a c i d ) . Each molecule i n the monolayer then occupied a known area at a given temperature [45]. The waxed thread kept the p i s t o n o i l separated from the monolayer which was confined w i t h i n the thread b a r r i e r . The area of the monolayer was recorded and then the sample was slowly drawn upwards through the f i l m . A lead screw device was used to withdraw the sample so that the f i l m was evenly deposited as a monolayer f i l m without "steps". A c c i d e n t a l stops or j e r k s give a discontinuous f i l m thickness over the surface of the sample. I t has been shown [45] that the monolayer deposits i t s e l f on the specimen so that the geometrical area of the specimen i s covered. The f i l m thus bridges the l o c a l topography of the surface. (The cohesive strength of most f i l m s i s so great that Bilcerman [51] was able to deposit monolayers onto a f i n e wire grid.) During the withdrawal of the specimen, the area of the monolayer l e f t on the surface p r o p o r t i o n a l l y decreased. However, as more water surface was exposed, part of the lens of the p i s t o n o i l spread to cover the new area so that a constant 39 pressure was maintained on the f i l m . Because of the p i s t o n o i l there was some assurance that the monolayer was uniform i n p r o p e r t i e s across the sample. By measuring the area of the f i l m remaining on the water surface a f t e r deposition was complete and by comparing the d i f f e r e n c e between the o r i g i n a l area and f i n a l area to the geometrical area of the sample, i t was p o s s i b l e to determine the extent of monolayer coverage. This f i g u r e i s a rough guide to the success or f a i l u r e of the d e p o s i t i o n . Only those samples having t r a n s f e r r a t i o s of 1 ± .05 were accepted f o r f r i c t i o n t e s t s . A f t e r t r a n s f e r was complete, the sample was a i r d r i e d f o r 15-20 minutes and i t was then tested at atmos-pheric pressure and temperature. (b) Monolayer Deposition by the Abrasion Technique A monolayer t r a n s f e r r e d from a water surface to a s o l i d i s an a r t i f a c t and may be quite d i f f e r e n t from a monomolecular f i l m adsorbed from s o l u t i o n or from the gas phase since the s o l i d surface w i l l always have a surface roughness on a scale l a r g e r than molecular dimensions. I t i s much more l i k e l y that the machining technique developed by Smith and A l l e n [52] and Smith and M c G i l l [53] to study the adsorp-t i o n mechanism of a long chain f a t t y a c i d (e.g., n-nonadecanoic acid) from a non-polar hydrocarbon (e.g., cyclohexane) more c l o s e l y simu-l a t e s a c t u a l f i l m formation conditions during f r i c t i o n t e s t s than the Langmuir-Blodgett t r a n s f e r method. A machining/abrasion technique requires equipment that w i l l generate a f r e s h metal surface under the s o l u t i o n so that newly-exposed metal atoms are a c c e s s i b l e to the polar component of the s o l u -t i o n . While Smith and M c G i l l used n-nonadecanoic a c i d i n cyclohexane as the s o l u t i o n and a planing-type c u t t i n g machine f o r generating a A O f r e s h surface, i n the present work s t e a r i c a c i d (n-octadecanoic acid) was used as the adsorbate, n-hexanes as the solvent and a r o t a t i n g wire cup-brush was used to generate the f r e s h surface. P r i o r to immersion i n the s t e a r i c acid-n-hexanes s o l u t i o n , the samples were wire-brushed i n a i r . Obviously, these surfaces were oxid i z e d but t h i s technique was used p r i m a r i l y to remove a l a y e r of l o o s e l y adhering metal oxide s c a l e , p r i o r to an adsorption run. The samples were immediately placed i n the s t e a r i c acid-n— hexane s o l u t i o n and were wire-brushed under the s o l u t i o n f o r 5 minutes, l e f t f o r 2 minutes i n the s o l u t i o n , r i n s e d i n pure n-hexane, a i r - d r i e d , and then tested at atmospheric pressure. The question a r i s e s as to the existence of a monolayer f o l l o w i n g t h i s treatment. Smith, and M c G i l l [53] spend considerable time and e f f o r t determining i f a mono-la y e r was formed. They a l s o showed that the organic a c i d was chemi-sorbed on " r e a c t i v e " surfaces and that the net r e a c t i o n was: Fe + 3H(St) -> F e ( S t ) 3 + | - H 2 where (St) represents the stearate ion (C^y H^ ,. COO) . They demon-str a t e d that the mechanical a c t i v a t i o n energy which was supplied to the surface by c u t t i n g or brushing, a s s i s t e d the r e a c t i o n . Thus, although an evaluation of the f r e e energy change during the proposed r e a c t i o n might show that the r e a c t i o n i s not spontaneous, the r e a c t i o n may proceed i f the energy required can be supplied by the mechanical a c t i -v a t i o n energy -(the Kramer e f f e c t energy). For metals more e l e c t r o p o s i -t i v e than s i l v e r , they found that the corresponding m e t a l l i c soap was formed. Furthermore, based on the apparent area of metal substrate involved, the amount of soap formed was s u f f i c i e n t to give a monolayer of coverage. Even though t h i s method more c l o s e l y represents a c t u a l 41 f r i c t i o n c o n d itions, i t had some shortcomings f o r the purposes of the present work since m e t a l l i c soaps such as calcium or barium s t e a r a t e could not be placed on the s t e e l surface. 4.2 Pretest Preparation of Samples The samples were a l l C 1020 s t e e l , annealed at 1600°F, then, sand-blasted to remove the oxide s c a l e formed during the anneal. The surfaces were then ground g i v i n g a surface roughness of 17 y i n s . CLA. A f t e r g r i n d i n g , the samples were vapor-degreased with T r i c l o r o e t h y l e n e to remove r e s i d u a l machining o i l and loose d i r t . A f t e r the degreasing treatment, the surfaces were wire-brushed. This procedure should have generated a new org a n i c - f r e e surface and the wire-brushing roughened the surface so that, according to the work of Greenwood and Williamson [7], the contact w i l l be p l a s t i c . The roughness of the surfaces a f t e r wire-brushing was 50 y i n s . CLA. 4.2.1 Vacuum F r i c t i o n Tests Following the wire-brushing, specimens to be tested i n the vacuum were q u i c k l y t r a n s f e r r e d to the chamber and the pumpdown was -3 commenced. A pressure of. 10 t o r r was achieved i n approximately 30 minutes; 10 ^ t o r r a f t e r 1 hour. For the r e s u l t s given i n Figure 12, —8 the t e s t pressure of 2 x 10 t o r r was reached a f t e r approximately 12 hours. Very l i t t l e bakeout was needed so that the temperature of the t e s t surfaces never exceeded 100°F. An a n a l y s i s of the r e s i d u a l gas at t h i s pressure showed that the p r i n c i p a l r e s i d u a l gases were hydrogen, helium, water vapour, and nitrogen. The oxygen content was very low (a p a r t i a l pressure of 5 x 10 t o r r ) , as was the hydrocarbon content. The t e l l - t a l e s i g n of hydrocarbon contamination, the 43 amu 42 peak, was v i s i b l e only at very high a m p l i f i e r gains so that the hydro-carbon content was l e s s than 10 t o r r . Since the vacuum f r i c t i o n t e s t s were expected to y i e l d i n f o r -mation about the - 0 pr o p e r t i e s of a s t e e l - s t e e l i n t e r f a c e , f r e e of s i g n i f i c a n t amounts of contamination, the pretest surface prepara-t i o n must y i e l d a surface that i s s u f f i c i e n t l y "clean". The d e f i n i t i o n of surface c l e a n l i n e s s i s an oper a t i o n a l one and i s t i e d to the measuring technique. F i e l d i o n i z a t i o n , f o r example, can r e v e a l contami-nates on the atomic l e v e l but adhesion and f r i c t i o n s t u d i e s are only a f f e c t e d i f the surface i s 10% or more covered with contaminants [28]. There are two general methods f o r producing c l e a n s u r f a c e s . In the f i r s t category are methods which synthesize a clean surface by de p o s i t i n g atoms of the d e s i r e d surface m a t e r i a l on a s o l i d s u r f ace. Obviously, t h i s deposited l a y e r can d i f f e r from the substratum, i n hardness and strength, so that i n a f r i c t i o n t e s t , i t might a c t as a low shear-strength s o l i d l u b r i c a n t . In the'second category are tech-niques which remove contaminants from the surface — high temperature heating to desorb gases from the surface as w e l l as crushing and c l e a v i n g to generate new surfaces. In a d d i t i o n , Hordon et a l [28] s u c c e s s f u l l y used a method of surface abrasion to prepare aluminium and copper samples f o r adhesion s t u d i e s . A f t e r two minutes of abra s i v e cleaning with a r o t a t i n g s t a i n l e s s s t e e l wire brush, the adhesion c o e f f i c i e n t of copper increased from 0 ( n e g l i g i b l e bonding) to a maxi-mum constant value of 0.32 at ZO^C. The method used i n the present study was based, to a c e r t a i n extent, on the work of Hordon, but also on the work of Bowden and Leben [16], who showed that r e p e t i t i v e s l i d i n g over areas d e l i b e r a t e l y covered 43 with monolayers and m u l t i l a y e r s of l u b r i c a n t s r a p i d l y wore the layers from the surface and the c o e f f i c i e n t of f r i c t i o n increased as did the amount of surface damage. Afte r the desired vacuum l e v e l was obtained, the s l i d e r was repeatedly rubbed across the test surface, immediately p r i o r to te s t i n g . I t was expected that the d i s r u p t i o n of the surfaces would v i r t u a l l y destroy a l l of the o r i g i n a l surface. I t was not implied that the surfaces were contaminant-free during the t e s t . At the pressures used, the fresh surface would be covered with a monolayer of adsorbed gas i n about two minutes. The f r i c t i o n values, although higher than normally seen i n boundary f r i c t i o n t e s t s , also ind i c a t e that the surfaces were not "clean". However, the consistency i n the f r i c t i o n values i n d i c a t e that a c e r t a i n constant l e v e l of surface pre-paration had been achieved. The V~ 6 properties of surfaces treated i n t h i s way were very d i f f e r e n t from the y^ - 9 values obtained by other i n v e s t i g a t i o n s [15], [19], [21] and both i n terms of maximum y g values and the shape of the y g - 9 curve. Since these i n v e s t i g a t o r s had used boundary l u b r i c a t e d surfaces, the di f f e r e n c e i n r e s u l t s suggested that the pre-test cleaning technique was adequate. The y g - 0 values were obtained by running several tests at d i f f e r e n t 9 values across the same surface and measuring y g at each 9 value. The y - 0 values were tested f o r "run-in". No e f f e c t s were s noticeable. The normal loads used i n the set of r e s u l t s shown i n Figure 12 were i n the 50 l b . range, and the high 0 values were obtained by using higher tangential loading rates and not by decreasing N. 4.2.2 A i r Those samples to be a i r - t e s t e d were l e f t exposed to the atmos-44 phere f o r the a l l o t t e d time, then tested both i n a i r and under vacuum. In Figure 13, values of 6 > 1.0 were obtained by reducing N from 50 to approximately 25 l b s . That t h i s would not change the y vs 8 values, was tested by extending the N = 25 l b . 