Rajendrakumar, P K

etd@IISc Electronic Theses and Dissertations at Indian Institute of Science

Synopsis Wear and fatigue charactenstrcs of engmeenng surfaces are dependent on the contact pressures and the resultmg subsurface stress distnbutrons in the bodies whlch are m A contact Real surfaces are rough and hence the contact between two red surfaces can be considered m general as a contact between two curved rough bo&es Th~s  thesis analyses the above problem m its slmplest form as a plane s h n  problem of a ng~d cylinder of radms r, mdentmg an elashc half space c q n g  a regular array of undulations, shape of wbch can be represented by a simple mathemahcal functron The problem is transformed Into the problem of lndentat~on of an elastic half-space by a system of normally loaded connected n g d  punches wth base profile represented by the funcfion of separabon h(x) between the two bodes m contact Th~s  is now a Class-A punch indentation problem w~th incomplete contact at the base of the punch profiles so that the contact pressures are bounded (and equal to zero) at the ends of the regions of contact Using the method of complex vanables, the above problem has been reformulated in terms of a complex potential O(z) , where r= x+y ,  oa, to yeld 2N number of non-linear simultaneous equations in 2N vanables (whch are the end points of the regions of contact of N punches) whch can be solved by Newton's ~teratwe scheme The extent of contact regons and the contact pressure &stnbution on each regon emerge from the analys~s a postenon -- Chapter 1 descnbes the significance of the problem of contact of rough surfaces and reviews some of the early models and methodologies for tackling this problem The need for a more realistic and tractable method of dealing with the problem has also been highlighted The method of complex variables has been identified to be one such method Since the problem of rough contact can be converted to an equivalent multiple punch indentation problem, Chapter 2 gives relevant details of the complex vanable solution to the problem of indentation of an elastic half-space by a system of connected ngid punches In Chapter 3 the contact configuration and contact pressure distnbution over the contact regions of an elastic half-space carryrng uniformly spaced cylindncal aspenties indented by a ngid smooth cylinder has been analysed using complex vanable method over a range of normal displacements The approach has been validated by modelling the same problem using boundary element method (BEM) and the results have been compared wlth those obtained using a pnon Hertzian pressure distnbution It has been observed that the contact is non-Hertzian especially when the aspenty tip radius is large compared to the radius of the indenting cylinder The dynamic nature of the aspenty contact has also been established When two rough bodies are in normal contact the point where the peak equivalent stress is induced is of particular mterest to tnbologists and surface engineers since the onset of plasticity occurs at this point which in turn strongly influences the mechanism of wear Indented by a large ngid smooth cylinder, the equivalent shear stress field induced in an elastic half-space carrying equi-spaced cylindncal aspenties on its surface, has been analysed in Chapter 4, for different aspenty tip radius-aspenty pitch-applied load combinations For every combination, it has been observed that there exists two peaks of equivalent shear stress, one at the individual aspenty (local) and the other, in the subsurface (global) Using complex vanable analysis, it has been shown that there exists such combinations for whch the global subsurface maximum (equwalent) shear .L stress is more than the maximum local (equivalent) shear stress at any aspenty Thus, it is possible that the subsurface starts yielding even when the aspenbes are elastic A finite element (FEM) model using a commercial FEM package called ABAQUS has been used to compare and venfy the above result The process of the development of contact or what happens to the aspenties under load is of great englneenng importance since ( I )  the quantitabve development of the real area of contact provides informabon about the dynamics of load support which in turn influences hcbon and wear and (zz) the ability or otherwise of the aspentles to persist under load have important beanngs on how and what amount of heat IS generated at contact and for electncal contact it determines microscopic au gaps and constriction to the flow of electnc~ty Hence, in Chapter 5, the approach using complex vanable method has been used to obtam a relationsh~p between the applied load and the corresponding contact regions developed for a simple configuratron of a half space carrying sinusoidal elashc aspenties being indented by a hard cylinder It has been shown that a power law relationship exists between the load and contact area and the load power factor vanes between 0 5 and 1 0 as the surface topography changes from perfectly smooth to very rough For realistic engineenng topography the global nature of contact is Hertzian It has also been shown by calculating the closure of the gap between the mrddle and the next aspenty that closely spaced aspenties have a tendency to persist while wrdely spaced short aspentles drsappear under modest normal loads The complex vanable method used for the present analyses is seen to produce good results for surfaces of finrshed engrneenng products, but has the llrnitation that ~t < ceases to be valid once plasticity is developed somewhere ins~de the matenal 

Analysis Of Non-Hertzian Contact Between Rough Surfaces

http://etd.iisc.ac.in/static/etd/abstracts/2754/G14912-Abs.pdf

Analysis Of Non-Hertzian Contact Between Rough Surfaces

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etd@IISc Electronic Theses and Dissertations at Indian Institute of Science