טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentMorag Yahav
SubjectA Fractal Model for the Contact of Rough Surfaces
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Emeritus Izhak Etsion
Full Thesis textFull thesis text - English Version


Abstract

This thesis suggests a revision to the elastic-plastic contact model of fractal rough surfaces offered by A. Majumdar and B. Bhushan (the MB model) [Journal of Tribology, 113, 1 (1991)]. According to the MB model, the contact mode of a single fractal asperity transfers from plastic to elastic when the load is increased, and the asperity's contact area becomes larger than a critical area, which is scale-independent. This surprising result of the MB model is in contrast to classical contact mechanics where an increase of contact area due to increased load is associated with a transition from elastic to plastic contact. The present study describes a revised elastic-plastic contact model of a fractal surface showing that the critical area is scale- dependent, contrary to the MB model prediction. For a given single contact spot, several specific related expressions are obtained. For example, the fractal deformation level (n), and the interference between the summit of the fractal asperity and the rigid flat at that fractal level (w). In addition, the critical values at the inception of deformation mode change are obtained, namely, the critical interference between the asperity and the rigid flat (wc­­), and the critical contact area (ac). The comparison between w and wc enables us to state the deformation regime, i.e., elastic, elastic-plastic or fully plastic. For each case, the relevant set of expressions for the deformation, load and contact area are obtained. The new model shows that a fractal asperity behaves as would be expected in classic contact mechanics, namely, as the load and contact area increase beyond a scale dependent critical value, a transition from elastic to plastic contact takes place in this order. Having obtained the solution for the single asperity, the model is expanded to the overall surface, in order to evaluate the elastic and plastic components of the load and the contact area, and their change during decreasing the separation distance. As done in a similar manner by Greenwood and Williamson (the GW model,1966), a "Fractal plasticity index" is developed, and as in the GW model, this index was found to give a good indication of the deformation mode.