8 values into the N = 50 l b . range of 8 values. The s i x points obtained i n the range .0001 < 6 < 1.0 by using N = 25 l b s . agreed very w e l l with the values of u , obtained when N = 50 l b s . 4.2.3 Oxide Films i ) furnace formed A f t e r degreasing and wire-brushing the samples were heated at 250°C i n the a i r f o r 2 hours and were then allowed to furnace c o o l . The r e s u l t was a t h i c k , blue-black oxide f i l m . Films of t h i s type were tested both i n —8 a i r and i n vacuum (2 x 10 t o r r ) . i i ) water formed Thinner oxide f i l m s were obtained by immersing the sample i n H 20 at 20°C and pH = 5.0 (HCl) f o r 15 minutes followed by a i r drying. These f i l m s were tested at room temperature and pressure immediately a f t e r d r y i n g i n a i r . 4.2.4 Monolayer Deposition i ) abrasion A f t e r the vapor, degreasing and f i n a l wire-brushing procedure, samples undergoing monolayer d e p o s i t i o n by abrasion were immediately placed i n the s t e a r i c a c i d - n -hexane s o l u t i o n and abraded, then rinsed i n n-hexane and 45 tested immediately a f t e r drying. A l l the monolayer-covered samples were tested at atmospheric pressure because there can be up to a 50% l o s s i n monolayer coverage under vacuum conditions [45]. i i ) Langmuir-Blodgett f i l m s The de p o s i t i o n technique has been described e a r l i e r i n t h i s chapter. A f t e r c o n t r o l l i n g the pH and metal ion concentration, the samples were immersed i n the bath, the f i l m was spread and the samples emerged "wet" from the trough. They were allowed to dry, then test e d immediately at atmospheric pressure and temperature except i n the temperature studies of the calcium st e a r a t e f i l m s . Four d i f f e r e n t Langmuir-Blodgett monolayers were formed with o l e i c a c i d as. p i s t o n o i l (TT = 29.7 dynes/cm): 1) S t e a r i c a c i d , pH = 4.0; 2) O l e i c a c i d , pH = 4.0; -4 ++ 3) S t e a r i c , pH = 9.0 - 10.0; 10 M Ca ; 4) O l e i c a c i d , pH = 9.0 - 10.0; 10~4M Ca"*"*". 4.2.5 Temperature Studies of Calcium Stearate Monolayers For the temperature s t u d i e s , calcium stearate monolayers were deposited on the s t e e l samples using the Langmuir-Blodgett technique. A f t e r drying, the f i l m covered p l a t e s were tested at atmospheric pressure and at temperatures ranging from 22°C to 70°C. A p a i r of quartz-iodide lamps (2,000 watts) were used as the heat source and a YSI Telethermometer equipped with a surface temperature probe was employed to monitor the temperature of the p l a t e , see Figure 11. 46 The temperature was regulated to within T ± 2°C by manual operation of the c o n t r o l s f o r the heating lamps. Besides the usual precaution of measuring d e p o s i t i o n r a t i o s to determine i f f i l m d e p o s i t i o n was s a t i s f a c t o r y , the samples to be heated were tested f o r - 0 c h a r a c t e r i s t i c s p r i o r to heating. The temperature t e s t s l a s t e d approximately 3 hours f o r each - 9 curve. 4.3 General Experimental Procedure A f t e r each sample had received the appropriate p r e - t e s t preparation, the upper s l i d e r was wire-brushed then placed i n contact with the sample and N,. the normal load was applied. N v a r i e d s l i g h t l y from one group of t e s t s to another but was g e n e r a l l y kept at approxi-mately 50 l b s . In a few instances, N had to be decreased so that U at higher 9 values could be obtained; these cases are noted on the appropriate graphs i n Chapter V. A f t e r N was a p p l i e d , F was a p p l i e d at a constant r a t e u n t i l gross s l i p occurred. F and N were released and the s l i d e r was moved to a new area (with the exception of the vacuum t e s t s described e a r l i e r ) . The s l i d e r was always moved to a new t e s t area because surface f i l m s are.disrupted during a t e s t and the r e t e s t i n g of that area would have y i e l d e d higher values. A t y p i c a l data run would c o n s i s t of at l e a s t 25 data p o i n t s covering the range of 9. Many separate data runs of monolayer-covered surfaces were c a r r i e d out and the r e s u l t s given i n the graphs are an accumulation of s e v e r a l separate runs. 4 7 V. RESULTS AND DISCUSSION . 5.1 Introduction The f i r s t part of the experimental work was concerned with i d e n t i f y i n g the source of the observed rate-dependence of s t a t i c f r i c -t i o n . The p o s s i b i l i t y that the s t a t i c f r i c t i o n force was r a t e -dependent because the deformation of s t e e l i s s t r a i n - r a t e s e n s i t i v e was checked experimentally by determining u g vs 6 values f o r s t e e l / s t e e l f r i c t i o n couples under high vacuum conditions. Testing a f r i c t i o n couple under these conditions was the most s a t i s f a c t o r y method of minimizing the e f f e c t s of o x i d a t i o n or of hydrocarbon adsorption on f r i c t i o n c h a r a c t e r i s t i c s . Following the high vacuum work, s t a t i c f r i c t i o n t e s t s were also c a r r i e d out on s t e e l samples which had been d e l i b e r a t e l y o x i d i z e d and on samples which had been coated with a monolayer of metal-organic soap. In the second h a l f of the study, a d d i t i o n a l y g - 0 data f o r se v e r a l monolayer-covered s t e e l surfaces were obtained as a check of the v a l i d i t y of the proposed t h e o r e t i c a l model f o r s t a t i c f r i c t i o n . F i n a l l y , the experimental work was extended to cover the e f f e c t of small temperature increases on the y^ - 9 c h a r a c t e r i s t i c s of monolayer-covered surfaces. 5.2 Obtaining S t a t i c F r i c t i o n Information f o r the S t e e l / S t e e l System • -8 5.2.1 y vs 0 curves at 2 x 10 t o r r s Figure 12 summarizes two separate data runs of s t e e l vs s t e e l —8 at 2 x 10 t o r r . The data points f o r t h i s graph were obtained from more 48 extensive data by averaging four u g values at a given 6. This graph i s -8 t y p i c a l of u - 9 curves obtained at 2 x 10 t o r r and at lower pressures. -9 The e f f e c t on y g of lowering the vacuum pressure to 5 x 10 t o r r was not noticeable. The most important feature of t h i s curve i s that i t i s inde-pendent of 9 through the range .001 < 9 < 5. This means that some other com-ponent of the i n t e r f a c e i s responsible for the v i s c o e l a s t i c behaviour of the i n t e r f a c e . The f r i c t i o n value of 0.75, although higher than values obtained during other boundary l u b r i c a t i o n studies, e.g., Johannes [19], Marion [21], i s r e l a t i v e l y low compared to values observed by some workers. Rittenhouse [28] for example, has observed values of 1.08 with "clean" s t e e l . The low f r i c t i o n value can be explained by considering the pre-test preparation. Before they were placed i n the test chamber, the test sur-faces were prepared by degreasing them over b o i l i n g t r i c h l o r o e t h y l e n e to remove r e s i d u a l machining o i l s and loose d i r t , then wire-brushing them. The brushing disturbed the surface and exposed new s t e e l which immediately oxidized i n a i r . In a matter of seconds, the surface was o covered with a th i n layer of oxide about 20 A thick [55]. However, t h i s procedure removed the majority of the scale and accumulated hydro-carbons from the surface. The specimens were placed i n the vacuum chamber immediately a f t e r cleaning and the pumpdown procedure was commenced. A pressure of 10 ^ t o r r was reached i n approximately 1-1/2 —8 hours and 10 t o r r i n about 12 hours. What i s the state of the surfaces at test time? From the work of Kruger and Yolken [55] who studied the oxida-t i o n k i n e t i c s and the i n i t i a t i o n of oxidation on i r o n surfaces*, i t i s obvious that the i n i t i a l oxidation rate of the f r e s h l y brushed surfaces 49 i s very high, but decreases exponentially with time. At the end of 17 hours i n pure, dry oxygen at 760 t o r r , the f i l m thickness would only o have reached about 30 A. Since the p a r t i a l pressure of 0^ i n the vacuum chamber, as measured by the RGA, was very low (approximately 10 ^ t o r r ) during the major part of the 12 hour pumpdown time, i t was doubtful i f o the f i l m thickness exceeded 30 A. Also, even when the bakeout heat was app l i e d , the temperature of the specimen never exceeded 50°C. Because of the low temperature, low 0^ p a r t i a l pressures and the high con-tent of the r e s i d u a l gas during bakeout (the hot ion pumps emit hydrogen during bakeout), i t i s u n l i k e l y that any f u r t h e r o x i d a t i o n would have occurred i n the chamber. P r i o r to the a c t u a l f r i c t i o n t e s t s , the specimens were abraded together se v e r a l times thus d i s r u p t i n g the oxide f i l m s . However, even i f t h i s procedure completely removed the oxide l a y e r , the newly-exposed surfaces would not remain f r e e of adsorbed —8 gases i n d e f i n i t e l y . At 10 t o r r and room temperature, the number of gas molecules remaining i n the chamber was s t i l l so l a r g e than the cleaned area would have been covered with a monolayer of adsorbed gas i n about 3 minutes. Thus, i t was l i k e l y that during the f r i c t i o n t e s t s , the t e s t surfaces were covered with at l e a s t a monolayer of adsorbed gas, probably a mixture of and N 2- These f i n d i n g s a s s i s t i n e x p l a i n i n g why the observed f r i c t i o n c o e f f i c i e n t was r e l a t i v e l y low compared to values observed by other workers. The minimal e f f e c t of t h i s adsorbed gas monolayer i s i n t e r e s t i n g when compared to the e f f e c t of adsorbed organic monolayers found i n subsequent t e s t s . 5.2.2 A i r Exposed A more i n t e r e s t i n g observation i s that i f the t e s t surface used i n vacuum was exposed to the atmosphere f o r 24 hours then 50 retested, the maximum f r i c t i o n value f e l l to 0.55, and the y vs 0 s behaviour i s c l o s e r to that reported by Johannes [19] and Marion [21]. The 24-hour exposure r e s u l t s are compared with the vacuum r e s u l t s i n Figure 13. What caused the s h i f t i n the f r i c t i o n value and the change i n the shape of the y vs 0 curve? The f i r s t thought was that the sur-face oxidized with further exposure to a i r . The second was that a i r -borne hydrocarbons were adsorbed onto the surface. There i s some inde-pendent evidence to suggest that hydrocarbon contamination could be present. When Coelho [60] was examining the i n f r a r e d spectra of organic acids adsorbed on metal mirrors, he found that extraneous hydrocarbon bands appeared i n the spectra before the acids had been deposited. These bands appeared when the mirrors had been exposed to the open atmos-phere for approximately 18 hours. He concluded that t h i s was the r e s u l t of the adsorption of hydrocarbons from the atmosphere. The p o s s i b i l i t y that oxide fi l m s could be contributing to the v i s c o e l a s t i c behaviour was checked by growing oxide fi l m s on the sur-faces and t e s t i n g t h e i r y^ vs 0 c h a r a c t e r i s t i c s . Subsequently, a study of d e l i b e r a t e l y deposited hydrocarbon monolayers was also performed. 5.2.3 Oxide Films The f i r s t f ilms tested were thick oxide fi l m s formed by heating the specimens to 250°C. The f r i c t i o n c o e f f i c i e n t s were high, 0.79, and appear to be independent of 0. They decreased very s l i g h t l y at higher 0 (see Figure 15). When f a i l u r e or s l i p occurred, the o x i d e ^ f i l m was torn from the base metal, exposing sections of s t e e l . These f r i c t i o n values probably r e f l e c t the bond strength between oxide and parent metal rather than metal vs oxide f r i c t i o n . The f r i c t i o n values are s l i g h t l y higher than those obtained for the 51 vacuum tests and they are also higher than values of subsequent tests on the water formed oxide f i l m s shown i n Figure 15. Other workers have observed t h i s behaviour also [29]. When the oxide f i l m s are t h i n , the f r i c t i o n values are usually lower than values of the corresponding oxide-free surface, but increasing the f i l m thickness can increase the f r i c -t i o n c o e f f i c i e n t . In Figure 16, the r e s u l t s of the f r i c t i o n tests on a i r formed and water formed f i l m s are plotted along with the r e s u l t s of Johannes [19] and Marion [21] f o r comparison. I t i s obvious that oxide fi l m s by themselves do not render the s t e e l / s t e e l i n t e r f a c e v i s c o e l a s t i c over the ranges of 0 considered. 5.2.4 Monolayers of Polar Organic Compounds a) Abraded A f t e r the experiments showed that oxide-films were not responsible for the v i s c o e l a s t i c i t y observed by other workers, a monolayer of an organic m e t a l l i c soap was deposited on the s t e e l surface by abrading i t under a hexane s o l u t i o n containing s t e a r i c a c i d . Unlike the oxide f i l m s j u s t discussed, t h i s f i l m did give a y - 6 curve s i m i l a r to the one Johannes had reported s (see Figure 17). I t shows an upper and a lower asymptote for y^. The values of these asymptotes compare favorably with those obtained by Johannes: Johannes Present Work y 0.38 0.39 max. y . 0.18 0.22 mm. Another encouraging feature i s that the general shape of 5 2 the curves i s quite s i m i l a r . These r e s u l t s were the •» f i r s t c l e a r i n d i c a t i o n that the u - 0 curves f o r s t e e l s were strongly influenced by hydrocarbons. The abrasion technique c l o s e l y simulates the film-formation process under ordinary f r i c t i o n conditions with one exception: the f i l m formed by the abrasion technique was l i m i t e d to a monolayer i n thickness. Depending on su r f a c t a n t con-c e n t r a t i o n , the f i l m formed during the " r u n - i n " period of ordinary f r i c t i o n t e s t s may be t h i c k e r . In e i t h e r case, p r o t e c t i o n was obtained because the f a t t y a c i d reacted with newly exposed Fe atoms on the surface to form a m e t a l l i c soap. Th i s soap was r e l a t i v e l y immobile because i t i s strongly bound to the surface and because i t possesses an i n t e r n a l cohesiveness due to the l a t e r a l i n t e r a c t i o n s of the chains of the orie n t e d a c i d molecules Unfortunately, the abrasion technique was not very f l e x i b l e and i t was impossible to deposit soaps of other metals onto a s t e e l surface. Consequently, i t was f e l t that the Langmuir-Blodgett method o f f e r e d more p o t e n t i a l so i n other t e s t s , monolayers were deposited using that technique. b) Langmuir-Blodgett Monolayers A f t e r the r e s u l t s of the abrasion-formed monolayer were analyzed, f u r t h e r i n v e s t i g a t i o n of the r e s u l t s of the studies on the rheology of surface f i l m s at the a i r / water i n t e r f a c e indicated that i t might be p o s s i b l e to 53 provoke the s t e e l / s t e e l i n t e r f a c e i n t o g i v i n g d i f f e r e n t U g - 6 curves by changing e i t h e r the metal i o n or the f a t t y a c i d i n the monolayer. The r e s u l t s are as f o l l o w s . 5.2.5 S t e a r i c Acid and O l e i c Acid at pH = 4.2 The f i r s t organic f i l m s to be deposited were formed by de p o s i t i n g s t e a r i c or o l e i c a c i d on a water surface. HCl had been added to reduce the pH to 4.2. At t h i s pH, c a r b o x y l i c a c i d s are undisso-c i a t e d but Spink and Saunders [41], have shown that b a s i c i r o n soaps can be formed i f a f e r r i c s a l t has been added to the aqueous s o l u t i o n . E a r l i e r work by Wolstenholme and Schulman [70] using m y r i s t i c a c i d (n-C^^H^^COOH) as the long chain polar compound i s more e x p l i c i t . I l l . They found that the Fe ions themselves do not produce s o l i d f i l m s but that when the pH value i s greater than 2, the f i l m i s condensed I | because b a s i c i r o n ions [FeCOH)^ or Fe(OH) ] i n t e r a c t with the undisso-c i a t e d organic a c i d molecules. Wolstenholme and Schulman a l s o proposed a mechanism of f i l m condensation i n which hydrogen bonding between the hydroxyl groups of the basic metal ions was responsible f o r condensing the f i l m . The b a s i c metal ions form a complex network s i t u a t e d j u s t beneath the monolayer. At pH > 5.5, no s o l i d f i l m s could -be detected. Above pH 5, the b a s i c metal ions form c o l l o i d a l aggregates i n the s o l u ^ t i o n and network formation under the monolayer w i l l no longer take place. In the present study, the s t e e l sample was the source of the basic metal ions. P r i o r to d e p o s i t i n g the monolayer on i t s surface, the sample was submerged i n the water f i l l e d (pH 4) trough and held there f o r approximately 20-30 minutes. Thus, i t i s expected that the deposited f i l m s are not s t e a r i c or o l e i c a c i d monolayers but monolayers of the 54 appropriate b a s i c i r o n soap. The mechanical p r o p e r t i e s of these f i l m s have not been studied i n d e t a i l , but from t h e i r performance during f r i c t i o n t e s t s , they are l i k e l y to be l e s s viscous than calcium stearate f i l m s . The ^ vs 0 curves f o r both f i l m s are shown in. F i g u r e 18. Both curves show a pro-nounced v a r i a t i o n of with 9 . The upper and lower asymptotes are 0.70 and 0.47 r e s p e c t i v e l y . The u value of 0.70 i s c l o s e to max. values obtained f o r the water formed oxide. The curves are s i m i l a r i n shape to the u - 0 curves obtained by Johannes but are d i s p l a c e d upward and to the r i g h t . 5.2.6 Ca-stearate and Ca-oleate at pH = 9.5 As noted e a r l i e r [36], [38], Ca ions cause s t e a r i c and monolayers to become h i g h l y viscous with an a c t i v a t i o n energy f o r flow of approximately 11 Kcal/mole over c e r t a i n ranges of pH. On the - H -other hand, Ca ions have very l i t t l e e f f e c t on o l e i c a c i d monolayers because Ca i s s t e r i c a l l y hindered from forming the same h i g h l y s t r u c -tured polymer-like f i l m with o l e i c a c i d as i t does with s t e a r i c a c i d . Deamer and Cornwell [36] found that the v i s c o s i t y of an o l e i c a c i d monolayer on water (at pH 2.0) was not s i g n i f i c a n t l y increased by the a d d i t i o n of Ca ions at pH 10 even though a calcium oleate di-soap was formed. However, s t e a r i c a c i d monolayer became so s o l i d - l i k e that -4 i t s v i s c o s i t y increased from 4 x 10 to greater than 0.2 dyne-sec. per cm which was the upper l i m i t of t h e i r viscometer. The e f f e c t of t h i s s o l i d i f i c a t i o n on s t a t i c f r i c t i o n i s shown i n the u g - 0 curves given i n Figures 19 and 20. The Ca-stearate f i l m s h i f t s the u - 8 curve to the l e f t so that u i s lower f o r a given 0j while Ca-oleate leaves the curve i n approximately the same p o s i t i o n as 55 i t had at pH = 4.0. The upper and lower asymptotes remain c l o s e to 0.70 and 0.47 i n each case. I t i s obvious that the p r o p e r t i e s of the deposited monolayer can a f f e c t the U g - 0 curve d r a m a t i c a l l y . These r e s u l t s w i l l now be i n t e r p r e t e d i n terms of the model proposed i n Chapter I I I . 5.3 Discussion of H - 0 Results s 5.3.1 Applying the V i s c o e l a s t i c Model to U g - 0 R e s u l t s Consider the composition' of a t y p i c a l i n t e r f a c e and i t s response to the applied f o r c e s . Both surfaces consist of a s o f t s t e e l substratum covered by a l a y e r of deformed metal about 0.1 microns deep o-which i s , i n turn, covered with an oxide l a y e r at l e a s t 30 A t h i c k . In a d d i t i o n , the s t a t i o n a r y h a l f of the f r i c t i o n couple i s covered by a d e l i b e r a t e l y deposited monolayer of organic m a t e r i a l . The a p p l i c a t i o n of N causes p l a s t i c y i e l d i n g i n the substrata immediately beneath the highest points of each surface so that small d i s c r e t e areas of contact are formed. Independent work by Courtney-Pratt and E i s n e r [14] and Green [15] has shown that these contact areas are at l e a s t p a r t i a l l y m e t a l l i c , probably because the oxide f i l m cracks and new metal i s exposed. Any oxide or organic m a t e r i a l trapped i n a contact zone w i l l experience reasonably high compressive s t r e s s e s as the y i e l d pressure, p^, f o r s t e e l i s about 200 Kg/mm. When the t a n g e n t i a l s t r e s s i s a p p l i e d , the shear s t r e s s : 1) w i l l be transmitted to the substratum causing the t o t a l contact area to grow; 2) may squeeze a portion of the oxide-monolayer m a t e r i a l out of the contact zone thus i n c r e a s i n g the m e t a l l i c area of contact.' During t h i s time, the surfaces w i l l show small amounts of v e r t i c a l as w e l l as h o r i z o n t a l movement as the i n t e r f a c e adjusts to the s t r e s s e s . At some point, however, the applied t a n g e n t i a l f o r c e w i l l cause gross s l i p of one surface over the other. a) What i s T q , to the shear strength/unit area of the i n t e r f a c e , when s l i p occurs? In the most extreme case, the majority of the con-t a c t area would be m e t a l l i c and the average shear s t r e n g t h per u n i t area would approach the shear strength of the metal substrata, S^. i s approximately 0.2 p^ [ 3 ] . (Note that may vary from j u n c t i o n to j u n c t i o n as the substratum i s a n i s o t r o p i c but only average values are considered.) A more usual circumstance i s that only a a f r a c t i o n , a, of the t o t a l contact area i s m e t a l l i c , the r e s t , (1 - a ) , c o n s i s t s of an oxide-monolayer mix-ture with shear strength per u n i t area, S , which i s nm l e s s than S,,. (If S > S„, shearing would take p l a c e M nm M . . . . . i n the underlying weaker metal.) Therefore, at f r a c t u r e t Fj. = A_ r (1 - a)S + a S„ I = T v A-. . Thus, the shear f f [_ ran M J o f strength per u n i t area of the i n t e r f a c e , ' T , has a maxi-mum value of S^. Therefore, £ ^ 0^P m J < 0.2 approximately b) When w i l l the area growth end? Measurements of the e l e c t r i c a l r e s i s t a n c e of the i n t e r f a c e show that the f i n a l amount of contact area at a given normal load i s a f u n c t i o n of the r a t e at which the t a n g e n t i a l f o r c e was applied. Because of the complex nature of the i n t e r f a c e , p r e d i c t i n g the amount of area growth by considering the 57 deformation of each component i s d i f f i c u l t . In Chapter I I I , a more general approach was taken and i t was assumed that the contact area growth shows a v i s c o e l a s t i c type . of behaviour so that at f r a c t u r e : F f = A f T o = A ± [ l + e ( t f ) ] T D = ^ T o [ l + e ( t f ) ] and - T - r [1 + e-<v ] rm 1 J Also, i n Chapter I I I , two possible types of v i s c o e l a s t i c models were used to p r e d i c t u^. From the experimental data obtained from s t a t i c f r i c t i o n tests of surfaces covered with Langmuir-Blodgett monolayers, the two models w i l l be evaluated. 5.3.2 Kelvin-Voigt-Prandtl Model In the simplest case, the i n t e r f a c e i s assigned one e l a s t i c parameter, k, and one viscous parameter, c, and treated as i f i t s deformation behaviour was that of a Kelvin-Voigt body. S l i p occurs when a f r a c t u r e s t r e s s , T q , i s reached. Using t h i s approach, equation (6) was derived e a r l i e r . It i s i n t e r e s t i n g to evaluate c, k and T /p ° p m for each of the four cases. Considering equation (6) i n Chapter I I I : the upper asymptote i s 58 the lower asymptote i s u . . = T /p . mm o m From the data f o r the monolayers y 0.47 i n a l l four cases so that: = 0.70 and y max. mm. 0.47 = ' m and 0.70 = -2-m 1 -From (6) with y 0.70, y max. = 0.47, the y - 0 curve i s : s s mm-r - y i • 1.46 + f 0 1 - e c s + 2.08 y = 0 s .... (11) and — = 1.46, — = 0.47, f = a P P k m *m .. (12) The value f o r a the " r e t a r d a t i o n time" i s d i f f e r e n t f o r each • monolayer. I t i s obtained by s o l v i n g (11) given a data p o i n t (y 0.) from the experimental curves. Given that p^ = 200 Kg/mm2 i s a reasonabl y i e l d value f o r s t e e l (published values range from 100 to 300 Kg/mm2), then c, k, T q are c a l c u l a t e d from the set of equations (12) f o r each f i l m (see Table. I ) . The value of c gives a bulk e f f e c t i v e v i s c o s i t y f o r each i n t e r f a c e . As expected from the r e l a t i v e p o s i t i o n s of the y^ - 0 curves the i n t e r f a c e with calcium stearate as the monolayer shows the highest bulk v i s c o s i t y value. At t h i s point, i t i s obvious that one d i f f i c u l t y with using the simple model to describe s t a t i c f r i c t i o n i s that i t p r e d i c t s an TOT'l"-.,i1.,CTft1i"iltl'.r n.lUil lllillHIll 'I'JITInVJhWil il^lLMTiUCT MONOLAYER . DEPOSITED , c/k T 0 k* c (sec.) (kg/mm2) (kg/nnn2) (poise) Ca-oleate Ca-stearate Fe (OH)2 Oleate Fe (OH)2 Stearate .69 40 .92 •34 94 94 94 94 292 292 292 292 1.97 x 10 1 0 111.4 x 10 1 0 2.63 x 10 1 0 .96 x 10 1 0 i n 9 *k = 2.86 x 10 u dyne/cm . TABLE I. Calculated Values of Relaxation Time, Viscosity, Elastic Modules and Shear Strength for the 2-Parameter Model. 6 0 unreasonably large value for the f r a c t u r e s t r e s s , T q . £ ^ o^ PmJ ''"S expected to have a maximum value i n the 0 . 2 0 range and t h i s model pre-d i c t s a value \ T /p 1 = 0 . 4 7 which i s almost 2 - 1 / 2 times the maximum • L ° m J value. 5.3.3 3-Parameter (Standard Linear Solid) - Prandtl Model In developing the 3-parameter model, two e l a s t i c m o d u l i i k^ and were used to describe the e l a s t i c i t y of the i n t e r f a c e while c described i t s viscous p r o p e r t i e s . The f a i l u r e c o n d i t i o n Is that s l i p occurs when T i s reached. From ( 8 ) : ° r 6T m k l + K 2 1 - e - 1 Ttfhere: The asymptotes are: T = k l + K 2  k l K 2 max. y. mxn. • m k - T m i l o k l + K 2  k l + K 2 " T o For a l l four i n t e r f a c e s , y = 0 . 7 0 , y s s max. min. 0 . 4 7 . (13) (14) (15) Using these values, ( 1 3 ) becomes: y. The r a t i o - 1.46 + TQ k, + k„ 1 s 0 T + 2.08 y = 0 s k l K 2 ( 1 6 ) c = T i s the r e l a x a t i o n time f o r a p a r t i c u l a r 6.1 i n t e r f a c e . Values of T f o r each i n t e r f a c e are d i f f e r e n t and are deter-mined from the experimental data by s u b s t i t u t i n g (Us^> 6^) i n t o (16). As can be seen from the graphs i n Figures 21 to 24, the t h e o r e t i c a l U g - 0 r e l a t i o n s h i p f i t s the data reasonably w e l l . It i s i n t e r e s t i n g to determine the magnitudes of c, and k^, k^ f o r each i n t e r f a c e . To do t h i s , the value T /p i s needed. In the o m development of t h i s model, i t was assumed that T^ i s known f o r each i n t e r f a c e . Unfortunately, t h i s i s not the case. By rearranging (15), i t i s obvious that (15) has s o l u t i o n s only when [~T /p "1 < U . ; • |_ o mj mm. since k^ and are p o s i t i v e q u a n t i t i e s . . k 1 + k 2 T o 1 - y . mm. Pm (17) Thus, T /p has an upper l i m i t of 0.47- The c, k, k„ parameters f o r o m 1 2 . . each i n t e r f a c e were c a l c u l a t e d f o r a range of | T /p 1 < u . . In [_ o m J min. Table I I , these parameters are given f o r s e v e r a l ^ Q / ] ? m values up to 0.47 which represents the l a r g e s t p o s s i b l e T Q / p m r a t i o . However, as discussed e a r l i e r , a more reasonable value of T /p would be about o m 0.20 or l e s s . I f T /p = 0.15, then the bulk v i s c o s i t y of the i n t e r -o m face i s 2 x 10"^ poise f o r calcium stearate, f o r example. The bulk v i s c o s i t i e s f o r the i n t e r f a c e s may be compared to published values of the v i s c o s i t i e s of some common mater i a l s given i n Table I I I . If the i n t e r f a c e v i s c o s i t y values are compared to published values f o r the v i s c o s i t i e s of monolayers at the air-water i n t e r f a c e , then they seem unusually large. The surface v i s c o s i t y of calcium oleate -4 f o r example, was measured by Deamer and Cornwell as 3 x 10 surface T o Pm 1 2 [mm h + ka] ^ u -1 [mm k 2 M 2 2 k l + k2 k l k2 c Ca S t 2 c Ca 0&2 c Fe (0H) 2 St c Fe (0H) 2 Oil (poise) (poise) (poise) (poise) 0.05 10.8 11.20 .4 2.59 21.5 x 10 1 0 4.7 x 10 8 2.3 x 108 6.26 x 10 8 0.1 23.3 25.4 2.1 0.52 4.3 x 10 1 0 .9 x 10 8 .45 x 10 8 1.2 x l l O 8 0.15 38 44 6 0.19 2 x 10 1 0 .3 x 10 8 .15 x 10 8 .4 x 10 8 0.20 56 69.6 13.6 0.09 .747 x 10 1 0 .16 x 10 8 .08 x 10 8 .2 x 10 s 0.30 105 165 60 0.026 .216 x 10 1 0 .04 x 10 8 .02 x 10 8 .05 x 10 8 0.40 187 537. 350 0.008 0.66 x 10 1 0 .015 x 108 .007 x 10 8 .02 x 10 8 0.46 268 4324 405.6 0.004 .03 x 10 1 0 .007 x 10 8 .003 x 10 3 .009 x 10 8 0.47 OO 00 TABLE I I , E l a s t i c M o d u l i i and V i s c o s i t y Values as a Funct ion of T /p f o r the 3-Parameter Model . o m MATERIAL BULK VISCOSITY g l y c e r i n e (0°C) **,J""*""'" *'11111 N" i H i i i i i M J i H i j<ii)i'?nr..Uiii.'inin'Tli..n wi.iirrTi 2 5 x 10 poise butter (20°C) 2 5 x 10 poise p i t c h (0°C) 5 x 10 poise p i t c h (15°C) 1.3 x 1 0 1 0 poise greases (20°C) ranges from 10 to 1 0 1 1 poise g l a c i e r i c e 1.2 x 10"^ poise glass (20°C) i n 2 2 10 poise TABLE I I I . V i s c o s i t i e s of Some Materials. 64 poise. The corresponding bulk viscosity (using 20 A as the monolayer 3 thickness) i s 1.2 x 10 poise, which i s much smaller than the viscosity value just obtained for the calcium-oleate covered interface. This apparent discrepancy in viscosity values indicates that the substratum strongly influences the rheology of the interface. This i s not sur-prising when.one considers that the apparent vis c o s i t i e s of monolayers at the air/water interface are known to be strongly influenced by the liq u i d substratum. When the surface viscosity values for the monolayers are converted to 3-dimensional bulk v i s c o s i t i e s , the apparent bulk v i s -cosities are much higher than those obtained for the actual materials. However, i f the measured viscosity i s considered to be the sum of two components, the viscosity of the monolayer i t s e l f plus a viscosity contri-bution due to the substratum, then when the substratum's contribution i s estimated and subtracted from the apparent viscosity, the monolayer viscosity values are much closer to the bulk values. In view of these observations, i t i s reasonable to expect that the measured interface viscosity may be much higher than the viscosity of the monolayer i t s e l f or the bulk soap. 5.4 Dimensionless y - 8 Curves [_s After examining the y^ - 8 data, i t i s apparent that the • • y - 0 relationship f i t s each set of data reasonably well. The y - 0 s s curves for each interface have the same asymptotes and are separated on the 6 axis because their relaxation times are different. It i s also apparent that a more general form of f r i c t i o n curve could be obtained by making 6 dimensionless and that a l l the experimental y^, 0 data should collapse onto this curve. Multiplying 8 by the relaxation time 65 w i l l g i v e a d imens i on le s s parameter, x*, as the a b s c i s s a and the g e n e r a l f r i c t i o n curve w i l l be i n the form of u vs x A . s The r e l a x a t i o n t ime x . f o r each of the f ou r i n t e r f a c e s was 1 determined e a r l i e r . The data f o r a l l f ou r i n t e r f a c e s were p l o t t e d as U g v s x ^ 9. The r e s u l t s a re g i ven i n F i g u r e 25. I t i s apparent t ha t the e xpe r imen ta l da ta w i l l c o l l a p s e onto a s i n g l e curve wh ich has t he form: - 1.46 + X * What use i s t h i s ? For the f o u r i n t e r f a c e s a l r e ady t e s t e d , the use i s obv ious — knowing x ^ a l l o w s one to p r e d i c t a t any 9. U n f o r t u n a t e l y , f o r o the r meta l soaps x ^ , and k^, k^ must be determined by e xpe r imen ta -t i o n . 5.5 E f f e c t of Temperature on S t a t i c F r i c t i o n The temperature s t u d i e s were not meant to be an e xhau s t i v e examinat ion of the e f f e c t s of heat on the f r i c t i o n c h a r a c t e r i s t i c s of mono layer -covered s u r f a c e s . They were c a r r i e d out as a supplementary check of the p o s t u l a t e d v i s c o e l a s t i c i t y of the i n t e r f a c e s i n c e i t i s w e l l known t h a t the r e l a x a t i o n t imes of v i s c o e l a s t i c m a t e r i a l s a re a f f e c t e d by temperature. The c a l c i u m s t e a r a t e f i l m was s e l e c t e d f o r the temperature s tudy because i t s room-temperature — 0 curve i s s i t u a t e d so that i f temperature e f f e c t s do a l t e r the r e l a x a t i o n t ime , the p o s i t i o n of the new - 6 curve should s t i l l be w i t h i n the expe r imenta l range of 9 v a l u e s . A l s o , the m e l t i n g p o i n t of bu l k c a l c i um s t e a r a t e i s r ea sonab l y h i g h (180°C as compared to 84°C f o r c a l c i u m o l e a t e ) so t ha t h i g h e r t e s t 1 - e s x * + 2.08 u = 0 (18) bb temperatures are p o s s i b l e before f i l m melting e f f e c t s might i n t e r f e r e . Heating the monolayer-covered s t e e l surface to 35°C, Figure 26, s h i f t e d the y - 0 curve s l i g h t l y to the r i g h t so that Xor-o r i - s * reduced to 10 sec. S i m i l a r l y , heating to 50°C s h i f t e d the y^ - 0 f u r t h e r to the r i g h t , Figure 25, and T „ i s f u r t h e r reduced to .5 sec. compared to a value of 40 sec. f o r T22 ° c ' Comparing room tempera-ture curves f o r Ca-stearate, Figure 21, with these two higher tempera-ture curves, Figures 26, and 27, i t i s obvious that the e f f e c t of temperature increase i s to decrease the r e l a x a t i o n time of the i n t e r -face. There i s a l s o some i n d i c a t i o n that the increase i n temperature has caused the upper asymptote to s h i f t upwards s l i g h t l y . The maximum value of y^ p r e v i o u s l y obtained f o r Ca-stearate f i l m s at room temperature i s 0.705 compared to y = 0.73 f o r the higher temperature t e s t s . max. • However, i f the data f o r these curves i s compared to the data p l o t t e d on the general curve of Figure 25, then i t appears that 0.73 i s w e l l w i t h i n the experimental s c a t t e r shown by a l l the f r i c t i o n data. There-f o r e , y , y are considered to be unaffected by temperature max. min. increases f o r the l i m i t e d temperature range i n v e s t i g a t e d . 5.5.1 Discussion of Temperature Results In l i g h t of t h i s information and by f u r t h e r examination of equations (6) and (8), which show that the upper and lower asymptotes f o r y are determined by p , T and k , k„, the e l a s t i c m o d u l i i , i t s m o JL z. appears that temperature has very l i t t l e e f f e c t on the. e l a s t i c modulii of the i n t e r f a c e . I t has however a s i g n i f i c a n t e f f e c t on c, the v i s -c o s i t y parameter. Q u a n t i t a t i v e l y then, over a l i m i t e d range of tempera-ture, the y^ - 0 equations would be modified by s u b s t i t u t i n g c(T) f o r 67 c as fo l l o w s : c - c ( T ) = p e ( A E / B T ) [47] .... (19) using the viscosity-temperature r e l a t i o n s h i p derived f o r monolayers. AE i s the a c t i v a t i o n energy f o r flow, B i s Boltzman's constant and p i s a s u i t a b l e constant. I t i s i n t e r e s t i n g to estimate AE as M a t i j e v i c [47] has given a value of 11 Kcal/mole f o r the a c t i v a t i o n energy f o r flow i n calcium stearate monolayers. From (19): . AE m c = p + — Given t h e . r e l a x a t i o n times, x , f o r 22°C, 35°C and 50°C, AE i s deter-mined from a semilog p l o t , F i g u r e 28 to be 28.5 (Kcal/gm-mole). Over a l i m i t e d range of temperatures, the u - 8 equations would be modified as f o l l o w s : - i.46 + ^p- e k 1 - e C ( T ) e J + 2.08 y = 0 s .. , • (21) or - 1.46 + T(T) k 2 k-r*- 6x(T) + 2.08 y g = 0 (22) I f the surface temperatures are kept w i t h i n a l i m i t e d range . ( c e r t a i n l y below the decomposition or desorption temperatures of the f i l m ) , then 6 and temperature e f f e c t s on s t a t i c f r i c t i o n would give the V -~ 8 - T curve shown i n Figure 29(a). The upper and lower asymptotes are not functions of T. If temperature increases a f f e c t the asymptotes (k values as w e l l as c values are temperature dependent but as discussed e a r l i e r 68 T and p are unaffected) then the y - 0 - T surface of Figure 29(b) o m s would be expected. One s i n g l e c r o s s - s e c t i o n a l curve of the " f r i c t i o n surface" described by y , 8 and T was obtained and i t i s shown i n Figure 30. -1 0 was kept constant at 0.345 sec. while the temperature of the calcium stearate covered surface was r a i s e d to 60°C i n 5°C increments. The f r i c t i o n c o e f f i c i e n t gradually climbed from 0.50 at 22°C to 0.68 as the temperature was r a i s e d to 60°C. Since changing the temperature changes the r e l a x a t i o n time, T , and not the asymptotes, the y - § - T s data should also c o l l a p s e on the general - T * curve obtained e a r l i e r . The r e l a x a t i o n times at each temperature, T^^> were determined from the appropriate y ^ - 8 data. Using T * = T 0, the experimental data was r e p l o t t e d i n Figure 31. The agreement i s good. The s i g n i f i c a n c e of t h i s f i n d i n g i s that, once AE has been determined, then the r e l a x a t i o n time at any other temperature, 1\ , can be c a l c u l a t e d using equation (15). Knowing the r e l a x a t i o n time means that the y - 8 curve at T. can be s J p r e d i c t e d . Of course f o r t h i s approach to be v a l i d , T. must not exceed the l i m i t s set e a r l i e r . More extensive t h e o r e t i c a l and experimental s t u d i e s of the y ^ - 0 - T r e l a t i o n s h i p may y i e l d a general method f o r normalizing f r i c t i o n curves f o r both s t a t i c and k i n e t i c f r i c t i o n . E x c e l l e n t r e s u l t s have already been obtained i n developing a "master curve" which gives temperature and s l i d i n g v e l o c i t y e f f e c t s on the f r i c t i o n of rubber on glass [27]. 69 VI. SUMMARY AND GENERAL DISCUSSION OF RESULTS 6.1 Summary The experimental part of t h i s i n v e s t i g a t i o n showed that a monolayer of an organic compound w i l l cause the s t a t i c f r i c t i o n c o e f f i -c i e n t , u , of a s t e e l / s t e e l f r i c t i o n couple to e x h i b i t a r a t e depen-dency. Four organo-metallic soap monolayers, deposited on mild s t e e l samples by the Langmuir Blodgett technique were i n t e n s i v e l y studied. Over c e r t a i n ranges of 6, the s t a t i c f r i c t i o n values were r e l a t i v e l y low, 0.47. When 6 dropped below a c r i t i c a l value, however, the u g values rose u n t i l a maximum of u = 0.70 was reached. The u - 9 data f o r a l l s s four monolayer-covered surfaces were adequately described by a modified v e r s i o n of the, t h e o r e t i c a l model f o r y g - 0 introduced by Johannes [19]. The model i s based on the premise that the r e a l area of contact between the surfaces determines u and that the amount of t h i s contact area i s determined by 9 and the p h y s i c a l properties of the i n t e r f a c i a l region. In the t h e o r e t i c a l p r e d i c t i o n of u - 8 values, the contact • s area at any r a t e 0 was derived by assuming that the deformation of the " i n t e r f a c e " could be represented by a mechanical model made up of e l a s -t i c and viscous elements. The f a i l u r e c o n d i t i o n was that s l i p occurred when T was exceeded. Unfortunately, the exact value f o r T i s not o J o a v a i l a b l e but i t should be l e s s than 0.2 p which represents the shear m strength/unit area of the metal substratum. Two mechanical model representations of the deformation were examined. For the simplest model, the a c t u a l value of (T /p ) was too high. This model was r e j e c t e d o m i n favor of the more general 3-parameter l i n e a r s o l i d - P r a n d t l model f o r area growth. 70 6.2 The Contact Area at S l i p I n i t i a l l y , the area of contact i s A = (N/p ). I t i s com-o m posed of regions of metal - nonmetal contact as well as metal - metal contact. *When s l i p occurs: T A o o (1 + e ( t f ) ) . H s N The contact area at s l i p can be calculated i f T , the shear strength/per unit area of the i n t e r f a c e i s known. If (T /p ) - 0.2, then the con-o m tact area at s l i p has a value of A (1 + e ( O ) = 3.5 A at u = u r o f o s max. • 0.70. This i s the maximum contact area (for (T /p ) - 0.2) for a l l 9. o -m It i s the contact area at very low loading rates, 9 << 1. The corres-ponding minimum value i s A (1 + e(t J.)) = 2.35 A when u = u . =0.47 ^ & o f o s mm. for 9 » 1. From the t h e o r e t i c a l p r e d i c t i o n f o r the upper and lower asymp-totes, u , u . and the preceeding discussion of contact area, i t i s max. "mxn. obvious that both the maximum and the minimum extent of area growth responds to the i n t e r f a c e T /p , k., , k„ values and not to the i n t e r f a c e v o m 1 2 v i s c o s i t y term: s max. rm 1 -and s mxn. T r o Pm 1 - T k 1 + k 2 At t h i s point, i t i s useful to consider the conditions under which a rate-dependency w i l l be observed. 71 a) Since f y - u . 1 represents the "spread" i n s t a t i c f r i c -[_ s max. s mm. J t i o n values, i t i s obvious that i f « f o r a given i n t e r f a c e , then I y - y . I ->• 0 and no rate-dependency w i l l be d i s -|_ s max. s mxn. J r c e r n i b l e . In these cases, y (6) - y f o r a l l 0. For most f r i c -s s max. t i o n experiments, the scatte r i s at l e a s t 5% so that small y g -y . values w i l l not be noticed, s mm. b) Even though the asymptotes are not s e n s i t i v e to the v i s c o s i t y term, c the r a t i o k 1 + k 2 , the r e l a x a t i o n time i s s t i l l an important property of an i n t e r f a c e . I t determines where the y g - 0 curve w i l l l i e on the 0 a x i s . Since small k 1 + k 2 r a t i o s s h i f t the y g - 0 curve to the r i g h t side of the 0 a x i s , i t i s p o s s i b l e that the f u l l shape of the curve w i l l only be v i s i b l e i f 0 i s r e l a t i v e l y l a r g e . I f t h i s i s the case f o r a p a r t i c u l a r i n t e r f a c e , then over the r e s t of the range of 0 values, y^ may appear constant at y = y . S i m i l a r l y , i f s s max. J k l + k 2 i s l a r g e , the y^ curve i s s h i f t e d to the l e f t and y g may appear constant at y = y . . s s mm. . Because of these two f a c t o r s , a given i n t e r f a c e may appear to show no r a t e - s e n s i t i v i t y over a p a r t i c u l a r 0 range. 6.3 A p p l i c a b i l i t y of Results to Lubricant S e l e c t i o n Although low s t a t i c f r i c t i o n values are not the sole c r i t e r i o n of boundary l u b r i c a n t performance, the y g - 8 curve should be of value i n l u b r i c a n t s e l e c t i o n . C e r t a i n l y i n some a p p l i c a t i o n s , such as switching gear, s t a t i c f r i c t i o n values are important. Unfortunately, relevant design data are scarce and poorly tabulated. I n d i v i d u a l y - 0 curves are u s e f u l because f i n d i n g y i s a simple matter: given s s any normal load at any ta n g e n t i a l loading speed, 0 i s r e a d i l y c a l c u l a t e d . 72 More generally, f o r a s e r i e s of l u b r i c a n t s which have known upper and lower asymptotes, only t h e i r i n d i v i d u a l r e l a x a t i o n times are required before a p a r t i c u l a r u - 0 curve or a (u ,0.) value i s f u l l y s s. 1 x defined. Although the majority of the preceeding d i s c u s s i o n concerns the f r i c t i o n behaviour of Langmuir-Blodgett monolayers, an examination of the f r i c t i o n behaviour of the f e r r i c s tearate monolayer deposited by the abrasion technique shows that t h i s f i l m has b e t t e r l u b r i c a t i n g q u a l i t i e s than any of the other soap monolayers. This observation i s not s u r p r i s i n g when one considers that monolayers formed i n t h i s way are strongly bound to the substratum through chemisorption while the Langmuir-Blodgett soap monolayers are only p h y s i c a l l y adsorbed i n the present case and thus more e a s i l y disrupted by the applied f o r c e s . Further consideration of the e f f e c t s of abrading a m e t a l l i c surface i n contact with a surfactant may ex p l a i n the frequently observed phenomenon of run-in during f r i c t i o n s t u d i e s . Generally, one observes that with repeated t r a v e r s a l s of the same tra c k , the f r i c t i o n c o e f f i c i e n t w i l l decrease u n t i l i t reaches a constant value. Since the s l i d i n g process i t s e l f generates "clean" areas which are i d e a l s i t e s f o r chemi-sorption, repeated t r a v e r s a l s cause the formation of an absorbed m e t a l l i c soap and a subsequent decrease i n f r i c t i o n . In a d d i t i o n , one must consider that c e r t a i n metals are capable of c a t a l y z i n g the oxida-t i o n of organic compounds [3]. The formation of these new s u r f a c t a n t s , which are also capable of forming f r i c t i o n reducing surface f i l m s , may be another f a c t o r i n run-in. The temperature work has shown that r e l a x a t i o n times are strongly influenced by temperature increases. I f the r e l a x a t i o n time 73 for each of two temperatures i s experimentally determined, the a c t i v a -t i o n e n ergycan be c a l c u l a t e d . Then, i t i s p o s s i b l e to construct the appropriate - 6 curve f o r any other temperature wi t h i n the given range. Unfortunately, i t i s not yet p o s s i b l e to p r e d i c t q u a n t i t a t i v e l y * the p — 0 behaviour of an i n t e r f a c e from a simple study of monolayer and substrata p r o p e r t i e s . A d d i t i o n a l work along these l i n e s i s necessary. 6.4 A Note on the Time-dependence of S t a t i c F r i c t i o n E a r l y i n v e s t i g a t o r s of s t a t i c f r i c t i o n observed that the s t a t i c f r i c t i o n values were not constant and proposed that the s t a t i c f r i c t i o n c o e f f i c i e n t was a f u n c t i o n of " s t a t i o n a r y contact time", meaning the time elapsed between the f i r s t a p p l i c a t i o n of the shearing f o r c e and the time at which macroscopic s l i d i n g occurred. Johannes tested t h e i r hypothesis by applying a t a n g e n t i a l load at a given r a t e , holding the load constant f o r time periods up to 100 seconds, then applying f u r t h e r t a n g e n t i a l force (at the i n i t i a l r ate) u n t i l macroscopic s l i d i n g occurred. He found that p g f o r the "delayed s t i c k " t e s t was not s i g n i f i c a n t l y l a r g e r than the y s value f o r corresponding t e s t s i n which the t a n g e n t i a l loading by uninterrupted by a delay period. In examining the v i s c o e l a s t i c models f o r s t a t i c f r i c t i o n (Equations 6, 10), i t i s obvious that time jus i n v o l v e d i n s t a t i c f r i c t i o n . However, i t i s probable that no increase i n s t a t i c f r i c t i o n was observed during Johannes creep t e s t s because the amount of area growth during the "delayed s t i c k " time was very small, and the r e s u l t i n g small increase i n p g was not considered s i g n i f i c a n t . Given the v i s c o e l a s t i c parameters of the i n t e r f a c e , i t s s t r e s s 74 h i s t o r y and appropriate creep compliance J ( t ) , i t i s possible to c a l -culate the increased area growth due to the delay time. Consider an i n t e r f a c e with calcium stearate as the monolayer and s t e e l as the sub-stratum: ^at 22°C, i f the i n t e r f a c e behaves as a Kelvin-Voigt sub-stance up to the fra c t u r e point, then c/k = 40 s e c , P m/k = 1/1.46. • m Given 6 = .005, = 50 sees., and the loading h i s t o r y shown i n Figure 32, the amount of area growth f or delayed s t i c k times of 1 second to <», was calculated as follows: A , the i n i t i a l contact area i s N/p . At time t„, A has o m I o grown to A (1 + e(t„)). The value of e(t„) i s found from the heredi-o 2 I tary i n t e g r a l given i n equation (3), for a loading time of t ^ . Therefore: A^ (1 + e(t )) = A o / o °2 °2 c " c C2 1 + (k t 2 - c) + — — e t 2 k t 2 k At t = t ^ , evaluating the same i n t e g r a l f o r the loading his-tory given by l i n e 2 of Figure 32 which includes the delay period ( t 3 - t 2 ) , the area w i l l be [31]: k (1 + E(t ) = A o 3 o °2 °2 c fc k c3 1 - e k c H i t . c 3 Therefore, the present area.increase due to area growth during the delay i s : A (1 + e ( t , ) ) - A (1 + e(t )) D = - 2 - 1- ^ — ^ x 100% A (1 + e ( t j ) o I 1 + e ( t 3 ) 1 + e ( t 2 ) x 100% where: 75 c k — = 40 sec. — = 1.46 t„ = 50 sec. k p 2 m Using these values, the area at t , immediately when the delay time begins, i s 1.07 A . The area at t„ i s A 1.171 - .34e o 3 o L -1 The % increase i n area due to delay time i s p l o t t e d i n Figure 33. For a delay time of 1 second, the area i s increased by 0.5%, an i n s i g n i f i -cant amount. The maximum area growth occurs when the delay time i s i n f i n i t e ; even then the area increase i n only 9.5%. For 0 = .005, f o r no delay t a n g e n t i a l loading i s 0.60. Therefore: F,. . f i n a l _ . r n V = ^ = T A. . = . 60 . s N o f i n a l I f , due to the delay time, the f i n a l area increases by the maximum amount, 10%, then U g would increase to approximately 0.66 from 0.60, and increase which might be considered s i g n i f i c a n t , depending on the amount of s c a t t e r i n the data. C e r t a i n l y considering the r e s u l t s obtained f o r calcium stearate, Figure 21, the s c a t t e r band i s such that area increases l e s s than 5% would not be considered s i g n i f i c a n t . There-f o r e , i n t h i s case, f o r delay times l e s s than 50 seconds, no time e f f e c t s would be n o t i c e a b l e . This c a l c u l a t i o n i n d i c a t e s why Johannes [19] d i d not observe s i g n i f i c a n t l y increased values and why the e l e c t r i c a l r e s i s t a n c e measurements of Green [16] d i d not i n d i c a t e appreciable area growth during the delayed s t a t i c contact period even though s t a t i c f r i c -t i o n i s time dependent. The experimental r e s u l t s of Seireg and Weiter [57] provide a d d i t i o n a l information on a v i s c o e l a s t i c model of s t a t i c f r i c t i o n . They conducted creep t e s t s i n much the same manner as Johannes with the exception that they were able to measure the very small amounts of micro-76 s l i p (of the order of .00005 inches) which took place during the creep t e s t . They a l s o considered using a v i s c o e l a s t i c model to explain t h e i r r e s u l t s and found that the 3-parameter model adequately approximated the observed creep. I t i s i n t e r e s t i n g to examine t h e i r r e s u l t s f u r t h e r . Based on t h e i r values f o r creep displacement, the r e l a x a t i o n time f o r the three parameter model has been c a l c u l a t e d as 0.13 sec. This com-pares very favourably with the r e s u l t s of the present study. Unfortu-n a t e l y , Seireg and Welter d i d not include s u f f i c i e n t data on loading r a t e s so that c a l c u l a t i n g a U g - 6 curve f o r t h e i r system was impossible. 77 VII. CONCLUSIONS Previous i n v e s t i g a t i o n s of s t a t i c f r i c t i o n have shown that the s t a t i c f r i c t i o n c o e f f i c i e n t of a s t e e l / s t e e l f r i c t i o n couple l a r g e l y depends on the magnitude of the rate parameter, 0, for the range .0001 < 0 < 10. The f i r s t part of the present experimental work was concerned with f i n d i n g the cause of t h i s observed rate dependence. S t a t i c f r i c -t i o n vs 8 studies under high vacuum conditions showed no rate e f f e c t over the range .0001 < 0 < 2 for s t e e l surfaces. The s t a t i c f r i c t i o n value y g , was somewhat lower than i n i t i a l l y expected but when the e f f e c t of r e s i d u a l surface contamination was considered, 0.70 was thought to be a reasonable value. No rate e f f e c t s were observed i n t h i s range of 0 values when oxide films were d e l i b e r a t e l y grown on the s t e e l surfaces. The f r i c t i o n c o e f f i c i e n t s were high (0.80 and 0.70) for oxide films formed by two methods: heating at 250°C i n a i r and by immersing the samples i n H 20 of pH 4.0. • When monolayers of organometallic soaps were deposited on i the surface, however, the s t a t i c f r i c t i o n c o e f f i c i e n t d i d show the expected rate dependency. One conclusion a r i s i n g from t h i s work was that, since the s t a t i c f r i c t i o n of reasonably clean s t e e l samples was independent of 8, the rheplogy of surface films was a large factor i n determining the s t a t i c f r i c t i o n c h a r a c t e r i s t i c s . The exact shape of the u - 0 curve depended on the m e t a l l i c soap deposited on the surface s as w e l l as on the method of deposition. F i v e soap monolayers were i n v e s t i -gated. Four monolayers, calcium oleate, calcium stearate, and the basic i r o n soaps of s t e a r i c a c i d were deposited using the Langmuir-78 Blodgett technique. The f i f t h monolayer, f e r r i c stearate was grown i n s i t u by abrading the s t e e l surface under a s o l u t i o n of s t e a r i c a c i d i n n-hexanes. For the s t e a r i c a c i d soap monolayer deposited by the abra-sion technique, u was 0.39 and u was 0.22. For the four max. min. soap monolayers deposited by the Langmuir-Blodgett method, u was max. 0.70 and u was 0.47. Although the upper and lower asymptotes were min. the same f o r each curve, the curves were displaced from one another on the 9 a x i s . An examination of p o s s i b l e t h e o r e t i c a l models showed that the s t a t i c f r i c t i o n behaviour f o r s t e e l surfaces covered with any of these four Langmuir-Blodgett monolayers i s adequately described by: - 1.46 + T0 where x i s the r e l a x a t i o n time f o r the i n t e r f a c e . The t h e o r e t i c a l model f or s t a t i c f r i c t i o n i m p l i c i t l y assumes that the o r i g i n of f r i c t i o n a l r e s i s t a n c e l i e s i n the breaking of the short-range metal-metal bonds formed at areas of contact. A f u r t h e r assumption i s that the f i n a l contact area between the surfaces i s a fu n c t i o n of 9 because the i n t e r f a c e has the deformation c h a r a c t e r i s t i c s of a v i s c o e l a s t i c s o l i d . I t i s a l s o assumed that s l i p w i l l occur only when the t a n g e n t i a l shearing s t r e s s exceeds a c e r t a i n value, T . Using (23), i t was p o s s i b l e to c a l c u l a t e r e l a x a t i o n times f o r each of the TTionolayer-covered surfaces from the experimental U g - 8 data. These r e l a x a t i o n times provide some i n d i c a t i o n of a p a r t i c u l a r monolayer's e f f e c t i v e n e s s as a boundary l u b r i c a n t . Monolayers which had high r e l a x a t i o n times gave low s t a t i c f r i c t i o n c o e f f i c i e n t s over the l a r g e s t part of the 6 range. Conversely low r e l a x a t i o n times mean u = u max. for most 0 values. •s x8 + 2.08 y = 0 (23) 79 The r e l a x a t i o n time of the calcium stearate-covered i n t e r f a c e decreased as the substratum temperature was increased. This e f f e c t i s important because i t shows how u g i s affected by temperature — a p a r t i c u -l a r monolayer may be adequate at room temperature but at 50°C, the s t a t i c f r i c t i o n c o e f f i c i e n t may be as high as y max. In the discussion section, the pr e r e q u i s i t e s for observing rate dependence were b r i e f l y discussed. They are: 1. the numerical values of and k^ f o r an i n t e r f a c e must be such that the d i f f e r e n c e between y and y i s s s max. min. detectable; 2. the r e l a x a t i o n time, k± + k 2 , must be large enough, or the range of 6 must be wide enough to show the expected y - 8 curve. s One of the inadequacies of f r i c t i o n research from the designer's point of view i s that i t i s s t i l l very d i f f i c u l t to f i n d the appropriate f r i c t i o n data i n a concise, useable form. Thus, the p o s s i b i l i t i e s of the general y g - x* curve look promising. I f 3 values for an i n t e r f a c e , 1) the asymptotes, 2) the re l a x a t i o n time, and 3) the temperature c o e f f i c i e n t were published, then the y g value at a given 8 for a given temperature could be calculated from the general y g - T * curve. 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Smith, H.A., A l l a n , K.A.; "The Adsorption of n-Nonadecanoic A c i d on Metal Surfaces", J . Phys. Chem,, 58, p. 449 (1954). 53. Smith, H.A., M c G i l l , R.M.; "The Adsorption of n-Nonadecanoic A c i d on Mechanically Activated Surfaces", J . Phys. Chem, 61, p. 1025 (1957). 54. Nelson, H.R.; "The Low Temperature Oxidation of Iron", J . Chem. Phys., 6, p. 606 (1938). 55. Kruger, J . , Yolken, H.T.; "Room Temperature Oxidation of Iron", Corrosion, 20, p. 99t (1963). 56. Langmuir, I.; "The Mechanism of the Surface Phenomena of F l o t a t i o n " , Trans. Faraday S o c , 15, Part 3, p. 62 (1920). .57. Seireg, A., Weiter, E.J.; " V i s c o e l a s t i c Behaviour of F r i c t i o n a l Hertzian Contacts Under Ramp-type Loads", Proc. Instn. Mech, Engs., V o l . 181, Pt. 3:0, p. 200 (1966-1967). 58. B a i l e y , A.I., Courtney-Pratt, J.S.; "The Area of Real Contact and the Shear Strength of Monomolecular Layers of a Boundary Lu b r i c a n t " , Proc. Roy. Soc. A, 227, p. 500 (1955). 59. T o l s t o i , D.M., Kaplan, R.L., L i n Fu-sheng and P'an Pin-yao; "New Experimental Data on Ext e r n a l F r i c t i o n " , p. 99, Research i n Surface Forces, B.V. Deryagin, ed., Consultant's Bureau, New York (1961) 60. Coelho, E.M.; " F l o t a t i o n of Oxidized Copper Minerals: An I n f r a r e d Spectroscopic Study", Ph.D. Thesis, Department of Mi n e r a l Engineering, The U n i v e r s i t y of B r i t i s h Columbia (1972). 61. Derjaguin, B.V., Push, V.E., T o l s t o i , D.M.; "A Theory of S t i c k -s l i p S l i d i n g of S o l i d s " , Proceedings of the Conference on L u b r i c a t i o n and Wear, p. 257, October (1957). 62. Howe, P.G., Benton, D.P., Puddington, I.E.; "London-Van der Waals A t t r a c t i v e Forces Between Glass Surfaces", Canadian J o u r n a l of Chemistry, 33, p. 1375 (1955). 84 63. Ko s t e r i n , J . I . , K r a g e l s k i i , I.V.; "Rheological Phenomena i n Dry F r i c t i o n " , Wear, 5, 190-197 (1962). 64. Rabinowicz, E.; "The Nature of the S t a t i c and K i n e t i c C o e f f i c i e n t s of F r i c t i o n " , Journal of Applied Physics, V o l . 22, No, 11, pp. 1373-1379 (1951). 65. Spurr, R.T.; "Creep and S t a t i c F r i c t i o n " , B r i t i s h Journal of  Applied Physics, V o l . 6, pp. 402-3 (1955). 66. Moore, A.C, Tabor, D.; B r i t i s h Journal of Applied Physics, V o l . 3, p. 299 (1952). 67. Atkins, A.G., S i l v e r i o , A., Tabor, D.; "Indentation Hardness and the Creep of S o l i d s " , Journal of the I n s t i t u t e of Metals, V o l . 94, pp. 369-378 (1966). 68. Mulhearn, T.O., Tabor, D.; "Creep and the Hardness of Metals: A P h y s i c a l Study", Journal of the I n s t i t u t e of Metals, V o l . 89, pp. 7-12 (1966). 69. Rosenfield, A.R., Hahn, G.T.; "Numerical De s c r i p t i o n s of the Ambient Low Temperature, and High S t r a i n Rate Flow and Fracture Behaviour of P l a i n Carbon S t e e l " , TRANS. ASM, 59, p. 962 (1966). 70. Wolstenholme, G.A., Schulman, J.H.; "Metal Monolayer I n t e r a c t i o n s i n Aqueous Systems — Part I", Trans. Faraday S o c , 46, p. 475 (1950). 85 APPENDIX I THE VACUUM SYSTEM The u l t r a - h i g h vacuum system used i n t h i s work was purchased from Ion Equipment Corporation of Santa C l a r a , C a l i f o r n i a . The b a s i c TTSB-200 system i s a bakeable, a l l metal u n i t , capable of reaching a t o t a l pressure of 5 x 10 t o r r i n 15 hours, i n c l u d i n g a two-hour bake-out at 250°C. The vacuum chamber c o n s i s t s of 2 major items — 1) a basewell assembly which houses two of the three gas pumping u n i t s plus ten 1-1/2" I.D. feedthrough p o r t s , and 2) a metal b e l l j a r which was custom b u i l t to our s p e c i f i c a t i o n s . A quadrupole type mass spectrometer, a l s o purchased from IEC was added to the vacuum system. I t was used as a t o t a l pressure gauge and a leak detector as w e l l as a r e s i d u a l gas analyzer. a) The Pumping System A rough vacuum i s produced by cryogenic pumping. The dual sorption-pump u n i t uses LN^ as a coolant and h i g h l y porous s y n t h e t i c (calcium or sodium aluminophosphate) z e o l i t e molecular sieve as the sorbant. These pumps are rated at 110 l i t r e s per second ^ and w i l l -3 produce a vacuum i n the 10 t o r r range which i s the s t a r t i n g pressure f o r the ion pumps. Although cryogenic pumping u n i t s handle r e l a t i v e l y small volumes of gas when compared with mechanical or d i f f u s i o n pumps, they are v i b r a t i o n f r e e . One other important advantage of using cryogenic pumping i n t r i b o l o g i c a l research Is that the p o s s i b i l i t y of contamination due to the backstreaming of pumping o i l s i s eliminated. 86 I f d i f f u s i o n pumps are poorly b a f f l e d , then the vacuum atmosphere w i l l be contaminated by small amounts of the heavy o i l s used as the pumping f l u i d Molecules of these o i l s can condense on the tes t surfaces and thus provid a l u b r i c a t i n g f i l m . The u l t r a high vacuum i s produced using titanium g e t t e r pumping and ion pumping. The titanium getter pump i s a four filament t i t a n i u m sublimator, capable of pumping 4300 l i t r e s per second N^. The titanium i s sublimed over 370 sq. i n . of the LN^ - cooled s t a i n l e s s s t e e l cryo-shroud. The work area i s shielded from the titanium sublimation pump. This type of pumping e f f e c t i v e l y pumps la r g e volumes of gas at high pressures. The ion pump c o n s i s t s of an array of eight 25 £/sec. magnetic diode u n i t s . These u n i t s are an i n t e g r a l part of the vacuum chamber. The ion pump assembly i s capable of pumping 200 £/sec. a i r ; 60 £/sec. helium or 40 £/sec. argon. The pumping s e c t i o n of the basewell assembly can be i s o l a t e d from the upper part of the chamber by a poppet valve. This allows the —8 pumps to maintain a vacuum l e v e l of 10 t o r r or lower i n the basewell assembly while the work area i s at atmospheric pressure. The basewell assembly a l s o contains 10 feedthrough ports of 1-1/2 inch I.D. b) Custom B e l l J a r The custom b e l l j a r u n i t i s shown i n s i t u i n Figure 8. I t Is 8" high and 12" i n diameter. I t contains 6 feedthrough p o r t s : 1) 4 port with .1-1/2" I.D. of which 2 ports are o p t i c a l ports, 1 port i s used f o r mounting a standard 3" l i n e a r motion mechanical feedthrough and the fo u r t port i s used f o r an e l e c t r i c a l feedthrough; 2) 1 large (2-1/2" I.D.) port used f o r a custom-made 6" l i n e a r motion mechanical feedthrough, and 87 3) 1 l a r g e (2-1/2" I.D.) o p t i c a l port on the b e l l j a r cover. The b e l l j a r u n i t also contains a 4" wide by 1" t h i c k work support platform. I t i s p o s itioned at the base of the chamber and i s welded to the inner f l a n g e at the chamber base. c) Measuring the System Pressure In f r i c t i o n and adhesion work, both system pressures and r e s i -dual gas composition are important. From a c a l i b r a t i o n curve of ion pump current vs Nitrogen-equivalent pressure supplied by the manufacturer, i t was p o s s i b l e to monitor the pressure i n the system down to 10 t o r r by measuring the ion pump current. However, ion pumps and i o n i z a t i o n gauges (a type of i o n pump) are s e n s i t i v e to the type of gas being pumped. Therefore, i n order to f i n d the true t o t a l pressure of the sys-tem, i t i s necessary to know the composition of the gases being pumped. To accomplish t h i s , a quadrupole-type r e s i d u a l gas analyzer was purchased -14 from IEC. This instrument has a s e n s i t i v i t y of 1 x 10 t o r r p a r t i a l pressure f o r Nitrogen, a mass range of 1 - 250 amu and i s capable of r e s o l v i n g adjacent mass peaks to mass 250 (10% v a l l e y d e f i n i t i o n of r e s o l u t i o n ) . The residual'gas analyzer formed an i n t e g r a l p art of the vacuum system. I t could be used i n the t o t a l pressure mode to give the Nitrogen-equivalent pressure i n the chamber and i t was used as a s e n s i -t i v e leak detector as w e l l as a mass spectrometer. This instrument was inva l u a b l e i n detecting small amounts of contamination i n a d v e r t e n t l y -9 l e f t i n the chamber. At the test pressures, 10 t o r r , a t y p i c a l a n a l y s i s would show that the r e s i d u a l gases were p r i m a r i l y l ^ , He, and Ar ( a f t e r bake-out). 88 APPENDIX II PROPERTIES OF REAGENTS USED a) S t e a r i c Acid (Octadecanoic Acid) CH (OH 2) l f i COOH Moi. Wt. = 284.49 m.p. •= 67-69°C This a c i d was obtained as laboratory grade from Fis h e r S c i e n t i f i c . b) Hexanes C 6 H14 F.W. = 86.18 A mixture of isomers. In the as received c o n d i t i o n , i t has a pH of 0.00. Actual Lot A n a l y s i s B o i l i n g Range: 66.1° - 68.1°C Density: g./ml. - 0.668 Residue A f t e r Evap.: 0.0004% A c i d i t y as CH 3 COOH P.T. Sulphur Cmpds. (as S): 0.004% Thiophene: P.T. c) HC1, Ca C0 3 Reagent grade. 89 d) H 20 Double d i s t i l l e d . e) O l e i c Acid Films O l e i c a c i d : (9-octadecenoic acid) Moi. Wt. = 282.46 C_ H CH: CH(OH_)_ COOH o 1 / 2. I Insoluble i n H^O. Approximate surface pressure on ^ 0 at 25°C, 30 dynes/cm. 90 APPENDIX I I I 1. Estimating the a c t i v a t i o n energy AE from the s h i f t r e l a x a t i o n time, T, due to temperature: AE T l k — = e T2 _1_ _ _1_ T T 1 2 £n 40 .5 £ n ^ = ^ T 2 k AE 1_ 1.98 cal/mole 295 323 •: AE = 28.7 Kcals/mole. FIGURES V V X A A A F t - F t •x- -AX-FIGURE 1. V i s c o e l a s t i c Model of S t a t i c F r i c t i o n Developed by Johannes [19]. 92 N F = F t LLLLL/ / Metoiiic Substrata Deformed Metal Layer Oxide — ^ Metallic Soap |_JL Oxide f Deformed Metal Layer Metallic Substrata FIGURE 2a. The Contact Area Between Two S o l i d Surfaces i s the Sum of A ^ J ^ J L ^ 8 0 ! 6 1 1 6 A r e a S ° f C o n t a c t Formed Where Opposing A s p e r i t i e s Meet. 9 3 A Contact Area Shear Strength of the Interface FIGURE 2b. The Area of Contact and the Shear S t r e n g t h as F u n c t i o n s of the Rate of A p p l i c a t i o n of the T a n g e n t i a l S h e a r i n g F o r c e . FIGURE 3. Tangential Loading During a S t a t i c F r i c t i o n Test. VsAAA cr(t) a) The Simplest Mathematical Model for S t a t i c F r i c t i o n Involves a Kelvin-Voigt Element Coupled with a Prandtl-Type Element. AAAAA A / W \ A To o-(t) b) More Complicated Model. The Interface Deforms as a General Linear S o l i d Having a F a i l u r e Strength per Unit Area of T Q . FIGURE 4. Models for S t a t i c F r i c t i o n . 96 l o g i o "C 3(dimensionIes^ FIGURE 7. The General Static Friction Curve. FIGURE 8. General Arrangement of Vacuum System and Experimental Apparatus. FIGURE 10. Schematic of the Hydraulic Control System. S u b - c i r c u i t A c o n t r o l s the a p p l i c a t i o n and the release of the normal load, c o n t r o l s the t a n g e n t i a l f o r c e F and the tangential loading rate F. Sub-ci r c u i t B o t—* FIGURE 11. Isometric Sketch of Friction Couple. T .8 .6. .4 .2 h O 2-IO"8torr _ j 1.0 4.0 3.0 2.0 1.0 0.0 l o g I O e(secr') FIGURE 12. S t a t i c F r i c t i o n of C1020 Steel i n Vacuum of 2 x 1 0 " ° t o r r at 20°C. O Ms .8 -" 7 1 O o o o o ° Q ° ° o o 0 c P o o o ° cP ° o oo 1 — .6 A A A • ± A A A A A AA ^ A A A A A A A A A . A A A ^ A -.4 A A A ^A A £ A £T A A A A * A A A A A A -.2 0 2-10"8 torr A air exposed-, 20or 48hrs. I 4.0 3.0 2.0 To o.o 1.0 log ! 0 9(sec:1) FIGURE 13. S t a t i c F r i c t i o n of C1020 Steel i n Vacuum and Af t e r Exposure to Atmosphere. § T o, o OO 000% o 0 c P o o ° cP. ° o o o A"^"A\.. A i l 4 _ O 2-!08torr A air exposed; 20or 48hrs. Marion Johannes J 1 4 . 0 3.0 2.0 0.0 l o g I O e(secr') FIGURE 14. Comparison of Static Friction of C1020 Steel in Vacuum and After Exposure to Atmosphere to Static F r i c t i o n Values Obtained by Johannes [19] and Marion [21]. 1—' o © Oxide B (water) A Oxide A(250°C-air) 4.0 3.0 2.0 1.0 0.0 ._ Ioglo 8 (sec:1) FIGURE 15. Static F r i c t i o n of C 1020 Steel Covered with Oxide Films. Ms 4-0 3.0 2.0 TO 0.0 1.0 .log-0 9 (sec:1) FIGURE 16. Comparison of S t a t i c F r i c t i o n of Oxide-covered C1020 Steel to S t a t i c F r i c t i o n Values Obtained by Johannes and Marion. O .8 .4 +• . A f t e r Abrading — . Johannes [19] l o g ! 0 e(secr') FIGURE 17. S t a t i c F r i c t i o n of C1020 S t e e l A f t e r A b r a d i m g Surface Under S t e a r i c Acid-Hexane Solut o oo i o n . .8 .4 m A A A £1 ,^0 4 V ^ A A " A • D D A A A ^ ^ AA. A Basic Iron Stearate .P Basic Iron Oleate FIGURE 18. iog 1 0 0(sec:') lllt?X«£ ^oV^^TS TVJ1^ " E i t h £ r \ ^  S t e a r a t e o r a o vO .8 © a A A A ^A - A A A A A A * A A ^ A A A ^ A AAA A A A A . est © A^ A A ' 9 ® Gg© ® © © ® A Fe(OH)2St * Ca(St) 0 log,0 9 (sec:1) FIGURE 19. The Effect of a Ca(St) 2 Monolayer on Static Friction as Compared to the Effect of an Fe(OH) <t Monolayer. PH of Substrata i s 4 for Iron-stearate Soap, 9 for Calcium-stearate Soap. T = 20°C i i O T T T .4 a s1 • a^ 3 a a • Fe(OH) 2 0£ 2 Ca(0£) o 4.0 3.0 2.0 1.0 0.0 _ j 1.0 log|0 e(sec:!) FIGURE 20. The E f f e c t of a Ca(0£) 2 Monolayer on S t a t i c F r i c t i o n Compared to the E f f e c t of an Fe(OH) 0£ Monolayer. pH of Substrate i s 4 f o r Iron-oleate Soap, 9 f o r Calcium-oleate Soap. T = 20°C. .6 3.0 - A - A — A _ & A ^ A — A ^ 3.0 A A A A 7 > A A A A ^ A A ^ , A A A A 2.0 1.0 log© 6 (sec: 1) 0.0 1.0 FIGURE 21. Experimental Data and Theoretical y - 0 Curve for Static Friction When Steel Surface is s Covered with Fe(0H) 2 St Monolayer. pH 4, T = 20°C. I T .8 .2 © © ® 4.0 3.0 2.0 1.0 0.0 1.0 l o g 1 0 0 ( s e c : ! ) no. FIGURE 22. Experimental Data and T h e o r e t i c a l ]i - 6 Curve f o r S t a t i c F r i c t i o n When Steel Surface i s Covered with Ca(St> 2 Monolayer. pH 9, T = 2 0 ° C . i—1 LO .8 4.0 3.0 2.0 0.0 . log,0 9(sec:!) FIGURE 23. Experimental Data and T h e o r e t i c a l ^ - 0 Curve f o r S t a t i c F r i c t i o n When Steel Surface i s Covered with Fe(0H> 2 01 Monolayer. pH 4, T = 20°C. •2 h 4 . 0 3.0 2.0 To o.o 1.0 FIGURE 24. fogi0 e(sec:!) Experimental Data and T h e o r e t i c a l y g - 6 Curve f o r S t a t i c F r i c t i o n When Steel Surface i s Covered with Ca(0£) 2 Monolayer. pH 9, T = 20°C. h-1 h-1 I I I I J I I I I I I I I I I I I I I I 1 I " I 1 1 A • s j i I I I I I I A Stearic Acid Fe(OH)2St pH=4 • Ca Stearate pH=9 • Oleic Acid Fe(OH)2OI pH=4 B Ca Oleate pH=9 .0001 .001 .01 0.1 1.0 T*- dimensionless 10 100 1000 FIGURE 25. Experimental Data Collapses on General y g - T * Curve Predicted from Mathematical Model. T = 20°C. T .8 .6 E a a I B H B s | a B a _ a S3 n Q a T = 35°C 4.0 3.0 2.0 1.0 0.0 _ l _ 1.0 Iog,0 e(secr') FIGURE 26. Effect of Raising'Surface Temperature to 35°C. Ca Stearate Soap Monolayer, T T T 1 A A A A A AA T= 50°C 4.0 3.0 2.0 1.0 0.0 LO l o g , 0 e ( s e c : ' ) FIGURE 27. Effect of Raising Surface Temperature to 50°C. Ca Stearate Soap Monolayer, 00 119 log c .1 .00300 .00325 .00350 .00375 .00400 t FIGURE 28. Log c vs c(T) = e , i/T f o r Calcium Stearate Soap Monolayers. Since ( A E / P T ) AE wa s Determined to be 28 K c a l s . 120 121 .8 •6 1 O O o o o o e=.345 o 20 30 40 50 60 70 r c FIGURE 30. y - T C h a r a c t e r i s t i c s of S t e e l Covered w i t h Ca l c ium S -3 S tea r a te Monolayer a t 0 =0 .345 sec. t FIGURE 31. Experimental Temperature-Friction Data Also Collapses on General U g - 0 Curve f o r Calcium Stearate Monolayer Covered Surface. '. . 123 FIGURE 32. Loading H i s t o r y During Delayed S t i c k . 10 -1 r — T 1 — l — l i | • - i 1 1—I—i l | n 1 i 1 — i—i—r-r 5 2 a) 6 D r -£ >> < o-CD C Q O 4 tn o a> o c o o o o o o o 0 0 i i i > i •—L. 10 I 1 I I I 100 Delay Time (sees) ' 1 1000 FIGURE 33. Area Growth Due to Delay Time i f the System has a Relaxation Time of 40 

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